Phonon Assisted Optical Absorption in an Electric Field

The optical absorption in crystals caused by interband transitions of electrons is altered in the presence of an external electric field (electro‐absorption effect). The theory presented here treats the effect for indirect (phonon‐assisted) transitions neglecting electron‐hole interaction. The transition rate is computed using a time dependent second order perturbation procedure based on the Houston representation for a lattice electron in an electric field. The theory yields a formula for the optical absorption as a function of the photon energy ħ ω which consists of two principal terms. The first one is just the usual zero field absorption rising from a threshold E proportional to (ħ ω ‐ E)2. The second term varies oscillatory (with decreasing amplitude) for ħ ω > E and falls off exponentially for ħ ω < E. The magnitude of the second term increases as the 4/3 power of the field strength in distinction to the shift of the zero values above the threshold and the width of the exponential decay below the threshold which increase as the 2/3 power of the field strength. In addition, the theory provides another absorption term of oscillatory structure (“Stark‐ladder”). However, this contribution vanishes if electron collisions are taken into account, their occurrence being, in fact, a necessary condition to prevent the crystal from electrical breakdown.