Probing strain modulation in a gate-defined one-dimensional electron system

Abstract

Gate patterning on semiconductors is routinely used to electrostatically restrict electron movement into reduced dimensions. At cryogenic temperatures, where most studies are carried out, differential thermal contraction between the patterned gate and the semiconductor often lead to an appreciable strain modulation. The impact of such modulated strain to the conductive channel buried in a semiconductor has long been recognized, but measuring its magnitude and variation is rather challenging. Here we present a way to measure that modulation in a gate-defined GaAs-based onedimensional channel by applying resistively-detected NMR (RDNMR) with in-situ electrons coupled to quadrupole nuclei. The detected strain magnitude, deduced from the quadrupole-split resonance, varies spatially on the order of 10 −4 , which is consistent with the predicted variation based on an elastic strain model. We estimate the initial lateral strain xx developed at the interface to be about 3.5 × 10 −3 .In many semiconductor-based quantum systems, electrons are manipulated by applying voltages to the surface metal gates. For example, a combination of nanoscale metal gates and GaAs based two-dimensional systems enables us to realize one-dimensional quantum channel and zero-dimensional quantum dot by depleting electrons under the gates[1]. These building blocks are integrated into many quantum devices, such as quantum computing/simulating systems based on electron spins [2][3][4]. Electron control in these systems is always accompanied by electron position change from the originally twodimensional sheet. One can expect microscopic strain distribution in such devices because surface metal gate and semiconductor system have different thermal expansion coefficients and complicated nanometer surface gates should produce a complicated strain pattern inside. Such phenomena are common for all semiconductor systems including silicon and other semiconductor groups. However, the strain variation felt by confined electrons has not received much attention up to now partly because a lack of appropriate and precise measurement tool to probe local strain in nanometer scale electron channel. Here, taking GaAs-based quantum-point-contact (QPC)[5, 6] as a prototypical example, we demonstrate that electrons flowing in the one-dimensional channel feel different strain even in the same device when the channel position is microscopically shifted by changing the gate voltage.There are a couple of methods to measure spatial strain distribution in materials. Examples include X-ray diffraction [7,8], electron microscopy [9,10], and Raman spectroscopy [11][12][13]. Although those techniques are capable of delivering a high-spatial resolution strain profile, they are only sensitive to strain magnitude larger than a factor of 10 −4 . Alternative technique such as solidstate NMR could provide an acceptable solution since it has the ability to detect ultra low-level strain variation of less than 10 −4 through nuclear quadrupolar interaction with the electric field gradient ...

Resistively Detected NMR Lineshapes in a Local Filling ν<1 Quantum Hall Breakdown

“…The quadrupolar splitting reflects strain field felt by the nuclear spin and its high sensitivity enables us to detect small strain difference on the order of of . [ 8 ] Figure 2 a shows calculated total strain distribution in the QPC device. The strain becomes maximum in between the metal gates and decreases under the gate.…”

“…Therefore, the quadrupolar splitting of the RDNMR signals reflects the strain in the electron channel of the QPCs. In the case of the experiments shown in Figure 2, [ 8 ] when we applied more a negative voltage (Vsg1) to the split gate 1 (SG1), the electron channel moved from beneath the SG1 to the region in between the gates as shown by the red arrow in Figure 2a. Correspondingly, the QPC conductance decreased as shown in Figure 2b.…”

“…Since the pioneering work of Wald et al in early 1990s, [ 5 ] resistively‐detected nuclear magnetic resonance (RDNMR) has emerged as a powerful tool to study characteristics of a quasi‐1D channel defined by a quantum point contact (QPC). The characteristics, which cannot be detected by any conventional transport measurements, such as ultra‐low strain distribution, [ 8 ] have been successfully detected as discussed in the following section. In these studies, we set the bulk two‐dimensional electron gas (2DEG) outside of the QPC at the filling of and inside filling factor in the QPC to be less than 1 ().…”

“…[ 5,6,9 ] Although the RDNMR signal is mainly dominated by positive nuclear polarization, that is, parallel to the applied magnetic field, due to forward edge‐channel scattering events when is tuned slightly lower than 1. [ 8–11 ] However, the negative nuclear polarization also plays a role and a complicated dispersive line‐shape signal appears in some conditions. [ 9 ] The observed dispersive lineshapes have been reported in a two‐dimensional system [ 12–19 ] and are interpreted due to the formation of spin unpolarized puddles in the sea of spin‐polarized background.…”

“…Previous RDNMR studies are overwhelmingly reported in a single QPC device and in a strong tunneling regime between the two‐edge channels at the lowest Landau level. [ 8–11,20–23 ] In attempt to comprehensively study local hyperfine‐mediated transport in the lowest Landau level, in this study, we investigate RDNMR spectra in a wide range of local filling factor , encompassing strong to weak tunneling regime between the inner and outer edge channel at the lowest Landau level. Furthermore, we use a QPC device with multiple gate structures to control a potential shape in and near the QPC channel.…”