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Yuk Nga Chen
To cite this version:
Yuk Nga Chen. Antenna Coupled Quantum Infrared Detectors . Quantum Physics [quant-ph]. Uni-versité Paris Diderot - Paris 7, 2015. English. �tel-01390461�
Antenna Coupled Quantum Infrared Detectors
D´etecteurs Quantiques Infrarouges Coupl´ees aux Antennes
by
Yuk Nga Chen
A thesis submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy in Physics
at UNIVERSIT´E PARIS DIDEROT - PARIS 7
SORBONNE PARIS CIT´E
Defended on: 21st April, 2015
Jury
Prof. Philippe Lafarge , President
Dr. Philippe Bois , Referee
Dr. Miriam Vitiello , Referee
Prof. Harald Schneider , Examiner
Prof. Vincent Berger , Invited
Prof. Carlo Sirtori, Advisor
In this research work, I investigate theoretically and experimentally the “antenna coupled microcavities” for intersubband (ISB) optoelectronic devices in the
mid-infrared (MIR) and THz spectral ranges. This innovative device geometry
relies on metal-dielectric-metal microcavities that support highly sub-wavelength modes concentrated in the dielectric core. The top metal is structured into arrays of patches which act as antennas that can effectively couple light in and out of the dielectric region.
In the first part of my thesis, I study the optical properties of the microcavities in the THz domain. To this end, I investigate the phonon-polariton modes arising from the strong coupling between the microcavity modes and the optical phonons in the semiconductor. I then concentrate on the light extraction from these modes and study the possibility of building narrow band THz emitters operating in the vicinity of the semiconductor restrahlen band. These are based either on thermal excitation or electrical injection of an ISB transition resonant with the phonon-polariton mode. In the second part, I study the implementation of the antenna coupled microcavity geometry for quantum well infrared photodetector (QWIP). In particular I present a model describing the physical properties of our devices and show that the antenna effect leads to a reduction of the dark current while the microcavity effect leads to an enhanced photo-absorption with few quantum wells. Finally, I illustrate how this new design can fundamentally enhance the detectivity of not only QWIPs but also that of all MIR/THz detectors.
These properties are experimentally validated in the third part, where I describe the first fabrication and characterization of an antenna coupled microcavity QWIP in the MIR domain. The noise properties of the device are also discussed. In the last part of the manuscript I draw some perspectives by presenting some preliminary results on novel devices based on this geometry, such as the polaritonic QWIP and the THz QWIP.
Dans ce travail de th`ese, j’´etudie th´eoriquement et exp´erimentalement des
dispositifs opto´electroniques intersousbandes (ISB) dans le moyen infrarouge
(MIR) et le domaine t´erahertz (THz) combin´es avec des microcavit´es. Ces
microcavit´es de type m´etal-semi-conducteur-m´etal supportent des modes fortement
sub-longueur d’onde, concentr´es dans le semi-conducteur. La couche m´etallique
sup´erieure est structur´ee en r´eseaux de patchs qui agissent comme des antennes
capables de coupler efficacement la lumi`ere incidente avec la couche
semi-conductrice.
Dans la premi`ere partie de ma th`ese, j’ai consid´er´e les propri´et´es optiques des
microcavit´es dans la r´egion THz. J’ai ´etudi´e les modes phonon-polariton qui
r´esultent du couplage fort entre les modes de microcavit´e et les phonons optiques
du semi-conducteur. En particulier, j’ai ´etudi´e l’extraction des photons `a partir
des modes coupl´es et la possibilit´e de construire des ´emetteurs THz `a bande ´etroite
op´erant au voisinage de la restrahlen bande. Les modes polaritoniques sont excit´es
soit thermiquement, soit par injection ´electrique d’une transition ISB r´esonante
avec le mode.
Dans la deuxi`eme partie, j’exploite cette g´eom´etrie de microcavit´es pour les
photo-d´etecteurs infrarouges `a puits quantiques (QWIP). J’ai d´emontr´e que l’effet
de l’antenne est de r´eduire le courant d’obscurit´e des d´etecteurs, alors que la
microcavit´e conduit `a une absorption am´elior´ee avec un nombre r´eduit des puits
quantiques. J’illustre ´egalement comment ces concepts peuvent am´eliorer la
d´etectivit´e des QWIPs et plus g´en´eralement des d´etecteurs quantiques de lumi`ere
infrarouge.
Les validations exp´erimentales de ces id´ees sont d´ecrites dans la troisi`eme
partie du manuscrit, o`u je d´ecris la premi`ere fabrication et la caract´erisation d’une
microcavit´e QWIP `a 9µm. Les mesures de bruit du d´etecteur sont ´egalement
discut´ees. Dans la derni`ere partie du manuscrit je pr´esente quelques r´esultats
pr´eliminaires sur d’autres dispositifs bas´es sur la g´eom´etrie en antenne patch, tels
qu’un QWIP op´erant en r´egime du couplage fort lumi`ere-mati`ere et un QWIP
Motivated by their potential as effective photon sources and detectors in the mid-infrared (MIR) and the terahertz (THz) ranges, research on intersubband (ISB) optoelectronic devices has been developing rapidly over the past decades. The most prominent examples are the quantum well infrared photodetector (QWIP) and the quantum cascade laser (QCL). Because of the limitations imposed by the polarization selection rule, an effective light coupling geometry is
often required to couple light in and out of these devices. As a result, much
research effort has been devoted to designing the host photonic structure to improve the device performance.
In this thesis work, we investigate theoretically and experimentally the use of antenna coupled microcavities for ISB optoelectronic devices operating in the MIR
and THz ranges. This innovative device geometry consists of a subwavelength
dielectric layer sandwiched between two layers of metal, while the top surface metal is periodically patterned with square patches of a specific dimension. Each of these square patches, in combination with the bottom metallic layer, forms a microcavity which supports a photonic cavity mode. They also act as antennas that allow light to couple with the dielectric cores of the device. The dielectric layer of the antenna coupled microcavity structure can naturally be filled with a
quantum engineered active medium, allowing the interaction between the
electronic states of the active medium and the photonic states of the cavity. In particular, these devices allow for an optimized spatial overlap of the photonic and electronic excitations inside the microcavities, and therefore a strong light-matter interaction can be achieved. In fact, they have been exploited to study devices operating in the strong and ultrastrong light-matter coupling regime in the MIR[1][2] and THz[3][4] ranges.
The main result of this work is the successful demonstration of the antenna coupled microcavity QWIP. A theoretical model describing the performance of such a device is presented. We show that the microcavity QWIP has intrinsically superior noise performance as compared to a QWIP in conventional geometries. This is a combined result of the antenna effect and the microcavity effect, which reduces the effective detector area and the dark current and enhances the absorption quantum efficiency of the device respectively. In addition, the performance of this device can be manipulated by adjusting the different device parameters. This optical coupling
of a microcavity QWIP with only 8 QWs. The complete characterisation of the QWIP devices is reported in this manuscript. In principle, this concept can be exploited to improve the performance of any detectors to yield a device with low dark current and high quantum efficiency. In the last part, we explore the antenna coupled microcavity geometry for novel detectors such as the polaritonic QWIP and the THz quantum well photodetector.
This Manuscript is Organized as Follows: Chapter 1 presents a general
introduction on the subject matter. The first part presents some of the applications of light sources and detectors in the MIR and THz range. The second part presents the basic physics of quantum wells (QWs) and the possibility of bandgap engineering in creating devices based on ISB transitions in QWs. Then we briefly introduce two of the most widely used ISB quantum devices, namely QCLs and QWIPs. The last part introduces the antenna coupled microcavity geometry, explaining how they are suited to be used for ISB quantum devices.
Chapter 2 presents the details of the modelling methods, fabrication processes and the experimental characterisation techniques used in this work.
Chapter 3 presents the physics of the antenna coupled microcavities. The
concept of the cavity mode is introduced. We present also the experimental
investigation of the antenna coupled microcavities on three different dielectrics,
namely GaAs, SiO2 and InP, in the THz. The optical properties of the cavity
modes in these devices are predicted and studied using a model based on the electromagnetic energy conservation and the antenna theory. The microcavities are used to probe different modes along the dispersion curves of different materials, including the phonon-polariton modes that are close to the restrahlen band of the material. The absorption and emission properties of these modes are investigated by means of reflectivity and thermal emission measurements respectively.
In the second part of this chapter, we attempt to build narrow band THz emitters. We have explored the optical properties of these cavities upon thermal excitation. Electrical injection could be achieved by replacing the dielectric core with a specially designed quantum cascade structure that has an ISB transition resonant with the cavity mode.
Chapter 4 presents the physics of QWIP devices. The first part presents the derivation of the figures of merit of QWIPs and discuss some of the conventional optical coupling geometries for QWIPs. We continue the discussion with the physics of the antenna coupled microcavity geometry on QWIP. We present an analytic model to describe the device, base on which we derive the different figures of merit in terms of the device parameters. Finally, we discuss the criterion for the optimization of the performance of a microcavity QWIP, with a comparison to conventional QWIP devices.
optical absorption, photo-responsivity, photoconductive gain, background limited performance (BLIP) and detectivity of the unetched and the etched devices. We present a comparison of the performance between the microcavity QWIPs and the conventional QWIP devices reported in the literature. The last part presents the results from the attempts to implement our geometry on a QWIP structure with bound-to-quasibound transition, and to further improve of the geometry design.
Chapter 6 presents some preliminary results on novel detectors based on the antenna coupled microcavity geometry, including a QWIP with a high well doping
(polaritonic QWIP) and a THz quantum well photodetector. The complete
characterisation of these devices are still in progress.
The growth sheets of the sample wafers studied in this work and some details of the clean room processing techniques are presented in Appendix.
1 General Introduction 1
1.1 Mid-Infrared and Terahertz Frequency Ranges . . . 1
1.1.1 Applications . . . 1
1.2 Intersubband Quantum Devices . . . 3
1.2.1 Quantum Well and Intersubband Transition . . . 4
1.2.2 Quantum Cascade Laser (QCL) . . . 6
1.2.3 Quantum Well Infrared Photodetector (QWIP) . . . 8
1.3 Antenna Coupled Microcavities . . . 9
2 Device Modelling, Fabrication and Characterisation 13 2.1 Device Modelling . . . 13
2.1.1 Simulation of the Band Structure . . . 13
2.1.2 COMSOL Multiphysics . . . 14
2.1.3 Modal Method . . . 14
2.2 Sample Growth . . . 15
2.2.1 Molecular Beam Epitaxy Growth . . . 15
2.2.2 Metalorganic Chemical Vapor Deposition . . . 15
2.3 Device Processing . . . 16
2.3.1 Double Metal Device Processing . . . 16
2.3.2 Clean Room Processing Techniques . . . 17
2.3.3 Device Processing Steps . . . 19
2.4 Sample Characterisation . . . 23
2.4.1 Device Mounting and Cryogenic Cooling . . . 23
2.4.2 Emission Measurements . . . 23
2.4.3 Reflectivity Measurements . . . 25
2.4.4 Spectral Photoresponse Measurements . . . 25
3 Antenna Coupled Microcavity in the THz 27 3.1 Microcavity Modes . . . 27
3.1.1 Planar Waveguide Modes . . . 27
3.1.2 Microcavity Modes . . . 29
3.2 Resonant Absorption and Antenna Effect . . . 34
3.3 Phonon-Polariton Modes in Microcavities . . . 39
3.4 Antenna Coupled Microcavity Emitter . . . 46
3.4.1 Microcavity QCL - Preliminary Results . . . 46
3.4.2 Microcavity Device with Electronic Injection Close to the Restrahlen Band . . . 49
4 Antenna Coupled Microcavity Enhanced QWIP: Theory 51 4.1 Basics of Thermal Detection . . . 51
4.2 Physics of QWIPs . . . 53
4.2.1 Intersubband Transition in QWIPs . . . 53
4.2.2 Light Coupling Geometries . . . 56
4.2.3 Dark Current and Photoconductivity . . . 58
4.2.4 Noise and Detectivity . . . 61
4.3 Antenna Coupled Microcavity Enhanced QWIP . . . 64
4.3.1 Responsivity of a Microcavity QWIP . . . 64
4.3.2 Detectivity of a Microcavity QWIP . . . 68
4.3.3 Designing an Optimized Microcavity QWIP . . . 71
4.4 Conclusion and Perspectives . . . 75
5 Antenna Coupled Microcavity Enhanced QWIP: Experiments 77 5.1 Quantum Well Layer Characterisation . . . 77
5.1.1 Current-Voltage Characteristics . . . 79
5.1.2 Spectral Photoresponses . . . 80
5.2 Microcavity QWIPs Characterisation . . . 84
5.2.1 Reflectivity Measurements . . . 86
5.2.2 Spectral Photoresponse . . . 88
5.2.3 Estimation of Responsivity . . . 91
5.2.4 Quantum Efficiency and Photoconductive Gain . . . 95
5.3 Etched Microcavity QWIPs Characterisation . . . 98
5.4 Background Limited Performance . . . 103
5.5 Detectivity . . . 108
5.5.1 Detectivity from the IV Characteristics . . . 108
5.5.2 Detectivity from Noise Measurements . . . 110
5.5.3 Summary . . . 113
5.6 Comparison with QWIPs in Conventional Geometries . . . 115
5.7 Further Developments . . . 118
5.7.1 Microcavity QWIP with a Bound-to-Quasibound Transition . 118 5.7.2 Microcavity QWIP with a Reduced Detector Size . . . 121
5.7.3 Summary . . . 125
6.1.1 Device Description . . . 130 6.1.2 Device Characterisation . . . 131 6.1.3 Discussion . . . 134 6.2 THz QWP . . . 135 6.2.1 Device Description . . . 136 6.2.2 Device Characterisation . . . 137 6.2.3 Discussion . . . 140
7 Conclusions and Perspectives 143 Bibliography 147 Appendix 156 A Growth Sheets 157 B Details of processing 161 B.1 Recipe for lithography . . . 161
B.1.1 Optical lithography . . . 161
B.2 Parameters for wet etching . . . 162
B.2.1 AlGaAs/GaAs etching . . . 162
B.2.2 Substrate removal - selective etching . . . 162
Publications List 163
Acknowledgements 165
General Introduction
1.1
Mid-Infrared
and
Terahertz
Frequency
Ranges
Figure 1.1: The electromagnetic spectrum, showing the different frequency ranges.
In this thesis work, we investigate the use of antenna coupled microcavities for semiconductor devices that generate or detect photon in the terahertz (THz) and mid-infrared (MIR) spectral frequency ranges. The THz and MIR ranges can be
defined to be between 0.5 − 15T Hz and 15 − 100T Hz respectively. Table 1.1
summarizes the corresponding energies and wavelengths of the photons in these ranges. As shown the electromagnetic spectrum in Fig. 1.1, these two ranges lie between the microwave and the visible light region. Motivated by many important applications in the MIR and THz spectral ranges, devices such as lasers and detectors have been intensively explored in the past two decades. In the following, we review some of these applications.
1.1.1
Applications
Spectroscopy A large number of molecules, such as CO2, CO, CH4, N2O, O3,
have distinct spectral features in the MIR and THz ranges which could be revealed
by means of spectroscopy. Spectroscopy in both ranges is interesting for many
applications such as environmental monitoring, pollution control, industrial process 1
Range Frequency Energy Wavelength THz 0.5-15T Hz 2 - 40meV 20-600µm MIR 15-100T Hz 40 - 410meV 3-20 µm
Table 1.1: The mid-infrared(MIR) and the terahertz (THz) spectral ranges expressed in
term of the photon frequencies, energies and wavelengths.
monitoring, non-invasive disease diagnosis and leak detection[5]. Spectroscopy in the THz range could also be useful for security screening of traces of explosive and drugs. Many chemical substances and explosive materials exhibit characteristic spectral responses in the THz range while materials such as clothes, plastics and paper are transparent to the THz waves[6].
Imaging The most common application for MIR detectors is for thermal imaging.
By detecting its emission in the MIR range, one could identify the temperature of an object. Indeed, according to the Planck’s radiation law, the emission of a blackbody at around 300K peaks in the MIR range. Thermal cameras based on QWIP focal plane arrays (FPAs) are already used as part of the enhanced vision system for military, aerospace and space applications[7]. The principal of thermal imaging is also discussed in section (4.1).
Terahertz radiation has the unique ability to non-destructively image physical structure, spectroscopic analysis can therefore be done without any contact with the object. Therefore THz imaging holds great potential for various application related to medical diagnosis[8], art conservation[9], security screening[10], and many others. Some of these applications have already been demonstrated. For example, the feasibility of using THz pulsed imaging to map margins of exposed breast tumors was demonstrated in 2006[11]. The inherent sensitivity to water molecules of the THz waves is exploited as a natural contrast agent to enhance cancer cell contrast. The use of THz imaging to identify different materials in delicate paintings and artifacts has also been demonstrated[9].
Free Space Optical Communication Free space data links using MIR and
THz sources have been explored for both commercial and military applications in
recent years. They have the potential to serve applications requiring high
bandwidth with relatively high security to eavesdropping and without the complexity of installing optical fibers. Laser sources with emission wavelengths at the atmospheric window region (3 − 5µm and 8 − 14µm in the MIR region) are often chosen for such application[12]. Research on the free space communication using carrier waves in these ranges are also being pursued because of the
availability of the frequency band and communication bandwidth, high
1.2
Intersubband Quantum Devices
Figure 1.2: (a) Schematic of the potential and the wavefunctions of the confined states in
a QW: the black line represents the potential energy V (z) of a quantum well (QW) along the growth direction z. The colored curves are the wavefunctions of the first two confined states in the QW, represented at their respective energies. (b) The energy dispersions of these two states as a function of the in-plane wave vector kk.
The term intersubband (ISB) transition is used to describe optical transitions between quasi-two-dimensional electronic states in semiconductors, which are formed due to the confinement of the electronic wavefunction in one dimension.
This confinement can be achieved in a quantum well (QW), which consists of a thin layer of semiconductor embedded in semiconductor layers with a lager bandgap. Depending on the band offset of the two semiconductor materials, the electrons can be confined in one direction in the conduction band and their allowed energy levels are quantized. Fig. 1.2(a) shows the schematic of the conduction band of a QW and the wavefunctions of the two confined states in the subbands along the growth direction z. Fig. 1.2(b) shows the dispersion of the two states as a function of the in-plane wavevector kk. An important characteristics is that these states have the same in-plane dispersion. As a result, the transitions between these joint densities of states, which are ISB transitions, are atomic like, leading to a narrow absorption peak[14]. In addition, the energy levels of these subbands, and therefore the energy of the ISB transition, can be fine tuned by adjusting the thickness and depth of the QW. This process is also known as the bandgap engineering[15].
Motivated by the potential of devices based on ISB transitions such as detectors, emitters and non-linear optics elements in the MIR and THz ranges, research on ISB transitions in QW have been quickly developing in the past decades. A major step to the realization of ISB quantum devices has been the invention of molecular beam epitaxy (MBE) by A.Y. Cho and J.R. Arthur in 1975[16], which opens up the possibility of growing epitaxial structures with a precision down to the atomic level and thus with well-defined interfaces. The QWs are created by epitaxial growth of a succession of different semiconductor layers (heterostructure). This technique is further introduced in section (2.2.1).
Focusing on the GaAs/AlGaAs material system used in this work, we consider only the transitions in the conduction band in the following discussion. In this first part of this section, we introduce the basic physics of ISB transitions in a QW and
derive the absorption coefficient for the induced ISB transition rate based on the Fermi’s golden rule following the discussion in Ref. [17]. In the second part, we introduce two of the most prominent examples of ISB quantum devices: quantum cascade laser (QCLs) and quantum well infrared photodetectors (QWIPs).
1.2.1
Quantum Well and Intersubband Transition
Energy States within the Semiconductor Heterostructures Using the
envelope function approximation, the total wave function ψ(r)i,ν can be written as
a product of the periodic Bloch function uν(r) of band ν at the center of the
Brillouin zone and an envelope function fi(r) that is slowly varying over a lattice period. The total wavefunction is written as:
ψi,ν(r) = uν(r)fi(r) (1.1)
where i denotes the quantum number of the state. This approximation provides reasonably a good description for the conduction band of many semiconductors including GaAs.
Assuming that uν(r) is the same in all constituent materials in the
heterostructure, we can derive the Schr¨odinger equation for the envelope function:
− ¯h
2
2m∗∇
2f
i(r) + V (r)fi(r) = Enfi(r) (1.2)
Taking z as the growth direction and considering the free motion of electron along the x and y direction, the envelope function can be expressed as:
fn,kk(r) = 1 √ Ae ikk·rϕ n(z) (1.3)
where kk = k(x, y) and A is the sample area. The solutions of the energy eigenvalues
to equation 1.2 then have the form:
En,kk = En+
¯
h2k2k
2m∗ (1.4)
where En is the energy of the confined states with quantum number n in the z
direction, which depends on the function V (z), ¯h is the reduced Plank’s constant,
and m∗ is the effective mass of the electron. The confined states with energies given
by En,kk forms the nth subband[17].
Consider the simplest case of an infinite symmetric QW of width L, the values
of En can be solved analytically:
En=
¯
h2π2n2
2m∗L2 (1.5)
For more complicated structures, only numeric solutions can be obtained. The
method used in this work to obtain these values in a QW structure is further discussed in section (2.1.1).
Fermi Golden Rule and Transition Rate The transition rate from state i to state f when induced by an external electromagnetic field is given by the Fermi’s golden rule: Wif = 2π ¯ h |hψi|H 0|ψ fi|2δ(Ef − Ei− ¯hω) (1.6)
with the H0 is the light-matter interaction Hamiltonian and H0 = 2me∗(A · p + p · A)
where A is the vector potential.
Under the one band effective mass model and the dipole approximation, the
transition rate of an ISB transition from the state n to the state n0 is given by[17]:
Wif = 2π ¯ h e2E2 0 4m∗2ω2|hφn|pz|φn0i| 2 δ(Ef − Ei− ¯hω) (1.7)
where E0 is the amplitude of the electric field. As implied from the matrix element
hφn|pz|φn0i, the external electric field must have a z-component in order to be coupled
to an ISB transition. This is known as the polarization selection rule, which is an important point to consider when designing an optical coupling geometry of ISB quantum devices.
For the ease of comparison between different physical systems, a dimensionless
oscillator strength fn,n0 is usually defined for the transition from state n to n0:
fnn0 = 2m∗ωn0n ¯ h |hn|pz|n 0i|2 = 2 m∗¯hωn0 n |hn|z|n0i|2 (1.8)
Note that it obeys the sum ruleP
n0
fn,n0 = 1, for the initial state n summing over all
possible final states n0. The value of fnn0 is positive for absorption and negative for
emission.
In the case of an infinite QW we have:
fn,n0 = 2m∗ω ¯ h hzi 2 n,n0 = 64 π2 n2n02 (n2− n02)3 (1.9)
In particular we note that f12 = 0.961. In fact, the oscillator strength for the
transition in an infinite QW is concentrated on the transition between the first two subbands.
Intersubband Absorption The absorption coefficient α2D of an ISB transition
between the first two subbands is expressed as[17]:
α2D(¯hω) =
n2De2h¯
20cnrm∗f12
Γ/2
(E2− E1 − ¯hω)2+ Γ2/4 (1.10)
where n2D is the 2D carrier density in the QW, e is the electronic charge, 0 is
the permittivity of the free space, nr is the refractive index of the semiconductor,
f12 is the oscillator strength of the ISB transition and Γ is the linewidth of the
homogeneous broadening. The expression is useful when optimizing the absorption of an ISB detector.
Under experimental conditions, the radiation is usually coupled in through an angle of θ onto a QW structure consisting of N periods. Since that the absorption can only be induced by the electric field along the z direction, the effective interaction length of the radiation is increased by 1/cosθ while the electric field is reduced by
sin2θ. Assuming that the absorption by individual QWs is small, the transmittance
T and absorption quantum efficiency η can be estimated by:
T = T0exp(−N α2Dsin2θ/cosθ) (1.11)
η = −ln(T
T0
) = N α2Dsin
2θ
cosθ (1.12)
where T0 denotes the absorption of the system other than that of the ISB transitions.
This includes the absorption by the device itself, such as at the contact layer or the interfaces of the heterostructure, or the absorption of the components of the experimental set-up, such as windows and lenses.
1.2.2
Quantum Cascade Laser (QCL)
Figure 1.3: (a) Schematic conduction band energy diagram of a quantum cascade laser,
showing two active regions and an intermediate injection region. The laser transition and the electron flow are indicated by the wavy and straight arrows respectively[18]. (b) Schematics of the THz QCL waveguides (i) the surface-plasmon and (ii) the metal-metal waveguides[19].
The first proposal for the light amplification by means of stimulated emission in superlattice structures was put forward by Kazarinov and Suris in 1971[20]. However, these schemes were found to be unsuitable for lasing because of the difficulties in achieving population inversion and their tendency to break into high field domains[21]. The first laser based on ISB transition is the quantum cascade laser (QCL), demonstrated at the Bell Laboratories in the group of Federico Capasso in 1994[22]. This laser was grown in the InGaAs/AlInAs/InP material system and emitted at 4.2µm at cryogenic temperatures.
Since its first demonstration, there has been a tremendous progress in the
continuous wave and room temperature operation were demonstrated[23]. The first QCL emitting in the THz range based on the GaAs/AlGaAs heterostructure was
demonstrated in 2002 by K¨ohler et al.[24]. To date, lasing in QCL has been
achieved over a wide range of wavelengths from 3.5 to 150µm. The QCL
technology is nowadays accepted as the dominant one that provides compact and robust semiconductor lasers for MIR and THz radiation. They are widely used in spectroscopic and imaging applications.
Operation Principle Fig. 1.3 show the schematic conduction band diagram of
a typical QCL. Each period of a QCL structure consists of an active region and an injection region. A photon is created when an electron relaxes from the upper laser level to the lower one. Electrons are injected into the upper laser level (3) by resonant tunneling across a potential barrier. On the other hand, the electron extraction from the lower lasing level (2) is usually obtained by the resonant emission of longitudinal optical (LO) phonons, or by elastic scattering into a narrow miniband followed by thermalization via electron-electron scattering. After the extraction, electrons are re-injected to the next period through the injection region. Following the well-known cascading principle, this period is repeated N times in a QCL. Ideally, each electron passing through the QCL generates N photons[14].
Optical Coupling A functional QCL requires an optical coupling mechanism that
provides optical confinement and allows for light extraction. Laser cavities based on optical waveguides are routinely used for QCLs. In the MIR, waveguiding is achieved using either metallic or dielectric confinement. On the other hand, for THz QCLs, two main types of waveguides are used as illustrated in Fig. 1.3(b)[19]: (i) For the surface-plasmon waveguide, the active region is sandwiched between the top metallic contact and a bottom doped contact layer where the surface plasmon mode is generated. (ii) For the double metal waveguide, the confinement is achieved with the active region confined between the two layers of metal. As implied in the polarization selection rule, the photon emission from a QCL is polarized along the growth direction and therefore the light extraction is usually from the ridge of the laser.
By employing a suitable photonic architecture, light can also be extracted from
the surface of a QCL. Surface emitting QCL based on second-order
distributed-feedback (DFB) structures[25][26] and two dimensional photonic crystals[27][28] have been demonstrated.
1.2.3
Quantum Well Infrared Photodetector (QWIP)
The first demonstration of the quantum well infrared photodetector (QWIP) was performed at the Bell Laboratories in 1987 by Levine et. al.[29]. Since then, there has been rapid developments in both the understanding of the photoconductive mechanism and the fabrication of two dimensional (2D) array based on QWIP for thermal imaging[30].
(a) (b)
Figure 1.4: (a) Scanning electron microscope image of 640×514 pixel QWIP array with
24µm pixel size[31]. (b) Picture of a 1024×1024 pixel QWIP FPA on a leadless-chip-carrier with a U.S. quarter for size comparison (Jet Propulsion Laboratory, NASA)[32].
The active region of a QWIP device is a superlattice structure with N identical QWs, each with an ISB transition at the desired photon detection energy. The physics and applications of GaAs/AlGaAs QWIPs are now well established[30], and they are further discussed in Chapter 4.
The development of 2D focal plane arrays (FPAs) based on QWIP structures for thermal imaging has reached maturity. They are widely available for various space, aerospace, military applications and some civilian use. The optical coupling mechanism in FPA is typically done using diffraction gratings processed onto the QWIP wafer. Fig. 1.4(a) shows the scanning electron microscope image of 640×514 QWIP array with 24µm pixel size[31]. Fig. 1.4(b) shows the picture of a 1024×1024 pixel QWIP FPA[32]. QWIP FPAs based on the corrugated QWIP have also been demonstrated[33]. The different light coupling geometries for QWIP devices are discussed in section (4.2.2).
There are several reasons for the success of GaAs based QWIP FPAs for thermal imaging. Firstly, as discussed earlier, the detection based on ISB transition means the possibility of band gap engineering and the versatility in designing the detection energies of QWIP devices. The devices can also be designed for single or wide band detection[34]. Secondly, with the maturity of the III-V semiconductor growth technology and the corresponding processing techniques, affordable GaAs QWIPs wafer with excellent uniformity over a large area can be obtained. Large wafers (up to 4 inches) grown by MBE technique with dark current non-uniformity of less than 10% and defects of less than 0.1% can be fabricated[35]. The processing steps
required for the fabrication of diffraction gratings are also standardized. In addition, QWIPs are unipolar devices, which means that no passivation step is required in the processing. Thirdly, QWIPs are actually robust towards damages from external radiation because of the relatively high bandgap of GaAs (1.5eV)[30]. Lastly, when operating under low temperature, a good signal-to-noise ratio is often obtained, in particular, the 1/f noise is usually negligible in a QWIP[30].
The need for low temperature operation (77K) and the cost involved in building the cryogenic cooler are the main points that limit the use of QWIP FPAs for more commercial applications. The use of novel photonic structure have been explored to improve the noise performance of QWIP devices by increasing photon absorption or reducing the noise[30][36][37]. As we show in Chapter 4-6, the novel antenna coupled microcavity geometry for QWIP introduced and demonstrated in this thesis work addresses both of these points. The geometry holds great potential for raising the operation temperature of a QWIP device[38]. In particular, this improvement could be useful for QWIP devices operating in the THz range. The technology of THz quantum well photodetector is still in the developmental stage and operation under liquid helium temperature is often required[39]. The antenna coupled microcavity could serve as a mean to improve the high temperature performance of THz QWIPs. Another prominent example of photodetector based on ISB transitions is the quantum cascade detector (QCD). The active region of a QCD has N identical periods. Each period is comprised of a doped active QW and an undoped extraction cascades composed of thinner QWs[40]. QCDs are photovoltaic detectors, thus there is no noise contribution from the dark current. Comparing with photoconductive detectors such as QWIPs, QCD devices have in principle a relatively low gain but also low noise. Theoretical results show that they should have similar detectivities when compared with QWIP devices[41]. However, it has not been demonstrated experimentally.
1.3
Antenna Coupled Microcavities
Metal-dielectric-metal microcavities are able to support modes that are highly sub-wavelength with respect to the distance between the metal layers. When the top metal is structured into an array of patches, these microcavities act as antennas that can effectively couple light in and out of the dielectric. This concept is widely exploited in the microwave range in a device known as the microstrip patch antenna[42], which consists of a ground metal, a dielectric layer and a square patch of size s. The dielectric layer thickness L is usually much smaller than the
resonant wavelength λ = 2nef fs of the T M0 mode that the patch antenna support,
where nef f is the effective index of the resonator.
In this work, we explore the implementation of the concept of patch antenna for ISB optoelectronic devices in the MIR and THz ranges. With the advancement of nanofabrication technologies, patch antennas can be created for applications in the
Figure 1.5: (a) Scanning electron microscope (SEM) images of top view of the (i) 1D and (ii) 2D antenna coupled microcavities (top metal colored orange). (b) Schematics of the (i) 1D and (ii) 2D devices, with the indicated direction for electric and magnetic field for incident light at an angle θ to the normal of the surface (schematic not to scale).
MIR and THz ranges in the form of nano-antennas on top of a thin layer of quantum engineered heterostructure (typically L ≈ 1µm)[43]. In fact, this concept has already been exploited in the fundamental studies of light-matter interaction[1][2][3][44].
The antenna coupled microcavity geometries used in this work are based on arrays of patch antennas. The top view scanning electronic microscope pictures and the schematics of the 1-dimensional (1D) and 2-dimensional (2D) antenna coupled microcavities are shown in Fig. 1.5. The sizes of the gratings or the square patches s have a typical dimension of ∼ 10µm in the THz and ∼ 1µm in the MIR.
There are several advantages for the implementation of this antenna coupled microcavity geometry for ISB optoelectronic devices. First of all, the dielectric layer of the antenna coupled microcavities can naturally be filled with a quantum engineered active medium, e.g. an ISB quantum layer, allowing the interaction between the electronic states of the active medium and the photonic states of the cavities.
Secondly, the device geometry allows for the coupling of the dielectric with the electromagnetic wave in the free space. The electromagnetic energy is coupled in by the patch antenna, squeezed into the subwavelength microcavity while the
polarization of the radiation is changed. In fact, the electric field of the
fundamental T M0 cavity mode provide the right polarization to interact with the
ISB transition according to the polarization selection rule.
Thirdly, the antenna effect allows each patch antenna to collect light from an area larger than itself. This property can be exploited to reduce the dark current and improve the noise performance of ISB photodetectors. The effect is demonstrated in this work for a QWIP structure and is discussed in Chapter 4 and 5.
Figure 1.6: Reflectivity spectra of the antenna coupled microcavities with highly doped quantum wells: The reflectivity dips indicates the absorption from the ISB polariton resulting from coupling of the ISB transitions and the cavity modes in the antenna coupled microcavities in the (a) THz[3] and (b) MIR[2] frequency ranges.
Another interesting property of this device geometry is the fact that the subwavelength confinement in the microcavity boosts the light-matter interaction between the resonant cavity mode and the ISB transitions. As the fundamental
T M0 mode is homogeneous in the growth direction, the use of metallic surfaces for
this confinement allows for the complete overlapping of the photonic mode and the polarization of the electronic excitation. As a result, a high coupling strength can be achieved. This effect has been demonstrated in the MIR and THz ranges by combining the antenna coupled microcavities with highly doped QWs. Fig. 1.6 shows the data from Ref. [2] and [3] for this kind of devices in the MIR and THz
respectively. Ultrastrong light-matter coupling is observed from the reflectivity
spectra of these devices, where the Rabi splitting becomes comparable to the
transition energy[45]. This strong light-matter coupling could be exploited to
enhance the performance of ISB quantum devices. Some preliminary results on the pursuit of this concept is presented in Chapter 6.
Device Modelling, Fabrication and
Characterisation
In this chapter, we provide some details of the modelling methods, the fabrication processes of the devices and the experimental set-ups for the device characterisations used in this work.
2.1
Device Modelling
The aim of this thesis work is to study the antenna coupled microcavity on intersubband (ISB) quantum devices in the terahertz (THz) and mid-infrared (MIR) region. The first step is to design the band structure of the quantum device depending on the desired application, followed by choosing the appropriate device
parameters in the device architecture. Here we provide some details of the
modelling methods used for the design.
2.1.1
Simulation of the Band Structure
In section (1.2.1), we have described the equations for the ISB wavefunction, the oscillator strength and the absorption coefficient for ISB transitions. While it is possible to obtain solutions for these quantities in an infinite quantum well,
numerical solutions are needed for an arbitrary heterostructure. The band
structure of multi-quantum well (QW) systems are obtained using a program
developed in our team based on the transfer matrix method[46]. The Schr¨odinger’s
equation (equation 1.2) in each semiconductor layer is solved individually under
the k · p approximation. The coefficients are obtained by implementing the
boundary conditions between the layers. In addition to calculating the
wavefunction of the energy levels, the program also provides the dipole moment, the oscillator strength and the energy for the transition between different states. However, the energy of the transition obtained from the program does not take
into account many body effects which becomes prominent in highly doped QW structures.
In the context of this work, this program is used to confirm the band structure of the lasers used in Chapter 3. It is also used to design the quantum cascade structure in section (3.4.2) and the QWIP structures in chapter 5 and 6.
2.1.2
COMSOL Multiphysics
The RF module in the software “COMSOL Multiphysics” is used to study the electromagnetic field distribution around a unit cell of the patch antenna. The program is based on the finite element method (FEM), in which the continuous
domain is mesh discretized into a set of non-overlapping sub-domains,
interconnecting the nodes. In a steady state, the solutions to the Maxwell’s
equations (partial differential equations) can be approximated locally with a set of algebraic equations, which can be solved numerically. The advantage of using this software is that it can easily handle complicated geometry using adaptive
discretization routines. Secondly, in addition to the EM field distribution, the
software can also compute other quantities such as the charge distribution and power flow within the domain. Reflectivity and absorption spectra of devices can also be simulated. However, the computation time required can be long depending on the size of mesh chosen and the solutions obtained often require careful post-processing analysis to confirm their validity.
In the context of this work, this software is used to simulate the EM field distributions and the absorption of the cavity mode of the etched and unetched microcavity devices.
2.1.3
Modal Method
A program based on the modal method and the approximation of the surface impedance boundary conditions is also used to study the EM field distributions in the antenna coupled microcavity devices. This program has been developed by Yanko Todorov and the detail formulation are described in Ref. [47] and [48]. This program allows for the simulation of the optical absorption and reflectivity spectra of a rectangular slit metallic gratings lying on an arbitrary multilayered medium, for incident radiation of any polarization and direction. The surface impedance boundary conditions serve as an excellent approximations in the MIR and THz
frequency ranges[49]. Therefore this program is able to reproduce well the
reflectivity spectra of the devices with 1D antenna coupled microcavities, i.e.
metallic gratings lying on top of a layer of dielectric and ground metal. The
computation power requirement for this program is relatively low. It also allows for the study of the coupling of the cavity modes in the antenna and the quantum
microcavities but not the 2D ones. It also does not predict the effect of etching on the cavity modes.
In the context of this work, this software is used to simulate the EM field distributions and the absorption of the cavity mode of the microcavity devices.
2.2
Sample Growth
Following the design of the QW band structure, the QW layers are grown according to the growth sheets such as those provided in Appendix A. Two major techniques are used to grow thin epitaxial layers of semiconductors: molecular beam epitaxy (MBE) and metal organic chemical vapor deposition (MOCVD). In this section we briefly introduce these two methods.
2.2.1
Molecular Beam Epitaxy Growth
Molecular beam epitaxy is an ultra-high vacuum (UHV) evaporation technique for the growth of thin epitaxial layers of semiconductors, metal or insulators, developed by Cho in 1975[16]. Inside the MBE growth chamber, the sources are evaporated or sublimated in the form of beams of atoms or molecules at a controlled rate onto a crystalline substrate surface (GaAs wafers used in this work) kept at a suitable temperature, allowing the epitaxy layers to crystallize on the
heated substrate surface. The thickness, composition, and doping level of the
epitaxial layer can be very precisely controlled by an accurate control of the beam flux and by employing various in situ surface sensitive diagnostic methods[23].
All of the GaAs/AlGaAs QWs samples studied in this work are grown with molecular beam epitaxy (MBE) method by Giorgio Biasiol in TASC (Trieste, Italy), except the passive GaAs samples studied in Chapter 3 which are provided by TU Wien (Vienna, Austria) and the quantum cascade lasers (QCLs) used in chapter 3 are from University of Leeds.
2.2.2
Metalorganic Chemical Vapor Deposition
MOCVD is a chemical deposition method for thin film growth of semiconductor, metal or ceramics. This technology is able to produce epitaxial layers with thickness as thin as a few atomic layers. In this method, the heated substrate in the chamber reactor is exposed to a controlled amount of metalorganic and hydride precursors using a carrier gas. The decomposition of the various gases on the substrate leads to chemical reactions and the growth of crystalline structure on the surface of the substrate[23].
The InP sample studied in chapter 3 is grown by metalorganic chemical vapor deposition (MOCVD) by Isabelle Sagnes at the LPN (Marcoussis, France).
2.3
Device Processing
After the material growth, the wafer samples with the desired QW design are
processed into devices with different geometries for optical or electrical
characterisation.
All the processing steps on the devices studied in this work are done in the clean room facility at the Laboratoire MPQ in Universite Paris 7, except for the wafer
bondings performed either at the IEF at Universit´e Paris Sud (Paris, France) or by
an external subcontractor. The electron beam lithography processes are done in the
clean room of the ´Ecole Normale Sup´erieure (Paris, France).
2.3.1
Double Metal Device Processing
In this part, we describe the processes required to prepare the wafer for the double metal geometry. The direct fabrication of GaAs based structures on gold surface is not realizable, therefore a processing step called the wafer bonding is required to create the bottom metal layer.
During the MBE growth of the wafers to be processed into double metal devices,
an Al0.5Ga0.5As etch stop layer (300 − 400nm thick) is first grown on the substrate
before the growth of the active QWs. After the growth of the whole structure, a metal deposition of Pd/Ge/Ti/Au: 25/75/10/500nm is made on the top of the wafer. The Pd/Ge layer is for the creation of the ohmic contact while the Ti layer acts as an adhesive for the Au layer. On the other hand, a host undoped GaAs substrate with a metal layer of Ti/Au 10/500nm deposited on top is also prepared. The sample wafer with the desired QW layers and the host substrate, both with
metallic layers on its surface, are thermally compressed together at 250◦C for an
hour with the metallic layers facing each other. During this process, the sample wafer and the host substrate are bonded together as the gold layers fused together. The process is known as the wafer bonding.
After the wafer bonding, the substrate of the sample wafer is etched away using
a solution of citric acid (H2O/H2O2/C6H8O7) with an etching rate of
150µm/hour. Careful surface monitoring of the etching rate is obtained using a DEKTAK profilometer throughout the process. To achieve uniform etching over the surface, the etching solution is changed to a diluted one with an etching speed of ∼ 20µm/hour when only 100µm thick of the substrate is left. The etching rates for the solution under different concentration and solution temperature is summarized in table B.2. The end of the etching is marked by the observation of the revealed etch stop layer with a distinctive color. Finally, the etch stop layer can be removed by immersing in a HF solution. A pre-processing under the oxygen plasma for 3 minutes is often done to facilitate the removal of the etch stop layer
by the HF solution. The removal of the etch stop layer is marked by the
disappearance of the distinctive color, which often takes less than 1 minute.
layer lying on top of a metallic layer, on top of a GaAs substrate. Double metal devices are fabricated through the deposition of metallic contacts or structures on top on the sample surface and other required processes.
2.3.2
Clean Room Processing Techniques
In this part we discuss the different techniques and recipes used for individual processing steps.
2.3.2.1 Metallic Contact Deposition
For the deposition of metallic contacts for wire bonding, standard optical lithography technique using AZ5214 as a negative tone resist is used, followed by a deposition of metallic layers using electron beam evaporation. The contact pads are left on
the samples after the lift-off process. The components of the different metallic
contacts used, the corresponding component thickness and the post lift-off annealing processes used are summarized in table 2.1.
Metallic Layers Thickness of the components (nm) Post lift-off annealing process
Ti/Au 10/180 nil
Pd/Ge 25/75 350◦C for 4 minutes
Ni/Ge/Au/Ni/Ge 10/60/120/20/200 420◦C for 1 minute
Table 2.1: Details of the metallic contacts used in this work.
2.3.2.2 Patch Antenna Deposition
THz Patch Antenna The technique used is the same as the deposition of the
metallic contact. Either Ti/Au (10nm/180nm) metallic layer or Pd/Ge/Ti/Au
(25nm/75nm/10nm/180nm) ohmic contact are used.
MIR Patch Antenna The MIR patch antenna has a typically dimension of
1µm with the connecting wires of ∼ 150nm Standard electron beam lithography technique is used to fabricate the antenna in MIR. The resist used is a solution of A6 PMMA:aniso (5:1) spin coated on the surface. The thickness of the resist on
the device is ∼ 300nm. The top metallic layers Ti/Au (2nm/50nm) are
subsequently deposited on the surface followed by a lift-off process leaving only the antenna patterns on the surface.
2.3.2.3 Plasma Enhanced Chemical Vapour Deposition Si3N4 and SiO2
Thin films of silicon nitride Si3N4 and silicon dioxide SiO2 are deposited by means
of plasma enhance chemical vapour deposition (PECVD). In the context of this
at 280◦C or 150◦C. They are used as insulating layers for the metallic contact pads. The formation of the thin film is done by the creation of plasma of the relative gases
involved (SiH4, N H3, Ar and N2 ). The growth rate of the Si3N4 layer is around
1nm/s. The SiO2 layer of thickness 1.5µm studied in chapter 3 is grown with the
same method and deposition rate while the substrate temperature is kept at 280◦C.
2.3.2.4 Etching
Wet Etching of AlGaAs/GaAs Sulphuric acid solution (H2SO4 : H2O2 : H2O)
is used to etch the AlGaAs/GaAs layer to define the edges of the device. Standard optical lithography technique with either S1805 or S1818 positive resist is used
to protect the device from the acid solution. The solution H2SO4 : H2O2 : H2O
(1 : 8 : 120) used has an average etching rate of 230nm/minute. A summary of the etching rates for the solution with different concentrations is shown in table B.1.
Inductive Coupled Plasma etching of AlGaAs/GaAs Inductive coupled
plasma (ICP) etching is used to etch AlGaAs/GaAs layers (100nm − 400nm) using the TiAu layer on the device surface as a mask. Inside the chamber, the plasma is
formed with silicon tetrachloride SiCl4 and Ar, and the ions are accelerated and
bombarded onto the surface of the device. The recipe used has an etching rate for AlGaAs/GaAs is ∼ 14nm/s while the metallic layers are etched in a much slower rate. The recipe has been developed by Maria Amanti in our team (MPQ, Paris, France).
Reactive Ion Etching of Si3N4 Standard optical lithography technique using
S1805 resist and subsequent reactive ion etching (RIE) is performed to remove the
insulating layer (Si3N4) in the unwanted area. The plasma created in the chamber
is composed of fluoroform CHF3, sulfur hexafluoride SF6 and O2, and the ions are
accelerated up an down the chamber by the RF source that initiated the plasma.
The fluoride ions bombarding the surface of the device etch the Si3N4 layer both
2.3.3
Device Processing Steps
A summary of all the device geometries used in this work is shown in Fig. 2.1. In this section we discuss the steps involved in producing devices with these geometries.
2.3.3.1 Mesa Structures
Substrate Coupled (SC) Geometry with 45◦ facet coupling To fabricate
the mesa structure, the MBE grown sample is first wet etched using a sulphuric acid solution into individual mesas, each with a dimension slightly larger that the size of the intended top contact. The etching reaches around 100nm above the bottom contact layer. A second lithography is made to deposit the bottom metallic contact Ni/Ge/Au/Ni/Au and subsequence thermal annealing processes are done with parameters indicated in table 2.1 to create a diffused ohmic contact. Finally, a last optical lithography is done to deposit the top metallic contact of Ti/Au or Pd/Ge. The device fabricated is then cleaved along the mesa edge, and the edge is
mechanically polished to create the 45◦ facet.
Double Metal Mesa (DMM) The wafer bonded sample, after the process
described in section (2.3.1), is wet etched into individual mesa until the bottom metal is revealed. Each mesa has a dimension slightly larger that the intended size
of the top contact. An optical lithography is done to deposit the top metallic
contact of Ti/Au or Pd/Ge on top of the mesa.
The processing steps for realizing both the antenna coupled microcavity geometries in the MIR and THz are shown schematically in Fig. 2.2.
2.3.3.2 MIR Antenna Coupled Microcavities
200× 200µm2 Microcavity QWIP The wafer bonded sample, after the process
described in section (2.3.1), is deposited with MIR patch antennas using standard electron beam lithography technique, as described in section (2.3.2.2). The MIR
patch antenna consists of an area of 200 × 200µm2 filled with square patches, each
of dimension s, arranged in a periodicity p electrically connected by wires of 150nm
thick. The top contact (TiAu 100 × 100µm2) is then deposited on the side of the
patch antenna, connecting all the patches electrically. In the last step, the sample is wet etched into individual devices until the bottom metal is revealed. For the etched microcavity device studied in section (5.3), an ICP etching process is done using the top metallic patterns as a mask. A depth of ∼ 100nm of the QW layer is removed in parts not covered by the top metal. The scanning electron microscope images of this type of device are found in Fig. 5.6.
50×50µm2 Microcavity QWIP The wafer bonded sample, after the process
described in section (2.3.1), is wet etched into individual mesa (70 × 70µm2) until
the bottom metal is revealed. A 300nm thick layer of Si3N4 is deposited on the
device surface using PECVD. Subsequent optical lithography and RIE etching is done to reveal some parts with the semiconductor mesa for the deposition of the patch antennas. The MIR patch antenna is then deposited on top of the center of the mesa using standard electron beam lithography technique, as described in section
(2.3.2.2). It consists of an area of 50 × 50µm2 filled with square patches, each of
dimension s, arranged in a periodicity of p electrically connected by wires of 150nm
thick. The top contact (TiAu 120 × 100µm2) connecting the patch antennas is then
deposited, which lies partially on top of the semiconductor mesa and partially on
top of the Si3N4 layer. Finally, an ICP etching process is done using the top metallic
patterns as a mask. A depth of ∼ 100nm of the QW layer is removed in parts not covered by the top metal. The scanning electron microscope images of this type of device are found in Fig. 5.30.
2.3.3.3 THz Antenna Coupled Microcavities
Three different masks for the deposition of the top metallic THz antenna patterns are used, as shown in the optical micrographs in Fig. 2.2, for either passive or active (electrical injection) study of the devices. The steps involved in the fabrication of all of them are essentially the same.
The process starts with the wafer bonded sample, after the process described in section (2.3.1), is deposited with the corresponding THz patch antenna patterns using standard optical lithography technique described in section (2.3.2.2). The sample is wet etched into individual devices until the bottom metal is revealed. For some devices, an ICP etching process is done to remove the top contact layer in parts of the device that is not covered by the top metal. Detailed optical micrographs of the THz microcavities for electrical injection are shown in Fig. 3.14.
Figure 2.1: Summary of the device geometries fabricated in this work (schematics not to scale).
Figure 2.2: Steps in the processing of the antenna coupled microcavity devices (schematics not to scale).
2.4
Sample Characterisation
In this section, we discuss the details of the experimental set-ups for the
measurements made in this work. We first put a note on the mounting and
cryogenic cooling of the device. We then discuss the details of the set-up for the common characterisation techniques used in this work, including the emission
measurements, reflectivity measurements and the spectral photocurrent
measurements. All measurements are made with a Bruker IFS 66 Fourier
Transform Infrared spectrometer (FTIR). Additional experimental set-ups specific to some parts of the thesis are discussed within the chapters of the experimental results.
2.4.1
Device Mounting and Cryogenic Cooling
In all the measurements, the device is mounted onto a copper holder by indium soldering or using silver paint, which is then attached to the cold finger of the open cycle Janis (ST-300) cryostat. For the measurement involving electrical injection, the device is wire bonded to ceramic pads with conducting surfaces, which are connected to the BNC cable in the cryostat. For measurements involving the device
at 4K or 77K, a continuous liquid helium He4 or nitrogen N2 flow through the
cryostat is maintained.
2.4.2
Emission Measurements
Electroluminescence The set-up used for the electroluminescence
measurements is shown in Fig. 2.3. The device is operating in a pulse mode, with the bias produced by a pulse generator, modulated by a step function generated at the function generator at a modulation frequency. The electroluminescence from the device is then collected by a parabolic gold mirror and directed to the FTIR. The modulated signal is then detected by a bolometer and processed using a
lock-in amplifier, subtracting all the non-modulated signal (noise). The signal
recorded is then fed back to the FTIR for spectral information of the emission.
Thermal Emission The set-up used for the thermal emission measurements is
shown in Fig. 2.4. The device is mounted to a copper holder attached to a Peltier
heater with a tunable temperature in the range of 30 − 80◦C. The thermal emission
from the sample is guided by parabolic mirrors and detected by the built-in room temperature THz pyroelectric detector (PE/DLaTGS D201) in the FTIR.
Figure 2.3: Schematic of the experimental set-up for the electroluminescence measurements (not to scale).
Figure 2.4: Schematic of the experimental set-up for the thermal emission measurements
(not to scale).
Figure 2.5: Experimental set-up for the reflectivity measurements, with the excitation
2.4.3
Reflectivity Measurements
The set-ups used for the reflectivity measurements at 10◦ and 45◦ incident angles
are shown in Fig. 2.5(a) and (b) respectively. The Globar in the FTIR is used as an excitation source for the measurements. The irradiation is guided by parabolic
mirrors through the interferometer onto the sample. For the 10◦ incident angle
measurements, a reflectivity unit from Bruker Corporation that allows the incident
light to impinge on the device at 10◦ with respect to the normal of its surface is
used. The reflectivity signal is then detected by either the same bolometer mentioned
above, or a MCT detector cooled at 77K. For the 45◦ incident angle measurements,
the set-up is arranged as shown in Fig. 2.5(b).
The signal from the detector is fed back into the FTIR to obtain spectral information of the reflected light. However, the spectral shape obtained would be depending on the spectral shape of the Globar radiation and the spectral responsivity of the detector itself. The reflectivity spectrum of the device, which represents the net absorption by the device itself, is obtained by making a ratio between the spectrum of the reflected light by the device and that of a reference gold surface.
2.4.4
Spectral Photoresponse Measurements
Figure 2.6: Experimental set-up for the spectral photoresponse measurements (not to
scale).
The set-up used for the spectral photoresponse measurements is shown in Fig. 2.6. The Globar of the FTIR used as an excitation source is guided by parabolic mirrors through the interferometer and focused by a germanium lens onto the device. The device is connected to a low noise current amplifier (DLPCA-200) that applies a small voltage on the device and amplifies the photocurrent generated by the incident radiation. The magnified signal is fed back to the FTIR to obtained the spectral photoresponse of the device.
Antenna Coupled Microcavity in
the THz
In this chapter, we present the physics of the antenna coupled microcavities and discuss its optical properties in the THz. The first part describes the microcavity modes, followed by the experimental investigation of the nature of these modes. The second part describes the resonant absorption and antenna effect in an array of microcavities, together with a discussion of the emission and absorption properties of this structure, which is the basis of our geometry. The third part discusses the use of this geometry to probe the phonon-polaritons in polar materials including GaAs and InP, and the possibility of extracting emission from these modes by thermal
excitation. The last part presents some preliminary results on exploiting these
structures to extract light from quantum cascade laser (QCL) and a discussion on the possibility of using the phonon-polariton modes for photon generation.
3.1
Microcavity Modes
3.1.1
Planar Waveguide Modes
Let us start by considering the electromagnetic (EM) modes in a planar cavity, as shown in Fig. 3.1(a), which consists of a layer of dielectric with a thickness L embedded between 2 layers of metal. The solutions for the propagating EM modes within this planar waveguide is well known and can be solved by considering the Maxwell’s equation and the boundary conditions at the metallic walls[50]. The allowed modes inside this cavity can be divided into 2 distinct categories, namely the transverse magnetic (TM) waves and transverse electric (TE) wave, which would form a complete set of modes to describe the EM disturbance inside the waveguide.
(a) 0 2 4 6 0 20 40 60 80 100 TM 1 , TE 1 TM 2 , TE 2 F r e q u e n c y ( T H z ) In-plane w avevector k // (mm -1 ) TM 0 = c / (b)
Figure 3.1: (a) TM and TE cavity modes inside a planar cavity. (b) Dispersion relation
of the TM and TE modes for GaAs slab of L = 1.5µm as a function of the in-plane wavevector k//, assuming homogeneous dielectric with the refractive index n = 3.55. The
region below the dotted line represents the frequency range where only the T M0 mode
exists.
The solutions for the TM and TE modes in this planar cavity have the forms of: T Mmmodes Ez ∝ cos(mπzL ) Ex ∝ sin(mπzL ) Hy ∝ cos(mπzL ) T Emmodes Ey ∝ cos(mπzL ) Hx ∝ sin(mπzL ) Hz ∝ cos(mπzL ) (3.1)
where m is a positive integer indicating the order of the mode along the z direction. The shape of the wavefunction for the zeroth-, first- and second-order modes are
shown in Fig. 3.1(a). The wavevector of these modes can be expressed as (k//, kz),
where kz = mπ/L is quantized along the z direction and the in-plane wavevector
k//forms a continuum. The dispersion relation of the mth-order TM or TE cavity
modes with frequency ω is given by Helmholtz’s relation:
k//2+ π 2 L2m 2 = ω2 c2(ω) or k//= r ω2 c2(ω) − π2 L2m 2 (3.2)
for both the T Mm or T Em modes and (ω) is the dielectric constant of the material.
Therefore for any given frequency ω, only certain values of wavenumber k// can
exist. Fig. 3.1(b) plots the relationship between the in-plane wavevector k// and
the corresponding energies of the cavity modes for a planar cavity filled with GaAs of thickness L = 1.5µm and assuming that it has a homogenous dielectric tensor
(p(ω) = √ = n = 3.55 in the THz range, where n is the refractive index of the
material). Notice that for each eigenmode of the planar cavity, there exists a cutoff frequency at: ωcutof f,m = πm L c √ (3.3)
for the mth-order mode, where m is an integer and m ≥ 0. For the modes in the
exception is the T M0 mode which has a dispersion relation that coincides with the light cone: ω c √ = k// (3.4)
Therefore the T M0 mode does not have any cutoff frequency and is independent on
the semiconductor thickness L, allowing the confinement of EM field in arbitrary thin cavities.
Monomode Conditions In fact, the subwavelength planar cavity is often
operating under a monomode situation, i.e. only the T M0 mode is excited. From
Fig. 3.1(b), the monomode condition is met if: ¯ hω ≤ ¯hωcutof f,1 or L ≤ πc ω√ or L ≤ λ 2n (3.5)
where λ = 2πc/ω is the corresponding wavelength for the propagating mode at frequency ω. If we have GaAs as the dielectric layer, we consider λ ' 100µm and
the refractive index n = √ = 3.55 in the THz range[51], then the monomode
condition is achieved if we have L ≤ λ/7 ≈ 14µm. From now on we shall assume this to be true ( we have L ≈ 1.5µm for devices studied in this chapter), and we
continue the discussion considering only the T M0 modes.
In fact, this type of planar waveguide provides a strong mode confinement within the subwavelength layer in the z direction. They are routinely used in the microwave and the submillimeter frequency range owing to their low propagation loss and high confinement factor. However it is difficult to couple these modes with the free space because of the impedance mismatch and the small dimension at the ends of the cavity, leading to a severe mode mismatch between the waveguided mode and the radiation modes in the free-space[42]. As a result, a transitional structure is required to couple the guiding modes with the free space. Different approaches have been used to couple light out of the double metal planar waveguide, for example, the distributed feed back (DFB) gratings[26][25], horn antennas[52], etc.
3.1.2
Microcavity Modes
Now we replace the top metallic layer of the planar cavity with a periodic array of metallic gratings with a strip width s and a period p. The schematics of the structure and its cross-section are shown in Fig. 1.5(b)(i) and Fig. 3.2 respectively. The presence of the metallic strips imposes additional boundary conditions to the allowed modes inside the cavity, resulting in the formation of standing waves under the strips with frequencies equivalent to integral multiples of c/2s, along the x direction indicated in Fig. 3.2.
Confinement Mechanism The confinement mechanism can be understood by
