Impurity Band Conduction in Germanium and Silicon
Impurity Band Conduction in Germanium and Silicon
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DOI：
10.1103/physrev.103.51
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发表时间：
1956-07
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影响因子：
--
通讯作者：
E. Conwell
中科院分区：
文献类型：
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作者：
E. Conwell
在本文中，我们试图在锗和硅的更坚实的理论基础上建立杂质能带传导的思想。 Baltensperger 对杂质产生的能带的计算适用于这些材料，用合适的氢近似代替杂质态的波函数。这些用于估计杂质带与导带的其余部分基本上合并的浓度，并且发现该估计与实验相当吻合。还对通常能带类型理论可能适用于杂质能带中的电子的浓度范围进行了估计。发现大约在这个范围内，简单能带理论对于杂质能带表现良好。顺便说一句，这凸显了即使在相对较高的温度下也必须考虑简并和近简并样品的杂质态传导的必要性。对于低于这些的浓度，描述了对传导的粗略处理，这可以解释杂质带电阻率随着杂质浓度的降低而急剧增加、这些样品中补偿的重要性，甚至电阻率的数量级。然而，它并没有预测电阻率与温度的正确关系，并且提出了其可能的起源。讨论了杂质能带中载流子的符号问题，结果表明，在杂质能带中观测到的热电势的符号反转并不一定意味着有效质量符号的变化。
In this paper, we attempt to establish the idea of impurity band conduction on a firmer theoretical basis for germanium and silicon. Calculations by Baltensperger of energy bands arising from the impurities are adapted for these materials by replacing wave functions of impurity states with suitable hydrogenic approximations. These are used to estimate the concentration for which the impurity band substantially merges with the remainder of the conduction band, and this estimate is found to agree reasonably well with experiment. An estimate is also made of the range of concentrations for which the usual band type of theory might be applicable to electrons in the impurity band. It is found that approximately within this range the simple band theory does well for the impurity band. This, incidentally, highlights the necessity of taking into account conduction in impurity states for degenerate and near-degenerate samples even at relatively high temperatures. For concentrations lower than these a crude treatment of conduction is described which can account for the sharp increase in impurity band resistivity with decreasing impurity concentration, the importance of compensation in these samples, and even the order of magnitude of the resistivity. It does not, however, predict the correct temperature dependence for the resistivity, and a possible origin for this is suggested. The question of the sign of carriers in the impurity band is discussed, and it is shown that the sign reversal of thermoelectric power observed for the impurity band need not imply a change in sign of the effective mass.