Transitions between Electron Energy Bands in Solids

Transitions between Electron Energy Bands in Solids 

The assembly of atoms into an array to form a solid leads to the formation of bands of allowed states separated by an energy gap. This results from the fact that when 

the absorption coefficient a(hv) for a given photon energy hv is proportional to the probability, Pjf, for the transition from the initial state to the final state (governed also by the conservation of momentum), the density of electrons in the initial state, Wi, and also the density of electrons in the final states, Wf. This process must be summed for all possible transitions between states separated by an energy difference equal to hv  

By using the paraboUc valley model, an expression of a(hv) for each type of transition (allowed or forbidden in dependence on selection rules) has been obtained [25-27]. As a common feature, for crystalline solids, a(hv) appeared expressed in all cases in the form  

A plot of [a(hv)] against E(hv) (values of the energy range the absorption edge is spread over) should then result in a linear relationship, the intercept with the 

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