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In a p-n junction diode, the current I can be expressed as I=I0(exp(eVKBT)1), where I0 is called the reverse saturation current, V is the voltage across the diode and is positive for forward bias and negative for reverse bias, and I is the current through the diode, KB is the Boltzmann constant (8.6×105eV/K) and T is the absolute temperature. If for a given diode I0=5×1012A and T=300K, then
(a) What will be the forward current at a forward voltage of 0.6V?
(b) What will be the increase in the current if the voltage across the diode is increased to 0.7V?
(c) What is the dynamic resistance?
(d) What will be the current if the reverse bias voltage changes from 1V to 2V?

Answer
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Hint: This problem can be solved by using the expression for the current in the p-n junction diode as given in the question and using it to solve the part questions one by one by plugging in the proper information in the equation.

Formula used:
Rdynamic=ΔVΔI

Complete answer:
It is given that the current I can be expressed as
I=I0(exp(eVKBT)1) --(1)
where I0 is called the reverse saturation current, V is the voltage across the diode and is positive for forward bias and negative for reverse bias, and I is the current through the diode, KB is the Boltzmann constant (8.6×105eV/K) and T is the absolute temperature.
Also,
I0=5×1012A
T=300K
Therefore, let us solve the question parts one by one.
(a) Given forward voltage V=0.6V and we have to find I.
Using (1), we get
I=(5×1012)(exp(1×0.68.6×105×300)1)=(5×1012)(exp(23.256)1)=(5×1012)(1.26×10101)
I0.063A
(b) Now the voltage is increased to V=0.7V, we have to find out the increase in current.
I=(5×1012)(exp(1×0.78.6×105×300)1)=(5×1012)(exp(27.132)1)=(5×1012)(6.07×10111)
I3.035A
Therefore, the increase in current is
ΔI=3.0350.063=2.972A
(c) The dynamic resistance Rdynamic is given by
Rdynamic=ΔVΔI --(2)
Where ΔV,ΔI are the change in voltage and current respectively.
The change in voltage when going from V=0.6V to V=0.7V is ΔV=0.70.6=0.1V.
The change in current for both the cases as found out in (b) is ΔI=3.0350.063=2.972A.
Hence, using (2), we get
 Rdynamic=0.12.972=0.0336Ω
Therefore, the dynamic resistance is 0.0336Ω.
(d) When the voltage is changed from 1V to 2V in reverse bias, the current will stay the same, that is, the reverse saturation current I0=5×1012.
This is because in the reversed bias state, the p-n junction diode is said to have infinite resistance and hence, from (2), we can see that if the resistance is infinite, the change in current will be zero.

Note: A p-n junction diode is a non-ohmic device which means that it does not follow Ohm’s law and therefore, the resistance of the device does not remain constant. Hence, we cannot find out the resistance by simply dividing the voltage by the current. We can only get the dynamic resistance of the diode for a certain change in voltage that brings about the respective change in current.