Rafeindatækni fastra efnaDjelloul Seghier
Haynes – Shockley experiment
Marel Helgason, Ólafur Davíð Bjarnason and Valdemar Örn Erlingsson
Setup
The Haynes-Shockley experiment describes the motion of minority carriers in a semiconductor. By measuring the time it takes for a LED to ionize a Silicon bar applied with a known drift voltage, we can calculate using an oscilloscope and a voltmeter the drift velocity, electric field, mobility and lifetime of minority carriers (in our n-type bar, holes).
Measurement of drift velocity
By measuring the time t1 it takes for a light pulse to ionize a Si n-type bar (length 23 mm) and travel along the bar to a known distance d, we can calculate the drift velocity of holes (the minority carriers in an n-type semiconductor). We plot d as a function of t1 for 4 different voltages.
Voltage [V] / Drift velocity vd [m/s]16,1 / 33,3
14,0 / 28,8
12,0 / 25,8
9,0 / 19,1
Electric field can be found with the equation where l is the length of the Si bar (23 mm) and V is the applied voltage to the bar.
Voltage [V] / Electric field ϵ [V/cm]16,1 / 698
14,0 / 609
12,0 / 522
9,0 / 391
Mobility of the minority carriers can be found with the equation where vp is the drift velocity of holes and ϵ is the electric field.
Voltage [V] / Mobility μp[cm2/V⋅ s]16,1 / 477
14,0 / 473
12,0 / 490
9,0 / 488
This is close to the expected value of 480 cm2/V⋅s for Si type semiconductor.
Diffusion constant
Diffusion constant can be found with the equation where Δ t is the width of half maximum of the peak, t1is the time between the light pulse and the peak measured value. These values should satisfy the Einstein equation where is roughly 0.0259 V at T = 300K. We plot as the function of
By dividing the slope of each graph with μpwe should get roughly 0.0259.
Voltage [V] / Dp / μp[ V ]16,1 / 0.0414
14,0 / 0.0334
12,0 / 0.0268
9,0 / 0.0290
As we can see these values are very close to correct value at low voltages but differ a bit at higher voltages.
Lifetime of holes
By measuring the height of the peak V, and the width at the half maximum Δt, we can get approximation of the peak area . The area can also be expressed exactly as
Or as
And by plotting ln(S) against t we get the slope and we can find out τp
Voltage [V] / τp [µs]16,1 / 202
14,0 / 185
12,0 / 173
9,0 / 207
From these results we get the average lifetime of holes is approximately τp = 192µs
Conclusion
Our result shows that the mobility of minority carriers does not change with different electric fields which the drift velocity is proportional to. The diffusion constant should be the same but in our observation we found minor inconsistencies but probably within range. We calculated the lifetime of holes but got a large variance.
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