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A NbTiN superconducting nanowire single photon detector (SNSPD) on a silicon-on-insulator substrate Yan, Xiruo 2017

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A NbTiN Superconducting Nanowire Single PhotonDetector (SNSPD) on a Silicon-on-Insulator SubstratebyXiruo YanB.Sc., The University of Waterloo, 2014A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Physics)The University of British Columbia(Vancouver)January 2017© Xiruo Yan, 2017AbstractSingle photon detectors are essential part of most optical quantum informationapplications. Among all candidates, superconducting nanowire single photon de-tectors (SNSPD) have the advantages of low jitter, low dark count rates and highmaximum count rate. Commercial systems based on these detector elements cur-rently cost on order $50-100K. In this project a circular meander design of a free-space SNSPD is fabricated and tested in house. Although the absolute absorptionefficiency of the detector is low, because it was fabricated on a substrate optimizedfor other applications, the measured and modelled values for both incident po-larizations agree within the uncertainties. The bias current dependence is almostconstant from 50% to 100% of the breakdown threshold value, which should allowoperation at intrinsic dark count rates extrapolated to be < 1 Hz at 2.05 K.iiPrefaceFor the work in Chapter 2 and Chapter 3, I was responsible for the entire nanofab-rication process and design optimization, instructed by related lab notes left by ourformer postdoc Dr. Mohsen K. Akhlaghi, and was also helped by Dr. Akhlaghihimself via emails.The idea of experiment method in Chapter 4 is mainly given by my supervisorDr. Jeff F. Young. I was responsible for all of the optics setup for the measurementsand calibration.Data collection of the cryogenic experiment in Chapter 5 is mainly conductedby Dr. Akhlaghi. I was responsible for experiment preparation, assisting him dur-ing the experiment, and post-experiment data analysis.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 Call of Quantum Information . . . . . . . . . . . . . . . . 11.1.2 Why SNSPD . . . . . . . . . . . . . . . . . . . . . . . . 41.2 Detection Mechanism . . . . . . . . . . . . . . . . . . . . . . . . 71.3 State-of-the-art . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.3.1 SNSPD in Cavity . . . . . . . . . . . . . . . . . . . . . . 101.3.2 Waveguide SNSPD . . . . . . . . . . . . . . . . . . . . . 111.3.3 Multiplexed SNSPD Array . . . . . . . . . . . . . . . . . 121.4 About This Project . . . . . . . . . . . . . . . . . . . . . . . . . 132 Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.1 General Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 152.1.1 Sample Preparation . . . . . . . . . . . . . . . . . . . . . 16iv2.1.2 Positive Electron Beam Lithography . . . . . . . . . . . . 162.1.3 Electron Beam Evaporation and Lift-off . . . . . . . . . . 172.1.4 Negative Electron Beam Lithography . . . . . . . . . . . 182.1.5 Plasma Etching . . . . . . . . . . . . . . . . . . . . . . . 192.2 Electron Beam Lithography . . . . . . . . . . . . . . . . . . . . . 202.3 Electron Beam Evaporation . . . . . . . . . . . . . . . . . . . . . 222.4 Plasma Etching . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.1 Design Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 263.2 Current Crowding . . . . . . . . . . . . . . . . . . . . . . . . . . 273.3 Proximity Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.4 Sequencing Issues . . . . . . . . . . . . . . . . . . . . . . . . . . 333.5 Residual Imperfections . . . . . . . . . . . . . . . . . . . . . . . 344 Experiment Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.1 Experiment Design . . . . . . . . . . . . . . . . . . . . . . . . . 374.1.1 Electronic Part . . . . . . . . . . . . . . . . . . . . . . . 374.1.2 Optical Power Calibration Approach . . . . . . . . . . . . 384.1.3 Optical Set-up . . . . . . . . . . . . . . . . . . . . . . . 404.2 Measuring Cryostat Window Transmission Twindow . . . . . . . . 424.3 Measuring Beamwidth w: Knife Edge Measurement . . . . . . . . 434.3.1 Knife Edge Measurement . . . . . . . . . . . . . . . . . 434.3.2 Measuring Beamwidth . . . . . . . . . . . . . . . . . . . 454.3.3 Uncertainty Summary . . . . . . . . . . . . . . . . . . . 465 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.1 Absorption Simulation . . . . . . . . . . . . . . . . . . . . . . . 475.2 Experiment Results . . . . . . . . . . . . . . . . . . . . . . . . . 516 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586.1 Project Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 586.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59vBibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60viList of FiguresFigure 1.1 Two chosen basis and states for encoding information in singlephoton states. . . . . . . . . . . . . . . . . . . . . . . . . . . 2Figure 1.2 Schematic diagram of a PMT. Figure taken from Wikipedia.org 5Figure 1.3 Schematic diagram of a SPAD. Figure taken from spie.org . . 6Figure 1.4 Formation of resistivity barrier. Arrows indicate current den-sity. Figure taken from [31] . . . . . . . . . . . . . . . . . . 7Figure 1.5 Schematic implementation of SPD using superconducting nanowire.Elements in green dashed box is an analogy to the nanowire. . 8Figure 1.6 A meander design SNSPD. Figure taken from [31] . . . . . . 9Figure 1.7 SNSPD embedded cavity. ARC is anti-reflection coating. Fig-ure taken from [28] . . . . . . . . . . . . . . . . . . . . . . . 10Figure 1.8 Schematic diagram of a TW detector. Figure taken from [26]. 11Figure 1.9 Coherent perfect absorber SNSPD. Superconducting nanowirelies atop a one-dimensional photonic crystal cavity, scale barsare 200 nm for a) and 1 µm for b). Figure taken from [4]. . . . 12Figure 1.10 Multiplexed SNSPD array. Figure taken from [12]. . . . . . . 13Figure 1.11 Meander SNSPD designed by Dr. Akhlaghi. Figure takenfrom [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Figure 2.1 Cross section layout out the of superconducting chip (not toscale). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Figure 2.2 Schematic process for positive EBL . . . . . . . . . . . . . . 17Figure 2.3 Schematic process for metal deposition . . . . . . . . . . . . 18Figure 2.4 Schematic process for positvie EBL . . . . . . . . . . . . . . 18viiFigure 2.5 After plasma etch . . . . . . . . . . . . . . . . . . . . . . . . 19Figure 2.6 Optical image of a final chip. 3 out of 12 devices of on one chipare shown. Each device has two large contact pads on bothsides (blue C marks one set of contact pads) of and connectingto a centre detector (marked in blue circles). Scale bar is 100µm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Figure 2.7 SEM image of one full detector. Scale bar is 2 µm. . . . . . . 20Figure 2.8 Image of a small part of contact pads and two alignment marksafter development. Nanowires will be pattern between contactpads and connect with them. Scale bar is 10 µm. . . . . . . . 21Figure 2.9 Raster style schematics. Black dashed line indicates the de-signed polygon to be write. Blue arrows show the beam sweeps.Red dotted line is the preceding direction of sweeps . . . . . . 23Figure 2.10 Importance of appropriate metal thickness . . . . . . . . . . . 24Figure 2.11 Overlap between contact pad (left) and tapered nanowire (cen-tral strip). Scale bar is 100 nm. . . . . . . . . . . . . . . . . . 24Figure 2.12 Schematic structure of the main reactor chamber . . . . . . . 25Figure 3.1 Layout of the design. . . . . . . . . . . . . . . . . . . . . . . 27Figure 3.2 Top view of boundaries of the 180-deg bend. Red bound-aries are imposed with Dirichlet boundary conditions and blueboundaries imposed with Neumann boundary conditions. Dashedarrows indicate assumed input/ouput. . . . . . . . . . . . . . 28Figure 3.3 Calculated streamlines of K with boundary conditions givenin Figure 3.2. Black solid lines correspond to the boundarygeometry, and dashed lines (red and blue) are streamlines of K. 29Figure 3.4 SEM image of the meander bend part of a fabricated detector,with the bend optimized with the introduced calculation. Thescale bar is 200 nm . . . . . . . . . . . . . . . . . . . . . . . 30Figure 3.5 Schematic for proximity effect: area surrounding the exposurepixel get exposed. . . . . . . . . . . . . . . . . . . . . . . . . 31viiiFigure 3.6 Two types of scattering. Blue line is an example trajectory of aforward scattering electron. Red line is an example trajectoryof a back scattering electron. . . . . . . . . . . . . . . . . . . 32Figure 3.7 Scheme of writing dummy lines in sequence (from bottom totop) to avoid large jumps. Green box indicates nanowire. Bluesolid and dashed arrows show direction of beam rastering andjump respectively. Blue circular dots mark the beginning ofnanowires. . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Figure 3.8 Writing scheme for a nanowire bending. Two nanowires (blueand green lines) forming a 180-deg bending. Solid lines witharrows are beam writing path. Dotted lines are beam jump.Grey region is for normal raster style (see Figure 2.9). Thenumber of lines defining a nanowire needs to be odd to avoidbig beam jumps (5 lines are illustrated here). Circles and squaresare starting and ending points of the nanowire respectively. . . 35Figure 3.9 Improper connection between tapering and tapered nanowire.Blue dashed lines are designed pattern, where triangular taper-ing part was patterned in the writing sequence of the circularregion, while the rectangle tapered part was patterned in theend. The scale bar is 1 µm . . . . . . . . . . . . . . . . . . . 35Figure 3.10 Rectangle junction to tolerate shift. Blue dashed lines are de-signed pattern. The scale bar is 1 µm . . . . . . . . . . . . . 36Figure 3.11 Distortion at the bend. Scale bar is 200 nm . . . . . . . . . . 36Figure 4.1 A schematic diagram of the electronics set-up. Parts enclosedby the blue dashed line are inside the cryostat. The SNSPD isin series with an inductor L (100 nH) and resistor R (100 Ω).C is capacitor (122 pF) and LNA is low noise amplifier . . . . 38Figure 4.2 Photos of the final chip and electronics. . . . . . . . . . . . . 38Figure 4.3 Two possible schemes for obtaining actual input power on thedetector area. The schematic of the detector only shows theactive area, (dummy lines are omitted). Blue circular shadeindicates laser spot. . . . . . . . . . . . . . . . . . . . . . . . 39ixFigure 4.4 Optical set-up. HeNe laser (λ = 632.8 nm) is through neu-tral densty filter set (NDF1) and directed via mirrors M1 andM2 to a polarizer plrz. Power meter PM is used to measurethe power of polarized light. The meter is then removed andlight goes through another pre-calibrated set of neutral densityfilters NDF2 for precise attenuation. Then light goes throughcryostat windows and normally incident on the sample. . . . . 41Figure 4.5 Measuring cryostat windows transmission. BS is beam splitter.Reflector is a silicon chip. . . . . . . . . . . . . . . . . . . . 42Figure 4.6 Knife edge experiment. Straight knife edge translates along x-axis, cutting through Gaussian beam and blocking a part of it.Resulting unblocked power is measured by a power meter. . . 44Figure 4.7 Beamwidth measurement. The laser is pulled back a distance dand the beamwidth of a position at distance d from the sampleposition is measured. . . . . . . . . . . . . . . . . . . . . . . 45Figure 4.8 Knife edge measurement data and fitted curve. . . . . . . . . 46Figure 5.1 Simulated structure . . . . . . . . . . . . . . . . . . . . . . 47Figure 5.2 Simulated absorption of nanowire versus its width. Blue solidand dashed lines correspond to a source polarization that isparallel and perpendicular to nanowire respectively. Red lineis the ratio of two absorption (parallel over perpendicular) . . 49Figure 5.3 Simulated absorption of nanowire versus ZEP thickness. Thecolour coding is the same as the previous figure. . . . . . . . . 49Figure 5.4 Simulated absorption of nanowire versus silicon etch depth.The colour coding is the same as the previous figures. . . . . . 50Figure 5.5 Simulated absorption of nanowire versus BOX thickness. Thecolour coding is the same as the previous figures. . . . . . . . 50Figure 5.6 Simulated E field of source polarization along z axis, parallelto nanowires. . . . . . . . . . . . . . . . . . . . . . . . . . . 51Figure 5.7 Simulated E field of source polarization along x axis, perpen-dicular to nanowires. . . . . . . . . . . . . . . . . . . . . . . 51xFigure 5.8 IV curves of detector 1 (blue curve) and 4 (red curve), at tem-perature T = 2.05K. . . . . . . . . . . . . . . . . . . . . . . 52Figure 5.9 Electric pulse picked up by fast oscilloscope. Vertical scale is50 mV/div and horizontal scale is 5 ns/div. . . . . . . . . . . 53Figure 5.10 QE and background count rates versus bias current for parallelpolarization. . . . . . . . . . . . . . . . . . . . . . . . . . . . 54Figure 5.11 QE and background count rates versus bias current for parallelpolarization. . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Figure 5.12 QE and dark count rate (of photons with wavelength 1550nm) versus bias current of the detector shown in Figure 1.11.Dashed lines mark optimal bias current. Figure taken from [3]. 56Figure 5.13 Estimated dark count rates. Blue and red lines correspondto a source polarization that is parallel and perpendicular tonanowire respectively. Curves fitted with an exponential func-tion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57xiAcknowledgmentsI offer my enduring gratitude to my supervisor Dr. Jeff F. Young, who fundedme for this project, and whose penetrating questions helped me understand myproject more thoroughly and enlarged my vision of science. His wisdom inspiredme during the entire Master program.I owe particular thanks to Dr. Mohsen K. Akhlaghi for all the critical helps andinstructions for this project, and all the kind patience and encouragements when Imade horrible mistakes. Without his help, I would never have finished this project.I thank Dr. Mario Beaudoin for providing me all the cleanroom support andnumerous nanofabrication tricks he taught me.Thanks are also owed to my fellow lab mates: Ellen Schelew, Jonathan Massey-Allard and Hamed Mirsadeghi. They all helped me kindly whenever I neededhelps. Ellen babysat me since my first day in lab and patiently answered my endlessnaive questions. Jonathan’s inspiring spirit and all the pranks he pulled on me leftme with many happy moments. Hamed gave me valuable suggestions in careerbuilding based on his own experience of job seeking.All the people above not only helped me fulfil my project, but also kindly gaveme many important helps and suggestions on my future career.Finally, special thanks are owed to my parents, whose have supported methroughout my years of education, both morally and financially.xiiDedicationTo my parentsxiiiChapter 1Introduction1.1 MotivationA single photon is the known fundamental unit of electromagnetic radia-tion. The quantum mechanical nature of these photon states opens a wholerange of novel applications in the burgeoning field of quantum information(QI). Compared to other candidates for implementation of QI systems, op-tical or near infrared frequency photons offer many advantages: carryingno charges, there are less unwanted interactions with matter, so they can betransported over macroscopic distances in low-loss waveguides, etc [24].Most potential applications based on single photons, require detectorsthat have high-efficiency, low timing jitter, low dark count rates, and highmaximum signal count rates. Superconducting nanowire single photon de-tectors (SNSPD) represent one promising category of such detectors thathave been a topic with growing interest in the past twenty years.1.1.1 Call of Quantum InformationAreas where QI may have an impact ranging from metrology, through se-cure communication, and all the way to universal quantum computing. Al-though this application sector is in its infant stage of development, a handfulof entry-level commercial ventures already exist.1Quantum key distribution (QKD) [7] is one of most mature QI applica-tions, and is already commercialized by some companies, such as ID Quan-tique, MagiQ Technologies and so on. It provides unconditioned securecommunication that is guaranteed by laws of physics (quantum mechan-ics). Especially with the BB84 protocol, metropolitan QKD networks havebeen built and tested [29].In this protocol, the security stems from quantum indeterminacy and no-cloning theorem. No-cloning theorem states that it is impossible to createan identical copy of an arbitrary unknown quantum state, so that any eaves-dropper has to make a direct measurement on the communicating quantumstates to learn information about them. Quantum indeterminacy states thata measurement of a quantum state can in general have an indeterministicresult and disturb the state, unless the state is an eigenstate of the measure-ment. BB84 exploits these physics to detect the eavesdropper and distributesecure keys.For BB84 to work, two pairs of orthogonal basis (of the same 2-dimensionHilbert space) are chosen, for example, the rectilinear basis (horizontal andvertical direction) and the diagonal basis (45°and 135°direction) of pho-ton polarizations. For each pair, the bit information 0 and 1 is encoded bypreparing the photon in two basis states respectively, as shown in Figure 1.1.Figure 1.1: Two chosen basis and states for encoding information in singlephoton states.2There is a conjugation relation (in Dirac bracket notation) between thetwo sets of basis:| ↑>=√22(| ↗>+| ↘>)| →>=√22(| ↗>−|↘>)| ↗>=√22(| ↑>+| →>)| ↘>=√22(| ↑>−|→>).The information can be extracted exactly by measuring the photon withrespect to the same pair of states, but measurements with the wrong pairwill have a 50-50 probability of getting either 0 or 1 and leave the photonin a corresponding state of the wrong pair.In practise, suppose Alice (the sender) wants to generate and share asecret key with Bob (the receiver), she encodes random bit information tophotons, and for each bit, she uses a random pair of basis from the two dis-cussed above, and sends them to Bob via a quantum channel. Bob measuresthese photons choosing different basis also randomly. After transmission isfinished, they discuss only the basis they used to encode/measure photonsthrough a public channel, and only keep bits that are encoded/measuredwith the same pair of basis, for these bits held by both parties should beidentical in theory.Then they compare a subset of the selected bits through public channeland check for the error rate (there should be an expected instrumental errorrate), and discard these bits afterwards. If a third party Eve (the eavesdrop-per) intercepted the quantum channel and measured photons, she will have50% probability altering the photon state when measuring it with the wrongpair of basis, which results in a increased error rate, and thus can be de-tected. If the error rate remains under a threshold level, then remaining bits3will be subjected to a reconciliation [8] process for error-correction, andthen be applied by a universal hash function to generate a shorter key forprivacy amplification, such that Eve has negligible knowledge about thisfinal key. Otherwise if the error rate is beyond the threshold level, Aliceand Bob will just abort the communication and try with another quantumchannel.Clearly for this protocol to work, detectors capable of reliably recordingsingle photon absorption events are required. Deficiencies in the quantumefficiency and/or significant spurious dark count rates of such detectors willseriously compromise the potential data rate at which this protocol can beoperated.Besides QKD, there are other QI applications that rely on SPDs ofgood performance, such as linear optical quantum computing (LOQC) [19].LOQC is one ultimate QI goal. It still remains distant, because it has verystrict requirements for single photon sources and detectors. For detectors,it requires scalable SPDs of detection efficiency (ratio between accuratelydetected photon count rate and photon input rate) of at least 2/3 [33], whichis achieved only recently [21].1.1.2 Why SNSPDSingle photon detection is not a new subject, and to date conventional SPDsmainly consist of photomultiplier tubes (PMT) and single-photon avalanchephotodiodes (SPAD) [12].The main body of a PMT is a vacuum tube, inside which is a photo-cathode followed by a focusing electrode, a sequence of electrodes withincreasing bias voltages (called dynodes) and an anode, as shown in Fig-ure 1.2. If photons to be detected have an energy exceeding the work func-tion of photocathode material, photoelectons (called primary electrons) willbe emitted from the photocathode due to photoelectric effect. These pri-mary electrons get focused by the focusing electrode, then accelerated byand collide with the dynodes, which release more electrons (called sec-ondary electrons). Since each dynode is biased at a voltage higher than the4previous one, secondary electrons get multiplied and thus amplify the initialsignal and allow single photon detection.Figure 1.2: Schematic diagram of a PMT. Figure taken from Wikipedia.orgAn SPAD is in essence an reversely biased p-n junction (p side negativeand n side positive), as shown in Figure 1.3, with a very high voltage, creat-ing a large depletion region at the interface. This high voltage is supposedto be well above the breakdown voltage of the p-n junction, so once an extrasingle charger carrier is added to the depletion region, it will gain large ki-netic energy due to the strong field and knock off other bound charges thatwill then also get accelerated, thus triggering the avalanche effect, creatinga macroscopic detectable current. The triggering primary electron can beeither photo-generated by the absorption of a single photon (ideal case), orthermally generated (a source of dark counts).PMT and SPAD work in a similar way; they both rely on electron cas-cade and multiplication effect to give a significant amplification of the sin-gle photon signal, which inevitably can have large time lag and jitter[31].Their count rate is also low. Furthermore, the optoelectronic effects ex-5Figure 1.3: Schematic diagram of a SPAD. Figure taken from spie.orgploited to turn a photon into electric signal depend on the work function(PMT) and band gap (SPAD), which are constrained by materials. It willalso be very challenging to detect a telecommunication wavelength pho-ton (with lower energy): with low work function/band gap materials, unac-ceptable noise (dark counts) due to thermal fluctuations can be an intrinsicdraw-back for these detectors. Cooling technology has been applied to helpreduce dark count, but temperature is usually restricted to be above 200 Kfor normal operations. For the reasons stated above, conventional PMTsand SPADs capable of detecting infrared photons usually have a jitter ofhundreds of picoseconds, maximum count rate of KHz to tens of MHz, andKHz level of dark count rate.On the other hand, SNSPDs are made of metallic superconductors thathave picosecond level optoelectronic response [30], and connected to fastelectronics, which can limit jitter to tens of picoseconds. Short reset timeleads to a maximum count rate that can easily reach GHz level. Moreover,cryogenic environment guarantees low noise: dark count rates usually atbelow 100 Hz.61.2 Detection MechanismIn contrast to PMT and SPAD, the photon detection mechanism of SNSPDis based on the breakdown of superconductive state of a material. When asuperconducting material is cooled below a certain characteristic tempera-ture Tc (critical temperature), the resistivity of the material suddenly dropsto zero. However, this state can be destroyed when current density in thematerial is greater than a characteristic Jc (critical current density). For ananowire with fixed cross section, Jc corresponds to a characteristic Ic (criti-cal current). For a fixed J < Jc flowing through a superconducting nanowirewith T < Tc, a single photon can locally disturb the material superconduc-tive state and cause it to go normal in the vicinity of the absorption event[14].Figure 1.4: Formation of resistivity barrier. Arrows indicate current density.Figure taken from [31]Combining the above two effects allows formation of a detectable resis-tive barrier on a superconducting nanowire, as shown in Figure 1.4. Firstly,the nanowire is kept at a temperature much lower than Tc so that it is inthe superconductive state. Then the nanowire is DC biased at a currentclose to Ic. When a photon is absorbed by the nanowire, a localized non-superconducting ’hot spot’ with finite size is generated, which graduallygrows and forces super current to go around it. As a result, local current7densities on both sides of the ’hot spot’ become higher, and when they ex-ceed Jc, that entire region turns non-superconducting, forming a resistivebarrier [31].Moreover, because of high mobility carriers in superconductor, there isanother important physical quantity: kinetic inductance Lk. Since chargecarriers in the superconductor have inertia mass, it will take a finite timefor a change in electromotive force to effect the dynamics of these carriers,which means the wire behaves like an inductor in the circuit.Lk and the formation of a resistive barrier can be exploited to implementsingle photon detectors. The schematic diagram in Figure 1.5 shows thebasic idea behind the operation of an SNSPD. The SNSPD is representedin circuit form by the green box, and is DC biased by a current close to Ic.When no photon is absorbed, the switch is closed, and Rb is short-circuited(superconducting state, no resistance). The case where a photon is absorbedand a resistive barrier formed corresponds to opening the switch. The re-sulting LR circuit will then have a high frequency signal that can be pickedup by the amplifier and fed to the counter. Furthermore, energy relaxationtime constants for those resistive barriers are generally in picosecond range,resulting in GHz maximum counting rate [31].Figure 1.5: Schematic implementation of SPD using superconductingnanowire. Elements in green dashed box is an analogy to the nanowire.8Given this detection mechanism, there are two main factors for efficientsingle photon detection: absorption by nanowire and formation of effectiveresistive barrier. The first factor depends on the geometric structure of theSNSPD and the imaginary permittivity of the material. As for geometry,most SNSPD designs naturally take a meander structure with a detectingarea matching the light modal area of a single mode optical fibre at the op-erating wavelength, for example, Figure 1.6. As for materials, NbN, NbTiNand WSi are often chosen because of their low superconducting energy gap.Figure 1.6: A meander design SNSPD. Figure taken from [31]The second factor depends on the bias current density. Since the forma-tion of resistive barrier starts from the initial ’hotspot’, for the same materialand bias current density, photons with lower energy (long wavelength) cancreate a smaller ’hotspot’, and thus they are less likely to be detected. How-ever, if the bias current density is brought too close to Jc, intrinsic dark countrate will grow exponentially due to current-assist vortex-antivortex pair un-binding. Therefore, narrow nanowires (usually < 100nm for NbN/NbTiN)are required to enhance photon detection while keeping intrinsic dark countrate low.91.3 State-of-the-art1.3.1 SNSPD in CavityAs mention in last section, absorption of light is one important factor forSNSPD performance. Performance of a simple design as in Figure 1.6 willbe largely limited by reflection and transmission of incident light. One wayto enhance absorption is to make use of an optical cavity.An optical cavity traps light. The simplest example is the Fabry-Perotresonator, where two highly reflective mirrors are held close together. Em-bedding the SNSPD inside such a cavity can boost absorption.Figure 1.7 shows such a design using silica and gold mirrors to formcavity, which boosted the detection efficiency of a normal NbN SNSPDfrom below 10% to 57% at wavelength 1550 nm [28].Figure 1.7: SNSPD embedded cavity. ARC is anti-reflection coating. Figuretaken from [28]A more recent design of the WSi SNSPD, using stacks of dielectriclayers to form the cavity, further increased detection efficiency to over 90%10at a wavelength 1550 nm [21].1.3.2 Waveguide SNSPDThe SNSPDs discussed so far are all free-space detectors, where the light tobe absorbed is incident normal to the plane of the meander detector, eitherfrom free space or from a single mode fibre.5Figure 1.8: Schematic diagram of a TW detector. Figure taken from [26].In photonic integrated circuit (PIC), conventional bulk optical elementssuch as beam splitters, resonators, waveguides as well as SPDs, can be in-tegrated to a simple chip, making scalable QI applications possible.Different from free space or fibre optics, in PIC light propagates in on-chip slab waveguides, or even photonic crystal waveguides [16]. Conven-tional implementation of a waveguide SNSPD follows a travelling wavefashion (TW detector), where the nanowire simply lies atop the waveguide.An example of TW detector is shown in Figure 1.8. However, most ofthe light is confined inside the waveguide and only weak evanescent lightoutside the waveguide can be absorbed by nanowires. Therefore, for suchdesign long enough waveguide and nanowire have to be chosen to ensurea high absorption, resulting in a big foot print, higher dark count rate, etc.For the design shown in Figure 1.8, in order to get a absorption of > 95%,11the nanowire needs to be as long as 20 µm [26].Figure 1.9: Coherent perfect absorber SNSPD. Superconducting nanowirelies atop a one-dimensional photonic crystal cavity, scale bars are 200nm for a) and 1 µm for b). Figure taken from [4].The waveguide SNSPD can also be implemented with an optical cavity.The detector in Figure 1.9 is designed and fabricated in this group earlier byDr. Mohsen Akhlaghi. The geometry of the nanowire and photonic crystalcavity are carefully chosen to create a coherent perfect absorber (CPA).Such a design ensures a unity absorption of the nanowire, while keeping acompact foot print [4].Cavity-SNSPDs mentioned previously and CPA-SNSPDs share the sim-ilar idea where SNSPDs are put inside cavities to enhance absorption. How-ever, design approaches are different. Cavity-SNSPD cavities are simplyFabry-Perot cavities made with stack dielectrics. CPA-SNSPDs cavities aredesigned based on temporal coupled-mode theory [16] and can achieve atheoretical unity absorption.1.3.3 Multiplexed SNSPD ArrayThe multiplexed SNSPD array bias multiple SNSPDs independently andilluminate light broadly to this ’multi-pixel’ detector. This scheme can de-crease detector dead time dramatically, since even if one SNSPD ’fired’,other SNSPDs can still register photons, which gives a much higher maxi-12mum photon count rate.Figure 1.10: Multiplexed SNSPD array. Figure taken from [12].Furthermore, multiplexed SNSPD can even count the number of photonsincident in one pulse, while SNSPDs described above can only distinguishthe state of ’zero photon’ and ’one or more photon’ of a pulse. In someadvanced QI protocols, SPDs should not only be able to detection photonsefficiently, but also be photon number-resolvable [20].Figure 1.10 is an example, which can count up to 6 photons. Recently a64-pixel multiplexed SNSPD Array has also been reported [5].1.4 About This ProjectIn this project, a free-space meander SNSPD is designed, fabricated andtested in house. Commercial single photon detection systems (free-space)based these elements cost the order of $100K. Since we have the in-housenanofabrication capabilities, and the electronic circuitry (designed and madein the earlier CPA-SNSPD project) for building our own detection system,we wanted to see how easy it would be to make good free-space detectorsin house. The purpose of this thesis was to sort out the fabrication steps,before getting special, custom-made substrates with cavities as described inSection 1.3.1.The design is adopted from [3], as shown in Figure 1.11, which is orig-13inally designed for detecting infra-red photons.Figure 1.11: Meander SNSPD designed by Dr. Akhlaghi. Figure taken from[3].In the original design, Nanowires (NbTiN) are 80 nm wide, with a fillingfactor of 33% and the detecting area diameter was 12.6 µm, fabricated ona silica thin film (with thickness being a silica quarter-wavelength of thetarget wavelength λ = 1550nm) deposited on a silicon substrate.This project takes the same nanowire width and filling factor, but de-creases the detecting area size to match light spot of visible source (He-Nelaser λ = 632.8nm), and extended the dummy lines area (to be discussedin Chapter 3) to increase the quality of nanowires. The current detectorwas fabricated with NbTiN coated silicon-on-insulator (SOI) chips (to bediscussed in Chapter 2).The rest of this thesis is organized as follows. Chapter 2 describes thenanofabrication processes of the detector chip, Chapter 3 discusses reasonsand methodology of the SNSPD design, Chapter 4 covers experimentalset-ups and methods for reliable measurements, Chapter 5 presents the ex-perimental/simulated data and discussions regarding these data, and finallyChapter 6 gives a summary of the project and future work.14Chapter 2Fabrication2.1 General ProcedureThe SNSPDs were fabricated from SOI wafers (200 nm thick silicon toplayer and a 1270 nm thick silica buried oxide layer) coated with 8 nm thickNbTiN layers (STAR Cryoelectronics Inc.), as shown schematically in Fig-ure 2.1. This chapter explains methods and machines that are used to fabri-cate the detector chip. Chapter 3 will explain the detailed design idea of thedetector.The superconductor coated SOI wafer was spin-coated with acetone-soluble photoresist for protection, and diced into 7 mm x 7 mm chips. Fromthat, all fabrication procedures were finished in house.Figure 2.1: Cross section layout out the of superconducting chip (not toscale).15Because of the delicate thin layer of the superconductor, chips must behandled with great care, and most manual processes happened in clean-rooms located within the AMPEL building (one class 1000 cleanroom andone class 10000 cleanroom).The following subsections outline basic fabrication steps. Detailed ex-planations on the major steps such as E-beam lithography (EBL), E-beamevaporation and plasma etching are in next three sections.2.1.1 Sample PreparationThe chip was first blown with a nitrogen gas gun (N2 blow) to removepossible flakes coming from the dicing process. Those flakes may causescratches on the surface, and thus have to be removed. Then, the chip wassoaked in deionized water (DI) water, and underwent a 2-minute ultrasonicwash to further remove possible flakes.The chip was then given a 2-minute ultrasonic wash in acetone to re-move the protecting photoresist, then a 2-minute ultrasonic wash in iso-propanol (IPA) to remove the acetone, then a 2-minute ultrasonic wash inDI water to remove the IPA.After that the chip was taken out and N2 blown to remove residual DIwater. Finally, the chip was placed on a hotplate at 100 °C for 1 minute todehydrate the surface.At this point, the chip should be visually checked under the optical mi-croscope to make sure no visible dirt or scratches remained on the surface.If there was residual dirt, the previous cleaning sequences were repeated.2.1.2 Positive Electron Beam LithographyA schematic flow diagram for this crucial lithography step is shown inFigure 2.2. The dehydrated clean chip was spin-coated with 500 nm ofZEP520A (ZEON Corp.) as a positive e-beam resist. The spin-coating wasdone using a HEADWAY PMW 32 spinner, operated at 3000 ramps perminute (r.p.m), followed by a 3-minute hard baking on a hotplate at 180 °C.16Since the expensive resist was long passed its expiration date, the r.p.m forthe desired thickness was found via trial and error, and it was not consistentwith reported value in the original material datasheet.Twelve sets of contact pads and alignment marks were defined throughEBL, with the extra-high tension (EHT) voltage set to 25 kV , and a doseof 120 µC/cm2 (more details in Section 2.2). Our e-beam lithographer isbased on a Zeiss SigmaT M Field Emission Scanning Electron Microscopy(FESEM), controlled by Nanometer Pattern Generation Software (NPGS)[2] for EBL.The chip was then developed in o-xylene, followed by ultrasonic clean-ing in IPA and DI water for 30 seconds respectively.(a) Spin-coated chip (b) Contact pads and align-ment marks exposed by e-beam(c) After developmentFigure 2.2: Schematic process for positive EBL2.1.3 Electron Beam Evaporation and Lift-offMetal needs to be deposited on the uncovered regions from the last step toform real contact pads and alignment marks.The chip was first rinsed in 40:1 H2O : BHF (7 : 1 buffered hydrofluoricacid) solution for 1 minute to remove any oxidized layer on the NbTiNsurface, so that better Ohmic contact can be achieved later. The chip wasthen immediately transferred to the evaporation chamber of a DEEWONG-2000 e-beam evaporator, and an 8nm/90nm of titanium-gold bilayer wasdeposited onto the chip (more details in Section 2.3).After deposition, the lift-off was performed by soaking in sonicatedchlorobenzene for 1 minute. The chlorobenzene could remove unexposed17(a) After e-beam evaporation (b) After lift-offFigure 2.3: Schematic process for metal depositionZEP and corresponding deposited metals. The lift-off was followed by 30seconds in sonicated IPA and a 30 seconds DI water cleaning. A schematicsummary of this process is shown in Figure 2.3.2.1.4 Negative Electron Beam LithographyMeander nanowires were defined using EBL. However, this time the sameresist ZEP520A was used as nagative resist, i.e, exposed region remainsafter development (more details in Section 2.2).Anisole-diluted ZEP520A was spin-coated on the chip at 2200 r.p.m toget a 150 nm thickness, followed by a 3-minute hard baking on a hotplateat 180 °C.Then nanowires were patterned by EBL at 25 KV EHT and 100 mC/cm2,and developed in chlorobenzene. A schematic diagram of the nanowirelithography process is shown in Figure 2.4.(a) Spin-coated chip (b) Meander nanowirespattern exposed by e-beam(c) After developmentFigure 2.4: Schematic process for positvie EBL182.1.5 Plasma EtchingThe final step was to etch through the unprotected NbTiN layer to formsuperconducting nanowires, using a PLASMAQUEST Electron CyclotronResonance (ECR) etcher. The cross section of the final chip is as shown inFigure 2.5Since the etch rate at narrow trenches could be slower than a flat surface,the etching recipe was calibrated by etching through 8 nm thick NbTiNand 10 nm thick silicon on a dummy chip. After this step, the nanowireshave ~100 nm thick ZEP on top for protection. The gas flow rates wereCF4 : O2 = 15 : 2 etch, with chamber pressure 30 mTorr and RF power 50W , for 75 seconds (more details in Section 2.4).Figure 2.5: After plasma etchFigure 2.6 gives an optical image of part of a final chip.Figure 2.6: Optical image of a final chip. 3 out of 12 devices of on one chipare shown. Each device has two large contact pads on both sides (blueC marks one set of contact pads) of and connecting to a centre detector(marked in blue circles). Scale bar is 100 µm.19Figure 2.6 gives an SEM image of one full meander SNSPD.Figure 2.7: SEM image of one full detector. Scale bar is 2 µm.2.2 Electron Beam LithographyElectron beam lithography can pattern custom two dimensional patterns inthin eletron-sensitive resist layers by exposing them to a focused electronbeam that is scanned over the surface in a computer-generated pattern, witha computer-controlled electron dose. [22]. Compared to traditional pho-tolithography in the silicon industry, EBL has a higher resolution and ismaskless. However, EBL is limited by its low throughput and mainly usedin research and development.Typical commercial EBL systems are very expensive, so this project uti-lized a field emission scanning electron microscope with the beam positionand scan speed controlled by a commercial pattern writing software system(NPGS). At an accelerating voltage of 20 kV , the Gaussian electron beamfocus has a diameter of nominally <5 nm.One key parameter in EBL is the dose, as defined by the total chargeincident per unit area. The charge is controlled by the dwell time of thee-beam at each pixel for a certain value of beam current. For our EBL sys-tem, a square e-beam write field is discretized into 232 square lattice pixels,which gives a minimum point-to-point spacing. However, this minimumspacing is not always available. For a given beam current and area dose,smaller point-to-point spacing leads to shorter beam dwell time per pixel,20but this pixel dwell time has to be above a lower limit that the system canhandle, in our case ~0.2 µsec.The write field size were chosen empirically. For writing contact pads,a write field size of 1425 µm X 1425 µm was chosen as to include contactpads and alignment marks of 3 devices in a column (as shown in Figure 2.6),which gave a minimum point-to-point spacing of 21.74 nm. For writingnanowires, the write field size was 71 µm X 71 µm to include 1 nanowiredetector, corresponding to a minimum point-to-point spacing of 1.09 nm.Figure 2.8: Image of a small part of contact pads and two alignment marksafter development. Nanowires will be pattern between contact pads andconnect with them. Scale bar is 10 µm.When first patterning contact pads and alignment marks, ZEP is used aspositive resist. The accelerated electrons hit the ZEP and break the polymerinto small segments with lower molecular weight, increasing the solubilityin the developer (O-xylene in this case).The fabrication requires two separate EBL processes on the same chip,where patterns from the two process have well defined relative position, i.enanowires should connect with corresponding contact pads. To align thesecond write field to the first, only small regions in the vicinity of the goldalignment markers, formed in the first stage of the process, are exposed tothe imaging SEM beam. By comparing the imaged regions with the knownalignment marker pattern, in three separate alignment marker regions, theoffset and rotation of the coordinate system is corrected before writing thesecond pattern at higher resolution than the first. An image of two alignment21marks is shown in Figure 2.8. This whole alignment procedure can ensurea position precision of submicron level.When patterning nanowires, it is better to use a negative EBL exposuretechnique, because of both writing convenience and final etching process.In this process, a much higher electron dose is applied in areas that onewants the resist to remain after development. At these high doses the poly-mer actually cross-links, rather than fractures, and hence becomes more dif-ficult than the unexposed resist to dissolve in the resist remover (chloroben-zene in this case).Extra care must be taken when patterning nanowires, since the designednanowire width of 80 nm is close to the linewidth limit constrained both bythe type of resist and the EBL system. Normally, the e-beam will draw apolygon in raster style, starting with one edge, and sweeping parallel to thatedge. However, in the nanowire case, such a raster style results in roughedges. Therefore, when patterning a nanowire, the approach is that the e-beam scans along the wire back and forth, as shown in Figure 2.9.When nanowires encounter a 180-degree bend, more careful considera-tions are needed, where the design was mainly to account for current crowd-ing effect (to be elaborated in Section 3.2), and the writing scheme to avoidbig beam jumps in writing (Section 3.4).2.3 Electron Beam EvaporationThin metallic films are typically deposited using an electron beam evapo-rator. The target material sits in a water-cooled crucible that resides in avacuum chamber typically kept below a pressure of ∼5 µTorr. Electronsare extracted from a hot filament and accelerated to bombard the target ma-terial at an energy of ∼ 30 KeV , causing the material to vapourize. Theevaporated metal impinges and sticks to the sample which is suspendedabove the crucible, forming a thin film on the sample surface.In this project, metals were deposited onto the chip after contact padsand alignment marks were uncovered by the first development process on22(a) Normal raster style for writing a pentagon(b) Normal raster style for writing nanowire (narrow rectangle)(c) Special approach for writing nanowires (not treated as a polygon)Figure 2.9: Raster style schematics. Black dashed line indicates the designedpolygon to be write. Blue arrows show the beam sweeps. Red dottedline is the preceding direction of sweepsthe ZEP layer patterned using positive exposure.Gold does not stick particularly well to silicon, therefore an 8 nm thickof titanium layer is first deposited, to which a 90 nm thick layer of goldbonds well. The total thickness of metal needs to be comparable to or thin-ner than the thickness of negative resist used in the second lithography step.When patterning nanowire detectors, the nanowire pattern will extend outand overlap with contact pads to make good connections. If contact pads aremuch thicker than resist, the connection may break and the superconductorunderneath the broken area may not be protected and get etched away in thefinal process, as shown in Figure 2.10.Figure 2.11 shows an SEM image taken after metal deposition, showinga continuous connection across the resist layer has been achieved.23(a) Metal thickness is com-parable to or thinner than neg-ative resist(b) Metal is too thickand causes disconnection, aspointed out by blue arrowsFigure 2.10: Importance of appropriate metal thicknessFigure 2.11: Overlap between contact pad (left) and tapered nanowire (cen-tral strip). Scale bar is 100 nm.2.4 Plasma EtchingDry plasma etching has the advantage of a highly anisotropic etching profileand a small amount of reactants (gaseous) and byproducts, as compared towet etching [23]. For the PLASMAQUEST ECR etcher used in this project,reactant gases are first ionized in the ECR chamber by electron cyclotronresonance effect, which generates even denser plasma than usual reactiveion etcher (RIE).The main chamber was first pumped to < 10−7 torr. Flow rates ofreactant gases CF4 and O2 were adjusted to to 9 and 1.2 sccm respectively,and the operating pressure was set to 30 mtorr. Microwave power wasthen applied to resonantly ionize a dense plasma, and then an RF field wasapplied to the sample chuck to apply a (rectified) accelerating voltage forions of the plasma to strike surface of the sample to be etched. Figure 2.12.Plasma ions will be accelerated and drive plasma toward the sample,24Figure 2.12: Schematic structure of the main reactor chamberwhere both sputtering (by ions) and chemical reaction (with plasma radi-cals) contribute to the etching process.In the etching recipe, CF4 can give effective plasma etching of bothNbTiN and silicon, while a small portion of O2 can remove possible byprod-ucts, mostly carbon. The primary reactive plasma components are:CF4+ e− −→CF+3 +F,so the superconductor and silicon are removed by reacting with fluorineradicals and volatile chemicals such as NbF5, TiF4, SiF4 and so on.25Chapter 3Design3.1 Design OverviewGiven the basic detection mechanism as addressed in the Chapter 1, one nat-urally concludes that: (1) the nanowire meander pattern should be as denseas possible, i.e, a very high filling factor (the ratio of nanowire width overmeander pitch), to maximize the photon absorption rate; (2) the narrowerthe nanowire of an SNSPD is, the more likely a single photon absorptionevent will cause the wire to transition into the normal state, especially forlong-wavelength photons that carry less energy to create large enough localhotspots.The overall layout of the detector design is shown in Figure 3.1, whichis a modified version of Dr. Ahklaghi’s design [3], as mentioned in Sec-tion 1.4. The active detecting area is the central part, about 10 microns indiameter: it is designed to match the spot size of the focused input laser.Surrounding nanowires are dummy lines included to minimize proximityeffects on the perimeter of the main detector meander. The width of thestraight sections of the nanowires is 80 nm and the pitch is 240 nm. The 180degree turns at the ends of the nanowires are carefully designed to avoidcurrent crowding, as discussed in Section 3.2. The input and output endsof the meander wire flare out and connect to large contact pads that are not26shown here.Figure 3.1: Layout of the design.3.2 Current CrowdingMany early meander detectors suffered from a large suppression of the crit-ical current density compared to its bulk value. The cause of this behaviour,which was is referred to as ’constriction’ [17], was identified in 2011 [2011]when Clem and Berggren pointed out that unless carefully shaped, the 180degree bends at the ends of the wires will experience ”current crowding”[10], or a local increase in the current density over its value in the straightsections of the wire.Current crowding is not a new concept. In 1963. Hagedorn and Hallshowed, by means of conformal transformation, that when current in a stripconductor meets a right-angle turn, the current density is higher on the in-side corner of the bend than on the straight strip, for both normal metals anduniform thin superconductors [13]. This fact directly results in the suppres-sion of critical current for SNSPDs.However, Hagedorn and Hall also showed in the same paper that thissuppression at the bend could be eliminated by smoothly shaping the innerboundary, so that the resulting current density is equal or less than that27on the straight strip. The optimal bend shape is usually nontrivial, and ittypically limits the maximum practical filling factor. In fact, to avoid currentcrowding at the 180-degree bend, the filling factor should be no more than33% [3].For thin and narrow superconductors, as in this project, the sheet currentdensity K, to a good approximation, satisfies ∇ ·K= 0 and ∇×K= 0[10].In this project, the MATLAB® PDE (Partial Differential Equation) solveris used to numerically find the optimal geometry for a 180-degree bendconnecting two 80 nm wide wires by solving the analogous electrostaticproblem. The ”electric” potential associated with K is solved for usingappropriate boundary conditions, and its gradient yields the desired K.Figure 3.2: Top view of boundaries of the 180-deg bend. Red boundariesare imposed with Dirichlet boundary conditions and blue boundariesimposed with Neumann boundary conditions. Dashed arrows indicateassumed input/ouput.With reference to Figure 3.2, let n be the normal vector of correspondingboundaries, then we require that K× n = 0 on the red (input and output)boundaries, and that K ·n= 0 on the blue (lateral) boundaries. Without loss28of generality, we apply boundary conditions:V = 1 (upper red edge) (3.1)V = 0 (lower red edge) (3.2)∇V = 0 (blue edges), (3.3)where V is the scalar potential for K. Streamlines of K can then be plotted,as shown in Figure 3.3.Figure 3.3: Calculated streamlines of K with boundary conditions given inFigure 3.2. Black solid lines correspond to the boundary geometry, anddashed lines (red and blue) are streamlines of K.The streamlines in the uniform input and output sections are equallyspaced, indicating a uniform current density in the straight wire regions. In-side (outside) the inner red streamline in Figure 3.3, the current density ishigher (lower) than in the wire. Therefore, an 80 nm wide wire with bound-aries defined by both red streamlines will have the highest current density inthe uniform wire regions. The resulting pattern (fabricated example shownin Figure 3.4) has a filling factor in the uniform wire region of 33% (80 nmwide wires on a 240 nm pitch).29Figure 3.4: SEM image of the meander bend part of a fabricated detector,with the bend optimized with the introduced calculation. The scale baris 200 nm3.3 Proximity EffectWith reference to Figure 3.5, the ideal electron beam for lithography pur-poses would be focused to the smallest spot size allowed by the machine,on the Photoresist mask material, and all of the modification of the resistby the electrons would be limited to the material within that focused spot(typically just a few nanometres). However, electrons scatter from the resistand backscatter from the underlying substrate, modifying the resist over anarea considerably larger than the focused spot size. These scattered elec-trons thus modify the overall pattern of exposed resist from the pattern thatthe computer directs the beam to follow. For instance, if trying to write a setof parallel 80 nm lines on different pitches, the closer the pitch approaches80 nm, the wider the individual wires will become, due to excess exposurefrom adjacent wires. This phenomenon is known as the ”proximity effect”.There are two types of scattering happening when an electron beam isincident on the chip: forward scattering and back scattering. Each of themapproximately gives a 2-dimensional Gaussian exposure profile around theincident point, with 1/e radii being σ f and σb respectively [25]. Forwardscattering occurs when the beam electrons collide with electrons attached toatoms in the resist or substrate. During the collision, electrons from atomsget excited or even ionized, and the incident electrons lose energy and their30Figure 3.5: Schematic for proximity effect: area surrounding the exposurepixel get exposed.trajectory can deviate from the original direction for some angle. For thiskind of rather inelastic collision, the deviation angle is generally small. Theeffect of forward scattering can be estimated according to the empiricalequation [27]:σ f = 0.9(Rt/V )1.5, (3.4)where Rt is the resist thickness in nm and V is the EHT voltage of theelectron beam in kV .In this case, given the ZEP thickness of about 156 nm and the EHT volt-age of 25 kV , σ f is roughly 14 nm. Since the spacing between nanowires aredesigned to be 160 nm, there should be little influence of these inelasticallyscattered electrons from writing one wire, on the adjacent wire. Thus theactual dimensions of the nanowires in the meander pattern should be almostunaffected by this inelastic scattering (i.e. they should retain the dimensionsprogrammed into the beam patterning software).The real problem comes from back scattering, when the incident elec-tron beam collides with a heavy nucleus, especially those in the substrate.Such collisions are elastic, so electrons retain most of the kinetic energy andscattering angles can be large. Since the associated σb depends strongly on31Figure 3.6: Two types of scattering. Blue line is an example trajectory of aforward scattering electron. Red line is an example trajectory of a backscattering electron.substrate and electron energy, it is usually determined empirically. Basedon information in [15], σb should be around 1 µm for the SOI wafter andan EHT voltage of 25 kV .Since this extended area of electron dose is much larger than the wire-to-wire separation in the middle of the detector meander pattern, the wireswill typically be wider than the intended width as defined by the patternfollowed by the electron beam. This aspect of the ”proximity effect” isrelatively simple to deal with, by reducing the width of the lines defined bythe electron beam.There is an additional impact of the proximity effect at the extremi-ties of the 9 µm diameter meander pattern, since there is a relative lackof backscattered electrons effecting the dose in these regions (no beam isscanned outside the pattern). If only the 9 µm diameter meander patternwas written, The size and shape of the wires and 180-degree bend regionswould be distorted. To mitigate this problem, a set of dummy lines (notconnected to the meander), are written in a circular disk surrounding thedetector region (see Figure 3.1).The dummy lines are meant to ensure that the overall exposure of thewires of the ends is similar to that in the middle of the meander. They arestraight nanowire strips designed to have identical width and spacing as themain meander, but not connected to the main meander.32As a rule of thumb, the farther the dummy line area extends, the moreuniform the exposure at the centre will be, and the uniformity should even-tually saturate at some spatial extension of the dummy line area. Givenσb ∼ 1µm, the width of the dummy line disk was chosen to be 10 µm tominimize the overall time required to write the patterns, and the dummylines had a gap of 160 nm from the ends of the meander wires.3.4 Sequencing IssuesOnce the sample is aligned and the translation stage is moved so that thearea to be written is centred on the electron beam’s field of view, the com-puter takes over control of the electron beam position and raster speed.When writing continuous patterns the beam effectively makes small, dis-crete steps across the pattern, dwelling for a certain amount of time at eachpoint according to the required exposure dose. When jumping from onecontinuous patterned area to another, a relatively large jump in voltage oc-curs across the beam steering electrodes. The larger the jump, the moresignificant ”ringing” artifacts may be, thus it is desirable to minimize theneed for large voltage jumps. Another practical consideration for choos-ing the patterning sequence has to do with the potential drift in the system(beam and translation stage). Adjacent objects that require very accuraterelative positioning should ideally be written in sequence.Taking these issues into consideration, the first step in the exposure con-sists of writing the entire meandering nanowire pattern, from the bottomdummy to the top dummy line, including central meander area and flaredinput/output wires. As explained in the text associated with Figure 2.9, theindividual nanowires are written using multiple raster scans parallel to thewire axis, and the subtlety is to alternate the starting point in each wire,from left to right etc., in order to minimize the voltage jump on going fromwire to wire.The dummy line writing scheme and meander nanowires (particularly at180-degree bend) are illustrated in Figure 3.7 and Figure 3.8 respectively.33Figure 3.7: Scheme of writing dummy lines in sequence (from bottom to top)to avoid large jumps. Green box indicates nanowire. Blue solid anddashed arrows show direction of beam rastering and jump respectively.Blue circular dots mark the beginning of nanowires.Once the meander and dummy line sections are completed, the beammust jump by a large amount to start writing one of the relatively widewires that connects the flared input wire with the contact pad (see the or-ange outline in Figure 3.1). After writing that connecting wire, the beammust jump a large amount once again, to write the connecting wire fromthe output flared nanowire to the other contact pad. It was found that thealignment of these final connecting wires with the flared nanowires variedrandomly from device to device, and this was attributed to drift (see Fig-ure 3.9). To overcome this, a large rectangular termination to the flaredregion was added, to ensure that the two would make contact despite thisdrift issue. This rectangle was written as part of the connecting wire. Anexample is shown in Figure 3.10.3.5 Residual ImperfectionsWhile careful control of the beam rastering sequence led to major improve-ments in the fabricated devices, there still remained unresolved issues. Themost significant is illustrated in Figure 3.11, where the shape of some of the34Figure 3.8: Writing scheme for a nanowire bending. Two nanowires (blueand green lines) forming a 180-deg bending. Solid lines with arrowsare beam writing path. Dotted lines are beam jump. Grey region isfor normal raster style (see Figure 2.9). The number of lines defining ananowire needs to be odd to avoid big beam jumps (5 lines are illustratedhere). Circles and squares are starting and ending points of the nanowirerespectively.Figure 3.9: Improper connection between tapering and tapered nanowire.Blue dashed lines are designed pattern, where triangular tapering partwas patterned in the writing sequence of the circular region, while therectangle tapered part was patterned in the end. The scale bar is 1 µm180 degree bends is distorted. The reasons isn’t clear, partly because thiswas a seemingly random, and infrequent occurrence.It may possibly be related to the ”charging effect” common in EBL ap-plications involving insulators. When electrons are incident on resist, theycan accumulate on exposed areas. The negatively charged resist can gener-35Figure 3.10: Rectangle junction to tolerate shift. Blue dashed lines are de-signed pattern. The scale bar is 1 µmFigure 3.11: Distortion at the bend. Scale bar is 200 nmate a repulsive electrical force on the electron beam resulting in a distortionof the pattern. In order to reduce the effect when patterning nanowires, thesmallest e-beam aperture (φ = 10µm) was used to minimize the beam cur-rent, and thus maximize the dwell time of the beam at each pixel. The aimwas to give more time for any accumulated charges to dissipate.36Chapter 4Experiment Method4.1 Experiment DesignThe experiment set-up consisted of an electronic part and an optical part:these are described separately the in the following subsections.4.1.1 Electronic PartFigure 4.1 shows a schematic diagram of the electronic components in thesystem, all of which were designed, assembled, and tested by Dr. Ahklaghiprior to the start of this thesis work. The SNSPD is DC-biased, and when itabsorbs photons, the resulting high frequency signal is capacitively coupledto a low noise amplifier LNA, and further amplified before being input tothe counter.The counter used here is a PicoHarp 300. The SNSPD chip is wire-bonded to the circuit board which was placed in a liquid He bath withinan optical cryostat (SVT-300, Janis Inc.). An Edwards mechanical vacuumpump was used to pump on the liquid He reservoir, reducing the temperatureto 2.1 K. This is well below the superconducting critical temperature ofNbTiN (8.4 K in bulk form), and the He critical temperature, so there wereno bubbles in the chamber to scatter incident radiation.Figure 4.2 shows photos of the final chip and electronics.37Figure 4.1: A schematic diagram of the electronics set-up. Parts enclosed bythe blue dashed line are inside the cryostat. The SNSPD is in series withan inductor L (100 nH) and resistor R (100 Ω). C is capacitor (122 pF)and LNA is low noise amplifier(a) Final chip with a quarter coin. The chip is mounted on a cryostat sample holder, andwire-bonded to electronics(b) Our customized circuit board outside the cryostat.Figure 4.2: Photos of the final chip and electronics.4.1.2 Optical Power Calibration ApproachThe purpose of the optical system was to deliver a calibrated optical powerof HeNe laser radiation (lambda=632.8 nm) on the 9 µm diameter activearea of the detector. Two possible schemes were considered, as shown in38Figure 4.3.(a) Small laser spot (b) Large laser spotFigure 4.3: Two possible schemes for obtaining actual input power on thedetector area. The schematic of the detector only shows the active area,(dummy lines are omitted). Blue circular shade indicates laser spot.The first scheme is to focus the laser to a spot considerably smaller thatthe 9 µm diameter detecting area. In this case, one would only have to mea-sure the laser beam power hitting the sample to know the incident photonrate on the detector. The main reasons for abandoning this approach were i)getting an∼ 5 µm diameter beam focused on the sample, inside the cryostatusing external optical components is challenging, and ii) vibrations in thelaboratory would cause the beam to move randomly on and off the detectorarea during the experiment.The second scheme involves a focused light spot much bigger. In thiscase, if the concentrically focused laser is known to be Gaussian with awell-defined beam waist and total power, the fraction of that power incidenton the small detector can be easily calculated. If sufficiently oversized,uncertainty/variation in the incident power due to vibration-caused beamshifts can be largely reduced. Therefore, the second scheme was adopted inthis project.Suppose the laser has been centred at one SNSPD, with on-chip laserbeamwidth w, the optical intensity profile of the on-chip fundamental T EM00Gaussian is then given by [32]:I(r) = I0(w0w)2exp(−2r2w2), (4.1)where r is the distance from the point of evaluation to the Gaussian centre,39I0 is the maximum intensity (at r = 0) and w0 is the beamwidth at beamwaist. The optical power within a radius R can be obtained by integratingI(r):P(R) =∫ R0I(r)2pirdr. (4.2)Setting R = ∞, we can calculate the total beam power:Ptot =∫ ∞0I(r)2pirdr=I02(piw20).Setting R = rd , the detecting area radius of the SNSPD that sits at thecentre of the beam, we can calculate the actual input power:Prd =∫ rd0I(r)2pirdr= Ptot [1− exp(−2r2dw2)].From the above, a ratio of Prd/Ptot can be calculated:Prd/Ptot = Rp = 1− exp(−2r2dw2). (4.3)The Laser power Ptot can be easily measured with a optical power me-ter, rd can be directly measured from SEM images of the SNSPDs, and thebeamwidth w can be measured using the knife edge technique (see Sec-tion 4.3).4.1.3 Optical Set-upFigure 4.4 shows the optical set-up for the cryogenic experiment. Twoknobs for tilt adjustment on mirror M2 allow the laser spot on the sam-40ple chip to be repositioned, along the x and y directions respectively. In theactual experiment, M2 is used to sweep the laser spot and find the positionthat maximized the count rate of the detector signal. Then the SNSPD isconsidered to be at the centre of the laser spot. Uncertainties associatingwith this part will be further discussed in Section 4.3.Figure 4.4: Optical set-up. HeNe laser (λ = 632.8 nm) is through neutraldensty filter set (NDF1) and directed via mirrors M1 and M2 to a po-larizer plrz. Power meter PM is used to measure the power of polarizedlight. The meter is then removed and light goes through another pre-calibrated set of neutral density filters NDF2 for precise attenuation.Then light goes through cryostat windows and normally incident on thesample.The adjustable polarizer plrz polarizes the input laser. The two polariza-tions of interest were parallel and orthogonal to the nanowires. The powermeter PM is a detector head (Spectra-Physics Model 404) directly fed intoan oscilloscope (Tektronix TDS 350), giving a sensitivity of 10 nanowatt.The choice of NDF1 and NDF2 is not trivial, but is decided accordingto the constraints of both the PM range and the maximum count rate of thecounter (up to 10 MHz, which corresponds to a power of ∼ 3.14 picowattof red photons).Based on this set-up, a calibrated input power for an SNSPD can beobtained:Pin = PPM×TNDF2×Twindow×Rp, (4.4)41where PPM is the power measured by power meter PM, TNDF2 is the trans-mission of neutral density filters set NDF2, and Twindow is the transmissionof the cryostat windows.4.2 Measuring Cryostat Window Transmission TwindowThe set-up for measuring the cryostat windows transmission is as in Fig-ure 4.5.(a)(b)Figure 4.5: Measuring cryostat windows transmission. BS is beam splitter.Reflector is a silicon chip.Suppose the readouts from power meter PM in Figure 4.5a and Fig-42ure 4.5b are P1 and P2 respectively. They can be expressed as:P1 = P0 ·TBS ·Twindow ·Rre f ·Twindow ·RBSP2 = P0 ·TBS ·Rre f ·RBS,where P0 is the power of the laser measured right after mirror M2, TBS andRBS are the transmission and reflection of the beam splitter respectively, andRre f is the reflection of the silicon reflector chip.The transmission through the windows can then be calculated as:Twindow =√P1/P2. (4.5)Using this method, a transmission of Twindow = 0.85±0.01 is observed.There are two windows (outer and inner) in the light path, which haveidentical thickness of ∼ 0.48 cm. The simulation based on normal inci-dent Fresnel equations suggests a transmission of 0.9332 = 0.87±0.08, asaveraged for wavelengths around λ = 632.8 nm, for the window materialSUPRASIL™2. The measure transmission is therefore reasonable.4.3 Measuring Beamwidth w: Knife Edge MeasurementIn order to calculate Rp in equation 4.4, it is essential to measure the beamwidthof the focused laser spot on-chip.4.3.1 Knife Edge MeasurementThe Knife edge technique [1] is a common way to measure beamwidth andto evaluate the quality of a Gaussian beam. The basic set-up for such ameasurement is shown in Figure 4.6.Rewriting the optical intensity equation 4.1 in Cartesian coordinates(origin at beam centre), and supposing the knife edge in Figure 4.6 is placedat position x, the unblocked power can then be evaluated by this integral:43Figure 4.6: Knife edge experiment. Straight knife edge translates along x-axis, cutting through Gaussian beam and blocking a part of it. Resultingunblocked power is measured by a power meter.P(x) = Ptot− I0(w0w )2∫ x−∞exp(−2x2w2)dx∫ +∞−∞exp(−2y2w2)dy= Ptot− I0(w0w )2√pi2w∫ x−∞exp(−2x2w2)dx= Ptot− I0(w0w )2√pi2w[∫ 0−∞exp(−2x2w2)dx+∫ x0exp(−2x2w2)dx]= Ptot− I0(w0w )2√pi2w[√pi8w+∫ x0exp(−2x2w2)dx]= Ptot− I04 (piw20)−∫ x0exp(−2x2w2)dx=Ptot2− I0(w0w )2√pi2w∫ x0exp(−2x2w2)dxThe remaining integral in the above result is essentially an error func-tion. With a change of variable:I0(w0w)2√pi2w∫ x0exp(−2x2w2)dx =I04(piw20)∫ √2xw0exp(−u2)du=Ptot2er f (√2xw).44Therefore,P(x) =Ptot2[1− er f (√2xw)] (4.6)Finally, we have a fitting model for determining beamwidth w:P(x) =Ptot2[1− er f (√2(x− x0)w)], (4.7)where x0 is an offset parameter such that x coordinates don’t have to bemeasured from the beam centre.By translating the knife edge over a series of x coordinates, recordingthe corresponding power P(x), Ptot , x0 and w can be obtained by fitting withthis model.4.3.2 Measuring BeamwidthSince the sample is located in the cryostat, where it is impossible to performa knife edge measurement, the procedure shown in Figure 4.7 was devised.Figure 4.7: Beamwidth measurement. The laser is pulled back a distance dand the beamwidth of a position at distance d from the sample positionis measured.Figure 4.8 shows the data and fitted curve of the knife edge measure-ment. According to the measurement, a beamwidth of 1.025 ± 0.009 mmis obtained. From Equation 4.3, this means Rp = 3.93×10−5. It should be45Figure 4.8: Knife edge measurement data and fitted curve.noted that although the ’sample point’ and laser are both pulled back at dis-tance d, the light path is different. In the actual experiment, light has to gothrough the cryostat windows described above. The thin windows slightlyshift the position of the beam waist axially, but calculations show the netimpact on the above estimate is negligible.4.3.3 Uncertainty SummaryThe overall uncertainty of the incident power on the detector due to themeasurement uncertainties of the laser power, window transmission, andbeam waist at the sample is ∼ 5%. This is negligible in comparison to thenoise in the detected count rate, due to vibrations of the cryostat from thevacuum pump, as documented in the following chapter.46Chapter 5Results5.1 Absorption SimulationFigure 5.1: Simulated structureThe absorption of the nanowire array is simulated using Lumerical®FDTD Solutions, with the geometry the unit cell shown in Figure 5.1, on a240 nm pitch. The refractive indicies of ZEP (nZEP = 1.5539) and NbTiN(nNbTiN = 1.7+ 2.8i) at wavelength λ = 632.8nm are calculated from theZEON product data sheet and [9] respectively. This cross section of an infi-nite (into the page) nanowire was periodically replicated in the simulation,and it was excited by a normally incident plane wave.47The exact widths of the wires, the etched silicon depth, the residualZEP layer thickness, and the silica layer thickness are not known, sinceit would be necessary to destroy the detectors to measure them. As de-scribed in Chapter 2, a number of detectors were made with slightly differ-ent doses chosen to bracket the target wire width of 80 nm. From detector1 to 12, nanowire width was designed to gradually increase. The SEM im-ages shown in the previous chapter are all taken of the largest wire widthdetector 12. Its measured width is∼90 nm, which roughly indicates a rangeof widths for all detectors of between 70∼ 90nm.Apart from the bracketing design, some other variations due to fabrica-tion uncertainty should also be taken into consideration in simulations. Thethree most important variations are: (1) ±10nm of residual ZEP thickness(under go spin-coating and plasma etch); (2) ±5nm of silicon etch depth;(3) ±10nm of silica (BOX) layer thickness.Given all of these uncertain, but bounded parameters, the absorption ofthe structure was calcualated as a function of wire width, silicon etch depth,ZEP layer thickness, BOX layer thickness, for plane waves polarized paral-lel and perpendicular to the wire axis. The results are shown in Figure 5.2 -Figure 5.5 respectively.For each of the absorption simulations, a range of parallel and perpen-dicular polarized absorption values, and their ratios can be calculated foreach of the independent unknown device parameters in the simulations. Bytaking the average of the mean values and adding uncertainties quadrati-cally, the overall simulated absorption values and their ratio are:P‖ = 3.34%±1.01% (5.1)P⊥ = 2.91%±1.05% (5.2)ratio = 1.1562±0.1643 (5.3)The absolute values of the absorptions are very low because the structureof the SOI wafer on which the meander wires were fabricated results in there48Figure 5.2: Simulated absorption of nanowire versus its width. Blue solidand dashed lines correspond to a source polarization that is parallel andperpendicular to nanowire respectively. Red line is the ratio of two ab-sorption (parallel over perpendicular)Figure 5.3: Simulated absorption of nanowire versus ZEP thickness. Thecolour coding is the same as the previous figure.being a near anti-node of the incident plus reflected (from the multi-layer,high refractive index stacked structure) field right at the silicon surface (seeFigure 5.6 and Figure 5.7). These wafers were originally designed and usedto fabricate SNSPDs on silicon waveguides carrying light in the plane of thesilicon device layer. Others have designed substrates optimized to produce a49Figure 5.4: Simulated absorption of nanowire versus silicon etch depth. Thecolour coding is the same as the previous figures.Figure 5.5: Simulated absorption of nanowire versus BOX thickness. Thecolour coding is the same as the previous figures.near node in the incident plus net reflected field in the nanowire plane [28],and the current detectors could readily be fabricated on such substrates,increasing their absorption considerably.The absorption efficiency is basically the upper bound of the QE, sincethe detection mechanism explained in Chapter 1 shows that the absorptionof a photon does not necessarily results in the detection of it. Biasing thenanowire at a current closer to critical current can increase the QE for a50Figure 5.6: Simulated E field of source polarization along z axis, parallel tonanowires.Figure 5.7: Simulated E field of source polarization along x axis, perpendic-ular to nanowires.fixed absorption efficiency, but this also increases the intrinsic dark countrate, as shown below.5.2 Experiment ResultsFigure 5.8 shows the IV curves of the two detectors in super fluid Helium.The curves indicate good electrical connection of detectors, and the turn-ing points show clearly the breakdown of superconductivity at slightly dif-51ferent critical currents of 5.24 µA and 8.28 µA for detector 1 and 4 re-spectively. Because of the bracketing in fabrication, detector 4 has a widernanowire and thus higher critical current, as expected. However, the sup-plementary information of [4] shows a value of ∼29 µA is measured froma short straight 80 nm wide nanowire at the same temperature, of the samematerial and with the same set-up. The most likely explanation is a residualcurrent crowding effect due to fabrication imperfections in the 180 degreebends of the meander. A similar detector with a nominal nanowire width of80 nm in [3] has a critical current of ∼14 µAFigure 5.8: IV curves of detector 1 (blue curve) and 4 (red curve), at temper-ature T = 2.05K.Figure 5.9 shows an electric pulse detected using detector 4 and a fastoscilloscope. The negative polarity of the pulse is set on purpose to make itcompatible with the counter, and the frequency cut-offs of the chain of am-plifiers results in an under-damped shape, and cannot provide an estimationof detector reset time [4].In this project, timing performance is not directly measured. However,the reset time can be roughly estimated using a calculation from [11]. OurSNSPD has a kinetic inductance of Lk ∼ 300 nH and with the resistor andinductor integrated as in Figure 4.1, the reset time can be estimated as τ =(Lk + L)/R = 4ns. A 4 ns reset time corresponds to a count rate of 25052MHz.Figure 5.9: Electric pulse picked up by fast oscilloscope. Vertical scale is 50mV/div and horizontal scale is 5 ns/div.Figure 5.10 and Figure 5.11 show measurements of the QE for twosource polarizations: parallel and perpendicular to the nanowires respec-tively, where error bars are due to fluctuations of counts read from thecounter.As can be seen from the figures, the QE versus bias current shows anearly saturation for both polarizations. When increasing bias current, theSNSPD becomes more sensitive to photons, but the measured photon countstops increasing. This is not an artifact of an incident photon rate that ex-ceeds the detector count rate, since the maximum count rate was estimatedto be 250 MHz, while the maximum incident photon rate was ∼ 10 MHz.According to Figure 5.10 and Figure 5.11, the measured QEs are:QE‖ = 2.30%±0.63% (5.4)QE⊥ = 2.57%±0.72% (5.5)ratio′ = 0.90±0.35 (5.6)The measured QEs and the polarization ratio therefore agree with simu-53Figure 5.10: QE and background count rates versus bias current for parallelpolarization.lated results in equation 5.1, 5.2 and 5.3, within the (relatively large) mutualuncertainties.The saturation of the QE suggests that in that saturated range of biascurrents, every single photon that is absorbed by the nanowire is detected.Furthermore, the saturation happens when the bias current is about 4.5 µA,with the critical current being 8.28 µA.As a comparison, Figure 5.12 shows the QE and intrinsic dark countrates measured for the detector reported in [3], from which the design isadopted for this project. Recall from Section 1.4,that these detectors arevery similar in structure to those made in this thesis project, but they werefabricated on a substrate designed to maximize the absorption of 1.55 µmwavelength photons. While the optimized substrates result in much highermaximum QEs of these detectors, note that they do not exhibit saturationwith bias current. This difference in saturation behaviour can be at leastqualitatively explained by noting the nearly factor of two difference in en-ergies of 1.55 µm and 632.8 nm wavelength photons. Recall that the causeof a detection event is the formation of a resistive barrier, upon the local54Figure 5.11: QE and background count rates versus bias current for parallelpolarization.absorption of a single photon which depends on the significance of photon-induced local ’hot spot’. If the incident photon has weak energy (long wave-length), the induced ’hot spot’ will be less significant, which is more likelyto fail in formation of resistive barrier. Therefore, to enhance detection oflonger wavelength photons, the bias current has to be set closer to the crit-ical current. In other words, the saturation bias current is expected to becloser to the critical current for 1550 nm photons, as compared to 632.8nm photons, which is at least qualitatively consistent with the data in Fig-ure 5.12.The significance of the saturation of the QE with bias current can best beunderstood from Figure 5.12. Both the QE and the intrinsic (no background(eg. black body) photons present) dark count rates increase with bias currentbelow the critical current. The intrinsic dark count rate increases exponen-tially, so the more saturated the QE curve, the lower the bias current youcan operate at, and hence the lower the intrinsic dark count rate. The data inFigure 5.10 and Figure 5.11 does not show the exponential behaviour of thedark count rate because it was impossible to sufficiently shield the detector55Figure 5.12: QE and dark count rate (of photons with wavelength 1550 nm)versus bias current of the detector shown in Figure 1.11. Dashed linesmark optimal bias current. Figure taken from [3].from black body radiation. However, assuming that the dark count rate dueto this black body radiation also saturates for our detectors, a constant valuecan be subtracted off of the total dark count rate to obtain an estimate ofthe intrinsic dark count rate. The results of doing this subtraction for bothpolarization data sets is shown in Figure 5.13. Within the uncertainties, theresults are independent of incident polarization, as they should be.The relation between SNSPD dark count rate (DCR) and ratio of biascurrent over critical current I/Ic has been studied in detail: [34] gives a rig-orous explanation of the origin of dark count based on current-assist vortex-antivortex pair unbinding rate. Empirically, a relation DCR∝ exp I/I0 is ob-served [18]. Figure 5.13 shows estimated dark count rates, curves are fittedwith exponential functions.56Figure 5.13: Estimated dark count rates. Blue and red lines correspond toa source polarization that is parallel and perpendicular to nanowirerespectively. Curves fitted with an exponential function.57Chapter 6Conclusion6.1 Project SummaryIn this project a circular meander design of a free-space SNSPD was fab-ricated and tested in house. Although the absolute absorption efficiency ofthe detector is low (∼ 3% at temperature 2.05 K), because it was fabricatedon a substrate optimized for other applications, the measured QE and mod-elled nanowire absorption efficiency for incident polarizations both paralleland perpendicular to the wire axis agree within the uncertainties.The absorption efficiency remains flat (saturated) for bias currents above0.5 Ic. The intrinsic dark count rate at a bias current of 0.7 Ic was measuredto be ∼ 100 Hz at 2.05 K. Assuming a continuing exponential falloff atlower bias currents, the detectors should operate at maximum absorptionefficiency down and an intrinsic dark count rate of < 1 Hz at a bias currentof 0.5 Ic. These results suggest that using the same patterning techniquesand electronics, very useful in-house detectors at a wavelength of 632 nmcould be fabricated on appropriate substrates.The total cost of the SNSPD element including the chip, circuit boardsand nanofabrication equipment usage is conservatively estimated to be <$10K, which is significantly lower than the commercial element cost (onthe order of ∼ $50-100K).586.2 Future WorkThe highest priority extension of this work is to design and source or fabri-cate a substrate that would locate an antinode of the total field in the planeof the superconducting layer. Based on the literature, it should be possi-ble to obtain QEs on the order of 90%. Once this problem is solved, thenthe next highest priority is to develop a robust packaging scheme to convertthese detectors into useful laboratory instruments.A longer term project would involve exploring the potential benefits ofalternate superconducting materials, such as WSi.For example, to date a new material WSi is spreading its influence inthe field of SNSPDs rapidly. The lower superconducting gap energy of WSicompared to NbN/NbTiN makes WSi nanowires more sensitive to photons(larger ’hot spot’), resulting in a higher QE and earlier saturation [6]. Mostof the work in this thesis should carry over directly to samples made fromWSi rather than NbTiN.59Bibliography[1] Knife edge measurement.http://massey.dur.ac.uk/resources/grad skills/KnifeEdge.pdf, January2017. URLhttp://massey.dur.ac.uk/resources/grad skills/KnifeEdge.pdf. →pages 43[2] Npgs website. http://www.jcnabity.com/, January 2017. → pages 17[3] M. K. Akhlaghi, H. Atikian, J. F. Young, M. Loncar, and A. H.Majedi. 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