CN105718618A - PIN limiter electrothermal integration analysis method under high-power electromagnetic pulse action - Google Patents

Abstract

The present invention discloses a PIN limiter electrothermal integration analysis method under a high-power electromagnetic pulse action, and provides internal temperature distribution of a PIN diode in a limiter circuit under the high-power pulse action. According to the method, firstly, a semiconductor drift-expansion equation group is calculated by using a time domain spectral element method, so as to obtain carrier distribution and electric potential distribution inside the PIN diode; next, on the basis of resolving an internal electric field and a current density of a semiconductor, internal temperature distribution of the PIN diode is obtained through calculating by using a heat conduction equation; and finally, a newton iteration form of a circuit equation of the limiter is deduced, the circuit equation, the drift-expansion equation group, and the heat conduction equation are coupled to resolve, and practical voltages of two ends of the PIN diode in the circuit and the internal temperature distribution of the PIN diode are obtained through calculation by using a physical model.

Description

PIN amplitude limiter electric heating Method In The Whole-process Analysis under high-power electromagnetic impulse action

Technical field

The invention belongs to the electric heating integrated analysis of semiconductor device, especially for the numerical analysis method of PIN pipe amplitude limiter design.

Background technology

High-power electromagnetic pulse refers to that the pulse peak power of microwave is at more than 100MW, frequency electromagnetic pulse within the scope of 0.3～300GHz.High power microwave weapon is that the microwave produced by high-power microwave source radiates through gain directional antenna, with high intensity illumination target, anti-personnel and destruction electronic equipment (Tan Xianyu, the state of the art of high power microblogging new concept weapon and development [J]. airborne weapon, 2004,1:8-11).High-power electromagnetic pulse makes electric component burn, or the performance of electrical subsystem is impacted.The damage effect of electronic equipment is mainly had two ways by high-power electromagnetic pulse: under (1) high-power electromagnetic impulse action, metal surface or plain conductor produce induced voltage or electric current the effect that electronic devices and components are produced, as caused circuit devcie state turnover, device performance to decline and the puncturing of semiconductor device.(2) gathering of media interior heat energy under high-power electromagnetic impulse action, heating cause the effect caused that heats up, and this effect can be burnt device or cause that second breakdown etc. occurs in semiconductor junction.Device burns the knot ablation including semiconductor device, and metal connecting line fusing etc., this will result in permanent damage.Electronic system is not only destroyed by High-Power Microwave, after High-Power Microwave is coupled into circuit, also the performance of electronic system is produced impact.Such as by PN junction rectification, create the voltage equal with normal circuit running voltage, cause the upset of digital circuit, thus destroying systemic-function.

Since the seventies in last century, due to developing rapidly of computer technology, Computational electromagnetics obtains fast development.Relative to analytic method, numerical method can solve the problem that a very big class calculates huge, and structure is complicated and problem that analytic method is difficult to maybe to obtain precise results.For electromagnetic model numerical solution, current main stream approach is divided into time domain approach (such as Finite-Difference Time-Domain Method) and frequency domain method (such as finite element, moment method etc.) etc. by time-frequency domain.It is more general that the numerical analysis of quasiconductor is generally adopted the methods such as FDTD, FEM.Determining it yet with the Yee grid characteristics of FDTD cannot the complicated model of model configuration.FEM when being applied to time domain each time step be directed to solving system of linear equations, amount of calculation is very huge, loses time very much.And time domain spectral element method (Joon-HoLeeandQingHuoLiu, " A3-DSpectral-ElementTime-DomainMethodforElectromagneticS imulation; " IEEETransactionsonMicrowaveTheoryandTechniques., vol.55, no.5, pp.983-991, May2007) using identical grid discrete, flexibly, subdivision is convenient in modeling, the matrix formed has good openness, and solution efficiency is higher.

Summary of the invention

It is an object of the invention in conjunction with quasiconductor numerical analysis method, it is proposed to a kind of method of the electric heating integrated analysis of PIN amplitude limiter under high-power electromagnetic impulse action, its step is as follows:

The first step, sets up the physical model of the required PIN diode solved, and adopts bent hexahedron that this physical model is carried out subdivision, obtain the structural information of PIN diode physical model, i.e. the physical coordinates value of each node on the numbering of hexahedral element and hexahedron；

Second step, from Drift-diffusion Semiconductor Equations group, adopts the gold test of gal the Liao Dynasty, by unknown quantity (carrier concentration n, p and the electromotive force of required solution to equation group) launch on each node, obtain solving equation.Newton iteration method solving equation is utilized to obtain the carrier concentration on each node of PIN diode physical model and Potential Distributing；

3rd step, from the equation of heat conduction, adopts the gold test of gal the Liao Dynasty, required solution unknown quantity (temperature T) is launched on each node, obtain solving equation the equation of heat conduction.By power density P on each for PIN diode physical model node_dSubstitute into the equation of heat conduction, calculate and obtain PIN diode internal temperature T distribution；

4th step, for PIN amplitude limiter circuit, it then follows Kirchoff s voltage, current law derive circuit equation, adopts Newton iteration method to solve circuit equation, and the unknown quantity of required solution is PIN diode both end voltage in circuit.When given PIN diode sounds out voltage, in circuit, the electric current of PIN diode and temperature adopt the physical model in second step and the 3rd step to solve to obtain, and the PIN diode electric current tried to achieve substitutes into circuit equation and carries out next step Newton iteration；

5th step, constantly repeat second and third, four steps, until the PIN diode both end voltage tried to achieve meets convergence precision, the voltage now tried to achieve is in amplitude limiter circuit PIN diode two ends real voltage.Carrier concentration n within PIN pipe, p, electromotive forceDistribution with temperature T can also obtain simultaneously；

6th step, to PIN amplitude limiter circuit plus a high power pulse (such as lightening pulse), by the Temperature Distribution that the solution procedure described in the 5th step is tried to achieve in circuit in PIN diode both end voltage, electric current and PIN diode；

The present invention compared with prior art, its remarkable advantage: (1) PIN diode adopt physical model solve, it is possible to obtain the electrical characteristics of device inside and the distribution of thermal characteristics.(2) PIN diode is put in circuit, circuit equation and PIN diode physical model governing equation (drift-diffusion equation group, the equation of heat conduction) are carried out couple solution, it is possible to simulation PIN diode working condition in amplitude limiter circuit.(3) electrical characteristics of semiconductor device and thermal characteristics are integrated analysis, it does not have isolated and come.And influencing each other between electric heating can be connected by next step of external circuit equation Newton iteration.(4) SETD adopts bent hexahedron subdivision, and flexibly, subdivision is convenient, uses specific orthogonal polynomial as basic function in modeling, and along with the raising of polynomial order, calculating error will exponentially decline.

Accompanying drawing explanation

Fig. 1 calculates PIN pipe doping used.

Fig. 2 calculates PIN pipe amplitude limiter circuit used.

Fig. 3 is that amplitude limiter adds PIN pipe both end voltage during lightening pulse.

Fig. 4 is that amplitude limiter adds the internal maximum temperature of PIN pipe during lightening pulse.

Fig. 5 is that PIN pipe is burning moment interior temperature distribution.

Detailed description of the invention

Below in conjunction with accompanying drawing, the present invention is described in further detail.

1, set up the physical model of the required PIN diode solved, and adopt bent hexahedron that this physical model is carried out subdivision, obtain the structural information of PIN diode physical model, be i.e. the physical coordinates value of each node on the numbering of hexahedral element and hexahedron.

Calculating the PIN diode physical model adopted is p⁺nn⁺The one-dimensional device model of structure, substrate is n⁺Silicon materials, doping donor concentration is 10¹⁹cm^-3, doping adopts Gauss distribution.At the n-type epitaxial layer that Grown thickness is 10 μm, donor concentration 10 of adulterating¹⁵cm^-3.Acceptor impurity diffuses into epitaxial layer and forms p district, and Impurity Distribution is Gaussian, and pn-junction place (degree of depth is 3 μm) concentration is 10¹⁵cm^-3, dopant profiles is as shown in Figure 1.

2, according to carrier drift-diffusion theory, Poisson's equation, equation of current density, Current continuity equation are the one group of fundamental formulars characterizing semiconductor device inside electric parameter.Drift domination is mainly made up of following three prescription journeys:

Poisson's equation:

In Poisson's equation,Being electromotive force, q is unit charge electricity, and n is electron concentration, and p is hole concentration,It is net dopant concentration,WithRespectively donor impurity concentration and acceptor impurity concentration.

Equation of current density:

Current continuity equation:

$\frac{\∂n}{\∂t}=\frac{1}{q}\▿\·J_n+G-R$

$\frac{\∂p}{\∂t}=-\frac{1}{q}\▿\·J_p+G-R---\left(2.3\right)$

G represents generation rate and the recombination rate in electronics and hole respectively with R.

In the multidimensional simulation of semiconductor device, boundary condition is generally all more complicated, is often divided into fixed boundary condition and floating boundary condition two class.Fixed boundary condition refers generally to border, metal electrode place, and floating border refers to the border not having metal electrode.

Fixed boundary condition:

φ_n=φ_p=V_A

N-p-N=0

Pn=1

Wherein V_AIt is the voltage being added in Ohmic contact place, φ_n、φ_pIt it is the Fermi potential in electronics, hole.

Floating boundary condition:

R is the outer normal component of boundary.

In the process carrying out Semiconductor Physics numerical solution, first having to drift-diffusion equation is normalized, equation is carried out the gold test of gal the Liao Dynasty by recycling spectral element method basic function, by the equations turned matrix form that can solve for computer.Adopt coupling algorithm and Newton iteration method to solve above-mentioned Nonlinear System of Equations, try to achieve n, p,After, electric current density can be tried to achieve

$J=J_n+J_p+\mathrm{\ϵ}\frac{\∂E}{\∂t}---\left(2.6\right)$

3, by solving drift-diffusion equation group, it is possible to obtain the electrical characteristics within PIN diode, i.e. carrier n, p distribution and electromotive forceDistribution.How calculating the Temperature Distribution within PIN diode on this basis is important problem.In heat medium, the transmission of t heat meets heat conduction partial differential equation, i.e. the equation of heat conduction (HTE), the expression formula of heat diffusivity equation:

${\mathrm{\ρ}}_m{c}_m\frac{\∂T}{\∂t}=K_t{\▿}^{2}T-V_s(T-T_a)+P_d---\left(3.1\right)$

Wherein, ρ_mIt is the density (kg/m of object³),c_mBeing the specific heat capacity (J/ (kg K)) of object, T is the transient temperature (K) of object, and t is heat time heating time (s), K_tIt is heat conductivity (W (m K)), V_sLong-pending (W/ (the m of thermal capacitance stream for cooling stream³K)), T_aIt is the temperature (K) of cooling stream, P_dPower density (W/m for thermal source³)。

For simplifying problem, it is assumed that ρ_mAnd c_mNot being all the function of time, space and temperature, and ignore the effect of cooling stream, under rectangular coordinate system, heat transmission governing equation is rewritten as:

$\frac{\∂T}{\∂t}=D_t((\frac{{\∂}^{2}T}{\∂x^2}+\frac{{\∂}^{2}T}{\∂y^2}+\frac{{\∂}^{2}T}{\∂z^2})+\frac{P_d}{K_t})---\left(3.2\right)$

In above formula,

$D_t=\frac{k_t}{{\mathrm{\ρ}}_m{c}_m}---\left(3.3\right)$

D_tIt is thermal diffusion power.

Utilize spectral element method basic function that equation (3.2) carries out the gold test of gal the Liao Dynasty, by the equations turned matrix form that can solve for computer.Try to achieve carrier n, p concentration and electromotive forceAfter distribution, by calculating current density equation and electromotive forceGradient, it is possible to obtain PIN pipe internal current density J and electric field E, thus calculating power density P_d=E × J, substituting into the equation of heat conduction can in the hope of Temperature Distribution.

4, the PIN pipe amplitude limiter circuit will analyzed is as in figure 2 it is shown, two PIN manage positive and negative parallel connection R in circuit_A=R_L=50 Ω, V_D, I_DThe respectively voltage and current of PIN diode.

According to Kirchhoff's theorem, it is possible to obtain circuit equation:

$(I_{D1}+I_{D2}+\frac{V_D}{R_L})\·R_A+V_D=v---\left(4.1\right)$

Diode model has transient state relation: I_D=f_t(V_D)(4.2)

With the trial solution approximate representation derivative of two intervals:

${f_t}^{\′}\left(V_{D1}\right)=\frac{I_{D1}-I_{D0}}{V_{D1}-V_{D0}}---\left(4.3\right)$

Order

$F_t\left(V_D\right)\≡(I_{D1}+I_{D2}+\frac{V_D}{R_L})\·R_A+V_D-v=0---\left(4.4\right)$

(4.4) formula is carried out Taylor series expansion: F_t(V_D1)+F_t'(V_D1)(V_D2-V_D1)=0, finally gives:

$V_{D2}=V_{D1}-\frac{(I_{D1}+I_{D2}+\frac{V_{D1}}{R_L})\·R_A+V_{D1}-v}{(\frac{I_{D1}-I_{D10}}{V_{D1}-V_{D0}}+\frac{I_{D2}-I_{D20}}{V_{D1}-V_{D0}}+\frac{1}{R_L})\·R_A+1}---\left(4.5\right)$

V_D1Voltage, I is soundd out for first, PIN pipe two ends_D1For corresponding PIN tube current value.Voltage V soundd out by PIN pipe second_D0=V_D1-Δ V, Δ V can be set to 0.01V in advance, and try to achieve electric current I_D0.Then, (4.5) the 3rd tentative voltage V is tried to achieve_D2, and electric current I_D2.Such iteration, until meeting convergence precision | V_D2-V_D1| < ε stops, and the V now tried to achieve_D2Can as the V in next moment_D1。

When given PIN diode sounds out voltage, the Temperature Distribution within the electric current of PIN diode generation and PIN diode is all obtained (by calculating drift-diffusion equation and the equation of heat conduction) by physical model calculating.Under one Newton iteration step of external circuit equation, after trying to achieve PIN diode internal temperature T, the parameter that some in Drift-diffusion Semiconductor Equations are varied with temperature is needed to be updated when carrying out next Newton iteration step, as mobility, carrier produce recombination rate etc., thus achieve electric heating integration and calculate.

5, lightening pulse signal is a kind of high-power electromagnetic pulse, adds a lightening pulse signal at PIN amplitude limiter circuit voltage source, to analyze high power pulse to the damage effect of PIN diode in PIN amplitude limiter.American army mark MIL-STD-461E standard provides the waveform of lightning voltage and lightning current, and lightening pulse double-exponential function represents i.e. v (t)=kV₀(e^-αt-e^-βt).Wherein, V₀Representing the peak value of pulse, α, β represent the attenuation quotient of two exponential functions, and k is coefficient.

The attenuation constant of the conventional double-exponential function impulse waveform of lightening pulse is as shown in table 1.

Table 1 lightening pulse commonly uses waveform

Double exponential pulse waveform parameter

Attenuation constant α

Attenuation constant β

Coefficient k

1.2/50 μ s (lightning voltage ripple)	1.625×104	2.456×106	1.0409
				2.6/40 μ s (lightning current wave)	1.859×104	1.365×106	1.0758
10/350 μ s (lightning current wave)	0.211×104	3.513×105	1.0304

Because PIN diode pipe adopts voltage drive mode in program, it is added on power supply so choosing 1.2/50 μ s (lightning voltage ripple).Calculated PIN pipe both end voltage and PIN pipe maximum temperature are respectively as shown in Figure 3, Figure 4.As seen from Figure 4, the maximum temperature of PIN pipe alreadys more than 1680K (fusing point of silicon), and PIN pipe will be caused permanent damage by this.

PIN pipe is important problem in not internal in the same time Temperature Distribution, for this, calculating process has taken PIN pipe and has burnt the moment (device maximum temperature reaches 1680K) internal Temperature Distribution as shown in Figure 5.From burning moment interior temperature distribution it can be seen that PIN pipe intrinsic layer I district temperature rises higher, it it is the place being easier to burn.

This electric heating Method In The Whole-process Analysis can simulate PIN diode working condition in amplitude limiter circuit, and the change of PIN pipe interior temperature distribution in amplitude limiter circuit can be obtained, to analyzing semiconductor device anti-high power destruction in microwave limiter circuit, there is extremely important realistic meaning.And electric heating integration solves analysis and all adopts spectral element method, using identical grid discrete, flexibly, subdivision is convenient in modeling, and the matrix of formation has good openness, and solution efficiency is higher.

Claims (3)

1. PIN amplitude limiter electric heating Method In The Whole-process Analysis under a high-power electromagnetic impulse action, it is characterised in that comprise the following steps:

The first step, sets up the physical model of the required PIN diode solved, and adopts bent hexahedron that this physical model is carried out subdivision, obtain the structural information of PIN diode physical model, i.e. the physical coordinates value of each node on the numbering of hexahedral element and hexahedron；

Second step, from Drift-diffusion Semiconductor Equations group, adopts the gold test of gal the Liao Dynasty, by the unknown quantity carrier concentration of required solution to equation group、And electromotive forceEach node launches, obtains solving equation；Newton iteration method solving equation is utilized to obtain the carrier concentration on each node of PIN diode physical model and Potential Distributing；

3rd step, from the equation of heat conduction, adopts the gold test of gal the Liao Dynasty, by required solution unknown quantity temperature to the equation of heat conductionEach node launches, obtains solving equation；By power density on each for PIN diode physical model nodeSubstitute into the equation of heat conduction, calculate and obtain PIN diode internal temperatureDistribution；

4th step, for PIN amplitude limiter circuit, it then follows Kirchoff s voltage, current law derive circuit equation, adopts Newton iteration method to solve circuit equation, and the unknown quantity of required solution is PIN diode both end voltage in circuit；When given PIN diode sounds out voltage, in circuit, the electric current of PIN diode and temperature adopt the physical model in second step and the 3rd step to solve to obtain, and the PIN diode electric current tried to achieve substitutes into circuit equation and carries out next step Newton iteration；

5th step, constantly repeat second and third, four steps, until the PIN diode both end voltage tried to achieve meets convergence precision, the voltage now tried to achieve is in amplitude limiter circuit PIN diode two ends real voltage；Obtain the carrier concentration within PIN pipe simultaneously、, electromotive forceAnd temperatureDistribution；

6th step, to PIN amplitude limiter circuit plus a high power pulse, by the Temperature Distribution that the solution procedure described in the 5th step is tried to achieve in circuit in PIN diode both end voltage, electric current and PIN diode.

2. PIN amplitude limiter electric heating Method In The Whole-process Analysis under high-power electromagnetic impulse action according to claim 1, it is characterised in that: described step 3 utilize second step to try to achieve、、Obtain PIN diode internal electric fieldAnd electric current density, obtain each node power density thus calculating；Try to achieve PIN diode internal temperatureAfterwards, the parameter varied with temperature in Drift-diffusion Semiconductor Equations is updated, it is achieved electric heating integration calculates.

3. PIN amplitude limiter electric heating Method In The Whole-process Analysis under high-power electromagnetic impulse action according to claim 2, it is characterised in that: described in the parameter that varies with temperature include mobility and carrier produces recombination rate.