Semiconductor quantum dots: Theory and phenomenology

Research in semiconductor quantum dots (q-dots) has burgeoned in the past d ecade. The size (R) of these q-dots ranges from 1 to 100 nm, Based on the t heoretical calculations, we propose energy and length scales which help in clarifying the physics of this mesoscopic system. Some of these length scal es are: the Bohr exciton radius (a(B)*), the carrier de Broglie and diffusi on length (lambda(D) and l(D)), the polaron radius (a,), and the reduction factor modulating the optical matrix element (M-x). R<a(B) is an individual particle confinement regime, whereas the larger ones are exciton confineme nt regime wherein Coulomb interaction play an important role. Similarly a s ize-dependent dielectric constant epsilon(R) Should be used for R<a(p)<a(B) . An examination of Mr reveals that an indirect gap material q-dot behaves as a direct gap material in the limit of very small dot size, We have carri ed out effective mass theory (EMT) calculations to estimate the charge dens ity on the surface of the quantum dot. We present tight binding (TB) calcul ation to show that the energy upshift scales as 1/R-x, where x is less than 2 and the exponent depends on the orientation of the crystallite.