CN104156545A - Circuit modeling and simulation method representing terahertz quantum cascading laser device multimode effect - Google Patents

Abstract

The invention relates to a circuit modeling and simulation method representing the terahertz quantum cascading laser device multimode effect. The method includes the steps of firstly, establishing a multimode velocity equation set representing carrier transportation characteristics inside a THzQCL active layer; secondly, establishing a physical equation model representing the multimode effect inside the THzQCL; thirdly, obtaining a corresponding equivalent circuit model through variable substitution and simplification; fourthly, establishing an equivalent circuit model representing the electrical characteristics of the input end of the THzQCL; fifthly, establishing an equivalent circuit model representing the luminous power characteristics of the output end of the THzQCL; sixthly, establishing a circuit macro model which comprises an electrical port and an optical power output port, and conducting photoelectric property simulation and output spectral property testing on the basis of the circuit macro model. By means of the circuit modeling and simulation method, the influences of the temperature on various photoelectric properties of the THzQCL can be tested, and imitation and simulation for the photoelectric property and the output multimode effect of the THzQCL can be supported and achieved.

Description

Characterize the circuit modeling emulation mode of Terahertz quantum cascaded laser multimode effect

Technical field

The present invention relates to laser technology field, is mainly a kind of circuit modeling approach of Semiconductor Laser, especially relates to a kind of circuit modeling emulation mode that characterizes Terahertz quantum cascaded laser multimode effect.

Background technology

First Terahertz quantum cascaded laser (terahertz quantum cascade laser in the world from 2002, THz QCL) since succeeding in developing, in numerous THz radiation producing methods, the advantage such as QCL is high with its energy conversion efficiency, volume is little, light and easy of integration becomes the preferred light source of following Terahertz research field.The THz QCL device of trial-produceing successfully is at present mainly to take the QCL of GaAs/AlGaAs material system resonance phonon structure as main, and researchist has also carried out relevant design research to Ge/SiGe material system, InGaAs/Al InGaAs/InP material system in addition.

THz QCL is the semiconductor sublayer interband device of a multicycle cascade structure.Electronics gives off photon by the optical transition between the sub-energy level of the difference at active layer.Meanwhile, it can, by the interaction with phonon, impurity and other electronics, inject next cycle from one-period.To the further investigation of above device inside carrier transport process, can provide useful guidance for the design of device active layer and the improvement of device performance.To the research of THz QCL carrier transport characteristic, substantially can be divided three classes both at home and abroad at present:

(1) quantum dynamics method: the wave characteristic based on quasi particle in solid, interaction between quasi particle uses the interference technique of ripple to be described, the method of use amount subdynamics is processed various scattering mechanisms and the boundary condition in carrier transport process, and main method comprises non-equilibrium green function method, density matrix method and wigner Function method etc.

(2) monte carlo method: the method is by following the tracks of the motion of a large amount of charge carriers under Electric and magnetic fields effect, and the charge carrier that obtains device inside distributes.Charge carrier the motion of device inside be divided into drift under electromagnetic field effect and with scattering two parts of the quasi particles such as other charge carriers, impurity and phonon.In drift part, the motion of charge carrier is described by classical Newton's laws of motion, and the scattering probability of charge carrier and other quasi particles calculates by the fermi's golden rule in quantum mechanics.

(3) rate equation method: the electronics being caused by various scattering mechanisms by calculating is in the relaxation time of transition probability and the intersubband transitions of intersubband, and occupy several equations according to the particle that each relaxation time is write out one group of each subband, finally by this system of equations of self-consistent solution, obtain the electrons occupy number of each subband.

In above-mentioned research, to the modeling effort of THz QCL interior lights electrical characteristics, are all the achievements in research of infrared QCL in reference, with method for numerical simulation, calculate and emulation.The advantage of method for numerical simulation is that emulation is accurate, precision is high, but it also exists that calculated amount is large, simulation time is long, the shortcoming of bad adaptability.In addition,, when comprising parasitic elements and driving circuit, cannot adopt numerical method to carry out circuit simulation analysis to device.

Circuit modeling approach is as building semiconductor device equivalent-circuit model, realize a kind of important cover half method of the sunykatuib analysis of device circuitry level, it is the important component part of modern optoelectronic integrated circuit computer-aided design (CAD), in extensive, VLSI (very large scale integrated circuit), the research fields such as integrated optoelectronic circuit and electro-optic hybrid circuit design all have a wide range of applications.It is a kind ofly directly from the physical equation of outlines device performance, to obtain the method for device equivalent-circuit model by suitable arrangement.

Realize single mode, wide wavelength tuning, surface launching, high-power, working and room temperature Terahertz light source, be the emphasis of THz QCL device research always.For many years, by optimizing the distributed feedback Thz QCL of active layer and ducting layer inner structure, the multimode effect in suppression device output spectrum, realizes device single-mode output aspect and has obtained certain progress.For further optimised devices output spectrum performance, just need in the Optimal Structure Designing of active layer and ducting layer, to the multimode effect of device output spectrum, carry out quantitative analysis, discuss and study the inherent positive connection between device architecture parameter and device output spectrum characteristic, for carrying out the optimal design of device, providing effective theory and data supporting.Though the research of Chinese scholars research in various degree cause reason and the influence factor of Thz QCL device multimode effect, and attempted realizing single longitudinal mode by the waveguiding structure of raising coupling efficiency, employing low-loss, high distributed feed-back and selected, but be not formed with yet the method for effect by the photoelectric characteristic of the Optimal Structure Designing of device active layer and ducting layer and device, particularly the multimode effect analog simulation of device output spectrum is integrated together.Aspect the emulation of simulation THz QCL device multimode effect, still lack applicable method model at present.

Summary of the invention

The present invention solves the existing technical matters of prior art; Provide a kind of be effective to study multi-modal effect on THz QCL as a kind of circuit modeling emulation mode that characterizes Terahertz quantum cascaded laser multimode effect of the impact of the photoelectric properties such as the gain of light, threshold current, saturated light power.

It is to solve the existing technical matters of prior art that the present invention also has an object; Provide a kind of support to realize simulation and the emulation to THz QCL time domain and frequency domain photoelectric properties and spectral characteristic by general circuit simulating software, under the condition that guarantees simulation precision, improve simulation velocity and efficiency, and can meet a kind of circuit modeling emulation mode that characterizes Terahertz quantum cascaded laser multimode effect that in actual photoelectricity integrated circuit (IC) design application requires optoelectronic device to realize the needs of photoelectricity hybrid simulation.

Above-mentioned technical matters of the present invention is mainly solved by following technical proposals:

A circuit modeling emulation mode that characterizes Terahertz quantum cascaded laser multimode effect, is characterized in that,

Step 1, based on multimodes rate equation group, the envelope that definition laser instrument output spectrum distributes has gaussian-shape as the function of wavelength, when simulation, spectrum is not treated as continuous spectrum as discrete spectrum, and define photon density in device chamber and change continuously with wavelength, Noise, does not set up the physical equation model that characterizes the inner multi-modal effect of Thz QCL, and concrete form is as follows;

Described electronics rate equation is as follows,

$\frac{{\mathrm{dn}}_3}{\mathrm{dt}}=\frac{\mathrm{\ηI}}{\mathrm{eV}}-\frac{n_3}{{\mathrm{\τ}}_3}-{\∫}_0^{\∞}g\left(\mathrm{\λ}\right)(n_3-n_2)S\left(\mathrm{\λ}\right)\mathrm{d\λ}$ Formula nine

$\frac{{\mathrm{dn}}_2}{\mathrm{dt}}=\frac{(1-\mathrm{\η})I}{\mathrm{eV}}+(\frac{1}{{\mathrm{\τ}}_{32}}+\frac{1}{{\mathrm{\τ}}_{\mathrm{sp}}})n_3-\frac{n_2}{{\mathrm{\τ}}_{21}}+{\∫}_0^{\∞}g\left(\mathrm{\λ}\right)(n_3-n_2)S\left(\mathrm{\λ}\right)\mathrm{d\λ}$ Formula ten

$\frac{{\mathrm{dn}}_1}{\mathrm{dt}}=\frac{n_3}{{\mathrm{\τ}}_{31}}+\frac{n_2}{{\mathrm{\τ}}_{21}}-\frac{n_1}{{\mathrm{\τ}}_{\mathrm{out}}}$ Formula 11

Described photon velocity equation is as follows,

$\frac{\mathrm{dS}\left(\mathrm{\λ}\right)}{\mathrm{dt}}=\mathrm{\Γg}\left(\mathrm{\λ}\right)(n_3-n_2)S\left(\mathrm{\λ}\right)+\mathrm{\β}\left(\mathrm{\λ}\right)\mathrm{\Γ}\frac{n_3}{{\mathrm{\τ}}_{\mathrm{sp}}}-\frac{S\left(\mathrm{\λ}\right)}{{\mathrm{\τ}}_{\mathrm{ph}}}$ Formula 12

Wherein, S (λ) is unit wavelength interval inner laser device output photon density, and its functional form is as follows,

$S\left(\mathrm{\λ}\right)=S_p\exp \left[\frac{-4\ln 2{(\mathrm{\λ}-{\mathrm{\λ}}_p)}^2}{{\left({\mathrm{\Δ\λ}}_p\right)}^2}\right]$ Formula 13

S in formula _pfor photon number density peak value, S (λ) has identical central wavelength lambda with gain g (λ) and spontaneous radiation coupling coefficient β (λ) _p, Δ λ _pfWHM for this distribution function;

Step 2, on the inner carrier transport characteristic in sign THz QCL active area of setting up in step 1 and the basis of the multi-modal characteristic physical model of photon, carrying out abbreviation and parameter changes, set up to characterize the equivalent-circuit model of the inner carrier transport of THz QCL active layer and multi-modal characteristic, based on following formula:

$I_{\mathrm{inj}}=\frac{V_{n3}}{R_3}+C_3\frac{{\mathrm{dV}}_{n3}}{\mathrm{dt}}+I_{\mathrm{st}}$ Formula 14

$I_{\mathrm{leak}}+I_3+I_{\mathrm{st}}=\frac{V_{n2}}{R_2}+C_2\frac{{\mathrm{dV}}_{n2}}{\mathrm{dt}}$ Formula 15

$I_3^{\′}+I_2=\frac{V_{n1}}{R_1}+C_1\frac{{\mathrm{dV}}_{n1}}{\mathrm{dt}}$ Formula 16

Wherein, I _inj=Q η I; R ₃=τ ₃/ Q; C ₃=Q;

$\begin{array}{c}{I}_{\mathrm{st}}=Q{\∫}_0^{\∞}g\left(\mathrm{\λ}\right)(n_3-n_2)S\left(\mathrm{\λ}\right)\mathrm{d\λ}\\ =G(V_{n3}-V_{n2})[A_t{\mathrm{\Δ\λ}}_p-A_g{\mathrm{\Δ\λ}}_p^3]S_p\end{array};$

$G=Q\frac{e^2{f}_{32}}{{{2\mathrm{\πm}}^{*}n}_{\mathrm{eff}}^2{\mathrm{\ϵ\Δ\λ}}_g},A_t=\sqrt{\mathrm{\π}/4\ln 2},A_g=\frac{A_t}{4\ln 2\mathrm{\Δ}{\mathrm{\λ}}_g^2};$

I _leak＝Q(1-η)I； $I_3=Q(\frac{1}{{\mathrm{\τ}}_{32}}+\frac{1}{{\mathrm{\τ}}_{\mathrm{sp}}})V_{n3};$ R ₂＝τ ₂₁/Q；C ₂＝Q；

$I_3^{\′}=\frac{Q}{{\mathrm{\τ}}_{31}}{V}_{n3};I_2=\frac{Q}{{\mathrm{\τ}}_{21}}{V}_{n2};$ R ₁＝τ _out/Q；C ₁＝Q；

$I_{\mathrm{rrl}}+I_{\mathrm{sp}}=\frac{S_p}{R_{\mathrm{ph}}}+C_{\mathrm{ph}}\frac{{\mathrm{dS}}_p}{\mathrm{dt}}$ Formula 20

I _rr1=I _s+ I _gformula 21

According to Kirchhoff's current law (KCL) with electronic circuit respectively by formula 14, formula 15, formula 16, formula 20, formula 21 statements out, the equivalent-circuit model of setting up the sign THz inner carrier transport of QCL active layer and multi-modal effect is as follows:

Equivalent model one: the electronic circuit obtaining according to formula 14 is by controlled current source I _injwith capacitor C ₃, resistance R ₃, controlled current source I _stthe 1st the electricity branch road that after in parallel, one end ground connection forms, this branch node voltage is Vn ₃;

Equivalent model two: the electronic circuit obtaining according to formula 15 is by controlled current source I _leak, controlled current source I _st, controlled current source I ₃, capacitor C ₂, resistance R ₂the 2nd the electricity branch road that after in parallel, one end ground connection forms, this branch node voltage is Vn ₂;

Equivalent model three: the electronic circuit obtaining according to formula 16 is by controlled current source I ' ₃with controlled current source I ₂, capacitor C ₁, resistance R ₁the 3rd the electricity branch road that after in parallel, one end ground connection forms, this branch node voltage is Vn ₁;

Equivalent model four: the electronic circuit obtaining according to formula 20 is by controlled current source I _rr1with controlled current source I _sp, capacitor C _ph, resistance R _phthe 4th the optics branch road forming after in parallel, this branch node voltage is S _p;

Equivalent model five: the electronic circuit obtaining according to formula 21 is by controlled current source I _rr1with controlled current source I _s, controlled current source I _gthe 5th optics branch road after in parallel in the ground connection component model of one end, this branch node voltage is Δ λ _p;

Step 3, according to the I-E characteristic of the electric input interface of THz QCL, sets up the equivalent-circuit model that characterizes THz QCL input end electrical specification, comprises following sub-step:

Step 3.1, definition P ₁for equivalent electric signal input port, first use a desirable diode D ₁with a resistance R _dbe series at P ₁between, as the corresponding electronic circuit of equivalent-circuit model that characterizes THz QCL input electrical specification, the I ideal diode D that represents to flow through ₁electric current, the function V (I, T) that the voltage V of device input end is defined as to electric current I and temperature T is as follows:

$V(I,T)=\frac{\mathrm{KT}}{e}\ln (\frac{I}{I_s}+1)+{\mathrm{IR}}_s$ Formula 22

Wherein, KT/e is thermal voltage parameter V _t, K is Boltzmann constant, and e is electron charge, and T is kelvin degree, resistance R _dresistance be R _s, I _sreverse saturation current for diode;

Step 3.2, then, according to current-voltage (IV) curve of device input end actual measurement, uses the matching of Levenberg-Marquard method to obtain parameters R _s, I _s;

Step 3.3, last, ideal diode D will flow through ₁electric current I as controlled current source I in step 3 _injand I _leakcontrol current signal;

Step 4, the relation of Output optical power and photon density in the unit of utilization wavelength interval, tries to achieve the total Output optical power P of THz QCL light waveguide-layer _out, set up the equivalent-circuit model that characterizes THz QCL output terminal luminous power characteristic;

Step 5, in step 2, on the basis of step 3 and step 4, sets up the circuit macro-model that characterizes THz QCL photoelectric properties based on multimodes rate equation group, and this circuit macro-model is totally two ports, comprises an electrical port and a luminous power output port; Based on circuit macro-model, carry out photoelectric properties emulation and spectral characteristic test.

In above-mentioned a kind of circuit modeling emulation mode that characterizes Terahertz quantum cascaded laser multimode effect, in described step 1, multimodes rate equation group is to set up according to the transport property of the inner charge carrier of THz QCL active layer:

Described electronics rate equation is as follows,

$\frac{{\mathrm{dn}}_3}{\mathrm{dt}}=\frac{\mathrm{\ηI}}{\mathrm{eV}}-\frac{n_3}{{\mathrm{\τ}}_3}-\underset{m}{\mathrm{\Σ}}{g}_m(n_3-n_2)S_m$ Formula one

$\frac{{\mathrm{dn}}_2}{\mathrm{dt}}=\frac{(1-\mathrm{\η})I}{\mathrm{eV}}+(\frac{1}{{\mathrm{\τ}}_{32}}+\frac{1}{{\mathrm{\τ}}_{\mathrm{sp}}})n_3-\frac{n_2}{{\mathrm{\τ}}_{21}}+\underset{m}{\mathrm{\Σ}}{g}_m(n_3-n_2)S_m$ Formula two

$\frac{{\mathrm{dn}}_1}{\mathrm{dt}}=\frac{n_3}{{\mathrm{\τ}}_{31}}+\frac{n_2}{{\mathrm{\τ}}_{21}}-\frac{n_1}{{\mathrm{\τ}}_{\mathrm{out}}}$ Formula three

The photon velocity equation of described m pattern photon is as follows,

$\frac{{\mathrm{dS}}_m}{\mathrm{dt}}=\mathrm{\Γ}{g}_m(n_3-n_2)S_m+{\mathrm{\β}}_m\mathrm{\Γ}\frac{n_3}{{\mathrm{\τ}}_{\mathrm{sp}}}-\frac{S_m}{{\mathrm{\τ}}_{\mathrm{ph}}}$ Formula four

Wherein, photon stimulated radiation transition high swash penetrate energy level and low swash penetrate energy level, the auxiliary transition relaxation energy level of phonon is designated respectively sub-energy level 1,2,3, wherein n ₃and n ₂represent respectively high sharp energy level and low sharp penetrate the electron number volume density on energy level, the n of penetrating of photon stimulated radiation transition ₁electron number volume density on the relaxation energy level of the auxiliary transition of expression phonon, S _mfor the photon number volume density of m pattern photon in optical cavity, the Injection Current that I is quantum cascade laser, τ ₃, τ ₃₂be respectively the radiation transistion life-span between 3 electronics entire lives of sub-energy level and sub-energy level 3 and sub-energy level 2; τ ₃₁, τ ₂₁be respectively between sub-energy level 3 and sub-energy level 1, the nonradiative transition life-span between sub-energy level 2 and sub-energy level 1, wherein 1I τ ₃=1/ τ ₃₂+ 1/ τ ₃₁+ 1/ τ _sp; τ _sp, τ _phbe respectively the spontaneous radiation life-span of electronics between sub-energy level 3 and sub-energy level 2 and the photon lifetime in optical cavity, τ _outfor electronics is in the escape time of facing mutually between two cascade periodic structures; Γ is light restriction factor, and e is electron charge, and V is active area single-stage volume; η represents electric current injection efficiency parameter; g _mfor the gain of light of m pattern photon, its computing formula is as follows:

$g_m=g\left({\mathrm{\λ}}_m\right)=\frac{e^2{f}_{32}}{{4m}^{*}{n}_{\mathrm{eff}}^2\mathrm{\ϵ}}\·\mathrm{\γ}\left({\mathrm{\λ}}_m\right)$ Formula five

λ in formula five _mfor optical wavelength corresponding to m pattern photon, f ₃₂for the resonance intensity of radiation between sub-energy level 3 and sub-energy level 2, m ^*for the effective mass of active area mqw material electronics, ε is effective dielectric constant, n _efffor the equivalent refractive index in optical cavity; γ (λ _m) be line shape function, for characterizing the gain spectral distribution of laser radiation photon, this function adopts Lorentz lorentz's distribution function, γ (λ _m) computing formula is as follows:

$\mathrm{\γ}\left({\mathrm{\λ}}_m\right)=\frac{\frac{2}{\mathrm{\π\Δ}{\mathrm{\λ}}_g}}{1+4{({\mathrm{\λ}}_m-{\mathrm{\λ}}_p)}^2/\mathrm{\Δ}{\mathrm{\λ}}_g^2}$ Formula six

λ in formula six _pfor the centre wavelength of laser gain spectrum, Δ λ _gfWHM (Full Width at Half Maximum) for this distribution function;

In formula four, β _mspontaneous radiation coupling coefficient for m pattern photon; Under different mode, the spontaneous radiation coupling coefficient of photon also meets Lorentz lorentz's distribution function, and its computing formula is as follows:

${\mathrm{\β}}_m=\mathrm{\β}\left({\mathrm{\λ}}_m\right)=\frac{{\mathrm{\β}}_{\mathrm{sp}0}}{1+4{({\mathrm{\λ}}_m-{\mathrm{\λ}}_p)}^2/\mathrm{\Δ}{\mathrm{\λ}}_s^2}$ Formula seven

Δ λ in formula seven _sfWHM for this distribution function; β _sp0for the spontaneous radiation coupling coefficient of corresponding centre wavelength, its value determined by following formula,

${\mathrm{\β}}_{\mathrm{sp}0}=\frac{{\mathrm{\λ}}_p^4}{{4\mathrm{\π}}^2{n}_{\mathrm{eff}}^3\mathrm{\Δ}{\mathrm{\λ}}_{s}V{N}_{\mathrm{mod}}}$ Formula eight

N in formula eight _modnumber for Thz QCL cascade.

At above-mentioned a kind of circuit modeling emulation mode that characterizes Terahertz quantum cascaded laser multimode effect, parameter τ described in multimodes rate equation group ₃, τ ₃₂, τ ₃₁, τ ₂₁, τ _out, τ _sp, τ _phobtain manner comprises the following steps,

Step 3.1, under the condition of known THz QCL active layer mqw material, physical dimension and doping content, suppose that the direction of growth of material is along z axle, by self-consistent solution not time-dependent Schrodinger equation and Poisson equation, iteration is obtained each sub-energy levels Ei of active layer electronics, wave function ψ i (z), electron density distribution n (z);

Step 3.2, according to fermi's golden rule, the transition speed of definition electronics in i sub-band energy level is

formula 25

Wherein, for reduced Planck constant, τ ' _ifor the existence life-span of electronics at sub-band energy level i, Ei and Ef are respectively the electron energy of initial state sub-band energy level i and transition final states sub-band energy level f, for disturbance quantity, for transition matrix element;

By the sub-energy level of initial state, the average transition speed to the sub-energy level transition of final states can be expressed as definition electronics

$\mathrm{mean}\left(\frac{1}{{\mathrm{\τ}}_i^{\′}}\right)=\frac{\∫{\mathrm{\θf}}_i^{\mathrm{FD}}\left(\mathrm{\θ}\right)/{\mathrm{\τ}}_i^{\′}\mathrm{d\θ}}{\mathrm{\π}{N}_i}$ Formula 26

Wherein, for the plane wave number of electronics, for electronics is at i subband Fermi distribution function, definition electronics at the surface density Ni of i subband is:

formula 27

Wherein, m ^*for the effective mass of electronics, be that i subband plane wave number is the energy of k electronics;

According to different scattering mechanisms, be listed as respectively and write transition matrix element f wherein, i=1,2,3, and f ≠ i, use numerical method to calculate the existence life-span τ ' of electronics on sub-energy level 3 under different scattering mechanisms according to formula five ₃, electronics is at the nonradiative transition life-span τ ' of 2 of sub-energy level 3 and sub-energy levels ₃₂, electronics is at the nonradiative transition life-span τ ' of 1 of sub-energy level 3 and sub-energy level ₃₁with the nonradiative transition life-span τ ' of electronics 1 of sub-energy level 2 and sub-energy level ₂₁, and according to formula six and formula seven, calculate the electronics the average survival time life-span of electronics on sub-energy level 3 under different scattering mechanisms electronics between sub-energy level 3 and 2, electronics between sub-energy level 3 and 1, the average nonradiative transition life-span of electronics between sub-energy level 2 and 1 with

Step 3.3, the inverse of the electronics mean lifetime of calculating under different scattering mechanisms is added and asks its reciprocal value to obtain electronics total life-span τ on sub-energy level 3 again ₃, electronics between sub-energy level 3 and 2, between sub-energy level 3 and 1, total nonradiative transition life-span τ between sub-energy level 2 and 1 ₃₂, τ ₃₁and τ ₂₁;

Intersubband self-excitation radiation-emitting transition rate equation under step 3.4, utilization three-dimensional photon density-of-states distribution model

$\frac{1}{{\mathrm{\τ}}_{\mathrm{sp}}}=\frac{e^2{n}_{\mathrm{eff}}{\mathrm{\ω}}_0^2}{{6\mathrm{\π\ϵm}}^{*}{c}^3}{f}_{32}$ Formula 28

Calculate the spontaneous radiation life-span τ of electronics between sub-energy level 3 and sub-energy level 2 _sp, wherein for the resonance intensity based on electric coupling polar moment between sub-energy level 3 and sub-energy level 2, ω ₀for utilizing emitted light subcenter angular frequency, the effective mass that m* is electronics, ε is effective dielectric constant, n _efffor effective refractive index in optical cavity, c is the light velocity in vacuum, and e is electron charge;

Step 3.5, according to the optical cavity structure of device and material parameter, calculate the mirror loss α of optical cavity _mwaveguide loss α with optical cavity _w, and according to formula calculate parameter τ photon lifetime in optical cavity _p, n wherein _efffor effective refractive index in optical cavity; According to experimental data, extract and obtain electronics at the escape time parameter τ facing mutually between two cascade periodic structures _out.

In above-mentioned a kind of circuit modeling emulation mode that characterizes Terahertz quantum cascaded laser multimode effect, described step 4 comprises following sub-step:

The pass of unit wavelength interval Output optical power and photon density is,

$p\left(\mathrm{\λ}\right)={\mathrm{hc}}^2\mathrm{WD}/\left(2{\stackrel{\‾}{n}}_g\mathrm{\λ}\right)\·\ln (1/R_L{R}_R)/2\·S\left(\mathrm{\λ}\right)$ Formula 23

In formula, W, D are respectively broadband and the gross thickness of active area, R _land R _rfor the left and right end face reflection coefficient of optical cavity, for the group index of photon, λ penetrates photon wavelength for swashing, and constant h is Planck constant, and c is the light velocity in vacuum; Make integration can obtain total Output optical power P _out

$P_{\mathrm{out}}={\mathrm{hc}}^2\mathrm{WD}/\left(2{\stackrel{\‾}{n}}_g{\mathrm{\λ}}_p\right)\·\ln (1/R_L{R}_R)/2\·A_t{S}_p{\mathrm{\Δ\λ}}_p$ Formula 24

Adopt a voltage-controlled controlled voltage source E _outanalog laser Output optical power P _out, voltage-controlled controlled voltage source E _outvoltage-controlled signal be the node voltage signal S of the 4th optics branch road _pnode voltage signal delta λ with the 5th optics branch road _p, voltage-controlled controlled voltage source E _outthe optical power value of the corresponding laser output of output voltage values, voltage-controlled controlled voltage source E _outscale-up factor k _paccording to formula 23, pass through to calculate obtain; Voltage-controlled controlled voltage source E _outconnect equivalent luminous power output port P ₂as the equivalent-circuit model that characterizes the output of THz QCL luminous power.

In above-mentioned a kind of circuit modeling emulation mode that characterizes Terahertz quantum cascaded laser multimode effect, in step 5, the concrete grammar that foundation characterizes the circuit macro-model of THz QCL photoelectric properties based on multimodes rate equation group is: first, use the newly-built circuit macro-model Thz QCL Multimode Model with two-port of circuit simulating software instrument HSPICE, definition two-port attribute, port Nin is laser instrument electrical input terminal mouth, and port NPout is laser optical power stage port; Then use electronic circuit descriptive language that each electronic circuit of setting up in step 3,4,5 is explained out; Finally the equivalent electric signal input port P1 setting up in step 4 is connected with the port Nin of circuit macro-model Thz QCL Multimode Model, the equivalent luminous power output port P2 setting up in step 5 is connected with the port NPout of circuit macro-model Thz QCL Multimode Model.

Therefore, tool of the present invention has the following advantages: (1) can be effective to study multi-modal effect on THz QCL as the impact of the photoelectric properties such as the gain of light, threshold current, saturated light power; (2) can support to realize simulation and the emulation to THz QCL time domain and frequency domain photoelectric properties and spectral characteristic by general circuit simulating software, under the condition that guarantees simulation precision, improve simulation velocity and efficiency, and can meet the needs that in actual photoelectricity integrated circuit (IC) design application require optoelectronic device to realize photoelectricity hybrid simulation.

Accompanying drawing explanation

Fig. 1 is method flow schematic diagram of the present invention.

Fig. 2 is the circuit macro-model graphical diagram of THz QCL of the present invention.

Fig. 3 is the equivalent-circuit model electronic circuit figure that the present invention characterizes THz QCL input end electrical specification.

Fig. 4 a is that the present invention characterizes the 1st electricity branch road in the equivalent-circuit model electronic circuit figure of the inner carrier transport of THz QCL and multi-modal effect.

Fig. 4 b is that the present invention characterizes the 2nd electricity branch road in the equivalent-circuit model electronic circuit figure of the inner carrier transport of THz QCL and multi-modal effect.

Fig. 4 c is that the present invention characterizes the 3rd electricity branch road in the equivalent-circuit model electronic circuit figure of the inner carrier transport of THz QCL and multi-modal effect.

Fig. 4 d is for characterizing the optics branch road of THz QCL interior lights sub-feature.

Fig. 4 e is for characterizing the optics branch road of THz QCL interior lights spectral property.

Fig. 5 is the equivalent-circuit model electronic circuit figure that the present invention characterizes THz QCL output terminal luminous power characteristic.

Fig. 6 is the performance diagram of Thz QCL Output optical power, input current and the bias voltage of temperature 5K Imitating of the present invention.

Fig. 7 is the Thz QCL Output optical power of temperature 5K of the present invention and 78K Imitating and the performance diagram of input current.

Fig. 8 is the Thz QCL output spectrum performance diagram of temperature 5K of the present invention and 78K Imitating.

Embodiment

Below by embodiment, and by reference to the accompanying drawings, technical scheme of the present invention is described in further detail.

One, first, introduce theoretical method of the present invention (comprising derivation step), comprise the following steps:

Step 1, according to the transport property of the inner charge carrier of THz QCL active layer, sets up the multimodes rate equation group of describing laser instrument electro-optical properties;

Described electronics rate equation is as follows,

$\frac{{\mathrm{dn}}_3}{\mathrm{dt}}=\frac{\mathrm{\ηI}}{\mathrm{eV}}-\frac{n_3}{{\mathrm{\τ}}_3}-\underset{m}{\mathrm{\Σ}}{g}_m(n_3-n_2)S_m$ Formula one

$\frac{{\mathrm{dn}}_2}{\mathrm{dt}}=\frac{(1-\mathrm{\η})I}{\mathrm{eV}}+(\frac{1}{{\mathrm{\τ}}_{32}}+\frac{1}{{\mathrm{\τ}}_{\mathrm{sp}}})n_3-\frac{n_2}{{\mathrm{\τ}}_{21}}+\underset{m}{\mathrm{\Σ}}{g}_m(n_3-n_2)S_m$ Formula two

$\frac{{\mathrm{dn}}_1}{\mathrm{dt}}=\frac{n_3}{{\mathrm{\τ}}_{31}}+\frac{n_2}{{\mathrm{\τ}}_{21}}-\frac{n_1}{{\mathrm{\τ}}_{\mathrm{out}}}$ Formula three

The photon velocity equation of described m pattern photon is as follows,

$\frac{{\mathrm{dS}}_m}{\mathrm{dt}}={\mathrm{\Γg}}_m(n_3-n_2)S_m+{\mathrm{\β}}_m\mathrm{\Γ}\frac{n_3}{{\mathrm{\τ}}_{\mathrm{sp}}}-\frac{S_m}{{\mathrm{\τ}}_{\mathrm{ph}}}$ Formula four

Wherein, photon stimulated radiation transition high swash penetrate energy level and low swash penetrate energy level, the auxiliary transition relaxation energy level of phonon is designated respectively sub-energy level 1,2,3, wherein n ₃and n ₂represent respectively high sharp energy level and low sharp penetrate the electron number volume density on energy level, the n of penetrating of photon stimulated radiation transition ₁electron number volume density on the relaxation energy level of the auxiliary transition of expression phonon, S _mfor the photon number volume density of m pattern photon in optical cavity, the Injection Current that I is quantum cascade laser, τ ₃, τ ₃₂be respectively the radiation transistion life-span between 3 electronics entire lives of sub-energy level and sub-energy level 3 and sub-energy level 2; τ ₃₁, τ ₂₁be respectively between sub-energy level 3 and sub-energy level 1, the nonradiative transition life-span between sub-energy level 2 and sub-energy level 1, wherein 1/ τ ₃=1/ τ ₃₂+ 1/ τ ₃₁+ 1/ τ _sp; τ _sp, τ _phbe respectively the spontaneous radiation life-span of electronics between sub-energy level 3 and sub-energy level 2 and the photon lifetime in optical cavity, τ _outfor electronics is in the escape time of facing mutually between two cascade periodic structures; Γ is light restriction factor, and e is electron charge, and V is active area single-stage volume; η represents electric current injection efficiency parameter; g _mfor the gain of light of m pattern photon, its computing formula is as follows,

$g_m=g\left({\mathrm{\λ}}_m\right)=\frac{e^2{f}_{32}}{4m^{*}{n}_{\mathrm{eff}}^2\mathrm{\ϵ}}\·\mathrm{\γ}\left({\mathrm{\λ}}_m\right)$ Formula five

λ in formula five _mfor optical wavelength corresponding to m pattern photon, f ₃₂for the resonance intensity of radiation between sub-energy level 3 and sub-energy level 2, m ^*for the effective mass of active area mqw material electronics, ε is effective dielectric constant, n _efffor the equivalent refractive index in optical cavity; γ (λ _m) be line shape function, for characterizing the gain spectral distribution of laser radiation photon, this function adopts Lorentz lorentz's distribution function, γ (λ _m) computing formula is as follows,

$\mathrm{\γ}\left({\mathrm{\λ}}_m\right)=\frac{\frac{2}{\mathrm{\π\Δ}{\mathrm{\λ}}_g}}{1+4{({\mathrm{\λ}}_m-{\mathrm{\λ}}_p)}^2/\mathrm{\Δ}{\mathrm{\λ}}_g^2}$ Formula six

λ in formula six _pfor the centre wavelength of laser gain spectrum, Δ λ _gfWHM (Full Width at Half Maximum) for this distribution function.

In formula four, β _mspontaneous radiation coupling coefficient for m pattern photon.Under different mode, the spontaneous radiation coupling coefficient of photon also meets Lorentz lorentz's distribution function, and its computing formula is as follows,

${\mathrm{\β}}_m=\mathrm{\β}\left({\mathrm{\λ}}_m\right)=\frac{{\mathrm{\β}}_{\mathrm{sp}0}}{1+4{({\mathrm{\λ}}_m-{\mathrm{\λ}}_p)}^2/\mathrm{\Δ}{\mathrm{\λ}}_s^2}$ Formula seven

Δ λ in formula seven _sfWHM for this distribution function; β _sp0for the spontaneous radiation coupling coefficient of corresponding centre wavelength, its value determined by following formula,

${\mathrm{\β}}_{\mathrm{sp}0}=\frac{{\mathrm{\λ}}_p^4}{4{\mathrm{\π}}^2{n}_{\mathrm{eff}}^3\mathrm{\Δ}{\mathrm{\λ}}_s{\mathrm{VN}}_{\mathrm{mod}}}$ Formula eight

N in formula eight _modnumber for Thz QCL cascade.

Step 2, on the basis of the multimodes rate equation group of setting up in step 1, complicacy for simplified construction model, improve Model Practical, suppose that envelope that laser instrument output spectrum distributes has gaussian-shape as the function of wavelength, when simulation, spectrum is not treated as continuous spectrum as discrete spectrum, suppose that in laser chamber, photon density changes continuously with wavelength, and ignore the impact of noise, and set up the physical equation model that characterizes the inner multi-modal effect of Thz QCL, concrete form is as follows;

Described electronics rate equation is as follows,

$\frac{d{n}_3}{\mathrm{dt}}=\frac{\mathrm{\ηI}}{\mathrm{eV}}-\frac{n_3}{{\mathrm{\τ}}_3}-{\∫}_0^{\∞}g\left(\mathrm{\λ}\right)(n_3-n_2)S\left(\mathrm{\λ}\right)\mathrm{d\λ}$ Formula nine

$\frac{d{n}_2}{\mathrm{dt}}=\frac{(1-\mathrm{\η})I}{\mathrm{eV}}+(\frac{1}{{\mathrm{\τ}}_{32}}+\frac{1}{{\mathrm{\τ}}_{\mathrm{sp}}})n_3-\frac{n_2}{{\mathrm{\τ}}_{21}}+{\∫}_0^{\∞}g\left(\mathrm{\λ}\right)(n_3-n_2)S\left(\mathrm{\λ}\right)\mathrm{d\λ}$ Formula ten

$\frac{d{n}_1}{\mathrm{dt}}=\frac{n_3}{{\mathrm{\τ}}_{31}}+\frac{n_2}{{\mathrm{\τ}}_{21}}-\frac{n_1}{{\mathrm{\τ}}_{\mathrm{out}}}$ Formula 11

Described photon velocity equation is as follows,

$\frac{\mathrm{dS}\left(\mathrm{\λ}\right)}{\mathrm{dt}}=\mathrm{\Γg}\left(\mathrm{\λ}\right)(n_3-n_2)S\left(\mathrm{\λ}\right)+\mathrm{\β}\left(\mathrm{\λ}\right)\mathrm{\Γ}\frac{n_3}{{\mathrm{\τ}}_{\mathrm{sp}}}-\frac{S\left(\mathrm{\λ}\right)}{{\mathrm{\τ}}_{\mathrm{ph}}}$ Formula 12

Wherein S (λ) is unit wavelength interval inner laser device output photon density, and its functional form is as follows,

$S\left(\mathrm{\λ}\right)=S_p\exp \left[\frac{-4\ln 2{(\mathrm{\λ}-{\mathrm{\λ}}_p)}^2}{{\left(\mathrm{\Δ}{\mathrm{\λ}}_p\right)}^2}\right]$ Formula 13

S in formula _pfor photon number density peak value, S (λ) has identical central wavelength lambda with gain g (λ) and spontaneous radiation coupling coefficient β (λ) _p, Δ λ _pfWHM for this distribution function.

Step 3, on the inner carrier transport characteristic in sign THz QCL active area of setting up in step 2 and the basis of the multi-modal characteristic physical model of photon, carry out abbreviation and parameter and change, set up the equivalent-circuit model that characterizes the inner carrier transport of THz QCL active layer and multi-modal characteristic;

The concrete steps of carrying out abbreviation and parameter variation structure circuit model described in step 3 are as follows,

Q=eV is taken advantage of in the equation both sides of the formula in step 2 nine, formula ten, formula 11, use voltage V _n3, V _n2, V _n1difference substitute variable n ₃, n ₂, n ₁arrange

$I_{\mathrm{inj}}=\frac{V_{n3}}{R_3}+C_3\frac{d{V}_{n3}}{\mathrm{dt}}+I_{\mathrm{st}}$ Formula 14

$I_{\mathrm{leak}}+I_3+I_{\mathrm{st}}=\frac{V_{n2}}{R_2}+C_2\frac{d{V}_{n2}}{\mathrm{dt}}$ Formula 15

$I_3^{\text{'}}+I_2=\frac{V_{n1}}{R_1}+C_1\frac{d{V}_{n1}}{\mathrm{dt}}$ Formula 16

In formula 14, in formula 15, formula 16,

I _inj＝QηI；R ₃＝τ ₃/Q；C ₃＝Q；

$\begin{array}{c}{I}_{\mathrm{st}}=Q{\∫}_0^{\∞}g\left(\mathrm{\λ}\right)(n_3-n_2)S\left(\mathrm{\λ}\right)\mathrm{d\λ}\\ =G(V_{n3}-V_{n2})[A_t\mathrm{\Δ}{\mathrm{\λ}}_p-A_g\mathrm{\Δ}{\mathrm{\λ}}_p^3]S_p\end{array};$

$G=Q\frac{e^2{f}_{32}}{2\mathrm{\π}{m}^{*}{n}_{\mathrm{eff}}^2\mathrm{\ϵ\Δ}{\mathrm{\λ}}_g},A_t=\sqrt{\mathrm{\π}/4\ln 2},A_g=\frac{A_t}{4\ln 2\mathrm{\Δ}{\mathrm{\λ}}_g^2};$ I _leak＝Q(1-η)I；

$I_3=Q(\frac{1}{{\mathrm{\τ}}_{32}}+\frac{1}{{\mathrm{\τ}}_{\mathrm{sp}}})V_{n3};$ R ₂＝τ ₂₁/Q；C ₂＝Q； $I_3^{\text{'}}=\frac{Q}{{\mathrm{\τ}}_{31}}{V}_{n3};I_2=\frac{Q}{{\mathrm{\τ}}_{21}}{V}_{n2};$

R ₁＝τ _out/Q；C ₁＝Q；

Use respectively λ _p(λ _p+ Δ λ _p/ 2) two specific wavelengths are brought the formula 12 in step 2 into, use voltage V _n3, V _n2difference substitute variable n ₃, n ₂, and Q=eV is taken advantage of in both sides, arrange

$Q\frac{d{S}_p}{\mathrm{dt}}=G^{\text{'}}(V_{n3}-V_{n2})S_p-\frac{Q{S}_p}{{\mathrm{\τ}}_{\mathrm{ph}}}+{\mathrm{\β}}_{\mathrm{sp}0}{I}_{\mathrm{rr}}$ Formula 17

$\frac{d{S}_p}{\mathrm{dt}}\frac{2G^{\text{'}}(V_{n3}-V_{n2})S_p}{1+\mathrm{\Δ}{\mathrm{\λ}}_p^2/\mathrm{\Δ}{\mathrm{\λ}}_g^2}\frac{Q{S}_p}{{\mathrm{\τ}}_{\mathrm{ph}}}\frac{2{\mathrm{\β}}_{\mathrm{sp}0}{I}_{\mathrm{rr}}}{1+\mathrm{\Δ}{\mathrm{\λ}}_p^2/{\mathrm{\λ}}_s^2}$ Formula 18

In formula, $G^{\text{'}}=\mathrm{Q\Γ}\frac{e^2{f}_{32}}{2\mathrm{\π}{m}^{*}{n}_{\mathrm{eff}}^2\mathrm{\ϵ\Δ}{\mathrm{\λ}}_g},I_{\mathrm{rr}}=\mathrm{\ΓQ}\frac{V_{n3}}{{\mathrm{\τ}}_{\mathrm{sp}}};$

Make formula 17 and formula 18 left and right equate to obtain:

${\mathrm{\β}}_{\mathrm{sp}0}{I}_{\mathrm{rr}}=\frac{2\mathrm{\Δ}{\mathrm{\λ}}_s^2}{\mathrm{\Δ}{\mathrm{\λ}}_s^2+\mathrm{\Δ}{\mathrm{\λ}}_p^2}{\mathrm{\β}}_{\mathrm{sp}0}{I}_{\mathrm{rr}}+\frac{\mathrm{\Δ}{\mathrm{\λ}}_g^2-\mathrm{\Δ}{\mathrm{\λ}}_p^2}{\mathrm{\Δ}{\mathrm{\λ}}_g^2+\mathrm{\Δ}{\mathrm{\λ}}_p^2}{G}^{\text{'}}(V_{n3}-V_{n2})S_p$ Formula 19

Make R _ph=τ _ph/ Q, C _ph=Q, I _rr1=β _sp0i _rr, I _sp=G ' (V _n3-V _n2) S _pin substitution formula 17, obtain,

$I_{\mathrm{rr}1}+I_{\mathrm{sp}}=\frac{S_p}{R_{\mathrm{ph}}}+C_{\mathrm{ph}}\frac{d{S}_p}{\mathrm{dt}}$ Formula 20

Make I _rr1=β _sp0i _rr, $I_s=\frac{2\mathrm{\Δ}{\mathrm{\λ}}_s^2}{\mathrm{\Δ}{\mathrm{\λ}}_s^2+\mathrm{\Δ}{\mathrm{\λ}}_p^2}{I}_{\mathrm{rr}1},I_g=\frac{\mathrm{\Δ}{\mathrm{\λ}}_g^2-\mathrm{\Δ}{\mathrm{\λ}}_p^2}{\mathrm{\Δ}{\mathrm{\λ}}_g^2+\mathrm{\Δ}{\mathrm{\λ}}_p^2}{G}^{\text{'}}(V_{n3}-V_{n2})S_p,$ In substitution formula 19, obtain,

I _rr1=I _s+ I _gformula 21

According to Kirchhoff's current law (KCL) with electronic circuit respectively by formula 14, formula 15, formula 16, formula 20, formula 21 statements out, the equivalent-circuit model of setting up the sign THz inner carrier transport of QCL active layer and multi-modal effect is as follows,

The electronic circuit obtaining according to formula 14 is by controlled current source I _injwith capacitor C ₃, resistance R ₃, controlled current source I _stthe 1st the electricity branch road that after in parallel, one end ground connection forms, this branch node voltage is Vn ₃;

The electronic circuit obtaining according to formula 15 is by controlled current source I _leak, controlled current source I _st, controlled current source I ₃, capacitor C ₂, resistance R ₂the 2nd the electricity branch road that after in parallel, one end ground connection forms, this branch node voltage is Vn ₂;

The electronic circuit obtaining according to formula 16 is by controlled current source I ' ₃with controlled current source I ₂, capacitor C ₁, resistance R ₁the 3rd the electricity branch road that after in parallel, one end ground connection forms, this branch node voltage is Vn ₁;

The electronic circuit obtaining according to formula 20 is by controlled current source I _rr1with controlled current source I _sp, capacitor C _ph, resistance R _phthe 4th the optics branch road forming after in parallel, this branch node voltage is S _p;

The electronic circuit obtaining according to formula 21 is by controlled current source I _rr1with controlled current source I _s, controlled current source I _gthe 5th optics branch road after in parallel in the ground connection component model of one end, this branch node voltage is Δ λ _p;

Step 4, according to the I-E characteristic of the electric input interface of THz QCL, sets up the equivalent-circuit model that characterizes THz QCL input end electrical specification;

Concrete steps are as follows,

1. first, establish P ₁for equivalent electric signal input port, first use a desirable diode D ₁with a resistance R _dbe series at P ₁between, as the corresponding electronic circuit of equivalent-circuit model that characterizes THz QCL input electrical specification, the I ideal diode D that represents to flow through ₁electric current, the function V (I, T) that the voltage V of device input end is defined as to electric current I and temperature T is as follows:

$V(I,T)=\frac{\mathrm{KT}}{e}\ln (\frac{I}{I_s}+1)+{\mathrm{IR}}_s$ Formula 22

Wherein, KT/e is thermal voltage parameter V _t, K is Boltzmann constant, and e is electron charge, and T is kelvin degree, resistance R _dresistance be R _s, I _sreverse saturation current for diode;

2. then,, according to current-voltage (IV) curve of device input end actual measurement, use the matching of Levenberg-Marquard method to obtain parameters R _s, I _s;

3. last, ideal diode D will flow through ₁electric current I as controlled current source I in step 3 _injand I _leakcontrol current signal.

Step 5, the relation of Output optical power and photon density in the unit of utilization wavelength interval, tries to achieve the total Output optical power P of THz QCL light waveguide-layer _out, set up the equivalent-circuit model that characterizes THz QCL output terminal luminous power characteristic;

Concrete steps are as follows, and the pass of unit wavelength interval Output optical power and photon density is,

$p\left(\mathrm{\λ}\right)={\mathrm{hc}}^2\mathrm{WD}/\left(2{\stackrel{\‾}{n}}_g\mathrm{\λ}\right)\·\ln (1/R_L{R}_R)/2\·S\left(\mathrm{\λ}\right)$ Formula 23

In formula, W, D are respectively broadband and the gross thickness of active area, R _land R _rfor the left and right end face reflection coefficient of optical cavity, for the group index of photon, λ penetrates photon wavelength for swashing, and constant h is Planck constant, and c is the light velocity in vacuum.Make integration can obtain total Output optical power P _out

$P_{\mathrm{out}}={\mathrm{hc}}^2\mathrm{WD}/\left(2{\stackrel{\‾}{n}}_g{\mathrm{\λ}}_p\right)\·\ln (1/R_L{R}_R)/2\·A_t{S}_p\mathrm{\Δ}{\mathrm{\λ}}_p$ Formula 24

Adopt a voltage-controlled controlled voltage source E _outanalog laser Output optical power P _out, voltage-controlled controlled voltage source E _outvoltage-controlled signal be the node voltage signal S of the 4th optics branch road _pnode voltage signal delta λ with the 5th optics branch road _p, voltage-controlled controlled voltage source E _outthe optical power value of the corresponding laser output of output voltage values, voltage-controlled controlled voltage source E _outscale-up factor k _paccording to formula 23, pass through to calculate obtain; Voltage-controlled controlled voltage source E _outconnect equivalent luminous power output port P ₂as the equivalent-circuit model that characterizes the output of THz QCL luminous power.

Step 6, in step 3, on the basis of step 4 and step 5, sets up the circuit macro-model that characterizes THz QCL photoelectric properties based on multimodes rate equation group, and this circuit macro-model is totally two ports, comprises an electrical port and a luminous power output port; Based on circuit macro-model, carry out photoelectric properties emulation and spectral characteristic test.

And, in step 1, described parameter τ ₃, τ ₃₂, τ ₃₁, τ ₂₁, τ _out, τ _sp, τ _phobtain manner comprises the following steps,

(1) under the condition of known THz QCL active layer mqw material, physical dimension and doping content, suppose that the direction of growth of material is along z axle, by self-consistent solution not time-dependent Schrodinger equation and Poisson equation, iteration is obtained each sub-energy levels Ei of active layer electronics, wave function ψ i (z), electron density distribution n (z);

(2), according to fermi's golden rule, the transition speed of definition electronics in i sub-band energy level is

formula 25

Wherein, for reduced Planck constant, τ ' _ifor the existence life-span of electronics at sub-band energy level i, Ei and Ef are respectively the electron energy of initial state sub-band energy level i and transition final states sub-band energy level f, for disturbance quantity, for transition matrix element;

By the sub-energy level of initial state, the average transition speed to the sub-energy level transition of final states can be expressed as definition electronics

$\mathrm{mean}\left(\frac{1}{{\mathrm{\τ}}_i^{\′}}\right)=\frac{\∫\mathrm{\θ}{f_i}^{\mathrm{FD}}\left(\mathrm{\θ}\right)/{\mathrm{\τ}}_i^{\′}\mathrm{d\θ}}{\mathrm{\π}{N}_i}$ Formula 26

Wherein, for the plane wave number of electronics, for electronics is at i subband Fermi distribution function, definition electronics at the surface density Ni of i subband is

formula 27

Wherein, m ^*for the effective mass of electronics, be that i subband plane wave number is the energy of k electronics;

According to different scattering mechanisms, be listed as respectively and write transition matrix element f wherein, i=1,2,3, and f ≠ i, use numerical method to calculate the existence life-span τ ' of electronics on sub-energy level 3 under different scattering mechanisms according to formula 25 ₃, electronics is at the nonradiative transition life-span τ ' of 2 of sub-energy level 3 and sub-energy levels ₃₂, electronics is at the nonradiative transition life-span τ ' of 1 of sub-energy level 3 and sub-energy level ₃₁with the nonradiative transition life-span τ ' of electronics 1 of sub-energy level 2 and sub-energy level ₂₁, and according to formula 26 and formula 27, calculate the electronics the average survival time life-span of electronics on sub-energy level 3 under different scattering mechanisms electronics between sub-energy level 3 and 2, electronics between sub-energy level 3 and 1, the average nonradiative transition life-span of electronics between sub-energy level 2 and 1 with

(3) inverse of the electronics mean lifetime of calculating under different scattering mechanisms is added and asks again its reciprocal value to obtain electronics total life-span τ on sub-energy level 3 ₃, electronics between sub-energy level 3 and 2, between sub-energy level 3 and 1, total nonradiative transition life-span τ between sub-energy level 2 and 1 ₃₂, τ ₃₁and τ ₂₁;

(4) use the intersubband self-excitation radiation-emitting transition rate equation under three-dimensional photon density-of-states distribution model

$\frac{1}{{\mathrm{\τ}}_{\mathrm{sp}}}=\frac{e^2{n}_{\mathrm{eff}}{\mathrm{\ω}}_0^2}{6\mathrm{\π\ϵ}{m}^{*}{c}^3}{f}_{32}$ Formula 28

Calculate the spontaneous radiation life-span τ of electronics between sub-energy level 3 and sub-energy level 2 _sp, wherein for the resonance intensity based on electric coupling polar moment between sub-energy level 3 and sub-energy level 2, ω ₀for utilizing emitted light subcenter angular frequency, the effective mass that m* is electronics, ε is effective dielectric constant, n _efffor effective refractive index in optical cavity, c is the light velocity in vacuum, and e is electron charge;

(5) according to the mirror loss α of the optical cavity structure of device and material parameter calculating optical cavity _mwaveguide loss α with optical cavity _w, and according to formula calculate parameter τ photon lifetime in optical cavity _ph, n wherein _efffor effective refractive index in optical cavity.According to experimental data, extract and obtain electronics at the escape time parameter τ facing mutually between two cascade periodic structures _out.

And in step 6, the circuit macro-model implementation of setting up based on multimodes rate equation group sign THz QCL photoelectric properties is as follows,

First, use the newly-built circuit macro-model ThzQCL Multimode Model with two-port of circuit simulating software instrument HSPICE, definition two-port attribute, port Nin is laser instrument electrical input terminal mouth, port NPout is laser optical power stage port; Then use electronic circuit descriptive language that each electronic circuit of setting up in step 3,4,5 is explained out; Finally the equivalent electric signal input port P1 setting up in step 4 is connected with the port Nin of circuit macro-model ThzQCL Multimode Model, the equivalent luminous power output port P2 setting up in step 5 is connected with the port NPout of circuit macro-model ThzQCLMultimode Model.

Two, be below a specific embodiment that adopts method of the present invention.

As shown in Figure 1:

According to the structure of THz QCL active layer, material behavior, set up THz QCL active layer internal electron rate equation and multimode photon velocity equation, can realize in the following ways:

Step 1.1, adopts Lorentz lorentz's distributing line shape function γ (λ _m) characterize the gain spectral distribution of laser radiation photon, the gain of light that using formula five calculates the photon of m patterns.Resonance intensity f in formula five ₃₂, equivalent refractive index n in optical cavity _effetc. parameter, according to THz QCL active layer material characteristic and ducting layer structure and material behavior, calculate;

Step 1.2, adopts Lorentz lorentz's distribution function to characterize the spontaneous radiation coupling coefficient distribution of photon under different mode equally, utilizes formula seven to calculate the spontaneous radiation coupling coefficient β of the photon of m pattern _m.The spontaneous radiation coupling coefficient of the corresponding centre wavelength in formula seven is calculated by formula eight;

Step 1.3, is listed as electronics rate equation and the multimode photon velocity equation of writing three-level transition according to the transport property of THz QCL active layer charge carrier, and by the gain of light theoretical calculation formula g of the single-stage m pattern photon obtaining in step 1.1 _mspontaneous radiation coupling coefficient β with the m pattern photon obtaining in step 1.2 _mbring into;

Step 1.4, on the basis of the three-level electronics rate equation of step 1.3 gained, introduces Injection Current efficiency parameter, and the introducing by this parameter joins the heat leak of active layer charge carrier in model to the impact of device performance.Injection Current efficiency parameter maximal value is 1, with temperature, increases and reduces, and this is that more high carrier heat leak is more serious because of temperature;

Step 1.5, under continuum Model, use self-consistent solution method and Fermi's Gold Principle to calculate the scattering time of each energy inter-stage of THz QCL active layer charge carrier, then calculate charge carrier corresponding life-span on each energy level, and they are updated in the electronics rate equation and multimode photon velocity equation of step 1.4 foundation.

The concrete process of establishing of embodiment is as follows:

1. the Lorentz lorentz's distributing line shape function γ (λ that first adopts formula six to represent _m) characterize the gain spectral distribution of laser radiation photon, and as follows by obtaining multi-modal lower photon gain formula in the gain of light formula five of formula six generations people m pattern photon

$g_m=g\left({\mathrm{\λ}}_m\right)=\frac{e^2{f}_{32}}{{4m}^{*}{n}_{\mathrm{eff}}^2\mathrm{\ϵ}}\·\frac{\frac{2}{\mathrm{\π\Δ}{\mathrm{\λ}}_g}}{1+4{({\mathrm{\λ}}_m-{\mathrm{\λ}}_p)}^2/\mathrm{\Δ}{\mathrm{\λ}}_g^2}$ Formula 29

Each parameter in formula calculates according to THz QCL active layer material characteristic and ducting layer structure and material behavior.

2. then adopt equally the spontaneous radiation coupling coefficient distribution of photon under Lorentz lorentz's distribution function sign different mode, formula eight is updated to the spontaneous radiation coupling coefficient β of the photon that obtains m pattern in formula seven _mformula is as follows,

${\mathrm{\β}}_m=\frac{1}{1+4{({\mathrm{\λ}}_m-{\mathrm{\λ}}_p)}^2/{\mathrm{\Δ\λ}}_s^2}\·\frac{{\mathrm{\λ}}_p^4}{{4\mathrm{\π}}^2{n}_{\mathrm{eff}}^3\mathrm{\Δ}{\mathrm{\λ}}_{s}V{N}_{\mathrm{mod}}}$ Formula 30

3. according to the transport property row of THz QCL active layer electronics, write the electronics rate equation of three-level transition, and by g _mbring into

$\frac{{\mathrm{dn}}_3}{\mathrm{dt}}=\frac{I}{\mathrm{eV}}-\frac{n_3}{{\mathrm{\τ}}_3}-\underset{m}{\mathrm{\Σ}}{g}_m(n_3-n_2)S_m$ Formula 31

$\frac{{\mathrm{dn}}_2}{\mathrm{dt}}=\frac{I}{\mathrm{eV}}+(\frac{1}{{\mathrm{\τ}}_{32}}+\frac{1}{{\mathrm{\τ}}_{\mathrm{sp}}})n_3-\frac{n_2}{{\mathrm{\τ}}_{21}}+\underset{m}{\mathrm{\Σ}}{g}_m(n_3-n_2)S_m$ Formula 32

$\frac{{\mathrm{dn}}_1}{\mathrm{dt}}=\frac{n_3}{{\mathrm{\τ}}_{31}}+\frac{n_2}{{\mathrm{\τ}}_{21}}-\frac{n_1}{{\mathrm{\τ}}_{\mathrm{out}}}$ Formula three

As follows with the photon velocity equation of m pattern photon, and by g _mand β _mbring into

$\frac{{\mathrm{dS}}_m}{\mathrm{dt}}={\mathrm{\Γg}}_m(n_3-n_2)S_m+{\mathrm{\β}}_m\mathrm{\Γ}\frac{n_3}{{\mathrm{\τ}}_{\mathrm{sp}}}-\frac{S_m}{{\mathrm{\τ}}_{\mathrm{ph}}}$ Formula four

Here 3,2,1 energy level does not represent the absolute population of levels of electronics in band structure, and just according to photon stimulated radiation transition high swash penetrate energy level (being expressed as energy level 3), low swash penetrate the sequence that the size of energy level (being expressed as energy level 2) and the auxiliary transition relaxation energy level (being expressed as energy level 1) of phonon is carried out.N wherein ₃and n ₂represent respectively high sharp energy level and low sharp penetrate the electron number volume density on energy level, the n of penetrating of photon stimulated radiation transition ₁represent the electron number volume density on the auxiliary transition relaxation energy level of phonon, S _mfor the photon number volume density of the m pattern photon in optical cavity, the Injection Current that I is quantum cascade laser, τ ₃, τ ₃₂be respectively the radiation transistion life-span between 3 electronics entire lives of sub-energy level and sub-energy level 3 and sub-energy level 2; τ ₃₁, τ ₂₁be respectively between sub-energy level 3 and sub-energy level 1, the nonradiative transition life-span between sub-energy level 2 and sub-energy level 1, wherein 1/ τ ₃=1/ τ ₃₂+ 1/ τ ₃₁+ 1/ τ _sp; τ _sp, τ _phbe respectively the spontaneous radiation life-span of electronics between sub-energy level 3 and sub-energy level 2 and the photon lifetime in optical cavity, τ _outfor electronics is in the escape time of facing mutually between two cascade periodic structures; Γ is light restriction factor, and e is electron charge, and V is active area single-stage volume.

4. then utilize leakage current to characterize the hot leakage phenomenon of THz QCL device active layer electronics, concrete grammar is to introduce injection efficiency parameter η, uses respectively η I and (1-η) I to substitute original I and obtain in formula 31 and formula 32:

$\frac{{\mathrm{dn}}_3}{\mathrm{dt}}=\frac{\mathrm{\ηI}}{\mathrm{eV}}-\frac{n_3}{{\mathrm{\τ}}_3}-\underset{m}{\mathrm{\Σ}}{g}_m(n_3-n_2)S_m$ Formula one

$\frac{{\mathrm{dn}}_2}{\mathrm{dt}}=\frac{(1-\mathrm{\η})I}{\mathrm{eV}}+(\frac{1}{{\mathrm{\τ}}_{32}}+\frac{1}{{\mathrm{\τ}}_{\mathrm{sp}}})n_3-\frac{n_2}{{\mathrm{\τ}}_{21}}+\underset{m}{\mathrm{\Σ}}{g}_m(n_3-n_2)S_m$ Formula two

The function that wherein η is temperature T, injection efficiency η raises and reduces with temperature, uses fitting formula

η (T)=1-a ₁(T-T ₀)-a ₂(T-T ₀) ²-a ₃(T-T ₀) ³formula 35

Calculate injection efficiency η, wherein T0 represents that injection efficiency η is approximately 1 low temperature, a1, and a2, a3 is fitting parameter.Fitting parameter a1, a2, a3 obtains by the extraction to experimental data.

5. finally use self-consistent solution method and Fermi's Gold Principle to calculate the scattering time of each energy inter-stage of THz QCL active layer charge carrier, then calculate charge carrier corresponding existence life-span τ on each energy level, and they are updated in the electronics rate equation and multimode photon velocity equation of having set up.Circular is as follows:

First, under the condition of known THz QCL active layer mqw material, physical dimension and doping content, suppose that the direction of growth of material is along z axle, by self-consistent solution not time-dependent Schrodinger equation and Poisson equation, iteration is obtained each sub-energy levels Ei of active layer electronics, wave function ψ i (z), electron density distribution n (z), self-consistent solution is prior art, and it will not go into details in the present invention.

According to sub-energy levels Ei, electron density distribution n (z), can calculate thereby calculate the surface density Ni of i subband.According to wave function ψ i (z), calculate transition matrix element

Then, according to different scattering mechanism (electronics-longitudinally optical phonon scattering, Electron Electron scattering, electronics-acoustic phonon scattering), be listed as and write transition matrix element respectively f wherein, i=1,2,3, and f ≠ i, use numerical method to calculate the existence life-span τ ' of electronics on sub-energy level 3 under different scattering mechanisms according to formula 25 ₃, electronics is at the nonradiative transition life-span τ ' of 2 of sub-energy level 3 and sub-energy levels ₃₂, electronics is at the nonradiative transition life-span τ ' of 1 of sub-energy level 3 and sub-energy level ₃₁with the nonradiative transition life-span τ ' of electronics 1 of sub-energy level 2 and sub-energy level ₂₁, and according to formula 26 and formula 27, calculate the electronics the average survival time life-span of electronics on sub-energy level 3 under different scattering mechanisms electronics between sub-energy level 3 and 2, electronics between sub-energy level 3 and 1, the average nonradiative transition life-span of electronics between sub-energy level 2 and 1 with

Therefore,

${\stackrel{\‾}{\mathrm{\τ}}}_3^{\′}=\frac{\mathrm{\π}{N}_3}{\∫\mathrm{\θ}{f}_3^{\mathrm{FD}}\left(\mathrm{\θ}\right)/{\mathrm{\τ}}_3^{\′}\mathrm{d\θ}}$

$\mathrm{mean}\left(\frac{1}{{\mathrm{\τ}}_{\mathrm{if}}^{\′}}\right)=\frac{\∫\mathrm{\θ}{f_i}^{\mathrm{ED}}\left(\mathrm{\θ}\right)/{\mathrm{\τ}}_i^{\′}(1-f_f^{\mathrm{FD}}\left(\mathrm{\θ}\right))\mathrm{d\θ}}{\mathrm{\π}{N}_i}$

Therefore,

${\stackrel{\‾}{\mathrm{\τ}}}_{32}^{\′}=\frac{\mathrm{\π}{N}_3}{\∫{\mathrm{\θf}}_3^{\mathrm{FD}}\left(\mathrm{\θ}\right)/{\mathrm{\τ}}_3(1-f_2^{\mathrm{FD}}\left(\mathrm{\θ}\right))\mathrm{d\θ}}$

${\stackrel{\‾}{\mathrm{\τ}}}_{31}^{\′}=\frac{\mathrm{\π}{N}_3}{\∫{\mathrm{\θf}}_3^{\mathrm{FD}}\left(\mathrm{\θ}\right)/{\mathrm{\τ}}_3(1-f_1^{\mathrm{FD}}\left(\mathrm{\θ}\right))\mathrm{d\θ}}$

${\stackrel{\‾}{\mathrm{\τ}}}_{21}^{\′}=\frac{\mathrm{\π}{N}_3}{\∫{\mathrm{\θf}}_2^{\mathrm{FD}}\left(\mathrm{\θ}\right)/{\mathrm{\τ}}_2(1-f_1^{\mathrm{FD}}\left(\mathrm{\θ}\right))\mathrm{d\θ}}$

Subsequently, the inverse of the electronics mean lifetime of calculating under different scattering mechanisms is added and asks again its reciprocal value to obtain electronics total life-span τ on sub-energy level 3 ₃, electronics between sub-energy level 3 and 2, between sub-energy level 3 and 1, total nonradiative transition life-span τ between sub-energy level 2 and 1 ₃₂, τ ₃₁and τ ₂₁.According under different scattering mechanisms reciprocal addition asks its reciprocal value to obtain τ again ₃, according under different scattering mechanisms reciprocal addition asks its reciprocal value to obtain τ again ₃₂, according under different scattering mechanisms reciprocal addition asks its reciprocal value to obtain τ again ₃₁, according under different scattering mechanisms reciprocal addition asks its reciprocal value to obtain τ again ₂₁.

Then, use the intersubband self-excitation radiation-emitting transition rate equation under three-dimensional photon density-of-states distribution model

$\frac{1}{{\mathrm{\τ}}_{\mathrm{sp}}}=\frac{e^2{n}_{\mathrm{eff}}{\mathrm{\ω}}_0^2}{6\mathrm{\π\ϵ}{m}^{*}{c}^3}{f}_{32}$ Formula 28

Calculate the spontaneous radiation life-span τ of electronics between sub-energy level 3 and sub-energy level 2 _sp, wherein for the resonance intensity based on electric coupling polar moment between sub-energy level 3 and sub-energy level 2, ω ₀for utilizing emitted light subcenter angular frequency, the effective mass that m* is electronics, ε is effective dielectric constant, n _efffor effective refractive index in optical cavity, c is the light velocity in vacuum, and e is electron charge;

Then, according to the mirror loss α of the optical cavity structure of device and material parameter calculating optical cavity _mwaveguide loss α with optical cavity _w, and according to formula calculate parameter τ photon lifetime in optical cavity _ph, n wherein _efffor effective refractive index in optical cavity.According to experimental data, extract and obtain electronics at the escape time parameter τ facing mutually between two cascade periodic structures _out.

Finally, by gained parameter τ ₃, τ ₃₂, τ ₃₁, τ ₂₁, τ _out, τ _sp, τ _phbe brought in formula one, formula two, formula three and formula four.

On the basis of the multimodes rate equation group of setting up in step (1), simplify and set up the physical equation model that characterizes the inner carrier transport of THz QCL and multi-modal effect.

Can realize in the following ways:

Step 2.1, in setting laser device chamber, photon density changes continuously with wavelength, and its output spectrum distribution envelope is Gaussian, and ignores the impact of noise, the wavelength interval inner laser device output photon density formula S of the unit of foundation (λ).

Step 2.2, the S that step 2.1 is obtained (λ) is brought into and in formula four, replaces original S _m, a plurality of mode photon velocity system of equations are reduced to and take the single photon velocity equation that S (λ) is variable.

Step 2.3, on the basis of setting in step 2.1, the output spectrum of laser instrument is set as to continuous spectrum by discrete spectrum, in the electronics rate equation that is about to set up in step (2), owing to swashing, penetrates the summation operation that a plurality of mode photons cause that electron number density reduces and change integral operation into.

Embodiment concrete methods of realizing is as follows:

1. first photon density changes continuously with wavelength in setting laser device chamber, and sets its output spectrum and distribute and follow Gaussian distribution, ignores noise effect, and Ke get unit's wavelength interval inner laser device output photon density formula is as follows,

$S\left(\mathrm{\λ}\right)=S_p\exp \left[\frac{-4\ln 2{(\mathrm{\λ}-{\mathrm{\λ}}_p)}^2}{{\left(\mathrm{\Δ}{\mathrm{\λ}}_p\right)}^2}\right]$ Formula 13

S in formula _pfor photon number density peak value, S (λ) has identical central wavelength lambda with gain g (λ) and spontaneous radiation coupling coefficient β (λ) _p, Δ λ _pfWHM for this distribution function.

2. S (λ) is brought in the photon velocity equation formula four of the m pattern photon of setting up in step (1) and replaces original S _mvariable, a plurality of mode photon velocity system of equations are reduced to that to take the single photon velocity equation that S (λ) is variable as follows,

$\frac{\mathrm{dS}\left(\mathrm{\λ}\right)}{\mathrm{dt}}=\mathrm{\Γg}\left(\mathrm{\λ}\right)(n_3-n_2)S\left(\mathrm{\λ}\right)+\mathrm{\β}\left(\mathrm{\λ}\right)\mathrm{\Γ}\frac{n_3}{{\mathrm{\τ}}_{\mathrm{sp}}}-\frac{S\left(\mathrm{\λ}\right)}{{\mathrm{\τ}}_{\mathrm{ph}}}$ Formula 12

3. use original S in two electronics rate equations one setting up in S (λ) replacement step (1) and formula two _mvariable, and original summation operation to m mode photon in formula is replaced with to the continuous integration computing to wavelength, obtain two new electronics rate equations as follows,

$\frac{{\mathrm{dn}}_3}{\mathrm{dt}}=\frac{\mathrm{\ηI}}{\mathrm{eV}}-\frac{n_3}{{\mathrm{\τ}}_3}-{\∫}_0^{\∞}g\left(\mathrm{\λ}\right)(n_3-n_2)S\left(\mathrm{\λ}\right)\mathrm{d\λ}$ Formula nine

$\frac{{\mathrm{dn}}_2}{\mathrm{dt}}=\frac{(1-\mathrm{\η})I}{\mathrm{eV}}+(\frac{1}{{\mathrm{\τ}}_{32}}+\frac{1}{{\mathrm{\τ}}_{\mathrm{sp}}})n_3-\frac{n_2}{{\mathrm{\τ}}_{21}}+{\∫}_0^{\∞}g\left(\mathrm{\λ}\right)(n_3-n_2)S\left(\mathrm{\λ}\right)\mathrm{d\λ}$ Formula ten

In addition keep the electronics rate equation (formula three) that obtains in step (1) constant as follows,

$\frac{{\mathrm{dn}}_1}{\mathrm{dt}}=\frac{n_3}{{\mathrm{\τ}}_{31}}+\frac{n_2}{{\mathrm{\τ}}_{21}}-\frac{n_1}{{\mathrm{\τ}}_{\mathrm{out}}}$ Formula 11

Three electronics rate equations that step (2) obtains (formula nine, formula ten, formula 11), form the physical equation model that characterizes the inner carrier transport of THz QCL and multi-modal effect with step (2) together with the photon velocity equation (formula 12) obtaining.

According to the circuit cover half method of optoelectronic device, on the basis of physical equation model that characterizes the inner carrier transport of THz QCL and multi-modal effect, set up the equivalent-circuit model that characterizes the inner carrier transport of THz QCL and multi-modal effect.

Can adopt the concrete steps of the equivalent-circuit model of setting up the inner carrier transport of sign THz QCL and multi-modal effect as follows:

Step 3.1, on the basis of the THz QCL physical equation model of setting up in step (2), in order to obtain better convergence, to three electronics rate equation (formulas nine in model, formula ten, formula 11) carry out suitable arrangement and conversion, make its rule of Kirchhoff's current law (KCL) (KCL) in coincidence circuit theory in form, then with the node voltage variable in Circuit theory, simulate the electron density variables of each energy level in each rate equation, with circuit topological diagram by three the Representation Equation after conversion out, set up three equivalent sub circuit models that characterize the inner carrier transport of THz QCL.Concrete steps are as follows: first Q=eV is taken advantage of in the equation both sides of the formula nine in step (2), formula ten, formula 11, by the node voltage variable V in Circuit theory _n3, V _n2, V _n1difference substitute variable n ₃, n ₂, n ₁; Then by transposition, operate and contain independent variable V by each electronics rate equation _nithe item of (i=1,2,3) (comprising proportional and differential term) all moves on to equal sign the right, and all the other every equal sign left sides that all move on to; Then by conversion, the transformation of coefficient of equal sign the right independent variable proportional in all equations is substituted to denominator and with an equivalent resistance parameter; Scale-up factor before equal sign the right independent variable differential term in all equations is substituted with an equivalent capacitive parameter; The every apportion that carries out of independent variable in other equations that the part on the equal sign left side in all equations is comprised according to it respectively, and substitute with an equivalent controlled current source; Finally every sub-equation represented with a corresponding electronic circuit respectively, independent variable in every sub-equation is corresponding with the node voltage in electronic circuit, in every sub-equation, subitem substitutes by a current branch respectively, for example differential term corresponds to a capacitive branch, the corresponding resistance branch of proportional.Its corresponding branch current direction of item on sub-equation equal sign both sides is just in time contrary, and for example the direction of equal sign left side item corresponding current is to flow into node, and the direction of equal sign the right corresponding current is to flow out node.

Step 3.2, on the basis of the THz QCL physical equation model of setting up in step (2), utilize the distribution of output spectrum to belong to the special nature of Gaussian, photon velocity equation under two specific wavelengths in rewrite model (formula 12), and the equation of two rewritings is carried out to suitable abbreviation, arrangement and conversion, obtain two sub-equations of Kirchhoff's current law (KCL) (KCL) in coincidence circuit theory in form, then with the photon number density peak value variable S in simulated photons rate equation respectively of the node voltage variable in Circuit theory _pwith the FWHM variable Δ λ in spectral distribution function _p, with circuit topological diagram by two the Representation Equation after conversion out, set up two equivalent sub circuit models that characterize the multi-modal effect of the inner photon of THz QCL.Concrete steps are as follows: first Q=eV is taken advantage of in the equation both sides of the formula 12 in step (2), by the node voltage variable V in Circuit theory _n3, V _n2, V _n1difference substitute variable n ₃, n ₂, n ₁; Then by two specific wavelength λ _p(λ _p+ Δ λ _p/ 2) unit of bringing into wavelength interval inner laser device output photon density formula S (λ) respectively; Then result of calculation is obtained to two equations for people respectively in formula 12, two equations are subtracted each other to cancellation variable S _pdifferential term obtain the 3rd equation; Then first and the 3rd equation are arranged, will in first equation, contain independent variable S _pwith in the 3rd equation, contain independent variable Δ λ _pitem (comprising proportional and differential term) all move on to equal sign the right, and all the other every equal sign left sides that all move on to; Then by conversion, the transformation of coefficient of equal sign the right independent variable proportional in two equations is substituted to denominator and with an equivalent resistance parameter; Scale-up factor before equal sign the right independent variable differential term in two equations is substituted with an equivalent capacitive parameter; The every apportion that carries out of independent variable in other equations that the part on the equal sign left side in all equations is comprised according to it respectively, and substitute with an equivalent controlled current source; Finally two equations are represented with a corresponding electronic circuit respectively, (independent variable of the first equation is S to the independent variable in every sub-equation _p, the independent variable of the 3rd equation is Δ λ _p) corresponding with the node voltage in electronic circuit, in each equation, subitem substitutes by a current branch respectively, and for example differential term corresponds to a capacitive branch, the corresponding resistance branch of proportional.Its corresponding branch current direction of item on sub-equation equal sign both sides is just in time contrary, and for example the direction of equal sign left side item corresponding current is to flow into node, and the direction of equal sign the right corresponding current is to flow out node.

Embodiment concrete methods of realizing is as follows:

1. Q=eV is taken advantage of in the equation both sides of the formula nine in step (2), formula ten, formula 11, node voltage variable V _n3, V _n2, V _n1difference substitute variable n ₃, n ₂, n ₁here 3,2,1 energy level is with aforementioned, do not represent the absolute population of levels of electronics in band structure, and just according to photon stimulated radiation transition high swash penetrate energy level (being expressed as energy level 3), low swash penetrate the sequence that the size of energy level (being expressed as energy level 2) and the auxiliary transition relaxation energy level (being expressed as energy level 1) of phonon is carried out.Then by transposition, operate three electronics rate equations be organized into following form,

$I_{\mathrm{inj}}=\frac{V_{n3}}{R_3}+C_3\frac{{\mathrm{dV}}_{n3}}{\mathrm{dt}}+I_{\mathrm{st}}$ Formula 14

$I_{\mathrm{leak}}+I_3+I_{\mathrm{st}}=\frac{V_{n2}}{R_2}+C_2\frac{{\mathrm{dV}}_{n2}}{\mathrm{dt}}$ Formula 15

$I_3^{\′}+I_2=\frac{V_{n1}}{R_1}+C_1\frac{{\mathrm{dV}}_{n1}}{\mathrm{dt}}$ Formula 16

R wherein ₃=τ ₃/ Q; C ₃=Q; R ₂=τ ₂₁/ Q; C ₂=Q; R ₁=τ _out/ Q; C ₁=Q;

I _inj＝QηI；I _1eak＝Q(1-η)I； $I_3=Q(\frac{1}{{\mathrm{\τ}}_{32}}+\frac{1}{{\mathrm{\τ}}_{\mathrm{sp}}})V_{n3};I_3^{\′}=\frac{Q}{{\mathrm{\τ}}_{31}}{V}_{n3};$

$I_2=\frac{Q}{{\mathrm{\τ}}_{21}}{V}_{n2};$

$\begin{array}{c}{I}_{\mathrm{st}}=Q{\∫}_0^{\∞}\left(\mathrm{\λ}\right)(n_3-n_2)S\left(\mathrm{\λ}\right)\mathrm{d\λ}\\ =G(V_{n3}-V_{n2})[A_t\mathrm{\Δ}{\mathrm{\λ}}_p-A_g\mathrm{\Δ}{\mathrm{\λ}}_p^3]S_p;\end{array}$

Parameter $G=Q\frac{e^2{f}_{32}}{2{\mathrm{\πm}}^{*}{n}_{\mathrm{eff}}^2\mathrm{\ϵ\Δ}{\mathrm{\λ}}_g},A_t=\sqrt{\mathrm{\π}/4\ln 2},A_g=\frac{A_t}{4\ln 2\mathrm{\Δ}{\mathrm{\λ}}_g^2};$

Finally according to Kirchhoff's current law (KCL) (KCL), with electronic circuit, respectively formula 14 to formula 16 is explained out.N ₃, n ₂, n ₁the node that represents respectively each electronic circuit; Formula 14 is to V in formula 16 _n3, V _n2, V _n1the voltage of corresponding above each node of difference; I _inj, I _st, I ₃, I ' ₃, I ₂, I _leakcontrolled current source in the corresponding electronic circuit of difference, C ₃, C ₂, C ₁capacity cell in the corresponding electronic circuit of difference; R ₃, R ₂, R ₁to the resistive element in electronic circuit, each electronic circuit is as shown in accompanying drawing 4a-4c respectively.

2. Q=eV is taken advantage of in the equation both sides of the formula 12 in step (2), by the node voltage variable V in Circuit theory _n3, V _n2, V _n1difference substitute variable n ₃, n ₂, n ₁; Then by two specific wavelength λ _p(λ _p+ Δ λ _p/ 2) unit of bringing into wavelength interval inner laser device output photon density formula S (λ) respectively; Then that result of calculation is as follows to obtaining two equations in formula 12 for people respectively

$Q\frac{{\mathrm{dS}}_p}{\mathrm{dt}}=G^{\′}(V_{n3}-V_{n2})S_p-\frac{{\mathrm{QS}}_p}{{\mathrm{\τ}}_{\mathrm{ph}}}+{\mathrm{\β}}_{\mathrm{sp}0}{I}_{\mathrm{rr}}$ Formula 17

$Q\frac{{\mathrm{dS}}_p}{\mathrm{dt}}=\frac{2G^{\′}(V_{n3}-V_{n2})S_p}{1+{\mathrm{\Δ\λ}}_p^2/{\mathrm{\Δ\λ}}_g^2}-\frac{{\mathrm{QS}}_p}{{\mathrm{\τ}}_{\mathrm{ph}}}+\frac{2{\mathrm{\β}}_{\mathrm{sp}0}{I}_{\mathrm{rr}}}{1+{\mathrm{\Δ\λ}}_p^2/{\mathrm{\Δ\λ}}_s^2}$ Formula 18

In formula, $G^{\′}=\mathrm{Q\Γ}\frac{e^2{f}_{32}}{2{\mathrm{\πm}}^{*}{n}_{\mathrm{eff}}^2\mathrm{\ϵ\Δ}{\mathrm{\λ}}_g},I_{\mathrm{rr}}=\mathrm{\ΓQ}\frac{V_{n3}}{{\mathrm{\τ}}_{\mathrm{sp}}};$ Then two equations are subtracted each other to cancellation variable S _pdifferential term to obtain the 3rd equation as follows

${\mathrm{\β}}_{\mathrm{sp}0}{I}_{\mathrm{rr}}=\frac{2\mathrm{\Δ}{\mathrm{\λ}}_s^2}{{\mathrm{\Δ\λ}}_s^2+{\mathrm{\Δ\λ}}_p^2}{\mathrm{\β}}_{\mathrm{sp}0}{I}_{\mathrm{rr}}+\frac{{\mathrm{\Δ\λ}}_g^2-{\mathrm{\Δ\λ}}_p^2}{{\mathrm{\Δ\λ}}_g^2+{\mathrm{\Δ\λ}}_p^2}{G}^{\′}(V_{n3}-V_{n2})S_p$ Formula 19

Then by transposition, operate and parameter replacement by two independently photon velocity equation 17 and formula 18 be organized into following form,

$I_{\mathrm{rr}1}+I_{\mathrm{sp}}=\frac{S_p}{R_{\mathrm{ph}}}+C_{\mathrm{ph}}\frac{{\mathrm{dS}}_p}{\mathrm{dt}}$ Formula 20

I _rr1=I _s+ I _gformula 21

R wherein _ph=τ _ph/ Q, C _ph=Q, I _rr1=β _sp0i _rr, I _sp=G ' (V _n3-V _n2) S _p, $I_s=\frac{2{\mathrm{\Δ\λ}}_s^2}{{\mathrm{\Δ\λ}}_s^2+{\mathrm{\Δ\λ}}_p^2}{I}_{\mathrm{rr}1},I_g=\frac{{\mathrm{\Δ\λ}}_g^2-{\mathrm{\Δ\λ}}_p^2}{{\mathrm{\Δ\λ}}_g^2+{\mathrm{\Δ\λ}}_p^2}{G}^{\′}(V_{n3}-V_{n2})S_p.$

Out according to Kirchhoff's current law (KCL) (KCL) with electronic circuit respectively by formula 20, formula 21 statements finally.S _p, Δ λ _pthe node that represents respectively two electronic circuits; S in formula 20, formula 21 _p, Δ λ _pthe voltage of corresponding above two nodes of difference; I _rr1, I _sp, I _s, I _gcontrolled current source in the corresponding electronic circuit of difference, C _ph, R _phcapacity cell and resistive element in the corresponding electronic circuit of difference; Two electronic circuits are as shown in accompanying drawing 4d-4e.

Referring to Fig. 4, the equivalent-circuit model that characterizes the inner carrier transport of THz QCL and multi-modal effect in the present invention comprises 5 electronic circuits altogether: front 3 electricity branch roads for sign THz QCL internal electron transport property, rear 2 optics branch roads for sign THz QCL interior lights sub-feature.Each branch road intercouples by the control signal of controlled current source.

The 1st electronic circuit obtains according to formula 14, controlled current source I _injwith capacitor C ₃, resistance R ₃, controlled current source I _stthe 1st electricity branch road after in parallel in the ground connection component model of one end, the other end is designated as node n ₃, node n in circuit ₃on magnitude of voltage V _n3characterize the electron number volume density on THz QCL internal Excited State high level (sub-energy level 3).Controlled current source I _injsign is injected into active layer electric current item, and its controlled quentity controlled variable comprises current signal I and the temperature variable T of the diode D1 that flows through in accompanying drawing 3; Controlled current source I _stcharacterize stimulated emission item in active layer, its controlled quentity controlled variable comprises the node voltage signal V in the 1st and the 2nd electricity branch road _n3, V _n2, the node voltage signal S of the 4th optics branch road _pand the node voltage signal delta λ in the 5th optics branch road _p.

The 2nd electronic circuit obtains according to formula 15, controlled current source I _stwith controlled current source I _leak, controlled current source I ₃, capacitor C ₂, resistance R ₂the 2nd electricity branch road after in parallel in the ground connection component model of one end, the other end is designated as node n ₂, node n in circuit ₂on magnitude of voltage V _n2characterize the electron number volume density in THz QCL internal Excited State low-lying level 2.Controlled current source I _stcharacterize stimulated emission item in active layer, its controlled quentity controlled variable comprises the node voltage signal V in the 1st and the 2nd electricity branch road _n3, V _n2, the node voltage signal S of the 4th optics branch road _pand the node voltage signal delta λ in the 5th optics branch road _p; Controlled current source I _leakcharacterize the leakage item of active layer electric current, its controlled quentity controlled variable comprises current signal I and the temperature variable T of the diode D1 that flows through in accompanying drawing 3; Controlled current source I ₃controlled quentity controlled variable be the 1st the node voltage signal V in electricity branch road _n3.

The 3rd electronic circuit obtains according to formula 16, controlled current source I ' ₃with controlled current source I ₂, capacitor C ₁, resistance R ₁the 3rd electricity branch road after in parallel in the ground connection component model of one end, the other end is designated as node n ₁, node n in circuit ₁on magnitude of voltage V _n1characterize the electron number volume density on the inner relaxation state of THz QCL energy level 1.Controlled current source I ' ₃controlled quentity controlled variable be the 1st the node voltage signal V in electricity branch road _n3; Controlled current source I ₂controlled quentity controlled variable be the 2nd the node voltage signal V in electricity branch road _n2.

The 4th electronic circuit obtains according to formula 20, controlled current source I _rr1with controlled current source I _sp, capacitor C _ph, resistance R _phthe 4th optics branch road after in parallel in the ground connection component model of one end, the other end is designated as node S _p, node S in circuit _pon magnitude of voltage S _pcharacterize THz QCL interior lights subnumber density peaks.Controlled current source I _spcharacterize stimulated emission item in active layer, its controlled quentity controlled variable comprises the node voltage signal V in the 1st and the 2nd electricity branch road _n3, V _n2, the node voltage signal S of the 4th optics branch road _p; Controlled current source I _rr1characterize self-sustained emission item in active layer, its controlled quentity controlled variable is the 1st the node voltage signal V in electricity branch road _n3.

The 5th electronic circuit obtains according to formula 21, controlled current source I _rr1with controlled current source I _s, controlled current source I _gthe 5th optics branch road after in parallel in the ground connection component model of one end, the other end is designated as node Δ λ _p, node Δ λ in circuit _pon magnitude of voltage Δ λ _pcharacterize the FWHM of THz QCL photon output spectra.Controlled current source I _rr1characterize self-sustained emission item in active layer, its controlled quentity controlled variable is the 1st the node voltage signal V in electricity branch road _n3; Controlled current source I _scontrolled quentity controlled variable comprise the 1st the node voltage signal V in electricity branch road _n3with the node voltage signal delta λ in the 5th optics branch road _p; Controlled current source I _gcontrolled quentity controlled variable comprise the node voltage signal V in the 1st and the 2nd electricity branch road _n3, V _n2, the node voltage signal S of the 4th optics branch road _pand the node voltage signal delta λ in the 5th optics branch road _p.

Use the ideal diode equivalent-circuit model of revising to set up the equivalent-circuit model that characterizes THz QCL input end electrical specification,

In described step 4, due to the voltage-current relationship curve of THz QCL input end and the volt-ampere characteristic of diode component closely similar, therefore on the basis of desirable diode equivalent circuit model, do suitable correction and set up the equivalent-circuit model that characterizes THz QCL input electrical specification, can adopt concrete steps as follows:

First the voltage of device input end is defined as to the function of input current and temperature, then the circuit that the effect based on to laser instrument adopts ideal diode to connect with a resistance is simulated the volt-ampere characteristic of THz QCL, model parameter comprises the resistance Rs of resistance in series Rd, thermal voltage VT, the reverse saturation current Is of diode, wherein thermal voltage VT is the function of temperature variable T, VT=KT/q, K is Boltzmann constant, and q is electron charge, and T is kelvin degree.Subsequently, according to the measured data of device, use numerical method to carry out curve fitting and extract associated arguments in model the volt-ampere characteristic of THz QCL input end, complete the foundation of device input electrical specification equivalent-circuit model.Finally, using the current signal of the ideal diode of flowing through as input current, be incorporated in the inner carrier transport of THz QCL of foundation in step (3) and the equivalent-circuit model of multi-modal effect.

Embodiment concrete methods of realizing is as follows:

1. first with a desirable diode D1, connect with a resistance R D, the function V (I, T) that the voltage V of device input end (being the voltage of equivalent electric signal input port P1) is defined as to input current I and temperature T is as follows:

$V(I,T)=\frac{\mathrm{KT}}{q}\ln (\frac{I}{I_s}+1)+{\mathrm{IR}}_s$ Formula 22

Wherein KT/q is thermal voltage parameter VT, and K is Boltzmann constant, and q is electron charge, and T is kelvin degree, and the resistance of resistance R D is Rs, the reverse saturation current that Is is diode.As shown in Figure 3, P1 is equivalent electric signal input port to Thz QCL input end equivalent electrical circuit, and I represent the to flow through electric current of ideal diode D1, is series between P1 with a desirable diode D1 and a resistance R D.

2. then according to current-voltage (IV) curve of device input end actual measurement, use the matching of Levenberg-Marquard method to obtain the parameters R s in model, Is;

3. last, the middle controlled current source I using the electric current I of the ideal diode D1 that flows through as step (3) _injwith controlled current source I _leakcontrol current signal, belong to controlled current source I _injwith controlled current source I _leakone of control signal.

According to the structure of laser optical cavity, set up the equivalent-circuit model that characterizes THz QCL output terminal luminous power characteristic.

During concrete enforcement, can adopt the concrete steps of the equivalent-circuit model of setting up the output of sign THz QCL luminous power as follows: first according to the pass series of laser optical cavity configuration and left and right both ends of the surface unit wavelength interval Output optical power and photon number density, to write out the mathematic(al) representation of laser instrument unit's wavelength interval Output optical power to photon number density, parameter in expression formula comprises optical cavity left and right end face reflection coefficients R L and RR, the width W of active area and gross thickness D, the group index of photon swash and penetrate photon wavelength λ, the light velocity c in vacuum, the wavelength interval inner laser device output photon density S of unit (λ); Then within the scope of whole excitation wavelength, do the computing formula that definite integral obtains total Output optical power.Because result of calculation shows the total Output optical power of laser instrument and photon number density peak value S _pfWHM value Δ λ with photon number density distribution profile function _pboth products present a kind of linear relationship, therefore by a Voltage-controlled Current Source, simulate the luminous power output characteristics of THz QCL, the control signal of Voltage-controlled Current Source is the product of the node voltage signal in two optics electronic circuits that obtain in step (4), and scale-up factor is parameter S in the total Output optical power mathematic(al) representation of laser instrument _p, Δ λ _pthe product of all before product; Then according to the device architecture of laser instrument and feature extraction, go out parameter in optical output power of laser expression formula, calculate the scale-up factor of Voltage-controlled Current Source, finally set up out the equivalent electrical circuit of THz QCL luminous power output.

In embodiment, concrete methods of realizing is as follows:

1. be first listed as the mathematic(al) representation that writes out laser instrument unit's wavelength interval Output optical power and photon number density,

$p\left(\mathrm{\λ}\right)={\mathrm{hc}}^2\mathrm{WD}/\left(2{\stackrel{\‾}{n}}_g\mathrm{\λ}\right)\·\ln (1/R_L{R}_R)/2\·S\left(\mathrm{\λ}\right)$ Formula 23

Wherein W, D are respectively broadband and the gross thickness of active area, R _land R _rfor the left and right end face reflection coefficient of optical cavity, for the group index of photon, λ penetrates photon wavelength for swashing, and constant h is Planck constant, and c is the light velocity in vacuum.

It is 2. then as follows to the gross output of formula 20 triple-cropping integral and calculating laser instruments,

$P_{\mathrm{out}}={\mathrm{hc}}^2\mathrm{WD}/\left({2\stackrel{\‾}{n}}_g{\mathrm{\λ}}_p\right)\·\ln (1/R_L{R}_R)/2\·A_t{S}_p{\mathrm{\Δ\λ}}_p$ Formula 24

3. finally according to formula 24, adopt a voltage-controlled controlled voltage source Eout analog laser output terminal light power consumption Pout.The voltage-controlled signal of voltage-controlled controlled voltage source Eout is the node voltage signal S of electronic circuit in accompanying drawing 4d _pnode voltage signal delta λ with electronic circuit in accompanying drawing 4e _p, the total optical power value of the corresponding laser output of output voltage values of voltage-controlled controlled voltage source Eout, the scale-up factor of voltage-controlled controlled voltage source Eout is by calculating ${\mathrm{hc}}^2\mathrm{WD}/\left(2{\stackrel{\‾}{n}}_g{\mathrm{\λ}}_p\right)\·\ln (1/R_L{R}_R)/2\·A_t$ Obtain, as shown in Figure 5, P2 is equivalent luminous power output port to the equivalent electrical circuit of THz QCL output terminal, and voltage-controlled controlled voltage source Eout connects equivalent luminous power output port P2.

During concrete enforcement, the equivalent model that (3) (4) (5) build forms the multi-modal effect equivalent model of THz QCL device together, and therefore the step sequencing of (3) (4) (5) is not limit.

Foundation characterizes the circuit macro-model of THz QCL photoelectric properties and spectral characteristic based on multimodes rate equation.The equivalent-circuit model of the inner transport property of characterizing device is combined to the circuit macro-model that the sign THz QCL photoelectric properties of considering multimode effect are set up in encapsulation with the equivalent model of device input, output interface.

During concrete enforcement, can adopt and set up that based on multimodes rate equation, to characterize the concrete steps of circuit macro-model of THz QCL photoelectric properties as follows: first use circuit macro-model with two-port of circuit simulating software instrument definition, in two-port, one be that electrical port, one are luminous power output port; Then by step (3), the equivalent-circuit model of setting up in step (4) and step (5) uses electronic circuit descriptive language that its net table is explained out; Finally the input port of setting up in step (4) is connected with the electrical port of circuit macro-model, the luminous power output port of setting up in step (5) is connected with the luminous power output port in circuit macro-model, completes the encapsulation that characterizes the circuit macro-model of THz QCL photoelectric properties based on multimodes rate equation.

Embodiment concrete methods of realizing is: first use the newly-built circuit macro-model ThzQCL Multimode Model with two-port of circuit simulating software instrument HSPICE, definition two-port attribute, port Nin is laser instrument electrical input terminal mouth, and port NPout is laser optical power stage port; Then use electronic circuit descriptive language that each electronic circuit of setting up in step (3), (4), (5) is explained out; Finally the input port P1 setting up in step (4) is connected with the port Nin of circuit macro-model ThzQCL Multimode Model, the output port P2 setting up in step (5) is connected with the port NPout of circuit macro-model Thz QCL Multimode Model, and the circuit macro-model based on multimodes rate equation sign THz QCL photoelectric properties as shown in Figure 2.

Adopting the inventive method is that GaAs/Al0.3Ga0.7 adopts the 2.47THz QCL of three quantum well designs to set up equivalent circuit macro models (laser waveguide loss α to an active area materials _w≈ 1000cm ^-1light restriction factor Γ ≈ 0.83), can to the optical and electrical properties under device different temperatures, simulate based on this model use circuit simulation tools PSPICE, then contrast with test data of experiment, investigate the accuracy that model is described Thz QCL electro-optical characteristic under different temperatures, and verify the validity of the inventive method.Concrete analogue simulation mode can be set voluntarily by those skilled in the art.For example the Thz QCL Output optical power (Optical Power) of 5K temperature performance model simulation, input current (Current) are I-V with the relation curve of laser bias voltage (Bias), and L-V curve as shown in Figure 6; Under different temperatures the Thz QCL Output optical power (Optical Power) of (5K, 78K) performance model simulation and the relation curve of input current (Current) be L-I curve as shown in Figure 7, what in figure, symbol ' zero ' was corresponding is all test data of experiment.Comparative simulation curve and measured data are known, and the THz QCL equivalent-circuit model that method of the present invention is set up can characterize the optical, electrical performance of Thz QCL device under different temperatures very accurately.Under different temperatures the Thz QCL of (5K, 78K) performance model simulation bias voltage be output spectrum distribution curve under 1.6V as shown in Figure 8, temperature is that 5K can find out the laser instrument that simulates, and the sharp frequency of heart of hitting is that this is very approaching with the 2.47THz of design for 2.57THz, in addition the spectrum widening effect that the blackbody radiation causing due to temperature rising causes is also embodied in simulation curve, if FWHM at 5K temperature is 0.47THz, when temperature is upgraded to 78K, FWHM increases to 0.52THz.

Specific embodiment described herein is only to the explanation for example of the present invention's spirit.Those skilled in the art can make various modifications or supplement or adopt similar mode to substitute described specific embodiment, but can't depart from spirit of the present invention or surmount the defined scope of appended claims.

Claims (5)

1. a circuit modeling emulation mode that characterizes Terahertz quantum cascaded laser multimode effect, is characterized in that,

Step 1, based on multimodes rate equation group, the envelope that definition laser instrument output spectrum distributes has gaussian-shape as the function of wavelength, when simulation, spectrum is not treated as continuous spectrum as discrete spectrum, and define photon density in device chamber and change continuously with wavelength, Noise, does not set up the physical equation model that characterizes the inner multi-modal effect of Thz QCL, and concrete form is as follows;

Described electronics rate equation is as follows,

$\frac{{\mathrm{dn}}_3}{\mathrm{dt}}=\frac{\mathrm{\ηI}}{\mathrm{eV}}-\frac{n_3}{{\mathrm{\τ}}_3}-{\∫}_0^{\∞}g\left(\mathrm{\λ}\right)(n_3-n_2)S\left(\mathrm{\λ}\right)\mathrm{d\λ}$ Formula nine

$\frac{{\mathrm{dn}}_2}{\mathrm{dt}}=\frac{(1-\mathrm{\η})I}{\mathrm{eV}}+(\frac{1}{{\mathrm{\τ}}_{32}}+\frac{1}{{\mathrm{\τ}}_{\mathrm{sp}}})n_3-\frac{n_2}{{\mathrm{\τ}}_{21}}+{\∫}_0^{\∞}g\left(\mathrm{\λ}\right)(n_3-n_2)S\left(\mathrm{\λ}\right)\mathrm{d\λ}$ Formula ten

$\frac{{\mathrm{dn}}_1}{\mathrm{dt}}=\frac{n_3}{{\mathrm{\τ}}_{31}}+\frac{n_2}{{\mathrm{\τ}}_{21}}-\frac{n_1}{{\mathrm{\τ}}_{\mathrm{out}}}$ Formula 11

Described photon velocity equation is as follows,

$\frac{\mathrm{dS}\left(\mathrm{\λ}\right)}{\mathrm{dt}}=\mathrm{\Γg}\left(\mathrm{\λ}\right)(n_3-n_2)S\left(\mathrm{\λ}\right)+\mathrm{\β}\left(\mathrm{\λ}\right)\mathrm{\Γ}\frac{n_3}{{\mathrm{\τ}}_{\mathrm{sp}}}-\frac{S\left(\mathrm{\λ}\right)}{{\mathrm{\τ}}_{\mathrm{ph}}}$ Formula 12

Wherein, S (λ) is unit wavelength interval inner laser device output photon density, and its functional form is as follows,

$S\left(\mathrm{\λ}\right)=S_p\exp \left[\frac{-4\ln 2{(\mathrm{\λ}-{\mathrm{\λ}}_p)}^2}{{\left(\mathrm{\Δ}{\mathrm{\λ}}_p\right)}^2}\right]$ Formula 13

S in formula _pfor photon number density peak value, S (λ) has identical central wavelength lambda with gain g (λ) and spontaneous radiation coupling coefficient β (λ) _p, Δ λ _pfWHM for this distribution function;

Step 2, on the inner carrier transport characteristic in sign THz QCL active area of setting up in step 1 and the basis of the multi-modal characteristic physical model of photon, carrying out abbreviation and parameter changes, set up to characterize the equivalent-circuit model of the inner carrier transport of THz QCL active layer and multi-modal characteristic, based on following formula:

$I_{\mathrm{inj}}=\frac{V_{n3}}{R_3}+C_3\frac{d{V}_{n3}}{\mathrm{dt}}+I_{\mathrm{st}}$ Formula 14

$I_{\mathrm{leak}}+I_3+I_{\mathrm{st}}=\frac{V_{n2}}{R_2}+C_2\frac{d{V}_{n2}}{\mathrm{dt}}$ Formula 15

$I_3^{\′}+I_2=\frac{V_{n1}}{R_1}+C_1\frac{{\mathrm{dV}}_{n1}}{\mathrm{dt}}$ Formula 16

Wherein, I _inj=Q η I; R ₃=τ ₃/ Q; C ₃=Q;

$\begin{array}{c}{I}_{\mathrm{st}}=Q{\∫}_0^{\∞}g\left(\mathrm{\λ}\right)(n_3-n_2)S\left(\mathrm{\λ}\right)\mathrm{d\λ}\\ =G(V_{n3}-V_{n2})[A_t\mathrm{\Δ}{\mathrm{\λ}}_p-A_g\mathrm{\Δ}{\mathrm{\λ}}_p^3]S_p\end{array};$

$G=Q\frac{e^2{f}_{32}}{2\mathrm{\π}{m}^{*}{n}_{\mathrm{eff}}^2\mathrm{\ϵ\Δ}{\mathrm{\λ}}_g},A_t=\sqrt{\mathrm{\π}/4\ln 2},A_g=\frac{A_t}{4\ln 2\mathrm{\Δ}{\mathrm{\λ}}_g^2};$

L _leak＝Q(1-η)I； R ₂＝τ ₂₁/Q；C ₂＝Q；

$I_3^{\′}=\frac{Q}{{\mathrm{\τ}}_{31}}{V}_{n3};I_2=\frac{Q}{{\mathrm{\τ}}_{21}}{V}_{n2};$ R ₁＝τ _out/Q;C ₁＝Q;

$I_{\mathrm{rr}1}+I_{\mathrm{sp}}=\frac{S_p}{R_{\mathrm{ph}}}+C_{\mathrm{ph}}\frac{d{S}_p}{\mathrm{dt}}$ Formula 20

I _rr1=I _s+ I _gformula 21

According to Kirchhoff's current law (KCL) with electronic circuit respectively by formula 14, formula 15, formula 16, formula 20, formula 21 statements out, the equivalent-circuit model of setting up the sign THz inner carrier transport of QCL active layer and multi-modal effect is as follows:

Equivalent model one: the electronic circuit obtaining according to formula 14 is by controlled current source I _injwith capacitor C ₃, resistance R ₃, controlled current source I _stthe 1st the electricity branch road that after in parallel, one end ground connection forms, this branch node voltage is Vn ₃;

Equivalent model two: the electronic circuit obtaining according to formula 15 is by controlled current source I _leak, controlled current source I _st, controlled current source I ₃, capacitor C ₂, resistance R ₂the 2nd the electricity branch road that after in parallel, one end ground connection forms, this branch node voltage is Vn ₂;

Equivalent model three: the electronic circuit obtaining according to formula 16 is by controlled current source I ' ₃with controlled current source I ₂, capacitor C ₁, resistance R ₁the 3rd the electricity branch road that after in parallel, one end ground connection forms, this branch node voltage is Vn ₁;

Equivalent model four: the electronic circuit obtaining according to formula 20 is by controlled current source I _rr1with controlled current source I _sp, capacitor C _ph, resistance R _phthe 4th the optics branch road forming after in parallel, this branch node voltage is S _p;

Equivalent model five: the electronic circuit obtaining according to formula 21 is by controlled current source I _rr1with controlled current source I _s, controlled current source I _gthe 5th optics branch road after in parallel in the ground connection component model of one end, this branch node voltage is Δ λ _p;

Step 3, according to the I-E characteristic of the electric input interface of THz QCL, sets up the equivalent-circuit model that characterizes THzQCL input end electrical specification, comprises following sub-step:

Step 3.1, definition P ₁for equivalent electric signal input port, first use a desirable diode D ₁with a resistance R _dbe series at P ₁between, as the corresponding electronic circuit of equivalent-circuit model that characterizes THz QCL input electrical specification, the I ideal diode D that represents to flow through ₁electric current, the function V (I, T) that the voltage V of device input end is defined as to electric current I and temperature T is as follows:

$V(I,T)=\frac{\mathrm{KT}}{e}\ln (\frac{I}{I_s}+1)+{\mathrm{IR}}_s$ Formula 22

Wherein, KT/e is thermal voltage parameter V _t, K is Boltzmann constant, and e is electron charge, and T is kelvin degree, resistance R _dresistance be R _s, I _sreverse saturation current for diode;

Step 3.2, then, according to current-voltage (IV) curve of device input end actual measurement, uses the matching of Levenberg-Marquard method to obtain parameters R _s, I _s;

Step 3.3, last, ideal diode D will flow through ₁electric current I as controlled current source I in step 3 _injand I _leakcontrol current signal;

Step 4, the relation of Output optical power and photon density in the unit of utilization wavelength interval, tries to achieve the total Output optical power P of THzQCL light waveguide-layer _out, set up the equivalent-circuit model that characterizes THz QCL output terminal luminous power characteristic;

Step 5, in step 2, on the basis of step 3 and step 4, sets up the circuit macro-model that characterizes THz QCL photoelectric properties based on multimodes rate equation group, and this circuit macro-model is totally two ports, comprises an electrical port and a luminous power output port; Based on circuit macro-model, carry out photoelectric properties emulation and spectral characteristic test.

2. a kind of circuit modeling emulation mode that characterizes Terahertz quantum cascaded laser multimode effect according to claim 1, it is characterized in that, in described step 1, multimodes rate equation group is to set up according to the transport property of the inner charge carrier of THz QCL active layer the multimodes rate equation group of describing laser instrument electro-optical properties:

Described electronics rate equation is as follows,

$\frac{{\mathrm{dn}}_3}{\mathrm{dt}}=\frac{\mathrm{\ηI}}{\mathrm{eV}}-\frac{n_3}{{\mathrm{\τ}}_3}-\underset{m}{\mathrm{\Σ}}{g}_m(n_3-n_2)S_m$ Formula one

$\frac{{\mathrm{dn}}_2}{\mathrm{dt}}=\frac{(1-\mathrm{\η})I}{\mathrm{eV}}+(\frac{1}{{\mathrm{\τ}}_{32}}+\frac{1}{{\mathrm{\τ}}_{\mathrm{sp}}})n_3-\frac{n_2}{{\mathrm{\τ}}_{21}}+\underset{m}{\mathrm{\Σ}}{g}_m(n_3-n_2)S_m$ Formula two

$\frac{{\mathrm{dn}}_1}{\mathrm{dt}}=\frac{n_3}{{\mathrm{\τ}}_{31}}+\frac{n_2}{{\mathrm{\τ}}_{21}}+\frac{n_1}{{\mathrm{\τ}}_{\mathrm{out}}}$ Formula three

The photon velocity equation of described m pattern photon is as follows,

$\frac{d{S}_m}{\mathrm{dt}}=\mathrm{\Γ}{g}_m(n_3-n_2)S_m+{\mathrm{\β}}_m\mathrm{\Γ}\frac{n_3}{{\mathrm{\τ}}_{\mathrm{sp}}}-\frac{S_m}{{\mathrm{\τ}}_{\mathrm{ph}}}$ Formula four

Wherein, photon stimulated radiation transition high swash penetrate energy level and low swash penetrate energy level, the auxiliary transition relaxation energy level of phonon is designated respectively sub-energy level 1,2,3, wherein n ₃and n ₂represent respectively high sharp energy level and low sharp penetrate the electron number volume density on energy level, the n of penetrating of photon stimulated radiation transition ₁electron number volume density on the relaxation energy level of the auxiliary transition of expression phonon, S _mfor the photon number volume density of m pattern photon in optical cavity, the Injection Current that I is quantum cascade laser, τ ₃, τ ₃₂be respectively the radiation transistion life-span between 3 electronics entire lives of sub-energy level and sub-energy level 3 and sub-energy level 2; τ ₃₁, τ ₂₁be respectively between sub-energy level 3 and sub-energy level 1, the nonradiative transition life-span between sub-energy level 2 and sub-energy level 1, wherein 1/ τ ₃=1/ τ ₃₂+ 1/ τ ₃₁+ 1/ τ _sp; τ _sp, τ _phbe respectively the spontaneous radiation life-span of electronics between sub-energy level 3 and sub-energy level 2 and the photon lifetime in optical cavity, τ _outfor electronics is in the escape time of facing mutually between two cascade periodic structures; Γ is light restriction factor, and e is electron charge, and V is active area single-stage volume; η represents electric current injection efficiency parameter; g _mfor the gain of light of m pattern photon, its computing formula is as follows:

$g_m=g\left({\mathrm{\λ}}_m\right)=\frac{e^2{f}_{32}}{4m^{*}{n}_{\mathrm{eff}}^2\mathrm{\ϵ}}\·\mathrm{\γ}\left({\mathrm{\λ}}_m\right)$ Formula five

λ in formula five _mfor optical wavelength corresponding to m pattern photon, f ₃₂for the resonance intensity of radiation between sub-energy level 3 and sub-energy level 2, m ^*for the effective mass of active area mqw material electronics, ε is effective dielectric constant, n _efffor the equivalent refractive index in optical cavity; γ (λ _m) be line shape function, for characterizing the gain spectral distribution of laser radiation photon, this function adopts Lorentz lorentz's distribution function, γ (λ _m) computing formula is as follows:

$\mathrm{\γ}\left({\mathrm{\λ}}_m\right)=\frac{\frac{2}{\mathrm{\π\Δ}{\mathrm{\λ}}_g}}{1+4{({\mathrm{\λ}}_m-{\mathrm{\λ}}_p)}^2/\mathrm{\Δ}{\mathrm{\λ}}_g^2}$ Formula six

λ in formula six _pfor the centre wavelength of laser gain spectrum, Δ λ _gfWHM (Full Width at Half Maximum) for this distribution function;

In formula four, β _mspontaneous radiation coupling coefficient for m pattern photon; Under different mode, the spontaneous radiation coupling coefficient of photon also meets Lorentz lorentz's distribution function, and its computing formula is as follows:

${\mathrm{\β}}_m=\mathrm{\β}\left({\mathrm{\λ}}_m\right)=\frac{{\mathrm{\β}}_{\mathrm{sp}0}}{1+4{({\mathrm{\λ}}_m-{\mathrm{\λ}}_p)}^2/\mathrm{\Δ}{\mathrm{\λ}}_s^2}$ Formula seven

Δ λ in formula seven _sfWHM for this distribution function; β _sp0for the spontaneous radiation coupling coefficient of corresponding centre wavelength, its value determined by following formula,

${\mathrm{\β}}_{\mathrm{sp}0}=\frac{{\mathrm{\λ}}_p^4}{4{\mathrm{\π}}^2{n}_{\mathrm{eff}}^3\mathrm{\Δ}{\mathrm{\λ}}_{s}V{N}_{\mathrm{mod}}}$ Formula eight

N in formula eight _modnumber for Thz QCL cascade.

3. the circuit modeling emulation mode that characterizes according to claim 1 Terahertz quantum cascaded laser multimode effect, is characterized in that: parameter τ described in multimodes rate equation group ₃, τ ₃₂, τ ₃₁, τ ₂₁, τ _out, τ _sp, τ _phobtain manner comprises the following steps,

Step 3.1, under the condition of known THz QCL active layer mqw material, physical dimension and doping content, suppose that the direction of growth of material is along z axle, by self-consistent solution not time-dependent Schrodinger equation and Poisson equation, iteration is obtained each sub-energy levels Ei of active layer electronics, wave function ψ i (z), electron density distribution n (z);

Step 3.2, according to fermi's golden rule, the transition speed of definition electronics in i sub-band energy level is

formula 25

Wherein, for reduced Planck constant, τ _i' be electronics in the existence life-span of sub-band energy level i, Ei and Ef are respectively the electron energy of initial state sub-band energy level i and transition final states sub-band energy level f, for disturbance quantity, for transition matrix element;

By the sub-energy level of initial state, the average transition speed to the sub-energy level transition of final states can be expressed as definition electronics

$\mathrm{mean}\left(\frac{1}{{\mathrm{\τ}}_i^{\′}}\right)=\frac{\∫\mathrm{\θ}{f_i}^{\mathrm{FD}}\left(\mathrm{\θ}\right)/{\mathrm{\τ}}_i^{\′}\mathrm{d\θ}}{\mathrm{\π}{N}_i}$ Formula 26

Wherein, for the plane wave number of electronics, for electronics is at i subband Fermi distribution function,

Definition electronics at the surface density Ni of i subband is:

formula 27

Wherein, m ^*for the effective mass of electronics, be that i subband plane wave number is the energy of k electronics;

According to different scattering mechanisms, be listed as respectively and write transition matrix element f wherein, i=1,2,3, and f ≠ i, use numerical method to calculate the existence life-span τ ' of electronics on sub-energy level 3 under different scattering mechanisms according to formula five ₃, electronics is at the nonradiative transition life-span τ ' of 2 of sub-energy level 3 and sub-energy levels ₃₂, electronics is at the nonradiative transition life-span τ ' of 1 of sub-energy level 3 and sub-energy level ₃₁with the nonradiative transition life-span τ ' of electronics 1 of sub-energy level 2 and sub-energy level ₂₁, and according to formula six and formula seven, calculate the electronics the average survival time life-span of electronics on sub-energy level 3 under different scattering mechanisms electronics between sub-energy level 3 and 2, electronics between sub-energy level 3 and 1, the average nonradiative transition life-span of electronics between sub-energy level 2 and 1 with

Step 3.3, the inverse of the electronics mean lifetime of calculating under different scattering mechanisms is added and asks its reciprocal value to obtain electronics total life-span τ on sub-energy level 3 again ₃, electronics between sub-energy level 3 and 2, between sub-energy level 3 and 1, total nonradiative transition life-span τ between sub-energy level 2 and 1 ₃₂, τ ₃₁and τ ₂₁;

Intersubband self-excitation radiation-emitting transition rate equation under step 3.4, utilization three-dimensional photon density-of-states distribution model

$\frac{1}{{\mathrm{\τ}}_{\mathrm{sp}}}=\frac{e^2{n}_{\mathrm{eff}}{\mathrm{\ω}}_0^2}{6\mathrm{\π\ϵ}{m}^{*}{c}^3}{f}_{32}$ Formula 28

Calculate the spontaneous radiation life-span τ of electronics between sub-energy level 3 and sub-energy level 2 _sp, wherein for the resonance intensity based on electric coupling polar moment between sub-energy level 3 and sub-energy level 2, ω ₀for utilizing emitted light subcenter angular frequency, the effective mass that m* is electronics, ε is effective dielectric constant, n _efffor effective refractive index in optical cavity, c is the light velocity in vacuum, and e is electron charge;

Step 3.5, according to the optical cavity structure of device and material parameter, calculate the mirror loss α of optical cavity _mwaveguide loss α with optical cavity _w, and according to formula calculate parameter τ photon lifetime in optical cavity _p, n wherein _efffor effective refractive index in optical cavity; According to experimental data, extract and obtain electronics at the escape time parameter τ facing mutually between two cascade periodic structures _out.

4. the circuit modeling emulation mode that characterizes according to claim 1 Terahertz quantum cascaded laser multimode effect, is characterized in that: described step 4 comprises following sub-step:

The pass of unit wavelength interval Output optical power and photon density is,

$p\left(\mathrm{\λ}\right)=h{c}^2\mathrm{WD}/\left(2{\stackrel{\‾}{n}}_g\mathrm{\λ}\right)\·\ln (1/R_L{R}_R)/2\·S\left(\mathrm{\λ}\right)$ Formula 23

In formula, W, D are respectively broadband and the gross thickness of active area, R _land R _rfor the left and right end face reflection coefficient of optical cavity, for the group index of photon, λ penetrates photon wavelength for swashing, and constant h is Planck constant, and c is the light velocity in vacuum; Make integration can obtain total Output optical power P _out

$P_{\mathrm{out}}=h{c}^2\mathrm{WD}/\left(2{\stackrel{\‾}{n}}_g{\mathrm{\λ}}_p\right)\·\ln (1/R_L{R}_R)/2\·A_t{S}_p\mathrm{\Δ}{\mathrm{\λ}}_p$ Formula 24

Adopt a voltage-controlled controlled voltage source E _outanalog laser Output optical power P _out, voltage-controlled controlled voltage source E _outvoltage-controlled signal be the node voltage signal S of the 4th optics branch road _pnode voltage signal delta λ with the 5th optics branch road _p, voltage-controlled controlled voltage source E _outthe optical power value of the corresponding laser output of output voltage values, voltage-controlled controlled voltage source E _outscale-up factor k _paccording to formula 23, pass through to calculate obtain; Voltage-controlled controlled voltage source E _outconnect equivalent luminous power output port P ₂as the equivalent-circuit model that characterizes the output of THz QCL luminous power.

5. characterize according to claim 1 the circuit modeling emulation mode of Terahertz quantum cascaded laser multimode effect, it is characterized in that: in step 5, the concrete grammar that foundation characterizes the circuit macro-model of THz QCL photoelectric properties based on multimodes rate equation group is: first, use the newly-built circuit macro-model Thz QCL Multimode Model with two-port of circuit simulating software instrument HSPICE, definition two-port attribute, port Nin is laser instrument electrical input terminal mouth, and port NPout is laser optical power stage port; Then use electronic circuit descriptive language that each electronic circuit of setting up in step 3,4,5 is explained out; Finally the equivalent electric signal input port P1 setting up in step 4 is connected with the port Nin of circuit macro-model Thz QCL Multimode Model, the equivalent luminous power output port P2 setting up in step 5 is connected with the port NPout of circuit macro-model Thz QCL Multimode Model.