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June 16th, 2019

To this point, the discussion has been concerned with the general properties of semiconductors. However, the primary subject of this chapter is a semiconductor device, namely the photovoltaic cell. The basis for most semiconductor devices is the p-n junction, which forms between p and n-type semiconductors. A p-n junction can be formed in a p-type semiconductor by diffusing an n-type donor dopant into the p semiconductor. Similarly, a p-n junction can be formed in an n-type semiconductor by diffusing a p-type acceptor into the n semiconductor.

Figure 5.5 illustrates what happens when a junction is formed between p and n – type semiconductors. When the semiconductors are isolated, as in Figure 5.5a, the Fermi level, Ef, of the uniformly doped p-type semiconductor lies near the top of the valence band energy, EV. Similarly, the Fermi level of the uniformly doped n-type material lies close to the bottom of the conduction band, Ec. When the two materials are joined the large carrier density gradients (Vn and Vp) cause carrier diffusion. Holes from the p-type material diffuse into the n-type material leaving behind negative acceptor ions, Na, near the junction. At the same time, electrons diffuse from the n – type material into the p-type material leaving behind positive donor ions, ND, near the junction. Thus, an electric field is produced in the direction of the p-type material as shown in Figure 5.5b. As a result of the junction formation, the energy band diagram is as shown in Figure 5.5b. The Fermi energy, Ef, remains constant throughout the junction for steady state, equilibrium conditions as can be shown as follows.

At steady state, equilibrium conditions the net current flow for electrons and holes must be zero. Hence, the electrons that diffuse from n to p, are balanced by electrons that drift from p to n. Similarly, holes that diffuse from p to n are balanced by holes that drift n to p. For electrons from equation (5.56),

Jn = epn є + |i nkBTVn = 0 (5.82a)

where equation (5.59a) is used for Dn. Hence,

where – ee is the force acting on the electron. The force is also equal to minus the gradient in the potential energy of the electrons in the conduction band, En.

-ee = – VEn = – VEc (5.83)

Since the force is the same for all electrons in the conduction band VEn = VEc, where Ec is the energy at the bottom of the conduction band. Now use equation (5.41) to Vn

calculate —— . Substituting that result and equation (5.83) in equation (5.82) produces

n

the following result.

VEf = 0

Therefore, Ef is a constant. The same result can be obtained based upon the hole current condition, Jp = 0 (problem 5.4).

Because of the electric field, є, there is an electric potential difference across the junction. This potential difference, Vb, is called the built-in potential. For steady state conditions or no magnetic field, Faraday’s Law [equation (1.2)] allows the electric field to be defined as,

є = – VV (5.85)

where V is the electric potential. From equations (5.83) and (5.85) the following is obtained.

E

V =—— (5.86)

e

Thus, referring to Figure 5.5b the built-in potential, Vb, is the following,

eVb = Ec – Ev – Et – E2 = Eg – Et – E2 (5.87)

where Eg is the bandgap energy, E1 = Ef – EV and E2 = Ec – Ef. E1 is given by equation (5.51). Therefore,

Also, Eg can be expressed in terms of n;, Nv, Nc, and kBT by using equation (5.47). Hence, VB can also be written as follows.

As equation (5.88) indicates, p-n junctions in semiconductors with the largest bandgap energies and the highest doping levels have the largest built-in potentials. For Si, Vb ranges from 0.4 to 1 eV, and for GaAs, Vb ranges from 1 to 1.4 eV in going from dopant levels from 1014 to 1018cm-3. It is the electric field resulting from the built-in potential that sweeps minority carriers produced by incident radiation across the junction in a PV cell. Minority electrons in the p region are injected into the n region,

and minority holes in the n region are injected into the p region. These minority electron and hole currents make up the total current that is supplied to the load.

The region around the junction is called the space charge region or depletion region. It this region that fixed positively charged donor and negatively charged acceptor ions produce the space charge electric field. Nearly all mobile charge carrier electrons and holes are depleted from this region.

5.4 Current-Voltage Relation for an Ideal Junction in the Dark

Consider how a p-n junction, as shown in Figure 5.6, behaves if an electric potential is applied. If a potential Vf is applied to the p side of the junction, as shown in Figure 5.6a, it is called forward bias. If a potential Vr is applied to the n side of the junction, as shown in Figure 5.6b, it is called reverse bias. For the forward bias condition, the net potential across the junction will be Vb – Vf. The applied Vf reduces the built-in electric field, which reduces the drift currents of electrons and holes. Thus, the balance between diffusion current and drift current existing at equilibrium is disturbed. As a result, holes from the p side diffuse into the n side and electrons diffuse from the n side into the p side. Thus, minority carrier injection occurs. Minority electrons are injected into the p side, and minority holes are injected into the n side. This results in a current flow from the p side to the n side. Under reverse bias, Vr, the potential across the junction increases to Vr +Vb from Vb under equilibrium conditions. The resulting increased electric field increases the electron and hole drift currents moving from the n side to the p side so that they exceed the electron and hole diffusion currents moving in the opposite direction. As a result, reverse bias produces a small reverse current moving from the n to the p side.

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