CN108923258B - Design method of trap type double-phonon active region energy level structure in terahertz quantum cascade laser - Google Patents

Design method of trap type double-phonon active region energy level structure in terahertz quantum cascade laser Download PDF

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CN108923258B
CN108923258B CN201810760732.9A CN201810760732A CN108923258B CN 108923258 B CN108923258 B CN 108923258B CN 201810760732 A CN201810760732 A CN 201810760732A CN 108923258 B CN108923258 B CN 108923258B
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陈长水
李金锋
王腾飞
周文辉
莘杰
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    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01S—DEVICES USING THE PROCESS OF LIGHT AMPLIFICATION BY STIMULATED EMISSION OF RADIATION [LASER] TO AMPLIFY OR GENERATE LIGHT; DEVICES USING STIMULATED EMISSION OF ELECTROMAGNETIC RADIATION IN WAVE RANGES OTHER THAN OPTICAL
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    • H01S5/30—Structure or shape of the active region; Materials used for the active region
    • H01S5/34—Structure or shape of the active region; Materials used for the active region comprising quantum well or superlattice structures, e.g. single quantum well [SQW] lasers, multiple quantum well [MQW] lasers or graded index separate confinement heterostructure [GRINSCH] lasers
    • H01S5/3401—Structure or shape of the active region; Materials used for the active region comprising quantum well or superlattice structures, e.g. single quantum well [SQW] lasers, multiple quantum well [MQW] lasers or graded index separate confinement heterostructure [GRINSCH] lasers having no PN junction, e.g. unipolar lasers, intersubband lasers, quantum cascade lasers

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Abstract

The invention discloses a design method of a trap type diphone active region energy level structure in a terahertz quantum cascade laser, which comprises the following steps: (1) designing the width of a trap wide potential barrier of one period of an active region of the terahertz quantum cascade laser; (2) solving the energy level of the active region through Schrodinger equation, and determining energy level distribution and whether the energy level distribution meets the design requirement; (3) and solving an active region velocity equation to obtain the output characteristics of the active region of the laser so as to verify the design feasibility. According to the method, Schrodinger is used for solving the quantum well energy level theory to calculate, so that the accuracy of the energy level position is determined, the problems of thermal excitation and thermal leakage caused by overhigh temperature of electrons in the terahertz quantum cascade laser can be solved, and the higher operating temperature and the higher output characteristic of the laser are obtained.

Description

Design method of trap type double-phonon active region energy level structure in terahertz quantum cascade laser
Technical Field
The invention relates to a design method of an active region energy level structure in a terahertz quantum cascade laser, in particular to a design method of a trap type diphone active region energy level structure in the terahertz quantum cascade laser.
Background
The development of infrared and microwave technology on both sides of the terahertz wave band was relatively mature before the middle of the 80's 20 th century, but the understanding of the terahertz wave band is still very limited, forming the so-called "terahertz groove". The terahertz frequency range has remained relatively undeveloped compared to the adjacent millimeter wave and infrared spectral ranges, mainly due to the lack of an effective radiation source.
The terahertz quantum cascade laser is one of effective methods for obtaining terahertz waves, and is a novel unipolar semiconductor device based on the principle of electron transition and assisted fast resonant tunneling of a conduction band and phonons in a semiconductor quantum well. Each level of the terahertz quantum cascade laser consists of an injection region, an active region and a relaxation region. The maximum working temperature of the terahertz quantum cascade laser is kept about 200K at present, and the output power is in the milliwatt level at the temperature.
The energy of laser photons emitted by the terahertz quantum cascade laser is far less than that of the intermediate infrared quantum cascade laser, which causes difficulty in structural design of an active region in the terahertz quantum cascade laser. GaAs/AlGaAs material system is widely used in terahertz quantum cascade laser. And the resonant phonon of GaAs is at an energy of about 36 meV. The resonance phonon energy of GaAs is relatively close to room temperature thermal energy, so that thermally activated phonon scattering becomes significant in the vicinity of room temperature. As a result, the population inversion is reduced and the output optical power is small. Obviously, a material system with large resonance phonon energy will suppress these negative transitions. In recent years, GaN/AlGaN heterostructures with large resonance phonon energies have attracted attention from a large number of researchers. It is reported that the GaN/AlGaN material system can effectively reduce the thermal excitation of the laser emission state at higher temperatures.
The two-phonon resonant active region design is a dual resonant active region system designed to allow efficient injection of electrons into the next-stage photon emission level.
Disclosure of Invention
The invention aims to provide a design method of a trap-type diphone active region energy level structure in a terahertz quantum cascade laser, which uses Schrodinger to solve a quantum well energy level theory for calculation so as to determine the accuracy of an energy level position, and can solve the problems of thermal excitation and thermal leakage caused by overhigh temperature of electrons in the terahertz quantum cascade laser so as to obtain higher laser operating temperature and output characteristics.
The above object of the present invention is achieved by the following technical solutions: the design method of the trap type diphone active region energy level structure in the terahertz quantum cascade laser is characterized by comprising the following steps:
(1) designing the width of a trap wide potential barrier of one period of an active region of the terahertz quantum cascade laser;
(2) solving the energy level of the active region through Schrodinger equation, and determining energy level distribution and whether the energy level distribution meets the design requirement;
(3) and solving an active region velocity equation to obtain the output characteristics of the active region of the laser so as to verify the design feasibility.
In the invention, the specific process of the step (1) is as follows:
the active region is based on a terahertz quantum cascade laser with the emitting light wave frequency of 6.77 terahertz, the corresponding active region in one period consists of 4 GaN quantum wells and 4 Al0.15Ga0.85N barriers, and the layer thickness is as follows: 2.5/0.9/0.6/0.8/2.4/1.9/1.7/1.8In nanometers, where the underlined numbers indicate the layer thickness of the barrier.
In the invention, the specific process of the step (2) is as follows:
the Schrodinger equation expression describing the quantum well is as follows:
Figure BDA0001727798880000021
wherein the content of the first and second substances,
Figure BDA0001727798880000022
is Planck constant, m*(z) is the mass of electrons in the quantum well, z is the growth direction of the material, V (z) is an external electric field of 71kv/cm, the intrinsic energy state of E electrons, and psi (z) is the wave function of the electrons;
solving the Schrodinger equation to obtain the intrinsic energy state E and the wave function of electrons, thereby obtaining the energy states of the electrons in the active region in one period and calculating the intrinsic energy state and the wave function of the electrons;
according to the design and calculation results, an active region of the terahertz quantum cascade laser is composed of 4 main energy levels which are respectively marked as 4 energy levels, 3 energy levels, 2 energy levels and 1 energy levels, the flow direction of electrons is from 4 energy levels to 1 energy level, the difference between the 4 energy levels and the 3 energy levels is an energy interval of phonons, the energy interval of the difference between the 3 energy levels and the 2 energy levels is 28meV, the corresponding optical wave frequency is 6.77 terahertz, and the difference between the 2 energy levels and the 1 energy levels is an energy interval of phonons.
In the invention, the specific process of the step (3) is as follows:
adopting a rate equation of electronic energy level to analyze the output characteristics of the active region and the included physical mechanism, wherein the corresponding rate equation is as follows:
Figure BDA0001727798880000023
Figure BDA0001727798880000031
Figure BDA0001727798880000032
Figure BDA0001727798880000033
wherein J represents the density of the injected current, e is the amount of electron charge, Ni(i ═ 1, 2, 3, 4) is the number of electrons on subband i, P is the number of photons in the cavity, W and L are the propagation cross-sections of the photons in the cavity, τijTime, τ, taken for electrons to transition from subband i to subband j3And τ4The electron lifetime at energy level 3 and energy level 4 respectively, N is the period number of the terahertz quantum cascade laser, and taupIs the survival time of a photon in the cavity, G ═ vgσ32) The optical gain factor in the/V active region is a mode confinement factor, V is the volume of one period, and the stimulated emission cross section is determined by the following formula:
Figure BDA0001727798880000034
wherein z is32Is a 3-level and 2-level dipole matrix element,0is the dielectric constant in vacuum, λ0Is the lasing wavelength in vacuum, 2 gamma 32 being the electromagnetic spectrumHalf peak;
in steady state, the terms on the left of equations (1) - (4) are equal to zero, and then the equation is reduced to the following equations:
Figure BDA0001727798880000035
Figure BDA0001727798880000036
Figure BDA0001727798880000037
Figure BDA0001727798880000038
through the integrated simplification and solution of the above equations, the output characteristics of the laser active region are obtained as follows:
Figure BDA0001727798880000039
Figure BDA00017277988800000310
Figure BDA0001727798880000041
Figure BDA0001727798880000042
the design and calculation verification of the active region structure of the terahertz quantum cascade laser are realized through the steps.
The method is mainly characterized in that the Schrodinger equation is solved, the wave function and the electronic intrinsic energy state of the electrons are determined, and the energy states in the quantum wells can have dependent energy separation according to the design thought.
According to the terahertz quantum cascade laser, a trap type double-phonon active region structure design is adopted, the novel active region has two phonons to assist electron resonance, and two phonon energy levels are respectively positioned above a light-emitting upper energy level and below a light-emitting lower energy level, so that better laser particle number reversal can be realized, and the temperature characteristic and the output characteristic of the terahertz quantum cascade laser are improved. By utilizing the resonance characteristics of phonons and electrons, an electronic state is ingeniously added to the energy state with higher luminous upper energy level, and the energy interval between the electronic state and the luminous upper energy level is different from that of the phonons by one phonon energy.
Drawings
The invention is described in further detail below with reference to the figures and specific embodiments.
Fig. 1 is a structural design diagram of an active region in a design method of a trap-type diphone active region energy level structure in a terahertz quantum cascade laser of the present invention, which shows the structure of the active region for one period, and lines 1, 2, 3, and 4 in the diagram represent energy states 1, 2, 3, and 4, respectively, taking an emitted light wave frequency of 6.77 terahertz as an example;
fig. 2 is a schematic diagram of electron transmission of one period of the trap type diphone active region structure in the design method of the trap type diphone active region energy level structure in the terahertz quantum cascade laser of the present invention, wherein lines 1, 2, 3, and 4 in the diagram represent energy state 1, energy state 2, energy state 3, and energy state 4, respectively;
fig. 3 is a schematic diagram illustrating a situation that the number of electrons at each energy level in the trap type diphone active region structure is changed with the density of the injected current in the design method of the trap type diphone active region energy level structure in the terahertz quantum cascade laser according to the present invention, wherein the abscissa is the density of the injected current, the ordinate is the number of electrons, the dotted line in the diagram represents the number of electrons in the energy state 3, the star-shaped line represents the number of electrons in the energy state 2, and the solid line represents the number of particle number inversion;
fig. 4 is a schematic diagram of variation of intra-cavity photons with injection current density achieved by the trap type diphone active region structure in the design method of the trap type diphone active region energy level structure in the terahertz quantum cascade laser according to the present invention, and meanwhile, in addition to comparison with a conventional three-energy level structure quantum cascade laser, a solid line represents an energy level structure corresponding to the present invention, and a dotted line represents a conventional three-energy level structure.
Detailed Description
The invention relates to a design method of a trap type diphone active region energy level structure in a terahertz quantum cascade laser, which comprises the following steps:
(1) designing the width of a trap wide potential barrier of one period of an active region of the terahertz quantum cascade laser;
the specific process of the step (1) is as follows:
the active region is based on a terahertz quantum cascade laser with the emitting light wave frequency of 6.77 terahertz, and correspondingly, one period active region of the terahertz quantum cascade laser is composed of 4 GaN quantum wells and 4 Al0.15Ga0.85N barriers, wherein the layer thickness is as follows: 2.5/0.9/0.6/0.8/2.4/1.9/1.7/1.8In nanometers, where the underlined numbers indicate potential barriers. The width of each quantum well and the thickness of the potential barrier in the active region are shown in fig. 1.
(2) Solving the energy level of the active region through Schrodinger equation, determining energy level distribution and whether the energy level distribution meets the design requirement
The specific process of the step (2) is as follows:
the Schrodinger equation expression for describing the quantum well is as follows:
Figure BDA0001727798880000051
wherein
Figure BDA0001727798880000052
Is Planck constant, m*(z) is the mass of electrons in the quantum well, z is the growth direction of the material, V (z) is the applied electric field, 71kv/cm, the intrinsic energy state of the E electrons, and ψ (z) is the wave function of the electrons.
By solving the Schrodinger equation, the intrinsic energy state E and the electronic wave function of electrons can be obtained, and therefore each electronic energy state in one period of the active region can be obtained. Solving this equation is done by a number of methods, such as: the invention relates to a transfer matrix method, a finite difference method, a self-consistent method and the like.
According to the design and calculation results, one active region of the terahertz quantum cascade laser is composed of 4 main energy levels which are respectively marked as 4 energy levels, 3 energy levels, 2 energy levels and 1 energy level. The flow of electrons is from 4 to 1 level. The energy interval between the 4 level and the 3 level differs by one phonon, the energy interval between the 3 level and the 2 level differs by 28meV, which corresponds to the energy interval between the 2 level and the 1 level differing by one phonon with the optical wave frequency of 6.77 terahertz. The energy level structure and electron flow direction are shown in fig. 2.
(3) Solving an active region velocity equation to obtain the output characteristics of the active region of the laser so as to verify the design feasibility
The specific process of the step (3) is as follows:
in the step (1) and the step (2), the emission frequency of the designed quantum cascade laser is 6.77 terahertz, corresponding to the results designed in the two steps, the corresponding rate equation is as follows:
Figure BDA0001727798880000061
Figure BDA0001727798880000062
Figure BDA0001727798880000063
Figure BDA0001727798880000064
wherein J represents the density of the injected current, e is the amount of electron charge, Ni(i ═ 1, 2, 3, 4) is the number of electrons on subband i, P is the number of photons in the cavity, W and L are the propagation cross-sections of the photons in the cavity, τijTime, τ, taken for electrons to transition from subband i to subband j3And τ4The electron lifetime at energy level 3 and energy level 4 respectively, N is the period number of the terahertz quantum cascade laser, and taupIs the survival time of a photon in the cavity, G ═ vgσ32) The optical gain factor in the/V active region is a mode confinement factor, V is the volume of one period, and the stimulated emission cross section is determined by the following formula:
Figure BDA0001727798880000068
wherein z is32Is a 3-level and 2-level dipole matrix element,0is the dielectric constant in vacuum, λ0Is the lasing wavelength in vacuum, and 2 γ 32 is the half-height peak of the electromagnetic spectrum.
In steady state, the terms on the left of equations (1) - (4) are equal to zero, and then the equation is reduced to the following equations:
Figure BDA0001727798880000065
Figure BDA0001727798880000066
Figure BDA0001727798880000067
Figure BDA0001727798880000071
through the integrated simplification and solution of the above equations, the output characteristics of the laser active region are obtained as follows:
Figure BDA0001727798880000072
Figure BDA0001727798880000073
Figure BDA0001727798880000074
Figure BDA0001727798880000075
the parameters used in the calculation are as follows:
parameter(s) Trap type double phonon energy level structure Conventional three-level structure
Temperature of 230K 230K
W 2.8mm 2.8mm
L 200um 200um
neff 2.29 2.29
N 50 50
2γ32 3meV 3meV
αm 2cm-1 2cm-1
αw 16cm-1 16cm-1
τ43 0.22ps --
τ42 20ps --
τ41 35ps --
τ32 1.2ps 1ps
τ31 18.7ps 10ps
τ21 0.24ps 0.21ps
τp 1.4ps 1.4ps
The population inversion and output power are shown in fig. 3 and fig. 4.
The above-described embodiments of the present invention are not intended to limit the scope of the present invention, and the embodiments of the present invention are not limited thereto, and various other modifications, substitutions and alterations can be made to the above-described structure of the present invention without departing from the basic technical concept of the present invention as described above, according to the common technical knowledge and conventional means in the field of the present invention.

Claims (3)

1. The design method of the trap type diphone active region energy level structure in the terahertz quantum cascade laser is characterized by comprising the following steps:
(1) designing the width of a trap wide potential barrier of one period of an active region of the terahertz quantum cascade laser;
(2) solving the energy level of the active region through Schrodinger equation, and determining energy level distribution and whether the energy level distribution meets the design requirement;
(3) adopting a rate equation of electronic energy level to analyze the output characteristics of the active region and the included physical mechanism, wherein the corresponding rate equation is as follows:
Figure FDA0002627187500000011
Figure FDA0002627187500000012
Figure FDA0002627187500000013
Figure FDA0002627187500000014
wherein J represents the density of the injected current, e is the amount of electron charge, Ni(i ═ 1, 2, 3, 4) is the number of electrons on subband i, P is the number of photons in the cavity, W and L are the propagation cross-sections of the photons in the cavity, τijTime, τ, taken for electrons to transition from subband i to subband j3And τ4The electron lifetime at energy level 3 and energy level 4 respectively, N is the period number of the terahertz quantum cascade laser, and taupIs the survival time of a photon in the cavity, G ═ vgσ32) V is the optical gain factor in the active region, where is the mode confinement factor, V is the volume of one period, and the stimulated emission cross-section is determined by:
Figure FDA0002627187500000015
wherein z is32Is a 3-level and 2-level dipole matrix element,0is the dielectric constant in vacuum, λ0Is the lasing wavelength in vacuum, 2 gamma32Is the half-peak of the electromagnetic spectrum;
in steady state, the terms on the left of equations (1) - (4) are equal to zero, and then the equation is reduced to the following equations:
Figure FDA0002627187500000016
Figure FDA0002627187500000017
Figure FDA0002627187500000018
Figure FDA0002627187500000019
through the integrated simplification and solution of the above equations, the output characteristics of the laser active region are obtained as follows:
Figure FDA00026271875000000110
Figure FDA00026271875000000111
Figure FDA00026271875000000112
Figure FDA0002627187500000021
and verifying the design feasibility by using the output characteristics of the obtained laser active region.
2. The design method of the trap type diphone active region energy level structure in the terahertz quantum cascade laser as claimed in claim 1, wherein the specific process of the step (1) is as follows:
an active region is based on a terahertz quantum cascade laser with the emission light wave frequency of 6.77 terahertz, and the corresponding active region in one period consists of 4 GaN quantum wells and 4 Al0.15Ga0.85N-barrier composition, layer thickness: 2.5/0.9/0.6/0.8/2.4/1.9/1.7/1.8In nanometers, where the underlined numbers indicate the layer thickness of the barrier.
3. The design method of the trap type diphone active region energy level structure in the terahertz quantum cascade laser as claimed in claim 2, wherein the specific process of the step (2) is as follows:
the Schrodinger equation expression describing the quantum well is as follows:
Figure FDA0002627187500000022
wherein the content of the first and second substances,
Figure FDA0002627187500000023
is Planck constant, m*(z) is the effective mass of electrons in the quantum well, z is the growth direction of the material, v (z) is the applied electric field, 71kv/cm, the intrinsic energy state of E electrons, ψ (z) is the wave function of electrons;
solving the Schrodinger equation to obtain the intrinsic energy state E and the wave function of electrons, thereby obtaining the energy states of the electrons in the active region in one period and calculating the intrinsic energy state and the wave function of the electrons;
according to the design and calculation results, an active region of the terahertz quantum cascade laser is composed of 4 main energy levels which are respectively marked as 4 energy levels, 3 energy levels, 2 energy levels and 1 energy levels, the flow direction of electrons is from 4 energy levels to 1 energy level, the difference between the 4 energy levels and the 3 energy levels is an energy interval of phonons, the energy interval of the difference between the 3 energy levels and the 2 energy levels is 28meV, the corresponding optical wave frequency is 6.77 terahertz, and the difference between the 2 energy levels and the 1 energy levels is an energy interval of phonons.
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