heoretical model of influence of frequency on thermal breakdown in semiconductor device

Abstract

In order to analyze the influence of frequency on thermal breakdown in semiconductor device, the influences of frequency on heat generation and heat conduction in the hot zone are introduced into the theoretical model. The heat transfer equation is solved by the Green's function method, and the error function is approximated. Then, the expressions of temperature in the hot zone and failure power of semiconductor device including frequency and pulse width are derived. The change rules of failure power with the increasing of pulse width under different frequencies and with the increasing of frequency under different pulse widths are obtained. The result shows that the expression for center temperature in hot zone caused by the failure power is divided into four time regions, i.e., regions I-IV, by three thermal diffusion times ta, tb, and tc. The three diffusion times ta, tb, and tc are related to the side lengths a, b and c(c≤b≤a) of the hot zone represented by a rectangular parallelepiped, respectively. In region I(0≤t≤tc), the relation between failure power Pf and failure time t is Pf∝t-1. In this region, the failure time is short and little heat is lost from the surface of hot zone so that the adiabatic term(t-1) dominates. In region Ⅱ(tcttb), the relation between failure power Pf and failure time t is Pf t-1/2. In this region, it is indicative of heat loss from the hot zone to its surrounding medium. In region Ⅲ(tb≤t≤ta), the relation between failure power Pf and failure time t is Pf∝1/ln t. In region IV(t >ta), the failure power Pf is constant. In this region, the failure time is very large and thermal equilibrium can be established so that the steady state term dominates. The relation between failure power and frequency is divided into two parts. In part one, the failure power increases with the increasing of frequency; in part two, the failure power is nearly constant with the increasing of frequency. Meanwhile, the physical interpretation of the influence of frequency on failure power is given. From region I to region IV, each heat transfer rate increases with pulse width. The lower the frequency, the more the injection energy during region I or region Ⅱ is, when the total injection energy is constant. The heat transfer rate is slower in region I or region Ⅱ, so the energy converted into heat will be more and the temperature in the hot zone will be higher, thus the device is burned out easily.