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.
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 trr, necessary for the removal of the surplus charge Qrr, 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 Irr with a rate di/dt that is determined by the voltage applied as well as the parameters of an external electric circuit:
The duration of this stage equals to ts (Figure 1). Thus,
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 ts 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 Irr practically up to zero point :
Figure 1. Back current flowing through PSC at changeover from conducting to nonconducting state
where tf - 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
Thus, the surplus charge, which is stored there at the time of PSD activity in a conducting state (Figure 1) is
In the present study, a mathematical model is offered that describes the switching parameters ts, tf, trr, Irr and Qrr 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:
where y is one of the switching parameters (Irr, Qrr, trr, ts or tf). Thus factors am and bn 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 am and bn. 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 Tj which is explained by the pronounced dependence of the minority carriers lifetime tp in the n-base of a PSD : tp ~ Tj 3/2.
This study has shown that for the wide range of devices, the back current rise time ts and the time of its fall tf are determined by the formulas:
where α, β, γ and δ are empiric parameters of the model, which depend only on the design features of PSD, and ts0 and tf0 - the back current rise time and the fall time accordingly, measured at the temperature of Tj0 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 ts1(I1) and the time of its fall tf1(I1) at the temperature of semiconductor structure Tj1, at the forward current strength I1 and the rate of its fall (di1/dt)1. Let us assume that measured values ts2(I1) and tf2(I1) correspond to temperature Tj1 at the forward current strength I1 and the rate of its fall (di1/dt)2, values ts1(I2) and tf1(I2) to temperature Tj2 at the forward current strength I2 and the rate of its fall (di2/dt)1, and ts2(I2) and tf2(I2) to temperature Tj2 at current strength I2 and the rate of its fall (di2/dt)2. Then, as it is evident from (8) and (9),
Figure 2. Switching parameters ts, tf, trr and Qrr 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 Tj = 298 К.
where constants α, β, γ and δ are determined using the following expressions:
Figure 3. Switching parameters of a Thyristor
The expression (4) allows us to determine the transient duration trr(I,di/dt,Tj) of the PSD turn-off. The back current maximum rate Irr(I,di/dt,Tj) and the surplus charge Qrr(I,di/dt,Tj) 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.
The results obtained in the present study show that at the preset rate of the reverse current rise, the durations ts and tf 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 ts and tf 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
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