Implantation and Optical Characterization of Color Centers in Silicon Carbide

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Implantation and Optical Characterization of

Color Centers in Silicon Carbide

by Remmert Muller

Supervisors: Dr. Clara I. Osorio,

Prof. Dr. A. Femius Koenderink and Dr. Katerina Dohnalova

Graduation project for Masters degree in Physics with track Advanced Matter and Energy Physics

Januari 2015 - December 2015

University of Amsterdam, Amsterdam, The Netherlands

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Abstract

Single color centers, point defects in crystal structures, are widely studied for their optical and spin properties. The most famous color center is the nitrogen-vacancy (NV) center in diamond. Many indispensable operations for quantum computing have already been demonstrated with NV centers, plus single photon emission has been improved by coupling NV centers to a variety of photonic structures. The major bottleneck for quantum and photonic technologies in diamond is the difficult nanofabrication process. This work is concerns with the implantation and characterization of color centers in silicon carbide. Silicon carbide is a material with superb electrical, optical and mechanical properties, which already finds applications in electronics. Recently single fluorescent centers with addressable spin states have been revealed. Additionally, a wide variety of photonic cavities with moderately high quality factors have been reported. We aimed to implant silicon-vacancy carbon-antisite defects in silicon carbide wafers by means of fast electron irradiation and to characterize these luminescent centers in the irradiated samples with high NA confocal fluorescence microscopy and cathodoluminescence microscopy. While the antisite defect has not been detected, this work can be used as a guide to research color centers, specifically in silicon carbide, since it addresses many important issues such as the choice of wafers, defect implantation with fast electrons and characterization of the optical properties of color centers with photoluminescence and cathodoluminescence microscopy techniques.

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Chapter 1 Introduction

Cavities can tune the optical absorption and emission properties of single emitters. As emitters you could envision atoms, ions, molecules and ultracold atomic gasses or solid state sources such as quantum dots and color centers. Cavity-emitter systems are scien-tifically interesting because they provide a toolbox to study the dynamics of emitters and how photons and emitters couple and interact. Boosting these interactions to the regime of strong coupling is believed to be an essential building block for quantum simulation, quantum communication and quantum computation applications [1, 2]. Color centers -point defects in a solid state host from which fluorescence can be generated - could play a big role in the development of cavity-emitter systems because of their photostability and ability to be implanted in cavities [3]. Additionally, the spin ground state of color centers remains coherent for long times at room temperature and can be initialized and read out very efficiently with optical and microwave signals, which brings about many opportunities for quantum computation with spins [4]. This thesis presents work in the generation of color centers in silicon carbide and investigation of their optical properties.

1.1 Single photon sources

Photons are a very suitable carrier of information, because they travel at the speed of light, have a low coupling with the environment and information can be encoded in their various degrees of freedom [5, 6]. The first practical application that utilizes these properties is quantum key distribution (QKD), which delivers unconditional secure communication by providing the encryption key through a string of photons [6]. This unlimited security stems from the destruction of the photon state when it is measured, such that any interference from an eavesdropper can be detected. In fact, to provide this maximum security, QKD demands single photons [7]. QKD systems have already been tested outside the lab and commercial systems are readily available (e.g. Ref. [8]). These systems use laser pulses attenuated down to have a fraction of a single photon per pulse.

Another popular single-photon source is spontaneous parametric down conversion (SPDC) where a pump laser beam shines on a material with a χ2 non-linearity that converts an excitation photon into two photon,s which obey energy and moment conser-vation [5]. SPDC is used in fundamental quantum experiments to study entanglement between photons, e.g. [9], or one of the photons is used as a heralded photon to notify the experimenter that a photon is being produced [5]. Attenuated laser pulses or SPDC are practically set up such that only a fraction of the trigger pulses produces a photon, hence,

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2 Introduction

the probability of producing multiple photons is reduced. Since the experimenter can not decide when the photons are produced, these sources are classified as probabilistic [5].

The requirement that a source should only produce a single photon at a time is fulfilled with single quantum emitters. Such systems can be viewed as consisting of a ground state and an excited state. The system can be brought into the excited state by means of an ultrashort trigger pulse and some time later, quantified by the decay rate γ, the system relaxes back to the ground state by emission of a single photon. However, these processes are commonly not efficient enough for this type of source to be deterministic, because: (1) emitters have a small absorption cross-section such that for the high photon densities achieved in a typical confocal microscope setup the probability of an absorption event is around 10−5. (2) Not every emission cycle leads to a photon because of the presence of competing non-radiative decay channels (γnr). The quantum efficiency (QE), the ratio

of radiative decay rate γr to the total decay rate γtot = γr+ γnr, quantifies the radiative

efficiency. (3) In general photons, specified by their frequency and propagation direction, are not indistinghuisable. Emission is omnidirectional, therefore not every photon is captured by the detector or interacts with another system of interest. Additionally, sources can have a broad spectrum due to dephasing mechanisms, especially at room temperature. (4) Fluorescence applications may suffer a reduced photostability in the form of blinking or bleaching. I must note that these photon sources are termed deterministic since the probability of producing two photons is zero, however, because of the mentioned losses single emitters are in practice probabilistic as well. However, properties (1)-(3) have been improved by positioning the emitters close to cavities.

Cavities have the ability to store photons for long times quantified by the quality factor (Q) in small mode volumes (Vm) [10]. On the one hand, this enhances the probability that

a photon gets absorbed. On the other hand, it increases the QE as a consequence of the Purcell effect. Fermis Golden Rule states that the decay rate is proportional to the amount of photon states available. Purcell argued that a given optical cavity characterized by Q and V provides an extra contribution to the density of optical states above the vacuum with a factor of F = _4π32

Q

(V /λ)3, also known as the Purcell factor [10]. Since the cavity only contributes to the radiative density of states, the radiative decay rate is enhanced and therefore the QE. The consequences of this enhancement are that radiation profiles can be narrowed by the narrow cavity response and dephasing is reduced due to enhanced γr,

plus emission is directed into the cavity with an efficiency F/(1 + F ). These advantages can all improve the single-photon source properties. As a final note, the strong coupling regime is reached when the coupling rate of the emitter to the cavity is stronger than the spontaneous decay rate of the emitter or the decay rate of photons out of the cavity, which means that photons and emitters repeatedly interact [10].

Compared to ions, atoms or atomic ensembles which require ultracold temperatures and bulky trapping devices, solid-state emitters have a huge potential for on-chip appli-cations. One of the most popular solid sate emitters are quantum dots (QDs), which have been frequently combined with cavities because of their good optical properties, high absorption cross-section and narrow-band emission profile [11]. QDs embedded in micropillars showed the emission of photons with an indistinguishability of 81% [12]. Even strong coupling experiments of QDs to a cavity has been reported for QDs embedded in a Bragg-stack micropillar [13], microdisk [14] and photonic crystals [15]. Also, strong-coupling of a single QD in photonic crystal cavity has been demonstrated in the form of lasing [16] and optical switching [17]. However, these experiments are challenging and

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1.2 Color centers and properties of the host 3

difficult to scale since positioning of the QD in the mode maximum of the cavity is a probabilistic operation and usually low temperatures are required to reduce dephasing.

In what follows, I will focus on color centers which are another type of solid state emitter. Color centers are a good candidate for quantum photonics because of their good photostability at room temperature, no blinking or bleaching, and the possibility of cavity fabrication inside the host material [18]. Deterministic implantation of single defects by means of irradiation is advancing [19], which enhances the cavity-emitter coupling success rate. On top of that, the favorable spin properties have showed all the basic operations for quantum information processing, which brings about a whole new class of opportunities besides photonic quantum applications [4]. Finding good defects in technological advanced materials means easy integration in current electronic technologies.

1.2 Color centers and properties of the host

Color centers are point defects, usually related to a vacancy, in the crystalline structure of a wide-bandgap semiconductor. Dangling electrons are bound to these defects that form an energy level structure in which optical transitions can be driven. The energy levels to which the electrons are excited should be far away enough from decay channels supplied by the host such that the electrons remain bounded to the defect. Hence, these defects do not contribute to the conduction properties of the host [20]. Additionally, at certain charge configuration, the centers can have a paramagnetic ground state with spin resonances that can be driven with microwaves [21].

The most famous color center is the NV− center in diamond. This defect consists of a nitrogen impurity adjacent to a carbon vacancy. At room-temperature, the emission spec-trum is broad due to phonon coupling of the excited state, but a small zero-phonon line (ZPL) is observable in which the excited state looses its energy purely radiatively. Despite the photostability of these centers, only a fraction of the emission is into the ZPL, there-fore room-temperature photonic quantum applications are challenging. Research mainly exploited the remarkably strong spin properties of the NV− [4]. At room-temperature the ground state electron spin resonance (ESR) has coherence times up to 1.3 ms [22], which persists for so long because of the low magnetic moments of the nearby carbon atoms. Also, the spin ground state can be read-out extremely efficiently and purely through op-tics [23]. This is called optically detected magnetic resonance (ODMR) which exists in quantum systems that have spin-conserving optical excitation and optically resolvable spin-dependent decay paths. In the case of the NV−, the spin-excited state favorably decays through a longer-lived inter system crossing such that the fluorescence intensity will quench. From this also follows that the spin-ground state can be prepared solely by optical pumping. Concluding, the spin ground state is very robust and effectively initialized and read out. As such basic components of quantum computation have been demonstrated such as storing information [23] and quantum error correction [4, 24].

To fully profit from the spin-properties of NV−-centers and to develop larger scale devices with multiple coupled NV−-centers, cavities and waveguides need to be fabricated in the diamond. Various structures in diamond showing high Purcell factors and coupling to NV centers have been fabricated, but this fabrication is extremely difficult because no high quality thin diamond wafers exist. Current fabrication techniques rely on etching down thicker diamond wafers [3], however this compromises the quality of the diamond

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4 Introduction

wafer and also the optical properties of the NV centers close to the surface [25, 26]. Therefore, Weber et. al. [21] proposed new deep level defects in more technologically mature materials could potentially possess the properties of the NV center. In particu-lar, the authors proposed vacancy related defects in silicon carbide, which have motivated many experiments on the characterization of their spin- and optical properties [27]. More-over, several groups have demonstrated the fabrication of a variety of different cavities with high Purcell factors [27]. What mainly caught our attention were two reports on the silicon-vacancy carbon antisite in two different types of SiC that showed the highest brightnesses ever measured in color centers, a factor 100 times higher than a typical NV center [28, 29]. These bright defects bring about major opportunities as single-photon sources or potential interfaces in photonic quantum computation. Combining the at-tractive spin-properties of deep levels in general with the fabrication opportunities could possibly make these centers a highly attractive active photon material interface.

1.3 Motivation and outline of this thesis

The long-term goal of this research is to implant and identify single defects in SiC, and merge these defects in a cavity directly fabricated in the SiC. This work could serve as a guideline for defect implantation and characterization of the optical properties of color centers, despite that our efforts for defect implantation have not been successful. The thesis also describes cathodoluminescence measurements, performed to characterize the material.

In Chapter 2, I present a literature research on deep levels in SiC, which was done with the goal of choosing a center to work with. This selection was based on several criteria: (1) single defects should have been isolated and assigned to a particular defect center, (2) the optical properties of the single defects: brightness, excitation and emission wavelength and (3) whether an ODMR signature from these defects has been measured. As we attempted to implant defects by means of electron irradiation, in Chapter 3 I present theory on radiation damage to a material by fast electrons and calculated the displacement cross-section of silicon in the SiC crystal. Chapter 4 explains of the high-NA confocal fluorescence setups used and discusses the calibration of the photon detection efficiency. In Chapter 5, I discuss the procedure and present the results of fluorescence measurements on irradiated and unirradiated SiC samples. Chapter 6 describes the cathodoluminescence setup, experiments and results on the SiC samples. I conclude with a list of possible explanations on why defect implantation has not been successful which at the same time gives a list of important factors that need to be considered in any color center experiment.

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Chapter 2 Silicon Carbide

Silicon carbide (SiC) is a material with a high potential for applications in different fields owing to its outstanding electrical, optical, thermal and mechanical properties [30].

SiC has a high electronic breakdown field and high electron mobility. Together with a high thermal conductivity and large indirect bandgap (table 2.1), SiC outperforms silicon (Si) and gallium arsenide (GaAs) for high power and high frequency applications [30, 31]. SiC crystallizes in the very rigid diamond structure and this brings about a high hardness, large Young’s modulus and large abrasion resistance (9 out of 10 on Mohs scale). This hardness also remains at high temperatures, thence SiC is used as coatings for brakes in the fastest sports cars1_{. Silicon carbide is also chemically inert and combined}

with electrical and mechanical properties, which remain at high temperatures, SiC has been applied in hybrid platforms such as micro- and nanoelectromechanical systems [33]. To fully benefit from the exceptional properties of SiC, a lot of research and technology has gone into growing ultrapure SiC wafers (see section 2.2). The photonic community also benefits from the advances in wafer growth of SiC. At visible wavelengths, the large refractive index and low absorption losses of SiC compete with those of silicon nitride (Si3N4) in terms of optical field confinement and potentially obtainable quality factors

(see table 2.2). SiC could make a perfect platform for hybrid functionalizations when combining the different properties, e.g. field confinement and Young’s modulus in op-tomechanics or electrical and photonic properties for photonic on chip applications.

In the remainder of this chapter, I will introduce the special polymorph crystal

struc-1_{The new McClaren P1 for example}

Table 2.1: Properties important for high power high frequency electronics.

Property 3C-SiC 4H-SiC Si GaAs

Band gap [eV] 2.36 3.26 1.12 1.42 (direct)

Electric breakdown field [MV/cm] 1.4∗ 2.2 0.3 0.4 Electron mobility [cm2_/V/s] ₁₀₀₀∗ ₁₂₀₀ ₁₄₀₀ ₈₅₀₀

Thermal conductivity [W/cm/K] 3.3-4.9∗ 3.3-4.9∗ 1.3 0.55

The data for 3C and 4H were obtained from [30]. Estimated values are indi-cated with∗. Data for Si and GaAs were obtained from the IOFFE database [32].

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6 Silicon Carbide

Table 2.2: Comparison of optical constants [nm] 3C-SiC 4H-SiC Si Si3N4 n 500 2.69 2.68 4.29 2.03 600 2.65 2.64 3.94 2.01 700 2.63 2.62 3.78 2.00 k 500 – 0.0000 0.07 0.0000 600 – 0.0000 0.027 0.0000 700 – 0.0000 0.012 0.0000

Real (n) and imaginary (k) refractive indices were obtained from the Hand-book of Optical Constants from Palik, Ref. [34]. No reports were given on 3C-SiC.

ture of SiC in section 2.1 and the growth of highly-pure wafers in section 2.2. Section 2.3 reviews state-of-the-art fabrication of nanostructures applied to photonics. In section 2.4, I outline the identification and the optical- and spin properties of deep-levels. Based on sections 2.3 and 2.4, I supply the motivation for my choice to investigate the antisite defect in the 3C in section 2.5.

2.1 Crystal structure of SiC

SiC is built up from regular tetrahedrons with one carbon (silicon) atom in the middle and four silicon (carbon) atoms pointing outwards. One of the Si-C bonds is aligned with the c-axis and the others along the a1, a2 and a3 (see figure 2.1). Hexagonal close-packed

bi-layers consisting of a Si-layer and a C-layer are formed perpendicular to the c-axis. The set of Si-layers or C-layers are also called the Si- or C-sublattices. As demonstrated in figure 2.1, there are three possible positions for each bi-layer (A, B or C) and two successive layers can not occupy identical sites. In this way different stacking sequences known as polytypes, can be formed. Whereas most polytype materials only have one stable form, SiC has many [30].

Within a bi-layer the local crystal structure depends on the neighboring layers. When the orientation of the preceding bi-layer is unequal to the proceeding bi-layer, the middle bi-layer has locally a cubic structure (indicated by k) whereas, for equal orientations this crystal structure is hexagonal (indicated by h) (see figure 2.2). The stacking sequence ABC generates a purely cubic crystal structure (3C-SiC) and the stacking sequence AB a purely hexagonal (2H). Mixtures are also possible, such as ABCB (4H) and ABCACB (6H). In brackets, the polytypes are classified by Ramsdell notation where the number indicates the number of bi-layers within a stacking sequence and the letter the crystal classification. The stacking sequences of 3C, 4H and 6H are represented in figure 2.2. In the next section, I will describe how different polytypes of SiC can be grown.

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2.1 Crystal structure of SiC 7

Figure 2.1: Schematic of the possible positions of the bi-layers [30]. Each bi-layer is denoted by the letters A,B or C and the figure shows that each next layer has two options to position itself. The c-axis points out of the paper.

Figure 2.2: This figure represents the common 3C 4H and 6H polytypes. The polytypes are indicated on top of each schematic with Ramsdell notation. The layer positions are labeled by the letters A,B or C next to each layer and the local crystal structure in a bi-layer are characterized either cubic (k) or hexagonal (h), as proposed by Jagodzinski. The schematic is obtained from [30].

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8 Silicon Carbide

2.2 Wafer growth

The compound system Si and C does not have a molten phase in practical conditions. Instead, SiC sublimes at a temperature around 1800-2000◦C. For this reason, SiC is not grown from a liquid phase such as Si or GaN, but with vapor transport methods. There exist a large variety of growing methods for SiC that are still thoroughly researched and improved. For this thesis, I will discuss the physical vapor transport (PVT) method to grow 4H and the chemical vapor deposition (CVD) technique to grow 3C on Si(100). Growth of 4H-SiC

The most common method to grow wafer-sized single crystalline 4H (and also 6H) is by a particular PVT method called seeded sublimation growth or modified Lely method [35]. A polycrystalline or powdered SiC source, which can be obtained with a variety of processes, is heated in a crucible until it sublimes. A SiC seed is placed in the crucible on which the Si and C atoms crystallize. SiC also crystallizes without a seed, however, with an uncontrolled size and shape. These fragments can be used as seeds for growing larger SiC pieces. The crystallization is promoted by keeping the seed at a lower temperature and by lowering the pressure in the crucible. Additionally, the wafers can also be doped during growth by filling the cubicle with a nitrogen for n-type or adding aluminum to the SiC source for p-type [30, 36].

Up to 150 mm large 4H wafers can now be grown almost defect free [36]. The major defects that were found in the 4H polytype are micropipes; µm thick hollow tubes prop-agating along the c-axis that is often the growth direction, and basal plane dislocation (BPD); regions of the crystal that miss a layer or have an extra layer of atoms. These defects usually propagate from the seed. A major breakthrough initiated by Nakamura et al. [37], the repeated a-face growth method, made it possible to grow virtually defect free crystals. The principle is that the crystals are grown along different crystallographic di-rections in two steps, which suppresses defect formations in each step and by this method 4H-SiC became a interesting material for electrical applications [36].

Growth of 3C-SiC

Different SiC polytypes are stable, for which also single crystalline crystals can still be grown. Regimes of Si/C ratio, temperature and pressure in which one configuration is favorable where empirically found [30]. The 3C polytype is metastable. Nonetheless, pure 3C wafers can be epitaxially grown on Si(100). Commonly, low pressure chemical vapor deposition (LPCVD) is used to grow 3C where a propane gass supplies the carbon atoms and silane the silicon atoms. These two precursors are pumped into a hot chamber where the Si substrate sits on which the SiC grows [30, 38].

However, due to a large lattice mismatch between the lattice parameters of Si and SiC, 5.43 ˚A versus 4.53 ˚A, limits the crystalline quality. Additionally, an 8% difference between thermal expansion coefficients between SiC and Si induces a large strain on the interface which reduces the crystalline quality on the Si-SiC interface. These defects have been reduced by only pumping the propane precursor into the chamber at the initial stage of growth [39]. It was found that Si atoms from the substrate diffuse out to form the first layers of SiC, leaving voids in the Si substrate on the Si-SiC interface [40]. This first step is called carbonization and by varying the propane flow rate, temperature of the chamber

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2.3 Nanofabrication 9

and reaction time one could reach a few nm thick and uniform sealing layer of SiC on the Si substrate while at the same time leaving the void density at a minimum. It was found that the crystal quality could significantly be improved by optimizing this first step [39] and defect density is reduced further away from the Si. The major defects still present are microtwins, which are local shifts in orientation of the crystal a few atomic distances wide which extend along a certain crystallographic direction. I found two papers that report a density of these microtwins based on x-ray diffraction measurements: 0.25% of the crystal is displaced in 500 nm thick 3C [39] and 0.16% in 2µm thick 3C [41]. Additional structural defects in 3C grown on (100)Si could be stacking faults, local interruptions of the stacking sequence. However, no density of these defects was found in literature.

The difference between available wafers also sets conditions on the nanofabrication techniques that can be employed. In the next section I, will discuss fabrication techniques applied per polytype.

2.3 Nanofabrication

Nanofabrication in 3C

Since 3C can be grown on a substrate, freestanding structures can be fabricated by means of conventional etching techniques that rely on a etch-selectivity between the epitaxial layer and the substrate. The first etch step of 3C and Si is usually performed with either an HBr-Cl2 or CF4/Ar plasma and than subsequent undercuts are usually produced by liguid KOH or XeF2 gas. With these etches, microdisk resonators were fabricated with

resonances in the red-NIR part of the spectrum with Q-factors up to ∼2300 [42] (figure 2.3a) and in the telecome wavelengths with a Q up to 6.2 · 103 [43] and 1.14 · 104 [44]. Photonic crystal cavities have also been fabricated in 3C-Si. Two examples are from Ref. [45] and Ref. [46] that both operate in the telecome regime. The latter example implanted Ky5 defects by12_{C-irradiation of the fabricated structures. The physical origin of the Ky5}

defect is still unknown. Nanofabrication in 6H

The hexagonal 4H and 6H crystals do not grow on a substrate and therefore, conventional etching techniques, such as in 3C cannot be applied. For 6H, a smart-cut technique was developed that allowed the transfer of a thin 6H film to an SiO2 substrate. H+ ion

bombardment creates a highly defective region at a certain depth in the crystal along which the crystal is cut [47]. As an example, this technique enabled the fabrication of a photonic crystal cavity with a Q up to 4500 in the NIR [48] (figure 2.3 d). This method is rather crude and compromises the quality of the material, which reflects in the measured Q of 4500, which was modeled to be 78000.

Nanofabrication in 4H

Etch-selectivity in 4H was obtained by epitaxially growing a thin p-type 4H layer by CVD on a thick n-type substrate. In this method, the undercut is produced by liquid KOH while illuminating the material with UV. The illumination promotes holes in the n-type which enhances the oxidation reaction rate of the n-type substrate that forms

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10 Silicon Carbide

water-soluble SiO2 [49]. This process is called photoelectrochemical etching (PEC) and

was among other structures and functionalities, used to fabricate a disk resonator with a Q of ∼9000 in the NIR [50]. A last example of a device fabricated in SiC are nanopillars in the 4H polytype obtained by inductively coupled plasma etching with a SF6 or O2 plasma

of a patterned 4H surface with nickel cylinders. Etch conditions were varied to control the height and thickness of the nanopillars, which led to thicknesses down to 60nm [51] (figure 2.3c).

Figure 2.3: Examples of nano-devices in various SiC polytypes. A) SEM im-ages of microdisk resonators fabricated from 210nm 3C on a Si substrate [42]. B) SEM images of microdisk resonators fabricated with photoelectrochemical etching [50]. C) SEM image of 4H nanopillars fabricated by etching a 4H wafer patterned with nickel cylinders [51]. D) SEM image of a 6H photonic crystal slab on a SiO2 substrate fabricated with a smart-cut technique [48].

2.4 Color centers in SiC

Many deep-level defects in SiC that recombine radiatively have been observed [27]. Two publications from S. Castelletto et. al. [29] and A. Lohrmann et. al. [28], stood out because they reported one of the brightest single color centers: about 100 times brighter than NV centers [26] and comparable to silicon vacancy centers in diamond [52]. Addi-tionally, other reports on different color centers identified single spins in SiC and showed ODMR signatures [53, 54]. As such, SiC has entered the arena of quantum photonics and quantum spintronics on single color centers.

The defects of common interest are the silicon vacancy (VSi), di-vacancy (VSiVC) and

silicon-vacancy carbon-antisite (VCCSi). The silicon-vacancy carbon-antisite, or antisite

for short, is an empty silicon site with an adjacent carbon atom sitting on that site leaving its carbon site vacant. The defects can have a particular charge which in that case would also be indicated in the notation. The ZPLs, measured in low-temperature PL experiments, are characteristic for the defect-host combination and these are mostly

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2.4 Color centers in SiC 11

Table 2.3: Comparison of single defect measurements in SiC

Polytype - defect ZPL [nm] Brightness [counts/sec]

ODMR

(∆I) Additional remarks 3C - antisite 2+ _{∼ 650} _{6 · 10}6 _[29] _– _{Detected in nanocrystals}

4H - antisite+ 650−680 2 · 106 [28] – Detected in bulk 4H 4H - Si-vacancy − 850−900 10

4 _[55] _– LT of 7.6ns

σabs of 1.5 · 10−16 cm−2

4 · 104 [54] 0.8% SIL: 4x enhanced brightness 100 µs spin coherence time 4H - di-vacancy − 1043−1132 2 · 104 ∗ _[53] _10% ∗ _{1.2 ms spin coherence} ∗

Measurements are performed at room temperature except the di-vacancy in 4H was done at 20K (denoted by∗).

assigned to a particular defect center with density functional theory (DFT) calculations. These yield the wavefunctions of the bound electrons from which the energy levels can be obtained, e.g. [21]. The inequivalent sites, the h- and k-sites, in 4H and 6H also affect the wavefunctions of the bound electrons slightly and thus the ZPLs shift depending on their position in the crystal (figure 2.4). In most studies, defects are implanted by irradiation with either electrons, neutrons or 12_{C ions. Defects may also be intrinsic in the material,}

but most single defect studies did an implantation to control the density.

Zero Phonon Lines in SiC

The zero phonon lines (ZPLs) in SiC can only be clearly resolved at low temperatures. This is not the case for the NV− center in diamond which has a clear ZPL at room temperature, although a broad phonon side-band at higher wavelengths. At present, not all PL lines observed in the polytypes of SiC are assigned to a particular vacancy beyond doubt [27]. However, based on the current knowledge, there seems to be a consensus that the antisite radiates in the red and the silicon vacancy and di-vacancy in the NIR.

Various reports on the optical properties of single defects were published in the past few years. Single antisite defects have been detected in 3C [29] and 4H [28] and single di-vacancies [53] and silicon vacancies [54, 55] in 4H have been isolated as well (see table 2.3 for an overview). The antisites were shown to be extremely bright, 7 · 106 _counts

per second in 3C nanoparticles [29] (quantum confinement effects should not play a role but the curved nanoparticle surface could enhance the collection efficiency) and 2 · 106

counts per second in bulk 4H [28], both detected at room temperature. A single silicon vacancy in 4H was reported to have a maximum brightness of 2 · 104 counts per second at room temperature which was enhanced by a factor 4 with a solid immersion lens [54]. Another publications reported on the observation of a single silicon vacancy in 4H with a maximum brightness of 104 counts per second and also obtained an absorption cross-section of 1.5 · 10−16cm−2, both at room temperature. Finally, Ref. [53] detected a single di-vacancy in 4H with a single defect brightness of 2 · 104 _{counts per second at 20K.}

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12 Silicon Carbide

Optically Detected Magnetic Resonance in SiC

Recently, the ODMR of single di-vacancy defects in 4H was measured with an ODMR contrast of a few percent and a spin coherence time of 1.2 ms at 20 K [53]. A different article, in the same issue of Nature Materials, shows a weak ODMR signal from single silicon vacancy defects in 4H-SiC [54] and a spin coherence time of half a second at room temperature. Another interesting report on ODMR is from Falk and coworkers [56], who implanted the 3C, 4H and 6H polytype with fast12_{C ions. The resulting line in 4H belongs}

to the di-vacancy defect assigned earlier by Ref. [57]. The unidentified lines in 3C and 6H are a result of an equal treatment and are in the same wavelength range as the di-vacancy in 4H, thus are tentatively assigned to the di-vacancy defect as well. All these lines show an ODMR signature and wavelength-resolved ODMR made it possible to track the ODMR signature per line. This extensive ODMR study showed that all lines have a zero-field resonance and some lines possess two zero-field resonances at 20K and some lines also at room temperature. Additionally, the authors demonstrate a room temperature coherence times for the di-vacancy in 4H around 50µs. Up to date, no optically detected magnetic resonance (ODMR) in any polytype has been observed for the antisite.

2.5 Motivation for the antisite in 3C-SiC

As mentioned in the introduction, the factors to decide which defect-host combination to work with depend on: (1) The isolation assignment and optical properties of singe defects, (2) The nanofabrication possibilities in the host and (3) whether an ODMR signature has been reported. An important practical constraint in our case is the efficiency of our silicon detectors, which is too low above 700 nm (efficiency of about 10% around 700 nm) and therefore limits us to work with the antisite. Although the antisite defect has a paramagnetic ground state, ODMR has not been measured. Since 3C can be etched with standard etching techniques, we choose to work with this host. Although the antisite was only detected in 3C nanoparticles, and the wafer quality for 4H is higher than for 3C, we assumed that we could detect the antisite 3C bulk as well. Especially, because cavities with high quality factors have been fabricated in 3C, which can only be achieved if there are low losses in the material, hence a high quality crystal.

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2.5 Motivation for the antisite in 3C-SiC 13

Figure 2.4: Examples of milestone experiments on color centers in SiC. A) (top) PL graph of a single VCCSi defect center in a 3C-SiC nanocrystal.

(be-low) Confirmation of a single defect by measurement of the g2 _{[29]. B) PL}

map of 4H-SiC wafer that was irradiated with fast electrons and subsequent steps of annealing were performed to form VCCSi defects. Scans were made

at room-temperature with a 532nm CW excitation source and collected fluo-rescence passes through a narrow 694nm bandpass to only select the defects luminescence. A maximum brightness of 6 · 106 _{cts/sec for a single defect}

center was measured [28]. C) (bottom) PL map of a 4H wafer were blue spots indicate V−_Si defects. (top) A z-confocal PL scan plotted as side view, which makes the solid-immersion lens visible that was milled to enhance the collec-tion efficiency [54]. D) SEM image of the SIL from C) [54] E) PL lines from the SiC polytypes 3C, 4H and 6H treated with carbon ion implantation. Because all sites for the 3C polytype are equal, only one line is present in the PL map. 4H-SiC and 6H-SiC show multiple lines, whereas each line corresponds to a different location and orientation of the defect in the crystal. F) Spectrally resolved ODMR of the lines of 4H from E) [56].

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Chapter 3 Defect implantation

In this Chapter, I will discuss the preparation of the samples. As explained in the last section of Chapter 2, we decided to investigate the antisite defect, a silicon vacancy with an adjacent carbon atom sitting on the empty silicon site, in the 3C polytype. We ordered from NovaSiC an ultrapure 6 µm thick 3C-SiC epilayer, 4” diameter, on a 0.5 mm (100)-oriented silicon substrate [38]. The silicon vacancies were implanted by exposing the wafers with fast electrons. The irradiation procedure was performed at Leoni [58], where they have a beam of electrons that are accelerated to a kinetic energy around 1.1MeV and also options to reach 10 MeV. We varied the irradiation conditions to establish the procedure for a desired density of antisite defects. Beforehand, I performed calculations on the displacement cross-section, the probability of displacing an atom from its original site, of a silicon atom in 3C-SiC given the irradiation conditions offered by Leoni.

In section 3.1, I will start with a general review on the theory behind vacancy formation due to radiation. This theory section is based on Ref. [59]. I will focus on electrons as the irradiation particles, but the theory could also be applied to other particles. In section 3.2, this theory will be applied to the beam energy offered by Leoni to explicitly calculate the displacement cross-section. Finally, in section 3.3, other factors will be included that could affect the final defect density and based on the results the final irradiation procedure will be presented.

3.1 Principles of vacancy formation due to radiation

We attempted to form silicon vacancies by exposing the SiC with fast electrons. When the electrons (or projectiles for any kind of particle) penetrate a solid (target), the inter-actions can be separated into two classes: elastic collisions and inelastic collisions. Elastic collisions are interactions with the nuclei of the target that lead to momentum transfer and possibly displacements of the atoms from their original site. Inelastic collisions are interactions with the electron cloud that lead to electronic excitations or ionizations of the atom. Inelastic collisions are much more likely to occur due to the larger extend of the electron cloud, compared to the nucleus, but also because the electrons shield the nucleus. Thus, this class of interactions are the main source of energy dissipation in the target. However, if the projectiles have enough energy, the electrons may penetrate the atoms and collide with the nucleus. In this case, energy and momentum can be transferred to the nuclei. When this energy transfer is higher than the binding energy of the target atom and additional energy to move the target from its original site, a Frenkel pair is created; a

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3.1 Principles of vacancy formation due to radiation 15

Figure 3.1: (left) Transferred energy (T) from swift electrons to Si atoms in 3C-SiC. T is plotted as function of scattering angle and electron energy. The yellow line highlights the displacement threshold energy (25 eV) and the grey dotted line is at 1.1 MeV, the energy used to implant defects. (right) Cross-cut of the transferred energy plot along the grey dotted line. A minimum scattering angle to displace an Si atom is indicated by the black dotted line.

vacancy and an interstitial atom [59]. The elastic interactions are of main interest in this work, since these can lead to the antisite defects, and these interactions will be discussed next. However, inelastic collisions can also affect the density of defects and these will be discussed in section 3.3.

Elastic collisions

Due to an elastic collision event, energy and momentum are transferred from the projectile to the target. As a consequence, the projectile scatters off the target with a certain scattering angle θ. The geometry of such a scattering event is presented in figure 3.2. I assume a single projectile interacting with a single stationary target.

First, I focus on the right part of the figure. It shows that for a certain scattering angle, the projectile transfers energy T to the target. From conservation of energy and momentum it can be shown that the relation between θscat and T is [59]:

T = Tmaxsin2 θscat 2 with Tmax = 2meE M 2 + E mec2 . (3.1)

Where E is the energy of the electron, me the mass of the electron, c the speed of light

and the target is specified by its mass M . Tmax is the maximal transferred energy, which

happens at a scattering angle of 180◦. Because of the small mass of the electrons with respect to the target atoms, the electrons can only transfer a fraction of their energy. Therefore, electrons with energies from a few 100 keV and up are usually used to create vacancies in solids. In this energy range, electrons travel close to the speed of light and therefore relativistic corrections are made to obtain T .

On the left side of figure 3.1, T is plotted as function E and θ. The graph shows that more energy is transferred for larger scattering angles. The dotted line is at 1.1 MeV which is the electron beam energy at Leoni. For this energy, T as function of θ is plotted on the right side of figure 3.1. A silicon vacancy is created when T is high enough to

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16 Defect implantation

break the four bonds with the surrounding carbon atoms plus some additional energy to displace the silicon from its original site. The minimum energy required to accomplish this is called the displacement threshold energy and this value was measured in 3C-SiC at E_disSi = 25 eV [60]. The minimum scattering angle θmin associated with EdisSi is 48 degrees.

So far, I have assumed that an elastic scattering event takes place, without specifying the potential through which the electron and silicon atom interact. To incorporate this in the analysis, I need to introduce the cross-section. In general the cross-section σ (units of area) is defined such that given an atomic density N , the number of collisions per unit length n is given by N σ. Additionally, many independent scattering events will give a distribution of scattering angles, and as such, the cross-section can be written as a cross-section as function of solid angle of scattering, dσ/dΩ:

n = N σ = Z

Ndσ

dΩdΩ. (3.2)

dσ/dΩ is called the differential cross-section (DCS) and its definition holds for any scat-tering event. These definitions are also included in figure 3.2 which shows that an electron from the shell with area dσ scatters into solid angle dΩ. Once the DCS, the relation be-tween dσ and dΩ, for the possible interactions are known, the trajectory of any projectile can be fully described [59]. As a last note on figure 3.2, we could also have written dσ in terms of impact parameter b, which is the shortest distance between the trajectory of the electron and a line parallel to that trajectory that goes through the center of the target. Obtaining the differential cross-section is a mathematically demanding task. In our case the DCS involves complicated potentials that describe the various electromagnetic interactions between the fast electron and the charge distribution of the atom, that is electron-cloud and the nucleus. As I will describe in the next section, advanced numerical calculation techniques are developed that give the DCS for specific situations. In this case, we must consider the elastic DCS for an electron and an atom. In the next section I will describe how I obtained the elastic DCS for electrons and the silicon atom embedded in the 3C-SiC crystal with the code package ELSEPA (Elastic Scattering of Electrons and Positrons in Atoms) [61].

Given the elastic DCS, we can get to the momentum transfer DCS by multiplying the DCS by a correction factor 1 − cos(θ), from θmin to the maximum scattering angle π [61].

Than the total probability to displace a silicon atom is obtained by integration of the momentum transfer DCS over all scattering angles that can lead to an displacement:

σ_distot = Z π θmin (1 − cos(θ)) dσ dΩ el dΩ. (3.3)

3.2 Calculation of the displacement cross-section

The DCS for scattering of electrons in the silicon sub-lattice of 3C-SiC was obtained with the code package ELSEPA [61]. This package calculates the DCS for electrons in the energy range of tens of keV up to 1 GeV. At an energy range of 1 MeV, only the electrostatic interaction between the electron and the charge distribution of the nucleus are important. At these energies, even the crystal structure does not influence the obtained DCS with respect to a freestanding atom [61].

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3.2 Calculation of the displacement cross-section 17

Figure 3.2: Schematic of a scattering event. The projectile is an electron that with an impact parameter b or cross-section dσ scatters on a carbon or silicon atom into scattering angle θ or scatteirng solid angle dΩ.

The atoms, specified by atomic number of Z and charge ρ0, are modeled as a static

charge distribution . The Si nucleus is modeled as a Fermi charge distribution: ρn(r) =

ρ0

exp[(r − Rn)/z] + 1

. (3.4)

In this equation, r is the radial distance from the center of the nucleus, Rn is the nuclear

radius (3.25·10−13cm for Si) and z is a skin thickness (5.46·10−14cm for Si) which models how sharply the distribution falls off at the radius. The charge density of the electron cloud are numerical inputs in the model provided by the package.

In figure 3.3, the momentum transfer DCS (the formula under the integral sign in Eq. 3.3) is plotted as function of scattering angle θ (dΩ = 2π sin(θ)dθ). By integrating of Eq. 3.3 from the minimum scattering angle to generate a displacement, θmin, to the maximum

scattering angle π, a total displacement cross section is obtained: σdis = 1.7 · 10−23 cm2.

The total elastic scattering cross section is σtot = 1.0 · 10−18 cm2, which is obtained by

integrating all angles.

Figure 3.3: The differential cross-section for silicon and carbon in 3C-SiC under irradiation of 1 MeV electrons. The data was obtained with the code-package ELSEPA. The grey dotted line indicates the minimum scattering angle.

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3.3 Irradiation conditions

We aimed for a target density that results in roughly one defect per a volume spanned by a high NA focal spot, that is 1 defect per µm3_{. Given that the density of Si atoms}

in a single bi-layer is 1015 _cm2_{, the probability that an electron generates a displacement}

in one bi-layer P = 1.8 · 10−8. For 300 bi-layers in 1 µm, the total probability becomes P = 5.6 · 10−5 such that based on the displacement cross section, an electron dose of 1012_e/cm2 _{should be sufficient to meet the target density. The electrons penetrate the}

sample along the c-axis such that the Si atoms are are aligned with the beam and may shield each other. However, I assume that every layer has an equal probability to displace a Si because the cross-section for such an event is small. Additionally, it was shown that for these high electron energies, the cross-section or displacement energy threshold does not depend on incoming angle or crystal facet [60]. The mean free path between two collisions, λ = 1/(NSiCσ), is 10 µm between two collisions of any kind and 2 cm

between two displacements. Concluding, the defect density and any other damage will be homogeneously distributed throughout the sample.

There are a number of factors that can reduce the defect density. In principle not every Frenkel pair survives. In 4H, under similar irradiation conditions, it was established that around 10% of the Frenkel pairs do not anneal out during the irradiation [62]. Next, not every Frenkel pair becomes an antisite defect. I have not found specific numbers on formation efficiencies in 3C-SiC, however, a report from Lef`evre et. al. [60] showed that the ZPL of the antisite in low temperature ensemble fluorescence measurements on irradiated 3C-SiC is much weaker than other lines. This suggests to irradiate with higher doses than calculated from the cross-section. Taking these factors into account, we reasoned that a dose-sweep of 1014− 1016 _e/cm2 _{must be sufficient to meet our target density. I note}

that these dose-ranges used coincide with other works on 3C-SiC, e.g. [29, 60]. Finally, the antisite defect in 3C is not thermally stable and 50% of the defects anneal out at temperatures from 100 − 700◦C, and all defects anneal out around 1000◦C [63, 64]. In the next paragraph, I will argue that during the irradiation conditions, the temperature rise in the samples is not significant.

The last factor, which can decrease the defect density, is heating of the sample during the irradiation procedure. A picture of the sample in the sample mount and a schematic representation of the irradiation configuration are given in figure 3.4. The sample consists of a 6 µm SiC layer on 0.5 mm Si which is clamped to a copper mount. The electron beam at Leoni has a fixed energy but variable electron fluxes. The samples are placed on a belt that moves in and out of the electron beam. The velocity of the belt, the electron flux and the number of passes regulate the total dose. The belt is kept at 4◦C by a flowing water source. An overview of the irradiation conditions are given in table 3.2.

Assuming that all the energy the electrons loose is converted into heat, the temperature rise per second during the irradiation procedure in the various layers can be calculated with the heat capacity of the materials. The energy loss of the electrons as they move through the sample is the stopping power S(E) [59]:

S(E) = −dE dx −→ x = Z E1 E2 1 S(E)dE. (3.5)

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3.3 Irradiation conditions 19

Table 3.1: Energy loss per layer of the sample.

Layer Thickness [µm] dE/dx [MeV/µm/el] PIn [W ] (for 1013 el/s)

SiC 6 5 · 10−4 5.2 · 10−3

Si 500 5 · 10−4 0.4

(1) Cu 650 1.1 · 10−3 1.1

(2) Cu 50 3.6 · 10−3 0.3

The first column indicates the different layers where (1) Cu is the low energy region for the copper mount and (2) Cu the high energy region for the copper mount. The thickness column indicates over which penetration length the energy loss, given in the third column, persists. The last column gives the total power dissipated in each layer for an electron fluence of 1013 el/s.

6 µm SiC 0.5 mm Si

4 mm Cu

e

-T=4°C

Figure 3.4: (left) Four 1.2x1.2 cm2 samples are clamped to a copper mount (see picture) and placed in the large electron irradiation beam. The electrons penetrate the sample along the c-axis of SiC. The different layers of the sample are depicted and the copper mount sits on a water cooled belt which is kept at 4◦C. (right) Energy loss per cm for 1 MeV electrons as function of penetration depth in copper. The energy loss is almost constant in the first 650 µm and increases rapidly in the last 50 µ (shaded area) before they come to rest at a depth of 700 µ, 4.3 mm away from the cooled surface.

obtained from the ESTAR database [65]. By using the continuous slowing-down approxi-mation, the integral in equation 3.5 gives the electron penetration depth x when it looses dE = E1 − E2 of kinetic energy [65]. Now, the stopping power can be conveniently

ex-pressed as the energy loss per unit length as function of penetration depth, such that the amount of energy deposited in the various layers of the sample can be calculated. On average, an electron with incoming energy of 1.1 MeV deposits 0.54 keV per µm in the SiC and Si layer. The electrons come to rest in the copper mount 700 µm away from the silicon. Because the cross-section increases rapidly for lower energies, the energy de-posited per unit length increases when the electrons are almost at rest [59]. I plotted the

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Table 3.2: Irradiation conditions Dose [e/cm2_] Electron fluence [1012_e/cm2_/sec] Beam time [sec] Passes dTsample [◦C/sec] dTCu(1) [◦C/sec] dTCu(2) [◦C/sec] dT [◦C] steady state 1014 ₅ _7.5 ₄ ₂ ₃ _8.5 _0.25 1015 10 15 10 4 6 17 0.5 1016 ₃₀ ₃₀₀ ₁ ₁₂ ₁₈ ₅₁ ₁₄

Column two to four specify the irradiation conditions per electron dose. In the fifth column, the temperature rise per second in the SiC and Si are given. The sixth and seventh column give the temperature rise per second in the two regions of Cu as explained in 3.1. The final column is an estimation of the temperature difference between the sample and the cooling belt for each irradiation condition.

energy loss per cm (dE/dx) per electron in the copper mount in figure 3.4. The energy profile consists of two regions: in the first 650 µm, the energy loss 1.1 keV/µm and in the last 50 µm, indicated by the shaded area, the average energy loss of 3.6 keV/µm. An overview of these results is given in table 3.1.

With the deposited energy per layer (see table 3.1), the temperature rise per second in each layer is calculated and given in table 3.2 for the different irradiation conditions. The irradiation doses of 1014 and 1015 e/cm2 pass the beam multiple times and has time to thermalize when it is out of the beam, as such, the temperature rises are negligible. However, for the 1016 _e/cm2_{, temperature rise may be significant.}

To calculate the final temperature in the samples, the flow of heat to the cooling belt is taken into account. Assuming a linear temperature profile in which the cooling plate stays at 4◦C, the power that is dissipated towards the cooling plate is given by:

Pout = κ

A · dT

dx , (3.6)

with κ the thermal conductivity, dT the temperature difference between the cooling plate and the sample and dx the distance of the cooling plate to the energy source. I assume that all the power deposited in the SiC and Si flows into the copper. Then, the steady-state temperature can be calculated by setting Pout = Pin (see table 3.1 for Pin). Values

for dT are given in table 3.2. As was already anticipated on, the temperature rise for the doses 1014 _{and 10}15 _e/cm2 _{are negligible (0.25 and 0.75} ◦_{C, respectively). For the dose}

of 1016 e/cm2 the steady-state solution is a temperature rise of 14◦C. This calculation is valid with the condition that there is good contact between the copper mount and the cooling belt and that the water can dispose of the heat quickly. After discussion with the irradiation company, we concluded that we can indeed assume that during the irradiation procedures, the temperature will not rise above 700◦C, the temperature from which the majority of the antisite defects anneal out.

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Chapter 4 Fluorescence microscopy for defect

characterization

The SiC samples were first investigated using confocal fluorescence microscopy. Fluores-cence microscopy spatially maps the spontaneous emission of a sample upon excitation. This chapter describes and gives a detailed calibration of two fluorescent setups used in this work that have the sensitivity to characterize the optical properties of single-emitters. Both microscopes operate with a resolution close to the diffraction limit and are equipped with a highly-sensitive CCD camera, APDs with single-photon detection efficiency and a spectrometer with cooled CCD. With these devices, spatial fluorescence maps of the irradiated and unirradiated SiC samples were made. Bright spots in these fluorescence maps are assigned to a particular defect center based on their spectrum. We aim to look for the antisite defect, which has a ZPL at 650 nm, but other defective centers may have different spectral characteristics. Additionally, the setups are also equipped with timing cards that collect the photon arrival times and trigger pulses from a pulsed excitation source with which the decay dynamics of emitters and photon-photon correlations can be performed. These techniques will be briefly explained, but were not employed in this work.

I used two confocal fluorescence microscope setups to investigate the SiC samples. The main difference between these microscopes, that is relevant for this thesis, are the excitation sources. Section 4.1.1 describes the confocal fluorescence microscope with a continuous wave (CW) argon-krypton laser as excitation source which has multiple ex-citation lines that were used to look for bright fluorescent spots in the SiC. Because fluorescence is such a weak process and we intend to detect single color centers, it is im-portant to benchmark the photon detection efficiency. This was done with beads stained with fluorescent molecules, and is described for the CW microscope in section 4.1.2.

In the other microscope, I used a pulsed 532 nm excitation source. This setup is also equipped with a spectrograph with a high-sensitive cooled CCD that has a sensitivity to obtain the spectrum of single emitters. This microscope will be described in section 4.2.1 and the calibration of the detection efficiency of the CCD, APD and spectrometer are given in 4.1.2. Finally, I tested the the setup on novel nanodiamonds specifically fabricated to host bright NV-centers. I show some preliminary optical characterization of these NV centers in section 4.2.3.

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22 Fluorescence microscopy for defect characterization

4.1 Confocal microscope setup with continuous wave

excitation source

4.1.1 Description of the setup

The first confocal fluorescence microscope I describe, presented in figure 4.1, has a con-tinuous wave (CW) Argon Krypton laser as excitation source (Stabilite 2018RM from Spectra Physics, wavelengths range from 456 - 674 nm). The laser is coupled into a single mode fiber (not shown in figure 4.1) before it is send towards the sample. This fiber acts as the first pinhole that is imaged on the sample plane. The laser spot is scanned over the sample by two Galvo mirrors and before the light enters the objective, it passes a telescope (f1 = 50 mm and f2 = 200 mm) that enlarges the beam by a factor 4 such that

the back aperture of the objective is completely filled to obtain maximal focusing on the sample. In the measurements I show, the light is focused and collected by a 100x NA 1.4 oil-immersion objective (Nikon CFI Plan APO).

In confocal microscopy, the laser spot is scanned point by point where on each position the signal is collected. In this setup, scanning is achieved by two Galvo mirrors (Thorlabs, GS002). These mirrors make an angle proportional to the voltage that is applied which than correspond to a displacement of the focal spot in the sample plane. This displacement is set by the focal lengths of the telescope and objective. With the 100x objective, each Galvo mirror can scan the laser spot in steps of 15 nm over a range of 200 µm. However,

Figure 4.1: Schematic of the fluorescence microscope with continuous wave excitation source. The laser source used is a CW Ar-Kr laser with multiple excitation lines. The laser spot is scanned over the sample by two Galvo mirrors. Emission is collected by the same objective of which 20% is send to the CCD and 80% to the APDs. A dichroic mirror and bandpass filter suppresses the excitation light. The fluorescence is detected by two APDs that are connected to a timing card for time-correlated single-photon counting measurements.

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4.1 Confocal microscope setup with continuous wave excitation source 23

Figure 4.2: Field of view obtained with the scanning the laser spot over a calibration sample with the Galvo mirrors. The sample is chromium evap-orated on glass that is patterned with 2 µm-sized holes with a 5µm pitch. The field of view is 120 µm in the y-direction and 80µm in the x-direction. Additionally, step sizes are 5% off in the y-direction and 1% in the x-direction. Scale bar is 20 µm.

the field of view is limited by the size of the optics and was determined with a reflection measurement by scanning the laser spot in 350 nm steps over a grid of 2 µm-sized holes with a 5µm pitch in chromium on glass. The reflected light was collected with the APDs (figure 4.2). This calibration sample was fabricated with UV lithography and it can be seen that the field of view is 120 µm in the y-direction and 80µm in the x-direction. Additionally, the same scan was used to determine the accuracy of the scanning steps, and it was obtained that in the y direction step sizes are 5% off and in the x-direction 1%. Since these offsets were constant over the sample, we believe that the offset, and also the elongated shape of the field of view, is caused by a slight miss-alignment of the Galvo mirrors. However, this was not taken into account in the SiC measurements that I will show since absolute distances do not play a major role in these measurements.

The light scattered or emitted by the sample is collected with the same objective. 20% of the collected light is send to a thermoelectically cooled CCD (CoolSnap EZ) with a quantum efficiency of 60% at 600 nm. A tube lens with a focal distance of 200 mm focuses the light on the CCD and the magnification is set by the focal distance of the objective, in this work the magnification is 100x. The CCD has pixels of 6.45 µm in size, 1392x1040 pixels in total, leading to a 8.978 x 6.708 mm sized active area. One pixel images 64.5nm of the sample and the total field of view of is 89.79x67.08 µm. Two band passes, that suppress the excitation light by 12 orders of magnitude, can be placed in front of the CCD to image fluorescence.

The remaining 80% of the collected light follows the same path as the excitation source and then passes a dichroic mirror and two band passes that also suppress the excitation light by 12 orders of magnitude. The light is split by a polarizing beam splitter and send to the two APDs (MPD PD5C0C) that have a quantum efficiency of 40%. The active area of the APDs is 50 µm and acts as the second pinhole that should be confocally focused on the position of the laser spot in the sample. As such, our setup has a resolution set by the diffraction limit. The lenses in front of the APDs have a focal distance of 25 mm and

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together with the telescope and objective, the image is magnified 50 times such that the active area of the APD is almost completely filled by a diffraction limited spot. Finally, the APDs are connected to a Becker & Hickle (DPC-230) counting card for photon-photon correlations or for lifetime measurements when a pulsed laser source is installed.

4.1.2 Setup calibration with fluorescent beads

This section shows the detection efficiency of the setup with polystyrene beads that have a diameter of 100 nm and are stained with red fluorescent molecules (580/605, Invitrogen f-8801). The sample is excited with a power of 13 nW at 570 nm. The diffraction limit of the microscope, with the 100x NA 1.4 objective, is 290 nm for 570 nm excitation. Therefore, the sub-diffraction limited beads act as a point source. To find single beads, the laser spot is scanned over the sample in 300 nm steps and fluorescence is collected by the two APDs with an exposure time of 100 ms per pixel (figure 4.3a). The background signal in this particular scan is 25 counts per pixel. The laser spot is moved to a single bead (indicated by the white arrows) and the focus is adjusted to reach maximum count rates in the detector. A fine scan with the same excitation and collection settings but now a pixel size of 50 nm around a single bead is given in figure 4.3b from which a total count rate of 4.7·105 _{counts per second is deduced by summing the maximums of both}

intensity maps. Additionally, the size of the bright spot on the fine APD scan defines the spot size which is 500 nm, such that from this scan it is deduced that the setup operates a factor two away from the diffraction limit.

From the same bead, after the APD scan, an image with an exposure time of 2 s was taken with the CCD (figure 4.4a). The cross-cut of the intensity map of the bead (figure 4.4b) shows again a spot size with a radius of 500 nm and by summing the ADUs belonging to the pixels within this radius I obtain a total count rate for the bead of 3.5 ∗ 103 _ADU/s.

Since the ADU-to-electron conversion and quantum efficiency of the CCD are known, it is possible to estimate the number of molecules on a single bead by comparing the number of emitted photons detected by the CCD with the excitation photon flux. This calculation benchmarks the performance of the setup and allows to address each loss channel in the process of excitation and detection such that quantitative expectations on single-emitter fluorescence can be made. Additionally, the countrates of the APDs can be compared to the CCD such that a detection efficiency for the APDs can be obtained. Estimation of the number of molecules on a single bead

In this section, I estimate the number of molecules on a single bead by comparing the number of emitted photons detected by the CCD with the excitation photon flux. Figure 4.5 gives a graphical representation of the setup with a bead in the focus. The bead is excited with a photon fluence of Nin = 3.9 · 1010/s. For a 500 nm spot radius, the spot

size in the focus is σL= 7.9 · 10−13 m2, resulting in an excitation photon flux through the

focus off 5.0 · 1022 photons/s/m2.

The bead is expressed in terms of the number of molecules on a bead (nmol) and the

optical properties of a single molecule: the absorption cross-section σabs, which is typically

10−20 m2 _{[66], and the quantum efficiency QE, which is typically around 50% − 100%}

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4.1 Confocal microscope setup with continuous wave excitation source 25

when excited with 5.0 · 1022 photons/s/m2. Note that these are rough estimates because the exact values are not known.

The collection efficiency depends on the NA of the objective but it also but also the emission profile of the emitters are important. If I assume a spherical emission profile for molecules that are randomly distributed. Then, given the NA of 1.4 of our objective, the collection efficiency ηcol is 30%. However, the collection efficiency of a randomly oriented

molecule on a glass substrate in air imaged with an index-matched oil objective is 70% [67], because the emission goes favorably into the glass and oil because of the larger density of optical states than in air. The collection efficiency of emitters embedded in a bead is usually estimated to be 40%. Therefore, the number of photons collected by the objective, Nout, is 150·nmol photons/s.

Now I discuss the detection part of the setup. For the CCD, the transmission coefficient T = 6% which is so low because 7% of the collected light is send towards the CCD and two band passes with a transmission of 95% each block the excitation light. The CCD has a quantum efficiency (QECCD) of 60% and it was set to gain factor which correspond

to 7 electrons per ADU (G = 14%) (see figure 4.5). As such, with the transmission coefficients and the given CCD settings, a photon-to-ADU conversion of 170 is reached,

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(B)

Figure 4.3: APD scans of fluorescent beads. Sample is excited with 13nW with 570 nm. (a) Large scan to localize single beads, as indicated by the arrow. Scalebar is 3 µm and pixels are 300 nm. (b) Fine scan of a single bead. Scalebar is 300 nm.

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(A)

(B)

Figure 4.4: (a) CCD image of fluorescence from the bead. Scalebar is 500 nm. (b) Horizontal and vertical cross cut of the intensity map of (a). Shaded are indicates the spot size with a radius of 500 nm.

OBJ

Figure 4.5: Schematic representation of the fluorescence microscope indicat-ing all the quantities of the excitation source, emission and collection (box on the left) and transmission and detection by detectors (box on the right).

when we consider the photons that have been collected by the objective (Nout). This

setup could reach a photon-to-ADU conversion of 6 if all the emitted photons would be send to the CCD and the CCD would be set to the highest gain which corresponds to an electron-to-ADU factor of 3.5.

From the CCD image, I counted 3.5 · 103 _{ADU/sec in the spot of the bead. Given a}

photon-to-ADU of 170, I estimate that 6.0 · 105 _{photons/s are collected by the objective.}

Comparing this number to 150 photons/s collected by the objective from a single molecule, I estimate that 4000 molecules sit on a single bead. When 4000 molecules are distributed in a bead with 100 nm diameter, the average distance between two molecules would be 5 nm. Given that the average size of a dye molecule (∼ 50 atoms) is a few nanometers, the estimate of nbead is reasonable.

Comparison of count rates CCD and APDs

Now, I compare the count rates as detected by the CCD to that of the APDs. Since the photon-to-electron conversion factor of the CCD is calibrated and all the photons impinge on the large active area of the CCD, I use NCCD to benchmark the performance of the

Implantation and Optical Characterization of Color Centers in Silicon Carbide