太赫兹波段碲化镉介电常数的理论与实验研究

孙旺; 李粮生; 张景; 殷红成

doi:10.12000/JR17096

太赫兹波段碲化镉介电常数的理论与实验研究

doi: 10.12000/JR17096

电磁散射重点实验室北京 100854

基金项目: 国家自然科学基金(6149069502)

详细信息

作者简介:
孙　旺(1993–)，男，硕士研究生，研究方向为太赫兹波段材料的密度泛函方法

李粮生(1981–)，男，研究员，研究方向为太赫兹技术、量子技术和统计物理

张　景(1987–)，男，博士后，研究方向为太赫兹测量技术

殷红成(1967–)，男，研究员，博士生导师，主要研究方向为电磁散射、雷达目标特性、目标识别等

通讯作者:
李粮生 liliangshengbititp@163.com

中图分类号: TN952
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出版历程
- 收稿日期: 2017-11-03
- 修回日期: 2018-01-21
- 网络出版日期: 2018-02-01

Theoretical and Experimental Study on the Permittivity of CdTe in the Terahertz Band

Science and Technology on Electromagnetic Scattering Laboratory, Beijing 100854, China

Funds: The National Natural Science Foundation of China (6149069502)

摘要

摘要: 该文采用密度泛函理论研究了闪锌矿型碲化镉的声子色散谱、特征向量及晶格振动频率，获得了碲化镉介电常数随频率变化的理论值。通过太赫兹时域光谱系统测量碲化镉单晶的介电常数，该实验结果与局域密度近似修正、广义梯度近似修正和广义梯度近似修正的计算结果吻合较好。最后，3种近似交换关联势的计算结果之间存在一定差异性，该差异性结果表明太赫兹波段碲化镉的介电常数由电子声子耦合所主导，但是横波和纵波声子频率敏感于电子密度分布。
- 碲化镉 /
- 介电常数 /
- 反射率 /
- 横/纵光学模 /
- 时域光谱
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.
- Cadmium telluride /
- Permittivity /
- Reflectivity /
- Transverse/longitudinal optical mode /
- Time domain spectroscopy

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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

Figure 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

下载: 全尺寸图片幻灯片

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 $E_{\rm{c}}^{{\rm{LDA}}}{\rm{ = }}1225\ {{\rm{eV}}}$

Figure 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} $

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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

Figure 3. The total energy as a function of k-point. Black arrows indicate the selected k-point

下载: 全尺寸图片幻灯片

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 $a_{{\rm{LDA}}}^{{\rm{CA {^{\scriptsize{-}}} PZ}}} = 0.64424 \ {\rm{nm}}$

Figure 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 $a_{{\rm{LDA}}}^{{\rm{CA {^{\scriptsize{-}}} PZ}}} = 0.64424 \ {\rm{nm}}$

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图 5 CdTe的声子色散谱，使用3种交换关联势为LDA, PBE, PW91

Figure 5. Phonon dispersions of CdTe with three exchange correlations LDA, PBE, PW91

下载: 全尺寸图片幻灯片

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

Figure 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

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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

Figure 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

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图 8 理论计算与实验测量结果

Figure 8. The results of theoretical calculations and experimental measurements

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表 1 CdTe单晶材料： ${\text{ω} _{\text{LO}}}$ , ${\text{ω} _{\text{TO}}}$ , $\text{ε}$ (∞)和 $\text{γ} $ 理论和实验值

Table 1. CdTe single crystal: the theoretical and experimental values of ${\text{ω} _{{\text{LO}}}}$ , ${\text{ω} _{{\text{TO}}}}$ , $\text{ε}$ (∞) and $\text{γ} $

方法	光学声子横波模式 ${\omega _{{\rm{TO}}}}$ (THz)	光学声子纵波模式 ${\omega _{{\rm{LO}}}}$ (THz)	高频极限介电常数 $\varepsilon (\infty )$	碰撞频率 $\gamma $ (THz)	晶格常数 ${a_0}$ (nm)
LDA	4.402	5.111	7.55792	0.13	0.64424
GGA-PBE	4.518	5.301	6.62839	0.12	0.66594
GGA-PW91	4.533	5.309	6.72645	0.12	0.66541
实验值	4.25	5.01	6.93	0.125	0.64827^[33]

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