Detectors based on Magnesium Diboride
Simone Frasca
imply its endorsement by the United States Government or the Jet Propulsion Laboratory, California Institute of Technology.
The 2000’s will be remembered as the era of microsatellites. Thanks to
the compactness and lightness of the technology instrumentation, sending
in orbit smaller satellites is going to be the cheapest way to perform space
exploration. However, reducing the dimensions of the satellites is going
to underline even more one of the critical aspects of today’s and future’s
missions: the data transfer. The main constraint is the data rate of these
relatively small satellites. Also, due to planets and moons rotation, the
so-called telecommunication windows for interplanetary missions are pretty
narrow, which make big data transfers hard to perform.
Moreover, with the improvement of technology, the required data rate
will certainly increase, hence finding a way to increment the communication
bandwidth is a primary issue to improve future space mission efficiency.
From these considerations, the idea of optical telecommunication
sys-tems has grown in the last decade, and the Superconducting Nanowire Single
Photon Detectors (SNSPDs [1]–[2]) has proven to be an excellent candidate
to perform the role of the system detector. To date, this technology has yet
[3].
Optical telecommunication provides some advantages with respect to the
classic RF technology, as higher bit rates and immunity to electromagnetic
interference, i.e. it looks like the ideal technology for deep-space data
trans-mission. If working, an optical telecommunication system would provide 10
to 100 times the state-of-the-art RF system (Ka-band) capability, without
increasing the mission burden in mass, volume, power and/or spectrum.
SNSPDs are prevalently made of niobium nitride (NbN), tungsten
sili-cide (WSi), MoGe, niobium silisili-cide (NbSi), tantalum nitride (TaN).
Cur-rently SNSPDs are state-of-the-art in near IR single photon detection. WSi
SNSPDs have 90% system detection efficiency (SDE), low timing jitter
(50-100 ps), high max count rates (20 Mcps) and have wide spectral sensitivity
(UV to mid-IR).
However, WSi SNSPDs require sub-Kelvin temperatures to operate
op-timally, which means the cryogenics become complex, expensive, large and
resource intensive. To date, no SNSPD made of these materials has been
demonstrated to work above 10K, while NASA has a flight heritage in flying
compact cryocoolers at temperatures greater than 20K.
The purpose of this thesis will be a study about the feasibility of a ”high
critical temperature” material SNSPD, in particular devices made of
mag-nesium diboride (MgB2). Magnesium diboride has a critical temperature of 39K, which makes it one of the best candidates for easy-to-fly optical
We demonstrated single-photon sensitivity up to 18K for 1.55-µm light, which is the most interesting wavelength for optical telecommunication
pur-poses. However, some unexpected behaviors affect our devices, which will
This work was developed as my master thesis during my intern at Jet
Propulsion Laboratory, California Institute of Technology. This work was
possible thanks to the help of all the people around me, friends, colleagues
and family. I would like to thank in particular:
My thesis advisor Prof. Alessandro Quarta who has been patient with
me and has supported me during these tough months despite the huge
distance. Big thanks to Dr. Francesco Marsili and Dr. Matt D. Shaw,
who gave me the chance to come at Jet Propulsion Laboratory in the first
place.
My project advisor and mentor Angel E. Velasco, who I had the chance
to work with for almost the whole time at JPL. His continuous explanations
were the main sources for my personal growth during the whole internship
duration. I will never be grateful enough for that.
My team colleagues Emma E. Wollman and Jason P. Allmaras, who
helped me lots of times with their experienced comments and advices. It
was my pleasure to have the chance to work with you all.
re-member of a day in Pisa without any of the two of you. Of all I accomplished
during these two and a half years, more than just ”a part” of the merit is
yours. Also, a big thank you goes to Francesco, Antonio and Alessandro:
your presence and friendship helped me growing intellectually, and I am
extremely grateful to you all for that.
My family, who supported me every single day of my life, included this
adventure on the other side of the world. Without you I wouldn’t be the
person I am today, so, sincerely, thank you for the job you all did.
But the most special thanks go to my brothers. Federico and Alessandro
are the strongest reason why I realized all I accomplished so far, and for
sure they are the reason why I won’t stop doing my best, to make them
proud of their older brother. I love you.
This research was carried out at the Jet Propulsion Laboratory,
Califor-nia Institute of Technology, and was sponsored by the JPL Visiting Student
Research Program (JVRSP) and the National Aeronautics and Space
Abstract I
Acknowledgments III
1 Superconducting Nanowire Single Photon Detectors:
The-oretical Overview 1
1.1 The Hotspot Mechanics . . . 2
1.2 Optical Characterization . . . 4
1.2.1 Statistical Approach of Detection Events . . . 6
1.3 Electrical Characterization . . . 8
1.3.1 The Latching Effect . . . 13
1.4 Uncertainties Characterization . . . 15
1.4.1 The System Dark Count Rate . . . 16
1.4.2 The Afterpulsing Effect . . . 17
2 Devices Fabrication Process 20 2.1 Depositions Techniques . . . 21
2.1.1 MBE . . . 21
2.1.2 HPCVD . . . 23
2.2 Devices Writing Process . . . 25
3 Testing Process 28 3.1 Set-up Description . . . 29
3.3 The R vs T characteristics . . . 39
3.4 Photo-sensitivity Tests . . . 41
3.4.1 Single- or Multi-Photon Sensitivity Test . . . 43
3.4.2 Device Detection Efficiency and Afterpulsing . . . 44
4 Best Devices Results 50 4.1 v40 S4-3H . . . 52 4.2 v42 2B . . . 58 4.3 v43 5G . . . 62 4.4 Last Devices . . . 67 5 Conclusions 69 Bibliography I
1.1 The hotspot generation sequence . . . 3
1.2 Example of SNSPDs geometries . . . 5
1.3 Example of Single- and Two-photons detection events . . . . 7
1.4 DDE vs Ibias for a device capable of reaching QE saturation [3] 8 1.5 Pulse’s Rise and Fall times . . . 9
1.6 Example of paralysis on a scope trace . . . 15
1.7 Difference between a not-afterpulsing and an afterpulsing be-havior . . . 17
2.1 AFM image of as-grown (a) and rapidly-annealed (b) films [39] . . . 22
2.2 Surface morphology of films grown on different substrates . . 23
2.3 Image of surface morphology grown at 70 (A), 60 (B), 50 (C) and 40 (D) torr [37] . . . 24
2.4 Surface morphology of films grown at different thicknesses . 24 2.5 Fabrication process . . . 26
2.6 Examples of devices’ geometries . . . 27
2.7 Example of devices’ geometries with the addition of ”dummy wires” . . . 27
3.1 Device to SMP interface . . . 29
3.2 Equivalent electrical circuit of our set-up . . . 31
3.3 I –V curve . . . 33
3.5 I –V curve measured first increasing and then decreasing the
bias . . . 36
3.6 I –V curve with hotspot plateau . . . 37
3.7 Set-up scheme of the Fast–Isw measurement [44] . . . 38
3.8 Expected scope readout of the Fast–Isw measurement [44] . . 38
3.9 Fast–Isw measurement results . . . 39
3.10 Classic R vs T characteristic . . . 41
3.11 Classic shape of a Pulse . . . 42
3.12 Difference in the photo-sensitivity curves for a single- and a three-photons sensitive detectors. . . 45
3.13 DDE vs Ibias/Isw curve for a single-photon sensitive detector at different temperatures . . . 46
3.14 Classic DDE vs T curve . . . 47
3.15 Afterpulsing usual scope trace . . . 48
3.16 Inter-arrival time of an afterpulsing device . . . 49
3.17 Inter-arrival time of a not-afterpulsing device . . . 49
4.1 Design image of the Mask used for fabrication. . . 51
4.2 v40 S4-3H . . . 53
4.3 I –V characteristic of v40 S4-3H at different temperatures . . 53
4.4 R vs T characteristic of v40 S4-3H . . . 54
4.5 Single-photon sensitivity test at 1.55-µm wavelength for v40 S4-3H, T = 18K . . . 54
4.6 Pulse track of v40 S4-3H at three different temperatures . . 55
4.7 Inter-arrival time measurements of v40 S4-3H at three test temperatures . . . 55
4.8 DDE vs T curve of v40 S4-3H at Ibias/Isw = 99% and 99.5% 56 4.9 Pulses’ Peak to Peak amplitude vs T curve of v40 S4-3H . . 57
4.10 SDCR vs Ibias curve of v40 S4-3H at multiple temperatures . 58 4.11 v42 2B . . . 58
4.13 DDE vs T curve of v42 2B . . . 60 4.14 Rpolariz vs T measurement of v42 2B . . . 61
4.15 Inter-arrival time measurement of v42 2B at T = 9K . . . . 61 4.16 v43 5G . . . 62 4.17 I –V characteristic of v43 5G at different temperatures . . . 63 4.18 R vs T characteristic of v43 5G . . . 64 4.19 DDE vs T curve of v43 5G . . . 64 4.20 Persistance traces of v43 5G pulse at different temperatures 65 4.21 DDE vs T curve of v43 5G, making the distinction on the
trigger level . . . 66 4.22 Pulses’ Peak to Peak amplitude vs T curve of v43 5G . . . . 67 4.23 Pulse in superconducting state (a) and in slightly resistive
Superconducting Nanowire
Single Photon Detectors:
Theoretical Overview
Superconducting materials may be the future for space applications. Their
property to present no resistance and very low thermal conductivity below
the so-called critical conditions opened them to plenty of new technology
developments.
These critical conditions exists under the shape of two working-condition
constraints: the first one is the critical temperature Tc, above which the
ma-terial loses all its superconducting properties, while the other is the critical
magnetic field Bc, which behaves the same way. They are related to each
other through the equation:
Bc ≈ Bc(0) 1 − T Tc 2 (1.1)
wire through the Ampre’s law, we will, for the sake of simplicity, refer to
this property under the form of critical current Ic.
As will be explained later, this parameter is just theoretical. In fact,
for our devices, we will refer to the switching current Isw, which is the
experimental value at which the device switches to the normal state.
1.1
The Hotspot Mechanics
Superconducting Nanowire Single Photon Detectors were first developed by
G. N. Goltsman et al. at Moscow State Pedagogical University in
collabo-ration with C. Williams and R. Sobolewski of the University of Rochester
in 2001 [1].
As they demonstrated, for a superconducting nanowire at operating
tem-perature T lower than its critical temtem-perature Tc, biased at sub-critical
cur-rent Ibias, nominally a single photon, carrying an energy such that ~ω 2∆,
where 2∆ is the superconducting energy gap, impinging on the device, could
generate a perturbation strong enough to break the Cooper’s Pairs of the
superconducting state of the matter due to electron–electron and electron–
Debye–phonon interactions, generating a high temperature electron zone
which, exceeding Tc, creates the so-called hotspot [6]. A scheme of the
hotspot mechanics is shown in Fig. 1.1.
Due to the exceeding of the critical temperature, this part of the nanowire
(a) The nanowire is biased at subcriti-cal current Ibias
(b) A photon carrying enough energy impinge on the nanowire
(c) The Cooper’s Pairs broke and a re-sistive state portion of the nanowire appears
(d) The current is redirect to the read-out circuit. The nanowire than cools down and returns to the su-perconducting state where the cur-rent starts flowing again trough it (a)
Figure 1.1: The hotspot generation sequence
state. Hence, even if no general theory has been accepted so far [7], the
hotspot starts growing, creating the hotspot region. The growth happens
due to the Joule heating produced by the normal state region.
After the switch, the current is redirected in the readout circuit, which
usually has a resistance Rreadout = 50 Ω, since in theory the resistance
of the hotspot region is much higher than that, usually in the order of
MΩs. The current flowing through the nanowire hence decreases until the
nanowire cools down and restores its superconducting properties, allowing
the current to flow again. This double transition can be seen from the point
of view of the electrical circuit as a fast change of resistance from the zero
value (superconducting state) to the resistive one (which, in case of MgB2 nanowires, is on the order of kΩ). For that reason, when part of the current
is redirected to the source, generates a voltage pulse reading.
1.2
Optical Characterization
In order to characterize the quality of a SNSPD, some important parameters
need to be now introduced: first of all, the Device Detection Efficiency
(DDE), i.e. the ratio of the number of detected photons and the number that
impinge on it; the System Dark Count Rate (SDCR), which is the number
of recorded counts when the fiber and optics are connected to the SNSPD
and the laser is off, i.e. a sort of parameter which describes the robustness of
the system to external radiation and bias fluctuations; the Maximum Count
Rate (MCR), which depends on the minimum time interval at which each
pulse can be separated; the dead time τdead, which is the time window after
a detection event in which the device is unable to detect other photons;
the timing jitter (∆t), which is the deviation from the true periodicity of a
presumably periodic signal; the spectral sensitivity of the device.
The DDE is defined as the product of the optical absorption coefficient
(η) and the quantum efficiency (QE) of the device. For high-quality
de-vices, this value needs to be optimized by increasing the two parameters
that compose it. The absorption coefficient is an optical property, which
can be enhanced by increasing the thickness of the device or
implement-ing the so-called optical cavities [9]–[11]. The quantum efficiency is instead
de-(a) Bridge Structure (b) Meander Structure
Figure 1.2: Example of SNSPDs geometries
pendent, and can be enhanced only by fabricating nanowires with smaller
cross-sections.
The SNSPD has to be thought as a ultrathin (5–10 nm) and ultranarrow
(30–200 nm) nanowire, whose length can vary from several hundreds of
nanometers, while in ”bridge” configuration, to the order of magnitude of
millimeters, while in ”meander” configuration. In Fig. 1.2 it is possible to
see the two main geometric styles used during the study.
The nanowire is biased at a sub-critical current, while enlightened by a
photon source (usually a laser). The calibration of the light source has to be
very accurate, since a mis-evaluation of the actual number of photons
strik-ing the nanowire can end up in a wrong evaluation of the device detection
efficiency. The way it was done during the experiments will be explained in
the next chapter.
Let us now consider a light source pointing the device. We will define
Jin as the fluence of photon striking the device, which is the amount of
define Jabs = JinSdη, which is the fluence of photon which can be detected
by the device, where Sd is the active area of the device, η is the radiation
absorption coefficient of the metallic film given by:
η ≈ 4(Rs/Z0)/[(Rs/Z0)(nsub+ 1) + 1]2, (1.2)
nsub is the index of refraction of the SPD substrate (which presence will be
discussed later in the manufacturing chapter), Rs is the surface resistance
of the nanowire above Tc and Z0 = 377 Ω is the free-space impedance.
If the quantum efficiency reached 100% by fabricating perfect and
ultra-narrow nanowires, the absorption coefficient would be the physical limit of
the device detection efficiency. The goal of all the proven materials SNSPDs
is to find a way to fabricate devices able to achieve 100% quantum efficiency,
and then to design optical stacks (resonant cavities) in order to enhance the
absorption coefficient.
1.2.1
Statistical Approach of Detection Events
The next step is to define a constitutive law for the detection to happen.
This is necessary in order to define the properties of a ”single–photon”
operating condition device. In order to be single-photon sensitive, the
de-vice needs to have a low enough superconducting energy gap ∆(T ) and a
high enough bias current such that just one photon is able to perturb the
(a) Single-photon impinging on the SNSPD
(b) Two-photons impinging on the SNSPD
(c) Single-photon detection event (d) Two-photons detection event
Figure 1.3: Example of Single- and Two-photons detection events
due to the hotspot generation. When it does not happen, we can appreciate
two-, three- or multiple- photons detection mechanics (see Fig. 1.3).
The dependence on the bias current can be seen from the QE point of
view (see Fig. 1.4). For low bias, the quantum efficiency is low and the
energy of one photon is not enough to cause a detection event to occur.
However, more photons striking the same portion of the device in the same
time may be able to cause a detection event, allowing multi-photons
sensi-tivity. Increasing bias current, the QE increases and a single photon may be
able to carry enough energy to produce the detection event, allowing then
single-photon sensitivity. Then further increasing the current leads to the
QE saturation plateau, where the QE has reached its maximum value.
From a simplified statistical approach, the detection can be considered
as a Poisson distribution [13]–[14].
Figure 1.4: DDE vs Ibias for a device capable of reaching QE saturation [3]
then the probability for the device to detect n photons is given by:
P (n) ≈ e
−mmn
n! (1.3)
from which, considering that e−m is fully dependent on the photon power input, if m 1 , follows that P (n) ∼ mn/n! and then that the
probabil-ity to detect photons is proportional to m for a single–photon absorption
regime, to m2 for a two–photons absorption regime, and so on.
1.3
Electrical Characterization
After the absorption of a photon, the device switches, acquiring a resistance
value Rn [13]. What happens is that the current in the device then starts
decaying from its initial value to the normal state current
In= Ibias·
Rreadout
(Rreadout+ Rn)
Figure 1.5: Pulse’s Rise and Fall times
where Rreadout is the resistance of the readout circuit and Ibiasis the biasing
current. This decay happens with a time constant τrise= L/(Rreadout+ Rn),
where L is the inductance of the device. It is called rise time since in the
readout circuit the current increases from zero to its maximum value due
to the redirection of the current into it caused by the switch of the device
(see Fig. 1.5).
The current drop in the device is then stopped at a certain current value
Iret, at which the self-heating of the device due to Joule heating is reduced
enough to allow the wire to recover the superconducting state. At the same
time, the readout circuit sees the peak of the pulse, which has an amplitude
of:
Vpulse = Rreadout· Gampl· (Ibias− Iret) (1.4)
to its initial value (Ibias) with time constant τfall = L/Rreadout.
From the equations obtained above, it is possible to notice the main role
of the inductance L in the time response of these devices. In fact, in order
to manufacture ultrafast devices, its value should be minimized.
It has been proven [13] that the inductance of the nanowire is prevalently
dominated by the kinetic one, Lk. In order to appreciate the magnitude
difference between the geometric and the kinetic inductance, consider that
a 5 nm thick, 100 nm wide and 5 µm long bridge made of NbN has a geometric inductance Lgeom = 0.005 nH, and, in accordance with the results
obtained by Kerman et al. [13], biased at 11.4 µA it develops a kinetic inductance Lk = 6.10 nH. For that reason, from now on, we will consider
only the contribution of the kinetic inductance.
The kinetic inductance can be considered as the inertia of the charge
carriers, which becomes relevant when the direction of current flow
sud-denly reverses (i.e. during the switch). Its value is proportional to the
room-temperature resistance of the nanowire, since both have the same
de-pendence upon the wire geometry:
Lk = Lk Z wire ds/Acs(s) (1.5) R300K = R300K Z wire ds/Acs(s) (1.6)
where Lk is the kinetic inductivity and R300K is the room temperature
is the product of the width and the thickness.
An analytical expression for Lkcan be obtained from the one-dimensional
Ginzberg-Landau theory [15]:
Lk = µ0λ2· l/Acs ⇒ Lk = µ0λ2, (1.7)
where µ0 = 4π × 10−7 H m−1 is the magnetic permeability of free-space, l is
the length of the nanowire and λ is the magnetic penetration depth. This
is valid in the approximation of T near Tc and Ibias ≈ 0.
For a temperature independent calculation, we can use the BCS (Bardeen,
Cooper, Schrieffer) theory and obtain a more complex form of the kinetic
inductance [16]: Lk = l w Rsqh 2π2∆ 1 tanh2k∆ BT ⇒ Lk = ρh 2π2∆ 1 tanh2k∆ BT (1.8)
where Rsq= ρ/t is the ratio between the resistivity ρ and the thickness t of
the nanowire, h = 6.62607004×10−34m2kg s−1is the Planck’s constant, ∆ is
the superconducting energy gap and kB = 1.38064852 × 10−23m2kg s−2K−1
is the Boltzmann’s constant.
From all this, manufacturing shorter or thicker devices having the same
width implies reducing the kinetic inductance Lk, allowing ultrafast photon
detection. However, decreasing the kinetic inductance is limited by the
latching effect, as will be explained later.
unusual shape with respect to other technology fields: instead of speaking
of resistance and geometry, usually the devices are described through the
”sheet resistance” and the ”number of squares”. That is mainly because,
in this way, the characteristics of the film are easily recognized (the sheet
resistance can also be considered as a parameter for the thickness of the
original film).
In a regular conductor, the resistance can be written as R = ρl/Acs =
ρl/w · t. Combining resistivity and thickness, obtain:
R = ρ t · l w = Rsq· l w (1.9)
where Rsqis the so-called sheet resistance, and, as shown, takes into account
both the resistive properties of the material and the thickness of the device.
Defining now the number of squares will explain why such a choice. For
a device, the number of squares Nsq is given by:
Nsq =
Z
wire
ds/w(s) (1.10)
which in case of constant width device geometry becomes Nsq= l/w.
Mul-tiplying the number of squares by the sheet resistance gives the overall
resistance. Moreover, more squares also means higher kinetic inductance of
the device, hence slower devices, since the kinetic inductance is proportional
1.3.1
The Latching Effect
Despite the capability of these devices to reach, nominally, ultrafast
de-tection rates, an important role is played by the so-called latching. As we
explained before, the timing capability of the device is strictly related to
the device’s reset time constant τreset = Lk/R, where Lk is the kinetic
in-ductance and R is the impedance across it.
In order to make the devices ultrafast, it is necessary to reduce as much
as possible the value of τreset. It can be done in two ways: reducing Lk or
increasing R.
The first choice is more disadvantageous then else, since in order to
re-duce Lk we need to design shorter devices, hence meanders with smaller
active area or lower fill-factor. Anyway, even if it is feasible, this approach
leads to a very fast device, but on the other hand also to a very low
de-tection efficiency due to the small active area. Moreover, since the kinetic
inductance is also proportional to the resistance, an decrement of Lk means
also a reduction of R, which does not seem to be the optimal way to develop
these devices.
For that reason the choice made from Yang et al. [19] was to increase
the resistance. In order to do that, they added an on-chip Ti resistor (a
shunt resistor Rshunt [20]) in series with the SNSPD, increasing the total
load’s resistance. Using a shunt resistance of Rshunt = 192 Ω, they were able
to decrease the time constant τreset of a factor 5, leading to the speed-up of
In theory, using a larger resistor should lead to an even faster device,
but a consideration has to be made in that sense. In fact, increasing the
series resistance means also a decrement in the value of current redirected
after the switch, since the normal state current is given by:
In= Ibias·
Rreadout+ Rshunt
Rn+ Rreadout+ Rshunt
(1.11)
If In > Iret, then the device will not go back to its superconducting state
unless the current is brought back to the Iret value. If, on the other hand,
In < Iret, latching may occur. That happens when the heat generated by
Joule heating equals the heat dissipated into the substrate and along the
wire. That is why the limit imposed by the latching effect is that the reset
time constant of the SNSPD cannot overcome the thermal time constant,
the electron–phonon interaction time τe–ph, of the material. If this condition
is not satisfied, for the latching effect will follow the generation of a
self-sustained normal-state hotspot.
This self-sustained hotspot can be unstable, under the shape of the
so-called paralysis, in which case the hotspot will be cooled down after a while
(see Fig. 1.6), or it can be stable. In the second case, the device will switch
and remain in normal state until the current is then brought back to lower
Figure 1.6: Example of paralysis on a scope trace
1.4
Uncertainties Characterization
The devices, however, can not be considered as if they were perfectly
manu-factured, since every production process has its limits, which implies defects.
It is then necessary now to introduce the concept of the constrictions [17].
These manufacturing defects were in the beginning considered only as
geo-metrical issues, like a portion of the wire which has a different cross-section
or due to crystal boundaries. More recent studies [18] confirm that the
con-cept of these imperfections is wider than that, since a constriction can also
be a quantum deficit, like a portion of the material which does not behave
as a perfect superconductor, or a chemical defect.
Due to this effects, the actual critical properties of the devices usually
shift from the theoretical values. For example, let us consider a certain
Ic given by the relation:
Ic(T ) = Jc(T ) · Acs (1.12)
where Jc is the critical current density at a specific temperature. However
in the reality, due to the presence of constrictions, the actual (observed)
critical current of the device appears to be:
Icobs = Ic· C (1.13)
where C ≤ 1 is the so-called constriction factor. This means that the actual
critical current density is not Jc but instead a lower value Jcobs = Jc· C.
From now on, we will refer to the observed critical current as the switching
current, Isw.
1.4.1
The System Dark Count Rate
Another critical aspect of the SNSPDs is the System Dark Count Rate
(SDCR). This is the combination of two effects: the background photons,
which make the device trigger even when the laser is off, and the intrinsic
dark count rate. The origin of the latter phenomenon is not very clear to
date, but it is mainly addressed to two different theories: the theory of
the vortex-antivortex pair (VAP) unbinding due to
Berezinskii-Kosterlitz-Thouless (BKT) transition, and the theory of the vortex hopping from an
(a) Pulses train while not afterpulsing
(b) Pulses train in afterpulsing case
Figure 1.7: Difference between a not-afterpulsing and an afterpulsing be-havior
The system dark count rate is a parameter of major importance, since
depending on its value the signal to noise ratio (SNR) is altered.
1.4.2
The Afterpulsing Effect
Finally, it is necessary to introduce the concept of afterpulsing. This
phe-nomenon appears under the form of an extra triggering, i.e. one incoming
photon generates more than one pulse. Usually, the extra pulse shows up at
a constant time interval after the ”main” pulse (depending upon the device,
[28]).
It is not clear what is the origin of this phenomenon, since it may be
gen-erated by the device itself due to some mysterious effect or by the coupling
Fujiwara et al. [25] found out that the presence of afterpulsing was
re-lated to the reflection of the pulse inside the system electrical feed line. In
order to assess that, they analyzed the increment of counts adjusting the
background light, but since the increment was not proportional at the
differ-ent bias currdiffer-ents tested, they realized that it should not be a photosensitive
effect.
Burenkov et al. [28], on the other hand, studied the distribution of
de-tect events of their devices. The system dark count rate pulses should be,
in principle, equally spread in the time domain. From their analyses,
how-ever, they noticed an uneven distribution of dark counts, which according
to them was related to afterpulsing. They found the presence of trains of
pulses, equally time-spaced, of 2, 3, 4 or more pulses. After some
consider-ations, they changed the amplifiers suit to a more low-frequency sensitive
one, and what they found out was no more afterpulsing. Moreover, they
no-ticed that, unexpectedly, after the main pulse the detection efficiency of the
device does not increase monotonically, but presents an overshoot. Hence,
they speculate that afterpulsing, dark counts and detection efficiency of the
device are three correlated effects which arise due to a perturbation in the
bias current through the nanowire.
What has been found so far is, anyway, that afterpulsing is not a
pho-tosensitive effect, i.e. it appears also while the device is not enlightened by
a laser source and all the pulses are generated by the system dark counts,
current.
Finally, after explaining all the physics that rules these devices, in Tab.
1.1 we collect the most characterizing parameters of the several
supercon-ducting materials used for SNSPDs.
Material, formula Niobium Nitride, NbN Tungsten Silicide, WxSi1-x Magnesium Diboride, MgB2 Bulk Critical Temperature, Tc [K] 16 4.9 39 Electron– Phonon interaction time, τe–ph [ps] ∼5 ∼35 ∼2 Sheet Resistance, Rsq [Ω/sq] (thickness) 900 (5 nm) 380 (5 nm) 80 (7 nm, HPCVD) 150 (10 nm, MBE) RMS Roughness [nm] .35 ? ∼2 (HPCVD) 0.35 (MBE) Atomic Structure
Crystalline Amorphous Crystalline
Table 1.1: SNSPD’s materials characteristic properties
As shown by the table, not only the bulk temperature of the magnesium
diboride is the highest, but also the electron–phonon interaction time τe–ph,
which sets the speed limit of the devices, is lower both than the WSi and
NbN ones, which means that if the devices work properly, they will be a lot
Devices Fabrication Process
Our fabrication process consists in obtaining the nanowires starting from
MgB2ultrathin films. Since the discovery of superconductivity in MgB2[31], different techniques have been developed and optimized in order to obtain
high-quality thin films, like pulsed laser deposition (PLD), molecular beam
epitaxy (MBE) [32], hybrid physical-chemical vapour deposition (HPCVD)
[33] and reactive evaporation (RCE) [34].
The different growth processes of MgB2 impart different superconduct-ing characteristics for the films. For example, films grown with MBE are
much smoother than the one obtained by HPCVD, which is essential for the
proper fabrication of homogeneous nanostructures, but they show a strong
suppression of the critical temperature with respect to the bulk temperature
(Tc = 20 − 24K for thin films, i.e. a suppression of 39% with respect to bulk
Tc in the best case) even for relatively thick (∼200 nm) films. However,
this issue for MBE has been partially solved by Shibata [39] developing
30K-33K (i.e. a suppression of ”only” 15% in the best case) for thin films
(∼15 nm).
Moeckly and Ruby developed the reactive evaporation (RCE) method,
which seems to be the most promising for smooth, high critical temperature
thin films. However, to date no ultrathin film has been demonstrated using
RCE technique.
2.1
Depositions Techniques
Our devices were produced by two different types of films: the deposition of
films by MBE developed by Prof Shibata, who deposited the films at NTT
Basic Research Laboratories in Kanagawa, Japan, and the films obtained
by HPCVD developed by Prof Xi’s group from the Department of Physics
of Temple University in Philadelphia, Pennsylvania. Here we will discuss
briefly the fabrication processes of these films.
2.1.1
MBE
Molecular beam epitaxy growth takes place in a vacuum or ultra-high
vac-uum (UHV) chamber (10−8− 10−12torr). Mg and B are coevaporated using
e-guns with a film growth rate of 0.25 nm s−1 at 280◦C. After the deposition, the wafer is passivated with a SiO2coating, which thickness is around 20 nm,
and then annealed with the fast-annealing process described in [39]. The
(a) AFM of as-grown film. The RMS roughness of the films made in this way widths between 1.2 and 0.4 nm
(b) AFM of rapidly-annealed film. The RMS roughness of the films made in this way goes down to 0.35 nm
Figure 2.1: AFM image of as-grown (a) and rapidly-annealed (b) films [39]
This is because film grown with MBE process are magnesium deficient,
which affects the Tc. Also, and the thinner is the film, the more difficult
is to retain the magnesium, which is why the critical temperature degrades
even further.
However, despite also the critical current density was improved, the
resis-tivity of the films was higher than the one obtained with the other processes.
The root mean square roughness (RMS), however, after the annealing,
was lowered even further. For typical so-grown MBE deposition, the RMS
is usually around 1.2 to 0.4 nm, while after the rapid-annealing process this
value gos down up to 0.35 nm (see Fig. 2.1), which means very smooth
sur-face, of great importance for what concerns the fabrication of homogeneous
nanostructures.
Despite it has been demonstrated by Jo et al. [32] that deposition at
fur-Figure 2.2: Image of surface morphology grown on 6H-SiC (A and D), MgO (B and E) and stainless steel (C and F). For each substrate, two films grown with different deposition flow rates (upper image is lower deposition rate) [37]
ther the temperature gives even smaller grains, despite growth temperature
is only one of the factors that could affect the Tc. However, it seems that
RCE technique developed by Moeckly and Ruby (deposition at 500◦C) may be the most promising one for MBE-type of deposition.
2.1.2
HPCVD
Hybrid physical-chemical vapor deposition, on the other hand, has proven to
be the most effective technique so far [35]. In this technique, Mg is provided
by thermally evaporating bulk Mg pieces (physical vapor deposition), while
B is obtained from the diborane gas, B2H6 (chemical vapor deposition).
It has been proved [37] that the use of different substrates and the
depo-sition rate, as well as depodepo-sition temperature, diborane mixtures, substrate
Figure 2.3: Image of surface morphology grown at 70 (A), 60 (B), 50 (C) and 40 (D) torr [37]
Figure 2.4: AFM images of three film thicknesses of 7.5 (A), 10 (B) and 25 (C) nm [37]. At lower thickness the film grows by initial nucleation of discrete islands, then they start coalesce. The thicker is the film, the more homogeneous is the surface.
As general rule, a lower deposition rate implies smaller crystals (see Fig.
2.2). This rate, however, is dependent by the total environment pressure
during the deposition and by the flow rate of diborane. The lower the
pressure and the flow rate, the lower the deposition rate. In Fig. 2.3 it is
possible to notice how the environment pressure affects the morphology of
the surface of the films.
Finally, it has been shown that also the thickness of the film plays an
film, the higher will be the RMS roughness of the film. That is consistent
with the Volmer-Weber growth mode. As can be seen by Fig. 2.4, the
MgB2 film grows by initial nucleation of discrete islands, which coalesce with increasing thickness. However, in order to realize high-Tc ultrathin
films, the deposition has been made to grow thick films, which were then
etched to sub-10 nm films, retaining the critical temperature of 40K.
For the films we processed, the RMS roughness was around 2 nm.
How-ever, after Ar ion milling etch, the RMS rose to 2–4 nm, which, for 7 nm
thick nanowires, implies a very inhomogeneous nanostructure. However, the
critical temperature usually exceeded 39K, the bulk critical temperature of
MgB2, due to the strains in the film.
2.2
Devices Writing Process
The devices fabrication process started with a 50 nm thick MgB2 film grown on a SiC substrate and passivated with a thin gold layer (∼30 nm). Via
Ar-ion milling [40], the film was thinned down to 7 nm and then passivated
with 30 nm thick SiO2.
Then, via lift-off procedure, the gold contact pads were put in order
to allow the device connection through the passivation layer. A layer of
resist was deposited on the stack and then, using electron-beam lithography
(EBL), the nanowire shape was written. After that, using Fluorine ICP the
Figure 2.5: Fabrication process
film uncovered in the spacing between the nanowire shape.
Finally, using a Ar ion mill etching process the MgB2 film was written and then passivated with SiO2in order to avoid impurities and deterioration
of the device.
Using this method, we were able to design different geometries, from the
relatively easier bridges to the more complicated meanders structures (see
mean-(a) 100 nm wide 34 µm long Bridge structure
(b) 100 nm wide 10 × 10µm2 Meander
structure
Figure 2.6: Examples of devices’ geometries
(a) 100 nm wide 34 µm long Bridge structure
(b) 100 nm wide 2 × 2µm2Meander
struc-ture
Figure 2.7: Example of devices’ geometries with the addition of ”dummy wires”
der and bridge structures gave pretty different results. In fact, etching the
meanders used to give much better homogeneity than etching the bridges.
For that reason we decided to add ”dummy wires” around the bridges
ge-ometries, in order to recall as much as possible the meanders. Since the
quality of the bridges improved, we chose to add the dummy wires also to
Testing Process
After the theoretical and manufacturing process description of the SNSPDs,
let us now focus the attention on the testing process developed to
charac-terize the devices.
As will be shown in the following pages, the identification of the devices
is mainly related to a couple of ”characterizing curves”, which are the I –V
and the R vs T curves. Starting from these two graphics, some of the most
important properties of the devices can be extracted.
After this, the photo-sensitivity analysis is developed, sweeping the bias
of the device in a range close to its switching current Isw both shining light
on it (1.55-µm and 635-nm laser) and without the light (i.e. evaluating the SDCR).
If the device is photosensitive, then further analyses are developed on
it, checking the presence of afterpulsing, scanning the pulse looking for
eventual latching and evaluating the detection efficiency with respect to the
Figure 3.1: Sample bonded to the device–SMP interface PCBs. The sub-strate chip (10 × 10 mm2) is in contact with the copper holder
with grease and GE varnish. From the devices’ pads, the SNSPDs are connected with the PCB via bonding wires, where from the PCB pads the signal is transfered to SMP connectors.
3.1
Set-up Description
The device was cooled down to a base temperature of 3.15K inside a
Cry-omech 410 pulse tube cryostat. It was mounted on a oxygen-free high
ther-mal conductivity (OFHC) copper support and in contact with some grease
between the interfaces to allow a better thermal contact. GE varnish was
applied on the edges of the 10 × 10 mm2 substrate to firmly anchor it to the copper stage.
On the support, there were mounted two PCBs to allow device–SMP
be tested (see Fig. 3.1). For the optical coupling, a ThorLabs SMF 28e+
single mode fiber was connected to a ThorLabs ED1-S20-MD (20◦ Square Engineered Diffuser) with the purpose to spread the light on a 20 × 20 mm2
spot size centering the wafer.
Connected to the support there was a thermometer, connected to a
LakeShore 336 Temperature Controller, since the purpose of the project
is to develop an high temperature working device it was important to
prop-erly know the actual operating temperature of the device while testing it.
The electrical connection, from the device, came out of the ICE through
high frequency, coax cables with SMA connectors and was connected to a
Mini Circuit ZFBT-4R2GW+ bias-tee, which has a bandwidth of 0.1–4200
MHz. From the bias-tee, then, the DC termination was connected through
a Stanford Research System SIM900 mainframe to the SIM928 Isolated
Voltage Source with a SIM970 Quad Channel Voltmeter in parallel, while
the AC termination was connected to a suit of room-temperature amplifiers,
in order to increase the signal to noise ratio (SNR) of the device’s pulse.
The amplifiers suit changed depending on the height and sharpness of the
pulses, but we adopted mainly a combination of two of the ones in Tab. 3.1.
Then the feed line was connected to a 225 MHz Agilent 53131A Universal
Frequency Counter or to a 6 GHz LeCroy WaveMaster 8600 oscilloscope,
from which different measurements were carried out. A scheme of the set-up
is shown in Fig. 3.2
Amplifier Name Bandwidth [MHz] Gain [dB] Noise Figure [dB] Impedance [Ω] ZX60-100VH+ 0.3–100 36 4.0 50 ZFL-500LN+ 0.1–500 28 2.9 50 ZFL-1000LN+ 0.1–1000 24 2.9 50
Table 3.1: Amplifiers adopted to test the devices
Figure 3.2: Equivalent electrical circuit of our set-up
to test our devices, the 635-nm was obtained from a ThorLabs S1FC635
Benchtop Laser Source and the 1.55-µm from a General Photonics TLS-101 Tunable Light Source. From the source, the fiber was first connected in
series to a ThorLabs FPC561 Manual Polarization Controller, an attenuator,
and an optical switch. From the switch, one termination was connected
to a fiber case and then inside the ICE, while the other termination was
connected either to the ThorLabs PM100D (1.55-µm) or the Newport 2931-C (635-nm) optical power meter.
3.2
The I –V characteristics
The current–voltage characteristic (I –V curves) is, as explained before, one
of the ways to characterize the devices.
In order to carry out the I –V measurement, the amplifiers were usually
dismounted since their presence could, in principle, induce noise which could
suppress the switching current in the devices. The reason why we took such
a precaution will be discussed later in the chapter.
Starting from zero, the voltage source (in series with a bias resistor Rb)
increases the bias across the device by fixed ∆V steps, i.e. increases the
bias current Ibias passing through the device by ∆I = ∆V /Rb. At the same
time, the voltmeter evaluates the voltage across the device, measuring the
resistance of the nanowire at each step. There are some uncertainties related
to the SMA cables or to the bonding between the device and the PCB that
have to be considered. However, the overall resistance of the system never
exceeded the order of magnitude of some Ohms.
In Fig. 3.3 it is possible to see the usual shape of an I –V curve. Since
the device is superconducting at very low bias currents, what happens is
that the I –V curve presents itself as an initially vertical line because the
superconducting nanowire has zero resistance. Once the device reaches the
switching current Isw, a sudden increment in the resistance results as a
reduction of bias current and an increment of bias voltage. That is what
Figure 3.3: I –V curve for a 100 nm wide, 34 µm long bridge structure constant cross-section and no constrictions, nominally the switching current
should be just one value. Hence, once reached Isw, the whole device should
switch in normal resistive state, and we would observe only one big
transi-tion. However, what happens in reality is that small constrictions cause the
switch of small parts of the device. Then, further increasing the bias
cur-rent, other parts of the device switch, causing a certain number of smaller
transitions.
We noticed that the wider the nanowire, the lower the number of
tran-sitions. That may be due to higher density of constrictions in the thinner
wires, as noticed by Gaudio et al. [18], because of the complications related
to the manufacturing process of ultrathin nanowires, for width value lower
than 150 nm.
Figure 3.4: I –V curve vs T for a 100 nm wide 5 × 5µm2 meander detector
slightly with respect to the temperature. For example, it is possible to notice
that at lower temperatures, sometimes, the number of small transitions is
lower then the ones at higher temperatures. We think that this effect may be
related mainly to two effects: the first one may be some kind of temperature
dependence behavior of the constriction, which, since their origin in not
completely known and understood, can not be disregarded. The second
one, instead, may be related to the heat generated by the switched portion
of the nanowire: in other words, since the switching current for a wire
section decreases with the increasing temperature, maybe the Joule heating
generated by the nanowire switched portion is not as high as it used to be,
hence the heat power generated only makes switch an even smaller portion
that it used to switch at lower temperatures.
usually the higher are the switching current and the resistance after the first
transition, the higher is the chance for the device to be photosensitive. That
is because the contribute of quantum efficiency in the device detection
effi-ciency increases with the bias current. Hence, having a damaged nanowire
(constriction) means that the all the other portions of the device is subject
to work at low currents with respect to their critical values. Because of that,
their QE remains low, and the device only works properly in the region near
the constriction.
Also, since Isw will deteriorate with temperature, from Eq. (1.4) one
can notice that having a ”big” pulse at low temperatures is the only way to
hope to have a ”decent” pulse at higher temperatures. A ”sharp” transition
does not mean that the device is going to be photosensitive, but only that
it is a good candidate to be.
From Fig. 3.5 it is possible to see that there are two I –V curves, one
on top on each other, which do not exactly match. That is because the top
curve has been tracked increasing the bias from the superconducting to the
fully normal state, while the bottom one has been obtained reducing the
bias from the fully normal state to the superconducting condition.
This mismatch is given by the so-called hotspot current effect. In fact,
as Skocpol et al. [6] discovered in 1974, usually the switching current of a
bridge is up to 10 times higher than the current required from the device to
self-sustain the normal hotspot.
Figure 3.5: I –V curve measured first increasing and then decreasing the bias for a 90 nm thick, 1 × 1 nm2 meander structure. The arrows indicate the direction of the bias
3.6, which has been obtained by the I –V characteristic of a WSi SNSPD.
The importance of the hotspot plateau can not be neglected. In fact, in
order to properly bias the device for single–photon absorption, the bias level
should be in the zero voltage state, just below the critical condition. When,
due to photon absorption, the transition takes place, the device follows a
well defined load line and reaches the metastable region. This metastable
region is that between the superconducting branch and the beginning of the
plateau.
For that reason, not having a clear plateau in our I –V curves means
that we do not have an exact idea of the size of this metastable region. This
can be related to the low quality of the films or to the damage caused on
Figure 3.6: I –V curve with hotspot plateau of a 500 nm wide, 10 µm long bridge structure
3.2.1
Fast–I
swmeasurement
Due to the long time required from the I –V curves to obtain an accurate
estimate of the switching current of the devices Isw, we decided to build in
our set-up a slightly modified version of the fast–Iswmeasurement procedure
developed by Adam McCaughan at MIT [44]. We used an Agilent Wave
Generator in series with a resistance RB to bias the device with a sinusoidal
current signal, Isin(t). Then we used the LeCroy oscilloscope in order to
observe both the bias voltage (channel 1) and the device response (channel
2). The schematics of the set-up is shown in Fig. 3.7.
What happens is that, if the peak voltage of the wave, Vpeak, is such that
Vpeak/RB > Isw for the SNSPD, then the device will undergo a transition
during the bias waving. So on the scope one should see a flat response of
Figure 3.7: Set-up scheme of the Fast–Isw measurement [44]
Figure 3.8: Expected scope readout of the Fast–Isw measurement [44]
channel 1, while once switched, the device should follow the trend of the
bias voltage, hence jumping from the zero bias to a higher value due to the
sharp transition. What we expect is something like Fig. 3.8.
In order to evaluate the switching current, then, it is necessary to
eval-uate the magnitude of the wave voltage (channel 1) at the instant at which
the device shows the transition (jump on channel 2, say t0) and to divide
it by the bias resistor RB, hence evaluating Isin(t0). A LabVIEW program
was then developed in order to automatize all the process and to collect the
Figure 3.9: Fast–Isw measurement results
3.3
The R vs T characteristics
The R vs T test is the second test we used to do while ”screening” the
de-vices. Since our goal is to demonstrate working devices at high temperature
(∼20K), it is fundamental for our purposes to test devices which have high
critical temperature.
In order to do the R vs T measurement, we increased the temperature
of the device above 39K (which is the critical temperature for bulk MgB2). Using the Stanford Research Systems SIM921 AC Resistance Bridge, the
device was biased by an AC sinusoidal current (which we usually chose to
be Ipeak = 30 nA) in order to evaluate the resistance of the device itself. We
chose such a small current because, with increasing temperature, the
switch-ing current of the device is reduced, and we did not want the bias current
Then, simply switching the temperature controller’s heaters off, the
de-vice would start cooling down, a LabVIEW program would read both the
resistance and the temperature of the device and collect the data for the
curve.
It has to be said that the critical temperature of the film and the one of
each device obtained from it may differ very much. In fact, apparently the
production process of MgB2, as well as the one of NbN films (or Nb, MoGe, etc.. [42]), may affect the superconductivity properties of the devices.
On the other hand, knowing the critical temperature of the film before
processing is a good starting point, considering that usually the critical
temperature reduction is about 20% (in the best cases) up to the complete
loss of superconductivity even at base temperature (which usually happens
for very thin, i.e. w ≤ 90 nm, devices).
Again, a distinction between the ideal behavior of the device and the real
one has to be pointed out. Nominally, for a perfect nanowire, the critical
temperature should be homogeneous all over the film, and, consequently, all
over the device. What in reality happens, however, is that the Tc changes
slightly along the nanowire, due to modifications of the superconductivity
properties (film inhomogeneities or fabrication damages).
From Fig. 3.10 it is possible to appreciate a common R vs T curve. From
this curve, we need to focus our attention basically on two parameters: the
first one is the Tc, which is the temperature at which the device reaches
Figure 3.10: R vs T curve of a 100 nm wide, 5 × 5 µm2 meander structure.
For this device, the critical temperature Tc is around 15.5K,
while the transition width ∆T is ∼2.5K
transition, i.e. the ∆T between the conditions at which the device resistance
is R0.9 = 0.9Rn and R0.1 = 0.1Rn.
This is a very good value to have, since it is a meter of the homogeneity
of the device. The smaller is ∆T , the more homogeneous are the device’s
properties.
3.4
Photo-sensitivity Tests
After the previously described tests, the basic photo-sensitivity test was
performed at the base temperature. This test was basically the last one of
the ”preliminary tests” group.
In order to do that, the AC termination of the bias-tee was connected
Figure 3.11: Classic shape of a Pulse
very close to the switching current, using the high photon energy 635-nm
laser at high power levels (fractions of a milliwatt), the research of the pulse
was performed.
Before going on, it is necessary to make a little consideration. In order
to avoid latching, to study the photo-sensitivity of the devices we used to
add a series inductance Ls = 6.5 µH to the devices to slow down the decay
time τfall of the response.
If a pulses was present, like in Fig. 3.11, then, setting the voltage
trig-ger level of the Agilent universal frequency counter to half of its height, the
count rate was evaluated while reducing the laser power. That was made
because changing the amount of photons striking on the device should
rep-resent, for a properly working photo-sensitive device, a change in count
If the device was photo-sensitive, the next step was to check the
polar-ization sensitivity using the manual fiber polarpolar-ization controller. Biasing
at high current and using high laser power in order to maximize the
num-ber of counts per second, manually modifying the polarization of the light
should in principle change the count rate. This because the coupling of the
electromagnetic wave to the electrons increases when they are parallel to
each other. For that reason, when the polarization of the light is parallel to
the nanowire the count rate is maximum, while when it is perpendicular to
it is minimum. Once found the positions of the pads which maximize and
minimize the count rate, after subtracting the system dark counts rate, the
ratio Rpolariz = PCRmax/PCRmin between the photons count rate at the two
conditions was evaluated as reference parameter for the polarization effects.
3.4.1
Single- or Multi-Photon Sensitivity Test
This test was performed in order to check if the device was single-photon
sensitive. First of all, using the temperature controller, the device was
maintained to a fixed temperature, with a maximum fluctuation of the order
of tenths of millikelvins. The device was then illuminated with a fixed laser
power level, while the bias current was swept over a range which had as
upper limit the switching current. During every step, the bias current and
the count rate (CR) were collected. This procedure was repeated for several
laser power levels. After that, the light was shut off, and the system dark
Once all the data were collected, the first step was to evaluate the actual
photons count rate (PCR) as the difference between the count rate (CR)
and the system dark count rate (SDCR). Then, since the amount of photons
in the laser light flux is proportional to the laser power P, we plotted the
photons count rate divided by P, P2 and P3 vs Ibias. In fact, in accordance
with Eq. (1.3), nominally a single-photon sensitive device should manifest
a linear dependence between the PCR and the amount of photons
strik-ing on the device, a two-photon sensitive one should manifest a quadratic
dependence between PCR and amount of photons, and so on.
In order to be single-photon sensitive, the PCR/P curves evaluated at
different laser powers should in principle coincide. As a consequence, for a
two-photons sensitive device the PCR/P2 should coincide instead, and so on.
In Fig. 3.12 it is possible to appreciate the difference for the results
ob-tained for a single-photon sensitive device and for a three-photons sensitive
one.
3.4.2
Device Detection Efficiency and Afterpulsing
Even if the ratio PCR/P is very useful for qualitative data such as the
discrimination of a single- or a multi- photon sensitive device, it is necessary
(a) PCR/P for a single-photon sensitive device
(b) PCR/P for a three-photon sensitive device
(c) PCR/P3 for a single-photon sensi-tive device
(d) PCR/P3 for a three-photon sensi-tive device
Figure 3.12: Difference in the photo-sensitivity curves for a single- and a three-photons sensitive detectors. The single-photon sensitive device (Figs. (a)–(c)) was a 90 nm wide, 2 × 2 µm2 meander,
while the three-photon sensitive device (Figs. (b)–(d)) was a 100 nm wide, 1 × 1 µm2 meander
To do that, we used the equation:
PCR = DDE × µ = DDE × P P’ I’ 1 E × Adevice (3.1)
where µ is the mean number of photons striking on the device per unit time,
P’ and I’ are calibrated power and flux obtained for the optical diffuser, E
is the energy of a photon and Adevice is the active area of the device.
Figure 3.13: DDE vs Ibias/Isw curve for a single-photon sensitive detector
at different temperatures. The device was a 100 nm wide, 1 × 1 µm2 meander, enlightened with 635-nm laser at 200µW
power. It is possible to notice that the DDE vs T presents a negative slope for 3.15K < T < 6K and a positive slope for 7K < T < 14K
Ibias/Isw), is to slightly decrease with temperature [47]. However, as it was
demonstrated by Inderbitzin et al. [46], sometimes it is possible to see the
trend to move in the opposite direction, i.e. the efficiency may increase
with temperature at fixed reduced bias current. Examples of the possible
representations of a DDE vs Ibias/Isw and a DDE vs T curves are Figs.
3.13–3.14.
Another possible effect which may be hidden behind an unusual DDE
curve could be the presence of afterpulsing. This effect has no actual
expla-nation to date, but it is possible to see whether the device is afterpulsing or
not performing the inter-arrival time (IAT) measurement.
Figure 3.14: DDE vs T curve for a single-photon sensitive detector, a 100 nm wide, 1 × 1 µm2 meander, at Ibias/Isw = 99% and 99.5%
Ibias and illuminating it with a light source. It is useful to bias at some
relatively high current, since, as we know [28], the afterpulsing effect is
current-related, and having a device which is not afterpulsing at very low
bias, where the count rate is so low that is far from the operative conditions,
is not of any use. That is why we usually biased at the highest ”stable”
current we could reach with the device.
To perform the measurement, there are multiple modes. The one that
we used was made connecting the AC termination of the bias-tee to the
amplifiers suit and then to the oscilloscope, use a high photon energy CW
light source (λ = 635-nm) and, while triggering on the pulse, make an
histogram of the time difference between the main and the extra pulses
which appear on the oscilloscope screen in a time domain of about 5 µs after the main pulse. A correct IAT should present a dead time τdead where
Figure 3.15: Afterpulsing usual scope trace
the detector measures no counts, followed by a quick rise to a flat region.
Afterpulsing is detected by noting large peaks in the IAT histogram.
The difference between an afterpulsing and a not-afterpulsing detector
Figure 3.16: Inter-arrival time of an afterpulsing device. The device was a 90 nm wide, 1 µm long bridge structure. The IAT was performed using 635-nm wavelength laser at 200 µW power biasing at 98% of the switching current
Figure 3.17: Inter-arrival time of a not-afterpulsing device. The device was a 100 nm wide, 1 × 1 µm2 meander structure. The IAT was performed using 635-nm wavelength laser at 200 µW power biasing at 98% of the switching current
Best Devices Results
During the study, we had the chance to face some interesting devices. Here,
we report the most significant ones. The chapter will be built in sections,
each regarding one specific device. It seems a good choice not to overlap
concepts regarding different devices at the beginning. However, in the final
section a more general discussion will be addressed, combining the results
obtained during the whole period of study.
The devices we will discuss come from 4 different films. The properties
of the films are collected in Tab. 4.1.
Wafer No. Production process: Rsq [Ω/sq] TC [K] RMS Roughness [nm] 40 HPCVD 48–60 40 2.1 42 MBE ∼90 31 .4 43 HPCVD 48–50 40.5 1.9 45 HPCVD 85–95 39.5 1.71
Table 4.1: Films properties
(a) 4 Samples for each Wafer (b) 60 Devices each Sample
(c) Difference between rows A-B, C–H and the extra devices in the corners (R)
Figure 4.1: Design image of the Mask used for fabrication. In dark green there are the pads and the ground plane, in light green the inductors in series with the devices of rows A and B, and in purple the devices. R devices, since are very wide, are in green like the inductors.
were 4 samples. In each sample there were 8 rows (A to H), 4 columns for
A and B (since the devices were connected in series with inductors) and 8
columns for the other rows. Moreover, there were also 4 extra devices in the
4 corners of the sample, which where assigned the letter R. Usually these
devices were wider than the other SNSPDs, because they were mainly used
as a fabrication process comparison terms, to check if narrower devices had
more suppression in critical current density or critical temperature. The
wafer design is shown in Fig. 4.1(c))
The name of each device was unique. For example ”v35 S3-5F” stands
for ”device of the 35th fabrication run, sample (S) 3, row 5, column F”.
When no S is present in the name, it means that the wafer was designed
with only one sample.
4.1
v40 S4-3H
This device was a 2 × 2 µm2 meander structure made by a 90 nm wide
nanowire with 420 nm spacing (Nsq = 111). The film was obtained by
HPCVD deposition. The device’s geometry is represented in Fig. 4.2.
The device had a sheet resistance Rsq= 57 Ω/sq, which was within the
range of film’s original sheet resistance.
At the temperature of 4K, the switching current Isw was 172.5 µA (see
Fig. 4.3). The critical temperature, as shown by Fig. 4.4, was around
(a) Design of the device (b) SEM of the device
Figure 4.2: v40 S4-3H
Figure 4.3: I –V characteristic of v40 S4-3H at different temperatures. It is possible to notice how the transitions, with increasing temper-ature, become smoother and then disappear almost completely for 35K
implies, for such a high critical temperature, a pretty homogeneous device.
The device was single-photon sensitive up to the temperature of 18K,
as shown in Fig. 4.5, both at 635-nm and 1.55-µm wavelengths. Anyway, the DDE was pretty low, since biasing at 99.5% of the critical current was
around 5 × 10−7% at 4K and reached a maximum of 10−4% at 16K (see Fig. 4.8). This behavior of increasing DDE with temperature can be explained
since the device efficiency did not saturate. Due to that, increasing the
Figure 4.4: R vs T characteristic of v40 S4-3H
Figure 4.5: Single-photon sensitivity test at 1.55-µm wavelength for v40 S4-3H, T = 18K
may explain such mechanism [46].
However, at temperatures higher than 18K something unexpected
hap-pened. At 19K, the device started showing a second, smaller pulse from
the oscilloscope, which became the main pulse at 20K (Fig. 4.6). From the
inter-arrival time measurements, we got some interesting results. At 18K
the device does not show any sign of afterpulsing (see 4.7), while at 19K
(a) T = 18K (b) T = 19K (c) T = 20K
Figure 4.6: Pulse track of v40 S4-3H at three different temperatures
(a) T = 18K (b) T = 19K (c) T = 20K
Figure 4.7: Inter-arrival time measurements of v40 S4-3H at three test tem-peratures
usual afterpulsing shape. It may just be an increment in DDE.
We have no reasonable explanation for that, only some hypotheses. The
most possible guess could be that the device is becoming more efficient,
since now two or more constrictions of the detector are working together to
detect photons.
The reason why it only happens at a certain temperature has been
guessed in this way: let us say that the device shows two constrictions.
Constrictions induce a suppression both in switching current and critical
temperature. If the first constriction has lower switching current and higher
critical temperature of the second one, sooner or later, due to the Isw–T
re-lationship, the latter will take over, becoming the prevalent. Hence, instead
