Fotoconduction of semiconductors

On the surface of an intrinsic Silicon crystal it falls a monochromatic radiation having an energy flux density of $\Phi_e=1.92*10^{-4} J/(m^2*s)$.

Knowing that the incident photon energy is $\epsilon=1.2 eV$ and assuming that all incident radiation is absorbed find:

a) The rate of generation of charge carriers

b) The concentration of non equilibrium charge carriers,

c) The relative variation of the conductivity at light.

There are given: the absorption coefficient of light $\alpha =10^4 cm^{-1}$, the time of electron-hole pairs $tau =10^{-4} sec$, the intrinsic concentration of free charge carriers in Silicon, $n_i=2.5*10^16 m^{-3}$ and the quantum efficiency $\gamma =1$


The generation speed is computed from the equation

$g =\alpha*\gamma\Phi_0$

and because the number of incident photons on the surface unit and in the time unit is given by

$\Phi_0 =\Phi_e/\epsilon$

it follows that

$g =\alpha\gamma*(\Phi_e/\epsilon) =10^{21} m^{-3}/s$


The concentration of the charge carriers that are being generated by light is

$\Delta n= g\tau =10^{17} m^{-3}$


The relative variation of the conductivity at illumination is

$\frac {\sigma_f}{\sigma_i} =\frac {e\Delta n(\mu_n+\mu_p)}{en_i(\mu_n+\mu_p)} =\frac{\Delta n}{n_i} =4$

A CdS crystal having a surface $S = 5 mm^2$ is illuminated with a beam of monochromatic radiation having a wavelength of the incident radiation $\lambda =0.5 \mu m$. If the power of the incident radiation is $P=10^{-6} W$, find:

a) the number of the incident photons per unit area and unit time

b) the rate of recombination of the charge carriers, knowing that the band-band generation takes place and the time of electron-hole pairs is $\tau=10^{-5} s$

c) the photo-conductivity $\sigma_f$

There are given: the mobilities of charge carriers $\mu_n=0.035 m^2/(V*s)$ and $\mu_p =0.0015 m^2/(V*s)$; the coefficient of light absorption $\alpha =2*10^4 cm^{-1}$ and the quantum yield $\gamma =1$,


The flux of incident radiation is

$\Phi_0 =\frac {P*t}{h\nu S} =\frac{Pt\lambda}{h c S} =5*10^{17} photons/(m^2*s)$


The recombination rate is

$r =\frac {\Delta n}{\tau} =\frac{\alpha\gamma\Phi_0\tau}{\tau} =\alpha\gamma\Phi_0 =10^{24} m^3/s$


The photo-conductivity is

$\sigma_f =e\Delta n(\mu_n+\mu_p) =er\tau(\mu_n+\mu_p) =5.84*10^{-2} [1/(\Omega*m)]$