Impedance engineering in circuits

1
Impedance engineering in circuits for charge
metrology
S.V. Lotkhov and A.B. Zorin
Physikalisch-Technische Bundesanstalt,
Braunschweig und Berlin
Symposium on Quantum Phenomena and Devices at Low
Temperatures
Espoo, Finland, 28.-30.3.2008
2
Outline
? Single-electron tunneling and its
applications in metrology ? Dissipative on-chip
components - Low-ohmic and low-frequency
environment for Cooper-pair devices -
High-ohmic resistors for selective suppression
of cotunneling in R-pumps ? Future experiments
3
Single-electron tunneling (SET)
ne
4
Single-electron tunneling (SET)
e
tunnel barrier
Gate-control
Metal
ne
Vg
CT, RT
Cg
("SET-Box")
Charge quantisation
shows in experiment, if
5
Tunneling and Dissipation
tunnel coupling
H HL HR HT
HT
?F
without dissipation (or on the short time
scale) quantum superposition of microstates,
quantum evolution, non-equilibrium population
dissipation in normal metal appears in form
of inelastic scatter processes (e - e, e - ph, )
HL
HR
Dissipation makes the tunnel process irreversible
and "restores" charge quantisation important
for charge metrology!
6
Quantised charge transport for metrology
Fixed number of electrons is transferred per
cycle I nef
typically f I 1MHz 1pA 1GHz
1nA
needed for redifinition of Ampere!
Accuracy
Trade-off
Current magnitude
7
"Slow" and accurate charge transfer capacitance
standard
f 5 MHz I 1 pA t 20 s N 108 C
1.6 pF DV 10 V
Cryocapacitor
Feedback- electronics
C
SET-Pump
Q eN
0-Meter
Cint
DV
Electron pump
Josephson Voltage Standard VJ j fJ KJ-1
SET-Chip
SET-Electrometer

• Idea
• E.R. Williams, R.N. Ghosh, and J.M. Martinis, J.
  Res. Natl. Inst. Stand. Technol. 97, 299 (1992)
• The best results standard deviation of C
  0.3x10-6
• M.W. Keller, A.L. Eichenberger, J.M. Martinis,
  and N.M. Zimmerman, Science 285, 1706 (1999)

8
Quantum Metrology Triangle
U
1. Closing quantum metrology triangle
Josephson effect U j f J KJ-1
KJ-1
Single-electron tunneling C
QxN
U
A. Self-consistency check ? of
electrodynamics theory
h
Qx e (?)
(?)
2e
C
fJ?
h
2e
i? j
fJ
?
?
e 2
?
?
ac-impedance bridge with Quantum Hall
reference (??C) -1 Rk (?)
e2
h
?
N
h
B. Possible corrections to practical constants
1
ie2
i

• F. Piquimal and G. Geneves,
• Metrologia, 37, 207 (2000)
• M.W. Keller, in Recent Advances
• in Metrology and Fundamental
• Constants, TJ.Quinn et al. Eds.,
• Amsterdam, The Netherlands IOS,
• 291 (2001)

2. In combination with calculable capacitor
? adjustments with nonelectrical SI-units
(meter)
9
Electromagnetic Environment equivalent Impedance

• M.H. Devoret et al., PRL 64, 1824 (1990)
• G. Ingold and Yu.V. Nazarov, in Single Charge
  Tunneling, edited by H. Grabert and
• M.H. Devoret (Plenum Press, New York, 1992), pp.
  21-107.

(Thevenin theorem)
tunnel junction (TJ)
Zt(w)
V1
V2
Energy win e(V1-V2) inel. scattering
"recharging" losses
10
Impedance as infinite set of oscillators
(see for more details, e.g., H.Pothier, PhD
Thesis, Paris 1991 P.Joyez, PhD Thesis, Paris
1995)
L1
L2
Lk
Zt(w)
C1
C2
Ck
The energy of EM-environment includes the sum
energy of the oscillators
11
Normal-metal junctions modification of tunnel
rates
Tunnel rates orthodox theory
Spectral function of environment
T 0
G(V)
Modification due to environment
Z(w) 0
Z(w) gt Rk

V
0
12
Superconducting case rates of Cooper pair
tunnelling
The rate of tunnelling "mimics" the shape of
P-function!
Dissipative environment enables processes of
relaxation, which makes tunneling of Cooper
pairs irreversible!
Superconducting single junction provides a direct
and effective tool for environmental spectroscopy!
see e.g. R. Lindell, J. Penttilä, M. Paalanen
and P. Hakonen, Physica E, 18, 13 (2003)
13
A Example of low-ohmic environment (the best
way to study use superconducting contacts!)
supercurrent peak
RH 10W CH 100 pF
14
B Example of resonant environment
Re(Zt) ltlt Rk
For the experimental conditions
Z1 gt Z2 ReZx(w) gtgt Z22/Z1 ,
ReZ(w) is peaked at odd harmonics!
15
C Low-frequency impedance
(possible application in Cooper pair metrology)
Superconducting devices shuttle, sluice,
pump, Direct supercurrent contributes to an
error mechanism
Those devices operating at finite bias voltage
(sluice, shuttle) could benefit of a special
low-frequency environment
CT 0.1?1fF
T 0.1K
R/2
R/2
Ec / kBT 0.01 - rapid decay!
Cs 1pF gtgt CT
The supercurrent is expected to vanish
exponentially towards finite bias voltages!
16
Low-frequency environment Experiment on Cooper
pair transistor with RC-shunt
(PTB-2006, unpublished)
(simplified mask image)
V
T 25mK Vg max SC
Cstray ?
Cs 3pF
Cr, l 25µm
(Al/SiO2/Au)
R 2 ? 250k?
CPT RT 10kW (Al/AlOx/Al)
(symmetric to the left)
Vg
() partially "restored" supercurrent
(-) no suppression observed (???)
Layout must be reconsidered with more detail!
17
High-ohmic environment
2. Highly resistive on-chip microstrips
1. High-ohmic impedance of Josephson-Junction-Arr
ay
1? ? 1M?
F
F
F
F
Impedance tunable over many orders of
magnitude - Shot-noise because of
quasiparticle tunneling
0.1µm
Cr-resistor as on-chip component, fabricated
in-situ with Al-SET structure (Dolan's shadow
evaporation technique)
refs, e.g. Haviland et al. J. Low Temp. Phys.
118, 733 (2000)
Details Zorin et al. JAP 88, 2665 (2000)
18
Resistive microstripline cutoff frequency
Pure resistor vs. RC-Line Z(w)
The total impedance Zt(w)
RT, CT
Zt-1(w) iwCj Z-1(w)
V
fB
Characteristic frequencies WRC 1/(RC0) ? 2p?6
GHz (for w ltlt WRC impedance Z R) W0
8R/(Rk2C0) ? 2p?12 GHz (for w lt W0 impedance Z gt
Rk) Note for typical Ec 100µeV fB Ec/h
24 GHz !
WRC/2p
W0/2p
19
P(E)-function at T 0
G. Ingold and Yu.V. Nazarov, 1992
Fixed R 100 kW L (and R0) varied
Fixed R0 10 kW/µm L varied
Pronounced high-ohmic type of environment at R0 ?
5 kW/µm (Sheet resistance ? 500 W/square)
Saturation of P(E) at L ? 10 µm at E 1/2 Ec
20
Junction arrays selective suppression of
cotunneling
Z/2
Z/2
A
Direct tunneling Z partially "screened"
Cotunneling Z(w) applies as is
gate-control
N-junctions
I
(rotated 90)
30nm
For such values of R the cotunneling is
suppressed selectively!
22nm
21
R-pump extending the current plateaus
Typical parameters Cj ? 160 aF, Rj ? 70 kW, R ?
30-60 kW
Courtesy of LNE N.Feltin et al. 2006
PTB-2000
22
under construction at PTB
Cryocapacitor
Feedback- electronics
C
SET-Pump
Q eN
0-Meter
Cint
DV
Electron pump
Josephson Voltage Standard VJ j fJ KJ-1
SET-Chip
SET-Electrometer

• setup is running
• pumping plateaus are measured
• shuttle pumping experiment is calibrated
• trapping times of 1min are demonstrated, will
  be improved

23
Sample layout for capacitance standard
experiment at PTB
to cryocapacitor
5-junction R-Pump
SET-Electrometer
to cryocapacitor
Needle pad
d 90µm
1µm
5µm
24
New experiments!
Al
qp
Hybrid NSN-Turnstiles
N
S
N

• J. Pekola, J. Vartiainen, M. Möttönen, O.-P.
  Saira, M. Meschke and D. Averin, Nature Physics
  4, 120 (2008)
• D.Averin and J.Pekola arXiv0802.1364.
• A.Kemppinen et al. arXiv0803.1563.

Cu, AuPd,
Step 1
N
N
S
Step 2
Similar restrictions of low tunnel
transparency as for the normal-state SET (max I
10pA) but parallel connection is possible!
N
N
S
I
Leak rate 10-3 (N Cu), potentially much better!
25
Error mechanisms due to higher-order tunneling

• Andreev cycles (two-electron tunneling)
• can be avoided by gate settings,
• Cooper pair-electron cotunneling
• (three-particle process) to be suppressed!

1.
2.
IAndreev

possible improvement use of high-ohmic resistor
highly disordered N-electrode ( with low
e-h-coherence length LT )
Al
Cr(N)
Cr
Amplitude of multiple tunnel attempts reduced due
to inelastic scattering!
RA RT2 / Rcor , where Rcor LT / sS
Hekking und Nazarov, PRB 49,6847 (1994), H.
Pothier et al. Physica B 203 226 (1994)
26
Extremely high impedance for narrow-band Bloch
oscillations
EJ EC
IB
V
excited band
V 0
R
ground state
fB IB / 2e
E
2e
Spectrum of Bloch oscillations
LZ-tunneling
R1 gt R2
R ?
V gt 0
Bloch oscillations
fB
e
3e
microwave-irradiation
hf
f fB lt fLZ 1?10 GHz
current plateaus at I 2ef 1nA
27
Experiments
1991 First experiments on current biased
single junctions existance of Bloch
oscillations! see, e.g.. Kuzmin and Haviland,
"Observation of the Bloch oscillations in an
ultrasmall Josephson junction", Phys. Rev. Lett.
67, 2890 (1991).
2006 Resistively biased ( R 500kW per
50µm-length ) long array of small JJs Lotkhov,
Krupenin and Zorin, IEEE Trans. Instr. Meas. 56,
491 (2007).


?
2008 Proposal for the EU support "SCOPE" in
the second evaluation stage Focus on
simulations of charge (soliton) dynamics /
extremely high-resistivity films / viable
concepts of self-compensation of the offset
drifts will be thought of
28
Conclusion
? Quantised charge transport is of basic
interest for metrology both for "low-" and
"high-SET-current" devices ? Resistive
environment has been an important component of
several useful SET-circuits ? Scheduled
experiments - combined "deviceenvironment"
approach should be continued - advances in
fabrication of narrow and extremely high-ohmic
wires are required.
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30
(Co)tunneling in SET-"Trap use of R
Vg
R

• Retention time is limited by
• Thermal escape

e
Eeff
?E
e
?E

1. At low-T cotunneling (macroscopic quantum
   tunneling)

?cot ? ?E 2N-12? , ? R/Rk / D. Golubev
and A. Zaikin, Phys. Lett. A 140, 251 (1992) /
31
realisations of R-SET devices 4-junction R-trap
Experiment charge hysteresis at T 100mK
Thermally activated switchings at T 130mK
T lt 100 mK Trapping times over 8h ! (comparable
to 7-9 junction traps)
S.V. Lotkhov et al., APL 75, 2665 (1999)