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Majority carrier electrons in the nregion will begin diffusing into the pregion and majority carrier holes in the pregion will be diffusing into the nregion. If we assume there are no external excitation to the semiconductor, then this diffusion process cannot continue indefinitely. As electrons diffuse from the nregion, positively charged donor atoms are left behind. Similarly, as holes diffuse from the pregion, they uncover negatively charged acceptor atoms. The unneutralized ions in the neighbourhood of the junction are referred to as uncovered charges. The general shape of the charge density ‘ρ’ depends upon how the diode is doped. Since the region of the junction is depleted of mobile charges, it is called depletion region, the spacecharge region, or the transition region.
The net positive and negative charges in ‘n’ and ‘p’ regions induce an electric fields in the region near the metallurgical junction, in the direction from the positive to the negative charge, or from the n to the p region.
Density gradients still exist in the exist in the majority carrier concentrations at each edge of the space charge region and producing a “diffusion force” that acts on the majority carriers as shown in Figure 1. The electric field in the space charge region produces another force on the electrons and holes which in the opposite direction to the diffusion force for each type of particle. In thermal equilibrium, the diffusion force and the field force exactly balance each other.
Below figure indicates the characteristic curve consisting of three distinct regions:
pn Junction characteristic Note: When PN junction is reverse biased, the reverse voltage must be always less than breakdown voltage of device, otherwise the normal diode will be damaged.
Let the PN junction is kept either open circuit condition or unbiased condition.
Mathematically,
V_{0} = V_{bi}
Note
The electric field across the junction has a fixed polarity called barrier potential or height of the barrier. A popular semiconductor device is formed using a pn junction called pn junction diode.
No Applied Bias (VD = 0V): In the absence of an applied bias voltage, the net flow of charge in anyone direction for a semiconductor diode is zero.
Forward Bias (VD > 0V):
R_{s} = Current Limiting Resistance
V_{D} = Forward Voltage across diode
By KVL we get:
V = V_{R} + V_{D}
V = I_{f} R_{s} + I_{f} R_{f}
R_{f} = Forward resistance of diode
The General formula of forward current, if (diode current) is:
So,
AqD_{p}/L_{p}N_{D }= If due to flow of holes from P side to N side
AqD_{n}/N_{A}L_{n}_{ }= If due to flow of electrons from N side to P side
Also,
The reverse saturation current in the Forward bias diode i
AqD_{p}/L_{p}N_{D }= If due to flow of holes from P side to N side
AqD_{n}/L_{n}N_{A}_{ }= If due to flow of electrons from N side to P side
A = Cross Sectional Area of Junction
Reverse Bias (V_{D} < 0V):
When PN junction is reverse biased, the width of the depletion layer increases.
Note: When PN junction is reverse biased the majority carries of P & N region will move away from the junction and this increases the region of IMMOBILE CHARGES i.e. the width of the depletion layer is increased.
We have found that a pn junction biased in the reverse direction exhibits a small, essentially voltageindependent saturation current. This is true until a critical reverse bias is reached, for which reverse breakdown occurs [Fig. (18)]. At this critical voltage (V_{Br}) the reverse current through the diode increases sharply, and relatively large currents can flow with little further increase in voltage. The existence of a critical breakdown voltage introduces almost a rightangle appearance to the reverse characteristic of most diodes.
Reverse breakdown in a pn Junction
The static resistance of a diode is defined as the ratio V/I of the voltage to the current. At any point on the voltampere characteristic of the diode the resistance R_{f} is equal to the reciprocal of the scope of a line joining the operating point to the origin.
For smallsignal operation the dynamic, or incremental, resistance r is defined as the reciprocal of the slope of the voltampere characteristic. RºdV/dI. For a semiconductor diode, we find from equation that the dynamic conductance where I is forward current.
for a forward bias greater than a few tenths of a volt, I >> I_{0} and r is given approximately by
Note
Example 1: Find the voltage drop across each of the Silicon junction diodes shown in the figure below at room temperature. Assume that reverse saturation current flows in the circuit and the magnitude of the reverse breakdown voltage is greater than 5 Volts.
Solution:
V_{D1} + V_{d2} = 5V
V_{D}_{2} = 5 V_{d1}
For diode D_{1},
For diode D_{2},
from equation, (i) and (ii)
V_{D}_{2} = 4.964 V
Transition or depletion layer capacitance:
Cr = Cj = ∈ A/W = Unit farads.
A = Cross Sectional Area Of junction
W = Width of Depletion Region
C_{T} ∝ A
C_{T} ∝ 1/W
For better performance of diode or BJT, the value of C_{T} must be as small as possible.
In a reverse biased PN junction, the transition capacitance, C_{T}
C_{T} ∝ V^{n}
where
V = reverse Biased Voltage
n = constant
n = grading coefficient
n = 1/2; for Step graded diode (abrupt PN Junction diode)
= 1/3; for Linear graded diode
For a forward bias pn junction a capacitance which is much larger than the transition capacitance C, comes into picture. The origin of this larger capacitance lies in the injected charge stored near the junction outside the transition region. It is convenient to introduce an incremental capacitance defined as the rate of charge of injected charge with voltage, called the diffusion or storage capacitance C_{D}.
C_{D }= dQ/dV
where g = dl/dV the incremental conductance and r = ηV_{T}/l. is the
incremental resistance
Therefore,
Where η is a constant dependent upon semiconductor, and VT is volt equivalent temperature and τ is the mean lifetime of minority carriers.
Note:
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