Calibration of the Numerical Simulations in the Design of High Temperature IGBTs

A.R. Brown⁺, A. Asenov⁺, J.R. Barker⁺, P. Waind*, and D.E. Crees*

⁺ Department of Electronics and Electrical Engineering,
University of Glasgow, G12 8QQ, Scotland, UK

* GEC Plessey Semiconductors, Carhome Road, Lincoln, LN1 1SG, UK

ABSTRACT.

In this paper we report on the calibration of the modelling program recently developed in the Department of Electronics and Electrical Engineering at Glasgow University for the simulation of IGBTs and other power semiconductor devices. The devices used for this purpose were 600V IGBTs fabricated by GEC Plessey Semiconductors. The calibration involves the identification and proper description of the most critical parts of the device structure and selection of appropriate models for the material and transport parameters and their temperature dependence.

INTRODUCTION

After its invention in 1982 [1,2] the Insulated Gate Bipolar Transistor became one of the most commercially advanced power semiconductor devices. The combined field effect and bipolar action however makes the device operation rather complicated and the empirical approach to the device design difficult. It is widely recognised that IGBT design should rely on a competent use of numerical simulation tools not only for qualitative understanding of basic device physics, but for quantitative prediction of the device performance, sensitivity analysis and even yield prediction.

To achieve this requires a careful calibration of the device and material parameter models included in the simulation program against measured characteristics from existing devices with well known device structures. The IGBT model calibration is a difficult process. The field action of the device is related to the behaviour of a double diffused MOSFET which itself is rather complicated for simulation. The bipolar part of the device is a wide, low doped base BJT, extremely sensitive to both lifetimes and transport properties of the excess carries in the drift region. The self-heating effects and the series resistance modify the results of the device measurements. Because of all these problems most of the existing IGBT simulation works [3,4] are concerned with a qualitative study of idealised structures and do not show comparison with measured I-V characteristics.

In this paper we share our experience in the calibration of the IGBT simulation program being developed in our department [5]. The real devices were fabricated and measured by GEC Plessey Semiconductors. The calibration involves generation of large numbers of I-V characteristics and their comparison with the experimental data. To this end we use a Parsytec Supercluster Model 64 for the simulation, which is a parallel processing system with 64 processors. Up to 64 points of the IGBT characteristics may be calculated in parallel during the calibration process [6]. The effect of the lateral doping profile, the mobility models, the reduction of the lifetime as a result of irradiation, the external resistance and the temperature are highlighted in comparison with the measured IGBT characteristics.

THE SIMULATION PROGRAM

Our steady state IGBT simulator is based on the solution of the Poisson equation and current continuity equations for electrons and holes [5]. Heavy doping effects are included through bandgap and electron affinity variation in a manner similar to those used in the simulation of compound semiconductor devices. A finite difference method is adopted for discretization. Although it is well known that the global Newton procedure provides better convergence in the case of strongly coupled equations, a modified Gummel-like iterative scheme is used for non-linear iterations because it provides a simpler way towards the parallelisation of the simulation code which will be the next step of this development. Due to the lack of memory and speed the serial codes are usually restricted to the simulation of only one cell of the whole power device. In many cases, however, the electrical and thermal behaviour of the devices depend on the interaction between many individual cells and are also affected by the chip periphery. The parallelisation will allow simulation domains containing many cells to be distributed over a network of processors [6] utilising the large distributed memory and the parallel processing speed-up.

An appropriate logarithmic damping of the Newton procedure for the Poisson equation in combination with a bounded change in electron and hole concentrations ensure convergence in the whole dynamic range of applied on-state voltages up to latch-up conditions. In reverse bias mode the logarithmic damping provides convergence for the Poisson equation up to several thousand volts. A fast Incomplete LU Factorisation Biconjugate Gradient (ILUBCG) solver is employed for the solution of both Poisson and current continuity equations. The solution time of the three nonlinear equations in the Gummel cycle is significantly reduced if only a few ILUBCG steps follow each non-linear Newton-like step. In order to simulate properly the high temperature IGBT behaviour, appropriate semi-empirical expressions are included for all relevant silicon parameters. The mobility model [7] includes the carrier-carrier scattering in the drift region. The heat flow equation is coupled to the system of semiconductor equations in order to describe realistically the self heating effects.

Fig.1 Pipeline of processors, calculating in parallel an I-V characteristic

Although at present our IGBT simulator is a 'serial' code, a universal pipeline fileserver has been developed to run the program on MIMD machines like the Parsytec Model 64 transputer system (Fig.1). Using this approach multiple copies of the program can calculate, in parallel, results for separate sets of input device data. This extends dramatically the capability of the simulator for real design work such as structure optimisation, sensitivity analysis and yield prediction where several hundred simulations are often carried out for a single investigation.

CALIBRATION STEPS

The schematic cross section of a single cell of the 600V IGBT used for calibration is shown in Fig.2. Instead of the traditional p⁺ diffusion a trench etching is used to reduce the series resistance of the p-emitter region and to improve the latchup immunity of the device. The MOS part of the device is a double diffused (DD) MOSFET whose threshold voltage is determined by the doping concentration in a small part of the channel region near the maximum in the effective boron concentration. In our simulations the vertical spreading resistance doping profiles of phosphorous and boron were approximated by Gaussian distributions. These Gaussians were initially used to describe the doping distribution along the channel. The sensitivity of the threshold voltage on the maximum effective boron concentration is illustrated in Fig.3. The maximum concentration may be adjusted either by changing the parameters of the lateral phosphorous distribution which determine the n⁺p metallurgical junction position, or by changing the boron distribution. The Gaussian distribution however predicts faster decay in the boron concentration than in the actual profile. This affects the proper values of the electron mobility along the channel, which is concentration dependent. The lateral boron distribution near the channel end also affects the channel pinch-off and hence the current saturation. To avoid this discrepancy a modified distribution was used to match the boron profile.

Fig.2 Schematic cross section of a trench etched IGBT. Fig.3 The effect of the maximum effective boron concentration along the channel on the device I_D-V_G characteristics. The drain voltage is 6 V.

The normal-electric-field dependence of the surface mobility in the mobility model is treated empirically and also may need calibration. This however requires a separate test structure representing only the MOSFET part of the IGBT fabricated on a n-n⁺ substrate.

The bipolar part of the BJT is a low doped, wide-base transistor where the recombination in the base drift region in conductivity modulation mode plays a significant role. To increase the switching speed the diffusion length is normally reduced by irradiation. As a result of this the carrier lifetimes times become uncertain. The effect of the electron and hole lifetimes in the drift region is illustrated in Fig.4 where the I_D-V_D characteristics were simulated for lifetimes between 0.5 and 100us. The reduction in the lifetime leads to pronounced reduction in the current. For lifetimes equal to 1ms the calculated curve at V_G=8V matches closely the corresponding measured curve. The calculated current at V_G=12V however is approximately 20% above the experimental values.

In order to obtain better agreement, the self heating during the measurements was included through the coupling of the heat flow equation to the Poisson and current continuity equations. The effect of the self heating is illustrated in Fig.5. The corresponding potential, electron concentration and lattice temperature distributions in the device at V_G=12V are illustrated in Fig.6 (a,b,c).


Fig 4 The effect of the electron and hole lifetimes in the drift region	Fig 5 Calculated and measured I_D-V_D characteristics when the self-heating is included

(a) (b) (c)

Fig.6 (a) Potential, (b) electron concentration and (c) lattice temperature distributions at V_G=12 V, V_D=8V, T_o=300K at collector contact.

The steady state solution of the heat flow equation however overestimates the self heating effects because the device I-V characteristics were measured in pulse mode. The internal contacts and wiring resistance together with the resistance of the measuring equipment also modify the experimental characteristics.

CONCLUSIONS

In this paper we illustrated the main steps in the calibration of our numerical simulation program against the measured characteristics of a state of the art IGBT. The accuracy of the simulated results depends both on the adequate description of the MOS and bipolar parts of the device and on the appropriate choice for material parameters models.

The most critical structural parameter for the MOS part of the device is the lateral doping distribution of the impurities along the MOSFET channel. This distribution affects not only the threshold voltage, but also the mobility along the channel and the saturation conditions.

For the bipolar part of the device the mobility in the drift region in conductivity modulation mode and the carrier lifetimes were found to play a crucial role. The improvement of the device speed by irradiation introduces additional uncertainty in these parameters.

The complementary measurements on specially designed test structures may help to avoid some ambiguity in the parameter identification during the calibration process.

REFERENCES

1. Baliga, B.J., Adler, A.S., Gray, P.V., Love R.P., and Zomer, N., "The insulated gate rectifier (IGR): A new power switching device," IEDM Tech. Dig. pp. 264-267, 1982.

2. Russel, J.P., Goodman, A.M., Goodman, L.A., and Neilson, J.M., "The COMFET - A new high conductance MOS-gated device," IEEE Electron Device Lett., Vol. EDL-4, pp. 63-65, 1983.

3. Iwamuro, N., Okamoto, A., Tagami, S., and Motoyama H., "Numerical analysis of short-circuit safe operating area for p-channel and n-channel IGBTs,", IEEE Trans. Electron Dev., Vol. 38, pp. 303-309, 1991.

4. Brunner, H. Gerstenmaier, Y.C., and Mattaush, H.-J., "Impact of cell geometries and electrothermal effects on IGBT Latch-Up in 2D-Simulation," Simulation of Semiconductor Devices and Processes, vol. 5, Selberherr, S., Stippel, H., and Strasser, E. (eds.), pp. 45-48, 1993.

5. Brown, A.R., Asenov, A., Barker, J.R., Jones, S., and Waind, P. "Numerical simulation of IGBTs at elevated temperatures", Proc. of the International Workshop on Computational Electronics, Leeds University Press, pp. 50-54, 1993.

6. Reid, D., Asenov, A., Barker, J.R. and Beaumont, S.P., "Parallel simulation of semiconductor devices on MIMD machines", Proc. of the International Workshop on Computational Electronics, Leeds University Press, pp. 161-165, 1993.

7. Dorkel, J.M. and Leturcq, P., "Carrier mobilities in silicon semi-empirically related to temperature, doping and injection level" Solid State Electronics Vol.24 No.9 pp821-825 1981

This work is supported by SERC grant GR/H23085 which is a part of a LINK PEDDS scheme.


Fig.2 Schematic cross section of a trench etched IGBT.	Fig.3 The effect of the maximum effective boron concentration along the channel on the device I_D-V_G characteristics. The drain voltage is 6 V.