Question

For a silicon diode with long $P$ and $N$ regions. the accepter and donor impurity concentrations are $1\times {10}^{17}c{m}^{-3}$ and $1\times {10}^{15}c{m}^{-3}$, respectively. The lifetimes of electrons in $P$ region and holes in $N$ region are both $100\mu s$. The electron and hole diffusion coefficients are $49c{m}^2/s$ and $36c{m}^2/s$, respectively. Assume $kT/q=26mV$, the intrinsic carrier concentration is $1\times {10}^{10}c{m}^{-3}$, and $q=1.6\times {10}^{-19}C$.When a forward voltage of $208mV$ is applied across the diode, the hole current density (in $nA/c{m}^2$) injected from $P$ region to $N$ region is

• A. 0.5147

Answer 1

The correct option is A 0.5147
The hole current density injected from P region to N region is given by
$\frac{q{n}_i^2{D}_p}{N_D{L}_p}[exp\left(\frac{V_{FB}}{\eta V_T}\right)-1]$
where,
q= charge on electron
$n_i$ = Intrinsic carrier concentration in silicon
$N_D$ = Donor doping
$D_p$ = Hole diffusion coefficient
$L_p$= Mean diffusion length of hole
$V_{FB}$= Forward voltage applied across diode
$V_T=kT/q=26mV$
$L_p=\sqrt{{\tau }_p{D}_P}=\sqrt{100\times {10}^{-6\times 36}}$
$=0.06cm$
Using the above values, we get hole current density injected from P region to N region is
$=0.5147nA/c{m}^2$