Coupled distribute circuit-3D FEM model to simulate the transient electromagnetic performances of IGBTs

Abstract

In order to quantitatively compute the magnetic field and current distributions in an Insulated Gate Bipolar Transistor (IGBT) considering the displacement currents and 3D eddy current neighboring effect to the lead in the fast switching-on and –off transients, a coupled distribute circuit-three dimensional (3D) finite element method (FEM) is developed, and its accuracy and merits are validated by comparing the numerical and tested results on a case study.

Keywords

IGBT displacement current 3D FEM

1. Introduction

With the rapid advancement of power electronics, the switching frequency of a power electronic value, such as an IGBT, increases tremendously [1,2]. In this regard, the stray parameters of the circuits become more and more essential in deciding the system reliability and transient performance since they may cause not only surges and oscillations on voltages and currents; but also the increasing in the switching losses, even the damage to the module [3,4]. For example, the displacement currents in an IGBT model under extremely high switching frequencies will result in a significant different performance as compared to that obtained using existing analysis approaches [5,6]. Therefore, it is essential to develop accurate IGBT models.

Existing IGBT models can be broadly classified into five categories: numerical models, mathematical models, behavioral models, semi-mathematical models, and semi-numerical models. Numerical models and semi-numerical models are based on finite element methods and analytical models. A typical such model is the Hefner model, which is based on semiconductor physics equations. The numerical results of these types of models are very accurate but they will take a considerable computational time and processing power [7]. Behavioral models are designed to simulate IGBT behaviors without considering the actual physical mechanisms. However, although very efficient, the accuracy of the results is very low for this kind of models [8]. Semi-mathematical models are a combination of existing models for components in equivalent circuit and physics based equations. Although these models are not accurate as mathematical models, the computational efficiency is relatively high. However, the nonlinearity is not taken into account when considering the capacitance between the electrodes and the base region modulation resistor in the existed IGBT semi-mathematical models [9]. Moreover, in existing numerical models, the displacement current and the neighboring effect of the eddy currents in conducting materials are not approximately modeled. In this regard, a coupled distribute circuit-3D FEM model for the transient performance simulation of an IGBT is proposed. In the distribute circuit model, a modified semi-mathematical model based on N-channel IGBT models by considering the inter electrode capacitance as a current-controlled nonlinear capacitance and the modulated resistance of the base region as a current-controlled nonlinear resistance is introduced.

Fig. 1.

The distribution of the parasitic capacitances.

2. High order distribute circuit model of an IGBT module

There are obvious boundaries between the different regions because of the different semiconductor types or doping concentrations in various regions, and the parasitic capacitances will be produced between the adjacent areas. With the switching frequency increasing, the parasitic capacitance and the inductances of the gate and the emitter will cause greater impact on the performance of the device. To consider the base-width modulation effects (early effects), and the inter-pole capacitances and inductances, a modified IGBT model by introducing parasitic capacitances C _ge, C _gc, C _ce, a channel modulation resistor R _b, and the inductances of the gate and the emitter L _g, L _e are proposed, as shown in Figs 1 and 2.

Fig. 2.

The proposed improved IGBT model.

Fig. 3.

A bus bar (a), and its distribute circuit model (b).

The inter-pole capacitance has the greatest influence on the switching characteristics of an IGBT. Moreover, the inter-pole capacitances C _ge, C _gc, C _ce are given by: $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle C_{ge}=C_{gs}\end{eqnarray}$ (1) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle C_{cej}=(A-A_{gd})\sqrt{(qN_{c}{\varepsilon}_{si})/(2(V_{D}+V_{ds}))}\end{eqnarray}$ (2) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle C_{gc}=C_{gd0}∼(V_{ds}\leq V_{gs})\quad \text{or}∼(C_{gd0}C_{gdj})/(C_{gd0}+C_{gdj})?(V_{ds}>V_{gs})\end{eqnarray}$ (3) where, $\begin{eqnarray}\displaystyle C_{gd0}=C_{oxs}, & & \displaystyle\end{eqnarray}$ (4) A is the device active area, A _gd is the gate-drain overlap area, N _c is the collector-base space charge concentration, q is the electronic charge, V _ds is the intrinsic drain-source voltage, V _D is the p-n potential, ϵ_si is the permittivity of the silicon.

Fig. 4.

3D solid and finite element model: (a) solid model, (b) side view, of an IGBT.

The channel modulation resistor R _b is a parameter in suppressing the tail current. R _b is determined from: $\begin{eqnarray}\displaystyle R_{b}=W^{2}/(({\mu}_{n}+{\mu}_{p})Q_{B}+{\mu}_{n}Q_{0}) & & \displaystyle\end{eqnarray}$ (5) where Q ₀ is the background charge, W is the quasi-neutral base width, Q _B is the total excess carrier base charge, 𝜇_n, 𝜇_p are, respectively, the electron and the hole mobility.

To consider the effect of the stray parameters in extremely high fast switching conditions, a high order distribute circuit model including stray capacitances and inductances is derived. The stay capacitance/inductance includes both self and mutual ones. Moreover, to simulate the discrete characteristics of a segment, it is modelled using a multi-sectional circuit rather than one segment one. For example, the bus bar of a typical IGBT circuit [Fig. 3(a)] is modelled using a multi-sectional circuit [Fig. 3(b)]. It should be pointed out that the mutual capacitances and inductances for this case study are extremely smaller than those of the self ones. Consequently, the mutual stray capacitances and inductances are neglected. Once the distribute circuits of each segment are determined, it is readily to derive a high order distribute circuit model of the whole IGBT module. To determine the stray parameters of each segment, the Partial Element Equivalent Circuit (PEEC) method is used based on the solutions of Maxwell equations of all practical sized bars.

Fig. 5.

The computed current and the tested results of the total current: (a) The computed current and the tested results of the total current; (b) The computed results of the displacement current and the conduction current in IGBT; (c) The frequency domain results of the computed current and the tested results of the total current.

Fig. 6.

The distribution of currents in the channel: (a) The transient current distribution in the channels; (b) The transient currents of the channels 1, 2, 7.

3. 3D transient finite element model of an IGBT

3.1. 3D transient finite element model of an IGBT

In an IGBT, if the gate is applied a forward voltage greater than the threshold one, the surface of the P-well is inversely formed, a current path is then formed between the source and the drain. The electrons flow from the N ⁺ source region to the drain through the channel, and flow into the N ⁻ epitaxial region vertically. Since the inflow of the electrons reduces the potential of the N ⁻ region, the process of injecting holes into the N epitaxial region by the P ⁺ substrate is accelerated, the device is turned on soon. Most of the injected holes are combined with the electrons flowing through the channel to form a continuous channel current in the IGBT [10], forming thousands of current channels. In this regard, the skin effect of the eddy currents in the channels is not significant and should be neglected. Moreover, to compromise the numerical accuracy and computational speed, the channels are simplified to a 4 × 4 channel model, and the 3D finite element model is finalized in Fig. 4. As explained previously, to include the displacement current in the transient field simulation, a displacement current channel is geometrically designed in the 3D solid model.

3.2. An indirect iterative procedure in solving the proposed IGBT model

The proposed high order distribute circuit and 3D transient finite element models are inter-coupled together: the parameters, especially those of the lead and the IBGT body, of the circuit model are dependent on the 3D finite element solutions while the exciting current including the displacement one of the 3D finite element analysis are determined from solutions of the circuit model. To solve this issue, an indirect iterative procedure is introduced and explained as:

Step 1: Predict the circuit parameters of the high order distribute circuit model, and then compute the exciting currents including the displacement one of the coupled FEM based field-circuit model for the next time step using the high order distribute circuit model;

Step 2: Solve the FEM based field-circuit model at the new time step using the existing conditions of Step 1;

Step 3: Re-compute the parameters of the high order distribute circuit model from the solutions of the FEM based field-circuit model of Step 2;

Step 4: Compare the differences between the computed parameters in Step 1 and Step 3. If the error is under a tolerance, go to step 5; otherwise, correct the circuit parameters and go to Step 1;

Step 5: If the time exceeds the given one, stop; otherwise, go to Step 1 for the next time instant computation.

4. Application and validation

To validate the proposed model and method, a prototype IGBT system is constructed, and its transient performances in the switching –on and -off states are simulated and tested. Figure 5 gives the comparison of the computed and the tested currents of the IGBT.

As shown in Fig. 5, the numerical results of the total current are basically the same with the experimental results. And the displacement current takes a large part of the total current on the fast turning-on and turning-off transients of the IGBT. Therefore, Fig. 5 proved the accuracy of the IGBT module and the conclusion that the displacement currents in the IGBT model under extremely high switching frequencies could not be neglected.

Figure 6 presents the distribution of the currents in different channels, showing the non-uniform current distribution due to the neighbouring effect of the eddy currents to the lead.

Figure 7 presents the variation of the magnetic fields with times for an observing point in the inner IGBT considering and without considering the displacement currents.

From these numerical results, it is obvious that the computed results using the proposed method considering the stray parameters show good agreement with the tested ones as compared to those using the same model without considering the stray parameters, other things being equal; validating the accuracy and the merits of the proposed model and method.

5. Conclusion

With the rapid advancement of power electronics, the switching frequency of a power electronic valve increases tremendously. In this regard, the stray parameters of the circuits become more and more important. Developing a high-frequency model of IGBT is thus essential.

Fig. 7.

The magnetic field strength with time considering the stray parameters.

In this paper, a coupled high order distributed circuit and 3D FEM model and method is proposed. In the high order distributed circuit model, a modified semi-mathematical IGBT model based on the N-channel IGBT considering the stray parameters and other physical characteristics is introduced; and in the 3D FEM model, both the displacement current and the neighbouring effect of eddy currents to the lead are considered. The numerical and tested results on a case study validated the high accuracy of the proposed model and method as compared to existing semi-mathematical models of an IGBT. Moreover, the results have proved that the displacement current could not be neglected in the switching –on and -off states of an IGBT.

It should be pointed out that the order of the proposed high order distribute circuit model would be extremely high for a complex IGBT module. In such cases, an order reduction technique will be required to make the model to be computational feasible. Moreover, the authors are striving to extend the proposed model to multi-module IGBT system simulations.

Footnotes

Acknowledgement

This work was supported by the National Natural Science Foundation of China (NSFC) under Grants No. 51490682 and by the Science and Technology Department of Zhejiang Province under Grant No. 2016C31037

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