THE DEFORMATION EFFECTS CAUSED BY ELECTRONS IN ATOMIC LATTICES

Abstract

The only previous work known to us on the polaron problem in atomic lattices gives a result which would mean that polarons of the adiabatic type (in the first approximation, a self-trapping state with static deformation) should exist in crystals such as Ge and Si. (The method used in dealing with the elastic energy is shown to be in error.) We have reconsidered the problem and found that most probably the reverse is the case. The problem is then investigated on the basis of the perturbation theory. It is shown that the volume change, strongest at the electron, extends essentially as far as one de Broglie wave length of an electron moving with the speed of sound; beyond this distance, the elastic displacement is of the 1/r2 type. The volume changearound the electron totals E/(a+4/3μ)(E being the deformation potential constant, a and μ beingrespectively the bulk and shear molulus). This local volume change induces a uniform strain in the specimen, the two effects together gives a total volume change E/a. The elastic deformation caused by an electron in a hydrogen-like impurity state is also considered. The total volume effect turns out to be identical with the above. The effect is quite considerable; for instance, it can be comparable with the observed volume change caused by a Ⅲ,Ⅴ type of impurity atom in a Ge or Si lattice. Energy change of a low speed electron in a conduction band is roughly ((electron mass)/(mass of lattice cell))(E/(kΘD))E which amounts to 0.001-0.1 eV for E=1-10 eV in Ge. The corresponding change in effective mass is 1/1000-1/10 electron mass. The energy change for an electron in a hydrogen-like impurity state is much smaller, it thus appears theoretically possible that the electron-lattice interaction may render an impurity state unstable against ionization!