频率对半导体器件热击穿影响的理论模型

针对半导体器件中的热击穿,通过分析已有的理论模型,把频率对器件热区热产生和热传导的影响引入理论模型.利用格林函数求解热传输方程,同时对余误差函数进行近似处理,求解得到热区温度以及器件烧毁功率与频率和脉冲宽度的表达式.通过数值分析,求解得到不同频率下器件烧毁功率随脉冲宽度的变化规律以及不同脉冲宽度下器件烧毁功率随频率的变化规律,同时给出了频率对器件烧毁功率影响的物理解释.

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

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 t_a, t_b, and t_c. The three diffusion times t_a, t_b, and t_c 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≤t_c), the relation between failure power P_f and failure time t is P_f∝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(t_c< t< t_b), the relation between failure power P_f and failure time t is P_f t^-1/2. In this region, it is indicative of heat loss from the hot zone to its surrounding medium. In region Ⅲ(t_b≤t≤t_a), the relation between failure power P_f and failure time t is P_f∝1/ln t. In region IV(t >t_a), the failure power P_f 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.