Question

Consider a p-n junction diode having the characteristic $i=i_0(e^{eV/kT}-1)$ where $i_0=20\mu A.$ The diode is operated at $T=300K.$ (a) Find the current through the diode when a voltage of 300 mV is applied across it in forward bias. (b) At what voltage does the current double ?

Answer 1

(a) Given $I_0=20\times {10}^{-6}A$

$T=300K$

$V=300mV$

$i=i_0(e^{\frac{eV}{KT}}-1)$

$=20\times {10}^{-6}(e^{\frac{0.3}{8.62\times 300\times {10}^{-5}}}-1)$

$=20\times {10}^{-5}(e^{\frac{100}{8.62}}-1)$

$=2.18A=2A$

(b) Since

$\Rightarrow 4=20\times {10}^{-6}(e^{\frac{v}{8.62\times 3\times {10}^{-3}}}-1)$

$\Rightarrow e^{\frac{V\times {10}^3}{8.62\times 3}}-1=\frac{4\times {10}^6}{20}$

$\Rightarrow e^{\frac{v\times {10}^3}{8.62\times 3}}=200001$

$\Rightarrow \frac{V\times {10}^3}{8.62\times 3}=12.2060$

$\Rightarrow V=\frac{12.206\times 8.63\times 3}{{10}^3}$

$=318mV$