1 Introduction 2 The Haynes-Shockley Experiment

x f − x i = v d (t pf − t pi ) (15)
= v d ∆t p (16)
where ∆t p = t pf − t pi is the change in the time half-width between the successive travel times t i and
t f . Then
v diff = x f − x i
t f − t i
= v d∆t b
∆t
(17)
where ∆t = t f − t i .
Assume that the charge concentration is an approximately linear function of the distance from the
central part of the pulse. Then
δn
δx ≃ n x
(18)
where n is the mean concentration and x = v d t p is the half-width. Combining the equations (13) and
(17) yields
D = (v d ) 2 t p∆t p
∆t . (19)
In this equation ∆t p is the change in the time half-width during the time interval ∆t, whereas t p is the
average time half-width of teh pulse within the time interval ∆t. That is, t p = ¯t p = (t pf +t pi )
2
. Then
te quantity t p ∆t p = (t pf +t pi )(t pf −t pi )
2
= ((t pf ) 2 −(t pi ) 2 )
2
= ∆(tp)2
2
, so that the diffusion coefficient can be
presented in the form
D = (v d ) 2 ∆(t p) 2
2∆t
(20)
You should note that this expression is obtained by assuming that the concentration gradient is
constant. That is, the recombination rate is not taken into account. In general, we have to introduce
the a constant, a, which takes these effects into account:
D = a(v d ) 2 ∆(t p) 2
∆t
(21)
where for our sample and arrangement the constant a = 0.242.
f. Plot the graph of the squares of the half-widths of the pulses observed on the oscilloscope, (t p ) 2
versus their corresponding delay times t d , and use the slope of the resulting straight line to
calculate the diffusion constant.
g. Compare your result with that given by the Einstein relation (equations (9) and (10)).
The pulse area
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