Download Conversion of Photons to Electrons in a Single

Conversion of Photons to Electrons
in a Single Nanowire Quantum Dot
Towards realization of single exciton pump
MSc. Thesis
Ataklti G. W.
July 2007
EMM Master of Nanoscience and Nanotechnology
TU Delft and KU Leuven
Delft University of Technology
Faculty of Applied Sciences
Kavli institute of nanoscience
Quantum Transport Group
Drs. Maarten van Kouwen
Dr. Valery Zwiller
Prof. dr. ir. L.P. Kouwenhoven
Delft University of Technology
c Kavli Institute of Nanoscience
Copyright °
All rights reserved.
Abstract
Nanowire heterostructures are promising candidates to realize single photon sources for
quantum information processing and quantum communication.
In this project optical and transport measurements were combined on electrically contacted
single InP nanowires containing an InAsP quantum dot. Photoluminescence measurements
showed that the emission linewidth of both InP and InAsP is very broad. The broadening
can be attributed to surface states in general and charging in the case of the quantum dot.
Photocurrent measurements on intrinsic nanowires showed very fast photoresponse which is
on the order of ms. Whereas n-type nanowires photoresponse is very slow and is on the order
of minutes. This indicates that there is a low deep levels density in intrinsic InP nanowires
as compared to n-type nanowires.
Furthermore photocurrent was measured from a single quantum dot by tuning the excitation
energy below the bandgap of InP. This shows that an electric field was effectively applied in
the quantum dot which gave rise to band bending and hence creating a tunnel barrier for
electrons in the quantum dot. Furthermore, upon increasing the external voltage a shift in
PL peak was observed, which can be due to quantum confined Stark effect and discharging
of the dot.
Photocurrent and photoluminescence quantum efficiencies of nanowire heterostructures
showed that a significant number of the photoexcited carriers recombine nonradiatively.
M.Sc. thesis
Ataklti G.W.
Table of Contents
Abstract
iii
1 Introduction
1-1 Objectives and Motivations of the Research . . . . . . . . . . . . . . . . . . . .
1
1
1-2 Growth of Nanowires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
2 The Physics of Semiconductor Nano-heterostructures
5
2-1 The Schrödinger Equation in a Nanowire . . . . . . . . . . . . . . . . . . . . . .
5
2-2 The Schrödinger Equation in a Quantum Dot . . . . . . . . . . . . . . . . . . .
8
2-3 The Density of States
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
2-4 Excitons in Heterostructures . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-5 Optical Properties of Nanowires . . . . . . . . . . . . . . . . . . . . . . . . . .
13
14
2-5-1
2-5-2
Generation Mechanisms . . .
Recombination Mechanisms .
Band-to-band Recombination
Trap-assisted Recombination
Auger Recombination
Surface Recombination
2-6 Metal-Semiconductor Interface
2-7 Addition of an External Electric
2-8 Principle of Photoconductivity
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Field
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3 Device Fabrication and Experimental Setup
33
3-1
Device Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
3-2
Experimental Setup
35
M.Sc. thesis
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ataklti G.W.
vi
Table of Contents
4 Results and Discussions
4-1 Photoluminescence Measurement on a Single Nanowire . . . . . . . . . . . . . .
37
37
4-1-1
Photoluminescence Measurement on a Single InP Nanowire . . . . . . . .
37
4-1-2
Photoluminescence Measurement on a Single InP/InAsP Nanowire . . . .
39
4-2 Photocurrent Measurement on a Single Nanowire . . . . . . . . . . . . . . . . .
40
4-2-1
Photocurrent Measurements on n-type InP Nanowire . . . . . . . . . . .
41
4-2-2
Photocurrent Measurements on Intrinsic InP/InAsP Nanowires . . . . . .
42
Photocurrent Measurements on Intrinsic InP Nanowires . . . . . . . . . .
Photocurrent Measurements on Intrinsic InP/InAsP Nanowires . . . . .
42
45
5 Conclusions and Recommendations
5-1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
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50
Bibliography
Ataklti G.W.
51
July 17, 2007
Chapter 1
Introduction
Single crystalline semiconductor nanowires are being extensively studied because of their
interesting optical and electrical properties and their potential applications in electronic
and optoelectronic devices like nanoscale light emitting diodes[16, 31], lasers[19, 21, 23],
photodetectors[35, 46], waveguides[15], field effect transistors[10], biochemical sensors[8, 49],
nonlinear frequency converters[22], resonant tunneling diodes[5], single-electron transistors[41]
and single-electron memories[42]. The interesting physical properties of nanowires arise
because of their anisotropic geometry, large surface area to volume ratio and carrier
confinement in two dimensions[1]. Furthermore, the fact that the physical properties of
semiconducting nanowires can be tuned by varying their size and composition makes them
very versatile nanoscale structures. Therefore, semiconductor nanowires represent an ideal
system for investigating low dimensional physics.
Currently, a number of experiments are undergoing to synthesis nanowires with control over
their composition, structure and dopant concentration in order to support fundamental research and their integration into functional devices. With present day nanowire growing
techniques, optically bright quantum dots can be embedded in nanowires with promising potential applications in optoelectronics, at the single electron and the single photon level, for
realizing single photon sources for quantum communication and quantum computation.[6, 45].
Moreover, single semiconductor nanowires can be electrically contacted, so that transport and
optical measurements can be combined.[11, 31]
1-1
Objectives and Motivations of the Research
The main objective of the research is to realize a single photon source device in which a single
electron spin can be read out via single photon polarization measurements. A well known
structure is that of self assembled quantum dots, which are formed as a result of lattice
mismatch between two materials. However, the density of self assembled quantum dots is
very high and less controllable. Consequently, making electrical contacts and carrier injection
M.Sc. thesis
Ataklti G.W.
2
Introduction
into a single self assembled quantum dot only is difficult. The fact that the self assembled
quantum dots are embedded in a material medium makes light extraction efficiency very
low. These make combining optical and transport measurements on a single self assembled
dot difficult. Nanowire heterostructures therefore provide a better alternative to optically
and electrically access a single quantum dot[31]. This will enable both electrical as well as
optical characterization of a single quantum dot.
Here, the primary focus of this project is to realize a single exciton pump or optically triggered single-electron turnstile. This can be done by creating an electron hole pair within a
quantum dot in a nanowire heterostructure using an optimized laser pulse as suggested by Leo
Kouwenhoven[29], i.e. the photogenerated electron hole pair contributes to photocurrent instead of photoluminescence by applying an external electric field. Photocurrent measurements
from resonantly excited single self assembled quantum dots have been reported.[14, 24, 38, 50]
However, no work has been reported on resonant excitation and photocurrent measurements
from a single nanowire quantum dot. Figure (1-1) shows the contribution of a photogenerated exciton in to photocurrent or photoluminescence in a self assembled quantum under an
external electric field, based on the values of tunneling time and radiative lifetime.
energy (eV)
1.338
1.337
Photocurrent
Photo-
luminescence
1.336
1.335
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
bias voltage (V)
FIG. 1. Stark shift of the ground state exciton measured in the
Figure 1-1: conversion of photoexcited carriers to photocurrent by applying an external voltage
on a single self assembled quantum dot(picture taken from[39]).
In this specific project intrinsic InP nanowires with intrinsic InAsP section as quantum dots
are studied under the objective of realizing an optically triggered single exciton pump. To
achieve this objective, optical and electrical characterizations are made to probe the electron
and hole energy levels of the quantum dot. Probing the electron energy levels is crucial to
resonantly excite an electron in particular and to understand the physics of quantum dots in
nanowires in general.
As schematically represented in figure (1-2) a single intrinsic InP/InAsP nanowire is
electrically contacted. When an electron-hole pair is created in the nanowire by absorbing an
incoming photon of energy larger than the band gap energy, the electron can recombine with
the hole by giving back another photon as shown in figure (1-2c) or can be separated before
they recombine by applying an external voltage as shown in figure (1-2d). The objective is
therefore to create a single electron hole pair, by tuning an excitation energy resonant with
the energy levels of the dot, and separate them before they recombine
Ataklti G.W.
July 17, 2007
1-2 Growth of Nanowires
3
i-InP
i-InP
i-InP
i-InAsxP (1-x)
i-InP
i-InAsxP (1-x)
(a)
(b)
Ec
E
E
Ev
(c)
(d)
Figure 1-2: Nanowire heterostructure (a) Single nanowire heterostructure (b) electrically connected nanowire Energy band diagram (c) no voltage applied (d) under external voltage
1-2
Growth of Nanowires
The growth of free standing crystaline nanowires has been realized using metal nanoparticles
as catalysts. Growth of varieties of nanowires, for example Si and III-V nanowires, have been
reported using gold nanoparticles as growth catalysts[3, 16, 36]. Furthermore, the growth of
InP nanowires has been reported using indium monodisperses as catalysts[30].
Using the advanced Vapor-Liquid-Solid(VLS)[44] growth technique it has become possible
to grow nanowire heterostructures and superlattices. For example, the growth of nanowire
heterostructures with atomically sharp heterojunctions has been demonstrated in InAs/InP
and in Si/SiGe nanowires[16, 36, 48].
In the VLS growth mode, monodispersed gold particles of a few nanometers in diameter
are deposited on a growth substrate of a given crystal plane orientation (usually h111i).
It is therefore possible to control the size and the density of the gold nanoparticles which
determine the density and the diameter of the grown nanowires. The length of the wires is
controlled by the growth time and growth conditions.
There are three ways of depositing the gold particles on the growth substrate. The first
mechanism is by defining a pattern on the substrate using electron beam lithography,
followed by evaporation and lift off[36]. Hence the pattern and the density of the gold
M.Sc. thesis
Ataklti G.W.
4
Introduction
(a)
(b)
(c)
Figure 1-3: Nanowire growth (a) schematic growth a single nanowire. SEM image of (b) as
grown chip (c) single free standing nanowire.
particles follows the beam generated pattern on the substrate. The other mechanism
is cleaning the substrate with buffered HF and depositing a few Ȧngstrom thick gold
film by thermal evaporation on the top. Upon heating, the gold film breaks up into
small particles[3]. The third one is using a solution of commercially available gold colloids. The first mechanism gives a better control over the density and size of the gold particles.
The substrate with gold particles is transferred to a growth chamber of chemical beam epitaxy
(CBE) or metal-organic vapor phase epitaxy unit, where nanowires from different materials
can be grown. The role of the gold particles is to lower the growth temperature, hence free
standing nanowires are grown beneath the gold particles instead of a bulk layer as depicted
in figure (1-3a). During the epitaxial growth of nanowires it is possible to switch between
different materials to grow heterostructures and superlattices along the nanowire growth axis.
It is also possible to grow a layer of another material in the lateral direction, forming core-shell
nanowires.
Unlike in the case of bulk heterostructures, strain induced by lattice mismatch is not a big
issue, it has been reported[16, 36, 48] that the strain owing to the lattice mismatch can
be relaxed radially because of the small diameter of the nanowires. Therefore, strain free
heterostructures of materials of different lattice constants can be grown. The slow growth
rate of CBE and MOVPE, which is on the order of one monolayer per second, makes it possible
to grow heterostrutures with an abrupt interface. This makes nanowires highly promising in
photonic and electronic applications where abrupt heterojunctions are important.
Ataklti G.W.
July 17, 2007
Chapter 2
The Physics of Semiconductor
Nano-heterostructures
The semiconductor structures studied in this research are of nanometer dimensions in which
size reduction plays an important role in modifying physical properties. Therefore a brief
introduction to the physics behind these structures is important.
A reduction in the momentum degree of freedom of carriers gives rise to a dramatic change
in the physical properties of nanostructures. Nanowires and quantum dots are known as
one dimensional and zero dimensional structures respectively, despite their three dimensional
geometrical structure. The dimensionality, of course, refers to the momentum degree of
freedom the carriers have in the structures. If the number of degrees of freedom and number
of confinement directions are labeled as Df and Dc respectively[18], then
Df + Dc = 3
(2-1)
For a three dimensional solid state structure.
2-1
The Schrödinger Equation in a Nanowire
The general three dimensional Schrödinger equation for the motion of carriers (electrons and
holes) for a constant effective mass is given as
·
−
¸
~2
2
5
+V
(x,
y,
z)
Ψ(x, y, z) = EΨ(x, y, z)
2m∗
(2-2)
Where m∗ is the carrier effective mass in the nanowire. For mathematical convenience the total
potential of a carrier in the nanowire can be written as the sum of the potential along the
M.Sc. thesis
Ataklti G.W.
6
The Physics of Semiconductor Nano-heterostructures
x
z
y
Figure 2-1: One dimensional nanowire .
length of the nanowire, say the z-axis and the confinement potential in the plane orthogonal
to the length of the wire i.e. the xy plane as
V (x, y, z) = V (z) + V (x, y)
(2-3)
Furthermore, the wave function can be written as
Ψ(x, y, z) = φ(z)ψ(x, y)
(2-4)
The total energy can also be written as the sum of the terms associated with the two components of the motion along z and in xy plane.
E = Ez + Exy
(2-5)
Substituting equations (2-3)-(2-5) into equation(2-2)
¸
·
∂2
∂2
~2 ∂ 2
− ∗ ( 2 + 2 + 2 ) + V (z) + V (x, y) φ(z)ψ(x, y) = (Ez + Exy )φ(z)ψ(x, y)
2m ∂x
∂y
∂z
(2-6)
Equation (2-7) can be further decoupled in two equations associated with the two directions
of motion as
·
¸
~2 ∂ 2
− ∗ 2 + V (z) φ(z) = Ez φ(z)
(2-7)
2m ∂z
·
µ 2
¶
¸
~2
∂
∂2
− ∗
+
+ V (x, y) ψ(x, y) = Exy ψ(x, y)
(2-8)
2m ∂y 2 ∂x2
Since the particles are free to move along the direction of the wire i.e. along the z-axis
V(z)=0 and equation (2-9) can be further reduced to
−
~2 ∂ 2 φ(z)
= Ez φ(z)
2m∗ ∂z 2
(2-9)
and the general solution of equation () is given by a plane wave of form e(ikz z) , and the energy
eigenvalue Ez is given by the standard free electron dispersion relation
Ez =
Ataklti G.W.
~2 kz2
2m∗
(2-10)
July 17, 2007
2-1 The Schrödinger Equation in a Nanowire
7
Where kz is the component of the wave vector along the direction of z.
For the second equation (2-8), a potential V (x, y) is included. This can be solved by taking
boundary conditions into account. The simplest approach to solve the solution for this
equation is to model the nanowire as a potential well with infinite depth, i.e. carriers are
free to move in the plane perpendicular to the direction of the length of the nanowire, but
can not exit the wire.
For simplicity let’s consider a wire with a rectangular cross section of length Lx and Ly such
that
V (y, z) = 0
V (y, z) = ∞
0 ≤ x < Lx and 0 ≤ y < Ly
(2-11)
x < 0 and x > Lx and y < 0 and y > Ly
(2-12)
Therefore, inside the wire the Schrödinger equation is given by free electron equation of motion
as:
µ 2
¶
~2
∂
∂2
− ∗
+
ψ(x, y) = Exy ψ(x, y)
(2-13)
2m ∂x2 ∂y 2
which can be decoupled as
~2 ∂ 2 χ(x)
= Ex χ(x)
2m∗ ∂x2
~2 ∂ 2 ϕ(y)
− ∗
= Ey ϕ(y)
2m ∂y 2
−
(2-14)
(2-15)
where ψ(x, y) = χ(x)ϕ(y) and Exy = Ex + Ey
The solutions of equations(2-14) and (2-15) are also given by the free electron equation of
motion as
χ(x) = C sin(kx x) + D cos(kx x)
(2-16)
ϕ(y) = A sin(ky y) + B cos(ky y)
(2-17)
Where A, B, C and D are arbitrary constants to be determined from the boundary conditions.
Since the wire is modeled as an infinitely deep potential well, the wave function should be
zero at y = 0, x = 0 and at y = Ly and x = Lx . Solving the value of the constants from the
boundary conditions A = C = 1 and B = D = 0. The values of the components of the wave
vector along the x and y direction is no more a continuous value but given by
kx =
πnx
Lx
and
ky =
πny
Ly
(2-18)
where nx , ny =1,2,3..
Using the values of the constants and the equations (2-16)-(2-18)
r
2
πnx x
χ(x) =
sin
L
Lx
s x
πny y
2
ϕ(y) =
sin
Ly
Ly
M.Sc. thesis
(2-19)
(2-20)
Ataklti G.W.
8
The Physics of Semiconductor Nano-heterostructures
with the energy components given by
Ex =
~2 π 2 n2x
2m∗ L2x
and
Ey =
~2 π 2 n2y
2m∗ L2y
(2-21)
where nx , ny =1,2,3.. The total energy of an electron measured from the conduction band
edge is therefore given by
E = Ez + Exy
·
¸
n2y
~2 kz2 ~2 π 2 n2x
=
+
+
2m∗e
2m∗e L2x L2y
(2-22)
where m∗e is the effective mass of the electron in the conduction band, rewriting equation ()
E − Exy =
~2 kz2
2m∗e
(2-23)
In equation (2-23) the kx and ky components are absent since the motion in the xy-plane is
quantized. Each quantum level Exy corresponds to an energy subband.
In the same analogy the equation of motion of a hole in the valence band can be solved and
the total energy is given by
E = Ez + Exy
·
¸
~2 kx2
~2 π 2 n2y
n2z
=
+
+ 2
2m∗h
2m∗h L2y
Lz
(2-24)
where nx , ny =1,2,3...
where m∗h is the effective mass of the hole in the valence band.
2-2
The Schrödinger Equation in a Quantum Dot
The simplest model of a quantum dot is a quantum box, in which carriers are confined in
all three spatial dimensions. Consequently the particle has no momentum degree of freedom,
hence it is localized in all three dimensions. Thus the energy levels can no longer be referred
to as sub-band and are called sublevels. Let’s consider a quantum dot in a nanowire heterostructure, for example an InAsP quantum dot embedded in an InP nanowire, the same as
in the case of the nanowire in section 2.1 the quantum dot can be assumed to be surrounded
by an infinite potential in the radial direction. For simplicity the band offset along the growth
direction will first be considered as infinite so that the carrier can be assumed to be trapped
in a three dimensional infinite potential well. As we are interested in photocurrent from
the quantum dot the finite barriers will be taken into account. Since the particle is free to
move within the dot, the potential term of the total Hamiltonian is zero inside the dot. The
Schrödinger equation of motion of the carriers in quantum dot is the same as a free electron
motion given by
µ 2
¶
~2
∂
∂2
∂2
− ∗
+
+
Ψ(x, y, z) = EΨ(x, y, z)
(2-25)
2m ∂x2 ∂y 2 ∂z 2
Ataklti G.W.
July 17, 2007
2-2 The Schrödinger Equation in a Quantum Dot
9
The equation can be decoupled in the three equations associated with the three directions of
motion as
−
~2 ∂ 2 φ(x)
= Ex φ(x)
2m∗ ∂x2
(2-26)
−
~2 ∂ 2 ψ(y)
= Ey ψ(y)
2m∗ ∂y 2
(2-27)
−
~2 ∂ 2 χ(z)
= Ez χ(z)
2m∗ ∂z 2
(2-28)
where Ψ(x, y, z) = φ(x)ψ(y)χ(z) and E = Ex + Ey + Ez
The total energy eigen value is then given by
Exyz
·
¸
n2y
~2 π 2 n2x
n2z
=
+
+ 2
2m∗ L2x L2y
Lz
(2-29)
where nx ,ny ,nz =1,2,3.... Therefore the total energy of the electron in the conduction band of
the dot and the energy of the hole in the valence band is given by
·
¸
n2y
~2 π 2 n2x
n2z
+
+
2m∗e L2x L2y
L2z
(2-30)
·
¸
n2y
~2 π 2 n2x
n2z
E = Ev −
+
+ 2
2m∗h L2x L2y
Lz
(2-31)
E = Ec +
where nx ,ny ,nz =1,2,3....
respectively.
and Ec and Ev are the conduction and valence band edges
Ec
EE Eg
Ev
Figure 2-2: Electron and hole energy levels in QD.
M.Sc. thesis
Ataklti G.W.
10
The Physics of Semiconductor Nano-heterostructures
As can be seen from equations (2-30) and (2-31) and figure (2-2) due to the confinement
effect, the minimum energy levels of the electron in the conduction band and the hole in the
valence band are shifted with respect to the minimum energy levels of the bulk semiconductor
Eg .
The nanowire quantum dot studied in this research, however, cannot be modeled as a three
dimensional infinite potential well. The band offset between InP and InAsP along the growth
direction is rather finite. Consequently, the electron and the hole have a finite probability
to tunnel out of the dot. A more appropriate Schrödinger equation for the motion along the
growth direction can be given as
[−
~2 ∂ 2
+ V (z)]χ(z) = Ez χ(z)
2m∗ ∂ 2 z
(2-32)
Here the potential term V (z) is given by the conduction band offset ∆Ec for electrons in the
conduction band and by the valence band offset, ∆Ev for the holes in the valence band. This
equation can be solved by taking boundary conditions into account. The standard boundary
conditions are
χ(z) → 0 and
∂
χ(z) → 0 as z → ±∞
∂
(2-33)
Using the boundary conditions the wave function is given by
χ(x) = Aexp(kz)
inside the dot
(2-34)
χ(x) = Bexp(−κz)
outside the dot
(2-35)
q
Where A and B are constants, to be determined from the boundary conditions, k =
q
∗
and κ = 2m (V~(z)−E) .
2m∗ E
~
The effect of the size of a quantum dot width (along the growth direction) on the confinement
energy of the electrons and holes (light and heavy) measured from the conduction band and
valence band edges is numerically solved for an InAs quantum dot in an InP nanowire. As can
be seen from figure (2-3) due to their larger effective mass the heavy holes are more confined
towards the valence band edge than the light holes.
2-3
The Density of States
The density of state is defined as the number of states per unit energy per unit volume of
real space; mathematically written as
Ataklti G.W.
July 17, 2007
2-3 The Density of States
11
0.8
0.7
Heavy-hole confinement
Electron confinement
Light Hole confinement
Energy (eV)
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
10
20
30
40
InAs dot in InP size (nm)
Figure 2-3: Confinement energies for electrons and holes as function of quantum dot width for
an InAs section in an InP nanowire
ρ(E) =
dN (E)
dE
(2-36)
In semiconductor bulk structures since the carriers have three degrees of freedom the carrier
momentum is mapped out on a sphere in k-space, while in two dimensional structures the
carrier momenta fill successively larger circles. Whereas in one dimensional structures like in
nanowires due to the presence of only one degree of freedom the carrier momenta fills along
a line. For example let’s consider a single wire of length L the length per state in k-space is
given by 2π
L and the total number of states is given by the ratio of the total length and in
k-space to the length per state as,
µ
Nk1 = 2
2k
¶
2π
L
(2-37)
Where 2k is the total length in k-space. Here the pre factor 2 is to take spin degeneracy into
account. The total number of states per unit length in real space is then given by
N1 =
1 1 2k
N =
L k
π
(2-38)
Therefore,
dN 1
2
=
dk
π
(2-39)
The density of states per unit energy per unit length is given by
ρ1 (E) =
dN 1
dN 1 dk
=
dE
dk dE
(2-40)
From dispersion relation
E=
M.Sc. thesis
~2 2
k
2m∗
(2-41)
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12
The Physics of Semiconductor Nano-heterostructures
dk
1
=
dE
2
sµ
¶
1
2m∗
E− 2
2
~
(2-42)
Using equation (2-42) in equation (2-40)
1
ρ (E) =
π
r
1
2m∗ − 1
E 2
~2
(2-43)
Where E is measured upwards from sub band minimum. Since there are many confined states
within the nanowire with sub band minima Ei , the total density of states at a given energy
is the sum over all subbands below that energy. The total density of states is then given by
r
n
X
1
1 2m∗
1
(E − Ei )− 2 Θ(E − Ei )
ρ (E) =
(2-44)
2
π
~
i=1
where Θ(E −Ei ) is the heaviside equation which is unity when E > Ei and zero when E < Ei .
Dimensionality
ρ(E)
µ
3D
1
2π 2
2D
1
2π
1D
1
π2
µ
µ
¶3
2
2m∗
~2
1
E2
¶1
2m∗
~2
2m∗
~2
2
1E 0
¶0
E
−1
2
Table 2-1: Density of states
D
E
N
S
I
T
Y
Energy
Figure 2-4: Electron density of states in 3D (blue curve), 2D (red curve),1D (green curve),0D
(dark lines).
For a quantum dot however, due to the confinement in all spatial directions there are no such
dispersion curves and the density of states is dependent on the number of confined levels.
An isolated dot would therefore give two fold state (spin- degenerate) at the energy of each
confined level. Consequently the plot of the density of states versus energy would be a series
of δ functions as shown in figure 2.2.
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July 17, 2007
2-4 Excitons in Heterostructures
2-4
13
Excitons in Heterostructures
When an incoming photon of energy hν which is comparable to the energy band gap of the
semiconductor is absorbed by an electron forming a chemical bond between two neighboring
atoms in the lattice of the semiconductor, an electron hole pair is created. The electron
is promoted to the conduction band, while an empty state called the hole is left behind in
the valence band. Electrons and holes can radiatively or non-radiatively recombine. Here
however, let’s just focus on the electron-hole complex, the exciton. The electron in the
conduction band relaxes to the minimum possible energy level in the conduction band edge.
This is done by phonon emission. In a similar way the hole relaxes to the valence band edge.
E
Ec
Ee
Ex
Eh
Ec
Ev
Eb
E
Ex
Eg
Ev
(a)
(b)
Figure 2-5: Excitons levels (a) in bulk (b) heterostructure
Since the hole in the valence band behaves as a positively charged quasi-particle, it forms a
bound state with the electron in the conduction band as shown in figure (2-5). This bound
state is known as an exciton. This attractive Coulomb interaction gives rise to a reduction
of the total energy of the electron-hole complex.
Since the hole mass is generally much larger than the electron mass, the electron-hole
interaction can be described analogously to a hydrogen atom, in which a negatively charged
electron orbits a positively charged hole.
The exciton binding energy Ex from a two body system of electron-hole pair of reduced mass
µ given by
1
1
1
= ∗+ ∗
µ
me
mh
(2-45)
where m∗e and m∗h are the electron and hole effective masses respectively. Hence the exciton
binding energy EB is given by
EB = −
M.Sc. thesis
µe4
32π 2 ~2 ²2r ²2o
(2-46)
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14
The Physics of Semiconductor Nano-heterostructures
Where ²r and ²o are the permittivities of the crystal and free space respectively. The exciton
Bohr radius is given by,
λ=
4π²r ²o ~2
µe2
(2-47)
In bulk semiconductors the exciton Bohr radius is small as compared to the crystal size, hence
the exciton is free to wander in the crystal. In smaller structures like a quantum dot however
the Bohr radius is comparable to the physical dimensions of the structures hence the exciton is
confined. Therefore the size of the exciton Bohr radius determines how large a crystal should
be before its energy bands can be treated as continuous i.e. the exciton Bohr radius can define
whether a crystal is classified as bulk or as quantum dot. Let’s consider a semiconductor
heterostructure as shown in figure (2-5), where the motion of carriers is confined in one or
more dimensions, say a quantum dot embedded in nanowire heterostructure, the total energy
of the exciton is therefore given as;
Ex = Eg + Ee + Eh + EB
(2-48)
Where Ee and Eh are the minimum energy levels of the electron in the conduction band and
a hole in the valence band of the dot respectively, Eg is the bulk energy band gap and EB
is the Coulomb interaction potential energy, which is the exciton binding energy given by
Equation (2-46), and is dependent on the nature of the heterostructure.
At low temperatures excitons are very stable with a life time in the order of hundreds of
picoseconds to nanoseconds. Since exciton binding energy is in the order of few meV their
existence is usually limited only to very low temperatures, where kT is less than the exciton
binding energy.
2-5
Optical Properties of Nanowires
Because of their highly symmetric crystallinity and their high interaction with and response to
light, the study of the optical properties of nanowires is simple. Usually photoluminescence,
absorption and time resolved measurements are carried out to probe the optical properties
of semiconductors in general and nanowires in particular. For example optical measurements
constitute the most important means of determining the band structure of semiconductors.
Photo-induced electronic transitions can occur between different bands, which lead to the
determination of the energy band gaps.
Transmission coefficient T and reflection coefficient R are are the two important quantities
needed for the interpretation of optical measurements. For a normal incidence at a semiconductor air or vacuum interface they are given by[34, 40]
T =
Ataklti G.W.
(1 − R2 )exp( −4πx
λ )
−8πx
2
1 − R exp( λ )
(2-49)
July 17, 2007
2-5 Optical Properties of Nanowires
R=
15
(1 − n̄)2 + κ2
(1 + n̄)2 + κ2
(2-50)
Where λ is the wavelength of the incident light, n̄ is the refractive index, κ the absorption
constant, and x is the thickness of the sample. If κ = 0 the reflection coefficient for an
arbitrary angle of incidence θi is given by
(cos θi − n̄ cos θt )2
(cos θi + n̄ cos θt )2
RT E =
RT M =
(2-51)
(n̄ cos θi − cos θt )2
(n̄ cos θi + cos θt )2
n̄ sin θt = sin θi
(2-52)
(2-53)
where θt is the angle of transmission and RT E and RT M are the reflection coefficients when
the electric field is parallel and orthogonal to the surface of the semiconductor respectively.
The dependence of the reflection coefficients on the angle of incidence is given in figure (2-6)
1
0.9
0.8
Reflection
0.7
0.6
0.5
0.4
TE
0.3
TM
0.2
0.1
0
0
20
40
60
80
Incident Angle [Degrees]
Figure 2-6: dependence of reflection coefficient on incidence angle for a refractive index of n̄=3.5.
(picture taken from[34])
The absorption coefficient per unit length which is a measure of the fraction of photons
absorbed by the semiconductor material, for a given wavelength λ, can be written as
α(λ) =
4πk
λ
(2-54)
By analyzing the (T − λ) and (R − λ) data at normal incidence or by making observation of
R or T for different angles both n̄ and k can be obtained and related to the transition energy
between bands. Near the band edge, the absorption coefficient can be expressed as[2]
α = (hν − Eg )γ
(2-55)
Where γ is a constant. In the one electron approximation γ equals to 1/2 and 3/2 for direct
transitions and forbidden direct transitions respectively[34].
M.Sc. thesis
Ataklti G.W.
16
The Physics of Semiconductor Nano-heterostructures
400
350
3
Absiorption coefficient10 cm
-1
450
300
InAs
InP
GaAs
250
200
150
100
50
0
1.4
1.6
1.8
2.0
2.2
2.4
Energy(eV)
Figure 2-7: absorption coefficient of common bulk semiconductors, InAs (black), InP (green),
GaAs (red) (data taken from[2])
2-5-1
Generation Mechanisms
The most common mechanisms to generate electron-hole pairs are: optical absorption, impact
ionization by high energy electrons or holes, ionization as a result of high energy beam consisting of charged particles and electrical injection. In relation to the nature of the research
the first mechanism is discussed in more detail.
Figure 2-8: common mechanisms of electron-hole pair generation.
When a flux of photons of energy larger than the energy band gap of the semiconductor is
impinging on a semiconductor, the fraction of photons absorbed is given by the absorption
coefficient α in Eq. (2-55). The absorption coefficient is dependent on the energy of the photon,
therefore on its wavelength. Assuming a light flux of f (λ) impinging on a semiconductor, and
assuming that every absorbed photon generates one electron-hole pair, the concentration of
electron-hole pair generated at a depth x per unit time can be written as
G(α, x) = α(λ)f (λ)[1 − R]exp(−α(λ)x)
(2-56)
Here f (λ)R(λ) is the fraction of photons with wavelength λ reflected at the semiconductor
surface and f (λ)exp(−α(λ)x) is the light flux at depth x having been attenuated by absorption. The number of electron-hole pairs Ne−h created through a distance of length L can be
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July 17, 2007
2-5 Optical Properties of Nanowires
17
calculated as
Z
Ne−h =
L
G(α, x)dx
(2-57)
o
Since the absorption coefficient α is not a function of x, evaluation of the integration (2-57)
gives
Ne−h = No (1 − R)[1 − exp(−αL)]
(2-58)
where No is the number of incident photons.
The attenuation of optical power of steady flux of photon of wavelength λ impinging on the
surface can also be calculated for a given incident optical power Po and reflection coefficient
R. The optical power penetrating into the semiconductor is thus Po (1 − R). If the absorption
coefficient is α, the optical power at depth x is given by
Popt = Po [1 − R(λ)]exp(−α(λ)x)
(2-59)
Hence the optical power drops exponentially with depth because of absorption.
2-5-2
Recombination Mechanisms
When an electron-hole pair is created by absorption of a photon of energy greater than
the energy band gap of the semiconductor, the electron and the hole tend to relax to their
respective minimum energy levels in the conduction and valence band respectively by giving
out phonons in a process called non-radiative transition. The electron which relaxed to the
lowest energy level in the conduction band can recombine with the hole in the valence band by
emitting a photon. This process is called radiative transition. The lifetime of the photoexcited
carriers is determined by both the radiative as well as the non-radiative transitions. If the
radiative and non-radiative lifetimes are given by τrad and τnonrad respectively, the effective
lifetime and the radiative quantum efficiency, ηrad are given by
1
τef f
=
ηrad =
1
τrad
+
1
τnonrad
1
τrad
1
τrad
+
1
τnonrad
(2-60)
(2-61)
Band-to-band Recombination
This is a mechanism in which an electron in the conduction band recombines directly with a
hole in the valence band by giving out a photon. Hence it is a radiative process and involves
M.Sc. thesis
Ataklti G.W.
18
The Physics of Semiconductor Nano-heterostructures
Figure 2-9: recombination of excited electrons.
both carriers. Band-to-band recombination is the dominant recombination mechanism in
direct semiconductors. The radiative recombination mechanism rate can be expressed as
Rb−b = B(np − n2i )
(2-62)
where B is a material constant called bimolecular recombination coefficient and has a typical
value of 10−11 − 10−9 cm3 s−1 for common III-V semiconductors[37] and n and p are the
concentration of electrons and holes respectively. For an intrinsic nanowire, where the only
carriers are photo or thermally excited electron-hole pairs, the concentration of electrons and
holes is the same, i.e. n = p = nex
Rb−b = B(n2ex − n2i )
(2-63)
nex
τ
(2-64)
and if nex À ni
Rb−b = B(n2ex ) =
where
τrad =
1
Bnex
(2-65)
is the radiative lifetime of carriers, which is determined by the amount of photoexcited
carriers and the recombination coefficient.
Trap-assisted Recombination
This is a mechanism predominantly facilitated by energy levels that lie within the energy
gap of the semiconductor and are caused by the presence of impurity atoms or structural
defects. These levels are called deep levels. In this mechanism an electron from the conduction
band relaxes to the deep level and then to the empty state in the valence band, thereby
completing the recombination process. This recombination can be radiative, non-radiative or
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July 17, 2007
2-5 Optical Properties of Nanowires
19
might combine both, depending on the relative position of the deep levels with respect to the
conduction band, the valence band and other deep levels. This mechanism can also be referred
to as Schockley-Read-Hall recombination. These deep levels associated with impurities and
defects are highly pronounced in doped nanowires.[13, 25] The recombination rate is given by
USRH =
pn − n2i
N vth σP σn
−Et
−Et
σn [n + ni exp( EikT
)] + σp [p + ni exp( EikT
)]
(2-66)
where σp and σn are the hole andqelectron capture cross sections, respectively, vth is the
thermal velocity which is equal to 3kT
m∗ , Nt is the trap density, Et is the trap energy level
and Ei is the intrinsic energy level. Under thermal equilibrium, pn = n2i then U = 0. If we
assume that σp = σn = σ, equation(2-66) can be reduced to
USRH =
pn − n2i
N vth σ
−Et
p + n + 2ni cosh[ EikT
]
(2-67)
and for intrinsic semiconductors since n = p = nex the above equation can be reduced to
USRH =
n2ex − n2i
N vth σ
−Et
2nex + 2ni cosh[ EikT
]
(2-68)
According to equation (2-86), the recombination rate approaches its maximum as the energy
level of the trap center approaches the midgap i.e, when Et ≈ Ei . Hence the most effective
recombination centers are, therefore, the deep levels that lie near the center of the bandgap.
Auger Recombination
This is a process in which an electron in the conduction band recombines with a hole in
the valence band by imparting its energy to another electron or hole in the form of kinetic
energy, hence it is a non-radiative recombination. It is important to take this process into
account because the involvement of the third party affects the recombination rate. The Auger
recombination rate is given by
Uauger = Γn n(pn − n2i ) + Γp p(pn − n2i )
(2-69)
The two terms correspond to the involvement of an electron and a hole as a third party. This
mechanism is highly dependent on the carrier concentration, as it is highly dependent on the
rate of collision.
Surface Recombination
Because of the abrupt termination of semiconductor crystal at surfaces and interfaces, surfaces
and interfaces typically contain electrically active states acting as non-radiative recombination
centers. Besides, because of their exposure during device processing, surfaces and interfaces
M.Sc. thesis
Ataklti G.W.
20
The Physics of Semiconductor Nano-heterostructures
are likely to contain impurities, which can also give rise to deep energy levels. The surface
recombination rate is given by
Us,SRH =
pn − n2i
Nts vth σ
−Et
]
p + n + 2ni cosh[ EikT
(2-70)
This expression is very much the same as that of SRH recombination equation (2-67), except
that this recombination is due to a two dimensional density of traps Nts , as the traps exist
only at the surfaces and interfaces.
For intrinsic semiconductor however n = p = nex , the rate equation is given by
Us,SRH =
n2ex − n2i
v
−Et s
2nex + 2ni cosh[ EikT
]
(2-71)
Where Vs = Nst Vth σ is the surface recombination velocity at room temperature for common
semiconductors given by table(2-2)
Semiconductor
GaAs
InP
Si
Vs
106 cms−1
103 cms−1
10 cms−1
Table 2-2: Surface recombination velocity (Values taken from[37])
In low dimensional structures like nanowires, due to their high density of surface states the
effect of surfaces states on the properties of the semiconductor is highly pronounced.[30, 43]
2-6
Metal-Semiconductor Interface
Metal-semiconductor interfaces are of great importance since they are present in every
semiconductor device. They behave either as Schottky barriers or as Ohmic contacts
depending on the characteristics of the interface. When a semiconductor is brought into
physical contact with a metal, there is charge redistribution in which electrons flow from
the metal to the semiconductor or vice-versa, until thermal equilibrium is reached. At
thermal equilibrium the Fermi-levels in the semiconductor and metal should be coincident.
As the result of charge redistribution, a space charge region or depletion region, populated
by ionized impurities, is created at the semiconductor side of the interface, with a built in
electric field as shown in figure (2-10). This built in electric field gives rise to a potential
barrier, at the metal-semiconductor interface, called Schottky barrier. Owing to this built in
potential metal-semiconductor contacts demonstrate rectification behavior, very much like a
pn junction, when an external voltage is applied[17].
However, when the semiconductor in contact with the metal is intrinsic, with no ionized
dopants, the built in field can be due to two main reasons. The first reason can be electrically
active states at the interface which are predominantly because of charge fluctuations at
Ataklti G.W.
July 17, 2007
2-6 Metal-Semiconductor Interface
21
(a)
(b)
(c)
Figure 2-10: Metal-semiconductor energy band diagram (a) before contact (b) after contact (c)
after built in potential
the interface attributed to the difference in charge density between the metal and the
semiconductor side[4]. Furthermore chemical reactions and interdiffusion at the interface
give rise to local charge redistribution and an effective work function change[7]. The other
reason can be the Fermi level pinning at the semiconductor. The Fermi-level pinning can be
because of impurity like interface states increasing the density of states at the interface[28]
and as a result of surface states due to native oxide layer[33].
Let’s consider a semiconductor in contact with a metal; the barrier height, φB defined as the
potential difference between the Fermi-energy of the metal and the semiconductor band edge
is given by
φB = φm − χ
(2-72)
for an electron in the conduction band, and
φB =
Eg
+ χ − φm
e
(2-73)
for a hole in the valence band. Where χ is the electron affinity of the semiconductor and φm
is the work function of the metal. A metal-semiconductor interface therefore forms a barrier
for both electrons and holes. The built in potential as a result of charge redistribution is
given by
φin = φm − χ −
M.Sc. thesis
Ec − Ef
e
(2-74)
Ataklti G.W.
22
The Physics of Semiconductor Nano-heterostructures
for an electron in the conduction band and
φin = χ +
Ec − Ef
− φm
e
for a hole in the valence band. The width of the depletion region is given by
r
2²r ²o
φin
W =
eNa
(2-75)
(2-76)
where Na is the number of ionized dopants.
The built in potential can however, be lowered or increased for example by applying an
external voltage. In forward bias the potential across the interface is given by
φext = φin − Va
r
W =
2²r ²o
(φin − Va )
eNa
(2-77)
(2-78)
And for a case of reverse bias the potential across the interface is given by
φext = φin + Va
(2-79)
The depletion width is then
r
W =
2²r ²o
(φin + Va )
eNa
(2-80)
where Va is the applied external voltage. Therefore, equations (2-78) and (2-79) show that
the barrier height is lowered in forward bias and increased in the case of reverse bias.
The Schottky barrier can also be lowered by image charge built up on the metal electrode
of the metal-semiconductor interface. The electric field associated with the charge lowers
the effective potential across the barrier by screening the built in electric field. This barrier
lowering is experienced by the carriers at the vicinity of the interface.
The current across the metal-semiconductor is mainly because of three mechanisms namely,
diffusion, thermionic emission and quantum-mechanical tunneling. Diffusion current is
mainly because of carriers moving from the semiconductor into the metal. Thermionic
emission current is attributed only to carriers with energy equal to or greater than the
conduction band energy at the metal-semiconductor interface and can hop over the barrier.
While the tunneling current is because of the carriers tunneling through the barrier taking
advantage of their wave nature.
Ataklti G.W.
July 17, 2007
2-6 Metal-Semiconductor Interface
23
Figure 2-11: Energy band diagram in (a) forward bias (b) reverse bias .
The diffusion and thermionic current is given by
·
¸
−φb
Va
Jn = evNc exp(
) exp( ) − 1
Vt
Vt
(2-81)
Where e is the electron charge v carrier velocity, Nc is the density of available carriers in the
semiconductor located next to the interface and Vt is the thermal voltage given by,
Vt =
kT
e
(2-82)
Where k is Boltzman’s constant and T is the temperature in Kelvin. The velocity is given
by the product of the mobility of carriers and the electric field across the junction. The
minus one in equation (2-81) ensures that the current is zero when there is no applied voltage.
Separately, the diffusion-drift current is given by
s
·
¸
e2 Dn Nc 2e2 (φi − Va )ND
−φb
Va
Jn =
exp(
) exp( ) − 1
Vt
εs
Vt
Vt
(2-83)
From equation(2-83) we can see that the current exponentially depends on the applied voltage
Va and on the built in potential φi . The electric field Ein at the metal semiconductor interface
is given by
s
2e2 (φi − Va )ND
Ein =
(2-84)
εs
Substituting equation (2-84) into equation (2-83)
·
¸
−φb
Va
Jn = eµc Ein Nc exp(
) exp( ) − 1
Vt
Vt
M.Sc. thesis
(2-85)
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24
The Physics of Semiconductor Nano-heterostructures
Here the prefactor eµc Ein equals the drift current at the metal-semiconductor interface,
which for zero applied voltage exactly balances the diffusion current.
The thermionic emission theory assumes that only electrons with energy larger than the top
of the barrier can cross the barrier provided that they are in the vicinity of the interface.
Hence the actual shape of the barrier does not matter. The current can be expressed by
·
¸
−φB
Va
Jms = A∗ T 2 exp(
) exp( ) − 1
(2-86)
Va
Vt
where φb is the barrier height and A∗ is the Richardson constant given by
A∗ =
4πm∗ ek 2
h3
(2-87)
The expression for the thermionic current can also be written in terms of Richardson velocity
VR , the average velocity with which the carriers at the interface approach the barrier,
r
kT
VR =
(2-88)
2πm
So that equation (2-86) can be written as
Jms
·
¸
−φB
Va
= eVR Nc exp(
) exp( ) − 1
Va
Vt
(2-89)
The tunneling current is a function of the Richardson velocity VR and the density of the
available carriers and it is written as
Jt = eVR nΘ
(2-90)
where the tunneling probability Θ is given by
4
Θ = exp[−
3
Here the electric field is equal to E =
2-7
φB
L
3
√
2em∗ φb2
]
h
E
(2-91)
, where L is the width of the barrier.
Addition of an External Electric Field
The energy band structure across a semiconductor heterostructure can be modified by applying an external electric field along the growth direction. Let’s assume a quantum dot
in a nanowire heterostructure in which an external electric field is applied, (for example by
connecting to an external voltage source) along the growth direction. The effect of adding
the external electric field is to add a linear potential energy term to the total potential energy
in the total Hamiltonian of the Schrödinger equation of motion of electrons and holes in the
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July 17, 2007
2-7 Addition of an External Electric Field
25
quantum dot. For an electron in the conduction band and a hole in the valence band, these
linear terms can be given by −eF z and eF z respectively, where z is the confinement width,
F is the applied electric field and e the electron charge. The Schrödinger equation, in the
presence of an external electric field, for one dimensional motion can be written as
·
¸
~2 ∂ 2
− ∗ 2 + (Vo (z) − eF z) ψ(z) = Ez ψ(z)
2me ∂z
(2-92)
for an electron in the conduction band and
·
¸
~2 ∂ 2
− ∗ 2 + (Vo (z) + eF z) ψ(z) = Ez ψ(z)
2mh ∂ z
(2-93)
for a hole in the valence band. Where Vo (z) is the potential energy in the absence of the
electric field.
For small applied fields the effect of the field on the confined energy level can be treated as a
first order perturbation theory.
~ 1i
∆E 1 = hψ1 |(−eF~ · Z)|ψ
(2-94)
For an electric field applied along the confinement direction, the correction term is given by
Z ∞
∆E =
ψ1∗ (−eF Z)ψ1 dz
(2-95)
0
In equation (2-95) the wavefunction of the ground state of a symmetric potential well is an
even function; hence the integrand is an odd function. Consequently the evaluation of the
integral gives zero. This is physically true as the change in energy should not be dependent
on the the direction of the field. The first order addition of a small applied field to the energy
level has no effect. The effect of large electric fields can, however, be evaluated using the
second order perturbation theory which is more accurate and more precise.
+∞
X
|hψm |(−eF z)|ψ1 i|2
∆E =
Em − E1
2
(2-96)
m=2
Which can also be written as
∆E
(2)
=
+∞ |
X
m=2
R∞
2
∗
−∞ ψm (−eF z)ψ|
Em − E1
dz
(2-97)
The sum is over all the excited states, including those with an energy Em > E1 the so called
quantum level. Since the applied electric field is independent of z the second order correction
term to the energy E (2) is proportional to F 2 i.e. E (2) αF 2 . The ground state energy of the
electron and the hole in the presence of an external electric field can be written as
Ege = Eoe − aF 2
(2-98)
2
(2-99)
Egh = Eoh − bF
M.Sc. thesis
Ataklti G.W.
26
The Physics of Semiconductor Nano-heterostructures
respectively
where Eoe and Eoh are the ground state energy in the absence of an external field, a and b
are proportionality constants which can be determined form experiments or calculations. In
Eq. (2-97) for the lowest energy states, which are usually of interest, all the denominators
Em − E1 and numerators are always positive. As a result, the second order perturbation
correction term to the energy is always negative. Hence the values of the constants a and b
are positive.
F
F=0
Ec
E
E
Ev
(a)
(b)
Figure 2-12: Energy band diagram (a) zero external field (b) under external field
Since a charged particle prefers to move to the areas of lower potential as seen in figure (2-12b),
the electron in the potential well moves to the left hand side of the well, thus lowering
its total energy. This lowering of confined energy level by an electric field is called quantum confined stark effect, which is a common experimental observation in semiconductor
heterostructures.[12, 14, 32, 39] The electric field induced change of exciton excitation energy
is given by[20]
∆Eexc = δEe1 + δEh1 − δε
(2-100)
Where δEe1 and δEh1 are the change in first energy levels of the electron and the hole as a
result of the external field and δε is the change in the exciton binding energy. The change in
exciton binding energy is because of the relative shift in the spatial position of electron and
hole into the opposite sides of the well as shown in figure (2-12b).
The energy correction term can also be determined using a simpler approach; because the
electron moves to the side of lower energy it gets polarized and generates a dipole moment
p = −hxie. For small fields the dipole moment is proportional to the magnitude of the field.
Hence
p = ²o αF
(2-101)
where ²o is the permittivity of free space and α is the polarizability of the material.
Consequently the shift of the position of the electron wave function ( see fig. (2-12b)) lowers
the electron energy by − 21 ²o αF , which is the energy of an induced dipole.
However if the applied field is very large, it can no more be assumed as a perturbation;
consequently neither the perturbation theory nor dipole approximation is valid. Lets consider
Ataklti G.W.
July 17, 2007
2-7 Addition of an External Electric Field
27
the case of our quantum dot at a very high electric field, the tilting of the energy band
creates a triangular tunneling barrier, as seen in figure (2-13), whose width decreases with
an increase in the magnitude of the electric field. The bound state in the dot has a finite
tunneling probability to tunnel through the barrier. This process of tunneling under high
electric field is called Fowler-Nordheim tunneling.[9]
F
Figure 2-13: Electron tunneling as a result of electric field.
The tunneling probability can be derived from the time independent Schrödinger equation
·
¸
~2 ∂ 2
− ∗ 2 + V (z) ψ(z) = Ez ψ(z)
2me ∂z
(2-102)
which can be explicitly written for one dimension as
d2 ψ(z)
2m∗ (V (z) − E)
=
ψ(z)
dz 2
~2
(2-103)
Assuming that V (z) − E remains constant over an interval z and z + dz and the particle is
moving from left to right the above equation can be solved to give
ψ(z + dz) = ψ(z)exp(−κdz)
(2-104)
√
where κ =
2m∗ [V (z)−E]
~
For a slowly varying potential the wave functions at the the right edge of the well (z = 0)
and after the tunneling through the barrier (z = `) can be related as
· Z Lp ∗
¸
2m [V (z) − E]
ψ(L) = ψ(0)exp −
dz
(2-105)
~
0
The above equation is referred to as the WKB approximation. Based on this approximation
the tunneling probability T for a triangular barrier given by V (z) − E = ∆E is
M.Sc. thesis
Ataklti G.W.
28
The Physics of Semiconductor Nano-heterostructures
· Z ` √ ∗r
¸
ψ(`)ψ ∗ (`)
2m
z
T =
= exp −2
∆E(1 − )dz
ψ(0)ψ ∗ (0)
~
`
0
(2-106)
Up on evaluating the integral
3 ¸
√
·
4 2m∗ ∆Ec2
T = exp −
3
F~
(2-107)
Where ∆E is the barrier height, in this case it is given by the energy difference between the
conduction band of say InP and the occupied energy level of InAsP, and F is the electric
field given by F = ∆E
e` . For details of the derivation the reader can refer to[9]. According to
equation(2-107) we can see that in the absence of an external field the tunneling probability
approaches zero.
In line with the objective of the research let’s consider an electron promoted from the valence
band to an energy level En in the conduction band. Taking a semiclassical approach, the
kinetic energy of the electron and the energy En can be related as
En =
~kn2
m∗ v 2
=
2m∗
2
Therefore velocity of the electron can be given by v =
of tunneling by the electron per unit time is given by
q
2En
v
m∗
A=
=
2L
2L
(2-108)
~kn
m
q
=
2En
m∗ .
The number of attempts
(2-109)
Where L is the width of the quantum dot. Let’s take the rate equation of the quantum dot
(in this case other processes such as recombination are neglected.)
dN (t)
= −N (t)T A
dt
(2-110)
N(t) is the number of electrons in the dot at a given time t and is given by
N (t) = No exp(−T At)
(2-111)
If we assume that the initial number of electrons in the dot No , is one the occupation probability of the dot is given by;
R(t) = exp(−T At)
(2-112)
Numerical calculations have been made on the probability of the occupation of the conduction
band of InAsx P(1−x) quantum dot in InP nanowire, as a function of applied voltage, for
x = 0.25, and width of 10 nm and wire length 2 µm. In these calculations the effect of the
Ataklti G.W.
July 17, 2007
2-7 Addition of an External Electric Field
29
(a)
(b)
(c)
(d)
Figure 2-14: Occupation probability of the conduction band of an InAsP quantum dot under
external voltage (a) the ground energy level at 2V. And the first excited state (b) at 2 V (c)
The colors represent occupation probability at a given voltage (blue) zero and (red) one (d) three
dimensional plot
hole in the valence band on the occupation probability is not taken into account.
Numerical calculations show that only electrons occupying the excited electron states in the
conduction band can tunnel out of the dot at a reasonable time when an external voltage of
equal to or greater than 2 V is applied, for the given dot parameters as shown in figure (2-14).
However, in addition to tunneling out of the dot there are other fates for electrons in a
quantum dot. Let’s assume that electron-hole pairs are created within a quantum dot using
laser pulses of frequency f. If the τrad , τnonrad and τt are the radiative, nonradiative and
tunneling lifetimes of the dot respectively, the rate equation is given by
N (t)
N (t)
N (t)
dN (t)
=f−
−
−
dt
τrad
τnonrad
τt
(2-113)
The number of excitons at any time t is then given by
N (t) =
f
1
τef f
M.Sc. thesis
+ No exp(−
t
τef f
)
(2-114)
Ataklti G.W.
30
The Physics of Semiconductor Nano-heterostructures
Where τef f is the effective life time given by
1
τef f
=
1
τrad
+
1
τnonrad
+
1
τt
(2-115)
If initially the dot is neutral (No = 0),
N (t) =
2-8
f
1
τef f
= f τef f
(2-116)
Principle of Photoconductivity
The conductivity of semiconductors is proportional to the concentration of carriers within
the semiconductor. When a fraction of an incoming flux of photon is absorbed by a semiconductor, electron-hole pairs are created, this results in an increase in the conductivity of the
semiconductor. Let’s take a piece of semiconductor illuminated by photons of energy larger
than the energy band gap, the change in conductivity as a result of the photo-generated
carriers is given by
∆σ = e(µn ∆n + µp ∆p)
(2-117)
Where e is the electron charge, µn and µp are the electron and hole mobility, ∆n and ∆p are
the changes in the concentration of electrons and holes as result of the irradiation, respectively.
Since an incoming photon of lower energy than the band gap Eg can not be absorbed, the
cutoff wavelength λc is given by
λc =
hc
Eg
(2-118)
where c is the speed of light. For extrinsic semiconductors however, due to deep levels,
photons of energy less than the band gap can be absorbed and contribute to photoconductivity.
Let’s consider a nanowire of radius r and length l contacted between two metal electrodes. If
the nanowire is illuminated by an optical power P, the optical power decrease with distance
from the surface of the wire due to absorption is expressed as
dP (x)
= −αP (x)
dx
(2-119)
P (x) = Po (1 − R)exp(−αx)
(2-120)
This gives
Ataklti G.W.
July 17, 2007
2-8 Principle of Photoconductivity
31
where po is the incident optical power, R is the reflection coefficient, thus Po (1 − R) is the
fraction of the optical power transmitted at the surface of the nanowire. For constant photon
flux, the excess carrier density due to photon absorption is given by
nex =
τ αPo (1 − R)exp(−αr0 )
hν2πrl
(2-121)
Where τ is the carrier lifetime, ν is the frequency of the incoming photon and h is Planck’s
constant. The number of carriers generated within the nanowire depth, in this case in the
radial direction is given by
dN = nx 2πldr0 =
Z
2r
N=
0
τ αPo (1 − R)exp(−αr0 )
(2πldr0 )
hν2πrl
τ αPo (1 − R)exp(−αr0 )
(2πldr0 )
hν2πrl
(2-122)
(2-123)
which gives
N=
τ α(1 − R)Po
[1 − exp(−2αr)]
hν
(2-124)
If an external voltage V is applied across the two ends of the nanowire, the photo-generated
carriers can be swept out of the nanowire before they recombine, hence contributing to photocurrent. The photocurrent can then be written as
Iph =
eτ α(1 − R)Po
[1 − exp(−2αr)]
hνtr
(2-125)
Where e is the electron charge and tr is the carrier transit time. For a given applied voltage,
V and carrier mobility µ, assumed to be the same for electrons and holes, it is written as
tr =
l2
µV
(2-126)
The current can also be expressed in terms of photocurrent quantum efficiency ηph , the
probability that an incident photon will generate an electron-hole pair that will effectively
contribute to photocurrent, is
Iph = ηph
ePo
hν
(2-127)
Hence the photocurrent quantum efficiency is given by
ηph = (1 − R)ζ[1 − exp(−2αr)]
(2-128)
where ζ = tτr is is the fraction of photo-generated carriers that do not recombine and
contribute to current.
M.Sc. thesis
Ataklti G.W.
32
The Physics of Semiconductor Nano-heterostructures
The photocurrent is directly proportional to the incident optical power, as
Iph = RePo
(2-129)
e
The proportionality constant Re = ηph hν
is called responsivity. It is the ratio of the incident
optical power to the output current and has dimension of AW −1 and it is dependent on the
applied voltage.
The objective of the theoretical background is to point out all the possible processes an
electron-hole pair generated in the quantum dot section of a nanowire heterostructure might
undergo as drifted into the metal contacts by an applied electric field, so that it will contribute
to a current. Let’s assume that an electron-hole pair is generated within the InAsP quantum
dot by resonant excitation with a pulse of frequency f. If τp is the duration of the pulse,
which is normally longer than the time required to create an exciton, and τt is the tunneling
time out of the dot, τre is the effective lifetime associated with radiative and nonradiative
processes and tr is the transit time required by the electron/hole tunneling out of the dot to
travel the InP section of the wire, a quantized current given by f e can be measured provided
that
τt + tr < τre
(2-130)
If the rate of repetition of the laser pulse is longer than the tunneling time, the dot will be
populated by only one electron for every cycle.
Ataklti G.W.
July 17, 2007
Chapter 3
Device Fabrication and Experimental
Setup
The nature of this research demands electrically contacted nanowires, to combine optical and
transport measurements. To realize the device a number of processing steps are followed. In
this chapter basic processing and experimental set ups are discussed.
3-1
Device Processing
The InP/InAsP nanowires studied in this project are grown by VLS method using gold
nanoparticles, on InP(111) substrates. The nanowires are then transferred from the as-grown
chip to a Si substrate, with a SiO2 layer, for direct optical measurements or further
processing. For photoluminescence measurements nanowires are transferred to a bare Si
substrate whereas for making electrical contacts the nanowires are transferred to a Si chip
with predefined markers.
For making electrical contacts the following steps were followed
step 1 Wire transfer
In this research three transfer techniques were used.
The first wire transferring technique consists in flipping the as-grown chip on the top
of the processing chip, so that some of the wires break and fall onto the processing
chip. In this technique there is a high risk of damaging the wires remaining on the as
grown chip as well as the wires transferred. Furthermore the density of the transferred
nanowires can not be controlled
The second technique is by forming nanowires solution. In this technique a piece
of as-grown chip is put in a beaker containing IPA. The beaker is then put in a
M.Sc. thesis
Ataklti G.W.
34
Device Fabrication and Experimental Setup
sonicator for a few seconds. As a result of the vibration, the nanowires break off
from the substrate and form a solution in the IPA. The wires are then transferred by
dropping a droplet of the solution on the processing chip. The density of the nanowires
transferred can be controlled by optimizing the concentration of the solution. In this
technique, it was observed that most of the wires were not breaking off from the surface.
The third technique is transferring using a piece of tissue-paper. A piece of tissue-paper
with a very sharp end which looks more like an AFM probing-tip was prepared. Small
sections of the as-grown chip was scratched using the tip of the tissue, the tip was then
brought in a gentle contact with the processing chip, so that some of the nanowires fall
on the chip. All the above mechanisms are iterative processes.
step 2 300 nm thick MMA first layer resist and 200 nm thick PMMA as second layer were
spined on the processing chip.
step 3 Pictures of nanowires on the chip were taken to locate the position of the wire with
respect to the predefined markers on the chip. These pictures are used for making
design CAD pattern for the contacts.
step 4 A contact pattern is generated on the chip by electron beam pattern generator (EPBG).
step 5 The written pattern is developed using MIBK/IPA solution.
Marker
Nanowire
(a)
(b)
Figure 3-1: Optical microscope image of a nanowire (a) next to predefined marker (b) with metal
contacts
step 6 Oxygen plasma descum is used to remove the resist residue from the pattern generated
and buffered HF etching is done to remove the oxides formed on the pattern as a result
of descum.
step 7 The sample was then mounted in an ultra high vacuum evaporation chamber where a
first 100 nm Ti layer followed by 10 nm Al layer were evaporated for making electrical
contacts.
Ataklti G.W.
July 17, 2007
3-2 Experimental Setup
35
step 8 The last step of the processing is lift off. The sample is put in hot acetone (55o C)
followed by IPA rinsing. In this step, all evaporated metal is removed leaving only the
contacts.
3-2
Experimental Setup
The experimental set up in this project consists of both optical and transport instruments.
The µ − P L setup is schematically drawn as shown in figure (3-2)
Laser
Spectrometer
optical
density
wheel
LED
He- objective
flow NA=0.75
crystal
BS
filter
power meter
Figure 3-2: Schematic representation of the µ − P L setup. The optical path of the laser (green
line) the light emitted from sample (red line). figure taken from [26]
The sample is mounted on a stage inside a liquid helium flow optical cryostat which enables
both optical and electrical access to a single nanowire. The cryostat consists of a computer
controlled movable stage where the sample is mounted and an outlet that connects the
nanowire to a voltage source. The sample inside the cryostat can be cooled down to 4 K by
flowing liquid helium through a tube connected to a helium vessel.
As a source of excitation power two types of laser sources were used namely, a Ti:Saphh laser
whose output wavelength can be tuned from 700 nm to 1000 nm and can give an optical power
of up to 2 W and a frequency doubled Nd:YAG 532 nm green laser source which can give an
optical power up to 50 mW. The intensity of the laser beam is controlled by an optical density
wheel and is sent to a 50-50 beam splitter. The part of the incoming laser passing through
the beam splitter is sent to a power meter for optical power measurement and the part of
the beam reflected by the beam splitter is sent to the sample in the cryostat via an objective
which can focus the beam in a spot of 500 nm in diameter. The nanowire inside the cryostat
can be imaged using a CCD camera, hence a selected nanowire can be illuminated by the laser.
M.Sc. thesis
Ataklti G.W.
36
Device Fabrication and Experimental Setup
The light emitted by the nanowire is collected by the objective and sent to a spectrometer
through the beam splitter. For proper data collection the laser beam reflected from the
sample is filtered using an appropriate filter. The emitted light dispersed by a grating
and the spectrum is acquired by a detector array. Two types of detectors are used in this
experimental set up, namely, a Si-CCD camera and an InGaAs array, which are both cooled
by liquid nitrogen. The more efficient Si detector can only detect down to 1.2 eV and the
more noisy InGas detector can detect down to 0.7 eV . The data from the spectrometer is
collected by a computer.
For the electronics setup a home made rechargeable battery as a voltage source and digital to
analog converter for interfacing with computer were used. The electronics setup has different
gain setting and can measure a current as small as 0.1 pA.
Ataklti G.W.
July 17, 2007
Chapter 4
Results and Discussions
4-1
Photoluminescence Measurement on a Single Nanowire
Optical characterization of nanowires provide fast and straightforward techniques to assess
the material quality of nanowires and probe the electron and hole energy levels in nanowires.
In this project photoluminescence measurements were carried out on different types of InP
nanowires and InP/InAsP nanowire heterostructures. The wires were grown by MOVPE on
InP substrates using gold particles as growth catalysts. For direct optical characterization,
nanowires were transfered from the growth substrate to a Si substrate, with a thin layer of
SiO2 on top, and optical measurements were done using different excitation energies.
4-1-1
Photoluminescence Measurement on a Single InP Nanowire
In this subsection photoluminescence measurement results from single intrinsic and n-type
InP nanowires are discussed.
50000
45000
Intensity (a.u.)
40000
35000
0.54kWcm-2
5.30kWcm-2
26.3kWcm-2
30000
25000
20000
15000
10000
5000
0
1.2
1.3
1.4
1.5
1.6
1.7
Energy (eV)
Figure 4-1: PL spectra of a single intrinsic InP nanowire for different excitation intensities at
2.33 eV excitation energy and 4.2 K.
M.Sc. thesis
Ataklti G.W.
38
Results and Discussions
Normalized Intensity(a.u.)
Figure (4-1) shows PL spectra of an intrinsic InP nanowire at very high excitation powers
(up to 26 kW cm−2 ) and excitation wavelength of 532 nm. As can be seen from the graph the
linewidth is very large (about 50 meV). The broadening of the linewidth can be attributed
to the large density of surface states. The effect of surface states on the linewidth of InP
nanowire has been reported i.e. a significant change on the linewidth with surface etching
with HF was demonstrated[30].
1.0
intrinsic
n-type
0.8
0.6
0.4
0.2
0.0
1.2
1.3
1.4
1.5
1.6
1.7
Energy(eV)
Figure 4-2: Comparison of normalized spectra between intrinsic and n-type InP nanowire. At
2.33 eV excitation intensity and 4.2 K
Figure (4-2) shows the comparison between PL spectra of intrinsic and n-type InP nanowires.
Similar results were reported by Van Weert et al. [47], however, the PL peak of the nanowires
studied show blue shift for both intrinsic and n-type wires. This may be attributed to the
difference in the diameter of the nanowire studied and the difference in excitation intensity
used. As can be seen from Figure (4-2) in addition to the dominant peaks, shoulder like
features were seen for both the intrinsic and the n-type nanowires. In case of the intrinsic
nanowires the dominant peak can be attributed to conduction band edge to valence band
edge transitions and the shoulder like feature can be attributed to deep levels associated to
surface states. While in the case of the n-type nanowires the dominant peak can be attributed
to electron transitions from donor levels to valence band edge and the shoulder like feature,
which coincides with dominant peak from the intrinsic nanowire, can be due to conduction
band edge to valence band edge transitions.
B9374 wire 4 high low power
right
middle
left
Counts (a.u.)
1500
1000
500
1.41
1.44
1.47
Energy (eV)
Figure 4-3: Spatial dependence of peak intensities at low excitation power, 2.33 eV excitation
energy and 4.2 K
Ataklti G.W.
July 17, 2007
4-1 Photoluminescence Measurement on a Single Nanowire
39
When very low excitation powers (about 2.5 W cm−2 ) were used, the shoulder like feature on
the spectrum of the intrinsic nanowires, shown in Figure (4-3), was resolved into multiple
peaks. When photoluminescence spectra were collected by scanning along the length of the
nanowires, a relative shift on the intensity was observed. This shows that the features are
associated to localized states which can be due to surface states and defects.
4-1-2
Photoluminescence Measurement on a Single InP/InAsP Nanowire
In this subsection photoluminescence measurement results from InP/InAsP nanowire
heterostructures with InAsP as a quantum dot are discussed. The results are mainly from
two sets of nanowires which were grown for 10 minutes and 20 minutes. The objective of
this optical characterization is to probe the electron energy levels of electrons and holes in
the quantum dot, in line with the objective of the project.
26000
24000
22000
20000
18000
16000
14000
12000
10000
8000
6000
4000
2000
0
-2
3500000
-2
3000000
5.10 kWcm
-2
2.55 kWcm
0.51 kWcm
-2
0.25 kWcm
Intensity(Counts/s)
Intensity(counts/s)
Figure (4-4) shows power dependent photoluminescence spectra from nanowires grown for
different growth time. In this measurement, the part of the spectrum larger than 1.47
eV was filtered out. As a result, direct qualitative as well as quantitative comparison on
the linewidth of the peak expected to be from InP is difficult. As can be seen from the
photoluminescence spectra, however, there are two peaks around 1.45 eV and 1.32 eV which
can be attributed to the InP and InAsP sections of the nanowires respectively.
2500000
2000000
1500000
1000000
500000
1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50
0
Energy(eV)
2
4
6
8
10
8
10
power(uW)
24000
22000
20000
18000
16000
14000
12000
10000
8000
6000
4000
2000
0
(b)
1600000
-2
5.10 kWcm
-2
2.55 kWcm
-2
0.51 kWcm
-2
0.25 kWcm
1400000
Intesnsity(a.u.)
Intensity(counts/s)
(a)
1200000
1000000
800000
600000
400000
200000
1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50
energy(eV)
(c)
0
0
2
4
6
power(uW)
(d)
Figure 4-4: Excitation intensity dependence of photoluminescence/integrated intensity of InP/InAsP nanowire of different growth time (a)/(c) 10 minutes (c)/(d) 20 minutes at 1.720 eV
excitation energy and 4.2 K.
M.Sc. thesis
Ataklti G.W.
40
Results and Discussions
26000
24000
22000
20000
18000
16000
14000
12000
10000
8000
6000
4000
2000
0
4500
10 minutes
20 minutes
4000
Intensity(counts/s)
Intensity(counts/s)
Figures (4-4b&d) show that there is a nearly linear relation between the optical excitation
power and the integrated photoluminescence intensity. There is more linear response to
optical power from intrinsic InP nanowires than the results reported in [26], on n-type
and p-type InP nanowire. The more linear response can be attributed to the smaller
concentration of deep levels in intrinsic wires than in doped wires. These deep levels are
associated with doping and cause nonlinear response to excitation power mainly because of
their contribution to non-radiative recombinations.
10 minutes
20 minutes
3500
3000
2500
2000
1500
1000
500
1.2
1.3
energy(eV)
(a)
1.4
1.5
0
1.2
1.3
1.4
1.5
energy(eV)
(b)
Figure 4-5: Comparison of Photoluminescence peak of nanowires of different growth time (a)
emission from entire nanowire (b) emission from the quantum dot section
Figure (4-5) shows the effect of growth time on the position of the photoluminescence
peak of InP/InAsP nanowire. As can be seen from the graphs, the effect of the growth
time is more pronounced on the InAsP peak, this is because of the fact that the quantum dot section is confined in three dimensions, the change in the length of one of the
dimensions affects the nature of the confinement which can result in a change of optical
properties. Whereas in case of the InP section since carriers are confined only in the
radial direction, the change in the length of the wire as a result of growth duration has
no effect on the optical properties. Furthermore it can also be seen that linewidth of
the photoluminescence spectra from the nanowire quantum dot is very broad (about 30
meV) and an order of magnitude larger than the linewidth of the spectrum from self
assembled quantum dots which is in the order of µeV . Owing to this linewidth broadening in the spectrum of nanowire quantum dots, the precise probing of energy levels is difficult.
The above direct optical characterizations enable to find out the appropriate dimensions of
a quantum dot that will enable resonant excitation with the laser source and experimental
setup at hand.
4-2
Photocurrent Measurement on a Single Nanowire
Photocurrent measurements on electrically contacted single nanowires were carried out.
These measurements are mainly on n-type and intrinsic InP nanowires and InP/InAsP
Ataklti G.W.
July 17, 2007
4-2 Photocurrent Measurement on a Single Nanowire
41
nanowire heterostructures with InAsP as a quantum dot section.
4-2-1
Photocurrent Measurements on n-type InP Nanowire
In this subsection photocurrent measurements from single n-type InP nanowires are discussed.
An n-type InP nanowire was electrically contacted using 100 nm Ti as first layer and 10 nm
Al as second layer. The objective of this measurement is to make electrical and optical
characterization of the nanowires by photocurrent measurements.
off
on
Current(nA)
200
100
0
-100
-200
-200
-100
0
100
200
Voltage(mV)
Figure 4-6: I-V curve of n-type InP nanowire at 2.33 eV excitation energy, 0.51 kW cm−2
excitation intensity and 4.2 K.
Figure (4-6) shows photocurrent (red curve) and dark current (black curve) measurements
on a single n-type InP nanowire. As can be seen from the I-V curve the semiconductor metal
contact is Ohmic. Similar contact behavior has been reported on n-type InP nanowires[26].
Furthermore, the nanowires were highly conducting even with no illumination and at very
low temperature (4.2 K), with a resistance of up to few kΩ. The Ohmic nature of the contacts
and the high conductivity of the wires is due to the high level of doping. Owing to the
high level of doping the dark current was not quenched by applying a voltage on the back gate.
The dark current and the photocurrent were also measured at a given constant applied voltage. Figure (4-7a) shows the ratio of photocurrent to dark current for two different excitation
powers, red curve 2.7 kW cm−2 and dark curve 5.3 kW cm−2 , of the same excitation energy
(1.49 eV). It can be seen that the ratio of the photocurrent to dark current is very small,
about 1.014 for 5.3 kW/cm−2 excitation power, this is because of the fact that the wires are
highly doped: the change in the concentration of carriers as a result of photoexcitation is not
so significant. Consequently, there is only a small change on the conductivity of the nanowire.
As can also be seen from figure (4-8) when the excitation laser was blocked, a delayed
conductance or memory effect was observed. Similar results have been reported on doped
Si-nanowires[27] and doped ZnO-nanowires[13, 25]. The delay was observed to be about 4
minutes, however a delay of up to several hours was reported by Fan et al.[13] This effect
can be attributed to trapping and releasing of carriers in deep energy levels. These levels
are usually associated with impurities and structural defects. Furthermore, as can be seen
M.Sc. thesis
Ataklti G.W.
42
Results and Discussions
1.018
on
1.016
1.020
-2
5.3kWcm
-2
2.7kWcm
off
1.014
790nm
810nm
870nm
940nm
1.015
1.012
Ion/Ioff
Ion/Ion
1.010
1.008
1.010
1.006
1.005
1.004
1.002
1.000
1.000
0.998
0
100
200
300
400
500
600
700
0
800
200
400
time(s)
time(s)
(a)
(b)
Figure 4-7: photocurrent measurement on n-type InP nanowire (a) ratio of photocurrent to dark
current at 200 mV (b) excitation wavelength dependence of photocurrent at 2.7 kW cm−2 excitation intensity and 4.2 K. The photocurrent was measured by periodically blocking the excitation
laser
161.0
160.5
Current(pA)
160.0
159.5
159.0
158.5
158.0
157.5
0
100
200
300
400
500
time(s)
Figure 4-8: Delayed conductance in n-type InP nanowire
from figure (4-7b) photocurrent was measured for excitation energy of 1.3 eV, which is less
than the energy band gap of InP which is 1.4 eV. This can be because of electron transitions
facilitated by the deep levels.
The other feature observed was a fluctuation on the photocurrent, this fluctuation can be
attributed to instability in the laser source giving rise to the fluctuations in photon flux
arriving on the surface of the nanowires.
4-2-2
Photocurrent Measurements on Intrinsic InP/InAsP Nanowires
In this subsection photocurrent measurement results from intrinsic InP nanowire and
InP/InAsP heterostructures are discussed.
Photocurrent Measurements on Intrinsic InP Nanowires
Photocurrent measurements from intrinsic InP nanowires demonstrated the Schottky nature
of intrinsic semiconductor-metal contact figure (4-9 black curve). Owing to the intrinsic
Ataklti G.W.
July 17, 2007
4-2 Photocurrent Measurement on a Single Nanowire
43
nature of the wires and the built in barrier at the metal-semiconductor interface, the dark
current Figure (4-9 red curve)is below the detection limit of the experimental setup, which is
0.1 pA. Asymmetric behaviors were also seen between the two metal-semiconductor contacts
which can be attributed to the difference in the nature of the two contacts associated with
device processing.
700
1000
1200
800
5.1kWcm
0W
-2
Current(pA)
600
400
200
0
-200
-2
600
500
100
Current (pA)
5.1kWcm
0W
Current(log scale)
1000
10
400
300
200
100
-400
-600
0
-800
0
-2
-1
0
1
1
2
2
0
voltage(V)
(a)
10
20
30
40
50
60
70
Excitation Intesnity (kWcm-2)
voltage(V)
(b)
(c)
Figure 4-9: Photocurrent of intrinsic nanowire (a) linear scale (b) logarithmic scale (c) power
dependence at 1.5 V and 1.77 eV excitation energy.
In contrast to the photoresponse of n-type nanowires, the photoresponse of intrinsic nanowires
is much faster (20 ms) as can be seen from figure (4-11a). Similar results have been reported
on intrinsic silicon nanowires.[27] The fast photoresponse is an indication of the lower density of deep levels in intrinsic nanowires than in n-type nanowires that can cause a delayed
conductance. The lower density of the deep levels was also demonstrated by the absence of
photocurrent for excitation energy less than 1.38 eV as shown in figure (4-11). This is in good
agreement with the photoluminescence measurements discussed in subsection 4−1−2. It was
also demonstrated that there is a nearly linear relationship between the excitation power and
the photocurrent, in good agreement with theoretical calculations. The slope is calculated to
2
be 17.3 pAcm
kW
0
-50
current(pA)
-100
-150
-200
-250
-300
-350
-400
-450
-1.4
-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
Voltage(V)
Figure 4-10: Photocurrent at 1.65 excitation energy, 660 kW cm−2 excitation intensity and 4.2
K
For a device different from the one given in figure (4-9) two regimes in the IV curve were
observed as can be seen in figure (4-10). A non-linear regime at low bias which can be because
M.Sc. thesis
Ataklti G.W.
44
Results and Discussions
of the forward biased Schottky barrier. And a linear regime at higher voltage which can be
an indication that the limiting factor is the rate of carrier generation and carrier extraction
efficiency. This can be an explanation for the noisy current in this linear regime.
30
30
1.65eV
1.55eV
1.46eV
1.38eV
1.32eV
20
25
current(pA)
Current(pA)
25
15
10
5
20
15
10
5
0
0
0
200
400
600
800 1000 1200 1400 1600
1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70
time(s)
Energy(eV)
(a)
(b)
Figure 4-11: Photocurrent of intrinsic InP nanowire at a constant bias of 1 V (a) periodically
measured photocurrent (b) Excitation energy dependence of photocurrent.
As can also be seen from figure (4-11) the ratio of photocurrent to dark current is very high.
This is because of the intrinsic nature of the nanowires, the intrinsic carriers concentration
at low temperature (4.2 K) is low. Therefore, the change in carrier concentration as a result
of illumination is very high giving rise to a very large change in conductivity. Furthermore
the Schottky barrier prevents carriers to enter the wire electronically, but doesn’t block the
excited carriers from traveling to the contacts (forward biased Schottky).
Intensity(counts)
Since the photoexcited carriers contributing to photocurrent are those escaping the recombination processes, a decrease in photoluminescence intensity by applying an external
voltage was observed. Figure (4-12) shows the decrease in photoluminescence intensity with
increasing external voltage
35000
30000
25000
20000
15000
10000
5000
0
-5000
0V
1V
2V
800
900
1000
1100
ntensity counts/10 s)
Wavelength(nm)
Figure 4-12: Photoluminescence under external voltage:
5.1 KW cm−2 excitation intensity and 4.2 K.
Ataklti G.W.
Bias V
at 2.33 eV excitation energy,
July 17, 2007
4-2 Photocurrent Measurement on a Single Nanowire
45
Photocurrent Measurements on Intrinsic InP/InAsP Nanowires
22
20
18
16
14
12
10
8
6
4
2
0
-2
20
18
1.65 eV
1.55 eV
1.46 eV
1.38 eV
1.32 eV
16
14
current(pA)
current(pA)
This subsection focuses on the photocurrent measurements from InP/InAsP heterostructure
nanowires. Since the contact nature of the heterostructure nanowire is determined by InPmetal contact, the same Schottky, asymmetric behavior and zero dark current were observed
in the I-V curve of the heterostructure nanowire as in the intrinsic InP nanowire discussed in
the previous subsection.
12
10
8
6
4
2
0
0
200
400
600
1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70
800 1000 1200 1400 1600
Energy(eV)
time(s)
(a)
(b)
1.4
1.2
InP
InP/InAsP
1.0
current(pA)
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
200
400
600
800
1000
1200
1400
time(s)
(c)
Figure 4-13: Photocurrent InP/InAsP nanowire heterostructure at constant bias of 1 V (a)
periodically measured photocurrent (b) Excitation energy versus photocurrent (c) photocurrent
measured at 1.32 eV excitation energy.
As can be seen from figure (4-13), similar photoresponse and ratio of photocurrent to dark
current was seen from intrinsic nanowires. Unlike in the case of intrinsic nanowires, however,
photocurrent was measured from 1.32 eV excitation energy, which is below the energy gap of
InP. This photocurrent is attributed to the photogenerated carriers within the quantum dot,
i.e InAsP section. This argument is also supported by the quenching of the photoluminescence
intensity from the quantum dot by applying an external voltage. Figure (4-14) shows the
intensity quenching from nanowire heterostructure by an external voltage.
Upon applying an external voltage in addition to quenching photoluminescence intensity,
quantum confinement stark effect(qcse) was demonstrated on the quantum dot emission. As
can be seen from Figure (4-15) as the external voltage was increased the photoluminescence
peak attributed to the quantum dot was quenched and shifted to lower energies i.e undergo
a red shift. This is in agreement with the quantum confinement stark shift observed in self
assembled quantum dots[14, 50]. However, as can be seen from figure (4-15b) the relationship
M.Sc. thesis
Ataklti G.W.
46
Results and Discussions
350
Peak Intensity(a.u.)
Intensity(a.u)
400
0V
0.5V
1.0V
1.5V
2.0V
400
200
300
250
200
150
100
50
0
1.15
1.20
1.25
0
1.30
0.0
0.5
1.0
1.5
2.0
Bias voltage(V)
Energy(eV)
(a)
(b)
Figure 4-14: Photoluminescence intensity dependence on bias voltage at 2.33 eV excitation
energy and 4.2 K (a) PL quenching (b) peak counts
B
1.228
2000
Intensity(a.u)
1600
1400
0V
0.5V
1.0V
1.5V
2.0V
1.226
Energy(eV)
1800
1200
1000
800
1.224
1.222
600
1.220
400
200
1.218
0
1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50
Energy(eV)
(a)
0.0
0.5
1.0
1.5
2.0
Bias Voltage(V)
(b)
Figure 4-15: Photoluminescence quenching and qcse in a nanowire quantum dot (a) PL quenching (b) Emission energy as function of applied voltage
between the emission energy of the quantum dot and the applied voltage is semi-quadratic,
despite quadratic theoretical predictions. This can be attributed to the effect of charging on
the relative shift of the PL peak. Preliminary gating measurements showed that(figure (4-16))
there is relative shift of the PL peak with positive gating. A negative backgate could discharge
the dot.
Figure (4-17) shows the effect external voltage on the photoluminescence and photocurrent
quantum efficiency. As can be seen from the figure, the photocurrent efficiency is much
larger than the photoluminescence efficiency. However, the sum of the carriers contributing
to photocurrent and recombining radiatively is much less than the number of photogenerated
carriers. This indicates that a significant part of the photoexcited carriers recombine nonradiatively. This is consistent with the relatively low efficiency of nanowire LEDs, as is
indicated by the dashed blue line in figure (4-17).
Ataklti G.W.
July 17, 2007
4-2 Photocurrent Measurement on a Single Nanowire
47
Backgate Vg
0V
+10 V
+20 V
Counts/s
100
50
0
1.20
1.25
1.30
PL emission energy (eV)
Figure 4-16: Effect of backgate on emission PL peak position under zero external voltage
Quantum efficiency (%)
10
PL
PC
EL
1
0.1
0.01
1E-3
1E-4
0.0
0.5
1.0
1.5
2.0
Bias (V)
Figure 4-17: Photoluminescence and photocurrent quantum efficiencies under external voltage
M.Sc. thesis
Ataklti G.W.
48
Ataklti G.W.
Results and Discussions
July 17, 2007
Chapter 5
Conclusions and Recommendations
5-1
Conclusions
This report is on work done to realize an optically triggered single electron turnstile or single
exciton pump using a single semiconductor nanowire heterostructure quantum dot. Electrical
and optical characterizations were done on different types of nanowires to find out the effects
of doping on electrical and optical properties of nanowires and to probe the energy levels
of carriers in the quantum dot. It was demonstrated that doping modified the transport
properties of nanowires by trapping and scattering carriers.
Due to their lower density of trap centers, intrinsic InP/InAsP nanowires are promising
systems to realize single exciton pumps. Photocurrent measurements showed very high
photoresponse of both intrinsic InP nanowires and InP/InAsP nanowires heterostructures.
At excitation energies less than the band gap energy of InP, photocurrent was measured
only from InP/InAsP heterostructures showing the absence of deep energy levels in InP that
could be simultaneously resonantly excited with the quantum dot. As a result, resonant
excitation of carriers within the quantum dot is possible.
By applying an external voltage it was shown that photocurrent and photoluminescence are
complementary. Photoluminescence intensities were quenched by applying an external voltage, showing that the carriers that do not undergo recombination contribute to photocurrent.
Upon applying an external field, the band bending in the quantum dot energy bands were
observed, forming a tunnel barrier for carriers in the dot to tunnel out of the dot. A shift
in the positions of PL spectra was also observed which can be attributed to the quantum
confined Stark effect and discharging of the dot.
Simulation results show the increase in tunneling probability of carriers from a quantum dot
with increasing applied voltage. It was shown that only electrons occupying energy levels
M.Sc. thesis
Ataklti G.W.
50
Conclusions and Recommendations
above the ground state tunnel out of the dot in reasonable time frame.
However, a broad linewidth in the spectrum of nanowire quantum dots is a bottleneck in
realizing single exciton pump. Optical characterizations indicated that the emission linewidth
of nanowire quantum dot is about 30 meV . This linewidth broadening is an obstacle to
precisely probe the energy levels of the quantum dot for resonant excitation. This linewidth
broadening can be associated with charging effects. A change in linewidth before and after
device processing was also observed.
5-2
Recommendations
As an alternative way to probe energy levels in a quantum dot absorption measurements can
be done. Since absorption measurements show components of an incident excitation photon
flux absorbed by a given nanowire, it will be possible to relate the components to the energy
levels.
As a solution to solve linewidth broadening: the effect of surface states can be avoided using
surface etching by HF and growing a shell of another material in the lateral direction of the
nanowire; for example GaP on InP. The effect of charging on the linewidth of the quantum
dot might also be solved by back gating.
Degradation of contacts with time was observed on fabricated devices. This can be due to
oxidation of the metal contacts or formation of an oxide layer in the metal semiconductor
interface. Keeping the devices in liquid nitrogen can be a solution. Electrically contacted
nanowires were observed to be blown out as a result of electrostatic charging. Careful handling
of devices to avoid the charging effect is recommended.
Ataklti G.W.
July 17, 2007
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