experimental and theoretical study of quantum dot resonant...

Experimental and theoreticalstudy of quantum dot resonant

tunneling diodes for single photondetection

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 exami-

nation. The optical response of the QDRTD will be experimentally and theoretically

characterized in order to optimize the quantum efficiency for single photon detec-

tion. 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 Theoret-

ical 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 character-

istics 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 Agen 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 com-

ponent 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 in-

creases 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-

200

DRAM half pitch

MPU gate length

100

60

80

50

40

30

20

152000 2002 2004 2006 2008 2010 2012 2014

Year of Introduction

Feature Size (nm)

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 en-

ergy physics, space science, medical imagining as well as telecommunication. Fur-

thermore, 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 telecom-

munication has the character of secrecy, thus making it more advantageous than

traditional code telecommunication. The QKD technology critically requires sensi-

tive 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 sys-

tem [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.


InAs QD

Electron

h

z

y

x

b

B

W

InAs

QD

a

GaAs

AlGaAs

AlGaAs

GaAs

GaAs

hυ

EfEc Ev

E0

(a) (b)

Light

absorbing

layer

Emitter

Collector

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 semi-

conductor 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 in-

creased, 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

Fermi Level

Conduction Band

PI

V

Iv

Ip

Vp

Vv

Figure 1.4: Operation principle of the resonant tunneling diode (RTD).

V+

Write

Input Output

Multi-Peak RTD

(a)

(b)

(c)

(d)

(e)

(f)

Metal interconnect

Figure 1.5: (a) RTD memory circuit [25], (b) RTD-CMOS (complementary metal ox-

ide 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].

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

Γ

L

X

XK

ky

kx

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 = h/p, and its wave function is described as ei(k·r−ωt). Such an electron is described

by the following Schrodinger equation(− h2

2m0

∇2 + U

)ψ = Eψ (2.1)

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](

1

m∗

)

ij

=1

h2

∂2E

∂kikj

(2.2)

Note that different semiconductor materials have different effective masses. The

Schrodinger equation in the solid thus becomes(− h2

2m∗∇2 + U

)ψ = Eψ (2.3)

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:

ψ3Dnk (r) = unk(r)eik·r (2.4)

by which the density of states of a three-dimensional system is:

N3(E) =1

2π2

(2m∗

h2

)3/2

E1/2 (2.5)

Analogously, if the system becomes confined along the z axis direction such as a

QW, the density of states is

N2(E) =m∗

πh2Lz

(2.6)

2.2. THEORETICAL SIMULATIONS OF RTDS 17

valence band

Conduction band

Egap

k

E

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,

N1(E) =1

2πSyz

√2m∗

h2

1√E

(2.7)

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

N0(E) =1

Vxyz

∑δ(E − Ei) (2.8)

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 Fermi-

Dirac distribution function

f(E) =1

exp [(E − Ef )/kBT ] + 1(2.9)

The total number of electrons within the system can then be simply expressed as

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 Schrodinger and Poisson equations. We apply the transfer


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:

Aèik`z + Bè

−ik`z , ik`

(Aè

ik`z −Bè−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

Aèik`z + Bè

−ik`z = A`+1eik`+1z + B`+1e

−ik`+1z

ik`

(Aè

ik`z −Bè−ik`z

)= ik`+1

(A`+1e

ik`+1z −B`+1e−ik`+1z

)(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 eik0z. A part of it will get reflected due to

the potential variation, which is expressed in the form of rk0e−ik0z. The rest will get

transmitted. The wave function and its derivative in the emitter and collector read:

z ≤ 0 : eik0z + rk0e−ik0z , ik0

(eik0z − rk0e

−ik0z)

z ≥ L : tk0eikLz , ikLtk0e

ikLz (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.

iemitter(k0) =eh

2im∗

[⟨ψ(z)

∣∣∣∣d

dz

∣∣∣∣ ψ(z)

⟩− c.c

](2.14)

where “c.c.” denotes the complex conjugate. The total current coming from the

emitter to the collector is:

Iemitter =

∫f(Ek, Efe)i(k)

2dk

(2π)3(2.15)

2.3. THEORETICAL SIMULATIONS OF QDRTDS 19

A similar expression can be written for the carrier transport Icollector from the collec-

tor 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 Schrodinger

equation is not enough: Doping and external bias will affect the potential energy of

the electrons significantly via the Poisson equation

d

dz

(εdφ

dz

)= −e

(n−ND

)(2.16)

where ND denotes the doping profile and ε is the dielectric constant [41, 42]. The

Schrodinger equation is modified to include the Coulomb potential φ in the RTD

system (− h2

2m∗∇2 + U − eφ

)ψ = Eψ (2.17)

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 tem-

poral evolution by solving the time-dependent Schrodinger equation [43, 44, 45, 46].

First we choose the Gaussian wave packet form to describe the initial wave packet

exp [ikz − (z − z0)2/2σ2] at t = 0 along the transport direction (the z direction) cen-

tred 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

ψ(x, y, z, 0) =∑

i

∫ ∞

0

ψi(x, y)eikz−(z−z0)2/2σ2

√1 + e(E+Ei−Ef )/kBT

dk

2π(2.18)

The dynamic transport process of electrons can be described by the time-dependent

Schrodinger equation:

Hψ(x, y, z, t) = ih∂ψ(x, y, z, t)

∂t(2.19)

In order to transform the time-dependent Schrodinger equation into a finite differ-

ential equation, the time is discretized into nδt (δt is the time step) and spatial


position iδs (δs is the space step) so that ψ(x, y, z, t) is converted into ψni and the

time-dependent Schrodinger equation assumes the Cayley form:

(1 +

iδt

2hH

)ψn+1

i =

(1− iδt

2hH

)ψn

i (2.20)

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 mea-

surement 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

AlAs barriersFree-standing air bridge2µm

20 µm

(a)

(b) (c)

2 µm

Lu

A B

C

D

70 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 23

-1.0 -0.5 0.0 0.5 1.0-30

-20

-10

0

10

20

30

0.55 0.60 0.65 0.705

10

15

20

25

30

-2 -1 0 1 2

-300

-200

-100

0

100

200

300

400

Bias [V]

(b) 77 K

300 K

77 K

300 K

Current [µA]

(a)

300 K

77 K

F

R

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.

-3 -2 -1 0 1 2 3-300

-200

-100

0

100

200

300

Cur

rent

[µA

]

Bias [V]

300 K

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.


0.0 0.1 0.2 0.3 0.4 0.510

-9

10-7

10-5

10-3

10-1

0.0 0.1 0.2 0.3 0.4 0.50

2

4

6

8

10

12

1.60

1.65

1.70

1.75

1.80

Tra

nsitio

n p

robabili

ty

Kinetic energy [eV]

(a)

Tunnelin

g c

urr

ent

External bias [volt]

(b)

Charg

e

77 K

300 K

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.

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.00

100

200

300

400

Current [µA]

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

-2 -1 0 1 2-800

-600

-400

-200

0

200

400

600

800

Current [µA]

Bias [V]

with parallel

resistance

original

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 analy-

sis

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 semi-

insulated 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 air-

bridge 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


Table 3.2: The QDRTD structure. Layers from 4 to 8 are unintentionally doped.

material thickness [nm] doping [1018 cm−3]

1 GaAs 50 2.0

2 GaAs 150 Undoped

3 GaAs 10 InAs QDs embeded

4 GaAs spacer 2

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

(b)

2 µm

(a)

(b)

Figure 3.7: (a) QDRTD device cell under SEM, and (b) surface morphology of InAs

QD under AFM.

3.2. QDRTD EXPERIMENTAL AND THEORETICAL ANALYSIS 27

-4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

Current [µA]

Bias(V)

pre-bias [V]

4.0

2.6

1.7

1.5

-4.0

77K

0.0~-4.0 V sweep

(a)

-5 -4 -3 -2 -1 0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

Current [µA]

Bias [v]

Dark:

after 4.0 V

after -5.5 V

77 K

(b)

Figure 3.8: (a) Experimental I − V characteristics QDRTD device. (b) The InAs

material is in the form of a QW. T = 77 K.

-0.5 -0.4 -0.3 -0.2 -0.1 0.0

-8

-6

-4

-2

0

Conduction c

urr

ent

External bias [V]

(a)

12

3

0.2 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]

(b)incident wave

reflectedtransmitted

trapped

(c)

RTD QWRQDRTD QWR

time

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.


3.3 Future work on single photon detection

My future work will be made up of two main parts. One is the optical characteriza-

tions 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 condi-

tions and different illumination intensity, we wish to obtain a series of I − V char-

acteristics. 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 quan-

tum 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 de-

tection 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 fluo-

rescence spectroscopy of single biomolecules [57], fluorescence lifetime imaging [58],

3.3. FUTURE WORK ON SINGLE PHOTON DETECTION 29

Semi-insulating

substrate

QDRTD

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.

Bibliography

[1] G. E. Moore, “Cramming more components onto integrated circuits”, Electronics.vol.38, no.8, April 19, 1965.

[2] S. E. Thompson and S. Parthasarathy, “Moore’s law’s: the future of Si microelec-tronics”, Materialstoday. vol.9, p.20-5, 2006.

[3] P. K. Chatterjee and R. R. Doering, “The future of microelectronics”, Proceedingsof IEEE, vol.86, p.176-83, 1998.

[4] P. A. Gargini, “Sustaining Moore’s law-microelectronics, nanoelectronics, and be-yond”, ISO Focus, p.28-30, 2007.

[5] Editor: R.Compano, “Technology Roadmap For Nanoelectronics”, European Com-mission IST Programme Future and Emerging Technologies. Second Edition. p.9,2000.

[6] J.-F. Eloy and M. Depeyrot, “Nanometer range: a new theoretical challenge for mi-croelectronics and optoelectronics”, Microelectronics Journal, vol.37, p.630-4, 2006.

[7] N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography”, Re-views of Modern Physics, vol.74, p.145-95, 2002.

[8] C. Gobby, Z. L. Yuan, and A. J. Shields, “Quantum key distribution over 122 kmof standard telecom fiber”, Appl. Phys. Lett. vol.84, p.3762-4, 2004.

[9] P. Buzhan, B. Dolgoshein, L. Filatov, A. Ilyin, V. Kantzerov, V. Kaplin, A.Karakash, F. Kayumov, S. Klemin, E. Popova, and S. Smirnov, “Silicon photomul-tiplier and its possible applications”, Nuclear Instruments and Methods in PhysicsResearch A, vol.504, p.48-52, 2003.

[10] A. Yoshizawa and H. Tsuchida, “A 1550nm single-photon detector using a ther-moelectrically cooled InGaAs avalanche photodiode”, Jpn. J. Appl. Phys. vol.40,p.200-1, 2001.

31

32 BIBLIOGRAPHY

[11] A. Dorokhov, A. Glauser, Y. Musienko, C. Regenfus, S. Reucroft, and J. Swain,“Recent progress on cooled avalanche photodiodes for single photon detection”, J.Modern Optics, vol.51, p.1351-7, 2004.

[12] S. Vasile, P. Gothoskar, R. Farrell, and D. Sdrulla, “Photon detection with highgain avalanche photodiode arrays”, IEEE Transactions on Nuclear Science, vol.45,p.720-3, 1998.

[13] N. Faramarzpour, M. J. Deen, S. Shirani, and Q.-Y. Fang, “Fully integrated singlephoton avalanche diode detector in standard CMOS 0.18-µm technology”, IEEETransactions on Election Devices, vol.55, p.760-7, 2008.

[14] D. S. Bethune, W. P. Risk, and G. W. Pabst, “A high-performance integratedsingle-photon detector for telecom wavelengths”, J. Modern Optics, vol.51, p.1359-68, 2004.

[15] Z. L. Yuan, B. E. Kardynal, A. W. Sharpe, and A. J. Shields, “High speed singlephoton detection in the near infrared”, Appl. Phys. Lett. vol.91, p.041114(3), 2007.

[16] E. Charbon, “Towards large scale CMOS single-photon detector arrays for lab-on-chip applications”, J. Phys. D: Appl. Phys. vol.41, p.094010(9), 2008.

[17] A. J. Shields, M. P. O’Sullivan, I. Farrer, D. A. Ritchie, R. A. Hogg, M. L. Lead-beater, C. E. Norman, and M. Pepper, “Detection of single photons using a field-effect transistor gated by a layer of quantum dots”, Appl. Phys. Lett. vol.76, p.3673-5, 2000.

[18] B. E. Kardynal, S. S. Hees, A. J. Shields, C. Nicoll, I. Farrer, and D. A. Ritchie,“Photon number resolving detector based on a quantum dot field effect transistor”,Appl. Phys. Lett. vol. 90, p.181114(3), 2007.

[19] J. C. Blakesley, P. See, A. J. Shields, B. E. Kardynal, P. Atkinson, I. Farrer, and D.A. Ritchie, “Efficient single photon detection by quantum dot resonant tunnelingdiodes”, Phys. Rev. Lett. vol.94, p.067401-4, 2005.

[20] H. W. Li, P. Simmonds, H. E. Beere, B. E. Kardynal, P. See, D. A. Ritchie, andA. J. Shields, “Optimisation of quantum dot resonant tunnelling diodes for fibrewavelength detection”, phys. stat. sol.(c), vol.3. p.4035-8, 2006.

[21] H. W. Li, P. Simmonds, H. E. Beere, B. E. Kardynal, D. A. Ritchie, and A. J.Shields, “Quantum dot resonant tunneling diodes for telecom wavelength singlephoton detection”, Proc. of SPIE, vol.6766, p.67660N-1-6, 2007.

BIBLIOGRAPHY 33

[22] H. W. Li, B. E. Kardynal, P. See, A. J. Shields, P. Simmonds, H. E. Beere, and D. A.Ritchie “Quantum dot resonant tunneling diode for telecommunication wavelengthsingle photon detection”, Appl. Phys. Lett. vol.91, p.073516(3), 2007.

[23] R. Tsu and L. Esaki, “Tunneling in a finite superlattice”, Appl. Phys. Lett. vol.22,p.562-4, 1973.

[24] L. L. Chang, L. Esaki, and R. Tsu, “Resonant tunneling in semiconductor doublebarriers”, Appl. Phys. Lett. vol.24, p.593-5, 1974.

[25] A. C. Seabaugh, Y.-C. Kao, and H.-T. Yuan, “Nine-state resonant tunneling diodememory”, IEEE Electron Device Letters, vol.13, p.479-81, 1992.

[26] J. I. Bergman, J. Chang, Y. Joo, B. Matinpour, J. Laskar, N. M. Jokerst, M. A.Brooke, B. Brar, and E. Beam, “RTD/CMOS nanoelectronic circuits: thin-film InP-based resonant tunneling diodes integrated with CMOS circuits”, IEEE ElectronDevice Letters, vol.20, p.119-22, 1999.

[27] S. Thomas, D. H. Chow, K. Kiziloglu, C. H. Fields, M. Madhav, and A. Arthur,“Planar integration of heterojunction bipolar transistors and resonant tunnelingdiodes”, J. Vac. Sci. Technol. B, vol.18, p.2452-6, 2000.

[28] T. P. E. Broekaert, B. Brar, J. P. A. van der Wagt, A. C. Seabaugh, F. J. Morris,T. S. Moise, E. A. Beam, and G. A. Frazier, “A Monolithic 4-Bit 2-Gsps resonanttunneling analog-to-digital converter”, IEEE J. Solid-State Circuits, vol.33, p.1342-9, 1998.

[29] M. Reddy, S. C. Martin, A. C. Molnar, R. E. Muller, R. P. Smith, P. H. Siegel, M. J.Mondry, M. J. W. Rodwell, H. Kroemer, and S. J. Allen, Jr., “Monolithic Schottky-collector resonant tunnel diode oscillator arrays to 650 GHz”, IEEE Electron DeviceLetters, vol.18, p.218-21, 1997.

[30] E. R. Brown, J. R. Soderstrom, C. D. Parker, L. J. Mahoney, K. M. Molvar, and T.C. McGill, “Oscillations up to 712 GHz in InAs/AlSb resonant-tunneling diodes”,Appl. Phys. Lett. vol.58, p.2291-3, 1991.

[31] K. M. Indlekofer, A. Forster, and H. Luth, “Density-matrix description of a quan-tum dot system with variable lateral confinement in the single-electron tunnelingregime”, Physica B, vol.314, p.499-502, 2002.

[32] S. Sen, F. Capasso, A. Y. Cho, and D. L. Sivco, “Multiple-state resonant-tunnelingbipolar transistor operating at room temperature and its application as a frequencymultiplier”, IEEE Electron Device Letters, vol.9, p.533-5, 1988.

34 BIBLIOGRAPHY

[33] J. P. A. van der Wagt, “Tunneling-based SRAM”, Proceedings of The IEEE, vol.87,p.571-95, 1999.

[34] P. Mazumder, S. Kulkarni, M. Bhattacharya, J.-P. Sun, and G. I. Haddad, “Digitalcircuit applications of resonant tunneling devices”, Proceedings of The IEEE, vol.86,p.664-86, 1998.

[35] T. S. Moise,Y.-C. Kao, C. L. Goldsmith, C. L. Schow, and J. C. Campbell, “High-speed resonant-tunneling photodetectors with low-switching energy”, IEEE Photon-ics Technology Letters, vol.9, p.803-5, 1997.

[36] J. M. L. Figueiredo, A. R. Boyd, C. R. Stanley, C. N. Ironside, S. G. McMeekin,and A. M. P. Leite, “Optical modulation at around 1550 nm in an InGaAlAs opticalwaveguide containing an InGaAs/AlAs resonant tunneling diode”, Appl. Phys. Lett.vol.75, p.3443-5, 1999.

[37] P. Harrison, “Quantum wells, wires and dots–Theoretical and computationalphysics”, John Willey & Sons LTD, 1999. p.4.

[38] P. Harrison, “Quantum wells, wires and dots–Theoretical and computationalphysics”, John Willey & Sons LTD, 1999. p.6.

[39] Y. Fu and W. Lu, “Semiconductor Quantum Device Physics”, Chinese Science Press.First Edition, 2005. p.32-34.

[40] Y. Fu and W. Lu, “Semiconductor Quantum Device Physics”, Chinese Science Press.First Edition, 2005. p.310-316.

[41] P. Harrison, “Quantum wells, wires and dots–theoretical and computationalphysics”, John Willey & Sons LTD, 1999. p.105-112.

[42] A. Shik, “Quantum wells physics and electronics of two-dimensional systems ”,World Scientific, 1998. p.69-77.

[43] Y. Fu and M. Willander, “Electron wavepacket transport through nanoscale semi-conductor device in time domain”, J. Appl. Phys. vol.97, p.094311(7), 2005.

[44] Y. Fu and O. Engstrom, “Electron wave packet transmission through a Si quantumwire under the influence of an ionized impurity scattering potential”, J. Nanoelec-tronics and Optoelectronics, vol.1, p.108-13, 2006.

[45] Y. Fu and M. Willander, “Charge accumulation and band edge in the double barriertunneling structure”, J. Appl. Phys. vol.71, p.3877-82, 1992.

BIBLIOGRAPHY 35

[46] C. A. Moyer, “Numerov extension of transparent boundary conditions for theSchrodinger equation in one dimension”, Am. J. Phys. vol.72, p.351-8, 2004.

[47] J. Wang, P. H. Beton, N. Mori, H. Buhmann, L. Mansouri, L. Eaves, P. C. Main,T. J. Foster, and M. Henini, “Submicrometer resonant tunnelling diodes fabricatedby photolithography and selective wet etching”, Appl. Phys. Lett. vol.65, p.1124-6,1994.

[48] C.-D. Lee, H. J. Lee, S. K. Noh, C. Parky, C. G. Park, S.-J. Park, and K.-S.Lee, “Fabrication of self-assembled quantum dots in lattice-matched GaAs/AlGaAssystem”, J. Korean Physical Society, vol.33, p.262-265, 1998.

[49] P. M. Petroff, A. Lorke, and A. Imamoglu, “Epitaxially self-assembled quantumdots”, Physics Today, p.46-52, 2001.

[50] O. Engstrom, M. Malmkvist, Y. Fu, H. O. Olafsson, and E. O. Sveinbjornsson,“Thermal emission of electrons from selected s-shell configurations in InAs/GaAsquantum dots”, Appl. Phys. Lett. vol.83, p.3578-80, 2003.

[51] Y. Fu, O. Engstrom, and Y. Luo “Emission rates for electron tunneling from InAsquantum dots to GaAs substrate”, J. Appl. Phys. vol.96, p.6477-6481, 2004.

[52] S. Takeuchi, J. Kim, Y. Yamamoto, and H. H. Hogue, “Development of ahigh-quantum-efficiency single-photon counting system”, Appl. Phys. Lett. vol.74,p.1063-5, 1999.

[53] A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J.-P. Poizat, and P. Grangier, “Singlephoton quantum cryptography”, Phys. Rev. Lett. vol.89, p.187901-4, 2002.

[54] E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum compu-tation with linear optics”, Nature, vol.409, p.46-52, 2001.

[55] S. Takeuchi, “Experimental demonstration of a three-qubit quantum computationalgorithm using a single photon and linear optics”, Phys. Rev. A, vol.62, p.032301-4,2000.

[56] S. Pellegrini, G. S. Buller, J. M. Smith, A. M. Wallace, and S. Cova, “Laser-baseddistance measurement using picosecond resolution time-correlated single-photoncounting”, Meas. Sci. Technol. vol.11, p.712-6, 2000.

[57] S. Weiss, “Fluorescence spectroscopy of single biomolecules”, Science, vol.283,p.1676-83, 1999.

36 BIBLIOGRAPHY

[58] W. Becker, A. Bergmann, M. A. Hink, K. Konig, K. Benndorf, and C. Biskup, “Flu-orescence lifetime imaging by time-correlated single-photon counting”, MicroscopyResearch and Technique, vol.63, p.58-66, 2004.

[59] C. W. Wilkerson, Jr., P. M. Goodwin, W. P. Ambrose, J. C. Martin, and R. A.Keller, “Detection and lifetime measurement of single molecules in flowing samplestreams by laser-induced fluorescence”, Appl. Phys. Lett. vol.62, p.2030-2, 1993.

[60] A. Castro, F. R. Fairfield, and E. B. Shera, “Fluorescence detection and size mea-surement of single DNA molecules”, Anal. Chem. vol.65, p.849-52, 1993.

[61] L. Q. Li and L. M. Davis, “Single photon avalanche diode for single molecule detec-tion”, Rev. Sci. Instrum. vol.64, p.1524-9, 1993.

[62] W. Becker, A. Bergmann, G. Biscotti, and A. Ruck, “Advanced time-correlated sin-gle photon counting technique for spectroscopy and imaging in biomedical systems”,Proc. SPIE, vol.5340, p.1-9, 2004.

[63] F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delpy,“A 32-channel time-resolved instrument for medical optical tomography”, Rev. Sci.Instrum. vol.71, p.256-65, 2000.

[64] L. Alaverdian, S. Alaverdian, O. Bilenko, I. Bogdanov, E. Filippova, D. Gavrilov, B.Gorbovitski, M. Gouzman, G. Gudkov, S. Domratchev, O. Kosobokova, N. Lifshitz,S. Luryi, V. Ruskovoloshin, A. Stepoukhovitch, M. Tcherevishnick, G. Tyshko, andV. Gorfinkel, “A family of novel DNA sequencing instruments based on single-photon detection”, Electrophoresis, vol.23, p.2804-17, 2002.

[65] J.-P. Knemeyer, N. Marme, and M. Sauer, “Probes for detection of specific DNAsequences at the single-molecule level”, Anal. Chem. vol.72, p.3717-24, 2000.

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