Hyperspherical formulation of impurity-bound excitons in semiconductors

Abstract

A hyperspherical formalism is shown to be an appropriate approach for the investigation of the three-particle complex corresponding to an exciton bound to a Coulomb center in a semiconductor. The ground-and excited-state potential curves and binding energies are calculated as a function of the mass ratio of the hole and electron, and the concept of a critical mass is discussed. The results that we have obtained are in very good agreement with variational calculations for several semiconductor materials.

Binding energies of excitons trapped by ionized donors in semiconductors

“…28 -37 The application of this method for bound excitons without the nonadiabatic couplings has given good qualitative results. 13,14 Recently 15 a HS coupledchannel calculation has been performed, proving that this method also leads to very accurate results, with precision comparable to the variational energy values found in literature. Those results have been achieved for excitons bound to donor impurities in CdS ͓1/ϭ5 ͑Ref.…”

“…An alternative approach, i.e., the hyperspherical ͑HS͒ adiabatic method, has been used with efficiency to deal with systems with light holes. [13][14][15] This method brings together the high precision aspect of the variational calculation with the potential curves intuitive picture. The HS treatment is based on the use of hyperspherical coordinates, which are defined to correlate the radial variables of the electron (r e ) and hole (r h ) in an analogous way as the two-dimensional Cartesian coordinates are related to the polar coordinates.…”

Hyperspherical approach to description of electron correlation in negative ion of exciton

“…(6) and Eq. (8). The solution of the problem (6) gives the channel functions and the adiabatic potentials U~,(R).…”

“…The lower energy levels were obtained within the effective mass approximation in which effective masses were attributed to both electron and hole interacting through a Coulombian field in a semiconductor. Recently HCM was used for description of a negatively charged exciton [5][6][7][8].…”

“…where the brackets (fig) denote integration over independent angular variables on the surface of a sphere in the three dimensional space with the weight sin~a sin/9.For the solution of the boundary problem (6) the channel functions are presented as a series xv(R, a, 8) = ~-'~.gvnm(R)~flnm(OL,8) …”