- As the pulse drifts in the ξ field it also spreads out by diffusion.
- By measuring the spread in the pulse, we can calculate Dp.
- 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 (tp 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 td), we can use the above equ to calculate Dp 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.