University of Technology
Laser and Optoelectronics Engineering Department
Optoelectronics Engineering Branch
Detector Lab 2010-2011
EXP.NO. (4)
THE PHOTOCONDUCTIVITY OF SILICON AND
THE LIFE-TIME OF EXCESS MINORITY
CARRIERS
Exp .4
THE PHOTOCONDUCTIVITY OF SILICON AND THE LIFETIME OF EXCESS MINORITY CARRIERS
‫ ﻣﻜﺮم ﻋﺒﺪ اﻟﻤﻄﻠﺐ ﻓﺨﺮي‬.‫اﻋﺪاد م‬
THE OBJECTIVES
1- To illustrate the photoconductive property of the silicon.
2- To measure the lifetime of the excess minority carriers in silicon.
Equipment
1-Digital D.C power supply (2 amp).
2-Setrobscope
3-Silicon detector operates on the spectrum range (400nm-1100nm) fixed on
thermal
distribution base
4-Digital voltmeter.
5- Resistance
6- storage oscilloscope
THE THEORY: A photoconductor is essentially a bar-like piece of semiconductor material with ohmic
contacts at the two ends of the bar as shown in figure 1.
SEMICONDUCTOR
Ohmic
contacts
Figure 11
University of Technology
Laser and Optoelectronics Engineering Department
Optoelectronics Engineering Branch
Detector Lab 2010-2011
EXP.NO. (4)
THE PHOTOCONDUCTIVITY OF SILICON AND
THE LIFE-TIME OF EXCESS MINORITY
CARRIERS
The semiconductors used in fabrication of photoconductors have typically low carrier
concentrations under dark conditions. The resistivity of the material is high (ρ ∝ 1/σ, and σ ∝
carrier-concentration, ρ is the resistivity and σ is the conductivity of the semiconductor). When
the semiconductor is illuminated with photons of sufficient energy, due to the generated
additional carriers, the conductivity of the semiconductor increases (resistivity will decrease).
The Photoconductive property of semiconductors can be used to determine the excess minority
carriers lifetime.
The experimental set up is schematically illustrated in figure 2.
Light
Pulse
Semiconductor
0.37∆vL
+
RS(t)
VA
I(t)
RL
VL(t)
-
τ
SCOPE
Figure 2
The semiconductor sample is chosen to be a bar-shaped with a length of L and a crosssection of A. RS is the sample resistance, RL is a load resistance, VA is a dc voltage, τ is excess
minority carriers lifetime, and VL is the load or output voltage. RS, and therefore I and VL are
time dependent parameters. VL changes as the conductivity of the semiconductor varies.
The variation of VL with respect to changes in minority carrier concentrations inside the
semiconductor can be derived as follows. In the following derivation it is assumed that:
1) The semiconductor is an n-type.
2) Uniform photogeneration throughout the semiconductor bulk.
3) Negligible surface recombination.
4) No end effects.
2
University of Technology
Laser and Optoelectronics Engineering Department
Optoelectronics Engineering Branch
Detector Lab 2010-2011
EXP.NO. (4)
THE PHOTOCONDUCTIVITY OF SILICON AND
THE LIFE-TIME OF EXCESS MINORITY
CARRIERS
The excess hole concentration ∆p(t) inside the sample is described by the simplified minoritycarrier diffusion equation
⎛ ∆p ( t ) ⎞
d∆p(t )
⎟ + GL
= −⎜
⎜ τ ⎟
dt
p
⎝
⎠
(1)
Where GL is the generation rate of electron-hole pairs due to light. During the light pulse, ∆p(t)
increases to a maximum value of ∆po = τp·GL. After the light pulse (t ≥ 0), GL = 0 and Eq.(1) with
GL set to zero is readily solved to obtain the following:
⎡ −t ⎤
⎢ ⎥
⎦
∆ p ( t ) = ∆p o ⋅ e ⎣ τ
For t ≥ 0 (light-off)
(2)
The conductivity σ(t) of the semiconductor is defined as:
σ (t ) =
1
ρ
= q ⋅ [µ n ⋅ n(t ) + µ p ⋅ p(t )]
(3)
σ (t ) = q ⋅ [µ n ⋅ (no + ∆n(t ) ) + µ p ⋅ ( po + ∆p(t ) )]
σ (t ) = q ⋅ µ n ⋅ N D + q ⋅ (µ p + µ n ) ⋅ ∆p(t ) For no≈ND »po, and ∆n(t) = ∆p(t)
σ (t) = σ
O
+ ∆ σ (t)
(4)
(5)
(6)
at if we assume ∆σ(t) << σo, then the maximum output is obtained by setting RL= RSO. Also,
using Eq(2 to 6) we can get the following expression:
∆v L (t ) = ∆v Lo ⋅ e
⎛ −t ⎞
⎜ ⎟
⎝τ ⎠
(7)
Where ∆v Lo is a constant, and is given by:
µ ⎞ ⎛ 1 ⎞
⎛1⎞ ⎛
⎟ ⋅ (τ ⋅ G )
For N-type sample: ∆v Lo = V A ⋅ ⎜ ⎟ ⋅ ⎜⎜1 + p ⎟⎟ ⋅ ⎜⎜
µ n ⎠ ⎝ N D ⎟⎠ p L
⎝4⎠ ⎝
µ ⎞ ⎛ 1 ⎞
⎛1⎞ ⎛
⎟ ⋅ (τ ⋅ G )
For P-type sample: ∆v Lo = V A ⋅ ⎜ ⎟ ⋅ ⎜1 + n ⎟ ⋅ ⎜⎜
µ p ⎟⎠ ⎝ N A ⎟⎠ n L
⎝ 4 ⎠ ⎜⎝
3
(8)
(9)
University of Technology
Laser and Optoelectronics Engineering Department
Optoelectronics Engineering Branch
Detector Lab 2010-2011
EXP.NO. (4)
THE PHOTOCONDUCTIVITY OF SILICON AND
THE LIFE-TIME OF EXCESS MINORITY
CARRIERS
Procedure:
1-Both of the Silicon detector and the resistance are connected to an D.C power supply (220V
A.C).
2-The oscilloscope screen, shown in figure 2, will display a simple exponential decay from
which one can find τ. One can obtain the excess minority carriers lifetime τ is given as follows:
3-Take 5 different points (t, ∆vL(t)) from the displayed exponential decay curve on the
oscilloscope screen.
[t2 − t1 ]
on the data that you have obtained in step 1 to
4-Use this equation τ =
v
t
∆
(
)
⎡
⎤
L
1
ln
∆v L (t 2 )⎥⎦
⎢⎣
procure at least 4 values of τ .
5-The excess minority carrier lifetime τ will be the average value of these 4 values of τ
obtained in step 2. Now we are prepared to perform the experiment.
Result
∆vL1(t)mv
t1 - t2(µs)
372
348
311
286
259
∆vL2(t)mv
290
290
290
290
290
τ(µs)
1
1
1
1
1
4
65.6
61.4
54.9
50.44
45.7