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Chinese Journal of Quantum Electronics
Vol. 40, Issue 6, 899 (2023)

Band calculation and spectral analysis of diamond crystal

LI Haidong^1、2、3, SHEN Yu^1、2、*, WEN Ya⁴, ZHANG Shenjin^1、2、**, ZONG Nan^1、2, BO Yong^1、2, and PENG Qinjun^1、2

Author Affiliations

¹Key Laboratory of Functional Crystals and Laser Technology, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190, China

²Key Laboratory of Solid State Laser, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190, China

³University of Chinese Academy of Sciences, Beijing 100049, China

⁴Institute of Optical Physics and Engineering Technology, Qilu Zhongke, Jinan 250000, China

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DOI: 10.3969/j.issn.1007-5461.2023.06.010 Cite this Article

Haidong LI, Yu SHEN, Ya WEN, Shenjin ZHANG, Nan ZONG, Yong BO, Qinjun PENG. Band calculation and spectral analysis of diamond crystal[J]. Chinese Journal of Quantum Electronics, 2023, 40(6): 899 Copy Citation Text

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Multi-electron model of diamond tetrahedron. (a) Structure of diamond face center; (b) Polyelectronic structureof tetrahedron (Red balls represent electrons, and green balls represent carbon atoms. )

Fig. 1. Multi-electron model of diamond tetrahedron. (a) Structure of diamond face center; (b) Polyelectronic structureof tetrahedron (Red balls represent electrons, and green balls represent carbon atoms. )

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Structure of diamond tetrahedron

Fig. 2. Structure of diamond tetrahedron

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Fig. 3. The <1 1 1> crystal plane of diamond crystal

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Fig. 4. Band structure of diamond

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Fig. 5. High-symmetric point path diagram of the first Brillouin zone

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Fig. 6. Energy level structure of diamond carbon atoms

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Fig. 7. The state density of diamond

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Fig. 8. Band structure under electric field. (a) Band structure of <1 1 0> crystal orientation;(b) Band structure of <1 1 1> crystal orientation

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Fig. 9. Phonon spectra of diamond

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Fig. 10. Raman spectra of diamond

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Fig. 11. The density of phonon states of diamond

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Fig. 12. Display of triple degenerate T_2g modes

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Fig. 13. Transmission spectrum of diamond

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$Reflectivity, complex refractive index and complex$

Fig. 14. Reflectivity, complex refractive index and complex

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Fig. 15. Absorption spectra of diamond

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Fig. 16. Transmission spectra of diamond at 3.5 - 6 μm

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	文献[41]中LDA计算结果		本研究GAA计算结果		修正后的结果
高对称点及晶向	价带顶/eV	导带底/eV	价带顶/eV	导带底/eV	价带顶/eV	导带底/eV
W<2 1 0>	-8.525	10.670	-8.444	10.817	-8.444	11.917
L<1 1 1>	-2.849	8.528	-2.832	8.619	-2.832	9.719
G	0	5.630	0	5.701	0	6.801
X<1 0 0>	-6.418	4.836	-6.373	4.901	-6.373	6.001
K<1 1 0>	-5.466	5.749	-5.431	5.831	-5.431	6.931
导带底	-5.766	4.218	-5.750	4.269	-5.750	5.369

Table 1. Comparison of GGA calculation results，corrected results with LDA results in reference [41]

主量子数n取值	角量子数 $l$ 取值、能级符号		磁量子数m取值、原子轨道符号、原子轨道总数			自旋量子数m_s取值和符号、电子运动状态数
1	0	1s	0	1s	1	±1/2	↑↓	2
2	0	2s	0	2s	4	±1/2	↑↓	8
	1	2p	0	2p_z		±1/2	↑↓
			±1	2p_x		±1/2	↑↓
			±1	2p_y		±1/2	↑↓

Table 2. Quantum number of diamond

晶向	无电场	<1 0 0>	<1 1 0>	<1 1 1>	<2 1 1>	<3 1 1>
能带间隙/eV	5.369	3.527	4.035	4.496	4.071	3.901
G点间隙/eV	6.801	3.636	4.099	4.637	4.232	4.058

Table 3. Energy band gap and G point energy gap under electric field

振动模式	频率/cm^-1	简并(N_r)	红外活性强度/A⁴	拉曼活性强度/A⁴
A_2u	0	1	0	0
E_1u	0	2	0	0
E_2u	788.73	6	0	0
B_1u	1102.28	6	0	0
B_2u	1223.45	6	0	0
T_2g	1325.83	3	0	279

Table 4. Vibration modes，frequencies，infrared and Raman activity intensity at high symmetric G point

对称点及晶向	声子支代号	参考^[24]	参考^[23]	参考^[58]	本研究计算值
G	G(O)	1332.4±0.01	1332.5±1		1315±1
X<1 0 0>	L(A、O)	1170	1191±3	1184±21	1212±1
	TO	1088	1072±2	1072±26	1086±1
	TA	786	829±2	807±32	788±1
L<1 1 1>	LO	1245	1256±4	1242±37	1261±1
	TO	1208	1220±2	1210±37	1221±1
	LA	1009	1033±2	1035±32	1065±1
	TA	572	553±2	552±16	550±1
K<1 1 0>	Σ₁O	1236	1239±2	1232±27	1245±1
	Σ₂O	1112	1111±1	1110±21	1106±1
	Σ₃O	1051	1042±2	1046±21	1069±1
	Σ₁A	986	992±3	1009±16	1019±1
	Σ₃A	982	978±1	972±16	983±1
	Σ₄A	748	764±4	765±21	752±1
W<2 1 0>	L(A、O)	1164	1146±1	1168±53	1177±1
	TO	1012	1019±3	993±53	1006±1
	TA	915	918±12	918±11	922±1

Table 5. Phonon frequencies at high symmetry points and related experimental values^{[23，24，58]}（unit cm^-1）

编号	声子组合	波数/cm^-1	波长/μm	吸收系数^[66]/cm^-1
a	Σ₃A+Σ₄A	1735	5.76	1.79
b	Σ₁A+Σ₄A	1771	5.65	2.34
c	LO(L)+TA(L)	1811	5.52	3.24
d	Σ₂O+Σ₄A	1858	5.38	4.98
e	TO(X)+TA(X)	1874	5.34	5.43
f	Σ₁O+Σ₄A	1997	5.01	10.60
编号	声子组合	波数/cm^-1	波长/μm	吸收系数^[66]/cm^-1
g	L(X)+TA(X)	2000	5.00	10.74
h	Σ₁A+Σ₃A	2002	4.99	10.65
i	Σ₂O+Σ₃A	2089	4.79	7.65
j	Σ₂O+Σ₃O	2175	4.60	11.06
k	L(W)+TO(W)	2183	4.58	10.05
l	L(X)+TO(X)	2298	4.35	5.41
m	Σ₁O+Σ₃O	2314	4.32	3.01
n	LO(L)+LA(L)	2326	4.30	2.37
o	Σ₁O+Σ₂O	2351	4.25	2.56
p	2L(X)	2424	4.12	4.17
q	2TO(L)	2442	4.09	4.38
u	LO(L)+TO(L)	2482	4.03	4.32
r	2LO(L)	2522	3.92	4.33
s	2O(G)	2630	3.80	0.74

Table 6. Dual-phonon absorption combination，absorption wavelength and absorption coefficient of reference [66]

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Haidong LI, Yu SHEN, Ya WEN, Shenjin ZHANG, Nan ZONG, Yong BO, Qinjun PENG. Band calculation and spectral analysis of diamond crystal[J]. Chinese Journal of Quantum Electronics, 2023, 40(6): 899

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