---
abstract: 'Complete suppression of the native n-type Schottky barrier is demonstrated in Al/InGaAs(001) junctions grown by molecular-beam-epitaxy. This result was achieved by the insertion of Si bilayers at the metal-semiconductor interface allowing the realization of truly Ohmic non-alloyed contacts in low-doped and low-In content InGaAs/Si/Al junctions. It is shown that this technique is ideally suited for the fabrication of high-transparency superconductor-semiconductor junctions. To this end magnetotransport characterization of Al/Si/InGaAs low-n-doped single junctions below the Al critical temperature is presented. Our measurements show Andreev-reflection dominated transport corresponding to junction transparency close to the theoretical limit due to Fermi-velocity mismatch.'
address:
- 'Scuola Normale Superiore and INFM, I-56126 Pisa, Italy'
- 'Laboratorio Nazionale TASC-INFM, Area di Ricerca, Padriciano 99, I-34012 Trieste, Italy'
author:
- 'Silvano De Franceschi, Francesco Giazotto, and Fabio Beltram'
- 'Lucia Sorba, Marco Lazzarino, and Alfonso Franciosi$^{a)}$'
- 'To be published in Phyl. Mag. B'
title: 'Andreev reflection in engineered Al/Si/InGaAs(001) junctions '
---

In the last few years there has been an increasing interest in the study of semiconductor-superconductor (Sm-S) hybrid systems [@been; @klein; @lamb]. These allow the investigation of exotic coherent-transport effects and have great potential for device applications. The characteristic physical phenomenon driving electron transport at a S-Sm junction is Andreev reflection [@andreev]. In this process (originally observed in normal metal-superconductor junctions ) an electron incident from the Sm side on the superconductor may be transmitted as a Cooper pair if a hole is retroreflected along the time-reversed path of the incoming particle. High junction transparency is a crucial property for the observation of Andreev-reflection dominated transport. Different techniques have been explored to meet this requirement including metal deposition immediately after As-decapping [@kast], Ar$^+$ back-sputtering [@nguy], and [*in situ*]{} metallization in the molecular-beam epitaxy (MBE) chamber [@akaz]. All these tests were performed in InAs-based Sm-S devices where the main transmittance-limiting factor is interface contamination. On the contrary, for semiconductor materials such as those grown on either GaAs or InP, the strongest limitation arises from the presence of a native Schottky barrier. In this case, in order to enhance junction transparency penetrating contacts [@gao; @williams] and heavily doped surface layers [@kast; @tabo] were used. Recently we have reported on a new technique [@silv], alternative to doping, to obtain Schottky-barrier-free Al/n-In$_x$Ga$_{1-x}$As(001) junctions ($x \agt 0.3$) by MBE growth. This is based on the inclusion of an ultrathin Si interface layer under As flux which changes the pinning position of the Fermi level at the metal-semiconductor junction and leads to the total suppression of the Schottky barrier. In this work we show the behavior of such Ohmic contacts realized and furthermore demonstrate how this method can be successfully exploited to obtain high transparency Sm-S hybrid junctions [@franz]. Notably these are based on low-doped and low-In-content InGaAs alloys that are ideal candidates for the implementation of ballistic-transport structures.

Al/n-In$_{0.38}$Ga$_{0.62}$As junctions incorporating Si interface layers were grown by MBE. Their schematic structure is shown in Fig. 1. The semiconductor portion consists of a 300-nm-thick GaAs buffer layer grown at 600 $^\circ$C on n-type GaAs(001) and Si-doped at $n \sim 10^{18}$ cm$^{-3}$ followed by a 2-$\mu$m-thick n-In$_{0.38}$Ga$_{0.62}$As layer grown at 500 $^\circ$C with an inhomogeneous doping profile. The top 1.5-$\mu$m-thick region was doped at $n=6.5 \cdot 10^{16}$ cm$^{-3}$, the bottom buffer region (0.5 $\mu$m thick) was heavily doped at $n \sim 10^{18}$ cm$^{-3}$. After In$_{0.38}$Ga$_{0.62}$As growth the substrate temperature was lowered to 300$^\circ$C and a Si atomic bilayer was deposited under As flux [@silv]. Al deposition ($\simeq 150$ nm) was carried out [*in situ*]{} at room temperature. During Al deposition the pressure in the MBE chamber was below $5 \cdot 10^{-10}$ Torr. Reference Al/n-In$_{0.38}$Ga$_{0.62}$As junctions were also grown with the same semiconductor part but without the Si interface layer.

In order to compare the current-voltage ($I$–$V$) behavior of Si-engineered and reference junctions, circular contacts were defined on the top surface with various diameters in the 75–150 $\mu$m range. Standard photolithographic techniques and wet chemical etching were used to this aim. Back contacting was provided for electrical characterization by metallizing the whole substrate bottom. $I$–$V$ characterization was performed in the 20–300 K temperature range using a closed-cycle cryostat equipped with microprobes. Typical room-temperature (dashed lines) and low-temperature (solid lines) $I$–$V$ characteristics for both Si-engineered and reference diodes are shown in Fig. 2.

The reference diode exhibits a marked rectifying behavior which is enhanced at low temperatures. We have measured the corresponding barrier height by different techniques: thermionic-emission $I$–$V$ measurements in the 270–300 K temperature range, and linear fit in the forward bias region of log($I$)–$V$ characteristics measured at $\sim 200$ K. These two approaches yielded barrier heights of $0.22 \pm 0.05$ eV and $0.23 \pm 0.02$ eV respectively. These values include corrections for image-charge and thermionic-field-emission effects [@S]. The quoted uncertainties reflect diode to diode fluctuations and uncertainties in the barrier height determination.

The engineered diode shows no rectifying behavior even at low temperatures (20 K in Fig. 2). Its $I$–$V$ characteristics bear no trace of a SB and are linear over the whole 20–300 K temperature range. Their slope is only weakly affected by temperature. To investigate the possible existence of a residual SB whose rectifying effect might be hidden by the series resistance arising from the InGaAs bulk and the back contact, we modeled the low-temperature $I$–$V$ behavior of the engineered diode in terms of a residual barrier height $\phi_n$ and a series resistance $R$ [@PS]. We were able to reproduce the experimental $I$–$V$ curves only with $\phi_n < 0.03$ eV. As will be apparent from what follows, this value represents only an upper limit for the barrier height.

Doping effects do not play any significant role in the barrier suppression. In order to verify this, we annealed the engineered diode at 420 $^\circ$C for 5 seconds. Following this we observed a marked rectifying behavior analogous to that of the reference sample. This result is in line with the findings reported in Ref. [@S6B] on the thermal stability of Si-engineered SBs in Al/GaAs junctions and reflects Si redistribution at the interface. Wear-out tests on engineered diodes were also performed in order to verify the persistence of the ohmic behavior against prolonged high-current stress. To this end we monitored the $I$–$V$ characteristics during 24 hours of continuous operation at current densities of 200 A/cm$^2$. No changes were detected.

In order to demonstrate the applicability of this technique to the realization of high transparency Sm-S hybrid devices, rectangular 100$\times$160 $\mu$m$^2$ Al/n-In$_{0.38}$Ga$_{0.62}$As junctions were patterned on the sample surface using standard photolithographic techniques and wet chemical etching. Two additional 100$\times$50 $\mu$m$^2$-wide and 200-nm-thick Au pads were electron-beam evaporated on top of every Al pattern in order to allow four-wire electrical measurements. Samples were mounted on non-magnetic dual-in-line sample holders, and 25-$\mu$m-thick gold wires were bonded to the gold pads. $I$–$V$ characterizations as a function of temperature ($T$) and static magnetic field ($H$) were performed in a $^3$He closed-cycle cryostat.

The critical temperature ($T_c$) of the Al film was 1.1 K (which corresponds to a gap $\Delta \approx 0.16$ meV). The normal-state resistance $R_N$ of our devices was 0.2 $\Omega$, including the series-resistance contribution ($\approx 0.1 \Omega$) of the semiconductor. At $H=0$ and below $T_c$, dc $I$–$V$ characteristics exhibited important non-linearities around zero bias that can be visualized by plotting the differential conductance ($G$) as a function of the applied bias ($V$). In Fig. 3(a) we show a tipical set of $G$–$V$ curves obtained at different temperatures in the 0.33–1.03 K range. Notably even at $T=0.33$ K, i.e. well below $T_c$, a high value of $G$ is observed at zero bias. At low temperature and bias (i.e., when the voltage drop across the junction is lower than $\Delta /e$ [@nota]), transport is dominated by Andreev reflection. The observation of such pronounced Andreev reflection demonstrates high junction transparency. The latter can be quantified in terms of a dimensionless parameter $Z$ according to the Blonder-Tinkham-Klapwijk (BTK) model [@btk; @z]. To analyze the data of Fig. 3(a) we followed the model by Chaudhuri and Bagwell [@chau], which is the three-dimensional generalization of the BTK model. For our S-Sm junction we found $Z \approx 1$ corresponding to a $\sim$50 % normal-state transmission coefficient. We note that without the aid of the Si-interface-layer technique, doping concentrations over two orders of magnitude greater than that employed here would be necessary to achieve comparable transmissivity (see e.g. Refs. [@kast; @gao; @tabo; @tabo2]). This drastic reduction in the impurity concentration is a very attractive feature for the fabrication of ballistic structures. It should also be noted that our reported $Z$ value is close to the intrinsic transmissivity limit related to the Fermi-velocity mismatch between Al and InGaAs [@BT].

We should also like to comment on the homogeneity of our junctions. By applying the BTK formalism, $Z\approx 1$ leads to a calculated value of the normal-state resistance ($R_N^{th}$) much smaller than the experimental value $R_N^{exp}$: $R_N^{th}/R_N^{exp}=0.003$ . This would indicate that only a small fraction ($R_N^{th}/R_N^{exp}$) of the contact area has the high transparency and leads to the transport properties of the junction, as already reported for different fabrication techniques [@gao; @van]. Values of $R_N^{th}/R_N^{exp}$ ranging from $\sim 10^{-4}$ to $\sim 10^{-2}$ can be found in the literature (see, e.g., Refs. [@kast; @gao; @van]). Such estimates, however, should be taken with much caution. Experimentally, no homogeneities were observed on the lateral length scale of our contacts and we did observe a high uniformity in the transport properties of all junctions studied.

The superconducting nature of the conductance dip for $|V|<\Delta/e$ is proved by its pronounced dependence on temperature and magnetic field. Figure 3(a) shows how the zero-bias differential-conductance dip observed at $T=0.33$ K progressively weakens for $T$ approaching $T_c$. This fact is consistent with the well-known temperature-induced suppression of the superconducting energy gap $\Delta$. Far from $V=0$ the conductance is only marginally affected by temperature as expected for a S-Sm junction when $|V|$ is significantly larger than $\Delta/e$ [@btk]. A small depression in the zero-bias conductance is still observed at $T \simeq T_c$. This, together with the slight asymmetry in the $G$–$V$ curves, can be linked to a residual barrier at the buried InGaAs/GaAs heterojunction.

In Fig. 3(b) we show how the conductance can be strongly modified by very weak magnetic fields ($H$). The $G$–$V$ curves shown in Fig. 3(b) were taken at $T=0.33$ K for different values of $H$ applied perpendicularly to the plane of the junction in the 0–5 mT range. The superconducting gap vanishes for $H$ approaching the critical field ($H_c$) of the Al film ($H_c \simeq 10$ mT at $T=0.33$ K). Consequently, the zero-bias conductance dip is less and less pronounced and at the same time shrinks with increasing magnetic field. The latter effect was not as noticeable in Fig. 3(a) owing to the temperature-induced broadening of the single-particle Fermi distribution function [@btk].

In conclusion, we have reported on Ohmic behavior and Andreev-reflection dominated transport in MBE-grown Si-engineered Al/n-In$_{0.38}$Ga$_{0.62}$As junctions. Transport properties were studied as a function of temperature and magnetic field and showed junction transmissivity close to the theoretical limit for the S-Sm combination. The present study demonstrates that the Si-interface-layer technique is a promising tool to obtain high-transparency S-Sm junctions involving InGaAs alloys with low In content and low doping concentration. This technique yields Schottky-barrier-free junctions without using InAs-based heterostructures and can be exploited in the most widespread MBE systems. It is particularly suitable for the realization of low-dimensional S-InGaAs hybrid systems grown on GaAs or InP substrates. We should finally like to stress that its application in principle is not limited to Al metallizations and other superconductors could be equivalently used. In fact, to date the most convincing interpretation of the silicon-assisted Schottky-barrier engineering is based upon the heterovalency-induced IV/III-V local interface dipole [@bin]. Within this description Schottky-barrier tuning is a metal-independent effect.

The present work was supported by INFM under the PAIS project Eterostrutture Ibride Semiconduttore-Superconduttore and the TUSBAR program. One of us (F. G.) would like to acknowledge Europa Metalli S.p.A. for financial support.

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