半导体材料中类氢杂质的热电离能

N. Poklonski, S. A. Vyrko, A. N. Dzeraviaha
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引用次数: 4

摘要

本文用解析和数值方法分析了n型和p型半导体中类氢给体和受体的热电离能随其浓度的变化规律。考虑了半导体在浓度绝缘体-金属相变(莫特相变)的绝缘体侧的杂质浓度和温度。假设晶体中的杂质是随机分布的(根据泊松),它们的能级是正态分布的(根据高斯)。在准经典近似中,首次证明了杂质电离能的降低主要是由于两个原因的共同表现。首先,从电中性杂质的激发态出发,为n型晶体中的c带电子(或p型晶体中的v带空穴)形成允许能值的准连续带。这减少了电子从供体到c波段(从受体到v波段的空穴)的热激活跃迁所需的能量。其次,从杂质的基态(非激发态)形成一个经典的杂质带,其宽度在低温下仅由杂质离子的浓度决定。在适度补偿半导体(当少数杂质的浓度比多数杂质的浓度小于50%)费米能级位于接近边缘的群允许能量比杂质能带的中间值,这个问题可以减少热的杂质电离能州附近的费米能级(过渡的电子供体c波段,或从一个孔受体v频带)。以前,由于杂质浓度的增加而导致热电离能下降的这两个原因是分开考虑的。根据所提出的公式计算的结果与已知的一些半导体材料(锗、硅、金刚石、砷化镓和磷化镓、碳化硅、硒化锌)的实验数据在定量上一致,补偿比适中。
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Thermal ionization energy of hydrogen-like impurities in semiconductor materials
In the work the dependence of the thermal ionization energy of hydrogen-like donors and acceptors on their concentration in n- and p-type semiconductors is analyzed analytically and numerically. The impurity concentrations and temperatures at which the semiconductors are on the insulator side of the concentration insulator – metal phase transition (Mott transition) are considered. It is assumed that impurities in the crystal are distributed randomly (according to Poisson), and their energy levels are distributed normally (according to Gauss). In the quasi-classical approximation, it is shown, for the first time, that the decrease in the ionization energy of impurities mainly occurs due to the joint manifestation of two reasons. Firstly, from the excited states of electrically neutral impurities, a quasicontinuous band of allowed energy values is formed for c-band electrons in an n-type crystal (or for v-band holes in a p-type crystal). This reduces the energy required for the thermally activated transition of electron from the donor to the c-band (for the transition of the hole from the acceptor to the v-band). Secondly, from the ground (unexcited) states of impurities a classical impurity band is formed, the width of which at low temperatures is determined only by the concentration of impurity ions. In moderately compensated semiconductors (when the ratio of the concentration of minority impurities to the concentration of majority impurities is less than 50 %) the Fermi level is located closer to the edge of the band of allowed energy values than the middle of the impurity band, that issue reduces thermal ionization energy of impurities from states in the vicinity of the Fermi level (transition of electron from a donor to the c-band, or hole from an acceptor to the v-band). Previously, these two causes of decrease in the thermal ionization energy due to increase in the concentration of impurities were considered separately. The results of calculations according to the proposed formulas are quantitatively agree with the known experimental data for a number of semiconductor materials (germanium, silicon, diamond, gallium arsenide and phosphide, silicon carbide, zinc selenide) with a moderate compensation ratio.
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