Reduced effective mass

EXAMPLE 4.5 From the absorption spectrum in Figure 4.14, determine (a) the energy gap of CU2O, (b) the reduced effective mass of the exciton, assuming By = 10, and (c) the Bohr radius of the exciton n = 2. 

The effective mass model is based on the energy of the lowest-energy par-ticle-in-a-box configuration, taking into account that the relevant mass term is given by a reduced effective mass, p, where p, is given by... 

Fig. 10.5 Experimentally measured values of bandgap of PbSe films (horizontal bars The length gives the experimental uncertainty in size, mainly due to the size distribution). The broken curve gives the theoretical relationship between bandgap and crystal size based on the hyperbohc band approximation used for PbS in Ref. 40. The room-temperature reduced effective mass (0.034) was calculated from the low-temperature value (0.022) (R. Dalven, Infrared Phys. 9 141, 1969.) according to the temperature dependence given in H. Preier, Appl. Phys. 20 189, 1979. The dotted curve is a more recent calculation based on an envelope function calculation [41].

Here, /Xexc is the reduced effective mass of the exciton, in terms of the free electron mass, and e is the dielectric constant. In addition, there are also Frenkel excitons, which are spatially more localized than Mott-Wannier excitons. They cannot be represented by a series formula. Therefore, Frenkel excitons have been assigned to single low-lying absorption bands in the near-edge regime of solid rare gases. 

Eg is the band gap of undoped saniconductor m e is the reduced effective mass, which is given by... 

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