Bir-Pikus parameters

A6.4 Luttinger and Bir-Pikus parameters of GaN and AIN A6.5 Electron and hole effective masses of GaN and AIN A6.6 Deformation potentials of GaN and AIN A6.7 Momentum matrix elements of GaN A6.8 Subband structures of GaN/AlGaN quantum wells A6.9 Optical gain of bulk GaN and GaN/AlGaN quantum wells... 

TABLE 1 Bir-Pikus parameters of wurtzite GaN and AIN. All values except A7 are in units of h2/2mo. 

Here are Luttinger parameters, and me is an electron effective mass, av, b, d and ac are Bir-Pikus deformation potentials. As0 is a spin-orbit splitting energy. L and a denote orbital and spin angular momentum operators, respectively. [Lf, LJ is defined as [Lf, LJ = (LjLj + LjLj)/2. The summation of i,j runs through x, y, z. 

Here Ai are inverse mass parameters in WZ structure, corresponding to Luttinger parameters in ZB structure, me11 and me1 are k-dependent electron effective masses. D , aic and a2c are Bir-Pikus deformation potentials. Ai and 3A2,3 correspond to the crystal-field and spin-orbit splitting energies, respectively. The definition of several operators is given as L+ = (U iLy)/V2, a+ = (ax iay)/2,... 

The shift of the A line in the epilayers has been connected with the variation of the lattice parameters of GaN [1,11,12], The shift of this line was also measured in samples subjected to hydrostatic pressure (see Datareview A3.1). Combination of all these data permits one to obtain the whole series of excitonic deformation potentials [6,16], Two sets of data are available which are consistent with each other and are given in TABLE 1. The discrepancies between them are linked to the differences in the values of the stiflhess coefficients of GaN used by the authors. Gil and Alemu [6] in their work subsequent to the work of Shan et al [16] used data not available when Shan et al calculated their values. The notations are the same and are linked to the relationship with the quasi cubic model of Pikus and Bir [17], Deformation potentials as and a6 have been obtained by Alemu et al [8] who studied the anisotropy of the optical response in the growth plane of GaN epilayers orthorhombically distorted by growth on A-plane sapphire. For a detailed presentation of the theoretical values of deformation potentials of GaN we refer the reader to Suzuki and Uenoyama [20] who took the old values of the stiflhess coefficients of GaN [21]. 

Expanding the transformed operator H( ) = UH( )U l in a power series with respect to the preceding small parameter and keeping the terms up to the second-order ones, one can obtain the following expression for the matrix elements of the operator H ) in the basis of the vibronic states of the ground electronic term (Bir and Pikus, 1971) ... 

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