Fundamentals of
Semiconductor
Optoelectronic Materials
Jing Yang
Materials Science & Engineering
Tianjin University
Nov.,2015
References
Texts:

P. Bhattacharya, Semiconductor Optoelectronic Devices, 2nd edition,
Prentice Hall, 1997.

孟庆巨等，半导体器件物理（第2版），科学出版社，2009

刘恩科等，半导体物理学（第7版），电子工业出版社，
2011
Additional references:

S. O. Kasap, Optoelectronic and Photonics: Principles and Practices,
Prentice Hall, 2011.

曾谨言，量子力学导论，北京大学出版社, 1998

黄昆原著，固体物理学，高等教育出版社，1988
考核方式：

采取学术报告形式

分为5个小组(5,5,5,4,4)，每组选1人为组长。

从第2次课开始，每次最后两节课，由一个小组的组员轮流
讲解部分PPT课件内容。每人先讲解10分钟，然后回答同学
和老师的提问（5分钟）。组内分工合作、共同讨论课件内
容。主要参考中文版本课件，查阅参考书和文献，并适当增
加课件内容，如实例等。使用中文或英文课件讲解均可。

评分标准：
PPT讲解及回答问题 —— 60%
小组内表现 —— 20%（组内成员互相排序）
提问 —— 20% （给讲PPT的同学提问，至少提问4次）
各小组课件讲解内容：
小组1：非平衡载流子、PN结部分内容
参考E-learning 课程中英文课件“半导体物理基础、PN结”，
2.6-3.3节，30-56页。
小组2：金属-半导体结
参考 E-learning 课程中英文课件“PN结、金属-半导体结”，第
四章，29-50页。查阅相关文献，适当增加实例
小组3：太阳能电池部分内容
参考E-learning 课程中英文课件“半导体异质结构、太阳能电池
和光电二极管”，6.1-6.4节，30-57页。查阅文献，增加实例
小组4：量子点太阳能电池、光电二极管
参考E-learning 课程中英文课件“半导体太阳能电池和光电二极
管”，6.10-6.12节，37-57页。查阅文献，增加实例
小组5：激光器、量子点生物荧光探针
参考E-learning 课程中英文课件“发光二极管和半导体激光器、
量子点生物荧光探针”，32-67页。查阅文献，增加实例
Outline
Chap. 1 Introduction
Chap. 2 Basics of Semiconductor Physics
Chap. 3 P-N Junctions
Chap. 4 Metal-Semiconductor Junctions
Chap. 5 Semiconductor Heterojunctions
Chap. 6 Semiconductor solar cells & Photodiodes
Chap. 7 Light Emitting Diodes & Semiconductor Lasers
Chap. 8 Quantum Dots for Biological Fluorescent Probes
Chapter 1
Introduction
1.1 Semiconductor Optoelectronic Devices
and Materials

Semiconductor optoelectronic devices:
Semiconductor functional devices in which the interaction
of electronic processes with light and optical processes can
suitably take place, usually accompanied by an energy
conversion process (e.g., form electrical to optical, and vice).

Common semiconductor optoelectronic devices:
Optical  Electrical: Photodetectors, solar cells.
Electrical Optical: Light emitting diodes, injection lasers.
Optical  Optical: Optically-pumped semiconductor lasers,
fluorescent quantum dos.

Semiconductor optoelectronic materials: Semiconductor
materials used for making the above devices.
1.2 Common Semiconductor Optoelectronic
Materials
Semiconductor Optoelectronic Materials
IV or IV-IV
compounds
III-V
compounds
GaAs; GaP; GaN
Ge
Si
SiC
InAs; InP; InSb
II-VI
compounds
ZnS; ZnO;
ZnSe; ZnTe
AlAs; AlP
CdS; CdSe;
CdTe
GaAs1-xPx ;In1-xGaxP
HgS; HgSe
IV-VI
compounds
PbS;
PbSe;
PbSnTe;
PbSnSe
1.3 Application of Some Semiconductor
Optoelectronic Materials








Germanium (Ge): Photodetectors.
Silicon (Si): Photodetectors, solar cells.
Silicon Carbide (SiC): Electroluminescent devices.
Gallium Arsenide (GaAs): Lasers, light emitting diodes (LEDs),
solar cells.
Zinc Sulfide/Oxide (ZnS, ZnO): Electroluminescent and
photoluminescent probes.
Cadmium Sulfide (CdS): Solar cells, lasers.
Cadmium Telluride (CdTe): Solar cells, IR photodetectors,
fluorescent probes/bioimaging.
Lead Sulfide/Selenide/Telluride (PbS, PbSe, PbTe): Solar cells,
IR photodetectors, lasers.
1.4 Physics of Semiconductor Optoelectronic Devices

The band gap energy normally determines the
working wavelength of a semiconductor
optoelectronic device.

The conversion between electrical and optical
energies usually relates to the electron transitions
between the conduction band and valence band of a
semiconductor.
1.4 Physics of Semiconductor Optoelectronic Devices

Solar cells, optodetectors
Absorption, photoconductive effect, photovoltaic effect

LEDs, semiconductor lasers
Carrier injection, radiative recombination

Photoluminescent quantum dots for fluorescent
probes
Absorption, radiative recombination
Chapter 2
Basics of
Semiconductor Physics
2. Basics of Semiconductor Physics
2.1 Electron states in One Atom
2.2 Electron states and Band Structures in
Semiconductors
2.3 Impurity and Defect Levels
2.4 Carrier Distribution in a Semiconductor
2.5 Conduction Processes in Semiconductors
2.6 Non-equilibrium Charge Carriers
2. Basics of Semiconductor Physics
2.1 Electron states in One Atom
2.2 Electron states and Band Structures in
Semiconductors
2.3 Impurity and Defect Levels
2.4 Carrier Distribution in a Semiconductor
2.5 Conduction Processes in Semiconductors
2.6 Non-equilibrium Charge Carriers
2.1 Electron States in one atom

The Earlier Proposal of Quantum Theory

Probability Wave

Schrödinger Equation


Energy Eigenvalue and Eigenfunction of the
Hydrogen Atom Model
Electron Configuration
The Earlier Proposal of Quantum
Theory

In 1900, Planck firstly proposed a hypothesis of “quantum”, and
derived the blackbody formula, which perfectly matched the
observation results. —— Discrete energy of electromagnetic
radiation
E  h , p  h 

In 1905, Einstein tried to explain the difficulties in the
experiment of photoelectric effect, and put forward the concept
of light quantum. —— Light is particulate.

19121913, Bohr proposed the quantum theory of atomic
structure, which successively explained the line spectrum of
hydrogen atom. —— Discrete energy levels and quantum transition
Having limitations and problems！
The Duality of Matter Particles

Wave-particle duality of light:
Wavelike behavior: interference, diffraction, and polarization
Particulate nature: blackbody radiation and photoelectric effect

de Broglie wave (1924): In the atomic world, matter particles
(electrons, protons, neutrons, atoms, etc) have wavelike
properties, which have been verified by experiments, i.e.,
diffraction of electron beams by single crystals.
  E h,   h p

Wave mechanics of Schrödinger (1926) —— revealing the
laws of particle movement in the microscopic systems.
Statistical Explanation of Wave Functions
—— Probability Wave



Wave function  ( r , t ) —— describes the quantum states of a
microscopic particle.
Probability wave (Born, 1926)：unifying the wavelike and
particulate properties of microscopic particles. “Particulate” —
microscopic particles have certain masses and charges, but
different from classic particles. “Wavelike” — additivity of
waves, but different from classic waves, not the fluctuations of
physical quantities in the space.  (r , t ) is also called amplitude
of probability wave.
Probability density    * , the probability of finding
the particle in a unit volume near the position r at time t.
2
Schrödinger Equation
For a microscopic particle moving in a potential V ( r ) ,
 2 2


i  (r , t )   
  V (r )  (r , t )  Hˆ (r , t )
t
 2m

2
2
2
  2 2 2
x y z
2
, Ĥ : Hamiltonian
The Schrödinger equation, a fundamental equation in
quantum mechanics, provides the basic laws of matter
movement in the microscopic world. It’s actually a
hypothesis, which needs to be verified by experiments.
Energy Eigenequation
If V ( r ) is independent of t, the solution  (r , t ) can be
obtained using the separation of variables  (r , t )   E (r )e iEt /
where  E (r ) satisfies the time-independent Schrödinger
equation,
2
2


  2m   V (r )  E (r )  E E (r )



E: energy of the system.
In solving specific problems, the boundary conditions (bound
states, periodic) requires that only certain values of E are
acceptable, which are called the energy eigenvalues, and the
corresponding solutions  E (r ) are called energy eigenfunctions.
Equation  is the energy eigenequation of particles.
Energy Eigenfunction of the
Hydrogen Atom Model
Only one electron outside the nucleus, so the energy
z
eigenfunctions can be accurately solved！
e2
Coulomb attraction: V (r )  
4 0 r
1
In spherical coordinates:  (r )

+
 (r , ,  )
x
r
-

The energy eigenequation of the electron in a hydrogen atom,

me m p
me  m p
, reduced effective mass of electron.
 (r , ,  )  R(r )( )( )
y
 d 2
2

m
0
 2
①
d


 1 d
d
m2
(sin 
)  [l (l  1)  2 ]  0 ②

d
sin 
 sin  d
 1 d 2 dR  2 
e2
l (l  1) 
(r
)   2 (E 
)
 2
R0 ③
2
dr 
4 0 r
r 
 r dr
①: Periodic boundary condition (  2 )  ( )
②: Finite solution
m =0,±1,±2,…
|m|  l, l = 0,1,2,…
③: For E >0, solutions always exist. (continuum-states)
For E <0, bound-states boundary condition (r  , R
n-l-1=0,1,2,…
n=1,2,3,…
The energy levels
E are quantized.
0)
e2
2
2
E  En  
,
a

4


e
0
2an 2
(Bohr radius)
 nlm (r ,  ,  )  Rnl (r )Ylm ( ,  )
Three Quantum Numbers
1. Principal quantum number n, n＝1, 2, 3,…
2. Orbital angular momentum quantum number l，
l =0, 1, 2,…, (n – 1)
3. Magnetic quantum number m, m＝0, 1,  2，…,  l


Each set of quantum numbers n, l, m determines a wave
function of electron or an atomic orbital, and represent a state of
motion of atomic electron, different from the concept of
Bohr’s “atomic orbital”.
Electron cloud: describe the area around a nucleus where an
electron will probably be, with density of dots representing
the probability density ||2.
1. Principal quantum number n



Determining the energy levels of hydrogen atom. n are
positive integers, and the energy levels are quantized.
A larger n means the electron is most likely to be found
farther from the nucleus.
2
The most probable radius, rn  n a, n  1, 2,3,...
Atomic orbitals with the same principal quantum number n
are called one “electronic shell or shell”. The shells
corresponding to n=1, 2, 3, 4, 5, 6, etc. are represented by
labels K, L, M, N, O, P, etc.
2. Orbital angular momentum quantum
number l

Determining the value of orbital angular momentum vector L
of electrons,
L  l (l  1)
l  0,1,2,, (n  1)
Quantized orbital angular momentum



Describing the shape of atomic orbitals and electron clouds.
The orbitals with l=0,1, 2,3, are represented by s,p,d,f.
Wave functions with the same l are called one “subshell”.
In multi-electron atoms, l also determines the energy of
electrons.
3. Magnetic quantum number m


The orientation of orbital angular momentum vector is
quantized. The projection of orbital angular momentum in zaxis is:
Lz  m m＝0,1,2，…,l
Describing the orientation of atomic orbitals and electron
clouds.
 For s-orbital, l=0, m=0. The electron cloud is spherical
about the nucleus, no orientation.

For p-orbital, l=1, m=0,±1. The electron cloud has three
different orientations.

For d-orbital, l=2, m=0,±1,±2. The electron cloud has
five different orientations.
1s, 2p, 3d Electron Clouds of
Hydrogen Atom
1s: n=1, l=0, m=0
2p: n=2, l=1, m=±1, 0
3d: n=3, l=2, m=±2, ±1, 0,
Spin Angular Momentum Quantum
Number ms




The fourth quantum number, describing the electron state of
motion (the spin orientation of the electron).
Not deriving from the Schrödinger equation, and not related to
n, l, m.
Spin is the intrinsic property of electrons. The spin angular
momentum is,
Ls  s(s  1) s=1/2
The projection of electron spin in certain direction is,
Lsz  ms 
ms=1/2, the spin quantum number.
A Complete Description of the
Motion States of Electrons
 Each set of n, l, m quantum numbers describes
all the characteristics of one wave function, and
thus determines the characteristics of the
electron cloud.
 However, in order to completely describe the
motion states of atomic electrons, the spin
quantum number ms is also need to be nailed down.
Electron Configuration

Aufbau Principle (Lowest-energy principle)
Electrons enter orbitals of lowest energy first.

Pauli exclusion principle
Within an orbital there can only be two electrons and each
should have opposite spins. (One spins clockwise and one spins
counterclockwise.)

Hund’s rule
When electrons occupy orbitals of the same energy, electrons
will enter empty orbitals first, and with the same spins.
2. Basics of Semiconductor Physics
2.1 Electron states in One Atom
2.2 Electron States and Band Structures in
Semiconductors
2.3 Impurity and Defect Energy Levels
2.4 Carrier Distribution in a Semiconductor
2.5 Conduction Processes in Semiconductors
2.6 Non-equilibrium Charge Carriers
2.2 Electron states and Band Structures
in Semiconductors

Electron Sharing —— Qualitative explanation

Band Theory —— Quantitative explanation


Interpretation of Metals, Semiconductors, and
Insulators with Band Theory
Quantum Confinement Effect
Electron Sharing and Formation of Band

The periodicity in the structure of
single crystals.

Periodic potential
Under single-electron approximation, the
potential V ( r ) for every electron in the
single crystals is regarded as periodic
V (r )  V (r ')  V (r  Rm )
Rm arbitrary lattice vector.
Electron Sharing and Formation of Band
V(r)
r
One dimensional periodic potential
ATOM
Electron Sharing and Formation of Band

Electron sharing
Due to the overlap of electronic shells between adjacent
atoms that constitute a single crystal, electrons are not confined
to a certain atom, and can transfer to the neighboring atom. So,
electrons can move in the whole crystals, which is called
electron sharing.
The extent of overlap is larger for outer shells, therefore,
the electron sharing is more prominent in the ourtermost shell,
i.e. valence electrons.
Electron Sharing and Formation of Band

Electron sharing —— by Quantum Mechanics
Based on the tunneling effect of quantum mechanics,
electrons can cross the barrier between atoms and transfer to
another atom, leading to the electron sharing in the whole
crystal.
Electron Sharing and Formation of Band

Splitting of energy levels
Due to the potentials of other atoms, the energy of shared
electrons changes. The energy levels of isolated atoms will split.
H2 molecule
The closer of
atoms, the
stronger
interaction
between them,
and the wider
of band.
Electron Sharing and Formation of Band

Band structure
General rules:
 The band related to the outer shell is wider.
 Smaller lattice constants lead to wider band.
 Bands can overlap.
Atomic
level
Allowed
band
Forbidden band
Forbidden band
Atomic
orbit
Electron Sharing and Formation of Band

Band structure

The number of energy levels in each band is N(2l+1). N the
number of atoms, (2l+1) the degree of degeneracy of the
atomic level of isolated atoms.
E.g., If spin is ignored, since s-level is non-degenerate
(m=0), when N atoms form a crystal, the s-level splits into N
close levels. While, the degree of degeneracy of p-level is 3
(m=0,1), so a p-level splits into 3N close energy levels.
In practice, N~1023, energy levels in each band get so close,
that each band is considered as continuous, the so called “quasicontinuous”.
Electron Sharing and Formation of Band

Band structure

In practice, each band usually does not simply correspond
to each energy level of isolated atoms.
E.g., for Si and Ge, each atom has four valence electrons (2 selectron, 2 p-electrons). When crystals form, due to orbital
hybridization, the two bands do not correspond to s- and p-level,
respectively, but both contains 2N levels. Each band could take in
4N electrons.
Upper band: empty band
Lower band: filled band
Electron Sharing and Formation of Band

Electron configuration in band
Configuration rule:
 Lowest-energy principle
 Pauli exclusion principle

Band related terms:
Filled
band：electron
states are
completely
occupied by
Valence
band: the uppermost
filled
band of semiconductors,
electrons.
---- Non-conductive
filled by valence
electrons.
Partially-occupied band: parts of the states are occupied.
Conduction band: the empty band above the valence band.
---- Conductive
Empty band: none of the states are occupied. ---- Nonconductive
Conductive!
Band Theory
Quantitatively solving the electron states in
single crystals by using quantum mechanics.


The fundamental theory in current research of
electron movements in solids.

Clarifying the general rule of electron
movements in single crystals.

Demonstrating the differences among metals,
semiconductors, and insulators.
Band Theory

Approximate theory
Since a single crystal is consist of periodically arranged
atoms, each of which contains many electrons, the problem of
electron movements in crystals is a many-body problem,
which could not precisely solved.
Adiabatic approximation
Single-electron approximation
Nearly free electron
approximation
Tight binding
approximation
Band Theory
 Adiabatic approximation
Ignore the lattice vibration. Every ion core is fixed at its
equilibrium position. （1927, Born-Oppenheimer）

Single-electron approximation
Every electron is considered to move in an effective
potential, and the movement of every electron is independent
(Hartree-Fock) . For ideal single crystals, the effective potential
is periodic.
Band Theory

Wave equation of electrons in crystal
 2 2

  2m   V r  (r )  E (r ) 



where
V (r )  V (r  Rn )
Rn arbitrary lattice vector.
Band Theory


Wave function of electrons in crystal  ( r )
Bloch theorem —— if the potential is periodic, the solution
of the wave equation  should have the following form:


 r e u r
where
Another
expression:
i k r
 
u r  u r  Rn



—— Bloch function
k wave vector
Rn arbitrary lattice vector

 r  Rn  eik R  r
n
Band Theory

Bloch function
Expression 1:


 r e u r
i k r
Plane wave modulated by periodic potential.
Expression 2:


 r  Rn  e

 r
ik  Rn
The electron wave functions for equivalent sites in
different unit cells are differentiated by one factor with
modulus of 1. The probability of finding electrons at
equivalent sites in different unit cells is same.
Band Theory

Wave function of free electrons
For one freely moving
electron with mass m,
velocity v , its momentum p
and energy E:
2
1 p
p  mv, E 
2 m
de Broglie wave , for free
electrons, plane wave with
frequency , and wavelength :
 
 r , t  Ae
k
E  h , p  h 
2


i k r  2t

k wave vector
Band Theory

Wave function of free electrons
|  (r ) |2  A2 --- The probability of finding
 (r )  Ae
ik r
the electron at different places are the same --freely moving.
p  mv
2
1 p
E
2 m
E  h
p
h  2
k
E
k
v
m
2
Wave vector k
describes the
electron states.
2
k
E
2m
k
Band Theory



 r e u r
i k r
Periodic boundary condition and the value of
k
For a finite crystal in a cuboid shape, which has N1, N2, N3
unit cells along directions of a1 , a2 , a3 , so the Bloch function
should satisfied the following periodic boundary condition:
 k (r  Ni ai )   k (r )
ai (i  1, 2,3) —— lattice primitive vector
Band Theory



 r  e i k r u r
Periodic boundary condition and the value of
k
Due to the periodic boundary condition, the wave vector k
should take some discrete values.
l3
l1
l2
k
b1 
b2 
b3
N1
N2
N3
li integers, bi (i  1, 2,3) reciprocal lattice primitive vector.
Wave vector k represents the motion state of electrons in
crystals. k is not the momentum any more.
Band Theory


General conclusions for electron motion states
in crystals.
The states of Bloch electrons are decided by the two
quantum numbers n and k , and the corresponding energy
eigenvalue and wave function are E n (k ) and  (r )
nk

For given n, E n (k ) is a periodic function of k , which has
upper and lower limits.

Different n represents different bands. E n (k ) Constitutes
the band structure of crystals.


 r  e i k r u r
Band Theory
Brillouin zone
3rd 2nd 1st 2nd 3rd
k
E n (k ) as a function of k
k
2π
Energy Band
2π
Reduced
Brillouin Zone
Band Theory

Generally, in order to determine an electron
state, one should tell:
（1）Which band does it belong to (n=?）
（2）What is the reduced wave vector
k?
To solve the wave function of electrons in crystals,
different approximations should be adopted with
respect to different cases.
Band Theory

Nearly free electron approximation

For metals, the valence electrons are weakly bounded to the
positively-charged core, so the periodically varied part in
V(r) is very small compared to the average kinetic energy.
Consequently, the motion of electrons is very close to that
of free electrons, but affected by the periodic potential.
(Kronig-Penny)
Band Theory

Nearly free electron approximation
Replace V(r) with V , the average potential, and treat
V  r   V  as perturbation.


2

 0
2
0
0



V


E



 2m

(1)
The solution of (1) is that for free electrons moving in a
constant potential V :
1 ikr
0
k r  
e ,
Rn
2 2

k
0
Ek 
V
2m
Band Theory

Nearly free electron approximation
Due to the perturbation in potential, E(k) abruptly changed
at k =n/a：the original higher energy level rises, while the
original lower level falls. —— Repulsion
Band Theory

Nearly free electron approximation
E n (k ) as a function of k
Energy Band
Band Theory

Tight binding approximation

The 3d electrons in transition metals and the core
electrons in solids are tightly bound to the atoms.
Put isolated atoms onto the lattice points. The motion of
electrons is similar to that of bound electrons in isolated
atoms, but affected by the perturbation induced by the
potentials from other atoms .


Consider the electron wave function in crystals as a
linear combination of N degenerate atomic wave
functions.
Band Theory


Primary conclusions for tight binding approx.
When N atoms compose a crystal, due to the overlap
between the wave functions of neighboring atoms, the N
degeneracy is released, and form a band.
Interpretation of Metals, Semiconductors, and
Insulators with Band Theory
T=0 K
Fermi
Energy
EF
Empty Band
Partiallyoccupied
Band
Valence
Band
Filled Band
Empty Band
Conduction
Band
Eg
Eg
Filled Band
Filled Band
Filled Band
Filled Band
Metal
Filled Band
Semiconductor Insulator
Quantum Confinement Effect
 The quantum confinement effect (QCE) can be observed once
the dimension of the material is of the same magnitude as the
wavelength of the electron wave function. The electronic and
optical properties deviate substantially from those of bulk
materials.
 The confinement of the electron motion leads to discrete
energy spectrum and the band gap becomes size dependent.
 0D quantum materials: quantum dots, clusters.
1D: nanowires, nanorods.
2D: quantum wells.
 For semiconductors, the QCE occurs only when the
dimension of the material is smaller than the exciton Bohr
radius.
Quantum Confinement Effect
The variation of band
gap with the size of
PbS quantum dots.
Bulk
Quantum dot
Molecule
ACS Nano 3, 3023（2009）
Quantum Confinement Effect
 QCE ultimately results in a blue shift in optical illumination as the
size of the particles decreases.
CdS
CdSe/ZnS
2. Basics of Semiconductor Physics
2.1 Electron states in One Atom
2.2 Electron states and Band Structures in
Semiconductors
2.3 Impurity and Defect Levels
2.4 Carrier Distribution in a Semiconductor
2.5 Conduction Processes in Semiconductors
2.6 Non-equilibrium Charge Carriers
2.3 Impurity and Defect Levels

Formation of Impurity and Defect Levels

Impurity Levels

Impurities in III-V Compound Semiconductors

Deep Levels

Defect Levels
2.3.1 Formation of Impurity and Defect
Levels
In real semiconductors, various types of defects or
impurities exist, which will induce additional potentials in
semiconductors, and thus result in localized electronic states.
Therefore, the electrons and holes can be bound to the
vicinity of the impurities or defects, corresponding to
impurity or defect levels inside the forbidden band. ——
Extrinsic semiconductors.
Intrinsic semiconductors: semiconductors without any impurities
and defects.
2.3.2 Impurity Levels
Ionization
energy of
donor
Ec
Ed
Ei
Ev
Energy in the middle of the
forbidden band
Donor level
Electrons in the conduction band
Ionized donor
(a) Donor impurity in a Si single crystal.



(b) Donor level and ionization.
Donor impurities are those which offer energy levels containing
electrons in the forbidden band.
Group V atoms are donors in Si and Ge.
Semiconductors with donor impurities are referred to as n-type
semiconductors, since electrons are the charge carriers.
2.3.2 Impurity Levels
Ec
Ei
Ea
Ev
Energy in the middle of the
forbidden band
Ionization
energy of
acceptor
Acceptor level
Holes in the valence band
Ionized acceptor
(a) Acceptor impurity in a Si single crystal.



(b) Acceptor level and ionization.
Acceptor impurities are those which offer empty energy levels in the
forbidden band.
Group III atoms are donors in Si and Ge.
Semiconductors with acceptor impurities are referred to as p-type
semiconductors, since holes are the charge carriers.
2.3.2 Impurity Levels
• If a semiconductors has both donor and acceptor
impurities, the electrons in the donor level must firstly
fill the acceptor level, and the rest can be excited to
the conduction band.
• The cancellation between donor and acceptor
impurities are named impurity compensation.
• The type of conduction of a compensated
semiconductor is determined by the impurity with a
higher concentration.
2.3.3 Impurities in III-V Compound
Semiconductors

The numbers of valence electrons in the impurity and
lattice atom determine the impurity behavior.

For III-V compounds (i.e., GaAs), group VI atoms (Se, Te)
replace group V atoms (As), and are donor impurity.
While, group II atoms (Zn, Cd) replace group III atoms
(Ga), and are acceptor impurity.

The group IV atoms can replace groups III and V atoms.
The concentration of group IV atoms and temperature
determine the impurity behavior.
2.3.4 Deep Levels

The ionization energy of the donors and acceptors, in Si
or Ge doped with P or B atoms, or in GaAs doped with
Se or Zn atoms, is around 0.01eV, and the impurity levels
are called shallow levels.

Deep levels: impurity levels located close to the center
of the forbidden band.

Due to the large ionization energies, deep levels make no
contributions to the carrier density under thermal
equilibrium. But they might become combination
centers of electrons and holes, which reduce the lift time
of non-equilibrium carriers.
2.3.4 Deep Levels


A deep-level impurity may have several different ionized states,
corresponding to multi impurity levels in the forbidden band.
Impurities that can become both donors and acceptors are
named amphoteric impurity.
• One valence electron for
Energy levels of Au atoms in germanium.
each Au atom. ---- 3 holes
• The Au atom in Ge can
accept 1,2,3 electrons and
becomes Au-,Au2-,Au3-,
corresponding to three
acceptor levels Ea1, Ea2, Ea3.
• The Au atom is also able to
offer the outermost electron,
and becomes Au+,
corresponding to one donor
level Ed..
2.3.5 Defect Levels —— Point Defect
Example 1:
 Vacancy and interstitial atom
P-type
PbS can be obtained by manipulating PbS in a high
ionic crystals
(oxides,
partialFor
pressure
of sulfur,
whichsulfides,
leads to selenides)
Pb vacancies.
Example
 Positive2:center: cations as interstitial atoms, or anion vacancies
ZnO
can beanions
obtained
by deoxidizing
in vacuum,
 N-type
Negative
center:
as interstitial
atoms,ZnO
or cation
vacancies
which induces O vacancies.
Point defects in ionic crystals

Positive centers are donors
which can provide electrons.

Negative centers are
acceptors.

The conduction type of
semiconductors can be
controlled by nonstoichiometric ratio method.
2.3.5 Defect Levels —— Point Defect

Vacancy and interstitial atom
For covalence crystals —— Si or Ge
 The vacancy is an acceptor,
since the four nearest
neighbors of it have one
unpaired electron for each,
which tend to accept electrons.
 The interstitial atom is a
donor, for it has four unpaired
electrons which could be lost.
Vacancies in Si and Ge crystals
2.3.5 Defect Levels —— Point Defect

Vacancy and interstitial atom
For covalence crystals —— III-V compounds (GaAs, etc.)
There is no definite
answer for whether the
vacancies and interstitial
atoms are donors or
acceptors, which should be
determined by the
experiments.
Point defects in GaAs
2.3.5 Defect Levels —— Point Defect

Substitutional atom
For covalence crystals ——III-V compounds (GaAs, etc.)
Substitutional atoms in binary compounds

Two types of substitutional
atoms: A substitute B (AB),
B substitute A (BA).

AB is an acceptor, while BA
is a donor. E.g., GaAs
behaves like an acceptor, and
AsGa is a donor.

The substitutional atoms
almost don’t exist in
compounds with high
ionicity.