几种反常弛豫的宽带隙半导体（110）表面电子结构的理论研究
摘要
本文利用形式散射理论的格林函数方法及紧束缚最近邻sp~3s~*和spd模型计算
了两种在应用方面具有一些优异特性的反常弛豫的半导体材料Ⅲ族氮化物BN和Ⅰ-
Ⅶ族化合物CulCl（110）表面的电子结构。分别给出了理想表面和弛豫表面的投影带
结构及电子层态密度。比较详细地讨论了弛豫前后电子态的特征。结果表明：
（1）BN（110）表面的电子结构与大多数Ⅲ-Ⅴ族和Ⅱ-Ⅵ族化合物半导体（110）
表面的电子结构定性上是类似的。但在各表面态的能级位置、色散特性和轨道特性
等方面上均存在较大的差别。其中一个显著的区别是：弛豫后带隙中阴阳离子悬挂
键对应的表面态虽然分别向下和向上移动，但仍部分处在带隙中。这与普适的“弛
豫赶走了禁带隙内的表面态”的结论不一致。（2）CuCl（110）表面弛豫后电子态的
变化是Cu的d态电子和Cl的p态电子的重新杂化起了主要作用。表面弛豫是p-
p、p-d杂化的共同作用，而大多数Ⅲ-Ⅴ族和Ⅱ-Ⅵ族化合物半导体（110）表面的
弛豫是p-p杂化起主要作用。
In this paper, by using the nearest-neighbor tight-binding sp3s and spd model and
Green function method in the frame of the scattering theory, we have studied the (110)
surface electronic structure of two semiconductors, HI-nitride BN and I -VII componud
CuCI, which have some excelent properties and widespread applications. We have
presented the surface projected band structure and the wavevector-resolved layer
densities of states at the high-symmetry point in the two-dimensional Brollouin zone. We
have discussed in detail the characters of the surface states before and after relaxation.
The results show that: (1) The electronic structure of BN (110) surface is qualitatively
similar to those of (110) surface of most rn-v and II -VI compounds. But there are
relatively large differences of surface states in energy level, dispersion and orbitial. One
of the obvious differences is that although the ation-drived and cation-drived dangling
bond states in the gap have shifted up and down respctively after relaxation, part of them
is still in the gap. This is completely different from the general conclusion of 揜elaxation
have drived the surface states out of the gap.?(2) The changes of the eletronic structure
of CuCl (110) surface after relxation is mainly due to the rehybridization between Cu-d
electrons and Cl-p electrons. The mechanism for the relaxation is that the rehybridization
of both p-p and p-d electrons in the top two layers plays an important part in the surface
relaxation while the rehybridization of only the p-p electrons plays an important role in
the (110) surface relaxation of most Ill-V and IJ-VI compounds.
了两种在应用方面具有一些优异特性的反常弛豫的半导体材料Ⅲ族氮化物BN和Ⅰ-
Ⅶ族化合物CulCl（110）表面的电子结构。分别给出了理想表面和弛豫表面的投影带
结构及电子层态密度。比较详细地讨论了弛豫前后电子态的特征。结果表明：
（1）BN（110）表面的电子结构与大多数Ⅲ-Ⅴ族和Ⅱ-Ⅵ族化合物半导体（110）
表面的电子结构定性上是类似的。但在各表面态的能级位置、色散特性和轨道特性
等方面上均存在较大的差别。其中一个显著的区别是：弛豫后带隙中阴阳离子悬挂
键对应的表面态虽然分别向下和向上移动，但仍部分处在带隙中。这与普适的“弛
豫赶走了禁带隙内的表面态”的结论不一致。（2）CuCl（110）表面弛豫后电子态的
变化是Cu的d态电子和Cl的p态电子的重新杂化起了主要作用。表面弛豫是p-
p、p-d杂化的共同作用，而大多数Ⅲ-Ⅴ族和Ⅱ-Ⅵ族化合物半导体（110）表面的
弛豫是p-p杂化起主要作用。
In this paper, by using the nearest-neighbor tight-binding sp3s and spd model and
Green function method in the frame of the scattering theory, we have studied the (110)
surface electronic structure of two semiconductors, HI-nitride BN and I -VII componud
CuCI, which have some excelent properties and widespread applications. We have
presented the surface projected band structure and the wavevector-resolved layer
densities of states at the high-symmetry point in the two-dimensional Brollouin zone. We
have discussed in detail the characters of the surface states before and after relaxation.
The results show that: (1) The electronic structure of BN (110) surface is qualitatively
similar to those of (110) surface of most rn-v and II -VI compounds. But there are
relatively large differences of surface states in energy level, dispersion and orbitial. One
of the obvious differences is that although the ation-drived and cation-drived dangling
bond states in the gap have shifted up and down respctively after relaxation, part of them
is still in the gap. This is completely different from the general conclusion of 揜elaxation
have drived the surface states out of the gap.?(2) The changes of the eletronic structure
of CuCl (110) surface after relxation is mainly due to the rehybridization between Cu-d
electrons and Cl-p electrons. The mechanism for the relaxation is that the rehybridization
of both p-p and p-d electrons in the top two layers plays an important part in the surface
relaxation while the rehybridization of only the p-p electrons plays an important role in
the (110) surface relaxation of most Ill-V and IJ-VI compounds.
引文
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[2] For a review ,see: The Theory of the Inhomogeneous Electron Gas,Eds. S. Lundqvist, N.H.Marcgm(Plenum,New York) 1983.
[3] A.Pasguarello, K.Laasonen,R.Car,et al., Phys. Rev. Lett. 69(1992),1982.
[4] J.S.Nelson, S.J.Plimpton, M.P. Sears, Phys. Rev. B47(1993), 1765; K.Brommer,M.Needles,B.Larson ,et al. Phys. Rev. Lett. 68(1992), 1355.
[5] L.Ruan,F.Besenbacher, I.Stensgaard, et al. Phys. Rev. Lett., 69(1992),3523.
[6] Prutton, Surface Physics, Oxford(1980)
[7] 陆家和，陈长彦编著，表面分析技术，清华大学出版社，1986．
[8] A.Zangwill, Physics at Surface, Cambridge(1988).
[9] V.Heine, Surf.Sci., 2(1964),1.
[10] J.R.Schrieffer, P.Soven,Phys. Today28(1975),24
[11] J.A.Appelbaum, D.R.Hamann, Phys. Mod. Rev. 48(1976),479.
[12] C. A. Swarts, W. A. Goddard Ⅲ and T. C. McGill, J. Vac.Sci. Technol.,19(1981),551.
[13] Xie Xide, Zhang Kaiming, Prog. in Surf. Sci., 28(1988),71
[14] Liqing Zhu, Enge Wang, Liyuan Zhang, Phys. Rev., B56(1997), 10308
[15] Shangfen Ren et al. J. Vac. Sci. Technol., B13(1995),1711
[16] G.A. baraff, A. Appelbaum and D. R. Hamann, Phys. Rev. Lett., 38(1977),237
[17] B. Djafari-Rouhani, L.Dobrzynski et al. Surf Sci., 78(1978),24
[18] M. Nishida, Surf. Sci., 109(1981),557
[19] J.Callaway, J. Math. Phys. 5(1964),783; Phys. Rev. 154(1967),515.
[20] G.F.Koster,J.C.Slater, Phys. Rev. 95(1954), 1167.
[21] 贾瑜，范希庆，马丙现，物理学报，46 (1997)，1999．
[22] 杨仕娥，马丙现，贾瑜，物理学报，47 (1998)，1704
[23] A.Kahn, Surf. Sci. Rep.,3(1983 ), 193.
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[26] A.Filippetli,V.Fiorentini,G.Cappellini,et al. Phys. Rev., B59(1999) ,8026．
[27] Zhi-Qiang Li, Hao Zhen,Fan-Quan Kong, et al.Appl.. Phys.84(1998) ,1977．
[28] H.W.LeiteAlves,J.L.A.Alves,R.A.Nogueira,Braz.J.Phys.(Brazil)29(1999) ,817．
[29] R.Miotto,G.P.Srivastava,A.C.Ferraz, Surf. Sci., 426(1999) ,75．
[30] J.E.Jaffe,R.Pandey, P.Zapol, Phys.Rev.B53(1996) ,R4209．
[31] X.Chen,J.M.Langlois, W.A.Goddard, Phys.Rev.B52(1995) ,2348．
[32] C.A.Swart,T.C.McGill,W.A.Goddard, Surf. Sci., 110(1981) ,400．
[33] U.Grossner,J.Furtmuller,F.Bechstedt, Phys.Rev.B58(1998) ,R1722．
[34] R.Pandey,P.Zapol,M.Causa, Phys.Rev.B55(1997) ,R16009．
[35] B.K.Agrawal,PSrivastava,S.Agrawal, Surf. Sci., 405(1998) ,54．
[36] M.Ferhat,A.Zaoui,M.Certiers and B.Khelifa,Phys.Lett.A216(1996) ,187．
[37] A.Goldmann,Phys.Stat.Sol.(b),81(1977) ,9．
[38] M.H.Tsai, J.D.Dow,R.P. Wang and R.V.Kasowski, Phys.Rev.B40(1987) ,9818．
[39] M.H.Tsai,W.M.Hu,J.D.Dow & .F.Sankey,J. Vac.Ssi.Technol.A10(4) (1992-),2511．
[40] C.B.Duke, A.Paton ,A-Lazatides and A.Kahn,Phys.Rev. B54(1996) , 14692．
[41] A.Kahn,S.Asan,W.Chen et al., Phys.Rev.Lett.68(1992) ,3200．
[42] D.L.Lessor,C.B.Duke,A.Kahn and .K.Ford,J.Vac.Sci.Technol.All(1993) ,2205．
[43] S.Tanaka,M.Kamada,J.Electron.Spectro.Relat.Phenomena,88-91(1998) ,689．
[44] D.We stphal,A.Goldmann,Solid State Commun..35(1980) ,441．
[2] For a review ,see: The Theory of the Inhomogeneous Electron Gas,Eds. S. Lundqvist, N.H.Marcgm(Plenum,New York) 1983.
[3] A.Pasguarello, K.Laasonen,R.Car,et al., Phys. Rev. Lett. 69(1992),1982.
[4] J.S.Nelson, S.J.Plimpton, M.P. Sears, Phys. Rev. B47(1993), 1765; K.Brommer,M.Needles,B.Larson ,et al. Phys. Rev. Lett. 68(1992), 1355.
[5] L.Ruan,F.Besenbacher, I.Stensgaard, et al. Phys. Rev. Lett., 69(1992),3523.
[6] Prutton, Surface Physics, Oxford(1980)
[7] 陆家和，陈长彦编著，表面分析技术，清华大学出版社，1986．
[8] A.Zangwill, Physics at Surface, Cambridge(1988).
[9] V.Heine, Surf.Sci., 2(1964),1.
[10] J.R.Schrieffer, P.Soven,Phys. Today28(1975),24
[11] J.A.Appelbaum, D.R.Hamann, Phys. Mod. Rev. 48(1976),479.
[12] C. A. Swarts, W. A. Goddard Ⅲ and T. C. McGill, J. Vac.Sci. Technol.,19(1981),551.
[13] Xie Xide, Zhang Kaiming, Prog. in Surf. Sci., 28(1988),71
[14] Liqing Zhu, Enge Wang, Liyuan Zhang, Phys. Rev., B56(1997), 10308
[15] Shangfen Ren et al. J. Vac. Sci. Technol., B13(1995),1711
[16] G.A. baraff, A. Appelbaum and D. R. Hamann, Phys. Rev. Lett., 38(1977),237
[17] B. Djafari-Rouhani, L.Dobrzynski et al. Surf Sci., 78(1978),24
[18] M. Nishida, Surf. Sci., 109(1981),557
[19] J.Callaway, J. Math. Phys. 5(1964),783; Phys. Rev. 154(1967),515.
[20] G.F.Koster,J.C.Slater, Phys. Rev. 95(1954), 1167.
[21] 贾瑜，范希庆，马丙现，物理学报，46 (1997)，1999．
[22] 杨仕娥，马丙现，贾瑜，物理学报，47 (1998)，1704
[23] A.Kahn, Surf. Sci. Rep.,3(1983 ), 193.
[24] C.B.Duke,R.J.Meyer,P.Mark, J. Vac. Ssi. Technol.17(1980),971.
[25] C.B.Duke, J. Vac. Ssi. Technol. B1(1983), 732.
[26] A.Filippetli,V.Fiorentini,G.Cappellini,et al. Phys. Rev., B59(1999) ,8026．
[27] Zhi-Qiang Li, Hao Zhen,Fan-Quan Kong, et al.Appl.. Phys.84(1998) ,1977．
[28] H.W.LeiteAlves,J.L.A.Alves,R.A.Nogueira,Braz.J.Phys.(Brazil)29(1999) ,817．
[29] R.Miotto,G.P.Srivastava,A.C.Ferraz, Surf. Sci., 426(1999) ,75．
[30] J.E.Jaffe,R.Pandey, P.Zapol, Phys.Rev.B53(1996) ,R4209．
[31] X.Chen,J.M.Langlois, W.A.Goddard, Phys.Rev.B52(1995) ,2348．
[32] C.A.Swart,T.C.McGill,W.A.Goddard, Surf. Sci., 110(1981) ,400．
[33] U.Grossner,J.Furtmuller,F.Bechstedt, Phys.Rev.B58(1998) ,R1722．
[34] R.Pandey,P.Zapol,M.Causa, Phys.Rev.B55(1997) ,R16009．
[35] B.K.Agrawal,PSrivastava,S.Agrawal, Surf. Sci., 405(1998) ,54．
[36] M.Ferhat,A.Zaoui,M.Certiers and B.Khelifa,Phys.Lett.A216(1996) ,187．
[37] A.Goldmann,Phys.Stat.Sol.(b),81(1977) ,9．
[38] M.H.Tsai, J.D.Dow,R.P. Wang and R.V.Kasowski, Phys.Rev.B40(1987) ,9818．
[39] M.H.Tsai,W.M.Hu,J.D.Dow & .F.Sankey,J. Vac.Ssi.Technol.A10(4) (1992-),2511．
[40] C.B.Duke, A.Paton ,A-Lazatides and A.Kahn,Phys.Rev. B54(1996) , 14692．
[41] A.Kahn,S.Asan,W.Chen et al., Phys.Rev.Lett.68(1992) ,3200．
[42] D.L.Lessor,C.B.Duke,A.Kahn and .K.Ford,J.Vac.Sci.Technol.All(1993) ,2205．
[43] S.Tanaka,M.Kamada,J.Electron.Spectro.Relat.Phenomena,88-91(1998) ,689．
[44] D.We stphal,A.Goldmann,Solid State Commun..35(1980) ,441．