Advanced Solid State Physics

Figure 38: Lattice, primitive lattice vectors and reciprocal lattice of of graphene the energy shift (in a covalent bond) we des ...

Figure 39: Plot energy versuskxandky(2 dimensions). 7.2.5 Carbon nanotubes Carbon nanotubesare made of a sheet ofgraphenerolled ...

Figure 41: How to specify the kind of a nanotube. graphene out perpendicular to this line and role it up so that the end point f ...

band line corresponds toky = 0and it touches the band above at a certainkxpoint. If we increase kya little bit what happens is t ...

cell the energy of the bonding and antibonding state is never the same - there is always a band gap - boron nitride is always a ...

7.3 Bandstructure of Metals and Semiconductors Metals In a metal there are a bunch of bands that are electrically inert. They ar ...

Semiconductors In a semiconductor bands that are filled are also electrically inert. But now the fermi energy falls in between t ...

Semimetal A semimetal is a metal where the fermi energy is in the band but the electron density is pretty low. The right plot in ...

In fig. 48 the periodic table is shown with the tagged d- and f-band metals. For calculating the band structure of these metals ...

Fig. 49 displays the band structure of the transition metals (the dotted line is the fermi energy). From the left to the right t ...

How to calculate the Fermi Energy: One possibility to calculate the fermi energy of a certain material is to construct it straig ...

7.4 Direct and Indirect Bandgaps Generally semiconductors can be divided into two types. There are semiconductors with direct ba ...

Figure 53: Band structure of Silicon, example for indirect bandgaps Figure 54: Band structure of Gallium Arsenide, example for d ...

8 Crystal Physics The main subject of Crystal Physics is how the symmetries of the crystal affect the physical properties. Knowl ...

Figure 56: Forces applyable in the x-direction orthogonal direction. We can define a stress tensor: σkl =    Xx Ax Xy Ay Xz ...

For every system, on which we would like to perform experiments, using the extrinsic variables as the independent ones isn’t a g ...

Elastic deformation (stiffness tensor) Reciprocal piezo-electric effect Reciprocal piezo-magnetic effect Thermal dilatation 8. ...

Direct and reciprocal effects In the exact same way we can find relationships between direct and reciprocal effects. As an examp ...

E =    1 0 0 0 1 0 0 0 1   , C 4 =    0 −1 0 1 0 0 0 0 1   , C 2 =    − 1 0 0 0 −1 0 0 0 1   , C 43 =    0 ...

number of indices, crystallographers very often combine pairs of two indices using the following scheme: 11 →1 12→6 13→ 5 22 →2 ...