Kronig Penney Model | Extended, Reduced and Periodic zone scheme | Part 5 скачать в хорошем качестве

Kronig Penney Model | Extended, Reduced and Periodic zone scheme | Part 5

Kronig Penney Model Right hand side cos ka of equation is an even periodic function and its value does not change whether ka is positive or negative or it is increased by integer multiple of 2π. As a result, total energy E of the electron is an even periodic function of k with period 2π / a. This periodic repetition of energy is shown in Fig 5.2.6a. This may be considered as obtained by the repetition of the region -π/a and π/a, this is the first brillouin zone. This representation is known as repeated or periodic zone scheme but the disadvantage in this case is that we obtain a larger k values corresponding to a particular energy values E. However, these are two other schemes viz. extended zone scheme and reduced zone scheme. We find that discontinuties occur at k = ± nπ/a where n = 1,2,3... These k values define the boundaries of the first, second and third Brillouin zones. #learningscience #crystalstructure #kronigpenneymodel #bandtheoryofsolids #extendedzonescheme #reducedzonescheme #periodiczonescheme