跳跃机构与低渗杂半导体杂质电导

在渗杂度很低时,由于少数杂质电离后引起场的起伏,电子在杂质上主要处于局域状态,电声子作用使电子能够在不同杂质上跳跃,但由于电子坐标算符与电声子作用交换,在电场中电子的运动实际上是一种击穿效应,而由声子束补偿能量。针对低补偿情况,略去复杂能带结构,我们由刘维方程出发,把密度矩阵对电场,然后对电声子作用展开,得到电流表达式及密度矩阵对角元所满足的玻茲曼型方程.只取到重迭积分二次项,我们得到了Miller等的网络方程,可以简单地求出平均阻抗,在低温极限下,得到σ～e^{(-βε_{(Be-1.54(rd/a)3/2))}}N_A^1/8,βε₃=βe²/(εr_d) -1.93(βE_A)^3/4。借助网络模型,我们分析了密度矩阵各部分的贡献,特别是与通常输运过程的差别。最后利用Anderson的结果,若K<10^-2,在对电导起主要作用的链上,在Ge,Si中浓度要在10¹⁴及10¹⁶cm^-3以下才能形成局域态,我们认为,考虑了电子间库仑作用后,载流子非局域并不与目前实验矛盾。 关键词：

HOPPING PROCESS AND IMPURITY CONDUCTION IN VALENCE SEMICONDUCTORS

The impurity conduction in the low concentration limit has been analyzed in terms of hopping process. Starting from the Liouville's equation, we have derived an expression for the electrical current and a boltzmann-type equation for diagonal elements of the density matrix in the lowest order of the electron-phonon interaction. If we only take into account the lowest order of W (overlapping integral), the Miller-Abraham's network model has been obtained. By improving the method of averaging we have shown the resistance to be proportional to K^l/3 in low temperature limit, where K is the degree of compensation.Furthermore, using the network model we have analyzed the different parts of the density matrix. The behavior of the diagonal part is much different from that in the ordinary conduction process, and is connected with appearance of the activation energy.By estimating the overlapping integral and energy fluctuation, we conclude that the carriers are mainly not localized in the low compensation case (K<10^-2), if the impurity concentration is larger then a critical value (10¹⁴cm^-3 in Ge and 10¹⁶cm^-3 in Si). This does not contradict the experimental facts, if we take into account the Coulomb interaction between electrons.