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首页> 外文期刊>Physical review >Operator ordering and interface-band mixing in the Kane-like Hamiltonian of lattice-matched semiconductor superlattices with abrupt interfaces
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Operator ordering and interface-band mixing in the Kane-like Hamiltonian of lattice-matched semiconductor superlattices with abrupt interfaces

机译：具有突变界面的晶格匹配半导体超晶格的类似Kane哈密顿量的算子排序和界面带混合

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摘要

A Kane-like envelope function Hamiltonian is derived for the Γ_(15) valence and Γ_1 conduction states of lattice-matched, semiconductor superlattice structures, with metallurgically abrupt interfaces. The local microscopic potential is treated as a weak perturbation on that of a reference crystal and is expressed in terms of a one-dimensional profile function, G(z), which modulates the difference between the potentials of the well and barrier materials. In contrast to many previous treatments, all terms up to order ?=2 in δV·(ka)~? are included, where ?V is the typical band offset, hk is the average momentum modulus of the envelope function, and a is the bulk lattice parameter. Far from the interfaces, the Hamiltonian is identical to the familiar bulk Kane Hamiltonian, with the standard bulk parameters. However, the operator ordering in the valence band is revised from the commonly used Burt scheme. An operator ordering scheme has also been derived for the linear-k P terms that couple conduction and valence states. Expressions have been derived for the S functionlike, and derivative of a S functionlike, interface terms. These are off-diagonal and diagonal, respectively, in common atom superlattices like GaAs/Al_xGa_(1-x)As, where the antisymmetric contribution to G'(z) is expected to be small. For superlattices with no common atom, additional interface terms are introduced. If the difference in the spin-orbit splitting energy for the two superlattice materials is comparable with the valence-band offset, then relativistic corrections can introduce many more, weak interface contributions. Part of the relativistic interface matrix has been derived, which includes the most significant terms. Finally, a scheme is proposed for reducing the number of independent Luttinger parameters required, when using the Hamiltonian to fit experimental spectral data.
机译：对于具有冶金学突变界面的晶格匹配的半导体超晶格结构的Γ_（15）价和Γ_1导电态，推导了一个类似Kane的包络函数哈密顿量。局部微观电势被视为参考晶体的微弱扰动，并以一维轮廓函数G（z）表示，该函数可调节阱和势垒材料的电势之差。与许多先前的处理方法相反，所有项在δV·（ka）〜？中的阶数为阶= 2。包括，其中ΔV是典型的带偏移，hk是包络函数的平均动量模量，而a是体晶格参数。哈密​​顿量远离接口，与熟悉的散装凯恩哈密顿量相同，只是具有标准的散装参数。但是，从常用的Burt方案修订了价带中的操作员订购。还为耦合导电和价态的线性k P项导出了算子排序方案。已经为S函数式派生了表达式，并为S函数式派生了接口术语。在常见的原子超晶格（如GaAs / Al_xGa_（1-x）As）中，它们分别是非对角线和对角线，其中对G'（z）的反对称贡献很小。对于没有公共原子的超晶格，将引入附加的界面项。如果两种超晶格材料的自旋轨道分裂能之差与价带偏移相当，则相对论校正会引入更多弱的界面贡献。已经推导出了相对论接口矩阵的一部分，其中包括最重要的术语。最后，提出了一种方案，当使用哈密顿量拟合实验光谱数据时，减少所需的独立Luttinger参数的数量。

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