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?)