Lifetimes and diffusion lengths
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Transcript of Lifetimes and diffusion lengths
LIFETI
MES AND DIFFUSION
LENGTH
S
A ST U D Y I N
SE M I C
O N D U C T O R PH Y S I C
S
Ashley
Finger
and Dr. T
im
Gfroere
r
Davidso
n Colleg
e
INTRODUCTIO
N
P R O P E R T I ES A
N D BE H A V I O
R OF
S E M I CO N D U C T O R S .
WHAT ARE SEMICONDUCTORS?
University of Colorado at Boulder. “Semiconductor Fundamentals.” Accessed 4 Dec. 2013. ecee.colorado.edu.
Streetman, Ben G. Solid State Electronic Devices. 6th ed. Englewood Cliffs, N.J.: Prentice Hall, 2006. Online Resources. Image 3.4.
WHY ARE THEY USEFUL?
n-type p-type Voltage
Curre
nt Dar
k
Illuminated
THEORY
B A S I S F
O R OU R E
X P E R I ME N T
ELECTRON-HOLE PAIRS AND RECOMBINATION
DEFECTS IN SOLAR CELLS
DIFFUSION • τ is the effective lifetime: the average time before recombination.
• L is the effective diffusion length: the average distance before recombination.
OUR EXPERIMENT
S E T - U P AN D P
R O C E D U R E
EXPERIMENT 1: SET-UP
EXPERIMENT 1: ANALYSIS
𝑠𝑙𝑜𝑝𝑒=Δ𝑐𝑜𝑛𝑡𝑟𝑎𝑠𝑡Δ𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
1𝐿
EXPERIMENT 2: SET-UP
Pulsed Laser
EXPERIMENT 2: ANALYSIS
Low Excitation
High Excitation
Note: Models are consistent at intermediate excitation.
RESULTS
S U M M A R Y OF O
U R FI N
D I NG S
DATA COMPILATION
~1015
Exponential Behavior
Reciprocal Behavior
~1016
RATE EQUATIONS WITH TRAPPING
Orton, J.W. and P. Blood. The Electrical Characterization of Semiconductors: Measurement of Minority Carrier Properties. San Diego: Academic Press, 1990. p.20.
𝑑𝑛𝑑𝑡 =−𝑐𝑛 (𝑁 𝑡−𝑛𝑡 )+𝑒𝑛𝑛𝑡−𝐵𝑛2+𝐺
𝑑𝑛𝑡
𝑑𝑡 =𝑐𝑛 (𝑁 𝑡−𝑛𝑡 )−𝑒𝑛𝑛𝑡−𝐴𝑛𝑡
Steady State (Exp.1)
After Pulse (Exp. 2)
G≠0 G=0==0 ≠0 ≠0
MODEL RESULTS
Time (10-8
s)
1x1016
1x1014
1x1015
Carri
er D
ensit
y (c
m-3)
𝒏𝒕
Experimental fit
Theoretical response
2 4 6 8
1021 2x1013 1.5x1015
1022 2x1014 1.5x1015
1023 7x1015 1.5x1016
1024 8x1016 2x1016
1025 3x1017 2x1016
Steady State
After Pulse
1023 7x1015 1.5x1016
1024 8x1016 2x1016
1025 3x1017 2x1016
traps availabl
etraps filled
CONCLUSIONS
R E F L E C T I ON S A
N D DI R
E C T I ON O
F FU T U R E
W O R K
CONCLUSIONS• At moderate and high carrier densities, the lifetimes and
diffusion lengths behave as expected.• At low densities, the behavior is unexpected.• The difference in the threshold density is due to the nature of
the experiment.
WHAT NEXT?• Quantitative model of trapping.• Modelling the low density behavior of carriers (screening?)