Table Of ContentCapacitively Enhanced Thermal Escape in Underdamped Josephson Junctions
Y. Yoon,1 S. Gasparinetti,1 M. Mo¨tto¨nen,1,2 and J. P. Pekola1
1Low Temperature Laboratory, Aalto University, P.O.Box 13500, FI-00076 AALTO, Finland
2Department of Applied Physics/COMP, Aalto University, P.O.Box 14100, FI-00076 AALTO, Finland
We have studied experimentally the escape dynamics in underdamped capacitively shunted and
unshunted Josephson junctions with submicroampere critical currents below 0.5 K temperatures.
In the shunted junctions, thermal activation process was preserved up to the highest temperature
where the escape in the unshunted junctions exhibits the phase diffusion. Our observations in the
1 shunted junctions are in good agreement with the standard thermal activation escape, unlike the
1 results in the unshuntedjunctions.
0
2
n Underdamped Josephson junctions are routinely used help the junction escape from the phase diffusion regime
a asthresholdcurrentdetectorstoreadoutquantuminfor- by enhancing TA. This idea can be realized by either
J mationinasuperconductingcircuitbymeasuringswitch- decreasing I or increasing C . Among these two solu-
C J
4 ing events from the superconducting to the normal state tions, however, only the second one is applicable, since
(see, e.g. [1]). In addition, this technique has been used the junctionwithsmallIC hasalsoalowJosephsoncou-
]
l to identify between geometric and dynamic phases in a pling energy EJ, which lowers ∆U. Low ∆U implies a
l
a superconducting charge pump [2], and also to measure small tilt of the potential at the point of escape, hence
h collective quantum phase slips in the ground state of a the particle gains a small amount of energy when es-
- Josephson junction chain [3]. The detector sensitivity is caping and can get trapped in the next well instead of
s
e important in the measurement. One can improve it by running down the potential. Accordingly, CJ is the only
m reducingthecriticalcurrentofthejunction,butthenthe parameter remaining for decreasing Tcr. For a typical
. systemtypicallyentersthe phasediffusionregime,which junction, the capacitance per unit area is 45 fF/µm2.
t
a isnotdesirablesinceinthiscontextoneusuallywantsto With this value, although one can implement a large CJ
m fixthephasedifferenceofthesuperconductingcircuit. In by increasing the junction area, it becomes impractical
this letter, we present a technique to prevent the phase forthe detector junction, sinceI isalsoproportionalto
- C
d diffusion by adding a large shunt capacitance with the the area. Alternatively, alargeshunt capacitancecanbe
n help of atomic-layer deposition (ALD). added in parallel to C .
J
o
c The Josephsonjunction dynamics is well described by Motivatedbythisidea,weimplementedashuntcapac-
[
a model of a phase particle in a tilted washboardpoten- itance Csh by growing Al2O3 layer of 5.5 nm thickness d
2 tial [4]. In this model, as the bias current I is increased using ALD ontop ofan Al groundplane of40 nm thick-
v toward the critical value I , the barrier height ∆U is ness. Usingelectronbeamlithographyandshadowangle
C
1
loweredandtheparticle,oscillatingwiththeplasma(an- evaporation [10], Al/AlO /Al Josephson junctions were
x
4 gular)frequencyω =(2eI /C ~)1/2 inapotentialwell, fabricatedontheALDoxide. TheinsulatingAlO layers
5 p C J x
where C is the junction capacitance, can escape out of for the tunnel junctions were formed by standard room
0 J
. thewellbyeitherthermalactivation(TA)ormacroscopic temperature oxidation between the evaporation steps of
2
quantum tunneling (MQT) process. The crossover be- thetwoAllayers,whichallowsustomanipulatethejunc-
1
tween MQT and TA regimes occurs at the temperature tionresistanceandI byvaryingtheoxidationpressure.
0 C
1 Tcr ≃ ~ωp/(2πkB) [5]. Above Tcr, the dominant escape For large capacitance, two rectangles with 30×15 µm2
: mechanism is TA. The junction behavior also depends area were defined in the leads near the junctions, over-
v
on the magnitude of the quality factor Q of the junction lapping with the ground plane, as shown in Fig. 1(b).
i
X at its plasma frequency. In the case of junctions with The total overlap area Atot between the two parts con-
r Q ≪ 1, called overdamped, the escape dynamics occurs nected to the junction on the top and the ground plane
a over a dissipation barrier [6], which is undesirable for a at the bottom is roughly 500 µm2 each. As a result, the
threshold current detector. For Q ≫ 1, so-called under- Josephson junction is capacitively shunted by the paral-
dampedcase,thephaseparticlemovesdownfreely ordif- lelplatecapacitorwhichconsists oftwoshuntcapacitors
fusively fromonewelltoanotherdepending onthe effect C0 in series and on each side of the junction. The total
ofdissipation. Whendissipationisweak,thefreerunning shunt capacitance is Csh = C0/2 where C0 = ǫAtot/d
particle is still governed by TA process, while when dis- and ǫ is the permittivity of Al2O3. A similar tech-
sipation is strong, the escape dynamics enters the phase nique for adding shunt capacitance to proximity Joseph-
diffusion regime [5, 7–9]. The appearance of phase dif- son junctions was reported in Refs.[7, 8], where the ca-
fusion in a hysteretic junction was studied extensively pacitorchangesthedampingstrengthinsuperconductor–
two decades ago by Martinis and Kautz [11, 12]. How two-dimensional electron gas–superconductor Josephson
can one avoid the underdamped phase diffusion regime junctions. The leakage resistance from the junction to
andmaintainTAprocessathightemperatures? Accord- groundplanewaslargerthan10GΩ. Boththeunshunted
ing to the phase diagram in Ref. [5], decreasing Tcr can and shunted junctions were fabricated at the same time
2
(a) (b) (a) T increases
bath
1
A1
0.5
P
y
bilit
a 0
b
1 m o
2 m 10 m Pr (b) 240 280 320 360
e
ap 1
(c) (d) c
Es A2
0.5
R C R C C
J sh J 0
150 200 250 300
I(nA)
FIG. 1: Scanning electron micrographs of (a) an unshunted
and (b) a capacitively shunted junction. In (b), the junc-
FIG.2: Measured switching histograms of (a) theunshunted
tionandleads(purple,inforeground)overlapwithAlground
junctionA1and(b)theshuntedjunctionA2. Thebathtem-
plane(encircledbysolidwhiteline,inbackground). Thesizes
of the junctions in the panel (a) and (b) are 0.4 × 2.5 µm2 peratureTbath wassetto58,120,160,216,270,321,377,and
430 mK for the different sets of data from the right to the
and0.4×1.5µm2,andthecircuitschematicsofthejunctions
left.
correspond to (c) and (d),respectively.
calculation based upon the information above and the
onthesamechip. NotethatthetotalcapacitanceCtot is
Ctot ≃CJ intheunshuntedjunctionandCtot ≃CJ+Csh relativedielectric constant7.8 ofAl2O3 in ALD process-
in the shunted junction, as shown in Fig.1 (c) and Fig. ing, Csh was estimated to be 3.14pF. We also estimated
C fromthe specific capacitanceof 45 fF/(µm)2 and the
1 (d), respectively. All measured data were taken in a J
3He–4Hedilutionrefrigeratorwithabasetemperatureof junctionareasgiveninFigs. 1(a)and(b). Consequently,
thetotalcapacitancesoftheshuntedandunshuntedjunc-
50 mK.
tion were 3.2 pF and 45 fF, respectively.
We investigate the escape dynamics by applying a set
TABLEI:Parametersofthesamples. Rn isthenormal-state of current pulses with a fixed amplitude and duration
resistance, IC is the critical current, and EJ is the Joseph- throughthejunctionsandbydeterminingtheprobability
sonenergyobtainedfromAmbegaokar–Baratoff formula[13].
forthedevicestoswitchfromthezero-voltagestatetothe
Ctot is the total capacitance including the junction capaci-
finite-voltagestate. Ateachamplitude200currentpulses
tance CJ and the shuntedcapacitance Csh.
wereapplied. TheescapeprobabilityP wasmeasuredas
a function ofthe currentpulse amplitude I, whichyields
Rn IC EJ Ctot cumulative histograms of switching current. Figure 2
Sample Device
(Ω) (nA) (K) (pF) showsthemeasuredswitchinghistogramsofboththeun-
shunted (A1) and the shunted junctions (A2) in Sample
Unshunted(A1) 612 513 12.2 0.045
A Aatdifferentbathtemperatures. Asimilarmeasurement
Shunted(A2) 828 379 9.0 3.2
wascarriedoutwithSampleB,butthehistogramcurves
Unshunted(B1) 775 405 9.7 0.045 are not shown here. The histogram is typically charac-
B
Shunted(B2) 746 421 10.0 3.2 terizedbythe switchingpositionI50% =I(P =0.5),and
the width ∆I = I(P =0.9) − I(P =0.1), the measure-
ment results of which are shown in Fig. 3. Note that at
In Table I, we present the characteristics of the de- the lowest temperature, the switching position of A2 is
vices studied here. The normal-state resistance R was lowerthanthatofA1,asshowninFig. 3(a),andSample
n
obtained from current–voltage(IV) measurement,which B behaves in an opposite manner as shown in Fig. 3(b).
yieldsIC andEJ accordingtoAmbegaokar–Baratofffor- We observed that on increasing bath temperature Tbath
mula [13]. By the standard parallel plate capacitance the mean position shifts down in all cases, whereas the
3
SAMPLE A SAMPLE B toTcr ≈200mK,aspredictedwiththeMQTmodel,but
400 400 theydecreaseathightemperatures. Itwasreportedthat
(a) (b) the decreasing ∆I results from the influence of dissipa-
A) 300 300 tionbyaretrappingprocess[5,7–9]. Thisindicatesphase
n
( diffusion. TheTAmodelcannotexplainthephenomenon
%
50 200 200 becauseitneglectstheeffectofdissipation. Severalmod-
I
elshavebeenproposedtoaccountforthephasediffusion
100 100 of underdamped Josephson junctions incorporating the
retrapping process in the TA model [5, 7–9, 14].
Kivioja et al. [5] claim that when I is below a maxi-
30 (c) 30 (d)
mum possible phase diffusion currentI = 4I /πQ, the
m C
A) phase particle is retrapped after escape. The observed
n
I ( 20 20 Im is 265 nA in A1 and 190 nA in B1, obtained from
I50% curves at a certain temperature where ∆I starts to
10 10 decrease in Fig. 3. With those values and I given in
C
Table I, Q of the unshunted junctions is estimated to be
0.06 0.1 0.5 0.060.1 0.5 2.5 in A1 in and 2.7 in B1. Note that this Q may differ
BATH TEMPERATURE (K) from that introduced earlier since here it corresponds to
lowfrequencydynamics ofthe junction. Forthe shunted
junctions, however, it is not simple to determine Q with
FIG.3: Thetemperaturedependentvariationofthemeanpo- the presentinformation. Nevertheless,webelieve thatQ
sition(I50%)in(a)–(b)andthewidth(∆I)ofthehistograms mustbe atleastanorderofmagnitude largerthanthose
in(c)–(d). Theexperimentaldatainpanels(a)and(c)andin of the unshunted junctions, because of the large Ctot.
(b) and (d) were obtained from SampleA and Sample B, re-
In conclusion, we developed a technique to add a
spectively. Ineachgraph,diamond(⋄),circle(◦),anddashed
large shunt capacitance using atomic-layer deposition in
line correspond to the experimental data of the unshunted
aJosephsonjunction to preventthe junctionfromenter-
junction (A1 and B1), the experimental data of the shunted
ing phase diffusion. We compared the escape dynamics
junction (A2 and B2), and the theoretical simulation of the
of the capacitively shunted and unshunted junctions. In
shunted junction by the TA model, respectively. The simu-
lation was performed with IC of 379 nA for Sample A and theshuntedjunction,TAprocessispreservedatallmea-
with 369 nAforSampleBas fitparameters, andCtot = 3.17 sured temperatures; for the unshunted junctions we ob-
pF was employed. The latter IC differs by 12 % from the servephasediffusion. TheTAmodelyieldsasatisfactory
Ambegaokar–Baratoff value. In the TA model, ∆I does not discussion for our observations in the shunted junctions.
depend on Ctot, or at least the dependence should be very Itmaybe possiblethat,byengineeringthisshuntcapac-
week. itance for the experiments on the phase biased Cooper
pair pumps [2], we can not only improve the sensitiv-
ity of the detector junction but also protect the circuit
temperaturedependenceofthewidthisverydifferentde-
from high frequency noise. However,attention has to be
pending on whether the junction is capacitively shunted
paidonthefluctuationsinthe phasebiasdue tothermal
to the ground plane or not. According to the standard
effects.
MQT and TA discussed above, Tcr ≈ 11 mK ≪ Tbath
in the shunted junctions (A2 and B2). Thus the role of
theMQTisnegligibleandinstead,TAdominatesthees-
cape dynamics. In the TA model, the width obeys ∆I
∝ T2/3. Consistent with the prediction of the model, Acknowledgments
bath
we observed that in the shunted junctions the widths
are increasing as a function of temperature. The dashed The authors gratefully acknowledge discussions with
lines in Fig. 3 show that the theory is in quantitative P. Solinas, M. Meschke, and J. Peltonen. This work
agreement with our observations. For the corresponding was supported by the European Community’s Seventh
unshuntedjunctions (A1 andB1),onthe other hand, on Framework Programme under Grant No. 238345 (GE-
increasing Tbath the widths are more or less constant up OMDISS).
[1] D.Vion,A.Aassime,P.Joyez,H.Pothier,C.Urbina,D. netier, and W. Guichard, NaturePhysics 6, 589 (2010).
Esteve, and M. H. Devoret,Science 296, 886 (2002). [4] M. Tinhkam, Introduction to Superconductivity
[2] M.M¨ott¨onen,J.Vartiainen,andJ.P.Pekola,Phys.Rev. (McGraw-Hill International Editions, New York,
Lett.100, 177201 (2008). ed. 2, 1996).
[3] I. M. Pop, I. Protopopov, F. Lecocq, Z. Peng, B. Pan- [5] J. M. Kivioja, T. E. Nieminen, J. Claudon, O. Buisson,
4
F.W.J.Hekking,andJ.P.Pekola,Phys.Rev.Lett.94, [10] G. J. Dolan, Appl. Phys.Lett. 31, 337 (1977).
247002 (2005). [11] J. M. Martinis and R. L. Kautz, Phys. Rev. Lett. 63,
[6] D. Vion, M. G¨otz, D. Esteve, and M. H. Devoret, Phys. 1507 (1989).
Rev.Lett. 77, 3435 (1996). [12] R. L.Kautz and J. M. Martinis, Phys.Rev.B. 42, 9903
[7] V. M. Krasnov, T. Bauch, S. Intiso, E. Hu¨rfeld, T. (1990).
Akazaki,H.Takayanagi,andP.Delsing,Phys.Rev.Lett. [13] V. Ambegaokar and A. Baratoff, Phys. Rev. Lett. 10,
95, 157002 (2005). 486 (1963).
[8] V. M. Krasnov, T. Golod, T. Bauch, and P. Delsing, [14] J. C. Fenton and P. A. Warburton, Phys. Rev. B. 78,
Phys.Rev.B. 76, 224517 (2007). 054526 (2008).
[9] J. M¨annik, S. Li, W. Chen, V. Patel, S. Han, and J.E.
Lukens,Phys.Rev.B. 71, 220509(R) (1996).
