PARAMETERS ESTIMATION OF THERMAL Part MODEL OF SEMICONDUCTOR DEVICES

This paper deals with the problem of the estimation of the thermal model parameters of semiconductor devices. A new computer tool - MASTER2 for estimation of these parameters is presented. MASTER2 controlls the method of measuring the transient thermal impedance Z(t) as well as it estimates both the values of Z(t) parameters: R-th, a(i), tau(thi) (i = 1, 2, 3,...,N) and the values of RC elements existing in the electrical analogues of a device thermal model of the form of Cauer or Foster network. The procedure of estimation of the parameters of the device thermal model is automatically realised on the authors' special algorithm implemented in MASTER2. In this algorithm, in the first place the values of the parameters: coefficients a(i), thermal time constant tau(thi) and the thermal resistance R-th are calculated using the measured Z(t) dependence. Next, the values of RC elements in the Foster and Cauer networks are computed. The considered algorithm is valid in the case when the values of the successive thermal time constants differ from each other at least a few times. Therefore, the dependence Z(t) normalized to R-th is a intervally linear function in the lin-log scale. The value of R-th results directly from Z(t) at the steady-state. Values of the remaining parameters are calculated by the last-square method used for approximation of any special function with Z(t)as an argument. At first the longest thermal time constant and the coefficient a[corresponding to them are calculated. The values of RC elements of the Foster network are calculated after analytical dependences containing the considered parameters. In turn, to calculate the values of the Cauer network, the operational thermal impedance Z(s) has to be formulated. Next, division of the values of coefficients corresponding to the highest degree of polynominals representing the numerator and the denominator of Z(s) respectively, have to be performed. The value of such division at the k-th iteration is denoted as D-k. In each iteration step, the product of the denominator value and the value of Dk is subtracted from the numerator and then the new numerator and the denominator are transformed to each other. The presented computer tool was verified experimentally by comparing the measured and calculated dependence of Z(t) of the VDMOS transistor IRF840. The very well agreement between measurements and simulations have been obtained.