A semiconductor photodiode consists of a light sensitive layer of thickness, \(d\), coupled to electronic circuitry that measures the current produced in that layer (Figure P5.33). Electrons are generated at a rate, \(\dot{M}\), by light striking the sensitive layer and are directly proportional to the light intensity. The light gets absorbed by the layer, so the intensity varies exponentially with depth.

\[I=I_{o} \exp (-\alpha x) \quad \dot{M}\left(\mathrm{~mol} / \mathrm{m}^{3} \mathrm{~s}\right)=m_{o} I\]

Once generated, the electrons diffuse toward the circuitry and a signal is issued proportional to the electron flux at \(x=d\).

a. Determine the concentration profile of electrons in the light sensitive layer and how the flux of electrons depends upon the current. (Hint: Use boundary conditions \(x=0\)

\[\left.c_{e}=0 ; x=d \dot{M}_{e}=A_{c} \int_{0}^{d} \dot{M} d x\right)\]

b. All photodiodes have a dark current, \(I_{d}\), electrons formed by random thermal means. This dark current is proportional to the volume of light sensitive material, \(I_{d}=I_{o} \mathrm{~V}\), and represents noise in the system. Develop an expression for the signal to noise ratio. Comment on how to operate the device.

Transcribed Image Text:

FIGURE P5.33 X D es circuitry d