Download Gol`tsman`s lecture for foreign students, part 1

Nonequilibrium Superconductivity and
Ultrasensitive Detectors and Mixers
Gregory Goltsman
Moscow State Pedagogical University
Moscow, Russia
Lecture 1. Nonequilibrium Superconductivity and Ultrasensitive Detectors and Mixers
Quasi-particle disequilibrium in BCS superconductors
- Energy-mode vs. charge-mode disequilibrium
- "Electrons" and "holes" in superconductors
- Enhancement and suppression of superconductivity by microwaves
- Normal metal - superconductor interface and Andreev reflection
- Electric field penetration into superconductor
- Time-dependent charge-mode disequilibrium: phase-slip centers
Superconducting single-photon detectors based on nonequilibrium
superconductivity (TES, STJ, SSPD)
- Operation principles of the detectors
- Comparison of the detector characteristics: response time, quantum
efficiency, operating wavelength range, dark counts rate, energy
resolution
Applications of single-photon detectors
- CMOS IC testing
- Quantum communication and quantum cryptography
Ground state in normal metal and in superconductor
Ground state in normal metal at T=0K, all
states with k<kF are occupied, all states
with k>kF are free. The excited state with
arbitrary small energy can be created by
moving of an electron from point o inside
the sphere to point x outside it.
Fermi surface
with energy eF
D
a
b
(a) Ground-state of normal metal.
Probability that single-electron state
with energy e is occupied, T=0K
(b) Ground state of superconductor.
It differs from metal ground state in
the small (~ D) region on the Fermi
surface, T=0K
Fundamentals of BCS Theory
Quasi-particle excitation energy in normal metal and in
superconductor.
In normal state:
for k>kF (electron)

2 2
Ek  e k 
k  k F2
2m
for k<kF (hole)

2 2
Ek  e k 
kF  k 2
2m

2

k F k  k F 
2m

2

k F k F  k 
2m
2
2
In superconducting state:

Ek  e k2  D2

1/ 2
where D is energy gap.
Spectrum of elementary excitations in
superconductor. The slope of the dashed
line is ћvc, where vc is critical velocity.
Energy-mode vs. charge-mode disequilibrium
Even ("energy") mode
T* >T
Odd ("charge") mode
"Branch imbalance"
Q* >0
Enhancement and suppression of
superconductivity by microwaves
Al bridges 1 mm wide and 100 mm long
20
max
Probabilities of quasiparticles
relaxation due to electron-phonon
interaction (EPI) and electronelectron interaction (EEI).
, GHz
15
10
Enhancement
pee  1  pe  ph
5
0
Suppression
pe ph   e1ph /( e1ph   ee1 )
min
0.04
0.06 0.08 0.1
-1
1/l, Å
l is electron mean free path
E.M. Gershenzon, G.N. Gol'tsman, V.D. Potapov, A.V. Sergeev, Physica B 169(1991) 629-630
Branch imbalance of the quasiparticle spectrum
Non-equilibrium distribution of
superconducting electrons vk2 and quasiparticle spectrum Ek in superconductor in
non-equilibrium state. The dashed line
shows equilibrium distribution vk2, when
ms=eF. Gap D retained its value, chemical
potential mn became greater than eF.
Andreev reflection
Normal metal
Superconductor
The charge of the quasiparticle (electron) is gradually changing as the
quasiparticle moves from normal metal to superconductor
Phase-slip centers
Schematic diagram of a model of the phase-slip
center. The oscillation of the gap magnitude
occurs in a core length ~2x, whereas the
nonequilibrium quasi-particles producing charge
imbalance diffuse a distance ~L in either
direction before mn relaxes to mp.
The oscillatory supercurrent in the
core region, which average value
~Ic/2.
Schematic I-V curve of a bridge containing
only a single phase-slip center. A is the crosssectional area of the filament and rn is its
normal resistivity.
[Tinkham M., Revs. Mod. Phys. 46, 587 (1974).)]
Phase-slip centers
Spatial variation of the
superconducting and normal electron
potentials, Vs and Vn, measured by
tunnel probes near a phase-slip center
in a tin film strip. (After Dolan and
Jackel.)
Phase-slip centers
Current-voltage characteristics of tin "whiskers" showing regular step
structures due to successive establishment of phase-slip centers. (Here
DT=Tc-T). (After Meyer)
Meyer J., v. Minnigerode G. Phys. Lett., 1972, 38A, 529
Lecture 1. Nonequilibrium Superconductivity and Ultrasensitive Detectors and Mixers
Quasi-particle disequilibrium in BCS superconductors
- Energy-mode vs. charge-mode disequilibrium
- "Electrons" and "holes" in superconductors
- Enhancement and suppression of superconductivity by microwaves
- Normal metal - superconductor interface and Andreev reflection
- Electric field penetration into superconductor
- Time-dependent charge-mode disequilibrium: phase-slip centers
Superconducting single-photon detectors based on nonequilibrium
superconductivity (TES, STJ, SSPD)
- Operation principles of the detectors
- Comparison of the detector characteristics: response time, quantum
efficiency, operating wavelength range, dark counts rate, energy
resolution
Applications of single-photon detectors
- CMOS IC testing
- Quantum communication and quantum cryptography
Semiconducting vs. superconducting singlephoton detectors for 1.3-1.5 mm wavelength
Semiconductors
Superconductors
a) One optical photon creates
only one
electron-hole pair
(typical bandgap 1-2 eV).
a) One optical photon creates ~100–
1000 excited electrons
(superconducting gap
~ 2 meV for NbN).
b) Room temperature and
cryogenic operation.
b) Relaxation times are picosecond.
c)
d) No gating required, simple biasing
source.
Large dark counts.
d) Complicated biasing
schemes.
c)
Extremely low dark counts.
Low temperature environment reduces background noise and thermal
fluctuations responsible for dark counts.
Transition-edge detector
(a) Microphotograph of a transition-edge, hot-electron quantum detector
and (b) the corresponding equivalent circuit. The device was a 20x20 μm2
square of 40 nm thick tungsten film having Tc=80 mK with a transition width
of 1mK. The device was operated at a bath temperature of 40 mK in a
voltage-bias regime that maintained the sensor within the transition region
via negative electrothermal feedback.
(Miller et al IEEE Trans. Appl. Supercond. 9 4205 ©1999 IEEE).
Hot-electron microcalorimeter based on superconducting
tunnel junction
Photon absorption gives rise to Te in a metal absorber and is measured using the I–V
characteristics of a normal-insulator-superconductor tunnel junction, in which a part of the
absorber forms the normal electrode. The current through the junction was measured with a
low-noise dc SQUID. The absorber had an area of 100x100 μm2 and was deposited on a silicon
nitride membrane. The microcalorimeter was operated at 80 mK with a time constant of 15 μs
and demonstrated an energy resolution of 22 eV for 6 keV photons.
(Nahum M. and Martinis J. M. 1995 Appl. Phys. Lett. 66 3203)
STJ microbolometer with Andreev
reflection of quasiparticles
A hot-electron microbolometer using
Andreev reflections of quasiparticles from
superconducting contacts and the
corresponding I–V characteristics.
The device relyes on Andreev reflections
of low-energy, thermal quasiparticles at
the edges of the stripe and on the weak
electron–phonon coupling at low
temperatures. Both effects confined the
energy delivered by the photons,
providing a large rise of Te. This was
subsequently read out by the
superconductor-insulator-normal metal
junction, for which the metal strip formed
the normal electrode.
(Nahum M. and Martinis J. M. 1993 Appl. Phys. Lett. 63 3075)
Single-photon detectors: desired
properties
• High quantum efficiency (QE reaching 100%)
• Broadband operation (200 nm to >2000 nm)
• Low dark count rates
– no false/unwanted counts
– no afterpulsing
• Very high speed
– fast, picosecond signal rise and recovery
– no “dead” time between counts
• Energy resolving - photon number resolving
Superconducting Single-Photon Detector (SSPD)
Mechanism of Photon Detection
Energy Relaxation Process
100
Photon h
e-e interaction
eV
10-1
Debye
phonons
e-e interaction
Quasi particles
2D
10-3
kbT
Cooper
pairs
Schematic description of relaxation process in an
optically excited superconducting thin film.
SSPD response mechanism
Concentration of nonequilibrium
quasipaticles across the width of the
film at different moments after the
photon has been absorbed. Time
delays are 0.8, 2.0 and 5.0 measured
in units of the thermalization time.
Distance from the absorption site is
shown in units of the thermalization
length. Inset illustrates redistribution of
supercurrent in the superconducting
film with the normal spot - the basis of
quantum detection. It shows the crosssection of the film drawn through the
point where photon has been
absorbed.
Semenov A., Gol'tsman G., Korneev A., Physica C 351 (2001) 349-356
SSPD response mechanism
Schematic of the resistive state formed
in the film after the current density in
sidewalks has exceeded the critical
value. The dark circle represents the
normal spot; grey zones correspond to
the area of superconductor with
penetrating electric field. Profiles of the
electric field (E) and the energy gap (D)
are shown along lines crossing the
normal spot (a) and the sidewalk (b).
Phase Slip Center
Semenov A., Gol'tsman G., Korneev A., Physica C 351 (2001) 349-356
Scanning Electron microscope image.
Fabrication:
• DC reactive magnetron
sputtering of 4-nm-thick
NbN film
• Patterning of meandershaped structure by direct ebeam lithography.
• Formation of Au contacts
with optical lithography.
Gol'tsman G. et al, Appl. Phys. Lett. 79 (2001) 705
Korneev A. et al, Appl. Phys. Lett. 84 (2004) 5338
SSPD placed inside a cryostat
10 mm
5 mm
meander
Au contacts
Resistance vs Temperature Curves for Sputtered NbN Film 3.5
nm Thick and for SSPD Device
Direct electron beam lithography and reactive ion etching process
IV-curves of the 3.5-nm thick film
devices at 4.5 K
25
Superconducting state
20
current, mA
Ic
A
15
Resistive
state
50  load line
10
B
5
0
Metastable
Region
0
1
2
Voltage, mV
3
4
Time-resolved SSPD photoresponse signal
The measured FWHM of the response signal is about 150 ps and includes
both the risetime and falltime jitter
Jitter of a NbN SSPD at 1.55 mm and 778
nm wavelengths is below 18 ps
1.0
0.8
778 nm
0.6
FWHM
0.4
~18 ps
0.2
0.0
1.0
0.8
1550 nm
0.6
FWHM
0.4
~18 ps
0.2
0.0
Oscilloscope: 50-GHz bandwidth Tektronix TDS-8000B
Laser source: Pritel OptiClock 1 GHz rate, 1.6 ps pulses, 70 fs jitter,
Signal amplifiers: Miteq JS3-00101800-24, 0.1-18 GHz bandwidth
Korneev et al., APL, 84, 5339 (2004)c
Counting speed of 3.5-nm-thick SSPDs is
above 2 GHz for 1.55-mm photons
T = 4.2 K
Detector
photoresponse
speed is
limited by the
acquisition
electronics:
 = 134 ps.
1-GHz-rate photoresponse train (real-time oscilloscope picture).
Korneev et al., APL, 84, 5339 (2004)
Experimental data for QE (open symbols) and the dark count rate
(closed symbols) vs. the bias current measured for 1.55-μm photons
10
7
10
6
0
10
5
-1
10
4
-2
10
3
-3
10
2
-4
10
1
-5
10
0
1
10
QE, %
10
10
10
10
10
10
10
12
14
16
Ib, mA
18
20
22
-1
2
10
Dark counts, s
T=4.2 K, Ic=16.9mA
T=3.2 K, Ic=19.5mA
T=2.2 K, Ic=21.5mA
,
,
,
Experimental quantum efficiency and dark counts rate
vs. normalized bias current at 2 K
2
6
10
10
4
10
10
0.56 mm
QE, %
0
2
10
10
0.94 mm
-1
0
10
10
1.26 mm
-2
-2
10
10
1.55 mm
-3
10
-4
0.4
0.5
0.6
0.7 0.8
Ib/Ic
0.9
1.0
10
Dark counts, cps
1
QE,%
Spectral dependencies of the quantum efficiency measured for
a NbN SSPD at 3 K temperature and different bias currents
10
1
10
0
10
-1
10
-2
10
-3
10
-4
10
-5
10
-6
Ib/Ic=0.94
Ib/Ic=0.88
Ib/Ic=0.82
Ib/Ic=0.78
T=3K
1
2
3
4
,μm
5
6
Ic =29.7mA at 3 K
Dark counts per second
The NEP and the dark counts (inset) measured at
1.26, 1.55 and 5.6 mm wavelengths at 2 K.
-16
10
-17
NEP, W/Hz
1/2
10
-18
10
4
10
2
10
0
10
10
-2
-4
10
0.88
0.92
0.96
1.00
Normalized bias current
-19
10
1.26 mm
1.55 mm
5.6 mm
-20
10

NEP 
2R
DE
-21
10
0.88
0.92
0.96
Normalized bias current
1.00
Comparison of traditional single-photon detectors and
superconducting single-photon detectors at ~1.3 mm wavelength
Detector Model
InGaAs PFD5W1KS
APD (Fujitsu)
R5509-43 PMT
(Hamamatsu)
Si APD SPCM-AQR16 (EG&G)
W bolometer- 0.1 K
(NIST)
Superconducting
Tunnel Junction
SSPD - 2 K
Counting rate
(Hz)
QE
(%)
Jitter
(ps)
Dark Counts
(s-1)
NEP
(W/Hz1/2)
5  106
20
200
6  103
310-17
9  106
1
150
1.6  104
10-16
5  106
0.01
350
25
10-16
2  104
90
N/A
<10-4
<210-21
5  103
60
N/A
N/A
N/A
2  109
30
18
<10-4
510-21
Lecture 1. Nonequilibrium Superconductivity and Ultrasensitive Detectors and Mixers
Quasi-particle disequilibrium in BCS superconductors
- Energy-mode vs. charge-mode disequilibrium
- "Electrons" and "holes" in superconductors
- Enhancement and suppression of superconductivity by microwaves
- Normal metal - superconductor interface and Andreev reflection
- Electric field penetration into superconductor
- Time-dependent charge-mode disequilibrium: phase-slip centers
Superconducting single-photon detectors based on nonequilibrium
superconductivity (TES, STJ, SSPD)
- Operation principles of the detectors
- Comparison of the detector characteristics: response time, quantum
efficiency, operating wavelength range, dark counts rate, energy
resolution
Applications of single-photon detectors
- CMOS IC testing
- Quantum communication and quantum cryptography
Application: CMOS Device Debug
• Normally operating nMOS transistor emits near IR photons
(0.9-1.4um) when current passes through the channel
• Time-correlated photon emission detection measures
transistor switching time
Vdd (1)
Vdd (1)
Vss (0)
Vdd (1)
Vss (0)
Vss (0)
Kash, J. A. and J. C.-H. Tsang (1999). Noninvasive optical method for measuring internal switching and
other dynamic parameters of CMOS circuits. USA, International Business Machines Corporation. US Patent
# 5,940,545
TRPE system setup
TRPE: Time-Resolved Photon Emission
OptiCA® System with NbN SSPD
commercialized by NPTest, Inc.
Compressed
He Lines
Vacuum
Manipulators
Cold
Shield
Coupling
Optics
Fiber
For more information:
http://www.nptest.com/products/probe/idsOptica.htm
Single-photon emission from CMOS transistors
Counts
0.35-mm linewidth, 3.3-V bias
Good CMOS circuit running at 100 MHz
Mepsicron II
detector
0
5
10
15
20
Time (ns)
0.13-mm linewidth, 1.3-V bias CMOS circuit running at 100 MHz
NbN SSPD
detector
Single-photon emission from both
nMOS and pMOS transistors
0.13-mm linewidth, 1.3-V bias CMOS circuit running at 100 MHz
120
100
Counts
80
60
FWHM = 62 ps
40
20
0
Time (200 ps/div)
Zhang et al., El. Lett, 39, 1086 (2003)
Quantum Cryptography (QC) based on
single-photon communication assures
unconditional security
Bob
(Receiver)
Alice
(Sender)
[from Simon Benjamin, Science 290, 2273 (2000)]
•
Unconditionally secret, quantum key distribution is possible in actual
physical environments due to Heisenberg Indeterminacy Principle:
It is impossible to measure the state of a quantum bit without altering it.
• Alice (Sender) - single-photon source.
• Bob (Receiver) - single-photon detector.
Free-space, satellite-based quantum key distribution will provide
us with high-speed
and unconditional security communications
(from www.space-technology.com)
Conclusion
- It is convenient to characterize the departure from thermal equilibrium
by introducing two parameters T* and Q*, representing the
nonequilibrium temperature and quasi-particle charge density,
respectively. These approaches are called energy-mode and chargemode disequilibrium.
- Nonequilibrium effects such as enhancement of superconductivity by
microwaves, Andreev reflection, phase-slip centers are widely used
in practical ultrasensitive detectors.
- Superconducting single-photon detectors outperform traditional
avalanche photodiodes and photon multiplier tubes. Superconducting
detectors are already used in science and industrial applications.
Andreev reflection
Schematic diagram of energy vs. momentum on the two sides of an NS interface.
The diagram includes degenerate states both inside and outside the Fermi surface
and on both forward and reverse sides of the Fermi sphere. The open circles
denote holes; the closed circles, electrons; and the arrows point in the direction of
the group velocity, ∂Ek/∂k. This describes an incident electron at (0), along with the
resulting transmitted (2, 4) and reflected (5, 6) particles. A refers to the Andreevreflected hole.
Enhancement and suppression of
superconductivity by microwaves
Al bridges 1 mm wide and 100 mm long
20
max
, GHz
15
10
Enhancement
5
0
Suppression
min
0.04
0.06 0.08 0.1
-1
1/l, Å
l is electron mean free path
Probabilities of quasiparticles
relaxation due to electron-phonon
interaction (EPI) and electronelectron interaction (EEI).
pe ph   e1ph /( e1ph   ee1 )
pee  1  pe  ph
E.M. Gershenzon, G.N. Gol'tsman, V.D. Potapov, A.V. Sergeev, Physica B 169(1991) 629-630
Equilibrium state of superconductor at
temperature T
Equilibrium at T
f k  f 0 ( Ek / T ) 
1
e Ek / k BT  1
Quasi-particle disequilibrium
Energy-mode
disequilibrium
Charge-mode
disequilibrium
Enhancement by extraction of quasi-particles
Schematic diagram of tunnel process
showing net extraction of quasi-particles
from the superconductor having the smaller
gap and hence a greater density of quasiparticles.
Phase-slip centers
a
b
Graphical representation of complex current-carrying Ginzburg-Landau
wavefunction in one-dimensional superconductors.
(a) Uniform solution. (b) Nonuniform solution just before phase-slip event.