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arXiv 0808.0729cond-mat.mtrl-sci
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精确计算半导体带隙的密度泛函理论近似

An approximation to density functional theory for an accurate calculation of band-gaps of semiconductors

Luiz G. Ferreira, Marcelo Marques, Lara K. Teles

摘要:

局域密度近似(LDA)和半占据(过渡态)方法在计算原子电离势方面是非常成功的。当涉及到扩展系统时,例如半导体无限系统,很难找到一种方法来半量子化,因为空穴往往会无限扩展(布洛赫波)。这个问题的答案在于LDA形式主义本身。证明了半占据等效于在薛定谔方程中引入空穴自能(静电能和交换关联能)。这样,论证就变得简单了:本征值减去自能必须最小化,因为原子具有最小能量。然后我们简单地证明了空穴是局域的,而不是无限延伸的,因为它必须具有最大的自能。在计算带隙和有效质量时,我们采用了原子的自能计算,得到了与GW近似的计算精度,但其优点是计算量不超过标准LDA。

英文摘要:

The local-density approximation (LDA), together with the half-occupation (transition state) is notoriously successful in the calculation of atomic ionization potentials. When it comes to extended systems, such as a semiconductor infinite system, it has been very difficult to find a way to half-ionize because the hole tends to be infinitely extended (a Bloch wave). The answer to this problem lies in the LDA formalism itself. One proves that the half-occupation is equivalent to introducing the hole self-energy (electrostatic and exchange-correlation) into the Schroedinger equation. The argument then becomes simple: the eigenvalue minus the self-energy has to be minimized because the atom has a minimal energy. Then one simply proves that the hole is localized, not infinitely extended, because it must have maximal self-energy. Then one also arrives at an equation similar to the SIC equation, but corrected for the removal of just 1/2 electron. Applied to the calculation of band gaps and effective masses, we use the self-energy calculated in atoms and attain a precision similar to that of GW, but with the great advantage that it requires no more computational effort than standard LDA.

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