Rafeindatækni fastra efna
Djelloul 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.
1
Rafeindatækni fastra efna
Djelloul Seghier
16,1 V
1,6E-02
y = 33,3x - 0,00
1,4E-02
d [m]
1,2E-02
1,0E-02
8,0E-03
6,0E-03
4,0E-03
2,0E-03
0,0E+00
0,0E+00
1,0E-04
2,0E-04
3,0E-04
4,0E-04
5,0E-04
6,0E-04
t1 [s]
14,0 V
1,4E-02
y = 28,8x - 0,00
1,2E-02
d [m]
1,0E-02
8,0E-03
6,0E-03
4,0E-03
2,0E-03
0,0E+00
0,0E+00
1,0E-04
2,0E-04
3,0E-04
4,0E-04
5,0E-04
t1 [s]
12,0 V
1,2E-02
y = 25,8x - 0,00
1,0E-02
d [m]
8,0E-03
6,0E-03
4,0E-03
2,0E-03
0,0E+00
0,0E+00
1,0E-04
2,0E-04
3,0E-04
4,0E-04
5,0E-04
t1 [s]
2
Rafeindatækni fastra efna
Djelloul Seghier
d [m]
9,0 V
1,0E-02
9,0E-03
8,0E-03
7,0E-03
6,0E-03
5,0E-03
4,0E-03
3,0E-03
2,0E-03
1,0E-03
0,0E+00
y = 19,1x - 0,00
0,0E+00 1,0E-04 2,0E-04 3,0E-04 4,0E-04 5,0E-04 6,0E-04
t1 [s]
Voltage [V]
16,1
14,0
12,0
9,0
Electric field can be found with the equation
is the applied voltage to the bar.
Voltage [V]
16,1
14,0
12,0
9,0
Drift velocity vd [m/s]
33,3
28,8
25,8
19,1
where l is the length of the Si bar (23 mm) and V
Electric field ϵ [V/cm]
698
609
522
391
Mobility of the minority carriers can be found with the equation
velocity of holes and ϵ is the electric field.
Voltage [V]
16,1
14,0
12,0
9,0
where vp is the drift
Mobility μp [cm2/V⋅ s]
477
473
490
488
This is close to the expected value of 480 cm2/V⋅ s for Si type semiconductor.
3
Rafeindatækni fastra efna
Djelloul Seghier
Diffusion constant
Diffusion constant can be found with the equation .
where Δ t is the width of half
maximum of the peak; t1 is the time for a light pulse to travel along the bar. These values should
satisfy the Einstein equation
as the function of 11.1#
where
is roughly 0.0259 V at T = 300K. We plot Δ!
16,1 V
3E-12
( d Δ t1)2 [m2s2]
2,5E-12
y = 1,977E-03x - 2,019E-14
2E-12
1,5E-12
1E-12
5E-13
0
0
2E-10 4E-10 6E-10 8E-10 1E-09 1,2E-09 1,4E-09 1,6E-09
11.1 t13 [s3]
( d Δ t1)2 [m2s2]
14,0 V
2E-12
1,8E-12
1,6E-12
1,4E-12
1,2E-12
1E-12
8E-13
6E-13
4E-13
2E-13
0
y = 1,582E-03x + 3,279E-14
0
2E-10
4E-10
6E-10
8E-10
1E-09
1,2E-09
11.1 t13 [s3]
4
Rafeindatækni fastra efna
Djelloul Seghier
12,0 V
1,6E-12
( d Δ t1)2 [m2s2]
1,4E-12
y = 1,313E-03x + 2,011E-14
1,2E-12
1E-12
8E-13
6E-13
4E-13
2E-13
0
0
2E-10
4E-10
6E-10
8E-10
1E-09
1,2E-09
11.1 t13 [s3]
9,0 V
2,5E-12
( d Δ t1)2 [m2s2]
2E-12
y = 1,414E-03x - 5,241E-14
1,5E-12
1E-12
5E-13
0
0
5E-10
1E-09
1,5E-09
2E-09
11.1 t13 [s3]
By dividing the slope of each graph with μp we should get roughly 0.0259.
Voltage [V]
16,1
14,0
12,0
9,0
Dp / μp [ V ]
0.0414
0.0334
0.0268
0.0290
As we can see these values are very close to correct value at low voltages but differ a bit at higher
voltages.
5
Rafeindatækni fastra efna
Djelloul Seghier
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 $ % ⋅ Δ . The area can also be expressed exactly as
$ Δ&' exp +, .
Or as
ln$ lnΔ&' ,
And by plotting ln(S) against t we get the slope
,
-
1
and we can find out τp
16,1 V
ln(S)
0,0E+00
-12,2
-12,4
-12,6
-12,8
-13
-13,2
-13,4
-13,6
-13,8
-14
-14,2
-14,4
1,0E-04
2,0E-04
3,0E-04
4,0E-04
5,0E-04
6,0E-04
y = -4.960x - 11,69
t1 [s]
14,0 V
ln(S)
0,0E+00
-12,2
-12,4
-12,6
-12,8
-13
-13,2
-13,4
-13,6
-13,8
-14
1,0E-04
2,0E-04
3,0E-04
4,0E-04
5,0E-04
y = -5.405x - 11,40
t1 [s]
6
Rafeindatækni fastra efna
Djelloul Seghier
12,0 V
ln(S)
0,0E+00
1,0E-04
-12
-12,2
-12,4
-12,6
-12,8
-13
-13,2
-13,4
-13,6
-13,8
-14
2,0E-04
3,0E-04
4,0E-04
5,0E-04
y = -5.764x - 11,17
t1 [s]
9,0 V
ln(S)
0,0E+00
-12
-12,2
-12,4
-12,6
-12,8
-13
-13,2
-13,4
-13,6
-13,8
-14
1,0E-04
2,0E-04
3,0E-04
4,0E-04
5,0E-04
6,0E-04
y = -4.832x - 11,32
t1 [s]
Voltage [V]
16,1
14,0
12,0
9,0
τp [µs]
202
185
173
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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