The dielectric function is one of the most important quantities that describes the electrical and optical properties of solids. Accurate modeling of the frequency-dependent dielectric function has great significance in the study of the long-range van der Waals (vdW) interaction for solids and adsorption. In this work, we calculate the frequency-dependent dielectric functions of semiconductors and insulators using the $GW$ method with and without exciton effects, as well as efficient semilocal density functional theory (DFT), and compare these calculations with a model frequency-dependent dielectric function. We find that for semiconductors with moderate band gaps, the model dielectric functions, $GW$ values, and DFT calculations all agree well with each other. However, for insulators with strong exciton effects, the model dielectric functions have a better agreement with accurate $GW$ values than the DFT calculations, particularly in high-frequency region. To understand this, we repeat the DFT calculations with scissors correction, by shifting DFT Kohn-Sham energy gap to match the experimental band gap. We find that scissors correction only moderately improves the DFT dielectric function in low-frequency region. Based on the dielectric functions calculated with different methods, we make a comparative study by applying these dielectric functions to calculate the vdW coefficients ( $C_3$ and $C_5$ ) for adsorption of rare-gas atoms on a variety of surfaces. We find that the vdW coefficients obtained with the nearly- free electron gas-based model dielectric function agree quite well with those obtained from the $GW$ dielectric function, in particular for adsorption on semiconductors, leading to an overall error of less than 7% for $C_3$ and 5% for $C_5$ . This demonstrates the reliability of the model dielectric function for the study of physisorption.
英文摘要：
The dielectric function is one of the most important quantities that describes the electrical and optical properties of solids. Accurate modeling of the frequency-dependent dielectric function has great significance in the study of the long-range van der Waals (vdW) interaction for solids and adsorption. In this work, we calculate the frequency-dependent dielectric functions of semiconductors and insulators using the $GW$ method with and without exciton effects, as well as efficient semilocal density functional theory (DFT), and compare these calculations with a model frequency-dependent dielectric function. We find that for semiconductors with moderate band gaps, the model dielectric functions, $GW$ values, and DFT calculations all agree well with each other. However, for insulators with strong exciton effects, the model dielectric functions have a better agreement with accurate $GW$ values than the DFT calculations, particularly in high-frequency region. To understand this, we repeat the DFT calculations with scissors correction, by shifting DFT Kohn-Sham energy gap to match the experimental band gap. We find that scissors correction only moderately improves the DFT dielectric function in low-frequency region. Based on the dielectric functions calculated with different methods, we make a comparative study by applying these dielectric functions to calculate the vdW coefficients ($C_3$ and $C_5$) for adsorption of rare-gas atoms on a variety of surfaces. We find that the vdW coefficients obtained with the nearly-free electron gas-based model dielectric function agree quite well with those obtained from the $GW$ dielectric function, in particular for adsorption on semiconductors, leading to an overall error of less than 7% for $C_3$ and 5% for $C_5$. This demonstrates the reliability of the model dielectric function for the study of physisorption.
Comments on "Giant Dielectric Response in the One-Dimensional Charge-Ordered Semiconductor (NbSe_{4})_{3}I" and "Colossal Magnetocapacitance and Colossal Magnetoresistance in HgCr_{2}S_{4}"
对“一维电荷有序半导体（NbSe_{4}）_{3}I中的巨介电响应”（D. Staresinic等人，物理修订版信函96，046402（2006））和“Colossal Magnetocapacitance and Colossal Magnetoresistance in HgCr_{2} S_{4}“（S. Weber等人，物理修订信函157202（2006））
Electronic structure and phase stability of oxide semiconductors: Performance of dielectric-dependent hybrid functional DFT, benchmarked against $GW$ band structure calculations and experiments
Finite-momentum dielectric function and excitonic effects from time-dependent density-functional theory with dielectrically screened hybrid functionals
REPLY to Comments on "Giant Dielectric Response in the One-Dimensional Charge-Ordered Semiconductor (NbSe4)3I" and "Colossal Magnetocapacitance and Colossal Magnetoresistance in HgCr2S4" (cond-mat/0607500)
Synthesis and study of alpha-Fe1.4Ga0.6O3: An advanced Ferromagnetic Semiconductor
本文报道了α-Fe_（1.4）Ga_（0.6）O_3化合物的合成及其结构相稳定性和有趣的磁性、介电和光吸收性质。在我们的工作中，Ga掺杂的α-Fe_2 O_3样品很好地稳定在α相（空间群为R3 C的菱形晶体结构）。本发明的Ga掺杂的α-Fe 2 O 3系统的组合物的性质与最近大多数研究的FeGa O 3组合物相比是显著先进的。在室温下，样品是典型的软铁磁体，同时也是直接带隙半导体。介电研究表明，样品的介电损耗较低，在较高频率下交流电导率大幅增强。在可见光范围内的光吸收增强了4%至5%。该组合物已表现出大范围的剪裁室温铁磁矩和光学带隙，通过改变晶粒尺寸和非环境（真空）热处理的机械合金化制备的样品。
Dielectric/semiconductor interfacial doping to develop solution processed high performance 1 V ambipolar oxide-transistor and its application as CMOS inverter
Accurate and efficient prediction of the band gaps and optical spectra of chalcopyrite semiconductors from a non-empirical range-separated dielectric-dependent hybrid: Comparison with many-body perturbation theory
本文用一种快速、实用的方法计算了半导体合金的带隙和能带弯曲参数。该方法是一个介电缩放近似的基础上，一个近似。它增加了一个能移的带隙所提供的局域密度近似（LDA）的密度泛函理论（DFT）。能量位移由高频介电常数的倒数加权的材料无关常数组成。该方法的显著特点是通过紧束缚线性松饼-锡轨道（TB-LMTO）的格林函数（GF）在原子球近似（ASA）下快速计算合金的介电常数。当将其应用于高度失配的半导体合金（HMA）（如Zn Te $_x$ Se $_{1-x}$）时，该方法提供了与用LDA计算的带弯曲参数不同的带弯曲参数，这是由于高频介电常数也表现出弯曲。
PRISA: a simple software for determining refractive index, extinction co-efficient, dispersion energy, band gap, and thickness of semiconductor and dielectric thin films
Implementation of an all-electron GW Approximation using the Projector Augmented Wave method: II. Application to the optical properties of semiconductors
