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首页> 外文期刊>Physica status solidi, B. Basic research >Exponential series representation for heat capacities of semiconductors and wide-bandgap materials
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Exponential series representation for heat capacities of semiconductors and wide-bandgap materials

机译：半导体和宽带隙材料的热容的指数级数表示

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The Thirring series expansion is used as the starting point for the design of a structurally novel, dispersion-related analytical model for descriptions of the temperature dependence, of harmonic parts of isochoric hear capacities, C-Vh(T). The notorious problem of slow convergence of this conventional series expansion is satisfactorily resolved here by its transformation into an associated exponential series representation, which shows up markedly better convergence properties than the original Thirring expansion. Combining this unprecedented analytical C-Vh(T) model in a physically adequate way with the recently introduced power series expansion for contributions of lattice expansion and anharmonicity effects to the observable isobaric heat capacities, we get a novel effective tool for numerical simulations and analyses of corresponding C-p(T) data sets, which is suitable for applications to the practically important regions of intermediate to high temperatures. This model is usable, among other things, as a physically consistent substitution for various types of ad hoc chosen polynomials that are hitherto still frequently used, especially in the field of thermochemistry. In order to illustrate the considerable usefulness of the novel analytical tool, especially for the technologically important class of wide-bandgap materials, we perform simultaneous least-mean-square fittings of combined sets of available high- and low-temperature C-p(T) data for diamond, SiC-3C, the III-nitrides BN, AlN, and GaN, and the zinc chalcogenides ZnO, ZnS, and ZnSe. For a comparison with results obtained recently for Si and Ge on the basis of a three-oscillator model, we have re marnined the respective C,(T) data sets. As interesting by products of present fittings we evaluate several even-order moments of the respective phonon density of states spectral functions. The discussion of numerical results reveals, among other things, the basic physical cause of the obvious inapropriateness of the conventional Debye model with respect to the majority of the materials under study,
机译：Thirring级数展开被用作设计新颖的，与色散相关的分析模型的起点，该模型描述了等速听音能力的谐波部分C-Vh（T）的温度依赖性。通过将其转换为关联的指数级序列表示法，可以令人满意地解决此常规级数展开式缓慢收敛的臭名昭著的问题，与原始的Thirring展开式相比，它表现出明显更好的收敛性。将这种空前的解析C-Vh（T）模型以物理上合适的方式与最近引入的幂级数展开相结合，以实现晶格展开和非谐效应对可观测的等压热容的贡献，我们得到了一种新颖的有效工具，可用于数值模拟和分析相应的Cp（T）数据集，适用于中高温的实际重要区域。该模型尤其可以用作物理上一致的替代，以替代迄今仍经常使用的各种类型的即席选择的多项式，特别是在热化学领域。为了说明新型分析工具的巨大用处，特别是对于宽带隙材料的技术重要性类别，我们对可用的高温和低温Cp（T）数据的组合集进行了同时最小二乘拟合。用于金刚石，SiC-3C，III族氮化物BN，AlN和GaN，以及硫属锌化物ZnO，ZnS和ZnSe。为了与最近基于三振荡器模型获得的Si和Ge的结果进行比较，我们重新介绍了各自的C，（T）数据集。作为当前配件产品的有趣结果，我们评估了状态谱函数各个声子密度的几个偶数阶矩。数值结果的讨论揭示了，除其他外，基本的物理原因是传统Debye模型相对于大多数研究材料而言明显不适当，

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