By Professor Dr. Peter Y. Yu, Professor Dr., Dres. h.c. Manuel Cardona (auth.)
ISBN-10: 366203848X
ISBN-13: 9783662038482
ISBN-10: 3662038501
ISBN-13: 9783662038505
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Additional resources for Fundamentals of Semiconductors: Physics and Materials Properties
Sample text
The crystals in (a) and (c) are assumed to be three dimensional, although only one layer of atoms is shown for the purpose of illustration. If they are two dimensional, the glide operation in (c) becomes equivalent to that of the diad screw in (a). (0 and ® represent arrow pointing towards and away from the reader, respectively of a factor group. Let G be the space group and T its subgroup consisting of all purely translational symmetry operations. Let C = {a,,B, . } be the complex of all the elements of G not in T.
1]. The band structure plot resulting from restricting the wave vector k to the first Brillouin zone is known as the reduced zone scheme. In this scheme the wave functions are indexed by an integer n (known as the band index) and a wave vector k restricted to the first Brillouin zone. In Fig. 1 the band structure of a "nearly free" electron (i. , V -; 0) moving in a one-dimensional lattice with lattice constant a is shown in both schemes for comparison. Band structures are plotted more compactly in the reduced zone scheme.
It can be shown that there are 32 distinct crystallographic point groups in three-dimensional space (see, e. g. 3]). Of a total of 230 space groups there are only 73 symmorphic space groups. Thus the simpler, symmorphic space groups are more often the exception rather than the norm. We will now consider how to analyze the rotational symmetries of nonsymmorphic space groups. By definition, a nonsymmorphic space group must contain at least one symmetry operation that involves both translation and rotation such that the rotational operation is not a symmetry operation of G by itself.
Fundamentals of Semiconductors: Physics and Materials Properties by Professor Dr. Peter Y. Yu, Professor Dr., Dres. h.c. Manuel Cardona (auth.)
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