The previous lecture showed that a sequence of N wells confined by N+1 barriers results in the formation of band-like transmission coefficients. Each of the bands contains N individual transmission peaks and their energy dependence forms a cosine-like dispersion. This lecture compares this dispersion to the one obtained in a periodic potential model that is made up of a periodic structure, in effect an infinite number of wells. It is found that the two significantly different methodologies predict almost identical results.
The infinite periodic structure Kroenig Penney model is often used to introduce students to the concept of bandstructure formation. It is analytically solvable for linear potentials and shows critical elements of bandstructure formation such as core bands and different effective masses in different bands. For realistic heterostructure superlattice engineering however, the finite barrier structure analysis is much closer to reality and the formation of a discrete bandstructure that approaches the infinite periodic bandstructure with just a few quantum wells is reassuring.
The presentation also compares the finite superlattice calculations using the transfer matrix method and the discretized effective masss method (single band tight binding) and virtually identical results are found for the ideal structures.
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Università di Pisa, Pisa, Italy
- band structure
- course lecture