Ncert Exercises & Solutions

14.14 In a p-n junction diode, the current I can be expressed as $I = I_{0} e x p [\frac{e V}{2 k_{B} T} - 1]$

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, k_B is the Boltzmann constant (8.6×10^-5 eV/K) and T is the absolute temperature. If for a given diode I₀ = 5 × 10^-12 A and T = 300 K, then

(a) What will be the forward current at a forward voltage of 0.6 V?

(b) What will be the increase in the current if the voltage across the diode is increased to 0.7 V?

(d) What will be the current if reverse bias voltage changes from 1 V to 2 V?

(a)
Hint: Use the expression of current in a p-n junction diode.
Step: Find the forward current at a forward voltage of 0.6 V.
In a p-n junction diode, the expression for current is I=I₀$exp\Big[\frac{eV}{2k_BT}−1\Big]$
where I₀ is the reverse saturation current = 5×10⁻¹²A
T=Absolute temperature = 300 K
V is the voltage across the diode.
For the forward voltage V=0.6 V
$I=5\times10^{-12}\left[ exp\Big(\frac{1.6×10^{−19}×0.6}{1.376×10^{−23}×300}−1\Big)\right] $=5×10⁻¹²×exp[22.36]
=0.0256 A

(b)
Hint: The increase in the current= (I-I')
Step 1: Find the forward current at a forward voltage of 0.7 V.
In a p-n junction diode, the expression for current is I=I₀$exp\Big[\frac{eV}{2k_BT}−1\Big]$
where I₀ is the reverse saturation current = 5×10⁻¹² A
T=Absolute temperature=300 K
V is the voltage across the diode.
For the forward voltage, V=0.7 V
$I'=5\times10^{-12}\left[ exp\Big(\frac{1.6×10^{−19}×0.7}{1.376×10^{−23}×300}−1\Big)\right] $=1.257 A
Step 2: Find the increase in the current.
Hence, increase in current = 1.257 A−0.0256 A=1.23 A

(c)
Hint: $Dynamic~resistance,~\Delta~r=\frac{\Delta~V}{\Delta~I}$
Step 1: Find the change in current.
Change in current= 1.257 A−0.0256 A=1.23 A
Step 2: Find the dynamic resistance.
Dynamic resistance = Change in voltage /Change in current
=$\frac{0.7−0.6}{1.23}$=0.081Ω

(d)
Hint: Dynamic resistance in the reverse bias is infinite.
Step: Find the current.
If reverse bias voltage changes from 1 V to 2 V, the current will be almost constant, because dynamic resistance in the reverse bias is infinite.

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