Experimental and theoretical
study of quantum dot resonant
tunneling diodes for single photon
detection
Ying Hou
Department of Theoretical Chemistry
School of Biotechnology
Royal Institute of Technology
Stockholm, Sweden 2008
c Y Hou, 2008
°
ISBN 978-91-7415-117-6
Printed by Universitetsservice US AB, Stockholm, Sweden, 2008
3
Abstract
Single photon detection has a broad application in the medical, telecommunication,
as well as in infrared imaging fields. In this thesis I present my work in studying
quantum dot (QD) resonant tunneling diodes (RTD) for single photon detection.
The device was processed in the form of a free-standing small-area air bridge. A
detailed series of experimental and theoretical characterizations have been performed
to understand the electrical properties of the RTDs (without embedding any QDs)
and QD-embedded RTDs (QDRTDs). It has been shown that external series and
parallel resistances shift the resonant current peak to higher voltage, create the
bistability effect observed in I − V characteristics, and reduce the peak-to-valley
ratio. For the QDRTD device, three-dimensional wave packet carrier transport
simulations show strong influence of the long-range Coulomb potential induced by
the hole captured by the embedded InAs QDs, thus demonstrating the fundamental
principle of single photon detection.
Two works are planned for the continuation of the graduate study after Lic examination. The optical response of the QDRTD will be experimentally and theoretically
characterized in order to optimize the quantum efficiency for single photon detection. I will then concentrate on processing a one-dimensional photodetector array
aiming at practical biotechnology applications.
4
Preface
The work presented in this thesis has been carried out at the Department of Theoretical Chemistry, School of Biotechnology, Royal Institute of Technology, Stockholm,
Sweden, and the National Laboratory for Infrared Physics, Shanghai Institute of
Technical Physics, Chinese Academy of Science, Shanghai, China.
Paper I Effects of series and parallel resistances on the current-voltage characteristics of small-area air-bridge resonant tunneling diodes, Y. Hou, W.-P. Wang, N.
Li, W.Lu, and Y. Fu, J. Appl. Phys. in press.
Paper II Carrier wave-packet transport under the influence of charged quantum
dot in small-area resonant tunneling diodes, Y. Hou, W.-P.Wang, N. Li, W.-L. Xu,
W. Lu, and Y. Fu, Appl. Phys. Lett. in press.
Paper III Dark currents of GaAs/AlGaAs quantum-well infrared photodetectors,
N. Li, D.-Y. Xiong, X.-F. Yang, W. Lu, W.-L. Xu, C.-L. Yang, Y. Hou, and Y. Fu,
Appl. Phys. A. vol.89, p.701-705, 2007.
The paper not included in the thesis but related:
Paper IV High photoexcited carrier multiplication by charged InAs dots in AlAs
/GaAs/AlAs resonant tunneling diode, W.-P. Wang, Y. Hou, D. -Y. Xiong, N. Li,
W. Lu, W. -X. Wang, H. Chen, J. -M. Zhou, E. Wu, and H. -P. Zeng, Appl. Phys.
Lett. vol.92, p.023508, 2008.
5
Comments on my contribution to the papers
• I was responsible for the experiment, calculation and writing of paper I.
• I was responsible for parts of the calculation and writing of paper II.
• I was responsible for parts of the discussion of paper III.
• I was responsible for parts of the discussion of paper IV.
6
Acknowledgments
I would like to express my sincere gratitude to my supervisor Dr. Ying Fu.
The experimental work in the thesis was performed at the Shanghai Institute of
Technical Physics, Chinese Academy of Science under the supervision of Prof. Wei
Lu. My deep thanks go to him for his guidance and for introducing me to my studies
in Sweden.
Special thanks to Prof. Hans Ågen for giving me the opportunity to work in this
wonderful department.
Deep thanks to Prof. Yi Luo for his warm-hearted helps.
Many thanks to Wangping Wang in the collaborations of experiments and Prof.
Hong Chen in material growth. I further like to thank the experimental help from
Prof. Ning Li, Prof. Pingping Chen, and Dr. Zhaolin Liu.
Many thanks for all the colleagues of our department here in Stockholm. It is very
nice to be a member of the Department of Theoretical Chemistry.
Thanks to the Chinese Scholarship Council for its financial support.
Thanks to the friends for their warm help when I stay in Sweden, especially to
Magnus, Maria, and Jani. Special thanks for my family for their constant love and
support.
Computing resources was acknowledged from the Swedish National Infrastructure
for Computing. The project partially supported by the National Natural Science
Foundation of China (Grant No:10474020) and Chinese National Key Basic Research
Special Fund (2006CB921507).
Ying Hou
Contents
1 Introduction
9
1.1
Microelectronics development . . . . . . . . . . . . . . . . . . . . . .
9
1.2
Single photon detection . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3
Resonant tunneling diode
. . . . . . . . . . . . . . . . . . . . . . . . 12
2 Operation theories for RTDs and QDRTDs
15
2.1
Basic semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2
Theoretical simulations of RTDs . . . . . . . . . . . . . . . . . . . . . 17
2.3
Theoretical simulations of QDRTDs . . . . . . . . . . . . . . . . . . . 19
3 Experiment and theoretical analysis
21
3.1
RTD experimental and theoretical analysis . . . . . . . . . . . . . . . 21
3.2
QDRTD experimental and theoretical analysis . . . . . . . . . . . . . 25
3.3
Future work on single photon detection . . . . . . . . . . . . . . . . . 28
7
8
CONTENTS
Chapter 1
Introduction
1.1
Microelectronics development
Since the invention of integrated circuits in 1959 by Jack Kilby and Robert Noyce,
microelectronics technology has made great progress. In 1965, Gordon Moore, the
co-founder of Intel, made his famous empirical observation that semiconductor component capacity would double every year [1]. Moore revised his prediction in 1975
that increased the time interval of doubling component capacity to 1.5-2 years. More
than 40 years has passed, yet the component density on silicon chip persistently increases approximately at that rate, showing that Moores law stands correctly to
describe the pace of the microelectronics [2, 3, 4]. Fig. 1.1 shows this development
trend [5].
The development of microelectronics capacity has been largely concentrated on re-
Feature Size (nm)
200
100
DRAM half pitch
80
60
50
40
30
MPU gate length
20
15
2000 2002 2004 2006 2008 2010 2012 2014
Year of Introduction
Figure 1.1: Microelectronics minimum feature size versus year [5].
9
10
CHAPTER 1. INTRODUCTION
ducing the device feature size from its initial size of 10 micrometer forty years ago
down to nowadays 30 nm. On the other hand, 30 nm is roughly the physical feature
size limit of classical semiconductors. The key to further development lies most
probably in nanotechnology [6]. When the size is scaled down to the nano scale,
revolutionary and novel physical phenomena have emerged. Among them is the
quantum confinement effect that the electron is confined in a region whose feature
size is comparable to the order of its de Broglie wavelength. Quantum mechanics
applies and results in new properties of the electron system such as the discretization
of electron energy levels along the confining direction. In the effort of scaling down
microelectronics, the bulk crystal is gradually replaced by thin films in the form of
quantum wells (QW), further down to quantum wires (QWR) and even quantum
dots (QD).
Electron transport through two-dimensional (2D) QW systems is characterized most
significantly by the resonant tunneling effect, while QDs are characterized by their
total three-dimensional (3D) confinement. Much effort has been concentrated on
applying QWs and QDs in microelectronics and optoelectronics. In my thesis, I will
try to study and develop QWs and QDs for single photon detection.
1.2
Single photon detection
Single photon detection is needed in order to detect very weak light with very high
sensitivity and good signal-to-noise ratio. It has extended applications in high energy physics, space science, medical imagining as well as telecommunication. Furthermore, single photon detection is needed for quantum telecommunication [7, 8].
Here, the concept of quantum key distribution (QKD) is expected to be realized in
the near future. Based on the Heisenburg uncertainty law, quantum key telecommunication has the character of secrecy, thus making it more advantageous than
traditional code telecommunication. The QKD technology critically requires sensitive single photon detector.
Photomultipliers Tube(PMT) [9] and avalanche photodiodes (APD) [10, 11, 12, 13,
14, 15] have been traditionally used for single photon detection. A single-photon
avalanche diode (SPAD) is shown on Fig. 1.2. All these devices have their own
advantages and disadvantages. In the visible and UV spectral ranges, PMT has
high multiplication, while in the infrared wavelength its quantum efficiency is low.
Furthermore, PMT has limited spatial resolution and is susceptible to magnetic fields
[12]. Thus, APD is the main stream in the infrared wavelength region. However,
1.2. SINGLE PHOTON DETECTION
11
Circular
SPAD
Quenching
& Gating
Figure 1.2: Single-photon avalanche diode array and a single photon detection system [16].
APD has a serious after-noise problem because of the avalanche working process.
New technologies are thus needed to improve efficiency and sensitivity as well as to
circumvent technical problems including the after noise. Much effort has been done.
One of the latest developments is a field-effect transistor gated by a layer of quantum
dots [17, 18]. In 2005, Blackesley et al. reported a new kind of single photon detector
based on the quantum dot resonant tunneling diode (QDRTD) [19]. The geometric
scheme and energy band structure are shown on Fig. 1.3. The device was made
up of three parts: photon absorption layer, QDs and RTD structure. This device
utilizes the electron resonant tunneling process which is controlled by QDs acting
as the electrical switch. The device system was a GaAs/AlGaAs RTD embedded
with InAs QDs, and the detection wavelength is about 850 nm. By modifying the
layer materials to AlAs/InGaAs/AlAs, Li et al. in 2006 reported a much extended
detection wavelength of 1310 nm [20, 21, 22]. This makes the device available for
telecommunication applications where the optical spectral range lies between 1310
and 1550 nm.
The single photon detector consists of a resonant tunneling diode (RTD) embedded
with QDs. When the RTD layers have the right voltage alignment a current can
tunnel through the structure. If misaligned, only little current flows. The layers
can be purposely slightly misaligned in such a way that capture by the QD of a
hole excited in the RTD by an incident photon can re-align the device, allowing
the tunneling current to resume. In other words, the arrival of a photon in the QD
results in the switch-on of the RTD.
12
CHAPTER 1. INTRODUCTION
(a)
(b)
z
h
b
a
InAs QD
Collector
Light
absorbing
layer
GaAs
hυ
InAs
QD
AlGaAs
GaAs
AlGaAs
W
B
GaAs
Electron
E0
y
x
Emitter
Ef Ec
Ev
Figure 1.3: (a) Schematic geometry and (b) energy band structure of the QDRTD
single photon detector.
1.3
Resonant tunneling diode
I introduce the resonant tunneling diode (RTD) concept briefly in this section. In
1973, Tsu and Esaki discovered the tunneling effect in superlattices. In the next
year, Chang et al. reported the resonant tunneling effect in double barrier semiconductor structures [23, 24]. More than 30 years have passed and RTDs have now
been widely developed and utilized in microelectronics and optoelectronics. All these
applications are largely based on two unique properties of the RTD: the negative
differential resistance (NDR) and the bistability in the NDR region. Fig. 1.4 shows
schematically the operation principle of the RTD. When the bias is gradually increased, the difference between the Fermi level in the emitter and the quasi sublevel
in the QW between the two barriers approach each other. When the two levels are
aligned, the penetration of the electron wave function through the barriers becomes
very long and resonant tunneling occurs.
RTDs have been used in oscillator circuits to compensate the ohmic losses coming
from the RLC components. Because of the two stable states and one unstable
operating point near the NDR region, the RTD can be integrated into the memory
devices of logic systems as shown on Fig. 1.5(a-c) [25, 26, 27]. In optoelectronics,
RTDs have also many applications. Fig. 1.5(d-f) show some of their applications on
circuits and optoelectronics [28, 29, 30, 31, 32, 33, 34, 35, 36].
1.3. RESONANT TUNNELING DIODE
13
I
P
Ip
Iv
Vp
Vv
V
Fermi Level
Conduction Band
Figure 1.4: Operation principle of the resonant tunneling diode (RTD).
(b)
(a)
V+
Write
Input
Output
Multi-Peak RTD
(c)
(d)
Metal interconnect
(f)
(e)
Figure 1.5: (a) RTD memory circuit [25], (b) RTD-CMOS (complementary metal oxide semiconductor transistor) [26], (c) RTD-heterojunction bipolar transistor (HBT)
[27], (d) RTD-heterojunction field-effect transistor analogue-to-digital converter [28],
(e) 64-element Schottky-collector resonant tunnel diode oscillator array [29], (f) RTD
optical modulator [36].
14
CHAPTER 1. INTRODUCTION
Chapter 2
Operation theories for RTDs and
QDRTDs
2.1
Basic semiconductors
Semiconductors are composed of a periodic array of atoms. The structure can be
described as a Bravais lattice and basis. In every Bravais lattice point there exist
a group of atoms. In the 3D space, there are 14 kinds of Bravais lattice structures.
Most semiconductor materials have the face-centred cubic (FCC) Bravais lattice
structure, which is shown in Fig. 2.1. The commonly used GaAs has a zincblend
structure which is composed of two sets of FCC Bravais lattices.
An electron having a kinetic momentum p can be described as a de Broglie wave
(a)
(b)
kz
L
Γ
ky
X
K
kx
X
Figure 2.1: FCC Bravais lattice structure in real space [37] and Brillouim k space.
15
16
CHAPTER 2. OPERATION THEORIES FOR RTDS AND QDRTDS
λ = h̄/p, and its wave function is described as ei(k·r−ωt) . Such an electron is described
by the following Schrödinger equation
µ
¶
h̄2 2
−
∇ + U ψ = Eψ
(2.1)
2m0
where m0 is the free electron mass in vacuum. In a crystal, we apply the effective
mass approximation where the vacuum electron mass m0 is replaced by an effective
electron mass m∗ so that [38]
µ ¶
1
1 ∂2E
=
(2.2)
m∗ ij h̄2 ∂ki kj
Note that different semiconductor materials have different effective masses. The
Schrödinger equation in the solid thus becomes
µ
¶
h̄2 2
− ∗ ∇ + U ψ = Eψ
(2.3)
2m
In the simplest case, we only need to concern ourselves with two bands: the valence
band and the conduction band. The gap between the two bands has no electron
energy state and is called the forbidden band. We can categorize the solid state
material into insulators, semiconductors, and conductors according to their bandgap
sizes. The bandgap of a semiconductor is smaller than that of an insulator, but larger
than that of a conductor. The electrons occupy the energy levels from low to high
energy according to the Pauli exclusion principle. At temperature 0 K, the highest
occupied band is known as the valence band, and the lowest unoccupied energy
band is known as the conduction band. Fig. 2.2 shows a schematic description of a
semiconductor energy band structure.
The density of states denotes the number of electron states per energy near E per
unit volume. According to Bloch’s theorem, the eigenstates are periodic and can be
described as:
3D
(r) = unk (r)eik·r
(2.4)
ψnk
by which the density of states of a three-dimensional system is:
µ ∗ ¶3/2
1
2m
N3 (E) = 2
E 1/2
2π
h̄2
(2.5)
Analogously, if the system becomes confined along the z axis direction such as a
QW, the density of states is
m∗
N2 (E) =
(2.6)
πh̄2 Lz
2.2. THEORETICAL SIMULATIONS OF RTDS
17
E
Conduction band
Egap
k
valence band
Figure 2.2: Energy band schematics of semiconductor material.
Here, Lz is the effective confinement size in the z direction. When the number of
dimensions is further decreased to one, i.e., a QWR,
r
1
2m∗ 1
√
N1 (E) =
(2.7)
2πSyz
h̄2 E
where Sxy is the effective confinement area in the yz plane. Finally, when all the
dimensions become confined, i.e. a QD, the density of states is
1 X
N0 (E) =
δ(E − Ei )
(2.8)
Vxyz
where Vxyz is the effective confinement volume of the zero dimensional system [39].
We now introduce the concept of Fermi level Ef that the probability of an energy
state E to be occupied by one electron at temperature T is described by the FermiDirac distribution function
1
f (E) =
(2.9)
exp [(E − Ef )/kB T ] + 1
The total number of electrons within the system can then be simply expressed as
Z
n = f (E)N (E) dE
(2.10)
where N (E) is the density of states discussed previously.
2.2
Theoretical simulations of RTDs
We first approximate the RTD as one-dimensional (1D). A self-consistent method
will be applied to solve the Schrödinger and Poisson equations. We apply the transfer
18
CHAPTER 2. OPERATION THEORIES FOR RTDS AND QDRTDS
matrix method [40] to solve the effective mass approximation of Eq. (2.3) in order to
describe electrons in the RTD. By the standard finite element method, we discretize
the 1D system into N equal sublayers along the RTD growth direction which is
defined as the z axis. The sublayer is thin enough so that the potential energy
within the sublayer can be approximated as constant. In the `th sublayer, the
general solution of the wave function and its derivative is shown to be:
¡
¢
A` eik` z + B` e−ik` z , ik` A` eik` z − B` e−ik` z
(2.11)
for (` − 1)∆ ≤ z ≤ `∆. We can write the wave function and its derivatives in layer
(` + 1) in a similar way. Standard boundary continuous conditions at the interface
of z = `∆ require that
A` eik` z + B` e−ik` z = A`+1 eik`+1 z + B`+1 e−ik`+1 z
¡
¢
¡
¢
ik` A` eik` z − B` e−ik` z = ik`+1 A`+1 eik`+1 z − B`+1 e−ik`+1 z
(2.12)
The above two equations have four unknowns, A` , B` , A`+1 , and B`+1 . We can find
the values of two of the unknowns when the other two are known. Starting at ` = 1,
we can write a series of such matrices so that all A` and B` can be determined from
A1 and B1 . This is normally referred to as the transfer matrix method.
We first consider the electron wave function propagation from the emitter (z ≤ 0)
to the collector (z ≥ L). Here we assume that the electron enters the active region
of 0 < z < L in the form of a plane wave eik0 z . A part of it will get reflected due to
the potential variation, which is expressed in the form of rk0 e−ik0 z . The rest will get
transmitted. The wave function and its derivative in the emitter and collector read:
¡
¢
z ≤ 0 : eik0 z + rk0 e−ik0 z , ik0 eik0 z − rk0 e−ik0 z
z ≥ L : tk0 eikL z , ikL tk0 eikL z
(2.13)
Here rk0 , tk0 is the reflection and transmission coefficient, respectively. After the
transfer matrix method calculation, we can get the current contribution from the
carrier of vector k0 .
¯ ¯
·¿
À
¸
¯d¯
eh̄
¯
¯
ψ(z) ¯ ¯ ψ(z) − c.c
(2.14)
iemitter (k0 ) =
2im∗
dz
where “c.c.” denotes the complex conjugate. The total current coming from the
emitter to the collector is:
Z
2dk
(2.15)
Iemitter = f (Ek , Ef e )i(k)
(2π)3
2.3. THEORETICAL SIMULATIONS OF QDRTDS
19
A similar expression can be written for the carrier transport Icollector from the collector and emitter. The total current across the device is the sum of the two currents.
In order to describe the electron movement and find more information about the
wave function, eigenstate, transmission probability, only solving the Schrödinger
equation is not enough: Doping and external bias will affect the potential energy of
the electrons significantly via the Poisson equation
µ
¶
¡
¢
dφ
d
ε
= −e n − ND
(2.16)
dz
dz
where ND denotes the doping profile and ε is the dielectric constant [41, 42]. The
Schrödinger equation is modified to include the Coulomb potential φ in the RTD
system
µ
¶
h̄2 2
− ∗ ∇ + U − eφ ψ = Eψ
(2.17)
2m
2.3
Theoretical simulations of QDRTDs
In the previous simulation, we assumed a 1D steady state single plane wave approach
where the momentum of the wave function is well-defined. To simulate the electron
transport through a 3D QD in the QDRTD, we adopt the electron wave packet
transport model. Comparing to the 1D electron plane wave, the wave packet model
takes into account the couplings among the different plane waves during the temporal evolution by solving the time-dependent Schrödinger equation [43, 44, 45, 46].
First we choose the Gaussian wave packet form to describe the initial wave packet
exp [ikz − (z − z0 )2 /2σ 2 ] at t = 0 along the transport direction (the z direction) centred at z0 . The wave function in the xy plane is denoted by eigenfunction ψi (x, y)
so that the initial electron wave packet at t = 0 is
X Z ∞ ψi (x, y)eikz−(z−z0 )2 /2σ2 dk
√
ψ(x, y, z, 0) =
(2.18)
1 + e(E+Ei −Ef )/kB T 2π
0
i
The dynamic transport process of electrons can be described by the time-dependent
Schrödinger equation:
Hψ(x, y, z, t) = ih̄
∂ψ(x, y, z, t)
∂t
(2.19)
In order to transform the time-dependent Schrödinger equation into a finite differential equation, the time is discretized into nδt (δt is the time step) and spatial
20
CHAPTER 2. OPERATION THEORIES FOR RTDS AND QDRTDS
position iδs (δs is the space step) so that ψ(x, y, z, t) is converted into ψin and the
time-dependent Schrödinger equation assumes the Cayley form:
µ
¶
µ
¶
iδt
iδt
n+1
1+
H ψi = 1 −
H ψin
(2.20)
2h̄
2h̄
Chapter 3
Experiment and theoretical
analysis
To build the single photon detector based on a QDRTD three main stages are
necessary. Layered RTDs and QDRTDs were first grown by the molecular beam
epitaxy method (MBE). A single detector pixel was then processed and electrically
and optically characterized in the form of a free-standing small-area air bridge. The
final stage is to fabricate a photodetector array for practical applications. This thesis
reports the work up to the electrical characterizations of the RTDs and QDRTDs.
Optical characterization and photodetector array fabrication will be the aim of the
work after the Lic exam.
3.1
RTD experimental and theoretical analysis
In order to reach few even single photon detection, a small-area air-bridge device
structure is needed. We first concentrated on the RTD (without embedding QDs)
[47]. The double barrier layer structure is listed in Table 3.1, and the free-standing
air-bridge structure is shown in Fig. 3.1(a), a scanning electron microscopic picture
in 3.1(b), and an optical microscopic picture in Fig. 3.1(c).
The electrical measurement setup consists of a Dewar, Keithley 236 (source measurement unit), IEEE488 GPIB, and a computer labview. Fig. 3.2 shows the I − V
characteristics under forward and reverse sweeps at 77 and 300 K of two RTD devices
on different wafers.
Devices on wafer A and B have exactly the same design parameters and got through
21
22
CHAPTER 3. EXPERIMENT AND THEORETICAL ANALYSIS
Table 3.1: The RTD structure. Layers from 4 to 8 are unintentionally doped.
material
thickness [nm] doping [1018 cm−3 ]
1 GaAs
100
2.0
2 GaAs
80
0.2
3 GaAs
50
0.02
4 GaAs spacer
20
5 AlAs
3
6 GaAs
8
7 AlAs
3
8 GaAs spacer
20
9 GaAs
50
0.02
10 GaAs
80
0.2
11 GaAs
300
2.0
12 AlAs etch-stop layer 15
13 GaAs buffer
400
14 GaAs substrate
(a)
Free-standing air bridge
B
AlAs barriers
20
µm
A
D
2µ
m
Lu
C
70 µm
(b)
(c)
2 µm
Figure 3.1: The RTD structure. (a) Schematic structure of the free-standing air
bridge. (b) Scanning electron microscopy. (c) Optical microscopy.
3.1. RTD EXPERIMENTAL AND THEORETICAL ANALYSIS
400
23
30
77 K
(a)
300
(b)
77 K
20
F
Current [µA]
200
10
100
300 K
R
0
300 K
0
30
77 K
25
-100
-10
20
15
-200
10
-20
300 K
5
0.55 0.60 0.65 0.70
-300
-2
-1
0
1
2
-30
-1.0
-0.5
0.0
0.5
1.0
Bias [V]
Figure 3.2: I − V characteristics of two RTD devices on wafer A and B, respectively,
under forward (F) and reverse (R) sweep at 77 (solid lines) and 300 K (dashed lines).
(a) Wafer A; (b) Wafer B. For the device on wafer B, the forward and reverse I − V
curves almost overlap with each other, see inset.
300
Current [µA]
200
300 K
100
0
-100
-200
-300
-3
-2
-1
0
1
2
3
Bias [V]
Figure 3.3: Thick solid lines: current-voltage characteristics of device A with an
external series resistor of 3.9 KΩ at 300 K. Thin solid lines: without any series
resistor.
the same processing steps, their I − V characteristics are, however, significantly
different. We first considered the external resistance that might cause the difference,
as shown Fig. 3.3. It is concluded here that the external series resistance shifts the
current-peak bias to a higher value and also widens the bistability loop.
We have calculated the transmission probability as a function of the electron kinetic
energy, Fig. 3.4(a), two quasi sublevels in the central GaAs QW, one at 0.12 eV and
the other at 0.42 eV. Fig. 3.4(b) shows the theoretical I − V characteristics. Only
one current peak is observed at an external bias of 0.28 V, corresponding to the
resonant state at 0.12 eV at zero bias in Fig. 3.4(a). Furthermore, the theoretical
I −V characteristics does not show any bistability effect and the peak-to-valley ratio
is also much higher than the experimental one.
24
CHAPTER 3. EXPERIMENT AND THEORETICAL ANALYSIS
1.80
-3
10
-5
10
-7
10
77 K
1.75
300 K
8
1.70
6
4
Charge
Tunneling current
Transition probability
(b)
12
-1
10
1.65
10
2
(a)
-9
10
0.0
0.1
0.2
0.3
0.4
1.60
0.5
0
0.0
0.1
0.2
0.3
0.4
0.5
External bias [volt]
Kinetic energy [eV]
Figure 3.4: (a) Transition probability as a function of the electron kinetic energy
through the 1D RTD. T = 300 K. (b) Theoretical current- and charge-voltage
relationships. Thin lines: 77 K. Thick lines: 300 K.
Current [µA]
400
300
200
100
0
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Bias [V]
Figure 3.5: Thin lines: experimental I − V curves of RTD devices on wafer A at
300 K. Thick lines: extracted RTD I − V characterizations.
Through extracting the series resistance, we tried to deduce the intrinsic I − V
characteristics of four discrete RTD devices on wafer A, see Fig. 3.5. After extracting
a series resistance, the current-peak voltages were 0.42, 0.37, 0.26 and 0.36 V, which
agreed well with the theoretical current-peak voltage and the measured contact
resistance.
It has thus been concluded that the series resistance plays an important role in
determining the I − V characteristics of the RTD system.
Similar to the series resistance, Fig. 3.6 shows the parallel resistance effect to the
I − V characteristics which shows that while the parallel resistance does not affect
the current-peak voltage and the bistability, it modifies the peak-to-valley ratio.
3.2. QDRTD EXPERIMENTAL AND THEORETICAL ANALYSIS
25
800
with parallel
resistance
Current [µA]
600
400
200
0
original
-200
-400
-600
-800
-2
-1
0
1
2
Bias [V]
Figure 3.6: Thick solid line: I − V characteristics of device A with an external
parallel resistor of 3.9 KΩ at 300 K. Inset: “original” marks the experimental data
without parallel resistor; thin solid lines: theoretical extrapolation from the thick
solid lines by subtracting the parallel resistor.
3.2
QDRTD experimental and theoretical analysis
We now move on to the QDRTDs. By the self-assembled method [48, 49], the
QDRTDs were grown by a molecular beam epitaxy (MBE) system on a semiinsulated GaAs (100) substrate. The material layer structure is listed in Table 3.2.
The parameters for InAs QDs are: density about 5.7×1010 µm−2 ; lateral size 20 ∼ 28
nm; height about 8 nm. By the same processing technique as the RTDs, the airbridge structure QDRTD device has an active area of 0.7 × 7.1 µm2 . Fig. 3.7 shows
the structure of the QDRTD device and the surface morphology of the InAs QDs.
Using the same electrical characterization setup as in the previous RTD experiment,
we measured the dark I − V curve at 77 K shown in Fig. 3.8. Quite differently from
the RTD I − V characteristics, we applied an initial charging bias for about 2 s
before the I − V bias sweep in order to study the QD charging effect. Two current
peaks were observed at about -1.7 and -2.3 V, respectively. The weak peak at -1.7 V
gradually disappeared when the initial charging bias changes from -4.0 V to 4.0 V.
We have fabricated and characterized a reference sample where the InAs material is
in the form of a QW (not QDs). Only one current peak at -3.2 V was then observed
in Fig. 3.8(b). This implies that the QDs are responsible for the weak current peak
in the QDRTDs.
We simulate the QDRTD by using a 1D plane wave model where the QD layer is
approximated as an effective QW layer and the density of the hole state in this
26
CHAPTER 3. EXPERIMENT AND THEORETICAL ANALYSIS
Table 3.2: The QDRTD structure.
material
1 GaAs
2 GaAs
3 GaAs
4 GaAs spacer
5 AlAs
6 GaAs
7 AlAs
8 GaAs spacer
9 GaAs
10 GaAs
11 GaAs
12 AlAs etch-stop layer
13 GaAs buffer
14 GaAs substrate
Layers from 4 to 8 are unintentionally doped.
thickness [nm] doping [1018 cm−3 ]
50
2.0
150
Undoped
10
InAs QDs embeded
2
3
8
3
20
50
0.02
80
0.2
300
2.0
15
400
(a)
(b)
Figure 3.7: (a) QDRTD device cell under SEM, and (b) surface morphology of InAs
QD under AFM.
(b)
2 µm
3.2. QDRTD EXPERIMENTAL AND THEORETICAL ANALYSIS
Current [µA]
-0.2
0.0
77K
0.0~-4.0 V sweep
-0.4
pre-bias [V]
4.0
2.6
1.7
1.5
-4.0
(a)
-0.6
-0.8
-1.0
-1.2
-4.0
-3.5
-3.0
-2.5
77 K
-0.5
Current [µA]
0.0
27
-2.0
-1.5
-1.0
-0.5
(b)
-1.0
-1.5
Dark:
after 4.0 V
after -5.5 V
-2.0
-2.5
0.0
-5
-4
Bias(V)
-3
-2
-1
0
Bias [v]
Figure 3.8: (a) Experimental I − V characteristics QDRTD device. (b) The InAs
material is in the form of a QW. T = 77 K.
incident wave
0
Conduction current
1
-2
(b)
(c)
2
RTD QWR
3
-4
QDRTD QWR
time
trapped
reflected
transmitted
-6
-0.5
0.2
(a)
-8
-0.4
-0.3
-0.2
-0.1
0.3
0.4
0.5
0.6
0.7
0.8
0.2
0.3
0.4
0.5
0.6
0.7
0.8
z axis [µm]
0.0
External bias [V]
Figure 3.9: (a) Theoretical I − V characteristics of the QDRTD at 77 K. (b) Wave
packet transportations along the RTD QWR and the QDRTD QWR where the QD
is charged.
InAs QW is described by a single delta function. Theoretical I − V curves assuming
different hole concentrations are shown on Fig. 3.9(a), showing that there is only
one current peak which depends weakly on the hole concentrations.
We now study the QDRTD system using the 3D electron wave packet model. The
carrier transport is composed of two parts: the electron wave packet transmits
directly through the QDs and between the QDs. When the QDs are not charged,
electron transport properties of the two types are rather similar. When the QDs are
charged with holes, a low-energy peak will be induced in the I − V curve [50, 51].
Fig. 3.9(b) and (c) show the wave packet transportations along the RTD quantum
wire of Fig. 1.3 and the QDRTD quantum wire (QWR) where the InAs QD is
charged, respectively.
28
3.3
CHAPTER 3. EXPERIMENT AND THEORETICAL ANALYSIS
Future work on single photon detection
My future work will be made up of two main parts. One is the optical characterizations of the QDRTD, both experimentally and theoretically. The other is to process
a QDRTD array.
The optical characterization will mainly concentrate on the photon response which
was demonstrated by Fig. 2 of APL 92, 023508. By different initial charging conditions and different illumination intensity, we wish to obtain a series of I − V characteristics. By comparing these curves with Fig. 2 of PRL 94, 067401, in which the
NDR peak was shifted but not degraded, we will be able to understand the physical
factors that determine the multiplication effect and relevant quantum efficiencies. I
will also try to make time-resolved measurements in order to characterize the time
response of the photodetector. Further scaling down the active area is needed in
order to obtain a step-like current curve, where each step corresponds to one photon
count. I shall modify the device parameters to extend the detection wavelength from
visible to telecommunication, and even to the far infrared wavelengths.
After the study of individual QDRTD photon detector, the final main object is to
process 1D and even 2D detector arrays. This requires not only uniformity of the
system but also an effective light coupling structure and readout circuit. We propose
the following single photon detector system consisting of three parts. First: use the
nanolens to funnel the photons into the detector. Second: the photons are absorbed
in the light absorption layer. The photogenerated hole will be captured by the
QD, its Coulomb potential is expected to switch on the tunneling current. Third:
the current will be converted and recorded by an external readout circuit including
further signal amplification and processing including analogue-digital conversion.
Fig. 3.10 shows the schematic principle of such a single-photon detector system.
Through the experimental and theory study and development of a QDRTD-based
single-photon detector, we shall optimize its device properties including the quantum efficiency and the time resolution. In the future, we will apply the QDRTD
based single photon detector. In telecommunication and in quantum cryptography,
the single photon detection is the key technology to a quantum key distribution
system which encode a data bit to a single photon and requires only a modest time
resolution while having high quantum efficiency [19, 52, 53]. The single photon detection technology is thus very important for future quantum computing [54, 55].
With single photon detection, the distance can also be measured [56]. In chemistry
and biology, the single photon detection technology can broadly applied in fluorescence spectroscopy of single biomolecules [57], fluorescence lifetime imaging [58],
3.3. FUTURE WORK ON SINGLE PHOTON DETECTION
29
QDRTD
Semi-insulating
substrate
Nanolense
Figure 3.10: Schematic of a 2D single-photon detector array system.
fluorescence lifetime measurements of single molecules [59], fluorescence detection
of single DNA molecules [60], detection of single molecules [61], optical tomography
[62, 63], and DNA sequencing [64, 65], to mention some examples.
30
CHAPTER 3. EXPERIMENT AND THEORETICAL ANALYSIS
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