Книги по разным темам Pages:     | 1 | 2 | 3 | 4 | The results have been compared to those calculated within pseudopotential [46], k p [17,18,45] and semi-ab initio [14] theories, and to experimental data [17,18,45,46] m001 m011 m111 m001 m011 m111 m001 m011 mc c c hh hh hh lh lh lh AlP a0 0.176 0.176 0.176 0.489 6.272,0.490 1.270 0.187 0.139 0.ae 0.170 0.170 0.170 0.509 6.138,0.509 1.310 0.181 0.137 0.[14] 0.513 1.372 0.211 0.AlAs a0 0.115 0.115 0.115 0.465 5.199,0.465 1.183 0.121 0.098 0.ae 0.110 0.110 0.110 0.476 5.142,0.476 1.206 0.116 0.095 0.[14] 0.409 1.022 0.153 0.[46] 0.152 0.457 1.087 0.200 0.Experiment [46] 0.150 0.478 1.149 0.208 0.LDA [9] 0.122 0.480 0.Experiment [9] 0.124 0.491 0.AlSb a0 0.110 0.110 0.110 0.401 3.746,0.401 0.992 0.110 0.088 0.ae 0.100 0.100 0.100 0.419 3.769,0.419 1.029 0.100 0.083 0.[14] 0.336 0.872 0.123 0.GaP a0 0.128 0.128 0.128 0.305 2.444,0.305 0.731 0.122 0.090 0.ae 0.100 0.100 0.100 0.361 2.687,0.361 0.853 0.097 0.079 0.[14] 0.419 0.997 0.160 0.GaAs a0 0.058 0.058 0.058 0.304 2.353,0.305 0.726 0.058 0.049 0.ae 0.030 0.030 0.030 0.351 2.551,0.351 0.826 0.030 0.028 0.[14] 0.395 0.934 0.089 0.[45] 0.067 0.460 0.950 0.085 0.Experiment [17] 0.340-0.475 0.450-1.030 0.082-0.120 0.070-0.k p [18] 0.340-0.800 0.520-4.000 0.082-0.142 0.075-0.GaSb a0 0.035 0.035 0.036 0.272 2.074,0.272 0.646 0.035 0.031 0.ae 0.004 0.006 0.008 0.219 2.274,0.319 0.747 0.004 0.006 0.[14] 0.231 0.551 0.052 0.InP a0 0.095 0.095 0.095 0.389 2.570,0.389 0.895 0.093 0.078 0.ae 0.058 0.058 0.058 0.477 2.979,0.477 1.084 0.057 0.052 0.LDA [42] 0.570 0.430 0.970 0.SLDA [42] 0.060 0.400 0.900 0.SEPM [42] 0.095 0.470 1.030 0.Experiment [42] 0.079,0.081 0.520,0.610 0.630,0.950 0.104,0.InAs a0 0.028 0.028 0.028 0.381 2.524,0.381 0.878 0.028 0.026 0.ae 0.015 0.017 0.018 0.461 2.885,0.461 1.048 0.015 0.016 0.EPM [47] 0.480 0.LDA [10] 0.094 0.112 0.353 0.sX [10] 0.022 0.021 0.388 0.Experiment [10] 0.023 0.410 0.k p [2] 0.023 0.410 0.Experiment [2] 0.024 0.410 0.InSb a0 0.022 0.023 0.023 0.345 2.333,0.345 0.799 0.022 0.021 0.ae 0.023 0.024 0.025 0.416 2.638,0.416 0.949 0.022 0.023 0.well with that of Fu, Wang and Zunger [21,44] calculated approach gives better agreement with tight-binding and by direct diagonalization method. Also, Ep < Ep for the LMTO calculations [5] for ZnS, ZnSe and ZnTe, and with semiconductors except GaSb, InAs and InSb with zero k p calculations [2] for ZnS. However, for all AIIBVI band gaps in the LDA calculations using experimentally compounds considered except ZnTe, the value of Ep is determined lattice constans. much smaller than that calculated in Ref. 5, which found that the value of Ep is comparable with that of Ep. Note, that Momentum matrix elements calculated keeping the d d-electrons of group-II atoms in the core are bigger momentum matrix element between the semicore states than those found for the d-electrons included into the and conduction band minimum (not shown in Table 4) is valence complex. It indicates that the d-electrons result in in between 1 and 3 eV, which is smaller than Ep, but about underestimation of the coupling between the conduction 10 times is bigger than those between the other remote band minimum and valence band maximum. The former bands for all the AIIBVI compounds considered. It can Физика и техника полупроводников, 2005, том 39, вып. Ab initio studies of band parameters of AIIIBV and AIIBVI zinc-blende semiconductors Table 6. Effective masses (in units of the free-electron mass m0) for AIIBVI semiconductors including the d-electrons of atoms of group-II into the core (a0, ae) and into the valence complex (ad0, ade), and using the LDS (a0, ad0) and experimentally determined (ae, ade) lattice constants. In Refs. [2,37] all effective masses (except CdTe and m011 for ZnS, Ref. [37]) are given without specific directions and c determined experimentally [37] m001 m011 m111 m001 m011 m111 m001 m011 mc c c hh hh hh lh lh lh ZnS a0 0.193 0.193 0.193 0.601 8.463,0.601 1.578 0.215 0.161 0.ae 0.183 0.183 0.183 0.966 8.938,0.961 2.350 0.203 0.171 0.ad0 0.145 0.145 0.145 0.557 2.884,0.556 1.203 0.155 0.127 0.ade 0.142 0.141 0.141 0.602 3.071,0.602 1.297 0.151 0.126 0.Experiment [37] 0.340 0.184 1.760,1.121 0.230 0.k p [2] 0.ZnSe a0 0.146 0.146 0.146 0.557 7.505,0.561 1.462 0.164 0.129 0.ae 0.126 0.126 0.126 0.866 7.550,0.867 2.113 0.137 0.120 0.ad0 0.083 0.084 0.084 0.581 3.651,0.559 1.246 0.089 0.078 0.ade 0.081 0.081 0.081 0.569 3.078,0.571 1.248 0.084 0.075 0.Experiment [37] 0.142 0.147 0.Experiment [40] 0.130 0.170 0.570 0.k p [2] 0.[14] 1.814 0.784 0.191 0.ZnTe a0 0.146 0.147 0.147 0.485 5.501,0.484 1.236 0.152 0.118 0.ae 0.118 0.118 0.118 0.717 5.975,0.719 1.742 0.121 0.105 0.ad0 0.081 0.081 0.081 0.456 2.800,0.456 1.032 0.082 0.071 0.ade 0.073 0.073 0.073 0.501 2.988,0.501 1.126 0.074 0.066 0.Experiment [37] 0.122 0.128 0.Experiment [40] 0.130 0.k p [2] 0.[14] 0.541 1.354 0.155 0.CdS a0 0.196 0.197 0.197 0.962 12.800,0.953 2.400 0.227 0.184 0.ae 0.191 0.190 0.190 1.433 12.621,1.433 3.499 0.218 0.192 0.ad0 0.108 0.108 0.108 0.745 3.249,0.745 1.532 0.113 0.101 0.ade 0.107 0.107 0.107 0.754 3.285,0.754 1.551 0.112 0.101 0.Experiment [40] 0.140 0.[14] 0.929 1.935 0.201 0.CdSe a0 0.079 0.104 0.116 1.063 46.105,0.943 2.643 0.179 0.147 0.ae 0.134 0.133 0.133 1.289 8.295,1.309 2.982 0.146 0.133 0.ad0 0.045 0.045 0.045 0.711 3.282,0.712 1.491 0.045 0.043 0.ade 0.043 0.043 0.043 0.729 3.355,0.729 1.524 0.044 0.042 0.Experiment [37] 0.Experiment [40] 0.110 0.CdTe a0 0.145 0.146 0.146 0.743 7.910,0.742 1.874 0.157 0.132 0.ae 0.122 0.122 0.122 1.070 8.542,1.070 2.567 0.129 0.117 0.ad0 0.054 0.054 0.054 0.603 3.110,0.603 1.304 0.054 0.051 0.ade 0.047 0.048 0.048 0.647 3.292,0.647 1.393 0.048 0.045 0.Experiment [37] 0.094 0.096 0.095 0.720 0.810 0.840 0.130 0.120 0.Experiment [37] 0.Experiment [40] 0.90 0.720 0.840 0.k p [2] 0.[14] 0.478 1.114 0.125 0.be related ot LDA overestimation of the influence of the found that involvement of d-electrons into the core reduces valence band semicore d states. Matrix elements between the Luttinger parameters significantly compared to those c d the lowest conduction band and valence band, and with d-electrons in the valence complex (see Table 4).

1 c c remote conduction band states, is zero, which is However, the former approah gives better agreement with 1 related to symmetry properties of the crystal.

k p theory [2] and tight-binding and linear muffin-tin-orbital Luttinger parameters calculated in this work for AIIIBV (TBLMTO) calculations [5]. This analysis indicates that, compounds in Table 3 are much smaller than those found from LDA calculations, one can sometimes get the correct by k p theory and experiment, though the order of momentum matrix elements and Luttinger parameters, but magnitude is the same. For AIIBVI semiconductors, we it is not systematic.

Физика и техника полупроводников, 2005, том 39, вып. 186 S.Zh. Karazhanov, L.C. Lew Yan Voon 3.4. Effective masses hole effective masses (mlh) are in good agreement with experimental data for ZnS and CdTe. Due to the lack of Carrier effective masses are one of the important theoretical or experimental data we could not make such parameters in discussion of transport phenomena, exciton a comparison for the other AIIBVI compounds. Calculated effects, electron-hole liquids ets in semiconductors.

heavy-hole effective masses (mhh) differ significantly from They are usually determined by cyclotron resonance, those of Refs. [2,37,40] for all the AIIBVI compounds electroreflectance measurements or from analysis of considered except CdTe. For the latter good agrement is transport data. In this section we present the results of our achieved if the theoretical lattice constant is used.

calculations of electron effective masses at the conduction The effective masses for all the compounds considered band minimum and hole effective masses at valence band somewhat agree with those calculated by Huang and maximum. The results are given in Table 5 and Table Ching [14] using a minimal basis semi-ab initio approach for AIIIBV and AIIBVI compounds, respectively. For indirect and by Wang and Klein [13] using LDA, but the agreement gap semiconductors AlP, AlAs, AlSb and GaP mc is usually is not systematic. Based on the above analysis, one can say discussed for conduction band minimum at and other that by LDA calculations one can sometimes get the correct than (say X or L) points. In this work, we consider all values of conduction or valence-band effective masses along effective masses only for point.

some of the specific directions. However, it is not systematic.

Analysis of the Table 5 and 6 shows that the effective masses of conduction band electrons are isotropic, while those of holes are anisotropic. The effective masses for 4. Conclusion heavy-holes (mhh) and light-holes (mlh) correspond to v splitting of the state into a double and single degenerate In summary, band-structure calculations have been bands, respectively. Since we have neglected spin-orbit performed for AIIIBV and AIIBVI semiconductors with coupling, the split-off mass band is not descussed. Analysis zinc-blende structure. By a search of the total energy of the Table 5 shows that conduction-band effective masses minimum lattice constants have been found which differ for AlP, AlSb, GaP, GaSb and InSb are much smaller from the experimentally determined ones by < 3% for than mc = 0.25, 0.18, 0.17, 0.22, 0.13 calculated by k p AIIIBV compounds, and by 1.5 and 7% for the AIIBVI theory [2]. One can also see that conduction-band effective semiconductors with d-electrons of group-II atoms included masses calculated using the LDA lattice constant are into the valence shell and into the core, respectively.

closer to experimental data than those calculated using Band parameters calculated within the LDA show the the experimental lattice constant. Note that all the effective correct tendency to be smaller than those determined masses for AlP, AlAs, AlSb and InSb using the theoreticall experimentally or calculated theoretically within the k p, and experimentally determined lattice constants do not differ tight-binding or semi-empirical methods. From this point our from each other so much, while the difference is significant results are in general agreement with those obtained using for the other AIIIBV semiconductors studied. the other ab initio codes.

Analysis of the Table 5 shows that the values of Difference of the calculated direct band gaps for AIIIBV m001, m111 for AlAs, GaAs, InP, and InAs calculated in this compounds are in the range from 6.5 to 66% for hh hh work agree well with previous calculations and experimental theoretical lattice constants and from 15 to 100% for data, while such an agreement was not achieved for m001, experimental lattice constants. The difference for the AIIBVI lh m111. Due to the lack of experimental or calculated data, we semiconductors with d-electrons of group-II atoms included lh could not make such a comparison for other semiconductors into the core is in the range from 30 to 47% for theoretical and for effective masses along other directions. Note that for lattice constant and from 14 to 28% for experimental lattice InP, InAs and InSb not only band gaps, but also conduction- constant. If the d-electrons are included into the valence band effective masses are overestimated. It indicates that complex, then the error in calculation of the band gap there is a corelation between changes of the band gap and becomes significant due to p-d repulsion.

the conduction-band effective mass, which is qualitatively Momentum matrix elements Ep calculated in this work consistent with the k p theory (see e. g. Ref. [2]). Also, are smaller compared with those obtained within the k p distinct from Fiorentini and Baldereschi [8,9], none of the theory [2], since the latter is known to be closer to conduction-band effective masses for AIIIBV compounds experimental data. For AIIIBV compounds difference of the except AlAs agree with experimental data. values of Ep obtained within the two theories is in the range Analysis of Table 6 shows that the effective masses of from 2.9 to 35% for theoretical lattice constant and from all AIIBVI compounds calculated keeping the d-electrons 21 to 38% for experimentally determined lattice constants.

in the core is bigger than those found when including the For AIIBVI compounds with d-electrons of group-II atoms d-electrons into the valence complex. It indicates that the included into the core the difference is in the range from semicore d-electrons results in underestimation of not only 3.7 to 34.3% for theoretical lattic constant and from 27.band and coupling between the valence band maximum and to 48.1% for experimentally determined lattice constant.

conduction band minimun, but also change the dispersion Involvement of the d-electrons into the valence complex around the point. Our calculated values of the light- increased the error in calculation of Ep.

Физика и техника полупроводников, 2005, том 39, вып. Ab initio studies of band parameters of AIIIBV and AIIBVI zinc-blende semiconductors The effective masses of conduction band electrons are [3] M. Willatzen, M. Cardona, N.E. Christensen. Phys. Rev. B, 50, 18 054 (1994).

found to be isotropic, while those of holes are anisotropic.

[4] M. Willatzen, M. Cardona, N.E. Christensen. Phys. Rev. B, Calculated mc for the AIIIBV semiconductors differs from 51, 13 150 (1995).

experimentally determined ones from 13 to 23% for [5] M. Willatzen, M. Cardona, N.E. Christensen. Phys. Rev. B, theoretical lattice constant and from 26 to 55% for 51, 17 992 (1995).

experimental lattice constant. For AIIBVI compounds with [6] L.C. LewYan Voon, M. Willatzen, M. Cardona. Phys. Rev. B, d-electrons of group-II atoms included into the core 53, 10 703 (1996).

the difference of the calculated mc from experimentally [7] L.C. Lew Yan Voon, S. Karazhanov, W.A. Harrison. Phys. Rev.

determined one is in the range from 8 to 54% for B, 66, 23 5211 (2002).

theoretical lattice constant, while that for experimental [8] V. Fiorentini, A. Baldereschi. J. Phys.: Condens Matter., 4, lattice constant is in the range from 2 to 46%. We found 5967 (1992).

that the effective masses of all AIIBVI compounds calculated [9] V. Fiorentini. Phys. Rev. B, 46, 2086 (1992).

keeping the d-electrons in the core is bigger than those [10] C.B. Geller, W. Wolf, S. Picozzi, A. Continenza, R. Asahi, found when including the d-electrons itno the valence W. Mannstadt, A.J. Freeman, E. Wimmer. Appl. Phys. Lett., complex. It indicates that the semicore d-electrons result 79, 368 (2001).

[11] L.-W. Wang, A. Zunger. Phys. Rev. B, 51, 17 398 (1995).

in underestimation of not only band gaps and coupling [12] E.O. Kane. Phys. Rev. B, 4, 1910 (1971).

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