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Band Theory & Optical Properties in solids. Band Theory.
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Band Theory Useful way to visualize the difference between conductors, insulators and semiconductors is to plot the available energies for electrons in the materials. Instead of having discrete energies as in the case of free atoms, the available energy states form bands where m* is called the effective mass
Electronic propertiesEnergy Bands models for solids • The last completely filled (at least at T = 0 K)band is called the Valence Band • The next band with higher energy is the Conduction Band • The Conduction Band can be empty or partially filed • The energy difference between the bottom of the CB and the top of the VB is called the Band Gap (or Forbidden Gap)
Energy Bands for Solids An important parameter in the band theory is the Fermi level, the top of the available electron energy levels at low temperatures. The position of the Fermi level with the relation to the conduction band is a crucial factor in determining electrical properties.
Insulator Energy Bands Most solid substances are insulators, and in terms of the band theory of solids this implies that there is a large forbidden gap between the energies of the valence electrons and the energy at which the electrons can move freely through the material (the conduction band).
Conductor Energy Bands In terms of the band theory of solids, metals are unique as good conductors of electricity. This can be seen to be a result of their valence electrons being essentially free. In the band theory, this is depicted as an overlap of the valence band and the conduction band so that at least a fraction of the valence electrons can move through the material.
Semiconductor A semiconductor material is one whose electrical properties lie in between those of insulators and good conductors. Examples are: germanium and silicon. In terms of energy bands, semiconductors can be defined as those materials which have almost an empty conduction band and almost filled valence band with a very narrow energy gap (of the order of 1 eV) separating the two.
Intrinsic Semiconductors An intrinsic semiconductor is one which is made of the semiconductor material in its extremely pure form. Examples of such semiconductors are: pure germanium and silicon which have forbidden energy gaps of 0.72 eV and 1.1 eV respectively. The energy gap is so small that even at ordinary room temperature; there are many electrons which possess sufficient energy to jump across the small energy gap between the valence and the conduction bands Alternatively, an intrinsic semiconductor may be defined as one in which the number of conduction electrons is equal to the number of holes. Schematic energy band diagram of an intrinsic semiconductor at room temperature is shown in Fig. below. Fermi level" is the term used to describe the top of the collection of electron energy levels at absolute zero temperature. the highest energy level which an electron can occupy the valance band at 0k is called fermi energy.
b. Extrinsic Semiconductors: Those intrinsic semiconductors to which some suitable impurity or doping agent or doping has been added in extremely small amounts (about 1 part in 108) are called extrinsic or impurity semiconductors. Depending on the type of doping material used, extrinsic semiconductors can be sub-divided into two classes: (i) N-type semiconductors and (ii) P-type semiconductors.
N-type semiconductor: • When a small amount of pentavalent donor atoms (e.g., phosphorus (P) and Arsenic (As)) is added, a silicon atom in the lattice may be replaced by a donor atom with four of its valence electrons forming the covalent bounds and one extra free electron. This is an N-type semiconductor whose conductivity is much improved compared to the intrinsic semiconductors, due to the extra free electrons in the lattice, which are called predominant or majority current carriers. There also exist some tiny number of holes called minority carriers.
P-type semiconductor: • When a small amount of trivalent acceptor atoms (e.g., boron (B) and aluminum (Al)) is added, a silicon atom in the lattice may be replaced by an acceptor atom with only three valence electrons forming three covalent bounds and a hole in the lattice. This is a P-type semiconductor whose conductivity is also much improved compared to the intrinsic semiconductors, due to the holes in the lattice, which are called predominant or majority current carriers. There also exist some tiny number of free electrons called minority carriers.
P-N Junction Diode • Construction ; It is two terminal devices consisting of a P-N junction formed either in Ge or Si crystal. It is circuit symbol is shown in fig. (3.2-a). The P and N type regions are referred to as anode and cathode respectively. In fig. (1-b) arrowhead indicates the conventional direction of current flow when forward • biased. It is the same direction in which hole flow takes place. • Fig.3.2 • Working; A P-N junction diode is a one way device offering low resistance when forward biased and behaving almost as an insulator when reverse biased. Hence such diodes are mostly used as rectifiers for converting alternating current into direct current.
Semiconductor Energy Bands There are two cases; · Direct gap; · Indirect gap;
Temperature dependence of the energy bandgap The energy bandgap of semiconductors tends to decrease as the temperature is increased. The temperature dependence of the energy bandgap, Eg, has been experimentally determined yielding the following expression for Eg as a function of the temperature, T:
