GATE 2015 EC – Question 45
For a silicon diode with long P and N regions, the accepter and donor impurity concentrations are $1 \times 10^{17}$ cm$^{-3}$ and $1 \times 10^{15}$ cm$^{-3}$, 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 49 cm$^2$/s and 36 cm$^2$/s, respectively. Assume $kT/q = 26$ mV, the intrinsic carrier concentration is $1 \times 10^{10}$ cm$^{-3}$, and $q = 1.6 \times 10^{-19}$ C. When a forward voltage of 208 mV is applied across the diode, the hole current density (in nA/cm$^2$) injected from P region to N region is ________.
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Correct answer: 28 to 30
Explanation
The holes are minority carriers in the lightly doped N region, where $p_{n0} = \frac{n_i^2}{N_D} = \frac{10^{20}}{10^{15}} = 10^5$ cm$^{-3}$. The diffusion length is $L_p = \sqrt{D_p\tau_p} = \sqrt{36 \times 10^{-4}} = 0.06$ cm. The current density is $J_p = \frac{qD_p p_{n0}}{L_p}\left(e^{V/V_T} - 1\right)$ with $e^{208/26} = e^8 = 2981$. This gives $\frac{1.6 \times 10^{-19} \times 36 \times 10^5}{0.06} \times 2980 = 2.86 \times 10^{-8}$ A/cm$^2$, which is 28.6 nA/cm$^2$.