Approximation to density functional theory for the calculation of band gaps of semiconductors
Approximation to density functional theory for the calculation of band gaps of semiconductors
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DOI：
10.1103/physrevb.78.125116
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发表时间：
2008-09-01
影响因子：
3.7
通讯作者：
Teles, Lara K.
中科院分区：
文献类型：
--
作者：
Ferreira, Luiz G.;Marques, Marcelo;Teles, Lara K.
局域密度近似（LDA）和半占据（过渡态）在原子电离势的计算中是众所周知的成功。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实现半量子化，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（静电和交换关联）。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，我们采用了以原子为单位计算的自能，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。
The local-density approximation (LDA) together with the half occupation (transitionstate) 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 Schrodinger 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 self- interaction correction 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.