Question

A semiconductor, in thermal equilibrium, has a hole concentration of p0 = 2x1016 cm-3. The minority carrier life time = 3x10-7 s. (Assume, ni = 1010 cm-3)
(a) Determine the thermal equilibrium recombination rate of electrons.
(b) Determine the recombination rate of electrons if an excess electron concentration of În = 1013 cm-3 exists.
(c) Calculate the change in the recombination rate when excess electron concentration exists (compared to thermal equilibrium).

Answer 1

Answer:

$1.67\times 10^{9}\ \text{cm}^{-3}\text{s}^{-1}$

$3.33\times 10^{19}\ \text{cm}^{-3}\text{s}^{-1}$

$3.33\times 10^{19}\ \text{cm}^{-3}\text{s}^{-1}$

Explanation:

$p_0$ = Hole concentration = $2\times 10^{16}\ \text{cm}^{-3}$

$n_i$ = Intrinsic concentration = $10^{10}\ \text{cm}^{-3}$

$\tau_{n0}$ = Minority carrier life time = $3\times 10^{-6}\ \text{s}$

$\delta n$ = Excess concentration of electrons = $10^{13}\ \text{cm}^{-3}$

Majority carrier electron concentration is given by

$n_0=\dfrac{n_i^2}{p_0}\\\Rightarrow n_0=\dfrac{(10^{10})^2}{2\times 10^{16}}\\\Rightarrow n_0=5000\ \text{cm}^{-3}$

Recombination rate is given by

$R_{n0}=\dfrac{n_0}{\tau_{n0}}\\\Rightarrow R_{n0}=\dfrac{5000}{3\times 10^{-6}}\\\Rightarrow R_{n0}=1.67\times 10^{9}\ \text{cm}^{-3}\text{s}^{-1}$

The recombination rate is $1.67\times 10^{9}\ \text{cm}^{-3}\text{s}^{-1}$

Recombination rate is given by

$R_n=\dfrac{\delta_n}{\tau_{n0}}\\\Rightarrow R_n=\dfrac{10^{13}}{3\times 10^{-7}}\\\Rightarrow R_n=3.33\times 10^{19}\ \text{cm}^{-3}\text{s}^{-1}$

The recombination rate is $3.33\times 10^{19}\ \text{cm}^{-3}\text{s}^{-1}$

Change in the recombination rate is

$\Delta R_n=3.33\times 10^{19}-1.67\times 10^{9}\\\Rightarrow \Delta R_n=3.33\times 10^{19}\ \text{cm}^{-3}\text{s}^{-1}$

The change in the recombination rate is $3.33\times 10^{19}\ \text{cm}^{-3}\text{s}^{-1}$