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Nanotechnology Application for
Solar Cells: Using Quantum Dots
to Modify Absorption Properties
Prepared by
James Fodor
Kwok Mak
Viet Huynh
Introduction


How Classical Solar Cells Operate
Absorption Coefficient (α)



Light Absorption of Quantum Dot Layers







Reasons for Interest Into Quantum Dot Light Absorption
Definition of a Quantum Dot
Formula for Light Absorption of a Quantum Dot
Comparison of α versus Energy for Bulk Material and Quantum Dot
Researchers working on Light Absorption of Quantum Dots


Definition and Relevance of α
Physical Techniques for Measuring α
Dr. Sheila Baily
Dr. Ryne Raffaelle
Problem Statement – Determining the most optically absorbent
semiconductor material
Problem Solution


Explanation of Theory
Results
Introduction


How Classical Solar Cells Operate
Absorption Coefficient (α)



Light Absorption of Quantum Dot Layers







Reasons for Interest Into Quantum Dot Light Absorption
Definition of a Quantum Dot
Formula for Light Absorption of a Quantum Dot
Comparison of α versus Energy for Bulk Material and Quantum Dot
Researchers working on Light Absorption of Quantum Dots


Definition and Relevance of α
Physical Techniques for Measuring α
Dr. Ryne Raffaelle
Dr. Sheila Baily
Problem Statement – Determining the most optically absorbent
semiconductor material
Problem Solution


Explanation of Thoery
Results
How Classical Solar Cells Operate1,2
How Classical Solar Cells Operate1,2
How Classical Solar Cells Operate1,2
How Classical Solar Cells Operate1,2
How Classical Solar Cells Operate1,2
How Classical Solar Cells Operate1,2
How Classical Solar Cells Operate1,2
How Classical Solar Cells Operate1,2
Introduction


How Classical Solar Cells Operate
Absorption Coefficient (α)



Light Absorption of Quantum Dot Layers







Reasons for Interest Into Quantum Dot Light Absorption
Definition of a Quantum Dot
Formula for Light Absorption of a Quantum Dot
Comparison of α versus Energy for Bulk Material and Quantum Dot
Researchers working on Light Absorption of Quantum Dots


Definition and Relevance of α
Physical Techniques for Measuring α
Dr. Ryne Raffaelle
Dr. Sheila Baily
Problem Statement – Determining the most optically absorbent
semiconductor material
Problem Solution


Explanation of Thoery
Results
Absorption Coefficient α –
Definition and Relevance of α3

Definition of Absorption Coefficient α

A measure of the rate in decrease of
electromagnetic radiation (as light) as
it passes through a given substance;
the fraction of incident radiant energy
absorbed per unit mass or thickness of
an absorber.
Absorption Coefficient α –
Definition and Relevance of α3

Unit of Absorption Coefficient α

The units of α are per length (cm-1)
Absorption Coefficient α –
Definition and Relevance of α3

Unit of Absorption Coefficient α

The units of α are per length (cm-1)
Absorption Coefficient α –
Definition and Relevance of α4

Absorption Versus Transmission

Transmission (t): a measure of conduction of
radiant energy through a medium, often
expressed as a percentage of energy
passing through an element or system
relative to the amount that entered.
Absorption Coefficient α –
Definition and Relevance of α4

Absorption Versus Transmission

Transmission (t): a measure of conduction of
radiant energy through a medium, often
expressed as a percentage of energy
passing through an element or system
relative to the amount that entered.
Absorption Coefficient α –
Definition and Relevance of α4

Absorption Versus Transmission

Transmission (t): a measure of conduction of
radiant energy through a medium, often
expressed as a percentage of energy
passing through an element or system
relative to the amount that entered.
10
10
8
6
 ( t)
4
2
0
0
0
0.2
0.4
0.6
t
0.8
1
Absorption Coefficient α –
Physical Techniques for Measuring α5,6

Optical Transmission Measurement



t – Measured transmission
l – Sample thickness
R - Reflectance
2   l
t 
( 1  R) e
2  2  l
1  R e
Introduction


How Classical Solar Cells Operate
Absorption Coefficient (α)



Light Absorption of Quantum Dot Layers







Why We Are Interested
Definition of a Quantum Dot
Formula for Light Absorption of a Quantum Dot
Comparison of α versus Energy for Bulk Material and Quantum Dot
Researchers working on Nano-coating


Definition and Relevance of α
Physical Techniques for Measuring α
Dr. Ryne Raffaelle
Dr. Sheila Baily
Problem Statement – Determining the most optically absorbent
semiconductor material
Problem Solution


Explanation of Theory
Results
Light Absorption of Quantum Dots –
Why We Are Interested7,8,13


These structures have great
potential for optoelectronic
applications, one of which may be
solar cells
Standard solar cells have a
theoretical upper conversion rate of
33%, the theoretical limit on the
conversion of sunlight to electricity
is 67%
Light Absorption of Quantum Dots –
Definition of a Quantum Dot9
Quantum Dot
Light Absorption of Quantum Dots –
Definition of a Quantum Dot9
Quantum Dot Layer
Light Absorption of Quantum Dots –
Definition of a Quantum Dot9
Quantum Dot Layer
Light Absorption of Quantum Dots –
Formula7


_
Vav = Average Dot Volume

pfi = 2d momentum matrix element

a = polarization of light

N(ћω) = density of states
Light Absorption of Quantum Dots –
Formula12

Transmission for Quantum dots.


For transmission through n planes of dots, each
having the same dot density N and each dot
experiencing the same optical field amplitude, the
transmission fraction is:
Tn=(1-σN)n ≈ (1-nσN) ; (σN << 1)

σ represents a cross section of the layer
Light Absorption of Quantum Dots –
Comparison of α versus Energy for Bulk
Material and Quantum Dot9
Light Absorption of Quantum Dots –
Comparison of α versus Energy for Bulk
Material and Quantum Dot
Light Absorption of Quantum Dots –
Comparison of α versus Energy for Bulk
Material and Quantum Dot
Light Absorption of Quantum Dots –
Comparison of α versus Energy for Bulk
Material and Quantum Dot7
Light Absorption of Quantum Dots –
Comparison of α versus Energy for Bulk
Material and Quantum Dot7
Introduction


How Classical Solar Cells Operate
Absorption Coefficient (α)



Light Absorption of Quantum Dot Layers







Reasons for Interest Into Quantum Dot Light Absorption
Definition of a Quantum Dot
Formula for Light Absorption of a Quantum Dot
Comparison of α versus Energy for Bulk Material and Quantum Dot
Researchers working on Light Absorption of Quantum Dots


Definition and Relevance of α
Physical Techniques for Measuring α
Dr. Ryne Raffaelle
Dr. Sheila Baily
Problem Statement – Determining the most optically absorbent
semiconductor material
Problem Solution


Explanation of Theory
Results
Researchers Working on Light
Absorption of Quantum Dot Layers



Dr. Sheila Bailey
Using quantum dots in a solar cell to create an
intermediate band
IEEE Photovoltaic Specialist Conference (PVSC)
Executive Committee since 1987
http://www.grc.nasa.gov/WWW/RT2001/5000/5410bailey1.html
Researchers Working on Light
Absorption of Quantum Dot Layers11




Dr. Ryne Raffaelle
Rochester Institute of Technology
NanoPower Laboratories
Organic and Plastic Solar Cells Combined
with Quantum Dot Layers
http://www.physlink.com/News/Images/QDots1_lg.jpg
Introduction


How Classical Solar Cells Operate
Absorption Coefficient (α)



Light Absorption of Quantum Dot Layers







Reasons for Interest Into Quantum Dot Light Absorption
Definition of a Quantum Dot
Formula for Light Absorption of a Quantum Dot
Comparison of α versus Energy for Bulk Material and Quantum Dot
Researchers working on Light Absorption of Quantum Dots


Definition and Relevance of α
Physical Techniques for Measuring α
Dr. Ryne Raffaelle
Dr. Sheila Baily
Problem Statement – Determining the most optically absorbent
semiconductor material
Problem Solution


Explanation of Theory
Results
Problem Solution –
Explanation of theory
Photon Absorption
E  Eo exp[ i (
nr
z
 t )] exp(  )
c
2

z = propagation direction
nr = refractive index
omega = frequency
alpha = absorption coefficient

Laws of Conservation






Energy
Momentum
e 2 
 o cnr mo 2
Photon Emission
1
| (a * p) if |2 N cv ( )

2 (mr ) 3 / 2 (  E g )1/ 2
*
N cv ( ) 
 23
(a * p) if | 2  2 p 2 cv
3
p 2 cv
 20 ~ 24eV
mo
Figures based on Singh
textbook
Problem Statement – Determining the most
optically absorbent semiconductor bulk

Consider InP and GaAs as being the available
semiconductors to create a solar cell. This solar
cell will be a hybrid, consisting of a traditional
solar cell created with either InP or GaAs, and
coating layers of quantum dots of either InP or
GaAs. If maximizing absorption is the only
criteria for designing the solar cell, which material
should be used for the bulk? Which should be
used for the quantum dot layers? Assume the
density of states for quantum dot layers of both
materials is equal and occurs at the same point, E
= .1eV, and that the polarization-momentum
product sum is the same in both cases.
Problem Statement – Determining the most
optically absorbent semiconductor bulk


Material
Absorption coefficient of InP and
GaAs
Required constants by material14
Electron
Mass
(mo)
Hole Mass
(mo)
Calculated
reduced
mass (mo)
Eg
(eV)
Lattice
Constant
(A)
Refractive
index
(nr)
Gallium
Arsenide,
GaAs
0.067
mhh* = 0.45
mr*
=0.058
1.5
5.65
3.65
Indium
Phosphide,
InP
0.073
mhh* = 0.45
mr*
=0.058
1.34
5.87
3
Introduction


How Classical Solar Cells Operate
Absorption Coefficient (α)



Light Absorption of Quantum Dot Layers







Reasons for Interest Into Quantum Dot Light Absorption
Definition of a Quantum Dot
Formula for Light Absorption of a Quantum Dot
Comparison of α versus Energy for Bulk Material and Quantum Dot
Researchers working on Light Absorption of Quantum Dots


Definition and Relevance of α
Physical Techniques for Measuring α
Dr. Ryne Raffaelle
Dr. Sheila Baily
Problem Statement – Determining the most optically absorbent
semiconductor material
Problem Solution


Explanation of Theory
Results
Problem Solution –
Results: GaAs Bulk
Problem Solution –
Results: InP Bulk
Problem Solution –
Results
Problem Solution –
Results: GaAs Quantum Dot Layer
Problem Solution –
Results: InP Quantum Dot Layer
Conclusion


How Classical Solar Cells Operate
Absorption Coefficient (α)



Light Absorption of Quantum Dots







Reasons for Interest Into Quantum Dot Light Absorption
Definition of a Quantum Dot
Formula for Light Absorption of a Quantum Dot
Comparison of α versus Energy for Bulk Material and Quantum Dot
Researchers working on Light Absorption of Quantum Dots


Definition and Relevance of α
Physical Techniques for Measuring α
Dr. Ryne Raffaelle
Dr. Sheila Baily
Problem Statement – Determining the most optically absorbent
semiconductor material
Problem Solution


Explanation of Theory
Results
References
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Pierret, Robert F. Semiconductor Device Fundaments. Addison Wesley Longman, 1996. pp 198-205.
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<http://www.rit.edu/~physics/facstaff/profiles/raffaeller.shtml>. Accessed 04/10/2005.
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