Dispersion-related description of temperature dependencies of band gaps in semiconductors -: art. no. 085201
Dispersion-related description of temperature dependencies of band gaps in semiconductors -: art. no. 085201
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DOI：
10.1103/physrevb.66.085201
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发表时间：
2002-08-15
影响因子：
3.7
通讯作者：
Pässler, R
中科院分区：
文献类型：
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作者：
Pässler, R
我们已经开发了一种新的色散相关模型的单调温度依赖性的基本带隙，E-g（T），和相关的激子吸收和发射线的位置，E-gx（T），这是适合于详细的数值分析的实验数据可用于各种各样的半导体（包括宽带隙）材料和量子阱结构。本模型与以前的模型的区别在于以下特点：（1）它适用于一个非常大的幅度跨度的声子色散系数，δ等效toroot/（h）在酒吧（ω）在酒吧，从熟悉的玻色-爱因斯坦制度的消失色散，δ大于或等于0，直到极限制度的极大色散，δ小于或等于1。(ii)由此产生的分析E（T）函数的方法，在低温区域，二次渐近线，其中的曲率是整个显着弱于Varshni的特设模型所建议的。(iii)新颖的解析表达式能够直接、直接地确定间隙宽度的T->0极限、斜率的高温极限、平均声子温度Theta=（h）/bar（omega）/bar /k（B）以及相关的色散系数Delta，而不需要预先确定其他（辅助）量。最小均方拟合的各种组IV，III-V，和II-VI材料的结果给出，并与以前的研究中使用不太精细的模型所获得的。得到的参数集表明，物理上现实的范围内的分散系数被限制在一个区间从0到最大的约3/4。另一个，定性不同，色散相关的模型，它代表了极大的色散，德尔塔>1的假设制度，也在本文中开发的只是为了一个详细的色散相关的分析Varshni的模型功能。我们的分析和数值研究的结论是，Varshni的模型是与一个假设的情况下，极大的色散的特点是色散系数显着高于单位，德尔塔（V）=（π（2）/6-1）（-1/2）=1.245。这与低于1的经验Delta值明显矛盾。实际Delta值约3/4的上界与Varshni模型Delta（V）的5/4的高值之间的相对较大的差异是使用Varshni公式对E（T）数据集进行常规拟合所产生的参数值通常不足（较大程度的任意性）的根本原因。
We have developed a novel dispersion-related model for monotonic temperature dependencies of fundamental band gaps, E-g(T), and the associated excitonic absorption and emission line positions, E-gx(T), which is suitable for detailed numerical analyses of experimental data available for a large variety of semiconductor (including wide-band-gap) materials and quantum-well structures. The present model is distinguished from preceding ones by the following features: (i) It is applicable to an unusually large span of magnitudes for the phonon dispersion coefficient, Deltaequivalent toroot/(h) over bar(omega) over bar, extending from the familiar Bose-Einstein regime of vanishing dispersion, Deltagreater than or equal to0, up to the limiting regime of extremely large dispersion, Deltaless than or equal to1. (ii) The resulting analytical E(T) functions approach, in the cryogenic region, quadratic asymptotes, the curvatures of which are throughout significantly weaker than suggested by Varshni's ad hoc model. (iii) The novel analytical expressions enable direct, straightforward determinations of the T-->0 limits of gap widths, the high-temperature limits of slopes, the average phonon temperatures, Theta=(h) over bar(omega) over bar /k(B), and the associated dispersion coefficients, Delta, without requiring preliminary determinations of other (auxiliary) quantities. Results of least-mean-square fittings for a variety of group IV, III-V, and II-VI materials are given and compared with those obtained in previous studies using less elaborate models. The parameter sets obtained suggest that the physically realistic range of dispersion coefficients is confined to an interval from 0 up to a maximum of about 3/4. Another, qualitatively different, dispersion-related model, which represents the hypothetical regime of extremely large dispersion, Delta>1, is also developed in this paper solely for the sake of a detailed dispersion-related analysis of Varshni's model function. Our analytical and numerical study concludes that Varshni's model is associated with a hypothetical case of extremely large dispersion characterized by a dispersion coefficient significantly higher than unity, Delta(V)=(pi(2)/6-1)(-1/2)=1.245. This is in clear contradiction to empirical Delta values that range below unity. The relatively large discrepancy between the upper boundary of about 3/4 for realistic Delta values and the high value of Delta(V)congruent to5/4 for Varshni's model is the fundamental reason for the usual inadequacy (large degree of arbitrariness) of parameter values resulting from conventional fittings of E(T) data sets using Varshni's formula.