Room-Temperature Quantum Ballistic Transport in Monolithic Ultrascaled Al–Ge–Al Nanowire Heterostructures

Conductance quantization at room temperature is a key requirement for the utilizing of ballistic transport for, e.g., high-performance, low-power dissipating transistors operating at the upper limit of “on”-state conductance or multivalued logic gates. So far, studying conductance quantization has been restricted to high-mobility materials at ultralow temperatures and requires sophisticated nanostructure formation techniques and precise lithography for contact formation. Utilizing a thermally induced exchange reaction between single-crystalline Ge nanowires and Al pads, we achieved monolithic Al–Ge–Al NW heterostructures with ultrasmall Ge segments contacted by self-aligned quasi one-dimensional crystalline Al leads. By integration in electrostatically modulated back-gated field-effect transistors, we demonstrate the first experimental observation of room temperature quantum ballistic transport in Ge, favorable for integration in complementary metal–oxide–semiconductor platform technology.

A fter decades, following Moore's law 1 by continuously shrinking feature sizes of classical planar metal-oxidesemiconductor field-effect transistors (FETs), physical limitations and the dramatic repercussions of short-channel effects 2 have forced a shift of research efforts toward the integration of new materials, novel processing techniques, and ultrascaled device architectures. 3 Owing to miniaturization in engineering systems as well as increasing interest in fundamental research in accompanying quantum confinement effects and ballistic transport, quasi-one-dimensional nanostructures, such as semiconductor nanowires (NWs), gain particular interest. 4−6 As the minimum feature size approaches the bulk electron mean free path, novel physics due to the confinement of electrons and phonons may pave the way for future high-performance, nanoelectronic devices. 7,8 Although room temperature ballistic transport was demonstrated in constricted two-dimensional electron gases of high-mobility materials, 9−11 forming quantum point contacts, ballistic transport in NWs was restricted to high magnetic fields (>4 T) and ultralow temperatures. 12 Motivated by the relevance of ballistic transport for multivalued logic gates, 13 quantum computing, 14, 15 and, recently, the realization of topological superconductivity or Majorana Fermions, 16−19 ballistic transport observed in Si−Ge core−shell NWs 7,20,21 triggered further research activities on group IV NWs favorable for complementary metal−oxide−semiconductor (CMOS) process integration. In particular, Ge NWs represent a unique quasi-1D system for exploring quantum coherence phenomena because of the high hole mobility 22 and an exciton Bohr radius of a Ge = 24.3 nm, 23 approximately five times larger than that of Si (a Si = 4.9 nm), leveraging strong quantum confinement effects. 24 In addition, compared to III−V materials in which hyperfine coupling limits the electron-spin coherence, the prospect of long coherence times in group IV semiconductors with spin-zero nuclei has stimulated a lot of experimental effort also for spin-based quantum information applications. 25 Despite the above-mentioned beneficial properties of Ge to the study of quantum confinement effects, 26 ballistic transport was not observed for temperatures above T = 2 K, 27 which is also attributed to precise nanopatterning and contact-formation issues. Furthermore, in these quasi-1D structures, surface states create inhomogeneities in the local electrostatic environment, increasing the probability of electron reflections and backscattering. 12 In this letter, we demonstrate for the first time room temperature quantum ballistic transport in ultrascaled Ge NWs with diameters comparable to the Bohr radius of Ge of a Ge = 24.3 nm. Therefore, monolithic Al−Ge−Al NW heterostructures with ultrashort Ge segments are integrated in a back-gated FET architecture (Figure 1a) accomplished by a novel heterostructure formation process via a thermally controlled exchange reaction between the single-crystalline Ge NWs and Al contact pads. 28 As shown in the SEM image in Figure 1a, applying this fabrication technique enables an axial metal− semiconductor-metal arrangement featuring an ultrashort Ge segment connected by quasi-1D crystalline Al (c-Al) leads with abrupt metal−semiconductor interfaces (see the transmission electron microscope (TEM) image in the inset).
To achieve ultrashort Ge segments, vapor−liquid−solid (VLS) grown Ge NWs with diameters of around 25 nm, occasionally coated with 20 nm high-k Al 2 O 3 by atomic layer deposition, are drop-cast onto an oxidized highly p-doped Si substrate. For the subsequent exchange reaction and selfaligned contact formation, Al pads are fabricated by electronbeam lithography, sputter deposition, and lift-off techniques. Thus, the device resembles a fully featured back-gated FET, whereby the actual Ge channel length (L Ge ) can be controlled by a successive thermally induced exchange reaction between the single-crystalline Ge NWs and the Al contact pads by rapid thermal annealing at a temperature of T = 623 K in forming gas atmosphere. Details of the exchange reaction, TEM, and compositional analysis by high-resolution energy-dispersive Xray investigations revealing the perfect crystallinity and purity of the remaining Ge segments connected to single crystalline Al leads were already given in a previous Letter. 28 In contrast to common short-channel devices, utilizing this unique device architecture effectively prevents the screening of the gate electric field by extended source and drain contacts. 29 The transfer characteristics in Figure 1b for a device with a bare Ge NW segment and one covered by Al 2 O 3 demonstrate the necessity of the high-k passivation layer to achieve reliable and reproducible electrical performance of the device. Although intrinsic VLS-grown Ge NWs were used, negative surface charges accumulating in interband trap levels 30 lead to an overall p-type behavior of the back-gated FET device for both the bare as well as the Al 2 O 3 -covered NWs. As adsorbates influence the electrical behavior of Ge-NW-based devices, 31,32 it was mandatory to passivate the Ge NWs prior to the heterostructure formation to reduce interface traps and surface disorder 33,34 and thus ultimately gain the ability to observe ballistic transport at room temperature.
In agreement with previous reports, 35,36 using a high-k passivation layer results in less pronounced hysteresis effects. In addition, the ON-current and the I ON /I OFF ratio of the passivated FET increases by more than two orders of magnitude. However, even the passivated device shows a small hysteresis due to kinetic effects, mostly related to chargecarrier trapping at the interface, and the devices exhibit transient behavior, as shown in the left inset of Figure 1b. For a negative gate voltage of V G = −15 V, the accumulation of holes continuously neutralizes trapped electrons, resulting in an exponential decay of the drain current over time. 30 In accordance with Zhang et al., 37 we assume that during atomic layer deposition, a thin GeO x layer is formed at the interface between the Ge NW and the Al 2 O 3 passivation. Dedicated to a multiexponential time dependence, indicating a significant spread in the spatial and energetic distribution of the surface trap states as well as kinetic limitation by either a diffusion barrier or a tunnel barrier at the NW surface, the charging and discharging of trapped surface states are relatively slow processes. 30 Therefore, for the actual device geometry and under the given experimental conditions, steady state is achieved after a time span of approximately 1 h, which has to be taken into account to achieve reliable ballistic transport measurements.
Furthermore, as shown in the right inset, a combination of conformal high-k passivation and control of the trap population allows the effective tuning of the electronic transport characteristic of the back-gated Ge NW device. Whereas the devices with uncoated Al−Ge−Al NW heterostructures

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Letter provoke a distinct nonlinear I/V characteristic, the ohmic behavior and higher conductivity for the passivated devices after trap depletion indicates improved contact properties enabling effective carrier injection (see the Supporting Information).
Two-terminal I/V measurements of passivated Al−Ge−Al NW heterostructure devices with different Ge segment lengths, shown in Figure 2a, revealed a clear transition from a nonlinear behavior to an almost linear characteristic for devices with channel lengths below L Ge = 45 nm.
Essentially, one may assume that devices with Ge segment lengths of L Ge > 45 nm operate as back-gated Schottky barrier FETs, with I D ∝ exp(eV/kT) due to two back-to-back Schottky contacts, which is commonly addressed to explain nonlinear I/ V curves of semiconductor NW devices. 38 Figure 2b shows further that the thereof calculated overall resistance of longer devices is directly proportional to the Ge segment length in accordance with Ohm's law. In contrast, heterostructure devices with Ge segment lengths below L Ge = 45 nm reveal a linear I/V characteristic, with the resistance being independent of the Ge segment length. Assuming a square-well confining potential as well as periodic boundary conditions for a Ge NW with a diameter of 25 nm, the current from the continuous bands in the contact leads is redistributed to a maximum of four conductance channels inside the Ge NW (see the Supporting Information). 39,40 According to Figure 2b, we assume that under the given experimental conditions (V G = 0 V), we can only access one conductance channel. Thus, Figure 2b actually illustrates the modification of the transmission coefficient as a function of the channel length for the first conductance channel. This is supported by the enlarged view in the inset of Figure 2b, which shows that the resistance of Al−Ge−Al NW heterostructures with ultrascaled Ge channels is approaching the fundamental contact resistance of R C = 12.9 kΩ, which is a first indication of ballistic transport. 39 For thin Ge NWs with diameters of about 25 nm and, thus, close to a Ge , quantum confinement results in a band structure being composed of multiple 1D sub-bands. According to the schematic shown in Figure 3a with the NW axis being oriented along the x-direction due to the quantum confinement in the y−z direction, the respective dispersion relation E(k) for holes of such a quantum wire provokes the corresponding quantization of conductance, 42,43 with each 1D sub-band contributing a quantum unit of conductance of G 0 = 2e 2 /h. 41 Figure 3b shows the transient behavior of the measured conductance of three Al−Ge−Al NW heterostructure devices with Ge channel lengths of L Ge = 15, 45, and 150 nm at V G =   Figure 3a). In contrast, applying a positive gate voltage of V G = 15 V provokes the filling of empty traps below the Fermi energy, resulting in a morenegative "effective" gate. This process continues until equilibrium is reached, having a higher number of trap states filled, which results in a Fermi level slightly below the edge of the third sub-band (red line of Figure 3a).
Thus, to support the proposed model, the upper left inset of Figure 3b shows the transfer characteristic for the ultrascaled (L Ge = 15 nm) device for different trap filling levels. Initially, without any depletion or filling of the traps, sweeping V G from 0 to −15 V, two distinct step-like features are observed at 1 and 2 G 0 due to the quantization of the density of states, with each step attributed to the population of a single spin-degenerated 1D sub-band. As already discussed above and attributed to the almost-insignificant contact resistances, the injection barriers appeared to be negligible, 41 indicating effective carrier injection with hole tunneling at the abrupt Al−Ge interface. However, G−V G measurements conducted for different trap depletion times between 15 and 60 min show that due to gradually trap depletion, the Fermi level moves upward, and thus, finally, only the first sub-band contributes to ballistic current transport, which is indicated by a step-like feature at G 0 . Furthermore, operating the device with filled traps due to effective gating, the Fermi level lowers and populates the first three sub-bands, which is supported by distinct step-like features in the G−V G characteristic at integer multiples of G 0 .
Hence, by investigating the transient behavior of trap neutralization/filling on the electronic transport of ultrascaled Al−Ge−Al NW heterostructures, we demonstrate that although the Fermi level shifts in respect to the trap-filling level, conductance quantization persists.
With increasing channel length, carrier scattering, and, for NWs in particular, surface roughness scattering will influence charge transport, and finally, when exceeding the mean free path, carrier transport will become diffusive. Hence, for the device with L Ge = 45 nm in the steady state, the conductance level is in the order of 0.25G 0 , which is close to the ballistic limit. For the device with the channel length of 150 nm, exceeding the mean free path in Ge, the conductance level is only 0.1G 0 . For even longer devices in the steady state, the diffusive transport leads to the observed linear dependency of the resistance on the channel length. The upper-right inset in Figure 3b depicts a compilation of steady-state G−V G measurements at T = 300 K of Al−Ge−Al NW heterostructure devices with Ge segment lengths L Ge between 15 and 45 nm. However, with increasing channel lengths, the plateau is shifted to lower conductance values corresponding to an added series resistance and, thus, a decrease of ballistic traversing charge carriers due to increased scattering. Investigations on numerous devices revealed that for devices with Ge segment lengths above L Ge = 45 nm, all signs of conductance quantization at room temperature vanish.
Finally, we focus on the investigation of the temperature dependency of the ultrascaled Al−Ge−Al NW heterostructure devices. Figure 4a depicts the G−V G behavior of a device with a physical channel length of L Ge = 15 nm measured in the temperature range between T = 5 K and 300 K.
Distinct plateau-like features can be observed over the entire temperature range, and neither the overall conductance nor the steepness of the conduction plateaus change with increasing temperature. For the long-channel devices, drift current due to the applied electric field dominates the charge-carrier transport, and in accordance with the work of Jones et al., 42 we observed a distinct decrease of conductivity due to a freeze-out of charge carriers below T = 25 K. The lack of such a temperature dependence for the ultrascaled devices is thus further proof of ballistic transport.
In addition to the plateau at G 0 , the ultrascaled Al−Ge−Al NW heterostructure device with a Ge segment length of L Ge = 15 nm exhibits several resonances below G 0 . A plateau-like Figure 4. (a) G−V G plot for an Al−Ge−Al NW heterostructure device with a Ge segment length of L Ge = 15 nm for temperatures between T = 5 K and 300 K. The inset shows the G−V G behavior shifted in V G for presentation clarity. The conductance was directly obtained from the measured current according to G = I D /V D . (b) Bias spectroscopy dI D /dV D of the 1D sub-band structure at T = 70 K. The differential conductance dI D /dV D was directly obtained from I/V measurements at different gate-voltages and is plotted in units of G 0 .

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Letter feature at approximately 0.85G 0 could clearly be observed for temperatures up to T = 200 K and is assumed to be a result of spin effects, but so far, there is no generally accepted explanation for the origin of this conductance feature. 43 Further plateau-like features observed at T = 5 K, fading away for higher temperatures, can be classified in intrinsic and extrinsic mechanisms. 39,43−45 The origins of these conductance anomalies are assumed to be dedicated to tunneling resonances, 46 single-electron charging effects, 47 or geometric transmission resonances 48 arising from impurities. Figure 4b shows the bias spectroscopy at T = 70 K ( Figure  4b) in which the device was cooled down without prior trap neutralization. Based on I/Vs measured for different V G values, the depicted curves correspond to dI D /dV D versus V D . In the low-bias region (linear regime), due to overlapping of measurements at different V G values, dense regions appear at integer multiples of G 0 , which is consistent with quantized conductance plateaus for individual spin degenerate 1D subbands, where the influence of the gate voltage on dI D /dV D is insignificant. 20 With increasing bias voltage, we observed the evolution of conductance from integers multiples of G 0 to intermediate values at higher bias voltages (±10 mV). As reported previously in quantum point contacts 49 and 1D quantum wires, 20 such half-plateaus appearing at intermediate values of G 0 at higher bias voltages arise when the chemical potentials of source and drain occupy different sub-bands. 50 Furthermore, the bias spectroscopy clearly revealed a conductance anomaly at 0.7G 0 , which is considered to be an intrinsic low-temperature sub-G 0 feature of mesoscopic devices that is assumed to originate from many-body physics and was the first conduction anomaly that turned out to be independent of the material system. 44, 45,51 In conclusion, by utilizing a controlled thermal exchange reaction between single-crystalline VLS-grown Ge NWs and Al pads, we demonstrated room-temperature quantum ballistic transport in back-gated Al−Ge−Al NW heterostructure devices with ultrascaled Ge segments. In addition, we have shown that the number of populated sub-bands can be modulated with respect to the trap-filling level. Most importantly, the investigations provide a platform for the exploration of ultrascaled devices based on Ge NWs and, thus, are an important step toward the practical application of ballistic transport at room temperature.