Influence of etching processes on electronic transport in mesoscopic InAs/GaSb quantum well devices

We report the electronic characterization of mesoscopic Hall bar devices fabricated from coupled InAs/GaSb quantum wells sandwiched between AlSb barriers, an emerging candidate for two-dimensional topological insulators. The electronic width of the etched structures was determined from the low field magneto-resistance peak, a characteristic signature of partially diffusive boundary scattering in the ballistic limit. In case of dry-etching the electronic width was found to decrease with electron density. In contrast, for wet etched devices it stayed constant with density. Moreover, the boundary scattering was found to be more specular for wet-etched devices, which may be relevant for studying topological edge states.

Recently, InAs/GaSb composite quantum wells have gained a lot of interest due to the prediction of the quantum spin Hall (QSH) state in the inverted regime [1] of the bandstructure. In this state, transport is expected to be governed by counter propagating (helical) edge channels of opposite spins together with an insulating bulk and the system is referred to as a two-dimensional topological insulator (2D TI). The QSH state was first predicted [2] and observed [3] in HgTe/CdTe quantum wells. Electron-hole hybridization and the indication of a topological insulator phase were reported in InAs/GaSb quantum wells in recent transport experiments [4][5][6][7][8][9]. One important requirement to observe the 2D TI phase in electronic transport is to fabricate devices smaller than the inelastic scattering length (l in ). In reality, due to limited material quality often bulk transport is relevant and masks edge channel transport [5]. Moreover, edge scattering originating from rough edges as a result of fabrication processes, can also be detrimental to the observation of helical edge states [10][11][12]. Apart from being an emerging candidate for 2D TI, this system offers the potential to observe several physical phenomena such as exciton condensation [13], Majorana Fermions [14], or edge mode superconductivity [15]. In comparison to the HgTe/CdTe system, InAs/GaSb coupled quantum wells offer electric field tunability of the topological phase [16].
When the device size becomes smaller than the elastic mean free path (l e ), the transport properties are modified with respect to bulk samples [17][18][19]. As a consequence mesoscopic devices exhibit enhanced resistivity due to the lateral boundary scattering, studied extensively in narrow channels fabricated in GaAs twodimensional electron gases (2DEGs) [20,21]. The electronic confinement in narrow 2DEGs depends a lot on the material system and particularly on the fabrication processes. For example, quasi-1D channels fabricated by reactive ion etching (RIE) in InAs 2DEGs [22] show a degradation of the mobility due to surface damage caused by the energetic ions along with lateral side wall depletion. Electronic transport in sub-micron devices of InAs [23] and InSb [24] based 2D systems were studied extensively. However, mesoscopic transport in InAs/GaSb systems is relatively unexplored. Compared to the pure InAs well, the presence of a GaSb layer may change the depletion width and the confinement potential. Hence, it is necessary to explore the mesoscopic properties of InAs/GaSb devices for reaching an optimized fabrication recipe.
Here, we present a detailed characterization of a series of mesoscopic Hall bar devices made by dry and wet etching processes (see Table I for details). The effective electronic width (W electronic ) was determined by mea- suring the low field magneto-resistance peak appearing due to partially diffusive boundary scattering [17]. We find that W electronic decreases with decreasing density for dry-etched devices, whereas it remains constant for wetetched devices. The edge roughness in wet-etched devices was found to be smaller compared to dry-etched devices, which could be relevant for observing edge transport in this material. The devices were fabricated from wafers grown by molecular-beam epitaxy (MBE) with a similar growth structure as in Ref. 8. We present measurements on eleven Hall bar devices from three different wafers (W1, W2 and W3) with exactly the same nominal growth structure, but with different targeted lateral width. For the fabrication of the Hall bar devices, Ohmic contacts Ge (18 nm We found all of our wafers to be electron doped at zero gate voltage with a density n ≈ 7 × 10 11 cm −2 irrespective of the fabrication processes. All the experiments were done by ac lock-in technique with a bias current of 10 − 50 nA and carrier frequency of 31 Hz at 1.3 K. Both electron and hole transport can be observed by tuning the gate voltage from positive to negative. Transport measurements on large Hall bars (25 µm×50 µm) fabricated by both dry and wet etching possess similar carriermobilities and gate tunability as in Ref. 8.
Boundary scattering was characterized by measuring the longitudinal resistance (R L ) and its magnetic field dependence [20]. Figure 1c and 1d show typical low-field magneto-resistance (MR) data for dry and wet etched devices (devices D1 and D10 in Table I) at a similar electronic density, n ≈ 9.5 × 10 11 cm −2 . We find distinct MR peaks which are used to determine the electronic width of the devices. When the device width becomes smaller than the elastic mean free path (l e ), charge carriers face partially diffusive boundary scattering in long channels (L > l e ). This results in a positive zero-field MR reaching a maximum at a field B max (indicated by arrows in figure 1c and 1d) when the ratio of the wire width (W electronic ) and the cyclotron radius (R c ) follows the relation [17] W electronic /R c = W electronic eB max /hk F = 0.55, where k F = (2πn) 1/2 , is the Fermi wave vector. Figure 1e and 1f show the transverse MR (R H ) for the corresponding devices exhibiting quenching of the Hall resistance near zero field, a typical classical phenomenon of electron transport in ballistic crosses [19,21]. Boundary scattering was observed mainly for high mobility electrons as l e exceeds the device dimension only for densities larger than ∼ 7 × 10 11 cm −2 . No ballistic effects were observed for holes in this temperature range due to the low mobility and high effective mass. The roughness of the boundary can qualitatively be evaluated by calculating the quantity ∆R L (B)/R L (0) [20], where, ∆R L (B) = R L (B max ) − R L (0), which is zero for completely specular boundary scattering. From figure 1c and 1d, we see that ∆R L (B)/R L (0) is ∼ 0.2 for device D1 and ∼ 0.06 for device D10, confirming the smoother edge for the wet etched device.
Next we concentrate on the density (n) dependence of the electronic width (W electronic ). Figure 2a shows the density dependence of three dry-etched devices (de- vices D1, D2, D4) with mean W etch 2.0 µm, 4.1 µm and 2.1 µm, respectively. For all the three devices, W electronic was found to decrease with decreasing electron density. For device D2 (W etch ≈ 4.1 µm), W electronic saturates at around 2.2 µm above a density n ≈ 1.1 × 10 12 cm −2 and decreases to ≈ 0.8 µm at n ≈ 7.3 × 10 11 cm −2 , the lowest density where the MR peak was observed. Below this density the holes start populating the GaSb layer and transport is governed by both electrons and holes, where we see the signature of two band transport in both longitudinal and Hall resistance [26]. For devices D1 and D4 (W etch ≈ 2.1 µm), the saturation was not observed due to the limited gate range, however, a similar decrease in W electronic was observed. Figure 2b shows the density dependence of W electronic for all the wet-etched devices with a mean W etch ranging between 0.9 − 2.6 µm. For devices with W etch ≈ 2.6 µm (device D7) and ≈ 1.9 µm (device D6), W electronic was found to be 1.1 µm and 0.75 µm, respectively, with little variation with density. For devices D9 (W etch ≈ 1.7 µm) and D10 (W etch ≈ 0.9 µm), W electronic shows a similar value ∼ 0.5 µm. Due to the larger etching depth for device D9 (≈ 1.1 µm) the side wall etching is expected to be more compared to device D10 (etching depth ≈ 240 nm) and may provide coincidentally similar W electronic .
The density dependence of W electronic (figure 2) suggests a steeper confinement potential for wet-etched devices compared to the dry-etched ones (see insets of figure 2a and 2b), however, the exact shape of the confinement potential is difficult to model.
The depletion width is often used in literature to judge the quality of etching processes, defined as W depletion = 1/2(W etch − W electronic ). As W electronic varies with density for dry-etched devices, the depletion width is also not constant unlike for wet-etched devices, where W electronic remains constant with density. To get a reasonable comparison for the depletion width values, we have plotted average W electronic as a function of W etch only for the wet-etched devices in the top inset of figure 2b. The red dashed line indicates the line corresponding to W electronic = W etch . In wet etching we often find double step and corrugation at the edges due to the different etching rates for layers with different materials, in contrary to the dry etching where the etching is uniform (see figure 1a and 1b). This may lead to a larger uncertainty in determining the actual W etch for the wetetched devices. We find W depletion to be in the range ∼ 0.2−0.8 µm, which is rather large compared to the pure InAs quantum well devices [23]. Moreover, the lateral depletion was found to increase for wider devices, which is counterintuitive. We also looked at the W depletion as a function of etching depth. However, no systematic dependence of W depletion with etching depth was observed in these four devices.
Qualitatively, in these devices we found that the gate capacitance per unit area (e.dn/dV T G ) decreases for narrower devices. For a narrow channel with an ideal edge, one expects to have enhanced gate tunability due to the fringing field lines near the edge. We speculate that due to the etching process there could be depositions of non-volatile components, ionic charges etc., [27]. These etchant residues may create charge traps near the edges which may be populated by the application of gate voltage. These trapped charges may screen the gate voltage, as well as modify the confinement potential in the lateral direction.
We plan to look into the influence of etching processes on the local and non-local electronic transport properties.
Further work is necessary to reduce the bulk conduction either by improving the material quality or impurity doping [7] to observe the quantum spin Hall effect in this system.
In conclusion, we have been able to fabricate and characterize mesoscopic devices of InAs/GaSb quantum well, made by two different etching processes. The electronic width was obtained from the low field magneto-resistance peak appearing due to boundary scattering. For dry-etched devices the electronic width decreases with lowering electron density, whereas, it remains constant for wet-etched devices. Our observations suggest that wet chemical etching is less invasive compared to the dryetching and could be preferable to produce mesoscopic devices for studying topological insulators.