Band Structure of Silver Chloride and Silver Bromide

The valence and conduction bands of silver chloride and silver bromide were calculated using the augmented-plane-wave (APW) method. For both crystals the calculated bands were adjusted so that the experimental value of the direct band gap at $\Gamma$ was duplicated ($E_g=5.13\mathrm{}$ eV in AgCl, $E_g=4.29\mathrm{}$ eV in AgBr). Several possible correction terms to the APW potential were considered. The effects of the nonspherical cubic field inside APW spheres and the varying cubic field outside the spheres were negligible. The mass-velocity correction was large for states which arise from the ${\mathrm{Ag}}^{+}\mathrm{}\left(4d\right)\mathrm{}$ electron. The calculated indirect band gaps were 3.28 and 2.89 eV for AgCl and AgBr, respectively. These values are within 10% of the experimental values. The indirect gap may occur along the [110] direction or at the point $L$.