NS junctions using high-mobility GaAs:AlGaAs heterostructures

Superlattices and Microstructures, Vol. 25, No. 5/6, 1999 Article No. spmi.1999.0716 Available online at http://www.idealibrary.com on

NS junctions using high-mobility GaAs:AlGaAs heterostructures DAVID A. W ILLIAMS Hitachi Cambridge Laboratory, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, U.K. (Received 24 March 1999)

The fabrication, analysis and measurement of superconductor/semiconductor junctions with GaAs:AlGaAs heterostructure channels is described. Microscopic analysis was used together with electrical measurement to optimize the characteristics of the annealed Sn and In alloy contacts, leading to the observation of ballistic electron mediated supercurrents. These contacts also had a high critical magnetic field, allowing the study of Andreev reflection at high fields. Epitaxially grown and unannealed single-crystal Al contacts showed high transparency. c 1999 Academic Press

Key words: Andreev reflection, superconductor–semiconductor junction, GaAs.

GaAs:AlGaAs heterostructures are attractive substrates for superconductor/semiconductor junctions because of the high electron mobilities obtainable, potentially making the study of ballistic and geometric effects in such junctions more easily fabricable. However, the high-mobility electron channel is inevitably buried, usually 70–100 nm below the semiconductor surface, which makes contact formation difficult. This paper reports the development of contact fabrication in this material, in the collaboration between the Cambridge University Microelectronics Research Centre and the Hitachi Cambridge Laboratory, using four different contact strategies, and the subsequent electrical characteristics of such junctions. The problem of contact formation to buried GaAs:AlGaAs channels is not limited to the formation of superconducting contacts. It is also of intrinsic importance in the fabrication of devices for the investigation of the quantum Hall effects and other transport physics experiments, and in the fabrication of commercial electronic and optoelectronic devices. Although in the latter case contact resistances remain problematic, in the former, variations in contact behaviour are typically removed by performing four-terminal measurements, and the microscopic nature of charge transport at the interfaces has not been extensively studied. In the case of superconducting contacts, however, and the study of Andreev reflection processes in particular, the microscopic nature of the contact and charge transport across it is of crucial importance [1]. For this reason, most studies have concentrated on materials systems which are more straightforward to fabricate, and more amenable to analysis, particularly niobium contacts to silicon and indium arsenide-based semiconductors, however several groups have fabricated GaAs-based junctions [2–5]. The substrate material used was typically a standard high-mobility modulation-doped GaAs:AlGaAs heterostructure, with a typical depth of the channel from the surface of 40–100 nm. Many types of metallic superconducting contact were investigated, and four were used successfully for different investigations. 0749–6036/99/050701 + 09 $30.00/0

c 1999 Academic Press

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1. Slow-annealed indium contacts Plain indium contacts were used with strip-heater annealing for early experiments, which provided hightransmission contacts, but which were difficult to control, and delivered an extremely low yield. In these experiments, the carrier concentration and mobility of the 2DEG were 5.9×1011 cm−2 , and 1.1×105 cm2 V−1 s−1 , respectively at 4.2 K. The mobility corresponds to an electron elastic mean-free path, le , of 1.4 µm. The contacts were formed by thermal evaporation, with a gap of 1 µm on the surface of an AlGaAs/GaAs heterojunction with a channel 200 µm wide, then sintered at 420 ◦ C for 120 s in a N2 + 5%H2 forming gas. The contacts were superconducting with a critical temperature Tc of 4.3 K, higher than that of bulk In (3.4 K), due to alloying. A supercurrent was observed between the contacts, as seen in Fig. 1, which was the first to be seen in the GaAs:AlGaAs system [6]. It was shown to be mediated by ballistic electron transport in the channel by killing the channel mobility in the superconducting devices by electron irradiation, after which no supercurrent was observed. The other point of note in these experiments was the high critical voltage. The critical current– normal resistance product Ic Rn , known as the critical voltage Vc , is used as a figure of merit for weak links. Here, Vc (Ic = 100 µA, Rn = 35  at 1.6 K) is 3.5 mV, and the energy gap in the indium electrodes is 1.5 meV. The Ambegaokar–Baratoff [7] result (π1(0)/2e) is often used as an upper bound to Vc and in this case is 1.02 mV. Vc for these indium contact devices is much larger than this result, but the Ambegaokar–Baratoff system is not directly applicable to transparent contacts. The critical voltage was derived for a junction in the clean limit by Kulik and Omelyanchuk [8], and is given as, Is Rn = π 1/e sin(φ/2) tanh(1 cos(φ/2)/2kB T ),

(1)

where φ is the superconducting phase across the junction. In our experiment T /Tc = 0.37 so Vs (max) = Vc = 1.81 mV at a phase of φ = 2.08 radians. This result was also derived for a very short junction where lj  ξn , le , for a continuous metal weak link.

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The coherence length, ξn in a two-dimensional channel in the ‘clean’ limit is given by [9], ξnc = (~2 /2πm ∗ kB T ) (2π N )1/2 , and in the ‘dirty’ limit by, ξnd = (~3 µ/6π m ∗ ekB T )1/2 (2π N )1/2 . Well within −2 + ξ −2 )−1/2 [10] and at the transition between the limits (l /ξ = 1) [11], either limit the length is ξn = (ξnc e n nd −1/2 ∼ ξn = ξnd (1 + [le /ξnc (Tc )]) . The coherence length here was 90 nm at 4.2 K, (<1/10 of the contact separation), putting the structure well within the ‘clean’ limit. The approaches mentioned above did not consider a normal region of different effective mass and Fermi velocity from the electrodes, so the results were not dependent on the properties of the normal region. Bardeen and Johnson [12] and Golub and Horovitz [13] extended an earlier model [14] to calculate Vc for a superconductor/normal metal/superconductor junction and show the variation with length (lj  ξn ) and temperature. Scattering in the normal region is neglected, but thermal equilibrium of carriers in the normal region is assumed, rather than ballistic nonequilibrium transport. Using this approach, the calculated Vc [12] is ≈4.5 µV, clearly much smaller than measured. This is because the maximum critical current density in the calculation is limited by the density of electron states in the normal region. For ballistic transport, the density of states is not limited to the thermal equilibrium value.

2. Rapidly annealed tin alloy contacts The problems of yield with indium-based contacts led to attempts with other materials. Initial success was found using a simple layered contact consisting of tin, chromium and gold [15, 16], but this was subsequently refined to remove the possibility of introducing magnetic centres in the channel. In all cases, a metallic multilayer was deposited on the semiconductor surface, in a pattern defined by electron-beam lithography of polymethyl methacrylate and lift-off. Sintering of the contacts was performed using an ultra-rapid thermal annealing system, which heats the back surface of the chip or wafer with a rapidly-scanned high-current electron beam. This gives a time at peak temperature of ∼10 ms, with a thermal cycle of a very rapid linear temperature rise followed by a slower exponential decay as the sample cools in vacuum [12]. The effective anneal time is very much shorter than the nominal heating time, which is the duration of the linear section (heating with constant electron-beam power). Diffusion lengths are approximately exponentially dependent on anneal temperature and linearly dependent on time, so the most effective part of the cycle is the peak of the temperature–time curve, and the effective anneal time is of the order of 10 ms or lower. This method gives very precise control of the annealing process. Samples are annealed face-downwards to prevent electron-beam damage of the transport channel, and proximity capping is used to minimize arsenic out-diffusion during the heating in vacuum. Similar heating cycles are used routinely to make nonsuperconducting ohmic contacts to high-mobility 2DEGs for low-temperature measurements, and it it well established that there is little or no mobility degradation in the process. The first optimized contact metallization was a layer of tin 250 nm thick, with a 100 nm layer of chromium and a cap of 60 nm of gold. Such a multilayer was necessary to provide good contact properties, with the tin acting as a dopant for the semiconductor, with some remaining on the surface as the superconducting region. The chromium was used as a refractory cap, to hold the tin in place during annealing, and the gold was to prevent oxidation of the chromium and allow the application of subsequent bonding metallization. The contact morphology changes considerably after annealing; smoother on a micron scale, but with evidence of gross distortion of the surface, giving a bubbled appearance, and much voiding is seen. The edge of the contact is relatively undisturbed, and largely follows lithographic fluctuations, in contrast to the gross mass-flow observed if a chromium layer is not included. The cross-sectional structure of the contact after annealing can be seen in a cross-sectional scanning electron micrograph in Fig. 2, and a transmission electron micrograph in Fig. 3, and is highly heterogeneous. The contact metal has extensively alloyed with the semiconductor to a depth in excess of 200 nm in some regions. The structure is polycrystalline, with considerable faceting and voiding, and there is no trace of

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Fig. 2. Cross-sectional scanning electron micrograph of a tin/chromium based contact showing a characteristic rounded trapezoidal inclusion.

Fig. 3. Cross-sectional electron micrograph of a tin/chromium contact showing the inclusion structure. The arrow shows the original semiconductor surface.

the original heterostructure visible under most of the contact. Other regions show much less intermixing. Energy-dispersive X-ray analysis (EDX) was used to assess the elemental composition of various regions. Several alloy phases can be seen, with a predominance of an alloy of Sn4 Au, in a matrix which is chromium-rich and has a large proportion of CrAs. There is evidence in some regions of arsenic depletion from the GaAs up to 2 µm from the surface, but again this is not uniform across the sample. Many aspects of the general morphology are similar to those of gold:germanium:nickel ohmic contacts to GaAs heterostructures formed by the same annealing process, although the optimized annealing conditions are slightly different for the two materials. In particular, there is considerable evidence of rounded trapezoidal inclusions, qualitatively similar to the spikes seen in Au:Ge:Ni contacts, but shallower and broader. EDX analysis of the various regions shows there to be a gold–tin compound with a concentration ratio of 1:4. A comparison of the equilibrium phase diagram for Au:Sn and the diffraction patterns obtained for this phase confirms that this is almost certainly Sn4 Au, which is orthorhombic with a = 0.6445 nm, b = 0.6487 nm and c = 1.1599 nm. The diffraction patterns obtained fit this to an accuracy of 1.5%, the discrepancy probably being due to the addition of a component of gallium. The matrix regions in which the tin–gold alloy is interspersed are predominantly chromium, with a variable arsenic content. The presence of chromium was felt to be an unnecessary complication, as a magnetic scattering centre, so the structure was altered: a layer of tin is evaporated and then capped in situ with a gold layer to prevent oxidation during specimen transfer. On to this a layer of silicon nitride is sputtered and then a refractory layer of chromium and gold is evaporated. The contact was sintered using rapid electron-

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A

200 nm Fig. 4. Cross-sectional transmission electron micrograph of the optimized tin-based contact. At A, the superconducting contact is seen to be a single crystal.

beam annealing as described above. The layer of silicon nitride is used as a diffusion barrier to prevent chromium mixing and alloying with the tin and the semiconductor during annealing. A thin layer of aluminium oxide is used to prevent contact flow across the gap during sintering. The layers of silicon nitride and chromium are used as a refractory layer, to prevent contact movement during annealing. Figure 4 shows a cross-sectional transmission electron micrograph of the contact region near the edge of the channel. In these contacts, the AlGaAs region is breached by inclusions near the channel, which are typically largegrain crystals on the superconductor side. A combination of the differential heat flow, and stress relief in the nitride layer, causes the inclusion formation to be favourable in this region. The critical temperature, and the critical magnetic field, of the superconducting alloy contact material have been measured in separate structures and found to vary between specimens, lying in the ranges 4–7.5 K and 3–6.5 T, respectively. The effect of a magnetic field on Andreev reflection has recently received increasing theoretical attention. The low-field behaviour is now well understood, with many experimental results, mostly using Nb:InAs devices. However, Nb contacts tend to have a low critical magnetic field, with the result that the regime above 50 mT has been little studied experimentally. The high critical fields of these contacts allow the higher-field behaviour of Andreev reflection to be investigated. Figure 5 shows the magnetoresistance response of the device at 0.3 K compared with a result obtained at 6 K. Superficially, the magnetoresistance appears to be as expected for a device of this geometry, with a progressive rise in resistance with increasing field and the onset of Shubnikov–de Haas/quantum Hall oscillations at higher fields. (The measured magnetoresistance is effectively two-terminal across the two-dimensional 2 ). channel and so contains elements of both longitudinal and transverse conductance: ρxx = σyy /(σxx σyy +σxy Two-terminal measurements of such devices show positive magnetoresistance with steps and superposed oscillations, and have been extensively studied.) However, the region below 3 T shows an unusual curvature and a lower resistance relative to that at higher temperature or bias than is seen in control devices with normal contacts. The unusual behaviour is more easily seen in a plot of normalized conductance versus perpendicular magnetic field. This is shown in the figure. The conductance of the structure with superconducting contacts shows several distinct regimes. For very low fields, the normalized conductance is less than unity, and rises to one at a field of approximately 60 mT, due to the breaking of weak localization in the channel. At higher fields, the conductance rises linearly and then oscillates and falls, reaching values around unity near 4 T. Other differences are seen between the superconducting and normal contacts. With superconducting contacts, the absolute resistance of the structure, and the change with field d R/d B, are both lower. Also, the magnetoresistance oscillations are considerably less well resolved than with normal contacts. This is an indication of the inhibition of the Hall effect due

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to the superconducting contacts. The existence of the superconducting region immediately adjacent to the channel imposes a local lateral electrical equipotential which dampens the establishment of a Hall voltage across the channel. This is also seen with normal conductor contacts in similar geometry, but the effect is larger for exactly the same geometry with superconducting contacts. The excess conductance shown in the figure is a measure of the proportion of Andreev reflection in the transport across the interfaces. Both the normalized zero-bias conductance, and the character of the differential resistance at finite bias, indicate that the proportion of the electron transport which takes place by Andreev reflection is first increasing with applied magnetic field, up to a field of around 1 T, then decreasing. This is against a background of generally decreasing conductance with magnetic field. As the field increases, the overall number of conduction channels decreases and transport begins to take place via edge channels, giving the overall positive magnetoresistance seen with both normal and superconducting contacts. With superconducting contacts, in order for transport across the interface to occur at subgap biases by Andreev reflection, the conditions of energy, (E 1 + E 2 = 2E s ) wavevector and spin, k1,↑ = −k2,↓ , matching must occur for the electrons in the channel to enter the superconductor as a spin-singlet pair. With no applied field, the range of states available near the interface means that the probability of two incoming electrons satisfying these conditions is low (unless interference effects are considerable). With edge-channel transport, the matching conditions are more likely to be satisfied. A similar increase in Andreev reflection probability has been seen using niobium nitride contacts [18]. As the field is raised still higher, spin-splitting means that the matching conditions are no longer satisfied, and the probability of Andreev reflection falls. The field at which the turnover in excess conductance is seen corresponds to the field at which spin-splitting of the levels is seen. When the available channels are

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spin-polarized, although the wavevector and energy conditions may be met, spin-flip is needed for Andreev reflection to occur [17], and so the probability decreases.

3. Epitaxial aluminium contacts For these experiments, a 125 nm GaAs/AlGaAs superlattice buffer layer was grown on a semi-insulating GaAs substrate, followed by 400 nm of undoped GaAs and 35 nm thick AlGaAs with 2δ-doped layers, with 5 × 1012 cm−2 Si atoms. Finally, 60 nm of pure single crystalline aluminium was grown in situ after the substrate temperature had fallen to room temperature, without breaking vacuum. All of the aluminium is pure (001) single crystal, as determined by transmission electron microscopy and X-ray diffraction. The interface between the aluminium and the semiconductor is atomically abrupt. The aluminium had a resistivity of 2.9 cm and a Tc of 1.2 K. The carrier concentration and mobility of the 2DEG were determinated to be 6.1 × 1011 cm−2 and 8.0 × 103 cm2 V−1 s−1 at room temperature and 6.6 × 1011 cm−2 and 1.1 × 105 cm2 V−1 s−1 at low temperatures, respectively. A 400 × 460 µm2 mesa structure was defined by optical lithography and etched from the single crystalline aluminium and GaAs/AlGaAs layers, and bond-pads were deposited. The mesa was defined by etching the structure to a depth of 500 nm. Two fingers of 5 × 0.5 µm2 and spaced 0.3 µm apart were then defined in the single crystalline aluminium using conventional electron beam lithography with poly-methylmethacrylate resist. The GaAs/AlGaAs and aluminium were wet etched using citric acid solution: H2 O2 (25:3) and KOH (14 mM), respectively. Four-terminal electrical measurements were carried out in a HeIII refrigerator using lock-in techniques at a frequency of 17 Hz. The coherence length in the 2DEG of these devices is estimated to be 4 µm at 300 mK. A supercurrent was observed between these contacts, and the differential resistance of such a device is seen in Fig. 6. The critical current is 390 µA at 300 mK, decreasing slowly with temperature up to 0.4 K and the supercurrent disappears around 1.2 K. Vc for this structure (Ic = 400 µA, Rn = 200 m at 300 mK) is 80 µeV, compared to the energy gap in the aluminium electrodes of 0.18 meV. The Ambegaokar–Baratoff [7] result (π1(0)/2e) in this case is 0.28 mV. In our experiment T /Tc = 0.37 so Vs (max) = Vc = 1.81 mV. Vc is thus well within the theoretically expected limits, in marked contrast to the situation measured using annealed indium contacts to a GaAs 2DEG [6], where a critical voltage far in excess of the Ambegaokar–Baratoff value was observed. The observation of a supercurrent depends upon the lack of scattering of normal electrons in the semiconductor channel, and on the phase-coherent Andreev reflection between the contacts and the channel. In these devices, contact between the two regions is by tunnelling through the AlGaAs layer. It is necessary to rule out parallel conduction through the δ-doped layers in the AlGaAs, and to this end similar structures were fabricated with the only difference being that the undoped AlGaAs spacer layer between the lower δ layer and the 2DEG was an extra 20 nm thick. The transmission between the contacts and the 2DEG was very much reduced, and no supercurrent was observed, indicating that there is little or no contribution from parallel conduction. The proximity effect is generally considered to be entirely due to the overlap of the correlated electron wavefunctions from the superconducting region into the normal metal. The pairing potential due to the phonon interaction is considered to be zero in the normal metal. This is true for most superconductor/normal metal interfaces, where there is a large acoustic mismatch between the materials. However, in the case of an epitaxial link between the two regions, there is very little barrier to phonon transport across the interface, and the phonon distribution in the superconducting aluminium can pass ballistically into the semiconductor. The proximity effect is usually described by a finite pair amplitude hψ↑ ψ↓ i in the normal material. We propose that in the case of phonon-coupled proximity effect, there is a further real pair potential, although this does not imply a real induced gap in the semiconductor, as the phonon–electron coupling would only be

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strong for the electrons with the matched wavevector, which would be those which took part in the proximity effect coupling. There is no evidence for such a gap in these experiments, and as most of the coupling is through the AlGaAs layer, there is little chance of seeing such a gap in this material. The main effect is that the proximity coherence length is increased, coupling the superconductor to the ballistic 2DEG over larger than usual lengths. The observation of a supercurrent in this structure implies that transport between the superconductor and the two-dimensional electron gas is coherent, via proximity coupling or Andreev reflection. Experience of other superconductors in this geometry with a GaAs:AlGaAs heterostructure is that tunnel coupling over this length is not sufficiently coherent for the observation of a supercurrent.

4. Conclusion This paper has summarized recent work on SN contacts using GaAs channels, in the Hitachi Cambridge Laboratory/Cambridge University Microelectronics Research Centre collaboration. Acknowledgements—The author would like to acknowledge the considerable experimental contributions of Adrian Marsh, Tim Moore, and Moises Villalvilla, Simon Newcomb and the late Mike Stobbs for TEM analysis, Mohammed Missous and Colin Stanley for MBE growth, and Haroon Ahmed, Bruce Alphenaar and Colin Lambert for many useful discussions.

References [1] Other papers in this issue, and for a review see: C. J. Lambert and R. Raimondi, cond-mat/9708056.

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[2] K. M. Lenssen et al., Appl. Phys. Lett. 63, 2079 (1993). [3] J. R. Gao et al., 10th International Conference on the Electronic Properties of Two-Dimensional Systems (Englewood Cliffs, RI, 1993). [4] J. Kutchinsky et al., Phys. Rev. Lett. 78, 931 (1997). [5] W. Poirier et al., Phys. Rev. Lett. 79, 2105 (1997). [6] A. M. Marsh et al., Phys. Rev. B50, 8118 (1994). [7] V. Ambegaokar and A. Baratoff, Phys. Rev. Lett. 10, 486 (1963); erratum 11, 104 (1963). [8] I. O. Kulik and A. N. Omelyanchuk, Fiz. Nizk. Temp. 3, 945 (1977) [Sov. J. Low Temp. Phys]. [9] G. Deutscher and P. G. de Gennes, Superconductivity, edited by R. D. Parks (Marcel Dekker, New York, 1969) Vol. 2. [10] W. Silvert, J. Low Temp. Phys. 20, 439 (1975). [11] A. W. Kleinsasser, J. Appl. Phys. 69, 4146 (1991). [12] J. Bardeen and J. L. Johnson, Phys. Rev. B5, 72 (1972). [13] A. Golub and B. Horovitz, Phys. Rev. B49, 4222 (1994). [14] C. Ishii, Prog. Theor. Phys. 44, 1525 (1970). [15] A. M. Marsh et al., Semicond. Sci. Technol. 10, 1694 (1995). [16] A. M. Marsh et al., J. Vac. Sci. Technol. A14, 2577 (1996). [17] M. P. A. Fisher, Phys. Rev. B49, 14550 (1994). [18] H. Takayanagi and T. Akazaki, Physica B249–251, 462 (1998).