The influence of temperature on the average number of optical phonons in a polar slab of semiconductors (Q2412581)

The paper is devoted to the study of the relationship between the temperature and the average number of optical phonons, the phonon frequency and slab thickness in a polar slab by using a linear combination operator and unitary transformation methods. First, it is assumed that the effective-mass approximation is valid and the Hamiltonian of the system, which includes the interactions of electrons and bulk longitudinal-optical (LO) phonons, and surface longitudinal-optical (SO) phonons in the slab, is written. Then the Lee-Low-Pines transformation is applied to this Hamiltonian. The system of electron-bulk LO phonon coupling weak but coupling strong with the surface longitudinal-optical (SO) phonons is used. The effect of the temperature is stated, based on the quantum statistical theory and the statistical average number of optical phonons is defined. As a result, the vibrational frequency, the average number of optical phonons, slab thickness, and the phonon frequency are related to the temperature. The numerical results show that the phonon frequency increases with increasing temperature, but the average number of optical phonons and phonon frequency decrease with the increase in slab thickness.