Interband absorption of light in a semiconductor sphere

A very simple model is used to allow for the influence of size quantization on interband absorption in a semiconductor sphere. Expressions are obtained for the absorption coefficients of light in three limiting cases; when the radius of a semiconductor sphere a is less than the Bohr radii of electrons a, and holes a h ; when a h <a <a e ; finally, when a h <a and a e <a. It is shown that in the first two cases the short-wavelength shift of the maximum of the absorption coefficient is proportional to h 2 /m e a 2 , where m e is the electron mass. However, if the sphere radius obeys a<a e and e<a h , the shift is detemined by the total exciton mass M =m, + m, and it is proportional to h 2 /Ma 2 . The case of a mixture of spheres is considered and the distribution of the radii is described by the Lifshitz-Slezov formula.