Erratum: Elastic constants and related properties of tetrahedrally bonded BN, AlN, GaN, and InN [Phys. Rev. B 53, 16310 (1996)]
Erratum: Elastic constants and related properties of tetrahedrally bonded BN, AlN, GaN, and InN [Phys. Rev. B 53, 16310 (1996)]
复制标题
DOI：
10.1103/physrevb.56.7018.2
复制
发表时间：
1997-09
影响因子：
3.7
通讯作者：
Kwiseon Kim;W. Lambrecht;B. Segall
中科院分区：
文献类型：
--
作者：
Kwiseon Kim;W. Lambrecht;B. Segall
Mark van Schifgaarde1提请我们注意，分别由206和177 Gpa计算的GaN和InN的立方剪切模C44c的值比他用相同的全势线性松饼-锡轨道方法得到的142和79 Gpa的值大得多，但使用了包括所谓的局域轨道的改进基组。2这使得人们可以同时考虑4d半核Ga3d和5d态高位导带状Ga4d对价带的影响。同时，对闪锌矿AlN、GaN和InN的改进计算包括了Al2p、Ga3p和4p态的半核，并且对间隙Hankel函数的展开使用了比我们以前的计算更高的角动量截止值。本文给出了用马丁变换方法得到的纤锌矿AlN、GaN和InN的弹性常数的校正值。用这些更精确的立方弹性常数作为输入，在表I中。我们发现，变换得到的CHh(C11hC12h)/2C33h2C13h和C33h的值与用我们的基组重新计算的直接计算值比以前更符合。这并不令人惊讶，因为C44c与沿立方111方向的扭曲有关，这相当于沿着c轴的扭曲决定了C33h和CHh。我们注意到，与实验数据的一致性与我们之前的结果相当。改进的计算还影响纤锌矿的结构参数，如表II所示，与实验相比，InN的c/a比有明显的改善，避免了我们所讨论的依赖于松饼锡球半径选择的问题。C44c的新值也改善了表八16321中C44K/C44的比率。对于AlN、GaN和Inn，它们分别变为0.84、1.00和1.09。我们最后指出了以下印刷错误：第二个中间的方程式
It was brought to our attention by Mark van Schilfgaarde1 that the values of the cubic shear moduli C44 c of GaN and InN calculated by us 206 and 177 GPa, respectively are significantly larger than the values obtained by him 142 and 79 GPa using the same full-potential linear muffin-tin orbital method but using an improved basis set including so-called local orbitals. 2 These allow one to include simultaneously the effects of semicore Ga 3d In 4d and high-lying conduction-bandlike Ga 4d In 5d states on the valence bands. At the same time, these improved calculations for zinc-blende AlN, GaN, and InN included semicore Al 2p, Ga 3p, and In 4p states, and used higher angular momentum cutoffs for the interstitial Hankel function expansions than our previous calculations. Here we present corrected values for the elastic constants of wurtzite AlN, GaN, and InN obtained by means of Martin’s transformation method using these more accurate cubic elastic constants as input in Table I.We find that the values of Ch h (C11 h C12 h)/2C33 h 2C13 h and C33 h obtained from the transformation are in better agreement with the directly calculated ones recalculated with our basis set than previously. This is not surprising, since C44 c is related to distortions along the cubic 111 direction which is equivalent to the distortions along the c axis determining C33 h and Ch h. We note that agreement with experimental data is comparable to that of our previous results. The improved calculations1 also affect the wurtzite structural parameters, shown in Table II, with a marked improvement compared to experiment for InN in the c/a ratio, and avoid the problems with dependence on the choice of muffin-tin sphere radii we discussed in our paper. The new values of C44 c also improve the ratios of C44 K/C44 in Table VIII, on p. 16 321. These become 0.84, 1.00, and 1.09, respectively, for AlN, GaN and InN. We finally point out the following misprints: the equation in the middle of the second