The bound polaron in a cylindrical quantum well wire with a finite confining potential

The phonon modes of a quantum well wire, formed by a cylindrical polar semi conductor 1 (well material) (rho < R-1) embedded in another polar semicondu ctor 2 (barrier material) (R-1 <less than or equal to> rho < R-2), were stu died by using the dielectric continuum model. The confined longitudinal opt ical phonon modes both in the wire (LO1) and in the barrier materials (LO2) and the interface optical (IO) phonon modes as well as the corresponding e lectron-phonon interaction Hamiltonians are derived. With a two-parameter v ariational trial wave function, the bound-polaron binding energy has been c alculated numerically for different confining potential heights and wire ra dii. The result shows that the electron-phonon interaction can greatly modi fy the impurity binding energy. The IO modes are the main factor contributi ng to the modification. The influence of the LO1 modes increases as the wir e radius increases and reaches the bulk limit at large wire radius, while t he LO2 modes only show their influence at narrow wire radius.