硅锥场发射阴极电热状态的数值模拟

Simulation of Electric and Thermal States of Silicon Field Emitters

用有限差分法求解相互耦合的电流连续方程和导热方程 ,对硅锥阴极的电热状态进行了数值模拟。模拟中采用了与温度、电场相关电导率模型以及和温度相关的热导率模型。模拟的结果表明 ,锥体顶端的电位变化比较突出 ,在较小的电流下其内部电场即可以达到临界场强 ,使载流子漂移速度开始饱和 ,并表现出饱和的发射特性。在尖锥顶端内部电场达到临界场强直至发生碰撞电离时 。

The electric and thermal states of cone shaped silicon field emitters were simulated.In our simulation,both the coupled current continuity equations and the heat conduction equations were numerically solved in terms of temperature dependent and electric field dependent electric conductivity as well as temperature dependent thermal conductivity of silicon.The results show that the potential at the tip apex varies markedly with the emission current.For moderate emission current,the internal field can be very high,approaching the critical field;saturation of carrier drifting speed and saturated I U characteristics can be expected.Temperature rise at the tip apex can be negligible when the internal field at the tip apex reaches its critical value,which may result in collision ionization.