Branch : Computer Science and Engineering
Subject : Fundamental of Electronic Devices
Gaussian distribution
- As the pulse drifts in the ξ field it also spreads out by diffusion.
- By measuring the spread in the pulse, we can calculate D_{p}.
- To predict the distribution of holes in the pulse as a function of time, let us first reexamine the case of diffusion of a pulse without drift, neglecting recombination.
- The equation which the hole distribution must satisfy is the time-dependent diffusion equation.
- For the case of negligible recombination (t_{p} long compared with the times involved in the diffusion), we can write the diffusion equation as
The function which satisfies this equation is called a gaussian distribution
- where ΔP is the number of holes per unit area created over a negligibly small distance at t = 0.
- The factor in brackets indicates that the peak value of the pulse (at x = 0) decreases with time, and the exponential factor predicts the spread of the pulse in the positive and negative x-directions that is shown in figure.
- If we designate the peak value of the pulse as bp at any time (say t_{d}), we can use the above equ to calculate D_{p }from the value of ∂p at some point x.
- The most convenient choice is the point Δx/2, at which ∂p is down by 1/e of its peak value ∂p. At this point we can write
Since Δx cannot be measured directly, we use the haynes shockley experiment.