The Haynes-Shockley Experiment

This applet will simulate the Haynes-Shockley experiment, with an animated carrier density graph to show variation over time. Use the Start button to run or pause the simulation, and the Reset button to go back to the beginning.

Any changes made to parameters will not take effect until the simulation is restarted (either click Reset, or press the return key after editing a text field).

The initial density is a square function; the width and position may be changed using the fields provided. Similarly, the strength of the electric field may be adjusted.

Number of holes

The number of holes (ie. the integral of the graph) will be plotted in the upper-right corner. This value decays exponentially with time, at a rate determined by the carrier lifetime. Setting the carrier lifetime to a sufficiently large value (eg. 1e10) will cause the decay to become insignificant. The blue marker on this graph indicates the initial value, which should be the product of the height (1.0) and width (user defined) of the initial function.

This graph will "wrap around" once the available width has been filled.

Observed density

The graph in the lower-right of the applet plots the carrier density as measured by an observer (at a fixed position) over time. The position of the observer may be adjusted using the text field provided, or by dragging the red marker on the main graph.

Over time, the carrier density seen by the observer will be approximately Gaussian; the width of this Gaussian will be calculated and displayed as soon as there is sufficient data to do so. The width is calculated by taking the distance between the two half-maximal points on the curve. If the curve is so "flat" that the graph "wraps around" before the second of these points is displayed, then no width will be calculated.

As the maximum value for this graph cannot easily be determined from initial conditions, the scale will automatically adjust to fit the data. Once the maximum value has been reached, the scale will stop changing.

Notes

The simulation is performed on a finite interval (the size of which may be chosen). With a nonzero field strength, the function will "move" towards one end of the interval, and will eventually leave. Even with zero field strength, the function will (after a very long time) become sufficiently broad that some part extends outside the interval. This effect is usually only visible some time after the interesting part of the simulation is over, and manifests itself as a sudden turn towards zero in the upper right (integral) graph. The effect is an artifact of the simulation, and should be ignored.

The grey vertical lines (on the integral and observed density graphs) do nothing other than indicated where "now" is on the graphs, and are mostly for dramatic effect.

Documentation