Quantum Inf Process (2017) 16:57
The inﬂuence of temperature on the average number of
optical phonons in a polar slab of semiconductors
Received: 26 April 2016 / Accepted: 4 November 2016 / Published online: 21 January 2017
© Springer Science+Business Media New York 2017
Abstract The effects of temperature T , average number of optical phonons N ,the
phonon frequency ω and slab thickness d in a polar slab were investigated using the
linear combination operator and unitary transformation methods. The results showed
that the phonon frequency ω increases with increasing temperature T , but the average
number of optical phonons N and phonon frequency ω decreases with the increase in
slab thickness d. When the slab thickness is <5nm, N decreases sharply, and when
the slab thickness is <10 nm, the phonon frequency ω and slab thickness d changed
Keywords Temperature · Polaron · Mean number of optical phonons · Polar slab
With the fast development of the epitaxial technique and the manufacturing of semi-
conductor materials in recent years, considerable interest has been focused on the
investigation of the polar slab, quantum well and semiconductor superlattice because
of their wide range of applications.
Licari and Evrand  have deduced the Hamiltonian of the electron–phonon
interaction in a slab, which includes the interactions between electrons and bulk
This article is part of topical collection on Trapped Ion Quantum Information Processing.
Foundation item: Project Supported by Inner Mongolia University for the Nationalities (NJZY174).
College of Physics and Electromechanics, Inner Mongolia National University,
Tongliao 028043, China