Scaling rules for multiphoton interband absorption in semiconductors

A quasi-dimensional analysis is presented for the N-photon interband absorption coefficients (KN) of direct-gap semiconductors. Regardless of the value of N, we show that KN∝(e2ℏc)NℏN-1P2N-3nNEg4N-5FN(NℏωEg),where FN varies little over the relevant range of radiation frequencies. The dominant material dependence of KN is through the energy-gap factor; the N-photon coefficient decreases as Eg4N−5.