Physical Modeling and Parameter Extraction ... - Semantic Scholar
Physical Modeling and Parameter Extraction Procedure for p-i-n Diodes with Lifetime Control L. Lu, A. Bryant*, E. Santi, J.L. Hudgins**, P.R. Palmer*** Department of Electrical Engineering, University of South Carolina, Columbia, SC 29208, Email: [email protected] * School of Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom, Email: [email protected] ** Department of Electrical Engineering, University of Nebraska, Lincoln, NE 68588-0511 *** Engineering Department, Cambridge University, Trumpington Street, Cambridge CB2 1PZ, UK Abstract—. A physics-based model for diodes with lifetime control has been recently proposed. The model is an extension of a diode model that uses a Fourier series solution for the ambipolar diffusion equation in the drift region. In this paper a parameter extraction procedure for the diode with lifetime control is proposed. The procedure requires a forward characteristic and a reverse recovery measurement. The parameter extraction procedure is illustrated using finite element simulations. The physics-based model using the parameters so extracted shows excellent agreement with experimental results. Keywords- Power semiconductor modeling, pin diode model, physics-based model, lifetime control, variable lifetime
I. INTRODUCTION One of the main goals in the development of circuitoriented physics-based models for power semiconductor devices is to make models available that allow prediction of switching waveforms and conduction and switching losses for an arbitrary power converter application. High-voltage p-i-n diodes are an important element of switching power converters. The diode reverse recovery phenomenon at turn-on of the active switch causes a variety of problems such as increased switching losses, voltage overshoot and ringing with associated noise and EMI problems. Attempts to improve the reverse recovery performance of a diode typically cause increased forward conduction losses in the diode. This trade-off between reverse recovery and forward conduction performance is a prominent aspect of diode design. Lifetime control [1-3] in the drift region has been used to improve diode performance beyond what is possible with a diode with uniform lifetime. A variety of techniques have been employed to control lifetime, such as gold and platinum diffusion, and electron and proton irradiation. A recently developed physics-based diode model [4-5] is based on a Fourier series solution of the ambipolar diffusion equation (ADE) in the drift region. The model has proven quite accurate for transient simulation under clamped inductive load conditions. In particular the diode model has been quite successful in predicting diode reverse recovery characteristics over a wide temperature range. Moreover, a simple parameter extraction procedure has been proposed [6], which requires only a clamped inductive turn-off experiment
to extract all parameters needed for the model. This diode model assumes constant lifetime in the drift region. When applied to a commercial diode that employs lifetime control, this physics-based model has been incapable to predict both reverse recovery and forward voltage drop using a single set of model parameters. The drift region lifetime needed for accurate forward drop prediction is more than three times the value needed for accurate reverse recovery prediction. This fact is actually further proof of the accuracy of the developed model and shows the improvement in the forwarddrop/reverse-recovery trade-off achievable using lifetime control. It also indicates the need for a diode model that includes variable lifetime. Such a diode model has been recently proposed [7] as an extension of the Fourier series model and it has been validated against finite element simulations of a theoretical diode. Not surprisingly this variable-lifetime diode model has a larger number of parameters than the constant-lifetime original model, but no parameter extraction procedure is currently available and the model has not been validated against experimental results. In this paper we propose a novel parameter extraction procedure for the variable-lifetime diode. The procedure retains the simplicity of the original parameter extraction procedure and requires a clamped inductive turn-off experiment and static forward characteristics easily obtainable from a curve tracer. The procedure is applied to a commercially available diode with lifetime control and the experimental model validation includes both switching and static characteristics. II. ELECTRO-THERMAL PHYSICS-BASED MODEL The behavior of conductivity modulated devices, such as pin diodes and IGBTs, depends heavily on the excess carrier (charge) distribution in the wide drift region. Space-charge neutrality is maintained with the majority carrier profile closely matching the minority carrier profile (quasi-neutrality). Under these conditions, and assuming high-level injection, the charge dynamics are described by the ambipolar diffusion equation. D
∂ 2 p( x, t ) p( x, t ) ∂p( x, t ) . = + ∂x 2 τ ∂t
(1)
A Fourier based solution for this equation has been used to develop physics-based diode models for the case of constant lifetime τ ( x ) = τ 0 [4] and for the case of variable lifetime [7]. The 2nd order partial differential carrier diffusion equation is converted into an infinite set of 1st order linear differential equations with series coefficients p0…pk forming equivalent RnCn components. The representation requires the width of the undepleted region and the hole and electron currents at the boundaries of the region (x1 and x2), which provide the boundary conditions. Notice that the model provides the instantaneous carrier distribution profile in the drift region. The pin diode model described above can be implemented in circuit simulators such as the Virtual Test Bed (VTB) or PSpice. A typical simulation result for diode reverse recovery is shown in Fig. 1. The excellent agreement between simulation and experiment is clearly evident. 1000
150 Vd(Test) Vd(Simulation)
800
Id(Test) Id(Simulation)
50
400
0
200
-50
0 55.0 -200
55.5
56.0
56.5 Time(us)
57.0
57.5
has a bigger slope. Typical reverse recovery diode waveforms are shown in Fig. 4. The falling slope of the diode current is determined by the supply voltage and by the stray inductance LS. When the current becomes negative, charge is extracted from the drift region. The slope remains constant as long as the diode voltage is small. At time t1 a depletion layer starts forming close to the p+ region and the diode voltage increases. As a result, the voltage across the stray inductance decreases and the current slope becomes smaller in magnitude. At time t2 the diode voltage is equal to the supply voltage and the current slope is zero. At this point the diode current reaches the peak negative value Irrm. The reverse current then falls to zero in a manner dictated by the remaining charge in the drift region. In order to have a soft recovery with limited ringing across the diode, it is desirable that at time t2 there be significant charge stored in the drift region. If little charge is left, the diode recovery can be quite snappy. The diode softness factor SF is defined in Fig. 4 as the ratio of recovery time tr and storage time ts.
100
Current(A)
Voltage(V)
600
L = Dτ is smaller and therefore the carrier concentration
-100 58.0 -150
Fig. 1 Diode at room temperature. Comparison between the experimental result (dark blue-voltage & pink-current) and simulation (yellow-voltage & light blue-current) during turn-off
Fig. 2 Assumed layout of diode with lifetime control
III. REVERSE RECOVERY OF DIODES WITH LIFETIME CONTROL Consider a diode with lifetime control as shown in Fig. 2. It is assumed that the drift region consists of two regions having lifetimes τ1 and τ2. The low-lifetime region is placed adjacent to the p+ region [1]. A typical carrier distribution under forward conduction conditions is shown in Fig. 3. Notice that in the low-lifetime region the diffusion length
SF =
tr ts
(2)
The goal of lifetime control is to reduce the peak reverse current Irrm without a corresponding reduction of recovery time tr, i.e., maintaining a large value of softness factor SF. This is achieved by placing a narrow low-lifetime region near the p+ emitter. This reduces the charge that needs to be extracted to form a depletion region (see Fig. 3) while leaving significant stored charge in the undepleted region near the n+ emitter. The stored charge Q2 provides the desired soft recovery at turn-off. Moreover, if the low-lifetime region is narrow, the forward drop will depend mostly on the highlifetime region and it will be small due to conductivity modulation.
0
xd
WB
Fig. 3 Typical charge distribution during forward conduction
2.
Fig. 4 Typical diode reverse recovery current and voltage waveforms
IV. PARAMETER EXTRACTION PROCEDURE FOR DIODES WITH LIFETIME CONTROL The model parameters needed for the diode with constant and variable lifetime are listed in Table I. For the variable lifetime case the arrangement of Fig. 2 is assumed. Most parameters are the same except that for the variable-lifetime diode there are three parameters related to lifetime: lifetimes τ1 and τ2, and width of low-lifetime region xd. Model parameters Diode with constant Diode with lifetime lifetime control Active area [A] Drift region width [WB ] Drift region doping concentration [NB] Anode recombination parameter [hp] Cathode recombination parameter [hn]
Same Same Same Same Same
Low lifetime [ τ1] High lifetime [τ2] Width of low-lifetime region [xd] Table I Model parameters for diode with constant lifetime and with lifetime control.
Check that diode has variable lifetime. Measure the diode forward characteristic using a curve tracer. A way to verify that the diode indeed has lifetime control is to try to match both reverse recovery and forward drop characteristics using the constant-lifetime model. This will prove impossible for diodes with lifetime control. 3. Extraction of high lifetime τ2. Assume now that you have a diode with constant lifetime and match the measured forward characteristic. The extracted lifetime is the high lifetime τ2. This is a good approximation because the width of the low-lifetime region is typically small and has a small effect on forward drop. 4. Extraction of low lifetime τ1. Assume that you have a diode with constant lifetime and find the lifetime value needed to match the peak reverse current Irrm. This value is low lifetime τ1. This is a good approximation because, during the storage period, charge has to be extracted from the low lifetime region and the amount of charge in this region is a function of τ1. Fig. 5 shows a set of Silvaco Atlas finite element simulations of diode reverse recovery for several values of lifetime. The increase of peak reverse current as lifetime increases can be clearly observed. 5. Extraction of low-lifetime region width xd. This parameter can be extracted by matching the softness of the diode recovery. A change in width xd changes the amount of charge left in the diode drift region at the end of the storage interval (time t2 of Fig. 4) and affects the softness of the recovery. Fig. 6 shows a set of Atlas simulations for different values of width xd. Notice that the peak reverse recovery current decreases as width xd increases. In conclusion there are three more parameters to be extracted compared with the constant lifetime case: τ1, τ2, and xd. High lifetime τ2 can be extracted by matching the forward characteristic, low lifetime τ1 can be extracted by matching the peak reverse recovery current and low-lifetime region width xd can be extracted by matching the recovery softness. Some final refinement of these parameters may improve matching.
High-level lifetime [ τHL]
100
tau 0.66us tau 0.2us tau 0.05us
50
0 Current (A)
The parameter extraction procedure is a modification of the proposed parameter extraction procedure for constantlifetime diodes described in [6]. It consists of the following steps: 1. Extraction of A, WB, NB, hp and hn. Perform an extraction procedure for a diode with constant lifetime following [6]. This requires a reverse recovery experiment. This provides values for active area A, drift region width WB, doping concentration NB and recombination parameters hp and hn. It is preferable to open a diode package and actually measure active area A, rather than trying to estimate it.
Diode Reverse Recovery _ 400V 100A 150
-50
-100
-150
-200
-250 5.00E-07
1.00E-06
1.50E-06
2.00E-06
Time (s)
Fig. 5 Atlas simulation of reverse recovery waveforms of constant lifetime diode for various values of lifetime: 0.05µs, 0.2µs and 0.66µs. Time scale is 0.5µs/div.
Diode Reverse Recovery _ 400V 100A _tau (0.3-1.6us) 150
100
D15 D30 D45 D0
50
Current (A)
0
-50
-100
-150
-200
-250
-300 0.00E+00
5.00E-07
1.00E-06
1.50E-06
2.00E-06
2.50E-06
3.00E-06
Time (s)
Fig. 6 Atlas simulation of reverse recovery waveforms of variable lifetime diode for various values of width xd. The total drift region width is WB = 180µm. The values are 0µm, 15µm, 30µm and 45µm. Time scale is 500ns/div.
V. EXAMPLE OF PROPOSED PARAMETER EXTRACTION PROCEDURE The proposed extraction procedure is applied to a commercially available variable lifetime diode having a rated forward current of 100A and a blocking voltage of 600V. A sample of the diode has been opened and the chip area has been measured to be 0.5cm2. This particular diode has been optimized by the manufacturer to operate with IGBTs. For validation purposes a special setup has been built to measure the reverse recovery characteristic. The setup uses MOSFETs as the active switch in order to minimize diode-IGBT interaction. Given the high switching speed of MOSFETs, the active switch can be considered an ideal infinitely fast switch for simulation purposes. The setup also allows to vary the parasitic loop inductance, so that the model validation can be done for different values of this parameter. All these special features are not strictly needed for the parameter extraction procedure, but simplify and enhance the model validation. The static forward characteristic is measured using a Tektronix 371A high power curve tracer. The measurement is performed in an environmental chamber at temperatures of 150K, 300K, and 400K. 1. Extraction of A, WB, NB, hp and hn. The extraction procedure for constant lifetime diode using the experimental reverse recovery experiment of Fig. 7 gives A = 0.5cm2, WB = 120µm, NB = 1E14 cm-3, hp = hn = 1E-14cm4s-1, τHL = 0.3µs. 2. Check that diode has variable lifetime. The diode model with constant lifetime with the parameters extracted in Step 1 can predict the reverse recovery characteristic as shown in Fig. 8. Notice however that it cannot accurately predict the experimental forward drop characteristic as shown in Fig. 9. The temperature dependence of the forward characteristic does not match and in particular the high temperature curves are far off. 3. Extraction of high lifetime τ2. In order to match the forward characteristic a lifetime τHL = 1.6µs is needed as shown in Fig. 10. This is the extracted high
lifetime τ2. Notice however that the reverse recovery characteristic does not match the experimental result at all, as shown in Fig. 11. 4. Extraction of low lifetime τ1. The low lifetime is extracted by matching the peak reverse recovery current. From Fig. 8 it is clear that a value τ1 = 0.3µs gives a good matching. 5. Extraction of low-lifetime region width xd. A variable lifetime diode having lifetimes τ1 = 0.3µs and τ2 = 1.6µs is simulated in Atlas for various values of low lifetime region width xd. Reverse recovery waveforms similar to the ones shown in Fig. 6 are obtained. From these results a value xd = 30µm is chosen. This value could be improved by further refining the model parameters. This completes the extraction procedure. The forward characteristic and the reverse recovery waveforms predicted by the variable lifetime model are shown in Fig. 12 and Fig. 13, respectively. Table II and Table III show a comparison of forward drop for the various cases at 100A and 50A current level respectively. Diode Reverse Recovery @ 300V-100A Ls1/2/3/4
700
Vd_Ls1_Exp Id_Ls1_Exp
600
Vd_Ls2_Exp Id_Ls2_Exp Vd_Ls3_Exp
500
Id_Ls3_Exp Vd_Ls4_Exp
400
Id_Ls4_Exp
300 200 100 0 -100 -200 -300 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Time (us)
Fig. 7 Experimental reverse recovery waveforms of variable lifetime diode for four different values of parasitic loop inductance (60nH, 73nH, 94nH, and 128nH). Diode voltage and diode current are shown. Time scale is 200ns/div. Diode Reverse Recovery @ 300V-100A Ls2
700 600
Vd_Ls2_Exp Id_Ls2_Exp
500
Vd_Ls2_Constant Lifetime 0.3us Id_Ls2_Constant Lifetime 0.3us
400 300 200 100
0 -100 -200 -300 0
0.2
0.4
0.6
0.8
1 Time (us)
1.2
1.4
1.6
1.8
2
Fig. 8 Comparison of experimental reverse recovery waveforms with finite element simulation using a constant lifetime diode with the parameters given in step 1 ( τHL = 0.3µs). The parasitic loop inductance is 73nH. Diode voltage and diode current are shown. Time scale is 200ns/div.
600V-100A Diode Forward Characteristics
110 100
100
Constant Lifetime 0.3us_300K Constant Lifetime 0.3us_400K
90
Experimental 300K
70
60
60
Id (Ampere)
70
50 40
30 20
10
10
0
0
-10
-10
0.3
0.4
0.5
Experimental 150K
0.6
0.7
0.8
0.9
1 1.1 1.2 1.3 Vd (Voltage)
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
Experimental 400K
0
2.2
Fig. 9 Comparison of experimental forward static characteristic with finite element simulation using a constant lifetime diode with the parameters given in step 1 ( τHL = 0.3µs). 600V-100A Diode Forward Characteristics
110
Experimental 300K
40
20
0.2
Variable Lifetime 0.3-1.6us_400K
50
30
0.1
Variable Lifetime 0.3-1.6us_300K
80
Experimental 400K
0
Variable Lifetime 0.3-1.6us_150K
90
Experimental 150K
80
Id (Ampere)
600V-100A Diode Forward Characteristics
110 Constant Lifetime 0.3us_150K
0.1
0.2
0.3
0.4
0.5
0.6
0.7 0.8 Vd (Voltage)
0.9
1.4
Id_Ls2_Exp 500
Constant Lifetime 1.6us_300K
Vd_Ls2_Variable Lifetime 0.3-1.6us
Constant Lifetime 1.6us_400K
Id_Ls2_Variable Lifetime 0.3-1.6us
400
Experimental 150K Experimental 300K
70
Id (Ampere)
1.3
Vd_Ls2_Exp
600
80
1.2
Diode Reverse Recovery @ 300V-100A Ls2
Constant Lifetime 1.6us_150K
90
1.1
Fig. 12 Comparison of experimental forward static characteristic with finite element simulation for the variable lifetime diode model (τ1 = 0.3µs, τ2 = 1.6µs, xd = 30µm). 700
100
1
300
Experimental 400K
60
200
50 100
40 0
30 -100
20 -200
10
-300
0
0
-10 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7 0.8 Vd (Voltage)
0.9
1
1.1
1.2
1.3
1.4
Fig. 10 Comparison of experimental forward static characteristic with finite element simulation using a constant lifetime diode with the parameters given in step 3 ( τHL = τ2 = 1.6µs).
0.2
0.4
0.6
0.8
1
Time (us)
1.2
1.4
1.6
1.8
Fig. 13 Comparison of experimental reverse recovery waveforms with finite element simulation for the variable lifetime diode model (τ1 = 0.3µs, τ2 = 1.6µs, xd = 30µm). Diode voltage and diode current are shown. Time scale is 200ns/div.
Diode Reverse Recovery @ 300V-100A Ls2 650
Vd_Ls2_Exp
150K 1.29V 1.42V 1.24V
100A 300K 1.18V 1.57V 1.08V
400K 1.15V 2.03V 1.02V
1.27V
1.15V
1.15V
Id_Ls2_Exp
550
Vd_Ls2_Constant Lifetime 1.6us 450
Id_Ls2_Constant Lifetime 1.6us
Experimental Atlas τHL = 0.3µs Atlas τHL = 1.6µs Atlas τ1 = 0.3µs τ2 = 1.6µs xd = 30µm
350 250 150 50 -50
Table II Forward drop at 100A current level.
-150 -250 -350
150K 1.18V 1.25V 1.13V
50A 300K 1.04V 1.38V 0.97V
400K 0.96V 1.77V 0.89V
1.15V
1.02V
1.00V
-450 0
0.2
0.4
0.6
0.8
1 Time (us)
1.2
1.4
1.6
1.8
2
Fig. 11 Comparison of experimental reverse recovery waveforms with finite element simulation using a constant lifetime diode with the parameters given in step 3 ( τHL = τ2 = 1.6µs). The parasitic loop inductance is 73nH. Diode voltage and diode current are shown. Time scale is 200ns/div.
2
Experimental Atlas τHL = 0.3µs Atlas τHL = 1.6µs Atlas τ1 = 0.3µs τ2 = 1.6µs xd = 30µm
Table III Forward drop at 50A current level.
VI. PHYSICS-BASED MODEL VALIDATION
several values of parasitic loop inductance Ls. Diode voltage and diode current are shown. Supply voltage is 300V and time scale is 100ns/div.
The parameter extraction procedure has been demonstrated using finite element simulations. The parameters obtained are now used in the Fourier-series-solution diode model with lifetime control proposed in [7]. The complete list of parameters used is given in Table IV. Notice that the values of the recombination parameters have been adjusted. Reverse recovery results are shown in Fig. 14 and Fig. 15 for a blocking voltage of 200V and 300V respectively. The forward characteristics at various temperatures are shown in Fig. 16. Notice the excellent agreement with the experimental results. Active area [A] 0.5 cm2 Drift region width [WB ] 120 µm Drift region doping concentration [NB] 1E14 cm-3 Anode recombination parameter [hp] 4E-14 cm4 s-1 Cathode recombination parameter [hn] 30E-14 cm4 s-1 Low lifetime [ τ1] 0.3 µs High lifetime [τ2] 1.6 µs Width of low-lifetime region [xd] 30 µm Table IV Model parameters used for variable lifetime diode.
Diode current IA (A)
80
0
LS = 93nH LS = 128nH
VAK (V), IA (A)
300 200 100 0
-100 -200
0.8
0.9
300V 700 LS = 60nH 600
LS = 73nH LS = 93nH
500
LS = 128nH
VAK (V), IA (A)
400 300 200
1.
[1]
0 -100
[2]
-200
0.6
0.7 Time (µs)
1
1.2
1.4
0.8
0.9
1
Fig. 15 Comparison of experimental reverse recovery waveforms (dashed lines) with physics-based diode model with variable lifetime (solid lines) for
CONCLUSIONS
Diode manufacturers commonly use lifetime control to improve diode characteristics. In this paper it is shown that constant lifetime diode models are unable to accurately predict both forward drop and reverse recovery characteristics. Therefore a parameter extraction procedure is proposed for diodes with lifetime control. The procedure is validated using Atlas finite element simulations and is applied to a commercially available diode with lifetime control. The parameters are used in the Fourier series solution diode model proposed in [7]. The model predictions show an excellent agreement with experimental results.
100
0.5
0.6 0.8 Diode voltage VAK (V)
Fig. 16 Comparison of experimental (dashed lines) forward static characteristic with physics-based diode model with variable lifetime (solid lines).
1
Fig. 14 Comparison of experimental reverse recovery waveforms (dashed lines) with physics-based diode model with variable lifetime (solid lines) for several values of parasitic loop inductance Ls. Diode voltage and diode current are shown. Supply voltage is 200V and time scale is 100ns/div.
-300 0.4
0.4
The parameter extraction procedure illustrated above provides a simple systematic procedure for the extraction of the model parameters for a diode with variable lifetime. It also provides a method to verify whether a certain diode has lifetime control. This is important because typically manufacturers are very reluctant to give out any processing information for diodes. The parameter extraction task is greatly simplified by the realization that the forward characteristic is mainly determined by the high lifetime region and the reverse recovery behavior is mainly determined by the low lifetime region.
LS = 73nH
400
0.7 Time (µs)
0.2
VII. DISCUSSION LS = 60nH
0.6
40
0
200V
0.5
60
20
500
-300 0.4
T = 400K T = 300K T = 150K
100
[3]
REFERENCES E. Napoli, A. G. M. Strollo, P. Spirito, “Numerical analysis of local lifetime control for high-speed low-loss P-i-N diode design,” IEEE Trans Power Electronics, Vol. 14 N.4, pp.615-621, July 1999. M.T. Rahimo and N.Y.A. Shammas. Optimisation of the reverse recovery behaviour of fast power diodes using injection efficiency and lifetime control techniques. In EPE Conf. Rec., volume 2, pages 99– 104, Trondheim, 1997. B. J. Baliga, “Comparison of gold, platinum, and electron irradiation for controlling lifetime in power rectifiers,” IEEE Trans Electron Devices, Vol. ED-24, No. 6, June 1977.
[4]
[5]
[6]
[7]
Leturcq, Berraies, Debrie, Gillet, Kallala and Massol, "Bipolar semiconductor device models for computer-aided design in power electronics," 6th European Conference on Power Electronics, vol. 2, p. 84, Sept. 1995. P.R. Palmer, E. Santi, J.L. Hudgins, X. Kang, J.C. Joyce, P.Y. Eng, "Circuit simulator models for the diode and IGBT with full temperature dependent features," IEEE Trans. Power Electronics, Vol. 18, No. 5, pp. 1220-1229, Sept. 2003 X. Kang, A. Caiafa, E. Santi, J.L. Hudgins, P.R. Palmer, "Parameter extraction for a power diode circuit simulator model including temperature dependent effects," Proc. IEEE Applied Power Electronics Conference (APEC'02), Dallas, Texas, pp. 452-458, March 2002 A.T. Bryant, P.R. Palmer, E. Santi, J.L. Hudgins, “A compact diode model for the simulation of fast power diodes including the effects of avalanche and carrier lifetime zoning,” Proc. IEEE Power Electronics Specialists Conference (PESC'05), pp. 2042-2048, Recife, Brazil, June 2005
I. INTRODUCTION One of the main goals in the development of circuitoriented physics-based models for power semiconductor devices is to make models available that allow prediction of switching waveforms and conduction and switching losses for an arbitrary power converter application. High-voltage p-i-n diodes are an important element of switching power converters. The diode reverse recovery phenomenon at turn-on of the active switch causes a variety of problems such as increased switching losses, voltage overshoot and ringing with associated noise and EMI problems. Attempts to improve the reverse recovery performance of a diode typically cause increased forward conduction losses in the diode. This trade-off between reverse recovery and forward conduction performance is a prominent aspect of diode design. Lifetime control [1-3] in the drift region has been used to improve diode performance beyond what is possible with a diode with uniform lifetime. A variety of techniques have been employed to control lifetime, such as gold and platinum diffusion, and electron and proton irradiation. A recently developed physics-based diode model [4-5] is based on a Fourier series solution of the ambipolar diffusion equation (ADE) in the drift region. The model has proven quite accurate for transient simulation under clamped inductive load conditions. In particular the diode model has been quite successful in predicting diode reverse recovery characteristics over a wide temperature range. Moreover, a simple parameter extraction procedure has been proposed [6], which requires only a clamped inductive turn-off experiment
to extract all parameters needed for the model. This diode model assumes constant lifetime in the drift region. When applied to a commercial diode that employs lifetime control, this physics-based model has been incapable to predict both reverse recovery and forward voltage drop using a single set of model parameters. The drift region lifetime needed for accurate forward drop prediction is more than three times the value needed for accurate reverse recovery prediction. This fact is actually further proof of the accuracy of the developed model and shows the improvement in the forwarddrop/reverse-recovery trade-off achievable using lifetime control. It also indicates the need for a diode model that includes variable lifetime. Such a diode model has been recently proposed [7] as an extension of the Fourier series model and it has been validated against finite element simulations of a theoretical diode. Not surprisingly this variable-lifetime diode model has a larger number of parameters than the constant-lifetime original model, but no parameter extraction procedure is currently available and the model has not been validated against experimental results. In this paper we propose a novel parameter extraction procedure for the variable-lifetime diode. The procedure retains the simplicity of the original parameter extraction procedure and requires a clamped inductive turn-off experiment and static forward characteristics easily obtainable from a curve tracer. The procedure is applied to a commercially available diode with lifetime control and the experimental model validation includes both switching and static characteristics. II. ELECTRO-THERMAL PHYSICS-BASED MODEL The behavior of conductivity modulated devices, such as pin diodes and IGBTs, depends heavily on the excess carrier (charge) distribution in the wide drift region. Space-charge neutrality is maintained with the majority carrier profile closely matching the minority carrier profile (quasi-neutrality). Under these conditions, and assuming high-level injection, the charge dynamics are described by the ambipolar diffusion equation. D
∂ 2 p( x, t ) p( x, t ) ∂p( x, t ) . = + ∂x 2 τ ∂t
(1)
A Fourier based solution for this equation has been used to develop physics-based diode models for the case of constant lifetime τ ( x ) = τ 0 [4] and for the case of variable lifetime [7]. The 2nd order partial differential carrier diffusion equation is converted into an infinite set of 1st order linear differential equations with series coefficients p0…pk forming equivalent RnCn components. The representation requires the width of the undepleted region and the hole and electron currents at the boundaries of the region (x1 and x2), which provide the boundary conditions. Notice that the model provides the instantaneous carrier distribution profile in the drift region. The pin diode model described above can be implemented in circuit simulators such as the Virtual Test Bed (VTB) or PSpice. A typical simulation result for diode reverse recovery is shown in Fig. 1. The excellent agreement between simulation and experiment is clearly evident. 1000
150 Vd(Test) Vd(Simulation)
800
Id(Test) Id(Simulation)
50
400
0
200
-50
0 55.0 -200
55.5
56.0
56.5 Time(us)
57.0
57.5
has a bigger slope. Typical reverse recovery diode waveforms are shown in Fig. 4. The falling slope of the diode current is determined by the supply voltage and by the stray inductance LS. When the current becomes negative, charge is extracted from the drift region. The slope remains constant as long as the diode voltage is small. At time t1 a depletion layer starts forming close to the p+ region and the diode voltage increases. As a result, the voltage across the stray inductance decreases and the current slope becomes smaller in magnitude. At time t2 the diode voltage is equal to the supply voltage and the current slope is zero. At this point the diode current reaches the peak negative value Irrm. The reverse current then falls to zero in a manner dictated by the remaining charge in the drift region. In order to have a soft recovery with limited ringing across the diode, it is desirable that at time t2 there be significant charge stored in the drift region. If little charge is left, the diode recovery can be quite snappy. The diode softness factor SF is defined in Fig. 4 as the ratio of recovery time tr and storage time ts.
100
Current(A)
Voltage(V)
600
L = Dτ is smaller and therefore the carrier concentration
-100 58.0 -150
Fig. 1 Diode at room temperature. Comparison between the experimental result (dark blue-voltage & pink-current) and simulation (yellow-voltage & light blue-current) during turn-off
Fig. 2 Assumed layout of diode with lifetime control
III. REVERSE RECOVERY OF DIODES WITH LIFETIME CONTROL Consider a diode with lifetime control as shown in Fig. 2. It is assumed that the drift region consists of two regions having lifetimes τ1 and τ2. The low-lifetime region is placed adjacent to the p+ region [1]. A typical carrier distribution under forward conduction conditions is shown in Fig. 3. Notice that in the low-lifetime region the diffusion length
SF =
tr ts
(2)
The goal of lifetime control is to reduce the peak reverse current Irrm without a corresponding reduction of recovery time tr, i.e., maintaining a large value of softness factor SF. This is achieved by placing a narrow low-lifetime region near the p+ emitter. This reduces the charge that needs to be extracted to form a depletion region (see Fig. 3) while leaving significant stored charge in the undepleted region near the n+ emitter. The stored charge Q2 provides the desired soft recovery at turn-off. Moreover, if the low-lifetime region is narrow, the forward drop will depend mostly on the highlifetime region and it will be small due to conductivity modulation.
0
xd
WB
Fig. 3 Typical charge distribution during forward conduction
2.
Fig. 4 Typical diode reverse recovery current and voltage waveforms
IV. PARAMETER EXTRACTION PROCEDURE FOR DIODES WITH LIFETIME CONTROL The model parameters needed for the diode with constant and variable lifetime are listed in Table I. For the variable lifetime case the arrangement of Fig. 2 is assumed. Most parameters are the same except that for the variable-lifetime diode there are three parameters related to lifetime: lifetimes τ1 and τ2, and width of low-lifetime region xd. Model parameters Diode with constant Diode with lifetime lifetime control Active area [A] Drift region width [WB ] Drift region doping concentration [NB] Anode recombination parameter [hp] Cathode recombination parameter [hn]
Same Same Same Same Same
Low lifetime [ τ1] High lifetime [τ2] Width of low-lifetime region [xd] Table I Model parameters for diode with constant lifetime and with lifetime control.
Check that diode has variable lifetime. Measure the diode forward characteristic using a curve tracer. A way to verify that the diode indeed has lifetime control is to try to match both reverse recovery and forward drop characteristics using the constant-lifetime model. This will prove impossible for diodes with lifetime control. 3. Extraction of high lifetime τ2. Assume now that you have a diode with constant lifetime and match the measured forward characteristic. The extracted lifetime is the high lifetime τ2. This is a good approximation because the width of the low-lifetime region is typically small and has a small effect on forward drop. 4. Extraction of low lifetime τ1. Assume that you have a diode with constant lifetime and find the lifetime value needed to match the peak reverse current Irrm. This value is low lifetime τ1. This is a good approximation because, during the storage period, charge has to be extracted from the low lifetime region and the amount of charge in this region is a function of τ1. Fig. 5 shows a set of Silvaco Atlas finite element simulations of diode reverse recovery for several values of lifetime. The increase of peak reverse current as lifetime increases can be clearly observed. 5. Extraction of low-lifetime region width xd. This parameter can be extracted by matching the softness of the diode recovery. A change in width xd changes the amount of charge left in the diode drift region at the end of the storage interval (time t2 of Fig. 4) and affects the softness of the recovery. Fig. 6 shows a set of Atlas simulations for different values of width xd. Notice that the peak reverse recovery current decreases as width xd increases. In conclusion there are three more parameters to be extracted compared with the constant lifetime case: τ1, τ2, and xd. High lifetime τ2 can be extracted by matching the forward characteristic, low lifetime τ1 can be extracted by matching the peak reverse recovery current and low-lifetime region width xd can be extracted by matching the recovery softness. Some final refinement of these parameters may improve matching.
High-level lifetime [ τHL]
100
tau 0.66us tau 0.2us tau 0.05us
50
0 Current (A)
The parameter extraction procedure is a modification of the proposed parameter extraction procedure for constantlifetime diodes described in [6]. It consists of the following steps: 1. Extraction of A, WB, NB, hp and hn. Perform an extraction procedure for a diode with constant lifetime following [6]. This requires a reverse recovery experiment. This provides values for active area A, drift region width WB, doping concentration NB and recombination parameters hp and hn. It is preferable to open a diode package and actually measure active area A, rather than trying to estimate it.
Diode Reverse Recovery _ 400V 100A 150
-50
-100
-150
-200
-250 5.00E-07
1.00E-06
1.50E-06
2.00E-06
Time (s)
Fig. 5 Atlas simulation of reverse recovery waveforms of constant lifetime diode for various values of lifetime: 0.05µs, 0.2µs and 0.66µs. Time scale is 0.5µs/div.
Diode Reverse Recovery _ 400V 100A _tau (0.3-1.6us) 150
100
D15 D30 D45 D0
50
Current (A)
0
-50
-100
-150
-200
-250
-300 0.00E+00
5.00E-07
1.00E-06
1.50E-06
2.00E-06
2.50E-06
3.00E-06
Time (s)
Fig. 6 Atlas simulation of reverse recovery waveforms of variable lifetime diode for various values of width xd. The total drift region width is WB = 180µm. The values are 0µm, 15µm, 30µm and 45µm. Time scale is 500ns/div.
V. EXAMPLE OF PROPOSED PARAMETER EXTRACTION PROCEDURE The proposed extraction procedure is applied to a commercially available variable lifetime diode having a rated forward current of 100A and a blocking voltage of 600V. A sample of the diode has been opened and the chip area has been measured to be 0.5cm2. This particular diode has been optimized by the manufacturer to operate with IGBTs. For validation purposes a special setup has been built to measure the reverse recovery characteristic. The setup uses MOSFETs as the active switch in order to minimize diode-IGBT interaction. Given the high switching speed of MOSFETs, the active switch can be considered an ideal infinitely fast switch for simulation purposes. The setup also allows to vary the parasitic loop inductance, so that the model validation can be done for different values of this parameter. All these special features are not strictly needed for the parameter extraction procedure, but simplify and enhance the model validation. The static forward characteristic is measured using a Tektronix 371A high power curve tracer. The measurement is performed in an environmental chamber at temperatures of 150K, 300K, and 400K. 1. Extraction of A, WB, NB, hp and hn. The extraction procedure for constant lifetime diode using the experimental reverse recovery experiment of Fig. 7 gives A = 0.5cm2, WB = 120µm, NB = 1E14 cm-3, hp = hn = 1E-14cm4s-1, τHL = 0.3µs. 2. Check that diode has variable lifetime. The diode model with constant lifetime with the parameters extracted in Step 1 can predict the reverse recovery characteristic as shown in Fig. 8. Notice however that it cannot accurately predict the experimental forward drop characteristic as shown in Fig. 9. The temperature dependence of the forward characteristic does not match and in particular the high temperature curves are far off. 3. Extraction of high lifetime τ2. In order to match the forward characteristic a lifetime τHL = 1.6µs is needed as shown in Fig. 10. This is the extracted high
lifetime τ2. Notice however that the reverse recovery characteristic does not match the experimental result at all, as shown in Fig. 11. 4. Extraction of low lifetime τ1. The low lifetime is extracted by matching the peak reverse recovery current. From Fig. 8 it is clear that a value τ1 = 0.3µs gives a good matching. 5. Extraction of low-lifetime region width xd. A variable lifetime diode having lifetimes τ1 = 0.3µs and τ2 = 1.6µs is simulated in Atlas for various values of low lifetime region width xd. Reverse recovery waveforms similar to the ones shown in Fig. 6 are obtained. From these results a value xd = 30µm is chosen. This value could be improved by further refining the model parameters. This completes the extraction procedure. The forward characteristic and the reverse recovery waveforms predicted by the variable lifetime model are shown in Fig. 12 and Fig. 13, respectively. Table II and Table III show a comparison of forward drop for the various cases at 100A and 50A current level respectively. Diode Reverse Recovery @ 300V-100A Ls1/2/3/4
700
Vd_Ls1_Exp Id_Ls1_Exp
600
Vd_Ls2_Exp Id_Ls2_Exp Vd_Ls3_Exp
500
Id_Ls3_Exp Vd_Ls4_Exp
400
Id_Ls4_Exp
300 200 100 0 -100 -200 -300 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Time (us)
Fig. 7 Experimental reverse recovery waveforms of variable lifetime diode for four different values of parasitic loop inductance (60nH, 73nH, 94nH, and 128nH). Diode voltage and diode current are shown. Time scale is 200ns/div. Diode Reverse Recovery @ 300V-100A Ls2
700 600
Vd_Ls2_Exp Id_Ls2_Exp
500
Vd_Ls2_Constant Lifetime 0.3us Id_Ls2_Constant Lifetime 0.3us
400 300 200 100
0 -100 -200 -300 0
0.2
0.4
0.6
0.8
1 Time (us)
1.2
1.4
1.6
1.8
2
Fig. 8 Comparison of experimental reverse recovery waveforms with finite element simulation using a constant lifetime diode with the parameters given in step 1 ( τHL = 0.3µs). The parasitic loop inductance is 73nH. Diode voltage and diode current are shown. Time scale is 200ns/div.
600V-100A Diode Forward Characteristics
110 100
100
Constant Lifetime 0.3us_300K Constant Lifetime 0.3us_400K
90
Experimental 300K
70
60
60
Id (Ampere)
70
50 40
30 20
10
10
0
0
-10
-10
0.3
0.4
0.5
Experimental 150K
0.6
0.7
0.8
0.9
1 1.1 1.2 1.3 Vd (Voltage)
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
Experimental 400K
0
2.2
Fig. 9 Comparison of experimental forward static characteristic with finite element simulation using a constant lifetime diode with the parameters given in step 1 ( τHL = 0.3µs). 600V-100A Diode Forward Characteristics
110
Experimental 300K
40
20
0.2
Variable Lifetime 0.3-1.6us_400K
50
30
0.1
Variable Lifetime 0.3-1.6us_300K
80
Experimental 400K
0
Variable Lifetime 0.3-1.6us_150K
90
Experimental 150K
80
Id (Ampere)
600V-100A Diode Forward Characteristics
110 Constant Lifetime 0.3us_150K
0.1
0.2
0.3
0.4
0.5
0.6
0.7 0.8 Vd (Voltage)
0.9
1.4
Id_Ls2_Exp 500
Constant Lifetime 1.6us_300K
Vd_Ls2_Variable Lifetime 0.3-1.6us
Constant Lifetime 1.6us_400K
Id_Ls2_Variable Lifetime 0.3-1.6us
400
Experimental 150K Experimental 300K
70
Id (Ampere)
1.3
Vd_Ls2_Exp
600
80
1.2
Diode Reverse Recovery @ 300V-100A Ls2
Constant Lifetime 1.6us_150K
90
1.1
Fig. 12 Comparison of experimental forward static characteristic with finite element simulation for the variable lifetime diode model (τ1 = 0.3µs, τ2 = 1.6µs, xd = 30µm). 700
100
1
300
Experimental 400K
60
200
50 100
40 0
30 -100
20 -200
10
-300
0
0
-10 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7 0.8 Vd (Voltage)
0.9
1
1.1
1.2
1.3
1.4
Fig. 10 Comparison of experimental forward static characteristic with finite element simulation using a constant lifetime diode with the parameters given in step 3 ( τHL = τ2 = 1.6µs).
0.2
0.4
0.6
0.8
1
Time (us)
1.2
1.4
1.6
1.8
Fig. 13 Comparison of experimental reverse recovery waveforms with finite element simulation for the variable lifetime diode model (τ1 = 0.3µs, τ2 = 1.6µs, xd = 30µm). Diode voltage and diode current are shown. Time scale is 200ns/div.
Diode Reverse Recovery @ 300V-100A Ls2 650
Vd_Ls2_Exp
150K 1.29V 1.42V 1.24V
100A 300K 1.18V 1.57V 1.08V
400K 1.15V 2.03V 1.02V
1.27V
1.15V
1.15V
Id_Ls2_Exp
550
Vd_Ls2_Constant Lifetime 1.6us 450
Id_Ls2_Constant Lifetime 1.6us
Experimental Atlas τHL = 0.3µs Atlas τHL = 1.6µs Atlas τ1 = 0.3µs τ2 = 1.6µs xd = 30µm
350 250 150 50 -50
Table II Forward drop at 100A current level.
-150 -250 -350
150K 1.18V 1.25V 1.13V
50A 300K 1.04V 1.38V 0.97V
400K 0.96V 1.77V 0.89V
1.15V
1.02V
1.00V
-450 0
0.2
0.4
0.6
0.8
1 Time (us)
1.2
1.4
1.6
1.8
2
Fig. 11 Comparison of experimental reverse recovery waveforms with finite element simulation using a constant lifetime diode with the parameters given in step 3 ( τHL = τ2 = 1.6µs). The parasitic loop inductance is 73nH. Diode voltage and diode current are shown. Time scale is 200ns/div.
2
Experimental Atlas τHL = 0.3µs Atlas τHL = 1.6µs Atlas τ1 = 0.3µs τ2 = 1.6µs xd = 30µm
Table III Forward drop at 50A current level.
VI. PHYSICS-BASED MODEL VALIDATION
several values of parasitic loop inductance Ls. Diode voltage and diode current are shown. Supply voltage is 300V and time scale is 100ns/div.
The parameter extraction procedure has been demonstrated using finite element simulations. The parameters obtained are now used in the Fourier-series-solution diode model with lifetime control proposed in [7]. The complete list of parameters used is given in Table IV. Notice that the values of the recombination parameters have been adjusted. Reverse recovery results are shown in Fig. 14 and Fig. 15 for a blocking voltage of 200V and 300V respectively. The forward characteristics at various temperatures are shown in Fig. 16. Notice the excellent agreement with the experimental results. Active area [A] 0.5 cm2 Drift region width [WB ] 120 µm Drift region doping concentration [NB] 1E14 cm-3 Anode recombination parameter [hp] 4E-14 cm4 s-1 Cathode recombination parameter [hn] 30E-14 cm4 s-1 Low lifetime [ τ1] 0.3 µs High lifetime [τ2] 1.6 µs Width of low-lifetime region [xd] 30 µm Table IV Model parameters used for variable lifetime diode.
Diode current IA (A)
80
0
LS = 93nH LS = 128nH
VAK (V), IA (A)
300 200 100 0
-100 -200
0.8
0.9
300V 700 LS = 60nH 600
LS = 73nH LS = 93nH
500
LS = 128nH
VAK (V), IA (A)
400 300 200
1.
[1]
0 -100
[2]
-200
0.6
0.7 Time (µs)
1
1.2
1.4
0.8
0.9
1
Fig. 15 Comparison of experimental reverse recovery waveforms (dashed lines) with physics-based diode model with variable lifetime (solid lines) for
CONCLUSIONS
Diode manufacturers commonly use lifetime control to improve diode characteristics. In this paper it is shown that constant lifetime diode models are unable to accurately predict both forward drop and reverse recovery characteristics. Therefore a parameter extraction procedure is proposed for diodes with lifetime control. The procedure is validated using Atlas finite element simulations and is applied to a commercially available diode with lifetime control. The parameters are used in the Fourier series solution diode model proposed in [7]. The model predictions show an excellent agreement with experimental results.
100
0.5
0.6 0.8 Diode voltage VAK (V)
Fig. 16 Comparison of experimental (dashed lines) forward static characteristic with physics-based diode model with variable lifetime (solid lines).
1
Fig. 14 Comparison of experimental reverse recovery waveforms (dashed lines) with physics-based diode model with variable lifetime (solid lines) for several values of parasitic loop inductance Ls. Diode voltage and diode current are shown. Supply voltage is 200V and time scale is 100ns/div.
-300 0.4
0.4
The parameter extraction procedure illustrated above provides a simple systematic procedure for the extraction of the model parameters for a diode with variable lifetime. It also provides a method to verify whether a certain diode has lifetime control. This is important because typically manufacturers are very reluctant to give out any processing information for diodes. The parameter extraction task is greatly simplified by the realization that the forward characteristic is mainly determined by the high lifetime region and the reverse recovery behavior is mainly determined by the low lifetime region.
LS = 73nH
400
0.7 Time (µs)
0.2
VII. DISCUSSION LS = 60nH
0.6
40
0
200V
0.5
60
20
500
-300 0.4
T = 400K T = 300K T = 150K
100
[3]
REFERENCES E. Napoli, A. G. M. Strollo, P. Spirito, “Numerical analysis of local lifetime control for high-speed low-loss P-i-N diode design,” IEEE Trans Power Electronics, Vol. 14 N.4, pp.615-621, July 1999. M.T. Rahimo and N.Y.A. Shammas. Optimisation of the reverse recovery behaviour of fast power diodes using injection efficiency and lifetime control techniques. In EPE Conf. Rec., volume 2, pages 99– 104, Trondheim, 1997. B. J. Baliga, “Comparison of gold, platinum, and electron irradiation for controlling lifetime in power rectifiers,” IEEE Trans Electron Devices, Vol. ED-24, No. 6, June 1977.
[4]
[5]
[6]
[7]
Leturcq, Berraies, Debrie, Gillet, Kallala and Massol, "Bipolar semiconductor device models for computer-aided design in power electronics," 6th European Conference on Power Electronics, vol. 2, p. 84, Sept. 1995. P.R. Palmer, E. Santi, J.L. Hudgins, X. Kang, J.C. Joyce, P.Y. Eng, "Circuit simulator models for the diode and IGBT with full temperature dependent features," IEEE Trans. Power Electronics, Vol. 18, No. 5, pp. 1220-1229, Sept. 2003 X. Kang, A. Caiafa, E. Santi, J.L. Hudgins, P.R. Palmer, "Parameter extraction for a power diode circuit simulator model including temperature dependent effects," Proc. IEEE Applied Power Electronics Conference (APEC'02), Dallas, Texas, pp. 452-458, March 2002 A.T. Bryant, P.R. Palmer, E. Santi, J.L. Hudgins, “A compact diode model for the simulation of fast power diodes including the effects of avalanche and carrier lifetime zoning,” Proc. IEEE Power Electronics Specialists Conference (PESC'05), pp. 2042-2048, Recife, Brazil, June 2005
