href="#ulink_cf50b559-aa69-5345-b768-1b97219f7458">Figure 1.7 Current-voltage (I-V) characteristics of a semiconductor p-n junction.
Figure 1.8 The two biasing regimes of a diode, (a) reverse (b) forward, are shown in the above schematic. In reverse bias, the diode acts as an open switch, while it acts as a closed switch in case of forward bias.
In the reverse bias mode, the diode device acts as an open switch such that the positive terminal of the source will attract free electrons from n-type and negative terminals will attract holes from the p-type. As a result, concentration of ions in both the regions will increase enhancing the width of the depletion region. In any case, minority carriers will enter the depletion region and cross to other sides of the junction causing a small amount of current called as reverse saturation current (IS). The term “saturation” here means that there will not be any enhancement in the current on increasing the reverse bias potential. As can be seen from Figure 1.7, current change happens very quickly in small voltages initially reaching the saturation current and dependency of the current on further changes in voltages is lost. At a certain higher critical reverse voltage, usually after tens of voltages, a huge current is caused in the opposite direction. On increasing the reverse voltage, it creates an electric field impacting greater force on the electrons to move faster and an enhancement in kinetic energy (K.E.) of electrons follows. This higher K.E. is transported to valence shell of electrons of stable atoms by highly mobile electrons causing them to leave the atom and form the stream of reverse current flow. The critical voltage at which this rapid change happens is called the Zener voltage.
In forward biasing mode, an electric field forces free electrons in n-type block and holes in p-type block towards the depletion region. In this biasing, holes and free electrons recombine with ions in the depletion region to reduce the width of the depletion region. On increasing the forward voltage further, depletion region becomes thinner and a larger number of majority carriers are able to pass through the barrier. It needs to be pointed out that no net current flows in the diode in absence of an externally applied electric field.
1.1.3.1 Equilibrium Fermi Energy (EF)
In the state of thermal equilibrium, the individual hole and electron streams passing through the barrier are ideally zero. The state of thermal equilibrium can be defined as the steady-state condition at a given temperature when no externally applied field is present. In this case, the net current density due to both drift and diffusion currents should be zero for both holes and electrons. Thus, net current density for holes is given as [10,11,23,24],
(1.1)
where,
The expression for hole concentration,
Differentiating equation (1.3) with respect to x in the equilibrium condition,
From equation (1.2) with the help of equation (1.4),
(1.5)
Similarly, net current density for electrons is given as follows,
(1.7)
(1.8)
(1.9)
Hence,
It is apparent from equations (1.6) and (1.10) that the Fermi level (EF) is not dependent on x and remains uniform in whole of the semiconductor sample for zero net hole and electron densities. This is also apparent from the band diagram as shown in Figure 1.6(b). A typical space charge distribution happens at the barrier due to uniform EF in the steady state. Considering the 1D p-n junction when all donor and acceptor atoms are ionized, Poisson’s equation for electrostatic potential ψ and unique space charge distribution is given as follows [10,23,24],
The above situation is well represented in Figure 1.9(a) in the energy band diagram of an abrupt junction in the steady state. There is a unique space charge distribution at the semiconductor junction. At distances far away from the barrier, net hole density is equal to the net electron density such that the total space charge density is zero maintaining the charge neutrality. In this case, from equation (1.11) [10,11,23,24],
(1.12)
and,
In case of a p-type neutral region, ND = 0 and p >> n. Now, setting ND = n = 0 in equation (1.13), we get, p = NA and putting
