In a `p-n` junction diode, the currect `I` can expressed as `I=I_(0) exp((eV)/(2k_(B)T)-1)` where `I_(0)` 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, `K_(B)` is the Boltzmann constant `(8.6 xx 10^(-5) eV//K)` and `T` is the absolute temperature. If for a given diode `I_(o) = 5 xx 10^(-12) A` and `T = 300 K`, then
(a) What will be the forward current at a formward voltage of `0.6V` ?
(b) What will be the increase in the current if the voltage across the diode is increased to `0.7 V` ?
( c) What is the dynamic resistance ?
(d) What will be current if reverse bias voltage changes from `1 V` to `2 V` ?

Explanation

Here, `k=8.6xx10^(-5) eVK^(-1)`
`=8.6xx10^(-5)xx1.6xx10^(-19)JK^(-1)`,
`I_(0)=5xx10^(-12)A, T=300K`.
If `V=0.6V`, then forward current is `I=I_(0)[e^(eV//kT)-1]`
`=5xx10^(-12)[e^(((1.6xx10^(-19))xx0.6)/((8.6xx10^(-5)xx1.6xx10^(-19))xx300))-1]`
`=5xx10^(-12)[e^(23.255)-1]`
`=5xx10^(-12)[(2.718)^(23.255)-1]=0.063A`
If `V=0.7V`, then
`I_(1)=5xx10^(-12)[e^(((1.6xx10^(-19xx0.7)))/((8.6xx10^(-5)xx1.6xx10^(-19))xx300))-1]`
`=5xx10^(-12)[e^(27.1318)-1]=3.035A`
`:.` Increase in current
`DeltaI=I_(1)-I=3.035-0.063=2.972A`
Now `DeltaV=0.7-0.6=0.1V, DeltaI=2.972A`
Dynamic resistance, `=(DeltaV)/(DeltaI)=0.1/2.972=0.0336Omega`
For a change in voltage from 1 to 2 V, the current will remain to saturation stae, `I_(0)=5xx10^(-12)A`. It shown that the diode possesses practically infinite resistance in reverse biased.