Volume 2, number 43 MATERIALS LETTERS May 1984 CONDUCT~ITY IN SEMICONDUCTORS INDUCED BY VIBRATIONALTO-ELECTRONIC ENERGY TRANSFER Isidore LAST zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Applied Mathematics, Soreq Nuclear Research Center, Yavne, 70600 Israel and Thomas F. GEORGE and David S. PERRY Department of Chemistry, University of Rochester, Rochester, NY 14627, USA Received 15 March 1984 A theoretical approach is presented for vibrational-to-electronic energy transfer at a semiconductor surface due to an impinging polar molecule. Results for the HCl t InSb and HCI + PbSe systems under thermal conditions indicate transition probabilities in the range 0.1 to lo%, which can be readily observed by experimental measurements of the semiconductor electrical conductivity. 1. Introduction A vibrationally-excited polar molecule located at some distance R from a solid surface can transfer its vibrational energy to the solid-state electrons [ 11. In the case of semiconductors, the valence-band elec- trons can be excited to the conduction band if the vibrational zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA energy level spacing E, is larger than the energy gap. The resulting electron-hole pair forma- tion is detectable by measuring the semiconductor electrical conductivity. In section 2, we summar~e a theoretical approach designed to treat vibrational-to- electronic energy transfer at a semiconductor surface. The results of calculations for the HCl + InSb and HCl + PbSe systems are presented in section 3, along with a discussion of the appropriate exper~ent~ conditions for verifying the results. 2. Theory For sufficiently large R one can neglect the over- lap between the orbitals of the molecule and the solid state and consider the molecule as a point di- pole with an electrostatic interaction with the solid. As this interaction is a weak perturbation, one can use the golden rule to express the transition probabili- ty as the integral over the energy levels involved in the transition, max EV P=2nd s min ~vQ@V~~C@V + EvI EV X R’2@v, EV +Ev), (1) where P is the probability per second, Ev is the vaf- ence-band electronic energy, qv and qc are the Ievel densities in the valence and conduction bands, respec- tively, and W is the matrix element for the transition from the excited vibrational state to the ground state with a s~ultaneous electronic transition from the valence band to the conduction band. The upper limit of integration, EraY, is the top electronic level of the valence band, and the lower limit is EFln = .I?$‘= - (E, - Eg), where Eg is the energy gap. The coeffi- cient s4 = mee4/A3 = 4.134 X 1016 is introduced in order to express all values within the integrand in atomic units and to obtain Pin s -1 . By the dipole approximation, W is given as a prod- uct of the dynamic dipole moment for the 1 -+ 0 tran- 0 167-577x/84/$ 03.00 0 Elsevier Science Publishers B.V. (North-HoIland Physics Publishing Divisions 315