The Quasi-Hydrogenic Case

The effective Rydberg values for GaAs and InP in this table differ slightly from the ones 5.74 and 7.33 meV, respectively) given by [56]. 

Departure from the CB parabolicity results in a non-isotropic effective mass, whose value depends on the electron energy E in the CB. This is the main reason for the spread in the values of mn reported for semiconductors with CB minimum at k = 0, another being polaron coupling. Non-parabolicity has been addressed inter alia for w-GaN, without reference to a difference between mn// and mn . The most recent results give mn0 = 0.208 me at the CB edge (E = 0) and the increase of mn with E is given empirically by mn = mn0 (1 + 2KE/Eg), with K = 2.5 for GaN [60]. 

For c-GaN, the effective Rydberg value calculated for mn = 0.19me and s = 9.5 is 28.6 meV. For w-GaN, a difference between mn// and mn would produce a splitting of the n = 2 level into 2s, 2po and 2pm 1 1 states. Calculations including central-cell corrections have been performed by [42], resulting in Table 5.11. 

The splitting between the Is — 2p and Is — 2po transitions is due to the difference between the values of mn// and mni used for the calculation (0.19me and 0.22me, respectively), leading to a value of 7 1. This condition results in an energy of the 2po level, which is smaller than that of the 2p i level. 

4 This parameter is usually denoted by 7, but to avoid a confusion with the ratio of the transverse and longitudinal effective masses, it is denoted here by 7b. 

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