Switching Parameters for Power Semiconductor Devices

Switching parameters characterizing power semiconductor devices changeover from the conducting to a nonconducting state (turn-off) by a reverse voltage pulse are considered. The mathematical model describing the dependence of these parameters on forward current strength and its rate of fall before its turn off is proposed. The algorithms of this dependence recovery on the experimental data basis are designed.

Introduction

The switching parameters are related to the most important characteristics of  power semiconductor devices (PSD), since their dynamic properties, output capacity of devices, their efficiency, and conditions of their cooling depend upon them to a considerable degree. In the present study, the switching parameters that describe PSD changeover from the conducting state to a  nonconducting state (PSD turn-off) under the action of  the reverse voltage impulse are also reviewed.

As is well known ^[1-3], power semiconductor devices (diodes, thyristors) change to off-state for a finite time t_rr, necessary for the removal of the surplus charge Q_rr, that is stored during their activity in a conducting state. Thus the transient process associated with PSD turn-off consists of two main stages (Figure 1): the stage of a back current rise and the stage of a back current fall, as a result of a back resistance recovery.

At the first stage, the semiconductor structure of the PSD practically does not block voltage, as there is a large enough number of excess carriers in its layers. Therefore, under the action of a reverse voltage impulse, back current starts to flow through the PSD, which linearly rises to its maximum value I_rr with a rate di/dt  that is determined by the voltage applied as well as the parameters of an external electric circuit:

$$\begin{equation} i (t) =-\frac{di}{dt} t \end{equation}$$

The duration of this stage equals to t_s (Figure 1). Thus,

$$\begin{equation} I_{\gamma \gamma} =\frac{di}{dt} t_s \end{equation}$$

The back current flow through the structure promotes excess carrier density attenuation due to recombination processes and  their removal by the external electric field. At the instant of time t_s the stored charge is decreased to such an extent that it starts to limit back current. Thus, the device resistance increases sharply, and it takes upon itself the external voltage. From this point on, together with the excess carriers density attenuation, the back current flowing through the thyristor falls from its maximum rate I_rr practically up to zero point ^[2]:

Figure 1. Back current flowing through PSC at changeover from conducting to nonconducting state

$$\begin{equation} i (t) \approx -I_{\gamma \gamma} \hspace{7 px} exp \hspace{7 px} \Big (-\frac{t-t_s}{0.53t-f} \Big ) \end{equation}$$

where t_f - the time, which is used to take as the duration of a back resistance recovery stage (Figure 1).

The whole transient duration of PSD turn-off is given by

$$\begin{equation} t_{\gamma \gamma} \approx t_s + t_f \end{equation}$$

Thus, the surplus charge, which is stored  there at the time of PSD activity in a conducting state (Figure 1) is

$$\begin{equation} Q_{\gamma \gamma} \approx Q' _{\gamma \gamma} + Q" _{\gamma \gamma} = \frac{1}{2} I_ {\gamma \gamma} t _{\gamma \gamma} = \frac{1}{2} \frac{di}{dt} t_s (t_s + t_f) \end{equation}$$

In the present study, a mathematical model is offered that describes the switching parameters t_s, t_f, t_rr, I_rr and Q_rr dependence on the forward current strength and the rate of its fall before device turn-off . The algorithms of this dependence recovery on the experimental data basis are designed.

Mathematical model describing  the dependence of switching parameters of a PSD on the forward current strength and the rate of its fall before the turn-off

At present, to describe the switching parameters' dependence on the forward current strength I and the rate of its fall di/dt, power approximations of the following kind ^{[2, 4]} are used:  

$$\begin{equation} y (I) = \sum\limits_{m} a_m I^m \end{equation}$$

$$\begin{equation} y \frac{di}{dt} = \sum\limits_{n} b_n {\Big (\frac{di}{dt} \Big )} ^n \end{equation}$$

where y  is one of the switching parameters (I_rr, Q_rr, t_rr, t_s or t_f). Thus factors a_m and b_n and the exponents m and n are considered as constants (m, n = 1, 2, 3, …) and are selected from the best possible fit of curves (6) and (7) with the experimental data.

Thus, the expression (6) describes PSD switching parameters’ dependence on the forward current strength I  at only one predetermined  rate di/dt of its fall value, and the expression (7) sets these parameters’ dependence on the rate di/dt at only one value I of the forward current strength. In case these values are changed a new selection procedure is required, at least for factors a_m and b_n.  For that it is necessary to make use of new experimental data.

The main disadvantage of power approximations (6) and (7) lies here. Besides, these expressions do not keep in mind the PSD switching parameters dependence on the semiconductor structure temperature T_j which is explained by the pronounced dependence of the minority carriers lifetime t_p in the n-base of a PSD [1]: t_p ~ T_j ^3/2.

This study has shown that for the wide range of devices, the back current rise time t_s and the time of its fall t_f are determined by the formulas:

$$\begin{equation} t_s (I, di/dt, T_j) = t_{s0} {\Big (\frac{I}{I_0} {\Big)}^\alpha \Bigg (\frac{{(di/dt)}_0}{di/dt} \Bigg )}^{(\beta I)^{-0.25}} {\Bigg (\frac{T_j}{T_{j0}} \Bigg )} ^{3/2}\end{equation}$$

$$\begin{equation} t_f (I, di/dt, T_j) = t_{f0} {\Big (\frac{I}{I_0} {\Big)}^\gamma \Bigg (\frac{{(di/dt)}_0}{di/dt} \Bigg )}^{(\delta I)^{-0.2}} {\Bigg (\frac{T_j}{T_{j0}} \Bigg )} ^{3/2}\end{equation}$$

where α, β, γ and δ are empiric parameters of the model, which depend only on the design features of PSD, and t_s0 and t_f0 -  the back current rise time and the fall time accordingly, measured at the temperature of T_j0 of the semiconductor structure, at the value I₀ of a classification current, which falls with the rate (di/dt)₀ at PSDchangeover from the conducting to a nonconducting state.

Functions (8) and (9) are natural generalizations of expressions (6) and (7) and describe satisfactorily the obtained experimental data (Figure 2 - 4). Thus, taking into account equations (1) - (5), one should come to the conclusion that formulas (8) and (9)  determine completely all switching parameters which characterize  transients of the PSD changeover from the conducting state to a nonconducting state.

Experimental measuring of switching parameters of PSD and  their dependence recovery on the forward current strength and the rate of its fall before the PSD turn-off

The expressions (8) and (9) together with equations (1) - (5) allow us to recover all switching parameters dependences on the forward current strength and the rate of its fall by means of a small number of experimental data points. And, in contrast to (6) and (7), these dependences are true at any values of the current strength I and the rate of its fall di/dt.

Indeed, let us assume that we managed to measure the back current rise time t_s1(I₁) and the time of its fall t_f1(I₁) at the temperature of semiconductor structure T_j1, at the forward current strength I₁ and the rate of its fall (di₁/dt)_1. Let us assume that measured values t_s2(I₁) and t_f2(I₁) correspond to temperature T_j1  at the forward current strength I₁ and the rate of its fall (di₁/dt)_2, values t_s1(I₂) and t_f1(I₂) to temperature T_j2 at the forward current strength  I₂ and the rate of its fall (di₂/dt)_1, and t_s2(I₂) and t_f2(I₂) to temperature T_j2 at current strength I₂ and the rate of its fall (di₂/dt)₂. Then, as it is evident from (8) and (9),

$$\begin{equation} t_s (I, di/dt, T_j) = t_{s1} (I_1) {\Big (\frac{I}{I_1} {\Big)}^\alpha \Bigg (\frac{{(di/dt)}_1}{di/dt} \Bigg )}^{(\beta I)^{-0.25}} {\Bigg (\frac{T_j}{T_{j1}} \Bigg )} ^{3/2}\end{equation}$$

$$\begin{equation} t_f (I, di/dt, T_j) = t_{f1} (I_1){\Big (\frac{I}{I_1} {\Big)}^\gamma \Bigg (\frac{{(di/dt)}_1}{di/dt} \Bigg )}^{(\delta I)^{-0.2}} {\Bigg (\frac{T_j}{T_{j1}} \Bigg )} ^{3/2}\end{equation}$$

Figure 2. Switching parameters t_s, t_f, t_rr and Q_rr of a thyristor МТ3-500 and their dependence  on the forward current rate di/dt of fall: 1 - I = 500 А, 2 - I = 1000 А, 3 - I = 1500 А. Continuous curves - calculations with the help of empirical formulas (8) and (9),  markers - experimental data at the temperature of T_j = 298 К.

where constants α, β, γ and δ are determined using the following expressions:

$$\begin{equation} \alpha = ln \Bigg (\frac{t_{s1}(I_1)}{t_{s1}(I_2)} \bigg [\frac{{(di_1/dt)}_1}{{(di_2/dt)}_1} \bigg ] ^{(\beta I_2)^{-0.25}} \bigg ({\frac{T_{j2}}{T_{j1}} \bigg ) ^{3/2}} \Bigg ) \Bigg / ln \bigg (\frac {I_1}{I_2} \bigg) \end{equation}$$

$$\begin{equation} \beta = \frac{1}{I_1} \Bigg [ln \bigg (\frac{{(di_1/dt)}_1}{{(di_1/dt)}_2} \bigg ) \bigg / ln \Bigg (\frac{t_{s2} (I_1)}{t_{s1}(I_1)} \Bigg ) \Bigg ]^4 \end{equation}$$

$$\begin{equation} \gamma = ln \Bigg (\frac{t_{f1}(I_1)}{t_{f1}(I_2)} \Bigg [\frac{{(di_1/dt)}_1}{{(di_1/dt)}_1} \Bigg ]^{(\delta I_2)^{-0.2}} \Bigg (\frac{T_{j2}}{T_{j1}} \Bigg )^{3/2} \Bigg ) \Bigg / ln \bigg (\frac {I_1}{I_2} \bigg ) \end{equation}$$

$$\begin{equation} \delta = \frac{1}{I_1} \Bigg [ ln \Bigg (\frac{{(di_1/dt)}_1}{{(di_2/dt)}_2} \Bigg ) \Bigg / ln \Bigg ( \frac{t_{f2}(I_1)}{t_{f1} (I_1)} \Bigg ) \Bigg ]^5 \end{equation}$$

Figure 3. Switching parameters of a Thyristor

The expression (4) allows us to determine the transient duration t_rr(I,di/dt,T_j) of the PSD turn-off. The back current maximum rate I_rr(I,di/dt,T_j) and the surplus charge Q_rr(I,di/dt,T_j) that stored there at the time of PSD activity in a conducting state may be calculated  by formulas (2) and (5)

Thus, by results of six measurements all switching parameters' dependences that describe the PSD changeover from the conducting state to a nonconducting state, on the current I and the rate of its fall di/dt may be recovered.

4. Conclusion

The results obtained in the present study show that at the preset rate of the reverse current rise, the durations  t_s and t_f of the main stages of  the PSD turn-off determine completely all other switching parameters which characterize a PSD changeover from the conducting to the nonconducting state. The suggested mathematical model (8) - (9) that describes dependence of  t_s and t_f from the forward current strength and the rate of its fall before the turn-off, made it possible to recover similar dependences for any other switching parameters of a PSD on the grounds of the experimental data.

Figure 4. Switching parameters of a Diode

The above mentioned dependences are true at any values of the forward current strength and the rate of its fall before the turn-off and are in satisfactory agreement with the experiment (Figures 2 - 4).

List of literature

1. Yu. Evseev, P. Dermenzhi. Power semiconductor devices. – М.: Energoizdat, 1981.

2. M. Abramovich, V. Babailov, V. Liber and others.  Diods and thyristors in converter installations. – М.: Energoatonizdat, 1992.

3. A. Rabinerson, G. Ashkinazi. Load conditions of power semiconductor devices. – М.: Energia, 1976.

4. Westcode. Positive development in power electronics, – Westcode Semiconductors Ltd. Provisional Data Sheet. 2000

 

For more information, please read:

Modeling of Power Semiconductor Devices

Approaches to Mounting Power Semiconductor Devices

Device Failure due to Electrical and Thermal Conditions