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 雷达学报  2018, Vol. 7 Issue (1): 67-74  DOI: 10.12000/JR17096 0

### 引用本文

Sun Wang, Li Liangsheng, Zhang Jing, et al. Theoretical and experimental study on the permittivity of cdte in the terahertz band[J]. Journal of Radars, 2018, 7(1): 67-74. DOI: 10.12000/JR17096.

### 文章历史

(电磁散射重点实验室   北京   100854)

Theoretical and Experimental Study on the Permittivity of CdTe in the Terahertz Band
Sun Wang, Li Liangsheng, Zhang Jing, Yin Hongcheng
(Science and Technology on Electromagnetic Scattering Laboratory, Beijing 100854, China)
Foundation Item: The National Natural Science Foundation of China (6149069502)
Abstract: The phonon dispersion spectrum, eigenvector, and lattice vibration frequency of cadmium telluride with a zinc blende structure have been investigated using the density functional theory, and the permittivity of cadmium telluride crystal is numerically calculated. The permittivity of the crystal is measured using the terahertz time-domain spectroscopy system. The experimental results are consistent with the theoretical calculations on the modified local density approximation, the general gradient approximation, and the modified general gradient approximation. Finally, the differences among the three approximate exchange correlation potentials indicate that in the terahertz region, the permittivity of cadmium telluride is dominantly contributed by the coupling between electron and phonon; however, the phonon frequencies of transverse wave and longitudinal wave were sensitive to electron density distribution.
Key words: Cadmium telluride    Permittivity    Reflectivity    Transverse/longitudinal optical mode    Time domain spectroscopy
1 引言

2 理论模型及计算方法

 图 1 CdTe晶体结构：红球为Te原子，蓝球为Cd原子，绿色箭头表示晶体的主轴方向 Fig.1 The crystal structure of CdTe: The red spheres indicate Te atoms. The blue spheres indicate Cd atoms. The green arrow indicates the direction of crystal major axis

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3 结果与分析 3.1 CdTe晶体结构优化

 图 2 总能量与截断能的依赖关系。黑色箭头表示选取GGA的截断能位置 $E_{\rm{c}}^{{\rm{PBE/PW91}}}{\rm{ = }}680 \ {{\rm{eV}}}$ 。红色箭头表示选取LDA的截断能位置 $E_{\rm{c}}^{{\rm{LDA}}}{\rm{ = }}1225\ {{\rm{eV}}}$ Fig.2 The total energy vs the cut-off energy. The black arrow indicates the value of GGA cut-off energy $E_{\rm{c}}^{{\rm{PBE/PW91}}}{\rm{ = }}680 \ {{\rm{eV}}}$ . The red arrow indicates the value of LDA cut-off energy $E_{\rm{c}}^{{\rm{LDA}}}{\rm{ = }}1225\ {\rm eV}$
 图 3 总能量随k-point数量的依赖关系。黑色箭头表示合适的k-point选择 Fig.3 The total energy as a function of k-point. Black arrows indicate the selected k-point
 图 4 LDA, GGA-PBE和GGA-PW91方法计算的总能量与尝试晶格常数a的依赖关系。黑色箭头表示LDA计算总能量最小值的位置 $a_{{\rm{LDA}}}^{{\rm{CA-PZ}}} = 0.64424 \ {\rm{nm}}$ Fig.4 The total energy (calculated by LDA, GGA-PBE, and GGA-PW91 methods) vs the test lattice constant. The black arrow indicates the minimum of total energy, where $a_{{\rm{LDA}}}^{{\rm{CA-PZ}}} = 0.64424 \ {\rm{nm}}$
3.2 太赫兹波段介电常数理论与实验对比

 图 5 CdTe的声子色散谱，使用3种交换关联势为LDA, PBE, PW91 Fig.5 Phonon dispersions of CdTe with three exchange correlations LDA, PBE, PW91
 图 6 声子波矢方向与原子振动方向平行(a), (d)与垂直(b), (c)示意图。(a)和(b)中的声子波矢方向为CdTe主轴方向。(c)和(d)中的声子波矢方向为y轴方向。黑色箭头表示原子振动方向。绿色箭头表示声子传播方向 Fig.6 Schematic diagram: the phonon wave vectors are parallel (a), (d) and perpendicular (b), (c) to directions of atomic vibration. (a)-(b) the phonon wave vectors are parallel to the direction of CdTe principal axis. (c)-(d) The phonon wave vectors are parallel to the y-axis direction. Black arrows indicate the direction of atomic vibration. Green arrows indicate the direction of phonon propagation
 图 7 全空气太赫兹系统实验装置示意图。β-BBO为I型硼酸钡，PM为离轴抛物面镜，HV为高电压调制器，PMT为光电倍增管 Fig.7 Schematic diagram of full-air terahertz experimental system. β-BBO is type I barium borate, PM is an off-axis parabolic mirror, HV is a high-voltage modulator, and PMT is a photomultiplier tube
 图 8 理论计算与实验测量结果 Fig.8 The results of theoretical calculations and experimental measurements
4 结论