INTRINSIC SEMICONDUCTORS

Silicon Crystal and Energy Band Diagram

The electronic configuration of an isolated Si atom is [Ne]3s2p2. However, in the vicinity of other atoms, the 3s and 3p energy levels are so close that the interactions result in the four orbitals ^ (3s), ^ (3/?*), V’ (3 py), and ^ (3 pz) mixing together to form four new hybrid orbitals (called V’tyb) that are symmetrically directed as far away from each other as possible (toward the comers of a tetrahedron). In two dimensions, we can simply view the orbitals pictorially as in Figure 5.1a. The four hybrid orbitals, W» each have one electron so that they are half-occupied. Therefore, a V’hyb orbital of one Si atom can overlap a Vfyb orbital of a neighboring Si atom to form a covalent bond with two spin-paired electrons. In this manner one Si atom bonds with four other Si atoms by overlapping the half-occupied xlrhyb orbitals, as illustrated in Figure 5.1b.

INTRINSIC SEMICONDUCTORS

V’hyb orbitals

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INTRINSIC SEMICONDUCTORS
INTRINSIC SEMICONDUCTORS

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INTRINSIC SEMICONDUCTORS INTRINSIC SEMICONDUCTORS

Figure 5.1

A simplified two-dimensional illustration of a Si atom with four hybrid orbitals T/^yb – Each orbital has one electron.

A simplified two-dimensional view of a region of the Si crystal showing covalent bonds.

The energy band diagram at absolute zero of temperature.

Figure 5.2 A two-dimensional pictorial view of the Si crystal showing covalent bonds as two lines where each line is a valence electron.

INTRINSIC SEMICONDUCTORSEach Si-Si bond corresponds to a bonding orbital, yjrB, obtained by overlapping two neighboring V^hyb orbitals. Each bonding orbital (jfB) has two spin-paired electrons and is therefore full. Neighboring Si atoms can also form covalent bonds with other Si atoms, thus forming a three-dimensional network of Si atoms. The resulting structure is the Si crystal in which each Si atom bonds with four Si atoms in a tetrahedral arrangement. The crystal structure is that of a diamond, which was described in Chapter 1. We can imagine the Si crystal in two dimensions as depicted in Figure 5.1b. The electrons in the covalent bonds are the valence electrons.

The energy band diagram of the silicon crystal is shown in Figure 5.1c.[13] The vertical axis is the electron energy in the crystal. The valence band (VB) contains those electronic states that correspond to the overlap of bonding orbitals (irB). Since all the bonding orbitals (V^) are full with valence electrons in the crystal, the VB is also full with these valence electrons at a temperature of absolute zero. The conduction band (CB) contains electronic states that are at higher energies, those corresponding to the overlap of antibonding orbitals. The CB is separated from the VB by an energy gap Egy called the bandgap. The energy level Ev marks the top of the VB and Ec marks the bottom of the CB. The energy distance from Ec to the vacuum level, the width of the CB, is called the electron affinity x* The gen­eral energy band diagram in Figure 5.1c applies to all crystalline semiconductors with appropriate changes in the energies.

The electrons shown in the VB in Figure 5.1c are those in the covalent bonds be­tween the Si atoms in Figure 5.1b. An electron in the VB, however, is not localized to an atomic site but extends throughout the whole solid. Although the electrons appear localized in Figure 5.lb, at the bonding orbitals between the Si atoms this is not, in fact, true. In the crystal, the electrons can tunnel from one bond to another and exchange places. If we were to work out the wavefunction of a valence electron in the Si crystal, we would find that it extends throughout the whole solid. This means that the electrons in the covalent bonds are indistinguishable. We cannot label an electron from the start and say that the electron is in the covalent bond between these two atoms.

We can crudely represent the silicon crystal in two dimensions as shown in Figure 5.2. Each covalent bond between Si atoms is represented by two lines corre­sponding to two spin-paired electrons. Each line represents a valence electron.

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