reverse-biasing (-ve terminal of the battery connected to p-type having positive vacancies as majority carriers and +ve terminal of the battery connected to n-type having electrons majority carriers), zero current flows initially virtually. A schematic of the two biasing regimes, reverse Figure 1.8(a) and forward Figure 1.8(b). Only a small amount of current flows on increasing the reverse potential through the battery terminals. At a critical value of the reverse bias, the current suddenly increases which is called as the junction breakdown. The diode response is achieved at relatively lower voltages (~1 V) in forward-biasing case as shown in Figure 1.8(b). In reverse-bias, the breakdown voltage or reverse critical voltage generally varies from few volts to larger voltages. This is typically dependent on the amount of doping of foreign atoms to form two types of semiconductor blocks or layers and different device parameters [10].
Figure 1.6 Space charge region formed in between the joining region of p-type and n-type semiconductor blocks is shown in (a). The energy band diagram of a p-n semiconductor junction in thermal equilibrium is shown in (b).
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