Handbook of LUMINESCENTSEMICONDUCTORMATERIALS doc

Handbook of
LUMINESCENT
SEMICONDUCTOR
MATERIALS

Edited by
Leah Bergman
Jeanne L. McHale
K11562
ISBN: 978-1-4398-3467-1
9 781439 834671
9 0 00 0
Handbook of Luminescent
Semiconductor Materials
Bergman
McHale
Materials Science
Photoluminescence spectroscopy is an important approach for examining the
optical interactions in semiconductors and optical devices with the goal of
gaining insight into material properties. With contributions from researchers at
the forefront of this field,
Handbook of
Luminescent Semiconductor Materials

explores the use of this technique to study semiconductor materials in a vari-
ety of applications, including solid-state lighting, solar energy conversion,
optical devices, and biological imaging.
After introducing basic semiconductor theory and photoluminescence
principles, the book focuses on the optical properties of wide-bandgap
semiconductors, such as AlN, GaN, and ZnO. It then presents research
on narrow-bandgap semiconductors and solid-state lighting. The book also

covers the optical properties of semiconductors in the nanoscale regime,
including quantum dots and nanocrystals.
Features
• Provides a detailed examination of the photoluminescence properties
of semiconductors, along with applications to semiconductor-based
devices
• Offers a condensed introduction to semiconductor photoluminescence
that is ideal for nonexperts
• Covers the photoluminescence and applications of nanoparticles
• Presents a clear treatment of the role of impurities and defects in
specific systems
• Explores the application of narrow-bandgap and wide-bandgap
semiconductors in devices, such as light-emitting diodes, lasers,
and infrared detectors
This handbook explains how photoluminescence spectroscopy is a powerful
and practical analytical tool for revealing the fundamentals of light interaction
and, thus, the optical properties of semiconductors. The book shows how
luminescent semiconductors are used in lasers, photodiodes, infrared
detectors, light-emitting diodes, solid-state lamps, solar energy, and
biological imaging.
Handbook of
LUMINESCENT
SEMICONDUCTOR
MATERIALS


Handbook of
LUMINESCENT
SEMICONDUCTOR
MATERIALS

Edited by
Leah Bergman
Jeanne L. McHale
CRC Press
Taylor & Francis Group
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Boca Raton, FL 33487-2742
© 2012 by Taylor & Francis Group, LLC
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Version Date: 20110719
International Standard Book Number-13: 978-1-4398-3480-0 (eBook - PDF)
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vii
Contents
Preface vii
Editors ix
Contributors xi
1 Principles of Photoluminescence 1
Baldassare Di Bartolo and John Collins
2 AlN: Properties and Applications 21
Ashok Sedhain, Jingyu Lin, and Hongxing Jiang
3 GaN-Based Optical Devices 69
Hiroaki Ohta, Steven P. DenBaars, and Shuji Nakamura
4 Photoluminescence of ZnO: Basics and Applications 87
Klaus onke and Martin Feneberg
5 Novel Applications of ZnO: Random Lasing and UV Photonic Light
Sources 125
Hui Cao and Robert P.H. Chang
6 Luminescent ZnO and MgZnO 145
Leah Bergman, Jesse Huso, John L. Morrison, and M. Grant Norton
7 Luminescence Studies of Impurities and Defects in III-Nitride
Semiconductors 169
Bo Monemar and Plamen P. Paskov
8 Narrow-Gap Semiconductors for Infrared Detectors 191
Antoni Rogalski
9 Solid-State Lighting 255
Lekhnath Bhusal and Angelo Mascarenhas
10 Fundamentals of the Quantum Confinement Effect 279
Patanjali Kambhampati

11 Selenide and Sulfide Quantum Dots and Nanocrystals:
Optical Properties 307
Andrea M. Munro
viii Contents
12 Radiative Cascades in Semiconductor Quantum Dots 321
Eilon Poem and David Gershoni
13 Photoluminescence and Carrier Transport in Nanocrystalline TiO
2
365
Jeanne L. McHale and Fritz J. Knorr
14 Photoluminescence Spectroscopy of Single Semiconductor
Nanoparticles 391
Takashi Tachikawa and Tetsuro Majima
15 Biological Applications of Photoluminescent Semiconductor
Quantum Dots 411
Oleg Kovtun and Sandra J. Rosenthal
ix
Preface
In broad terms, photoluminescence is the science of light. e term luminescence means light emission,
and photoluminescence is luminescence that is excited by a photon source. Photoluminescence spec-
troscopy is a versatile technique enabling the study of light dynamics in matter, and it is an important
approach for exploring the optical interactions in semiconductors and optical devices with the goal of
gaining insight into material properties. is book is intended as a detailed examination of photolumi-
nescence properties of semiconductors with applications to semiconductor-based devices.
Chapter 1 provides the reader with an overview of basic semiconductor theory. e chapter presents
the formalisms of semiconductor aspects such as bandgap, doping, and p–n junctions; these concepts
are the fundamentals that underlie light emission and photoluminescence. In addition, it gives an out-
line of the radiative transition mechanisms in semiconductors. e following six chapters focus on the
optical properties of wide-bandgap semiconductors that include AlN, GaN, and ZnO. e bandgaps of
this family of materials are in the range of ∼ 3 eV–6.2 eV, which is well into the UV spectral range. In

particular, Chapter 2 addresses the electronic band structure and radiative recombination of AlN, as
well as doping issues and application to devices. e topic of GaN and GaN-based optical devices is pre-
sented in Chapter 3. at chapter describes the fundamentals of GaN-based blue light-emitting diodes
and lasers. Chapter 4 provides a comprehensive overview of near-UV and visible photoluminescence of
ZnO. Chapter 5 considers the applications of ZnO photoluminescence, including random lasing. e
topic of optical alloys is presented in Chapter 6, where the issue of bandgap-engineered Mg
x
Zn
1−x
O is
addressed. Chapter 7 covers luminescence studies of impurities and defects in GaN, AlN, and InN. In
particular, that chapter focuses on donors, acceptors, intrinsic point defects, and structural defects of
the III-Nitride group.
Chapters 8 and 9 present research on the topics of narrow-bandgap semiconductors and solid-state
lighting, respectively. Chapter 8 gives a comprehensive description of the optical and electronic prop-
erties of narrow-bandgap semiconductors and their application to infrared (IR) detectors. Among the
narrow-bandgap materials discussed are the HgCdTe ternary alloys, InAsSb, PbS, PbSe, and InGaAs.
It covers the properties of various optical devices such as photodiodes and IR detectors, as well as their
manyfold applications to defense technologies as well as IR astronomy. Solid-state lighting involves
materials in the visible spectrum, and is the topic of Chapter 9. e chapter covers the material and
optical characteristics of low- and high-brightness light-emitting diodes and solid-state lamps. e fun-
damentals of photometry, which is the science of luminosity, and colorimetry, which is the science of
measurement of color, are discussed in detail.
e next six chapters (Chapters 10 through 15) focus on the optical properties of semiconductors
in the nanoscale regime. Chapter 10 covers the fundamental aspects of quantum eects unique to
nanoparticles. Chapter 11 discusses the consequences of quantum connement in selenide and sulde
quantum dots and nanocrystals. Chapter 12 presents the formalism and experiments of radiative cas-
cade in semiconductor quantum dots. Chapter 13 considers the photoluminescence of nanocrystalline
TiO
2

and its relation to the carrier transport properties that are important in solar energy applications.
x Preface
Chapter 14 continues the discussion of TiO
2
and other semiconductor nanoparticles, as revealed by the
spectroscopy of individual nanoparticles. Finally, Chapter 15 reveals how the photoluminescence of
semiconductor nanoparticles is proving useful in biological imaging applications.
is handbook demonstrates that photoluminescence is a powerful and practical analytical tool for
the study of the optical properties of semiconductors. e knowledge gained through photolumines-
cence spectroscopy encompasses both the fundamentals of light interaction as well as valuable techno-
logical applications.
Leah Bergman
Jeanne L. McHale
xi
Editors
Leah Bergman is an associate professor of physics at the University of Idaho, Moscow, Idaho. She
received her PhD in materials science and engineering in 1995 from North Carolina State University,
Raleigh, North Carolina. She is a recipient of a CAREER award from the National Science Foundation
division of DMR and was a postdoctoral fellow for the National Research Council. Dr. Bergman’s
research is in the eld of optical materials with a focus on wide-bandgap luminescent semiconductors.
Jeanne L. McHale is a professor of chemistry and materials science at Washington State University,
Pullman, Washington. She received her PhD in physical chemistry in 1979 from the University of
Utah, Salt Lake City, Utah. She is the author of Molecular Spectroscopy and a fellow in the American
Association for the Advancement of Science. Dr. McHale’s research focuses on spectroscopic studies of
semiconductor nanoparticles and chromophore aggregates relevant to solar energy conversion.

xiii
Contributors
Leah Bergman
Department of Physics

University of Idaho
Moscow, Idaho
Lekhnath Bhusal
National Renewable Energy Laboratory
Golden, Colorado
and
Philips Lumileds Lighting Company
San Jose, California
Hui Cao
Department of Applied Physics
Yale University
New Haven, Connecticut
Robert P.H. Chang
Department of Materials Science and
Engineering
Northwestern University
Evanston, Illinois
John Collins
Department of Physics
Wheaton College
Norton, Massachusetts
Steven P. DenBaars
Materials Department
and
Electrical and Computer Engineering
Department
University of California
Santa Barbara, California
Baldassare Di Bartolo
Department of Physics

Boston College
Chestnut Hill, Massachusetts
Martin Feneberg
Institute for Experimental Physics
University of Magdeburg
Magdeburg, Germany
David Gershoni
Department of Physics
e Technion—Israel Institute of Technology
Haifa, Israel
Jesse Huso
Department of Physics
University of Idaho
Moscow, Idaho
Hongxing Jiang
Department of Electrical and Computer
Engineering
Texas Tech University
Lubbock, Texas
Patanjali Kambhampati
Department of Chemistry
McGill University
Montreal, Quebec, Canada
Fritz J. Knorr
Department of Chemistry
Washington State University
Pullman, Washington
Oleg Kovtun
Department of Chemistry
Vanderbilt University

Nashville, Tennessee
xiv Contributors
Jingyu Lin
Department of Electrical and Computer
Engineering
Texas Tech University
Lubbock, Texas
Tetsuro Majima
e Institute of Scientic and Industrial Research
(SANKEN)
Osaka University
Osaka, Japan
Angelo Mascarenhas
National Renewable Energy Laboratory
Golden, Colorado
Jeanne L. McHale
Department of Chemistry
Washington State University
Pullman, Washington
Bo Monemar
Department of Physics, Chemistry and Biology
Linköping University
Linköping, Sweden
John L. Morrison
Department of Physics
University of Idaho
Moscow, Idaho
Andrea M. Munro
Department of Chemistry
Pacic Lutheran University

Tacoma, Washington
Shuji Nakamura
Materials Department
and
Electrical and Computer Engineering
Department
University of California
Santa Barbara, California
M. Grant Norton
School of Mechanical and Materials Engineering
Washington State University
Pullman, Washington
Hiroaki Ohta
Materials Department
University of California
Santa Barbara, California
Plamen P. Paskov
Department of Physics, Chemistry and Biology
Linköping University
Linköping, Sweden
Eilon Poem
Department of Physics
e Technion—Israel Institute of Technology
Haifa, Israel
Antoni Rogalski
Institute of Applied Physics
Military University of Technology
Warsaw, Poland
Sandra J. Rosenthal
Departments of Chemistry, Physics and

Astronomy, Chemical and Biomolecular
Engineering, and Pharmacology
Vanderbilt University School of Medicine
and
Vanderbilt Institute of Nanoscale Science and
Engineering
Vanderbilt University
Nashville, Tennessee
and
Oak Ridge National Laboratory
Oak Ridge, Tennessee
Ashok Sedhain
Department of Electrical and Computer
Engineering
Texas Tech University
Lubbock, Texas
Takashi Tachikawa
e Institute of Scientic and Industrial Research
(SANKEN)
Osaka University
Osaka, Japan
Klaus onke
Institute for Quantum Matter
University of Ulm
Ulm, Germany
1
1.1  Introduction
Luminescence is the spontaneous emission of light from the excited electronic states of physical systems.
e emission is preceded by the process of excitation, which may be produced by a variety of agents. If
it is achieved by the absorption of light it is called photoluminescence, if by the action of an electric eld

electroluminescence, if by a chemical reaction chemiluminescence, and so on.
Following the excitation, if the system is le alone without any additional inuence from the exciting
agent, it will emit spontaneously.
Even in absolute vacuum, an excited atom devoid of any external inuence will emit a photon and
return to its ground state. e spontaneity of the emission presents a conceptual problem. A tenet of
physical science, expressed by the so-called uctuation-dissipation theorem sets forth the fact that any
dissipation of energy from a system is the eect of its interaction with some external entity that provides
1
Principles of
Photoluminescence
1.1 Introduction 1
1.2 Photoluminescent Solid Systems 2
1.3 Classication of Crystalline Solids 3
Insulators • Metals • Semiconductors
1.4 Density of One-Electron States 5
1.5 Intrinsic Semiconductors 6
1.6 Doped Semiconductors 8
n-Type Semiconductors • p-Type Semiconductors
1.7 Models for Doped Semiconductors 9
n-Type Semiconductors • p-Type Semiconductors
1.8 Direct Gap and Indirect Gap Semiconductors 11
1.9 Excitation in Insulators and Large Band Gap
Semiconductors 12
1.10 Radiative Transitions in Pure Semiconductors 12
Absorption • Emission
1.11 Optical Behaviors of Doped Semiconductors 15
1.12 Radiative Transitions across the Band Gap 15
1.13 Nonradiative Processes 16
1.14 p–n Junctions 17
Basic Properties • Junction Rectier • Radiative Processes in p–n

Junctions and Applications
Acknowledgments 20
References 20
Bibliography 20
Baldassare Di
Bartolo
Boston College
John Collins
Wheaton College
2 Handbook of Luminescent Semiconductor Materials
the perturbation necessary for the onset of the process. Such an entity seems to be missing in the case
of an isolated excited atom. If we hold the classical view of natural phenomena, we cannot explain the
presence of spontaneous emission.
In the quantum world things are dierent. e harmonic radiative oscillators that populate the
vacuum and that classically hold no energy when in their ground state have, each in this state, the energy
1/2 hv and may produce a uctuating electric eld at the site of the atom, setting the perturbation neces-
sary for the onset of spontaneous emission.
e rst reported observation of luminescence light from glow worms and reies is the Chinese
book Shih-Ching or Book of Poems (1200–1100 BC). Aristotle (384–322 BC) reported the observation of
light from decaying sh. e rst inquiry into luminescence dates ca. 1603 and was made by Vincenzo
Cascariolo. Cascariolo’s interests were other than scientic: he wanted to nd the so-called philosopher’s
stone that would convert any metal into gold. He found some silvery white stones (barite) on Mount
Paderno, near Bologna, which, when pulverized, heated with coal, and cooled, showed a purple-blue glow
at night. is process amounted to reducing barium sulfate to give a weakly luminescent barium sulde:

BaSO 2C BaS 2CO
22
+ +→
Cascariolo observed that the glow could be restored by exposing the powder to sunlight. News of this
material, the Bologna stone, and some samples of it reached Galileo, who passed them to Giulio Cesare

Lagalla. Lagalla called it lapis solaris and wrote about it in his book De Phenomenis in Orbe Lunae (1612).
It is rare when one can insert a literary citation in a scientic article. is happens to be the case here.
In Goethe’s e Sorrows of Young Werther, the protagonist is unable to see the woman he loves because
of an engagement he cannot refuse and so sends a servant to her, “only so that I might have someone
near me who had been in her presence….” is is then his reaction when the servant comes back [1]:
It is said that the Bologna stone, when placed in the sun, absorbs the sun’s rays and is luminous for
a while in the dark. I felt the same with the boy. e consciousness that her eyes had rested on his
face, his cheeks, the buttons of his jacket and the collar of his overcoat, made all these sacred and
precious to me. At that moment I would not have parted with him for a thousand taler. I felt so
happy in his presence.
e second important investigation on luminescence is credited to Stokes and dates back to the year
1852. Stokes observed that the mineral uorspar (or uorite), when illuminated by blue light gave out
yellow light. Fluorite is CaF
2
, colorless in its purest form, but it absorbs and emits light when it contains
such impurities as Mn, Ce, Er, etc. e term “uorescence” was coined by Stokes and has continued to
be used to indicate short-lived luminescence.
1.2  Photoluminescent Solid Systems
A Stokes’ law has been formulated, according to which the wavelength of the emitted light is always
longer than or equal to the wavelength of the absorbed light. e reason for this dierence is the trans-
formation of the exciting light, to a great or small extent, into a nonradiating vibrational energy of atoms
or ions.
When the intense radiation from a laser is used or when sucient thermal energy contributes to the
excitation process [2], the wavelength of the emission may be shorter than the wavelength of the absorp-
tion (anti-Stokes radiation).
It is convenient to subdivide the luminescent system into two categories, localized and delocalized.
For the rst category, the absorption and emission processes are associated with quantum states of opti-
cally active centers that are spatially localized at particular sites in the solid. For the second category,
these processes are associated with the quantum states of the entire solid.
Principles of Photoluminescence 3

e most important classes of localized luminescent centers are Transition Metal Ions and Rare Earth
Ions that are generally intentionally doped into ionic insulating host materials. e luminescence prop-
erties of these systems depend on both the dopant ion and the host. Another class of localized centers
is that of defects in solids. One such center is an electron trapped at a vacant lattice site. ese defects
oen absorb in the optical region giving the crystal color and, for this reason, are called color centers.
e category of delocalized luminescent centers includes semiconductor systems to which we shall
now dedicate our attention.
1.3  Classication of Crystalline Solids
Crystalline solids are arranged in a repetitive 3D structure called a lattice. e basic repetitive unit is the
unit cell. Prototypes of crystalline solids are (i) copper-metals, (ii) diamond-insulators, and (iii) silicon
semiconductors. We can classify the solid according to three basic properties:
1. Resistivity ρ at room temperature

ρ Ω=
E
J
( m)
where
E is the electric eld
J is the current density
2. Temperature coecient of resistivity

α
ρ
ρ
=
−
1
1
d

dt
(K )
3. Number density of charge carriers, n (m
−3
)
e resistivity of diamond is greater than 10
24
times the resistivity of copper. Some typical parameters
for metals and undoped semiconductors are reported in Table 1.1.
If we assemble N atoms, each level of an isolated atom splits into N levels in the solid. Individual
energy levels of the solid form bands, adjacent bands being separated by gaps. A typical band is only
a few eV wide. Since the number of levels in one band may be on the order of ~10
24
, the energy levels
within a band are very close.
1.3.1  Insulators
e electrons in the lled upper band have no place to go. e vacant levels of the band can be reached
only by giving an electron enough energy to bridge the gap. For diamond the gap is 5.5 eV, and the
TABLE 1.1 Comparison of the Properties of Metals
and Semiconductors
Unit Copper (Metal) Silicon (Semiconductor)
n m
−3
9 × 10
28
1 × 10
16
ρ Ω m
2 × 10
−8

3 × 10
3
α
K
−1
4 × 10
−3
−70 × 10
−3
4 Handbook of Luminescent Semiconductor Materials
possibility that one electron occupies a quantum level at the bottom of the conduction band (see
Equation1.5) at room temperature is on the order of 10
−46
, and as such is negligible.
1.3.2  Metals
e feature that denes a metal is that the highest occupied energy level falls near the middle of an
energy band. Electrons have empty levels they can go to!
A classical free electron model can be used to deal with the physical properties of metals. is model
predicts the functional form of Ohm’s law and the connection between the electrical and thermal con-
ductivity of metals, but does not give correct values for the electrical and thermal conductivities. is
deciency can be remedied by taking into account the wave nature of the electron.
1.3.3  Semiconductors
In this section, we shall treat semiconductors that do not contain any impurities, and that are gener-
ally called intrinsic semiconductors. We shall see later how the presence of impurities greatly aects the
properties of semiconductors. e band structure of a semiconductor is similar to that of an insulator.
e main dierence is that a semiconductor has a much smaller energy gap E
g
between the top of the
highest lled band (valence band) E
v

and the bottom of the lowest empty band (conduction band) E
c

above it. For diamond E
g
= 5.5 eV, whereas for Si, E
g
= 1.1 eV.
e charge carriers in Si arise only because at thermal equilibrium, thermal agitation causes a certain
(small) number of valence band electrons to jump over the gap into the conduction band. ey leave an
equal number of vacant energy states called holes. Both electrons in the conduction band and holes in
the valence band serve as charge carriers and contribute to the conduction. e resistivity of a material
is given by

ρ
τ
=
m
e n
2
(1.1)
where
m is the mass of the charge carrier
n is the number of charge carriers/V
τ is the mean time between collisions of charge carriers
Now, ρ
Cu
= 2 × 10
−8
Ω m, ρ

Si
= 3 × 10
3
Ω m, and n
Cu
= 9 × 10
28
m
−3
, n
Si
= 1 × 10
16
m
−3
, so that

ρ
ρ
Si
Cu
Cu
Si
≈ ≈10
11
and 10
13
n
n
e vast dierence in the density of charge carriers is the main reason for the great dierence in ρ.

We note than the temperature coecient of resistivity is positive for Cu and negative for Si. e atom
Si has the following electronic conguration:

Si s s p s p
core
:1 2 2 3 3
2 2 6 2 2
  
Each Si atom has a core containing 10 electrons and contributes its 3s
2
3p
2
electrons to form a rigid
two-electron covalent bond with its neighbors. e electrons that form the Si–Si bonds constitute the
Principles of Photoluminescence 5
valence band of the Si sample. If an electron is torn from one of the four bonds so that it becomes free
to wander through the lattice, we say that the electron has been raised from the valence to the conduc-
tion band.
1.4  Density of One-Electron States
Given a volume V = L
3
, the number of one-particle states in the range dp
x
dp
y
dp
z
is

V

dk dk dk
V
h
dp dp dp
x y z x y z
8
3 3
π
=
(1.2)
e number of one-particle states in the range (p, p + dp) is

g p dp
V
h
p d d dp
V
h
p dp( ) sin= =
∫∫
3
2
2
0
3
2
θ θ ϕ
π
ππ
0

4
(1.3)
and if the particles are electrons, taking the spin into account

2 2
2
4 1
2
2 4
2
1
2
2
4
3
2
3
3
g E dE g p
dp
dE
dE
V
h
p
m
E
dE
V
h

mE
m
E
dE
V
h
( ) ( )
(
=
= =
=
π π
π
22
8 2
3 2 1 2
3 2
3
1 2
m E dE
m
h
VE dE
)
/ /
/
/
=
π
(1.4)

Given a system of Fermions at temperature T, the probability distribution that species the occupancy
probability is

F E
e
E E kT
F
( )
( )/
=
+
−
1
1
(1.5)
In metals E
F
, the Fermi energy is the energy of the most energetic quantum state occupied at T = 0. At
T ≠ 0, E
F
is the energy of a quantum state that has the probability 0.5 of being occupied. e number of
available states in (E, E + dE) for a system of electrons is given by Equation 1.4. e Fermi energy at T = 0
is determined by

N g E dE
m
h
V E dE
m
h

VE
E E
F
F F
= =
=
∫ ∫
2
8 2
16 2
3
0
3 2
3
1 2
0
3 2
3
3 2
( )
/
/
/
/
π
π
(1.6)
6 Handbook of Luminescent Semiconductor Materials
en

E
m
N
V
h
m
n
F
=






=

2
2
2
2
3
0.121
π
2 3
2 3
/
/
(1.7)
where n = N/V.

1.5  Intrinsic Semiconductors
We shall now present a model for an intrinsic semiconductor. In general, the number of electrons per
unit volume in the conduction band is given by

n N E F E dE
c
E
c
( ) ( )
top
∫
(1.8)
where
N(E) is the density of states
E
c
is the energy at the bottom of the conduction band
We expect E
F
to lie roughly halfway between E
v
and E
c
: the Fermi function F(E) decreases strongly as E
moves up in the conduction band. To evaluate the integral in Equation 1.8, it is sucient to know N(E)
near the bottom of the conduction band and to integrate from E = E
c
to E = ∞. Near the bottom of the
conduction band, according to Equation 1.4, the density of states is given by

N E
h
m E E( ) ( )
/
/
=
(
)
−
4
2
3
*
π
e c
3 2
1 2
(1.9)
where m
e
*
is the eective mass of the electron near E
c
. en

n
h
m
E E
e

dE
c e
E E kT
E E kT
F
=
(
)
−
(
)
+
→
 →
−
(
)
∞
−
(
)
〉〉
∫
4
2
*

3
c
c F

π
3 2
1 2
1
/
/
E
c

( )
−
(
)
−
(
)
∞
∫
4
2
3
e
*
π
h
m
E E
e
dE
c

E E kT
E
F
c
3 2
1 2
/
/
(1.10)
e integral may then be reduced to one of type

x e dx
x1 2
0
1 2
2
/
/
−
∞
∫
=
π
(1.11)
and we obtain the number of electrons per unit volume in the conduction band:

n
m kT
h
e

c
E E kT
F c
=






−
2
2
*
e
3
π
3 2/
( )
(1.12)
Principles of Photoluminescence 7
Let us now consider the number of holes per unit volume in the valence band:

n N E F E dE
h
E
v
( )[ ( )]1 −
∫
bottom

(1.13)
where E
v
is the energy at the top of the valence band. 1 − F(E) decreases rapidly as we go down below the
top of the valence band (i.e., holes reside near the top of the valence band). erefore, in order to evaluate
n
h
, we are interested in N(E) near E
v

N E
h
m E E
h v
( )
*
( )
/
/
=
(
)
−
4
2
3
3 2
1 2
π
(1.14)

where m
h
*
is the eective mass of a hole near the top of the valence band. For E
F
− E
v
≫ kT

1 1
1
1
− = −
+
≈
−
−
F E
e
e
E E kT
E E kT
F
F
( )
( )/
( )/
(1.15)
Substituting (1.14) and (1.15) into (1.13), we obtain

n N E F E dE
h
m E E e
h
E
h
E E k
F
= −
[ ]
=
(
)
−
∫
−
(
)
( ) ( )
*
( )
/
/
1
4
2
3
3 2
1 2
bottom

v
v
π
TT
E
h
E E kT
v
F
dE
m kT
h
e
−∞
−
∫
=






2
2
2
3 2

π

*
/
( )
v
(1.16)
We now use the fact that

n n
c h
= (1.17)
and equate the two expressions for n
c
and n
h
given by Equations 1.12 and 1.16, respectively. We nd

E
E E
kT
m
m
F
c v h
e
=
+
+
2
3
4

ln
*
*
(1.18)
If
m m
e h
* *
=
, E
F
lies exactly halfway between E
c
and E
v
. Replacing the expression (1.18) in Equation 1.16,
we nd

n n
kT
h
m m e
c h e h
E
kT
g
= =







( )
−
2
2
2
3 2
3 4
2
π
/
/
* *
(1.19)
8 Handbook of Luminescent Semiconductor Materials
At room temperature,

2
2
10
2
3 2
3 2 19 3
πkT
h
m







≈
−
/
/
,cm
where m is the mass of the electron.
1.6  Doped Semiconductors
1.6.1  n-Type Semiconductors
Consider the phosphorus atom’s electronic conguration:

P s s p s p Z : ( )1 2 2 3 3 15
2 2 6 2 3
=
If a P atom replaces an Si atom, it becomes a donor. e h (extra) electron is only loosely bound to the
P ion core. It occupies a localized level with energy E
d
≪ E
g
below the conduction band. By adding donor
atoms, it is possible to greatly increase the number of electrons in the conduction band. Electrons in the
conduction band are majority carriers. Holes in the valence band are minority carriers.
Example
In a sample of pure Si, the number of conduction electrons is ≈10
16
m
−3

. If we want to increase this
number by a factor 10
6
, we should dope the system with P atoms creating an n-type semiconductor. At
room temperature, the thermal agitation is so effective that practically every P atom donates its extra
electron to the conduction band. The number of P atoms that we want to introduce in the system is
given by

10 ,
6
0 0
n n n
P
= +
where
n
0
is the number density of conduction electrons of pure Si (~10
16
m
−3
)
n
P
is the number density of P atoms
Then

n n n n
P
= − ≈ ≈ × =

−
10 10 10 10 10 m
6
0 0
6
0
6 16 22 3
The number density of Si atoms in a pure Si lattice is

n
N
A
Si
a
= = ×
−
ρ
5 10 m
28 3
where
N
a
is the Avogadro number
ρ is the density of Si = 2330 kg/m
3
A is the molar mass = 28.1 g/mol = 0.028 kg/mol
Principles of Photoluminescence 9
The fraction of P atoms we seek is approximately

n

n
P
Si
=
10
5 10
1
5 10
22
28 6
×
=
×
(1.20)
Therefore, if we replace only one Si atom in five million with a phosphorous atom, the number of elec-
trons in the conduction band will be increased by a factor of 10
6
.
1.6.2  p-Type Semiconductors
Consider the electronic conguration of an aluminum atom

Al s s p s p Z : ( )1 2 2 3 3 13
2 2 6 2
=
If an Al atom replaces an Si atom, it becomes an acceptor. e Al atom can bond covalently with only
three Si atoms; there is now a missing electron (a hole) in one Al–Si bond. With a little energy, an elec-
tron can be torn from a neighboring Si–Si bond to ll this hole, thereby creating a hole in that bond.
Similarly, an electron from some other bond can be moved to ll the second hole. In this way, the hole
can migrate through the lattice. It has to be understood that this simple picture should not be taken as
indicative of a hopping process since a hole represents a state of the whole system. Holes in the valence

band are now majority carriers. Electrons in the conduction band are minority carriers. We compare the
properties of an n-type semiconductor and of a p-type semiconductor in Table 1.2.
1.7  Models for Doped Semiconductors
Most semiconductors owe their conductivity to impurities, i.e., either to foreign atoms put in the lattice
or to a stoichiometric excess of one of its constituents. Energy level schemes for an n-type semiconduc-
tor and a p-type of semiconductor are shown schematically in Figure 1.1.
1.7.1  n-Type Semiconductors
At T = 0, all the donor levels are lled. At low temperatures, only a few donors are ionized: the Fermi
level is halfway between donor levels and the bottom of the conduction band. If we assume that E
F
is
TABLE 1.2 Comparison of the Properties of an
n-Type and a p-Type Semiconductor
Property
Type of Semiconductor
n p
Matrix material Silicon Silicon
Matrix nuclear charge 14 e 14 e
Matrix energy gap 1.2 eV 1.2 eV
Dopant Phosphorus Aluminum
Type of dopant Donor Acceptor
Majority carriers Electrons Holes
Minority carriers Holes Electrons
Dopant energy gap 0.045 eV 0.067 eV
Dopant valence 5 3
Dopant nuclear charge +15 e +13 e
10 Handbook of Luminescent Semiconductor Materials
below the bottom of the conduction band by more than a few kT, then we can use, in this case, formula
(1.12), that we rewrite as

n
m kT
h
e
c
e
E E kT
F c
=






−
2
2
2
π
*
( )/
(1.21)
is density is equal to the density of the ionized donors.
If E
F
lies more than a few kT above the donor level at E
i
, the density of the empty donors is equal to

n F E n e
d i d
E E kT
i F
1−
[ ]
≈
−
( )
( )
(1.22)
Equating (1.21) and (1.22), we obtain

E E E
kT n m kT
h
F i c
d e
= + +



















−
1
2 2 2
2
2
3 2
( )
*
ln
π
(1.23)
At T = 0, E
F
lies halfway between the donor level and the bottom of the conduction band. As T increases,
E
F
drops (see Figure 1.2). Using the expression for E
F
from Equation 1.23 in n
c
given by Equation 1.21,
we nd

n n
m kT
h
e
c d
e
E E
kT
c d
=






∗
−
−
( )2
2
1 2
2
3 4
2
π
(1.24)
1.7.2  p-Type Semiconductors
e case of p-type semiconductors can be treated in a similar way as the n-type semiconductors. n
h

has
an expression similar to that for n
c
. e Fermi level lies halfway between the acceptor level and the top
of the valence band at T = 0. As T increases, E
F
rises.
Figure 1.3 represents schematically the behavior of the Fermi level for an n-type and for a p-type
semiconductor. e gure illustrates the fact that as the temperature increases, the Fermi level for an
n-type semiconductor does not drop indenitely as indicated by Equation 1.23. As the temperature
increases, the intrinsic excitations of the semiconductor become more important and the Fermi level
tends to set in the middle of the gap. Similar eects take place for the p-type semiconductor. For addi-
tional considerations, the reader is referred to the book by Dekker (see Bibliography).
Conduction band
(a) (b)
Conduction band
E
c
E
c
E
i
E
i
E
υ
E
υ
FIGURE 1.1 Energy level scheme for (a) an n-type semiconductor and (b) a p-type semiconductor. E
i

is the energy
of the donor level (a) or the acceptor level (b).
Principles of Photoluminescence 11
1.8  Direct Gap and Indirect Gap Semiconductors
e energy of the band gap of a semiconductor determines the spectral region in which the electronic
transitions, both in absorption and emissions, take place. For visible or near-infrared transitions, we
need materials with gaps of ~1–1.7 eV. A list of such materials is provided in Table 1.3.
Direct gap transitions take place when the maximum energy of the valence band and the minimum
energy of the conduction band both occur in correspondence to a value of the linear momentum equal
to zero or at the same k
→
≠ 0. Such semiconductors are called direct gap semiconductors.
In other materials, the maximum of the valence band and the minimum of the conduction band
occur at dierent values of k
→
. Such materials are called indirect gap semiconductors.
0
–.1
–.2
–.3
–.4
0 200 400 600 800
Conduction band
Donor
level
10
18
3 ×10
17
10

17
T (K)
E (ev)
FIGURE 1.2 e variation of the position of the Fermi level with temperature with a donor level 0.2 eV
below the bottom of the conduction band for three dierent values of n
d
. (With kind permission from Springer
Science+Business Media: Handbook of Applied Solid State Spectroscopy, 2006, Vij, D.R.)
Conduction band
Donors
Acceptors
Intrinsic
1
2
T
E
F
Valence band
FIGURE 1.3 e variation of the position of the Fermi level with temperature. Curve 1 relates to insulators with
donors and curve 2 relates to insulators with acceptors.
12 Handbook of Luminescent Semiconductor Materials
It is interesting to consider the case of the semiconductor GaAs. By changing the chemical
compositionofthis material according to the formula GaAs
1−x
P
x
, it is possible to change the band gap from
1.52 eV with x = 0 to 2.3 eV with x = 1. In addition, for x > 0.4, the material changes its character from a direct
gap to an indirect gap semiconductor. Mixtures of InP and AlP can also yield gaps from 1.42 to 2.5 eV.
1.9   Excitation in Insulators and Large Band 

Gap Semiconductors
If a beam of light, with photons exceeding in energy the energy gap, goes through an insulator or a
semiconductor, it raises an electron from the valence band into the conduction band for each photon
absorbed, leaving behind a hole. e electron and the hole may move away from each other contributing
to the photoconductivity of the material. On the other hand, they may combine producing an exciton, a
hydrogen-like or a positron-electron pair-like structure. Excitons are free to move through the material.
Since the electron and the hole have opposite charge, excitons are neutral, and as such, are dicult to
detect. When an electron and a hole recombine, the exciton disappears and its energy may be converted
into light or it may be transferred to an electron in a close-by atom, removing the electron from this
atom and producing a new exciton.
Excitons are generally more important in insulators and in semiconductors with large gaps, even if
some excitonic eects in small gap materials have been observed. Excitons do not obey the Fermi–Dirac
statistics and, therefore, it is not possible to obtain a lled band of excitons. Excitons may also be created
in doped semiconductors. In these, however, the free charges provided by the impurities tend to screen
the attraction between electrons and holes and excitonic levels are dicult to detect.
Two models are generally used to deal with excitons in solids. ere are more than two dierent ways
of looking at the same problem, but, rather, they reect two extreme physical situations:
1. A model in which the electron, aer its excitation, continues to be bound to its parent atom.
2. A model where the electron loses the memory of its parent atom and binds together with a hole.
e rst case corresponds to the so-called Frenkel exciton and the second case to the Wannier exciton.
Experimentally, the Frenkel exciton is in principle recognizable because the optical transitions responsible
for the production of the exciton occur in the same spectral region of the atomic transitions. Experimentally,
the transitions responsible for the production of a Wannier exciton t a hydrogen-like type of behavior.
1.10  Radiative Transitions in Pure Semiconductors
1.10.1  Absorption
e absorption optical spectra of pure semiconductors generally present the following features (see
Figure 1.4):
TABLE 1.3 List of Typical
Semiconductors
Material Type Band Gap (eV)

Si Indirect 1.16
InP Direct 1.42
GaAs Direct 1.52
GaP Indirect 2.3
AlP Indirect 2.5
SiC Indirect 3.0