Full-band-structure calculation of first-, second-, and third-harmonic optical response coefficients of ZnSe, ZnTe, and CdTe

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{α} method, to obtain the energy band structures and optical matrix elements of each material. The expressions for {ε}{→}({ω}) and {χ}{→} ⁽²⁾(-2{ω};{ω},{ω}) are evaluated utilizing a linearized sampling method for integrating over an irreducible segment of the Brillouin zone; the expression for {χ}{→} ⁽³⁾(-3{ω};{ω},{ω},{ω}) is evaluated using a random-sampling method. The results of our calculations of {ε}→₂({ω}) are in good agreement with experimental results. Our calculated value of χ₁₄⁽²⁾(0)=24.8×{}10^-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 χ₁₄⁽²⁾({λ}=28 {μ}m)=(28±{}11)×{}10^-8 esu. We argue that the experimental results for χ₁₄⁽²⁾({λ}=10.6 {μ}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 {χ}{→} ⁽²⁾(0) and {χ}{→} ⁽³⁾(0) are positive for the materials considered in this work. We analyze the prominent features of {ε}→₂({ω}), {χ}{→} ⁽²⁾(-2{ω};{ω},{ω}), and {χ}{→} ⁽³⁾(-3{ω};{ω},{ω},{ω}) 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.