Full-band-structure calculation of first-, second-, and third-harmonic optical response coefficients of ZnSe, ZnTe, and CdTe.
Full-band-structure calculation of first-, second-, and third-harmonic optical response coefficients of ZnSe, ZnTe, and CdTe.
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DOI：
10.1103/physrevb.43.9700
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发表时间：
1991-04
期刊：
影响因子：
--
通讯作者：
E. Ghahramani;David J. Moss;J. Sipe
中科院分区：
文献类型：
--
作者：
E. Ghahramani;David J. Moss;J. Sipe
我们报道了全能带结构计算的频率相关的二次和三次谐波响应函数，以及我们的结果，这些半导体的介电函数。我们使用高斯轨道的线性组合技术，结合X-保证数学{-α}方法，得到了每种材料的能带结构和光学矩阵元。利用线性化采样方法对\ensuremath{\epsilon}\ensuremath{\rightarrow}(\ensuremath{\omega})和$^{(2)}$(-2\ensuremath{\omega}；\ensuremath{\omega}，的表达式进行求值，以在布里渊区的不可约段上进行积分；使用随机抽样方法进行评估。\ensuremath{\epsilon}${\ensuremath{\rightarrow}}_{2}$(\ensuremath{\omega})的计算结果与实验结果吻合较好。我们计算的${\mathrm{\ensuremath{\chi}}}_{14}^{(2)}$(0)=24.8\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$对镉的esu值与实测值非常吻合[G.H.Sherman和P.D.Coleman，J.Appl.太棒了。44,238(1973)[${\mathrm{\ensuremath{\chi}}}_{14}^{(2)}$(\ensuremath{\lambda}=28\ensuremath{\mu}m)=(28\ifmmode\pm\else\textpm\fi{}11)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$esu.我们认为，${\mathrm{\ensuremath{\chi}}}_{14}^{(2)}$(\ensuremath{\lambda}=10.6的实验结果保证了锌硒和锌碲[C.K.N.Patel，Phys.莱特牧师。16,613(1966)]可能不准确，需要额外的测量。我们的计算表明，对于本工作中所考虑的材料，确保数学{\chi}$^(2)}$(0)和确保数学{\chi}$^{(3)}$(0)都是正的。分析了\ensuremath{\epsilon}${\ensuremath{\rightarrow}}_{2}$(\ensuremath{\omega})，、$^{(2)}$(-2\ensuremath{\omega}；\ensuremath{\omega}，的显著特点，并对其进行了分析，提出了一种新的算法。确保数学{\omega}、\保证数学{\omega}、\保证数学{\omega})覆盖广泛的频率范围。结果表明，在二阶和三阶光学响应函数中，弱光学跃迁的影响比在线性响应函数中要明显得多。
We report full-band-structure calculations of the frequency-dependent second- and third-harmonic response functions of ZnSe, ZnTe, and CdTe, as well as our results for the dielectric function of these semiconductors. We use a linear combination of Gaussian orbitals technique, in conjunction with the X\ensuremath{\alpha} method, to obtain the energy band structures and optical matrix elements of each material. The expressions for \ensuremath{\epsilon}\ensuremath{\rightarrow}(\ensuremath{\omega}) and \ensuremath{\chi}\ensuremath{\rightarrow} $^{(2)}$(-2\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega}) are evaluated utilizing a linearized sampling method for integrating over an irreducible segment of the Brillouin zone; the expression for \ensuremath{\chi}\ensuremath{\rightarrow} $^{(3)}$(-3\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega}) is evaluated using a random-sampling method. The results of our calculations of \ensuremath{\epsilon}${\ensuremath{\rightarrow}}_{2}$(\ensuremath{\omega}) are in good agreement with experimental results. Our calculated value of ${\mathrm{\ensuremath{\chi}}}_{14}^{(2)}$(0)=24.8\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$ esu for CdTe is in excellent agreement with the measured value [G. H. Sherman and P. D. Coleman, J. Appl. Phys. 44, 238 (1973)] of ${\mathrm{\ensuremath{\chi}}}_{14}^{(2)}$(\ensuremath{\lambda}=28 \ensuremath{\mu}m)=(28\ifmmode\pm\else\textpm\fi{}11)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$ esu. We argue that the experimental results for ${\mathrm{\ensuremath{\chi}}}_{14}^{(2)}$(\ensuremath{\lambda}=10.6 \ensuremath{\mu}m) of ZnSe and ZnTe [C. K. N. Patel, Phys. Rev. Lett. 16, 613 (1966)] are likely to be inaccurate and that there is a need for additional measurements. Our calculations show that both \ensuremath{\chi}\ensuremath{\rightarrow} $^{(2)}$(0) and \ensuremath{\chi}\ensuremath{\rightarrow} $^{(3)}$(0) are positive for the materials considered in this work. We analyze the prominent features of \ensuremath{\epsilon}${\ensuremath{\rightarrow}}_{2}$(\ensuremath{\omega}), \ensuremath{\chi}\ensuremath{\rightarrow} $^{(2)}$(-2\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega}), and \ensuremath{\chi}\ensuremath{\rightarrow} $^{(3)}$(-3\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega}) over a wide range of frequencies. Our results indicate that the effects of weak optical transitions are much more pronounced in the second- and third-order optical response functions than in the linear-response functions.