Superconducting nanowire single-photon detectors for quantum communication applications

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Thesis

Reference

Superconducting nanowire single-photon detectors for quantum communication applications

CALOZ, Misael

Abstract

La technologie des détecteurs de photon unique a suscité un intérêt croissant au cours de la dernière décennie. Une des raisons majeures de cette tendance sont les applications en communication quantique, telles que la distribution de clés quantiques, qui nécessitent des détecteurs à hautes performances. Les détecteurs de photon unique à nanofils supraconducteurs (SNSPD) sont sensibles aux photons uniques aux longueurs d'onde allant des rayons X jusqu'à l'infrarouge moyen et offrent des performances inégalées sur de nombreux aspects. Ils présentent généralement des efficacités très élevées sur une large gamme de longueurs d'onde, ainsi qu'un faible bruit, une gigue temporelle faible, et un taux de répétition élevé. Le travail présenté dans cette thèse couvre tous les aspects essentiels des SNSPDs fabriqués en molybdène-silicium (MoSi). Alors que la nano-fabrication, la caractérisation, la recherche des limites intrinsèques et le mécanisme de détection constituent le cœur de ce travail, la motivation principale à l'origine de cette thèse a toujours [...]

CALOZ, Misael. Superconducting nanowire single-photon detectors for quantum communication applications. Thèse de doctorat : Univ. Genève, 2019, no. Sc. 5413

DOI : 10.13097/archive-ouverte/unige:129599 URN : urn:nbn:ch:unige-1295994

Available at:

http://archive-ouverte.unige.ch/unige:129599

Disclaimer: layout of this document may differ from the published version.

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Université de Genève Faculté des Sciences Groupe de Physique Appliquée Professeur Hugo Zbinden

Superconducting nanowire

single-photon detectors for quantum communication applications

Thèse

présentée à la Faculté des sciences de l’Université de Genève pour obtenir le grade de Docteur ès sciences, mention Physique

par

Misael CALOZ

de

Bretagne (France) et du Valais (Suisse)

Thèse n° 5413

Genève

Centre d’impression de l’Université de Genève 2019

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It ain’t what you don’t know that gets you into trouble.

It’s what you know for sure that just ain’t so.

Mark Twain

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Abstract

The past decade has seen an increase in interest in single-photon detector technologies.

A major reason of this trend has been the push towards optical quantum information applications such as quantum key distribution, that require extreme detector performance.

Superconducting Nanowire Single-Photon Detectors (SNSPD) are single-photon sensitive from X-ray to mid-infrared wavelengths and offer unequalled performance in many aspects.

They typically present high efficiencies over a broad range of wavelengths together with low dark count rates, low timing jitters and high repetition rates. The work presented in this thesis covers the essential aspects of molybdenum silicide (MoSi) superconducting nanowire single-photon detectors. While the fabrication, characterization, investigation of the intrinsic limits and the detection mechanism constitute the core of this work, the driving motivation behind this thesis was always focused on delivering high performance single-photon detectors for demanding quantum communication applications.

Despite an impressive amount of experimental work to improve the performance of SNSPDs since their invention, a full description of the detection mechanism has not been established yet. The motivation of the first part of this thesis is to address this question with MoSi detectors. The high performance achieved during the course of this thesis are discussed in the second part of this manuscript, where detectors combining high detection efficiency (> 85%) and low timing jitter (<30 ps) are presented. The third part deals with the investigation of the intrinsic limits of the timing jitter, partially performed at the NASA Jet Propulsion Laboratory (USA). The point behind this study was not only to improve the system jitter of amorphous MoSi SNSPDs, but also to probe, reach, and quantify the intrinsic component in order to have experimental evidences of the fundamental limits and insights of potential material differences. Notably, our work exhibited that there is a trade-off between the system jitter, the latching current, the kinetic inductance, and consequently the efficiency. Optimizing the signal-over-noise ratio by tuning the series kinetic inductances allowed us to obtain a system timing jitter of 6.0 ps at 532 nm and 10.6 ps at 1550 nm photon wavelength. In the last part of this thesis, recent and promising results on the maximum counting rate achievable are presented. Furthermore, preliminary results on detectors made out of niobium titanium nitride (NbTiN) material are discussed, opening up new opportunities and improvements in the SNSPD field.

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Résumé

La technologie des détecteurs de photon unique a suscité un intérêt croissant au cours de la dernière décennie. Une des raisons majeures de cette tendance sont les applications en communication quantique, telles que la distribution de clés quantiques, qui nécessitent des détecteurs à hautes performances. Les détecteurs de photon unique à nanofils supraconducteurs (SNSPD) sont sensibles aux photons uniques aux longueurs d’onde allant des rayons X jusqu’à l’infrarouge moyen et offrent des performances inégalées sur de nombreux aspects. Ils présentent généralement des efficacités très élevées sur une large gamme de longueurs d’onde, ainsi qu’un faible bruit, une gigue temporelle faible, et un taux de répétition élevé. Le travail présenté dans cette thèse couvre tous les aspects essentiels des SNSPDs fabriqués en molybdène-silicium (MoSi). Alors que la nano-fabrication, la caractérisation, la recherche des limites intrinsèques et le mécanisme de détection constituent le cœur de ce travail, la motivation principale à l’origine de cette thèse a toujours été de fournir des détecteurs de photon unique performants pour des applications de communication quantique exigeantes effectuées au sein même du groupe.

Malgré un grand nombre de travaux expérimentaux visant à améliorer les performances des SNSPD depuis leur invention, une description complète du mécanisme de détection n’a pas encore été établie. La motivation principale de la première partie de cette thèse est d’apporter une réponse à cette question. Les hautes performances obtenues sont discutées dans la deuxième partie de ce manuscrit, où sont présentés des détecteurs combinant une efficacité de détection élevée (> 85 %) et une gigue temporelle faible (<30 ps). La troisième partie de cette thèse porte sur l’étude des limites intrinsèques et fondamentales de la gigue temporelle, en partie réalisée au Jet Propulsion Laboratory de la NASA (USA). Notre travail a notamment montré qu’il existe un compromis entre la gigue temporelle, le courant de verrouillage, l’inductance cinétique et, par conséquent, l’efficacité des détecteurs. Après avoir optimisé le rapport signal sur bruit en réglant les inductances cinétiques en série tout en contrôlant l’effet de verrouillage, nous avons obtenu une gigue temporelle minimale de 6.0 ps à 532 nm et de 10.6 ps à 1550 nm.

Enfin, des résultats très récents et prometteurs sur le taux de comptage maximum sont présentés en dernière partie. Les résultats préliminaires sur des détecteurs fabriqués à partir de nitrure de niobium-titane (NbTiN) sont également discutés, ouvrant la porte à de nouvelles opportunités et améliorations dans le domaine des SNSPD.

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Remerciements

J’aimerais tout d’abord remercier mon directeur de thèse, professeur Hugo Zbinden, pour m’avoir donné l’opportunité d’entreprendre cette thèse. Je suis vraiment reconnaissant pour ta disponibilité et ton encadrement qui m’ont permis de devenir autonome au long de cette thèse. Je tiens également à remercier Dr. Félix Bussières, qui dirige les activités des SNSPD et qui m’a suivi de près pendant ces quatre années. Ta motivation et ta rigueur on été des éléments indispensables pour avancer dans ma thèse.

Je remercie spécialement Boris Korzh, avec qui j’ai eu le chance de travailler à mes débuts au GAP. Ta motivation, ton énergie et ton enthousiasme ont été des facteurs essentiels pour bien débuter cette thèse.

Merci à Matthew Shaw du Jet Propulsion Laboratory pour m’avoir accueilli quelques mois dans son groupe et m’a permis de vivre une expérience extraordinaire.

Tout au long de ma thèse je me suis fait de nombreux amis que j’ai malheureusement du voir partir du GAP au fils du temps, ils ont contribué à créer une ambiance merveilleuse que je n’oublierai pas. En particulier Cyril Laplane, Pierre Jobez, Anthony Martin, Tomer Barnea, Emmanuel Zambrini Cruzeiro et Raphaël Houlman. Je remercie également tous ceux qui sont encore là pour garder une merveilleuse atmosphère, tout particulièrement Alberto Boaron, Davide Rusca, Nicolas Maring, Farid Samara, ainsi que tous les autres étudiants du GAP en général !

Ce travail n’aurait pu être mené à bien sans l’aide du personnel du Centre de micro et nanofabrication de l’école polytechnique fédérale de Lausanne, toujours disponible pour répondre aux questions relatives à la nanofabrication, particulièrement Rémy Jut- tin, Cyrille Hilbert, Zdenek Benes, Joffrey Pernollet, Giancarlo Corradini et Julien Dorsaz.

Les progrès en physique expérimentale sont difficiles sans un support technique excep- tionnel. Pour cela, je tiens à remercier Claudio Barreiro, notre spécialiste en électronique, qui a contribué à beaucoup d’éléments utilisés au cours de cette thèse.

Ce fut un plaisir de travailler avec Matthieu Perrenoud, Emna Amri, Gaëtan Gras, et

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Claire Autebert, qui ont d’une façon ou d’une autre poursuivi certains travaux de cette thèse. Un remerciement spécial à Matthieu qui a travaillé sur la plus grande partie des résultas sur les SNSPD parallèles présentés trop brièvement dans cette thèse, et à Claire pour les miroirs diélectriques.

Je remercie les membres externes de mon jury, les professeurs Christian Schönenberger de l’université de Bâle et Andrea Fiore de Eindhoven University of Technologies.

Ma gratitude va également à tous les collaborateurs avec qui j’ai pu travailler. En particulier Simone Frasca de l’EPFL, que j’ai eu la chance de rencontrer au JPL. Markus Weiss et Daniel Sacker de l’université de Bâle, ainsi que Stefano Gariglio et Adrien Waelchli du Département de physique de la matière quantique.

Je remercie aussi Mikael Afzelius, Michel Moret, Nicolas Gisin, Rob Thew, Jean Etesse, Krzysztof Kaczmarek et tous ceux que j’aurais pu oublier, pour avoir toujours été disponible pour des discussions scientifiques et pour avoir garder une excellente ambiance de travail dans le groupe.

Enfin, j’adresse toute mon affection à mes amis, à ma famille, à Marine, et en particulier à ma maman qui m’a accompagné et soutenu toute ma vie. Ta confiance, ta tendresse, et ton amour me portent et me guident tous les jours. Merci pour avoir fait de moi ce que je suis aujourd’hui.

Misael Caloz Genève, 20 Septembre 2019

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1 Introduction

1.1 Single photon and quantum communication

After revolutionizing the field of modern physics early in the 20th century, quantum physics is nowadays a very active research field. Physicists realized that quantum theory is not only a good framework for describing fundamental phenomena, but also a tool to develop new technologies that rely on fundamental nature laws and were not possible before [1]. Quantum information and communication are the study of the information processing tasks and communication protocols that can be accomplished using quantum mechanical systems. They promise great revolutions in the way data are processed and transmitted. The bit (which can take the value 0 or 1) is the fundamental concept of classical information. Quantum information is built upon an analogous concept, the quantum bit (also called qubit) [2]. Different physical systems can be used to encode qubits and the photon is a system of choice, as it is an ideal carrier of information and is perfectly suited to transmit data over large distances. At the end of quantum communication protocols based on photons, the information has to be retrieved, and hence the photons detected. That is where single-photon detectors show their usefulness.

These single photons, commonly at telecom wavelength, carry an immensely low energy and are very challenging to detect.

1.2 Single-photon detectors

The past decade has seen an increase of interest in single-photon detector technologies.

A major reason of this trend has been the push towards optical quantum information applications such as quantum key distribution, that require extreme detector performance.

The performance of a single-photon detectors are assessed in terms of the spectral range, dead time, dark count rate, detection efficiency, timing jitter and ability to resolve photon number. The different single-photon detection technologies and their corresponding performance are listed in Table 1.1. Note that the best performance of each category are

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written and the values are only indicative of the technology potential, it does not mean that they combine the performance at the same time. In practice, it is more complicated since the categories are usually dependent on one another and one has to think about which technology fits the best the application requirements. Other specifications such as the afterpulsing effect, photon number resolving capabilities or power consumption have to be taken into account as well.

Table 1.1: Comparison of single-photon detectors. The values are indicative of the technology potential, i.e. the detectors does not necessarily combine the performance presented here at the same time. The data are updated from [3]. For high efficiency SNSPDs, see [4, 5, 6]. For InGaAs SPAD, see [7, 8, 9]. Otherwise, see [3].

Detector Temp. Detection Timing DCR Max. count Spectral

type (K) efficiency jitter rate range

PMT (NUV-NIR) RT 40% at 500 nm 300 ps 100 kHz 10 MHz NUV-NIR

PMT (IR) 200 K 2% at 1550 nm 300 ps 200 kHz 10 MHz IR

MCP-PMT RT 25% at 500 nm 55 ps 100 Hz 10 MHz NUV-NIR

Si SPAD (TJ) RT 65% at 650 nm 400 ps 25 Hz 10 MHz Visible

Si SPAD (SJ) RT 49% at 550 nm 35 ps 25 Hz 10 MHz Visible

CMOS SPAD RT 50% at 550 nm 80 ps 50 Hz 10 MHz Visible

VLPC 6 88% at 694 nm 270 ps 20 kHz - Visible

MKID 0.1 90% at 285 nm 50 ns 1 Hz 100 kHz X-ray–FIR

TES 0.1 98% at 1550 nm 100 ns 3 Hz 100 kHz NIR

InGaAs SPAD 240 K 55% at 1550 nm 50 ps 1 Hz 100 MHz NIR (free running)

SNSPD 1-3 95% at 1550 nm 3 ps 10⁻³ Hz 200 MHz X-ray–MIR

1.3 Superconducting nanowire single-photon detectors

The superconducting nanowire detector concept was demonstrated by Gol’tsman et al.

in 2001 [10]. This type of device, known as Superconducting Nanowire Single-Photon Detector (SNSPD), is single-photon sensitive from X-ray to mid-infrared wavelengths and offers unequalled performance in many aspects. They typically present high efficiencies over a broad range of wavelengths together with a low dark count rate, low timing jitter and a high repetition rate. Notably, they do not suffer from afterpulsing effect and, depending on their design, can exhibit photon-number resolving capabilities. Being superconducting, the main drawback of this technologiy is that they have to be cooled down to cryogenics temperature, typically ∼1-3 K. So far, SNSPDs demonstrated unequalled performance over a large range of wavelengths, making them a technology of choice for quantum applications. SNSPDs have been the subject of intense interest over the past decade and many research groups around the world have contributed to its development. Nowadays, SNSPDs are the best single-photon detection technology and offer the best combined performance [11]. A schematic of a SNSPD is depicted in Fig. 1.1.

A SNSPD consists of a superconducting nanowire that forms a meander covering a usual

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1.3. Superconducting nanowire single-photon detectors

Si wafer mirror

Superconducting nanowire Contact pads SiO2 (AR coating and spacer)

fibre core

wire bonding

(a)

Si wafer mirror Absorptive material Contact pads

SiO2 (spacer) SiO2 (AR coating) fibre core

(b)

Figure 1.1: (a) 3D representation of a fibre-coupled SNSPD. (b) Corresponding cross- section representation.

area of 15×15µm² to achieve a high coupling efficiency between the nanowire and the fibre mode. The nanowire is biased just below its critical current, defined as the point at which the wire becomes resistive. When a photon strikes the nanowire, a local resistive hotspot is formed, perturbing the current distribution and triggering a fast voltage pulse that can then be amplified and measured. More details on the detection mechanism are presented in Chapter 3. To achieve high efficiency, the nanowire is embedded in an optical cavity to enhance the photon absorption by mean of constructive interferences.

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1.4 Thesis outline

The work presented in this thesis covers the essential aspects of MoSi superconducting nanowire single-photon detectors. While the fabrication, characterization, investigation of the intrinsic limits and the detection mechanism constitute the core of this work, the driving motivation behind this thesis was constantly focused on delivering high performance single-photon detectors for demanding in-house quantum communication applications. During the course of this thesis several peer-reviewed articles were published and are presented in two different appendices: Appendix A includes the articles that are relevant and constitute the essential of this thesis, while the ones included in Appendix B concern the applications of SNSPDs in quantum communication experiments.

To present high performance detectors, the nano-fabrication was a substantial part of this thesis and is detailed in Chapter 2, where crucial processes are discussed.

Despite an impressive amount of experimental work to improve the performance of SNSPDs since their invention, a full description of the detection mechanism has not been established yet. This question is addressed with MoSi detectors in Chapter 3 and Appendix A.1. A particularly crucial feature of the detection models is the so-called energy-current relation, which we measured to be non-linear over a large range of energy, contrarily to other studies. In addition, new insights on Fano fluctuations are reported.

The performance achieved during the course of this thesis are discussed in Chapter 4, Chapter 5, and Appendix A.2, where detectors combining high detection efficiency (>85%) and low timing jitter (<30 ps) are presented. Notably, detectors obtained during this work were used in a remarkable long-distance quantum key distribution experiment, presented in Appendix B.1.

The investigation of the intrinsic limits of the timing jitter, partially performed at the NASA Jet Propulsion Laboratory (USA), is included in the second part of Chapter 5 and mentioned in the Appendix A.3. The goal behind this study was not only to improve the system jitter of amorphous MoSi SNSPDs, but also to probe, reach, and quantify the intrinsic component in order to have experimental evidences of the fundamental limits and insights of potential material differences.

Finally, recent and promising results on the maximum count rate are presented in Chapter 6. Furthermore, preliminary results on the parallel design and detectors made out of NbTiN material are discussed, opening up new opportunities and improvements in the SNSPD field.

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2 Nano-fabrication

Image credit: CMi, EPFL

Nano-fabrication constitutes a substantial part of this thesis. The first section of the present chapter introduces the basic knowledge of nano-fabrication processes required to make SNSPDs. The second section focuses on the superconducting materials properties, while the following ones correspond to each important step of the fabrication itself.

2.1 The basics of nano-fabrication

Nano-fabrication refers to fabrication processes of objects and structures at the nanometer- scale dimensions. The range of application is endless and numerous modern and everyday applications benefit from nanotechnology advances: from the processors in smartphones, semiconductor electronics, chemistry, medicine, molecular biology, aerospace engineering, to physics and beyond. Research in nano-fabrication requires joint effort across many scientific disciplines, such as collaboration between mechanical engineers, physicists, biologists, chemists, and material scientists. As nanotechnology processes are usually very sensitive to any kind of dust and temperature and humidity fluctuations, the fabrication

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is carried out in clean and regulated environment, so-called cleanroom.

Typically used in nano-fabrication and scientific research, a cleanroom is a controlled environment that has a low level of pollutant particles, and a regulated temperature and humidity. The cleanroom has a controlled level of contamination that is specified by the number of particles per cubic meter at a specified particle size. The air is coming from an outside source and filtered to eliminate dust, the inside air is recirculated constantly through filters that remove containments produced from within the cleanroom. Staff enters and leaves cleanrooms through airlocks, and wears protective clothing including face masks, laboratory coats, glove, aprons, hairnets, hoods, sleeves, glasses, and shoe covers.

The equipment inside a cleanroom is designed to generate minimal air contamination, with specialized paper sheets, pencils, etc... Cleanrooms are not a sterile environment as the attention is primarily to controlling dust particles.

The nano-fabrication processes performed during the course of this PhD was carried out mostly in the Centre de MicroNanotechnology (CMi, ISO 7-6) in Ecole Polythechnique Fédérale de Lausanne (EPFL), and partially at the University of Basel. The techniques used during this PhD are listed and briefly explained below.

Photolithography

Photolithography is a technique used in nano-fabrication to pattern 3D structures on a substrate, also called wafer. It uses light, generally in the UV range, to transfer a geometric pattern to a photosensitive chemical photoresist on the substrate. A series of chemical treatments then either etches the exposure pattern into the material or enables deposition of a new material in the desired pattern upon the material underneath the photoresist (lift-off process). To create complex structures, a wafer may go through many photolithography cycles. The principle is based on the fact that the illuminating light changes the solubility of the photoresist, enabling selective removal of either the exposed or non-exposed regions of the resist by immersing it in a solvent (developing step).

Photolithography method can create extremely small patterns, down to a few hundreds of nanometers in size. It provides precise control of the shape and size of the objects it creates. Photolithography is the standard method of printed circuit board (PCB) and microprocessor fabrication, for example. A standard photolithography process is sketched in the Fig. 2.1.

For the fabrication of SNSPDs, at least three photolithography processes are required: (i) for the mirror deposition, (ii) the electric contact pads, and (iii) the final wafer etching.

Each photolithographic step requires different dimensions and topology, the resist and the process have to be adjusted accordingly.

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2.1. The basics of nano-fabrication

substrate

light

mask

(a)

(b)

(c)

(d)

(e)

(f)

photoresist

Figure 2.1: (a) The photoresist is spin coated on the substrate. The photoresist is selected according to the desired specifications, such as positive tone or negative tone, smallest dimensions achievable, exposing light wavelength, etc... (b) A mask is aligned onto the substrate. For direct writing method, no mask is needed, the laser beam moves and prints directly the design. (c) Light is illuminating the photoresist. (d) Patterns are transferred to the photoresist and the mask is removed. (e) Development step, which involves chemical reactions with specific solvents that strip the exposed parts of the photoresist, and harden the non-exposed ones (for positive-tone resist, inversely for negative-tone resist). (f) The substrate is ready for etching process.

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Electron-beam lithography

Electron beam lithography (also called e-beam lithography or EBL) uses basically the same principle as the photolithography (see Fig. 2.1), except that direct writing electrons are exposing the resist instead of light, increasing the feature size resolution compared to diffraction-limited photolithography. With optimized process, the typical feature size achievable with EBL is under 10 nm. For the SNSPD fabrication, the nanowire typically ranging from 30 to 200 nm, are patterned with the EBL technique.

Etching

Etching is used in nano-fabrication to remove layers from the surface of a wafer. Etching is a critically important process, and wafers commonly undergoes many etching steps before completion. The term of etching regroups two categories: wet etching and dry etching. Dry etching refers to the removal of material, by exposing it to a bombardment of ions, usually a plasma of reactive gases such as fluorocarbons, oxygen, chlorine, boron trichloride, sometimes with addition of nitrogen, argon, helium and other gases. For wet etching, the wafer is directly immersed in a bath of etchant, usually strong acids that will etch through the materials.

Dry etching technique is used at numerous levels of the SNSPD fabrication process:

(i) nanowires patterning (ion beam etching (IBE) with argon, RIE with CF4, SF6 and Ar gases), (ii) electric contact pads (IBE), and (iii) wafer etching (deep reactive ion etching (DRIE) with Bosch process).

Physical vapor deposition

Physical vapor deposition (PVD) describes a variety of vacuum deposition methods which are used to grow thin films on a substrate. PVD is characterized by a process in which the material goes from a condensed phase to a vapor phase and then back to a thin film condensed phase onto the substrate. The most common PVD processes are sputtering and evaporation. As sputtering was a crucial technique to deposit high quality superconducting films during this thesis, this section introduces this technique in detail.

Sputter deposition involves ejecting material from a so-called target onto a substrate.

When multiple targets are used at the same time, it is referred as co-sputtering. A plasma with a inert sputtering gas, usually Argon is maintained closed to the target during the process. Argon atoms will strike the target and eventually eject atoms from the target.

Sputtered atoms ejected from the target have a wide energy distribution. The sputtered ions, typically only a small fraction of the ejected particles, can ballistically fly from the target and impact on the substrates, as shown in Fig 2.2.

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2.1. The basics of nano-fabrication

pump target

magnet

gas inlet

Ar O2

N2

gas inlet

pump

heating/cooling system substrat

target

target RF/DC generator

thin film

atom ejected

Ar

Ar Ar

substrate holder

Figure 2.2: Simplified schematic of a sputtering machine. The wafer is placed on a substrate holder, which can be heated up or cooled down during the deposition. The vacuum is maintained to a desired value, sputtering gases and reactive gases can be added in the chamber via inlets. Depending on the target composition, RF or DC generator are set up in order to maintain stable plasma during the process.

For reactive sputtering processes, reactive gases such as O2 and N2 can also be added in the chamber to sputter compounds. The compounds are chemically formed on the target surface, in-flight or on the substrate depending on the process parameters. The composition of the film can be controlled by varying numerous parameters such as the relative pressures of the inert and reactive gases, target power, pre-process target cleaning steps, etc... Film stoichiometry is a crucial parameter for optimizing functional properties of superconducting films. The availability of many parameters that control sputter deposition make it a complex process, but also allow a large degree of control over the growth and microstructure of the film. Those parameters are described in details in the next section.

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2.2 Superconducting absorptive films

The superconducting material is at the core of SNSPDs and impacts on all performance aspects. One of the important properties is the critical temperature Tc, defined as the upper bound temperature at which the superconductivity can be established. For type I superconductor, according to the Bardeen-Cooper-Schrieffer (BSC) theory, the superconducting energy gap is given by: ∆(T = 0) = 1.764kbTc. Intuitively,∆represents the excitation energy needed to brake a Cooper pair, and if the absorbed photon does not transfer enough energy to the electron, the superconductivity might not be broken and the photon would not be detected. This is directly linked to the detector internal quantum efficiency mentioned in Chapter 4. A high T_csignifies a large∆, and intuitively we understand that depending on the photon wavelength we want to detect, we have to choose the material accordingly. The main objective for this thesis was focused on detecting single photon at 1550 nm wavelength.

The Tc is not the only important parameter. One very important characteristics of superconducting films is the device repeatability, or production yield. If the films is not locally homogeneous, the same detector design fabricated at different locations on a wafer would lead to different characteristics. While this aspect is not critical to make working SNSPDs for single pixel applications, it becomes the key parameter when fabricating large detectors and arrays of pixels. The crystalline structure plays a big role in this aspects.

It is known that amorphous materials such as WSi or MoSi lead to a production yield close to unity, making them a material of choice to fabricate SNSPDs. Polycrystalline materials such as NbN or NbTiN usually exhibit a higher Tcthan WSi and MoSi but a lower production yield. Recently with NbN, it has been shown that by fine tuning the deposition conditions, the grain size of the lattice structure can be reduce and lead to better homogeneity [12].

The last important aspect is the material intrinsic electrical properties. Each material is intrinsically different in this regard, and this plays a crucial role in the maximum count rate and timing jitter. This point is mentioned in details in Chapter 5 and Chapter 6.

Table 2.1 summarizes different materials used for SNSPDs fabrication. The most common being, by order of occurrence : NbN, WSi, NbTiN and MoSi. During the course of this thesis, MoSi has been studied extensively. In the last chapter of this manuscript, preliminary results on NbTiN are presented.

Molybdenum silicide

MoSi is a material of choice to make SNSPDs as it is a very flexible and versatile material, for numerous reasons: (i) being amorphous, the yield approaches unity making the fabrication easier, (ii) theT_cis relatively higher than WSi, optimal operation temperature

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2.2. Superconducting absorptive films Table 2.1: List of common materials used for the fabrication of SNSPDs with their bulk superconducting transition temperatures and measured energy gap when available. Data updated from [13].

Material Nb NbN NbTiN NbSi WSi MoSi MoGe MgB2 YBCO

BulkTc(K) 9.26 16 16 - 5 8.2 7.36 39 89

Energy gap 3.3 4.9 5.1 - - - 1.1 6.8 -

2∆0 (meV)

References [14, 15] [14, 16] [17] [18] [19] [20, 21] [22, 13] [23, 24] [25]

is achieved under 1 K. (iii) The energy gap is smaller than NbN and NbTiN, making it a very sensitive material, consequently the internal quantum efficiency is easily saturated for 1550 nm wavelength photons and above.

The MoSi films have been developed in collaboration with the University of Basel. The films are deposited by co-sputtering by applying a DC and RF bias on the molybdenum and silicon targets, respectively. The films are capped with a few nanometer thick a-Si layer, by closing a mechanical shutter on the Mo target at the very end of the process.

The stoichiometry was controlled by varying the relative deposition rates of Mo and Si and has been tuned to optimize the T_c, Mo0.8Si0.2 showed the best results. The thin films and bulk Tc of MoSi films are shown in the Figure 2.3. To ensure that the material remains within the amorphous phase, X-Ray diffraction was carried out on a 40 nm sample and confirmed the amorphous nature of the film, see Fig. 2.4b. The structural peaks correspond to the silicon substrate.

. 55max

7 . 55max

(a)

. 55max

7 . 55max

(b)

Figure 2.3: (a) Resistance vs temperature measurement for 5 and 40 nm thick MoSi 80:20 films, from above 100 K down to 4.2 K. (b) Zoom of (a) close to the critical temperatures.

Since we are concerned by maximizing the optical absorption within the detector, it is crucial to characterize the optical constants of the MoSi films in order to achieve an efficient micro-cavity-enhanced structure. This enables accurate modelling of the

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micro-cavity, which is the topic of discussion in the Chapter 4. This characterization was carried using a spectroscopic ellipsometer. In order to improve the robustness of the material model, the measurement was done at different angles, for samples of different thicknesses, which is commonly done when characterizing absorptive films. The material model fitting was carried out using the open-source RefFit software. The optical constants from the resulting model are shown in Fig. 2.4a.

(a) (b)

Figure 2.4: (a) Optical constants of MoSi thin films extracted from ellipsometry measurement. (b) X-ray diffraction measurement.

2.3 Nanowire patterning

As shown in Fig. 2.5, a typical SNSPDs is constituted by a single nanowire that forms a meander covering the photon input area. For single mode fibre (SMF) at 1550 nm, a round area of approximately 8 µm diameter is necessary to cover the the optical gaussian mode. The fill-factor is defined as ff = _gap+width^width and represents the portion of active area of the detector. The typical nanowire width and thickness are 150 nm and 6.5 nm, respectively, while the fill-factor is commonly between 0.4 and 0.7. The extremely small feature of the meander makes it difficult to fabricate and a lot of optimization and fine tuning steps are crucial to ensure the detectors quality. Ultimately, one would like a meander as clean as the one presented in Fig. 2.6. But before achieving this quality, a lot of issues had to be addressed and techniques improved. In the next part of this section, the major issues that happened during the course of this thesis are presented together with their solution.

Oxygen plasma

A common way to remove EBL and photolithography resists is to place the wafer in an O2

plasma for few minutes. This step strips the resist in a clean and efficient manner. However,

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2.3. Nanowire patterning

Figure 2.5: SEM image of a MoSi nanowire (in blue) forming a meander. The active area is16×16µm². The dashed circle is the±3-sigma of the SMF gaussian mode, it represents where 99.7% of the photon are absorbed. Colours are added for clarity purposes.

when done repetitively, it can seriously damage metallic layers and more particularly MoSi. A systematic study of the effect of the O2 plasma on the nanowire shape was performed by imaging (SEM) and measuring the depth profile (AFM) before and after O2 process. Fig. 2.7 shows a SEM image and the corresponding AFM measurement after an O2 plasma step. During the plasma, the resist being stripped is still present on top of the nanowire and protects the MoSi from oxidation. The problem arises only when all the resist is gone, leaving the MoSi unprotected. Despite being capped by a 3 nm thick layer of Si, MoSi is not protected enough for oxidation. While the meander is still electrically connected, the internal quantum efficiency of such device is clearly limited and yields to non-saturating devices, see Chapter 4. This problem can be avoided by stripping the resists in a clean bath of NMP-based stripper, heated up for few hours.

Fences

A common etching technique used in nano-fabrication is called ion beam etching (IBE). In this process, argon ions are accelerated in a plasma and physically hit the wafer, while the resist acts like a shield and stops the material from being fired. Argon ions acceleration being very directional, this technique normally yields to very well defined edges, which is desired for SNSPD fabrication. In first attempts, this techniques was used to pattern the nanowire but had different drawbacks. Firstly, due to the high energy of the argon ions, the EBL resist can be transformed in a polymer-like structure, making it very difficult to remove without O2 plasma. Secondly, a redeposition process can happen. Due to its amorphous properties, MoSi adhesion is usually good on numerous materials. While this is normally a desired feature in nano-fabrication, it becomes a problem in this particular case. When the Mo and Si atoms are being hit, they have a significant probability to be

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500 nm

(a)

2 !m

100 nm 200

300

400

100 nm 200

300 400

0 13 nm

(b)

Figure 2.6: (a) SEM image of a nanowire after the etching process. (b) AFM images of the same devices shown in (a).

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2.3. Nanowire patterning

500 nm

(a)

(b)

Figure 2.7: (a) SEM image of damaged nanowire after O2 plasma process. (b) AFM images of the same devices shown in (a). The nanowire shape is clearly affected with bumps rising up from the edges. Despite being capped by a 3 nm thick layer of Si, MoSi is not protected enough from the O2 plasma oxidation.

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redeposited on the side of the resist, building up fences. When the resist is stripped off, the fence stays in shape, covering the nanowire and affecting the critical current and the photon absorption. This effect is visible in Fig. 2.8. Interestingly, the height of the fences corresponds exactly to the thickness of the EBL resist.

500 nm

Figure 2.8: SEM image after IBE etching showing large fences due to the redeposition process.

To tackle this issue, a different etching approach consisting of reactive ion etching (RIE) was taken. This technique involves a chemically-reactive etching, which is known to be more isotropic. In the case of very thin films though, the process time is so short that this feature was not observed to be an issue. Different gases and mixture of gases can be selected depending on the material to etch, SF6 and CF4 are commonly used in the SNSPDs fabrication. The device presented in Fig. 2.6 was etched with SF6 gas.

Patterning optimization

Another technique worth mentioning concerns the optimization of the electron beam exposition. As described in more details in Chapter 4 the current crowding effect arises at the maximum inflection point of the turns, limiting the device critical current. The turns are a particularly important limiting factor and they have to be properly designed to create the smoothest line possible. One technique is to over expose on purpose each pixel step of the electron beam shot, as depicted in Fig. 2.9. The blue pattern is the exposed part, the blue circles represent the step size of 5 nm where the electron beams will be shot. The black line draws the border of the pattern after exposition. The size of the pattern is adjusted accordingly.

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2.4. Mirrors

10 nm

Figure 2.9: Schematic view of electron beam shots and step compaction around a curved line. The blue pattern is the exposed part, the blue circles represent the step size of 5 nm where the electron beams will be shot. From left to right, for a fixed step size, the beam size is increased to visualize the edges smoothing of curved patterns. The black line represent the border of the pattern after exposition.

2.4 Mirrors

As shown in the introduction (Chapter 1, Fig. 1.1), the cavity structure is fabricated on top of a mirror. Mirrors deposition is a crucial fabrication step because it defines its reflectivity and the final production yield is closely related to its quality, see Fig. 2.10a.

During the course of this thesis, different mirror structures have been fabricated and compared, their reflectivity is plotted in Fig. 2.11.

Silver is a material of choice to make highly reflective mirrors for 1550 nm photon wavelength. It is well known that the adhesion of Ag on SiO2 (and SiO2 on Ag) is poor and Ag layers are commonly stacked in between two so-called adhesion layers, usually 5-10 nm titanium or chrome. However, to make highly reflective mirrors, the top adhesion layer has to be chosen with care, as it affects the final reflectivity of the mirror structure.

The first detector batches were fabricated with, from bottom to top: 5 nm of Cr, 50 nm of Ag, and 15 nm of Al2O3, its corresponding reflectivity is plotted in Fig. 2.11. However, this structure showed its limitations in the process yield. Fig. 2.11 shows cross-sectional SEM images of a detector with this particular mirror structure. Many defects coming from the poor adhesion of the SiO2 layer on the top of the mirror stack are visible. While those bubbles did not prevent the detectors from working, it can affect the nanowire critical current and of course the cavity quality, and consequently the absorption.

In order to improve the mirror quality and the yield, different structures have been tested, their reflectivity at the wavelength of interest are summarized in Table 2.2. The best compromise was the Ti-Ag-Ti (1.5 nm) which showed an excellent quality and a reflectivity of 97.0% at 1550 nm wavelength. We observed that the top adhesion layer thickness has a significant impact on the reflectivity. For example, the reflectivity of Ti-Ag-Ti (3 nm) is significantly reduced, 92.0% versus 97.0%. More recently, mirrors composed of many repetitive dielectric layers, also know as Bragg or dielectric mirrors

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have been designed and tested. While they show excellent reflectivity values at their central wavelength, they exhibited poor surface roughness which impacts on the detectors performance. The next section deals with this issue.

Silicon wafer SiO2 Ag mirror SiO2 Au

SiO2 MoSi

200 nm

200 nm (a)

Silicon wafer SiO2 Ag mirror SiO2

Au

Silicon wafer SiO2 Ag mirror SiO2

Au

SiO2 MoSi

200 nm

200 nm (b)

Figure 2.10: SEM cross-section images of a detector with a Cr-Ag-Al2O3 mirror structure.

(a) Visible defects coming from poor adhesion of the SiO2 layer on top of the mirror. (b) Same device as (a) but elsewhere. The thin layer of MoSi can be seen encapsulated in the optical stack.

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2.4. Mirrors

400 600 800 1000 1200 1400 1600 1800 2000

Wavelength (nm)

0 20 40 60 80 100

R ef le ct iv it y( % )

Cr₋Ag₋Al2O3

Cr₋Ag₋Ti (1.5 nm) Ti₋Au₋Ti (1.5 nm) Ti₋Au₋Ti (3 nm) Ti₋Ag₋Ti (3 nm)

(a)

1000 1500 2000 2500

Wavelength (nm)

0 20 40 60 80 100

R ef le ct iv it y( % )

980 nm 1550 nm

(b)

Figure 2.11: Reflectivity measurement for (a) metallic and (b) dielectric structures. See details in the text and in Table 2.2.

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Table 2.2: List of tested mirror structures and their corresponding reflectivity at 1550 nm wavelength.

Structure Top adhesion layer thickness Reflectivity, 1550 nm (from bottom to top)

Cr-Ag-Al₂O₃ 15 nm 97.2%

Ti-Ag-Ti 1.5 nm 97.0%

Ti-Ag-Ti 3 nm 92.0%

Ti-Au-Ti 1.5 nm 95.5%

Ti-Au-Tu 3 nm 93.0%

Bragg, 980 nm - 99.5% (at 980 nm)

Bragg, 1550 nm - 98.2%

2.5 Surface roughness

As mentioned previously, the surface roughness of the underlying layer is a crucial problem when fabricating SNSPDs, especially to obtain a saturated internal quantum efficiency.

The superconducting layer thickness being very thin, even a minor defect at the surface underneath may cause a major problem. In our case, the MoSi is deposited on top of a SiO2 layer so one has to look at the SiO2 roughness. SiO2 from thermally oxidized Si wafers is known to have one of the smoothest roughness achievable. Different deposition conditions have been tested and the roughness parameterRq, defined as the root mean square of the height of the surface, is summarized in Table 2.3, and the corresponding AFM measurement in Fig. 2.12. We observed that the roughness of the underlying Ag mirror is partially transferred to the SiO2 layer especially for recipe #1 and #2.

With the custom recipe #3, a roughness under 0.4 nm was obtained on the mirror structure. Intuitively one would like the smoothest roughness possible, however there is no experimental evidence that a device on a Rq∼0.4 nm surface would perform better than with a R_q ∼1 nm, this point was not investigated in more detail.

Table 2.3: List of SiO2 deposition processes and their corresponding R_q. Recipe #1 and #2 are deposited without and with addition of oxygen gas in the chamber while depositing, respectively. Recipe #3 is similar to #2 with the addition of a 25 W RF bias on the substrate.

Process recipe Underlying layer Rq (nm) Corresponding figure

Therm. ox. - 0.2 Fig. 2.12a

#1 Thermal oxide 1.4 -

Mirror 2.7 Fig. 2.12b

#2 Thermal oxide 1.0 -

Mirror 1.5 Fig. 2.12c

#3 Thermal oxide < 0.3 -

Mirror < 0.4 Fig. 2.12d

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2.5. Surface roughness

0.2 0.6

0.4 0.8 5.0

0 1.0

0.2 0.4 0.6 0.8 1.0

x (!m)

y (!m) z (nm)

Rq ≈ 0.2 nm

(a)

0.2 0.6

0.4 0.8 5.0

0 1.0

0.2 0.4 0.6 0.8 1.0

x (!m)

y (!m) z (nm)

Rq ≈ 2.7 nm

(b)

0.2 0.6

0.4 0.8 5.0

0 1.0

0.2 0.4 0.6 0.8 1.0

x (!m)

y (!m) z (nm)

Rq ≈ 1.5 nm

(c)

0.2 0.6

0.4 0.8 5.0

0 1.0

0.2 0.4 0.6 0.8 1.0

x (!m)

y (!m) z (nm)

Rq ≈ 0.3 nm

(d)

Figure 2.12: AFM surface roughness comparison for 4 different SiO2deposition conditions.

The SiO2 is sputtered on the metallic mirror structure presented in Section 2.4. (a) Thermally oxidized Si wafer. (b) Recipe #1. (c) Recipe #2. (d) Recipe #3.

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2.6 Detector packaging and setup

Packaging

Once the optical cavity process is finished, the final step consists in cutting a lollipop shaped devices through the wafer thickness. To optimize the alignment between the optical fibre core and the meander, the device are detached from the wafer by performing a deep reactive ion etching (DRIE) over the entire wafer thickness. The detectors are then detached and placed in a mounting as shown in Fig. 2.13. The alignment precision of this self-aligning technique has been characterized to be±3 µm [26].

Figure 2.13: Left: lollipop-shaped device in its mounting. The detector is aligned in the center of the white mating sleeve. The wire bondings, which connect the electrically the detector, are barely visible. Right: detectors mounted on the 0.8 K plate in the cryostat.

Electronic readout

Detector characteristics such as timing resolution, reset time, and maximum count rate, are heavily influenced by the readout electronics that sense and amplify the photon detection signal [27]. Different electronic readout circuits can be found in the literature [27, 5, 28, 27, 29]. The electric scheme used during the major part of this thesis is the following: a resistive bias tee at 40 K separates the RF signal and the DC current. After a detection, the nanowire needs sufficient time to cool down and becomes superconducting again. If the DC current comes back too quickly in the nanowire, the nanowire can be locked in a resistive state preventing it from working, see Section 5.3 for details. Depending on the application, different electronic scheme can be used, see Chapter 5 and 6 for details.

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3 Detection mechanism

3.1 Introduction

Despite extensive experimental studies to improve the performances of SNSPDs since their invention in 2001, a full description of the detection mechanism has not been established yet. Surprisingly, in the past few years, astonishing performances were achieved with a very limited comprehension of how SNSPDs really work. While the core of this chapter is already presented in details in the Appendix A.1, this chapter intends to add precisions on the experimental methods and discussion on the results.

The detection process can be decomposed in different steps, as depicted in the Fig. 3.1.

(i) A thin superconducting nanowire is biased near its critical current. (ii) An incoming photon is absorbed into the nanowire. (iii) The energy diffusion creates a cloud of excited electrons and phonons, so-called hotspot. (iv) This cloud then obstructs the current flow, leading to a non-superconducting cross-section in the nanowire that grows under the influence of Joule heating. (v) Because of the large resistive section (∼1 kΩor so), the current is redirected in the readout electrics, producing a voltage pulse. (vi) Due to the current division with the readout, the nanowire can cool down and becomes superconducting again, ready to detect another photon.

The points (i)-(ii) are well understood: by solving Maxwell’s equations for the appropriate structure, we can compute the absorption probability into the nanowire [30], as described in the Section 4.1 of this manuscript. The points (v)-(vi) are given by the electronic coupling and heating diffusion equation which describe the normal domain growth, this is also discussed in Chapter 6. The missing point is the central step of the detection process, where an absorbed photon converts its energy to create a cloud of excited electrons and phonons, i.e. the part (iii)(iv) in the Fig. 3.1.

Discussion about the core of the detection mechanism in SNSPDs began soon after their invention. Different theoretical detection models exist by now and in the past years,

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(i)

(ii)

(iii) (iv)

(v)

t ≈ 6 nm w ≈ 150 nm

(vi)

I

b

Figure 3.1: Schematic description of the full detection mechanism. (i) A thin superconducting nanowire is biased near its critical current. (ii) An incoming photon is absorbed into the nanowire. (iii) The energy diffusion creates a cloud of excited electrons and phonons. (iv) This cloud of quasi-particles obstructs the current flow, leading to a non-superconducting cross-section in the nanowire that grows under the influence of Joule heating. (v) Because of the large resistive section (∼1kΩor so), the current is redirected in the readout electrics, producing a voltage pulse. (vi) Due to the current division with the readout, the nanowire can cool down and becomes superconducting again, ready to detect another photon.

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3.2. Experimental setup scientists put a lot of effort to set up different experiments in the hope that one of the model would clearly emerge from the experimental data [31, 32, 33, 20, 34, 35, 36, 37].

However, although many studies highlighted very interesting behaviour, it turns out that this is a very complex phenomenon and no clear consensus has been found in the community yet. Very recently, Allmaras et al. [38] established a detection model for NbN taking into account the timing jitter experimental data. A particularly crucial feature of the detection models is the energy-current relation, which describes the bias current threshold needed at a given photon energy to create a detection event. The measurement of this relation is the primary method of investigation of the detection mechanism. A more detailed introduction of the different models and experimental methods is given in [32].

3.2 Experimental setup

Device under test

The device is fabricated out of a 5 nm thick film of amorphous Mo0.8Si0.2, with aTc= 5K, which is deposited by co-sputtering with a DC and RF bias on the molybdenum and silicon targets, respectively. The MoSi film is deposited on a thermally oxidized silicon wafer and is capped with a 3 nm a-Si layer. X-ray diffraction measurements have been performed, confirming the amorphous nature of the MoSi. The film is patterned into a meandered wire with a width of 170 nm and a gap of 160 nm as shown in the Fig. 3.2, and total surface area of 16×16 µm² by a combination of EBL and ion beam etching.

The detection efficiency at 1550 nm is 20%. The device has been selected out of tens of other detectors with different widths and fill factor by looking for the highest critical current and widest plateau region in order to have the largest energy range accessible.

16 !m

200 nm

Superconducting nanowires

Figure 3.2: Scanning electron microscope image of the device under test. The white1

dashed circle represents the region where the photons are absorbed. Inset: close-up look.

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The detector is mounted in a sorption cryostat reaching 0.75 K and biased with a current source and its critical current is 14.7 µA. The voltage pulses from detection events are amplified by a custom low-noise amplifier cooled to 40 K and by a secondary amplifier at room temperature. The detector is illuminated with unpolarized photons coming from a halogen lamp sent through a grating monochromator, as shown in Fig. 3.3. This provides a continuous spectrum from 750 to 2050 nm. We carefully calibrated the monochromator using laser lines at 632.8, 980.1, 1064.0, 1310.2 and 1550.8 nm. By using the second order of some of these wavelengths, we obtain 9 calibration points, extending up to 2128.0 nm with a 4 nm uncertainty. Appropriate low-pass filters were inserted to avoid crosstalk from higher diffraction orders.

monochromator

variable attenuator

fast

discriminator

cryostat

SNSPDs counter

current source

light

0.8 —> 2.5 K 40 K

room temperature amplifier low noise cryogenic amplifier

Figure 3.3: Schematic of the experimental setup. Broadband light is sent on a grating mirror, which narrows down the spectrum to a specific wavelength depending of the angle.

The filtered light is sent onto the device under test through a variable attenuator to fix the number of incoming photon constant. After a detection event, the electric signal goes through two stages of amplification to be discriminated and counted. The temperature of the device can be adjusted between 0.75 K and 2.5 K.

Discriminator settings

In order to assess that the experimental data have a physical meaning and are not affected by any electronic effect, we must pay attention to the pulse discrimination electronics. By decreasing the wavelength (increasing the energy) of the incident photon, the bias current needed to create an event decreases. As the signal amplitude depends only on the applied bias current, a problem can arise when the detector is operating at such low currents. If the discriminator threshold level is not set correctly, the consequence is that the photon counts cannot be distinguished from the amplifier noise and the shape of the PCR is affected. In Fig. 3.4a, the PCR is plotted as a function of the bias current for different discriminator threshold values at 750 nm photon wavelength. By increasing the threshold value, the bias current needed to overpass it increases and the PCR curves shift to the right. The transition width then represents the noise level of the amplification, which is non-physical and undesired. The discriminator level has to be set as low as possible,

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3.2. Experimental setup while still not under the noise level. In addition to this, the transition width becomes steeper, see Fig. 3.4b, where the transition width∆Ib =I_b^80%−I_b^20% and the bias value I_b^50% extracted from Fig. 3.4a are plotted as a function of the discriminator level.

2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

Bias currentIb(µA) 0.0

0.2 0.4 0.6 0.8 1.0

Countratenormalized

44 mV 4546 4748 4950 5255 6070

7580 8590 95100 110120 130140 150

(a)

40 50 60 70 80 90 100 110 120

Discriminator level (mV) 0.4

0.5 0.6 0.7 0.8 0.9 1.0 1.1

∆Ib(µA)

3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6

I50%b(µA)

(b)

Figure 3.4: Tuning of the discriminator settings. (a) Relative photon count rate (photon count rate subtracted by the DCR and divided by the maximum count rate) as a function of the bias current at 0.75 K for an incident photon wavelength of 750 nm. Each color represents one measurement run with a specific discriminator threshold value in millivolts.

Each solid line traces the error function fit for the respective data curve. The leftmost and rightmost curves correspond to 44 mV and 150 mV, respectively. When the discriminator level is too high, more bias current is required in the nanowire to overpass it. The sigmoid shape then represents the electrical noise. (b) Transition width extracted from (a) as a function of the discriminator setting value. The vertical dashed line represent

approximately the maximum reasonable discriminator level.

We verified that none of the curves are affected by scanning the discriminator level and restricting ourselves to the bias currents where the count rate was independent of the threshold level, corresponding to the safe region at the left of the red line in Fig. 3.4b.

During all the measurements, the discriminator level was set to 46 mV. The minimum detectable voltage pulse in the setup occurs at a bias current of approximately 2.5 µA.

A voltage pulse as seen on the oscilloscope for different detector bias currents is shown in Fig. 3.5. The discriminator setting of 46 mV is indicated as a blue dashed line in the figure. We see that even with the lowest pulse amplitude at 2.5 µA, the discriminator level is lower than the pulse amplitude by a significant amount. The second oscillation appearing around 60 ns for currents above 10 µA does not affect our response as the discriminator dead time is set to 80 ns. We also note the high-pass effect of our cryogenic amplification, which reduces the width the typical SNSPD output signal and creates an undershoot. However, this does not affect the shape of the curves that we measured.

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0 20 40 60 80 Time (ns)

−200

−100 0 100 200 300

Amplitude(mV)

Disciminator : 46 mV

3µA 45 8

1012 14

Figure 3.5: Oscilloscope traces of pulses for different bias currents. The dashed blue line indicates the discrimination level of 46 mV used during the measurement.

3.3 Results

Energy-current relation

The photon count rate and dark count rate measurements as a function of bias current and photon energy are shown in Fig. 3.6a. Each colour represents one measurement run with a specific incident photon wavelength. Each solid line traces the error function fit for the respective data curve, as explained later in this section. The dashed red line indicates the fraction η of the saturated detection efficiency η = 50% used to extract the energy-current relation. The integration time was 10 seconds at each bias current and energy point. In order to compare the PCR of various wavelengths, we normalise the data to a count rate value situated just below the critical current, i.e. in the plateau region where the efficiency is saturated.

The energy-current relation is shown in Fig. 3.7. For each wavelength we plot the amount of bias current I_b^η required to achieve a certain fraction η of the saturated detection efficiency. The setup allows to measure from 0.6 eV to more than 1.6 eV in the single- photon absorption regime. The relation is plotted for two different efficiency threshold, η = 50%andη= 1%, at 0.8 K and 1.5 K. The relation between bias current and photon energy is nonlinear throughout the entire energy range, for both temperatures, and for both η values.

Superconducting nanowire single-photon detectors for quantum communication applications

Thesis

Reference

Superconducting nanowire single-photon detectors for quantum communication applications

Université de Genève Faculté des Sciences Groupe de Physique Appliquée Professeur Hugo Zbinden

Superconducting nanowire

single-photon detectors for quantum communication applications

Thèse

Misael CALOZ

Abstract

Résumé

Remerciements

Contents

1 Introduction

1.1 Single photon and quantum communication

1.2 Single-photon detectors

1.3 Superconducting nanowire single-photon detectors

1.4 Thesis outline

2 Nano-fabrication

2.1 The basics of nano-fabrication

2.2 Superconducting absorptive films

2.3 Nanowire patterning

2.4 Mirrors

Wavelength (nm)

R ef le ct iv it y( % )

Wavelength (nm)

R ef le ct iv it y( % )

2.5 Surface roughness

2.6 Detector packaging and setup

3 Detection mechanism

3.1 Introduction

I

3.2 Experimental setup

3.3 Results