Physica E 2 (1998) 894—898

Induced superconductivity and residual resistance in InAs quantumwells contacted with superconducting Nb electrodes

Mason Thomas!,*, Herbert Kroemer!, Hans-Richard Blank!, Ki C. Wong"

! Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106, USA" Physics Department, University of California, Santa Barbara, CA 93106, USA

Abstract

We have investigated hybrid superconductor/semiconductor structures consisting of modulation-doped InAs quan-tum wells contacted by closely spaced niobium electrodes, and showing induced superconductivity in the InAs. Theresistance of these semiconductor-coupled weak links does not disappear abruptly with decreasing temperature, butinstead over a wide temperature range, in a continuous, thermally activated fashion. We present a detailed quantitativestudy of the temperature-dependence of the residual resistance, and of a peculiar interrelation between the rate ofresistance decrease and the geometry of the devices. ( 1998 Elsevier Science B.V. All rights reserved.

Keywords: Superconductivity; Low temperature; InAs; Quantum well

1. Introduction and background

Hybrid superconductor/semiconductor struc-tures show promise for combining the almost negli-gible losses of superconductors with the tunabilityand ease of processing of semiconductors. The mostpromising hybrid combination is superconductingniobium with an InAs quantum well [1,2]. Thiscombination has shown induced superconductivityeffects in the InAs [3,4], in addition to being com-patible with standard semiconductor processes. Inprevious work, we examined Nb—InAs structuresand found a unique temperature dependence of theresidual resistance [5]. Below the superconducting

*Corresponding author. Fax: 805 893 3262; e-mail:thomas@nemesis.ece.ucsb.edu.

transition temperature of the Nb, we found theresistance of the Nb—InAs junction to fall to negli-gible resistances over several Kelvin, but the formof the resistance did not fit well to any canonicaltheories for superconductors. In the present work,we extend those early measurements and also pres-ent a more detailed analysis of the temperaturedependence, and finally propose an explanation forthe observed behavior.

To test the temperature dependence we use agrating structure to generate a series array ofNb—InAs junctions. We begin with a molecularbeam epitaxially grown InAs quantum well withAl

0.5Ga

0.5Sb barriers. The quantum well is 15 nm

thick and is modulation-doped with Te to a con-centration above 5]1012 cm~2. Further details onthe MBE growth may be found in Ref. [6].

1386-9477/98/$19.00 ( 1998 Elsevier Science B.V. All rights reservedPII: S 1 3 8 6 - 9 4 7 7 ( 9 8 ) 0 0 1 8 2 - 9

Fig. 1. Schematic of grating structure from Ref. [5]. Top figureis a cross-section showing the Nb to InAs quantum well inter-face. Bottom shows the device used for four-point measurementsand relevant dimensions. The grating period is 1 lm, the spacingbetween voltage probes is typically 300 lm, and the width, w,varies from 16 to 200 lm in the experiments.

Fig. 2. Current—voltage characteristic of a w"200 lm grating.The solid line is taken at 2.4 K and the dashed line at 4.2 K.

We then selectively make contact to the InAswith Nb. A HeCd laser is used to holographicallydefine a 1 lm-period grating pattern on the semi-conductor. Then the sample is etched down to theInAs quantum well with Cl

2reactive ion etching.

Nb is then sputter-deposited on the InAs. After thedeposition, the Nb is lifted-off to form the gratingpattern. Finally, we define mesas on the gratingstructure to perform accurate four-point probemeasurements. The grating provides a series con-nection of Nb—InAs junctions, which enhance anyvoltages developed in the structure, which in turneases measurement. A schematic of the final struc-ture is shown in Fig. 1, with relevant dimensions.For more details on the processing, refer to [7].

We measure the samples using a four-pointprobe technique in a cryostat. The temperature ofthe sample can be controlled from about 1.8 to10 K. Since the Nb becomes superconducting atapproximately 8 K, this provides a sufficient rangeof temperatures for measuring superconductingeffects. With the four-point probe technique, cur-rent is passed through the outer contacts and anyvoltage developed is measured across the innercontacts (see Fig. 1). As previously mentioned, thegrating effectively multiplies any voltage generated

across one Nb—InAs junction by the number ofjunctions in series (typically &300). Thus, usinga lockin amplifier we can measure voltages as smallas 1nV per junction. The grating is the optimalstructure to use since we are looking for effectswhere the voltage becomes vanishingly small.

An example measurement of the current vs. volt-age (I—») of one of our grating structures is shownin Fig. 2. Unlike most semiconducting structures,our grating shows a very strong non-linearity whenthere is a very small voltage or none at all. Thisnon-linearity is a fundamental effect of a strongcoupling between the Nb electrodes, and can becharacterized by the slope of the I—» curve (i.e., thedifferential resistance) at zero bias and the value ofthe current when voltage rapidly increases (the“corner” current). The present paper is concernedwith the behavior of these two parameters asa function of temperature and the geometry of thegrating structure.

2. Temperature dependence

At high temperatures, where the Nb is not super-conducting, the I—» curve is a straight line, asexpected for a normal resistor. However, below thesuperconducting transition temperature of Nb, theindividual Nb lines in the grating couple together(due to the close spacing — approximately 0.5 lm —of the Nb lines) and the non-linearity of Fig. 2

M. Thomas et al. / Physica E 2 (1998) 894—898 895

Fig. 3. The differential resistance (at zero bias) of the sample ofFig. 2 is shown on a log scale vs. 1/¹ to show the thermallyactivated behavior of the resistance. The intermediate temper-ature range shows the resistance dropping over four orders ofmagnitude. The resistance matches an exponential (thermallyactivated) form with an activation energy of 23 meV.

Fig. 4. Differential resistance of samples of various widths,showing a clear trend of activation energy with width. Thewidest sample is the same as in Fig. 3. The narrowest sample hasan activation energy of only 0.7 meV.

arises. Initially, the non-linearity is weak, and thedifferential resistance at zero bias is not much lessthan the high temperature resistance. As the tem-perature falls, though, the differential resistancerapidly drops, while the corner current increasesslowly and becomes better defined. Over most ofthe temperature range, the non-linearity is onlyover a voltage »@k¹/q, which is an indication ofthe superconductive coupling behavior. The differ-ential resistance falls rapidly, but it appears neverto drop to a true zero-resistance state. This can beseen in Fig. 3 where the zero bias differential resist-ance is shown vs. the inverse temperature. In thehigh temperature regime, where the Nb is a normalmetal, the resistance is constant. In the low temper-ature regime, the measurement is in the noise floorand so is also constant. In between these ranges, theresistance falls over several orders of magnitude.However, there is no indication that the resistancedrops suddenly to zero. Instead, it falls smoothlyand continuously.

This exponential drop of resistance with inversetemperature is an indication of a thermally acti-vated process. The slope of the resistance on theplot of Fig. 3 gives the activation energy for thisprocess. In the example shown it is 23 meV. Thisvalue is, however, strongly sample dependent. Inthe course of processing different samples, the grat-ing uniformity or the Nb to InAs interface quality

may vary, and this could account for some variationin measured activation energies. In spite of this,there is still a consistent trend in activation energiesbetween samples of different widths (see Fig. 1).This variation is the subject of the next section.

3. Width dependence

Fig. 4 shows the results of temperature depen-dent measurements on a number of devices withdifferent widths. The widest sample, at 200 lm, hasan extracted activation energy of 23 meV. The nar-rowest sample, 16 lm, has an activation energy ofonly 0.7 meV. The activation energies of all samplesare not always well-defined, but it is neverthelessclear from the figure that wider samples have ahigher activation energy. Furthermore, three of thesamples shown in the figure are derived from onesample. The 95 lm wide sample shows an activa-tion energy of 5.5 meV. This same sample was thenpatterned and etched down to 38 lm. This was thenmeasured to have an activation energy of 2.5 meVas shown in the plot. The sample was again etchedto 16 lm wide and re-measured, with the finalmeasurement giving an activation energy of0.7 meV. The results on this one sample indicatethat the activation energy is in fact proportional tothe width.

896 M. Thomas et al. / Physica E 2 (1998) 894—898

Fig. 5. Differential resistance of four samples with widths 65and 90 lm, and lengths 300 and 425 lm. The two samples withwidth of 65 lm and lengths 300 and 425 lm have the sameactivation energy — 2.6 meV. Similarly, the two samples withwidth 90 lm have an activation energy of 3.6 meV.

To eliminate the uncontrolled processing vari-ations, we fabricated a set of four samples from thesame starting grating. Of course, the original grat-ing has an unknown Nb to InAs interface quality,but since the same grating is used for all fourdevices, they all have the same interface and uni-formity. The only variation between the samples isan intentional variation of the geometries for four-point measurements. The gratings are patterned asin Fig. 1 with two widths — 65 and 90 lm — and twolengths between the voltage probes — 300 and425 lm. This gives four combinations of length andwidth. The results of measuring these co-processedsamples are shown in Fig. 5. In the thermally ac-tivated temperature range (below &8 K), the ac-tivation energies are not a function of the length(and hence of the number of Nb—InAs junctions inseries), but are instead only a function of the widthof the sample. Furthermore, the activation energy isdirectly proportional to the width of the sample, sothat a sample with no width would have zero ac-tivation energy.

4. End effect or homogeneous effect?

There are two possible ways for the activationenergy to depend on the width. The first possibility

is a dependence of the activation energy on thecorner current of the sample and thus an implicitdependence on width. This is true in the more com-mon Josephson tunnel junctions [8]. In a tunneljunction, the corner current scales with the area ofthe junction (and hence with the width). Accordingto the theory of Ambegaokar and Halperin [9], theactivation energy of the zero bias resistance is pro-portional to the corner current as E

!"+I

#/qk¹,

which therefore also scales with the width. How-ever, the numerical factor in that equation isapproximately 4 eV per mA of corner current. Thisis two to three orders of magnitude greater thanour values. There are no adjustable parameters inthis formula so it is not clear that it is appropriateor even applicable to our hybrid structures.

Another way the activation energy might dependon the width of the sample is through an explicitdependence on the ends of the sample. In thisphenomenological model, a single junction isviewed as a distributed resistor. We propose thata resistance arises at the ends of the grating (per-haps due to inelastic scattering of electrons fromthe etched grating edge) and the resistance expo-nentially falls towards the grating center with acharacteristic decay length, ¸

D. A simple calcu-

lation then yields a resistance for the entire junctionof the form

RJo0exp(!w/2¸

D).

If we make another assumption that ¸D

is propor-tional to the temperature, then we can define anactivation energy, EJw¹/¸

D, which has the re-

quired dependence on width. Furthermore, E!

isconstant for a given width, since ¸

Dis proportional

to temperature. We believe this theory can accu-rately describe the observed temperature depend-ence of these hybrid structures.

Evidently, this phenomenological theory re-quires further verification and a more rigorousmicroscopic underpinning. One possible way totest the theory is by creating structures withoutends. This can be accomplished by connecting thetwo ends of a Nb line into a ring. The current andvoltage may then be measured through concentricrings or between an inner disk and a surroundingring. The circumference of the ring is then equiva-lent to the width of a grating line, and a comparison

M. Thomas et al. / Physica E 2 (1998) 894—898 897

of rings with different circumferences should help todetermine the role of end effects in the temperaturedependence of the Nb—InAs hybrid structures.

Acknowledgements

The authors would like to thank both the Officeof Naval Research and the NSF Science and Tech-nology Center for Quantized Electronic Structures(under grant dDMR 91-20007) for supporting thiswork.

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