The speed of semiconductor photodetectors is increased by applying a bias voltage. We can investigate this effect by assuming a constant electric field, \(E_{o}\), is applied across the light sensitive layer and this field forces the electrons to flow via a drift mechanism toward the detector circuitry. The mobility of the electrons can be estimated using the Nernst-Einstein relationship. Using the physical data and configuration in the problem above, determine the concentration profile of electrons in the light sensitive layer and the flux of electrons leaving that layer. Use boundary conditions from problem 5.33.

Problem 5.33

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. (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