Pis'ma v ZhETF, vol.96, iss.2, pp. 114-117
© 2012 July 25
Direct observation of standing electron waves in diffusively conducting InAs nanowire
A.A.Zhukov+, Ch. Volk*x, A. Winden*x, H. Hardtdegen*x, Th. Schäpers*xo
+ Institute of Solid State Physics of the RAS, 142432 Chernogolovka, Russia * Grünberg Institut (PGI-9), Forschungszentrum Jülich, 52425 Jülich, Germany
x JARA-Fundamentals of Future Information Technology, Forschungszentrum Jülich, 52425 Jülich, Germany
° II. Physikalisches Institut, RWTH Aachen University, 52056 Aachen, Germany
Submitted 20 June 2012
We investigate the disturbance of the InAs nanowire resistance by a conductive tip of a scanning probe microscope at helium temperature as a function of the tip position in close vicinity to the nanowire. At the tip displacement along the wire the resistance (Rwire — 30 kii. what is typical for diffusive regime) demonstrates quasi-periodical oscillations with an amplitude about 3%. The period of the oscillations depends on the number of electrons in the nanowire and is consistent with expected for standing electron waves caused by ballistic electrons in the top subband of the InAs nanowire.
Inhomogeneous distributions of the electron density in metallic systems caused by peculiarities of electron wave function are well established in a number of different electron systems. Electron density waves in 2-dimensional electron gases [1] and Friedel oscillations in an Ag covered Si-surface [2] are popular examples of such inhomogeneous distributions. The typical scale of these oscillations is conventionally microscopic one, comparable with atomic scale. Below we report on the direct observation of standing electron waves in an InAs nanowire with a period between micro- and nanoscale. Moreover, such long range electron density oscillations are observed in the wire with formally diffusive conductivity.
The possibility to change the density of the electrons in nanowire by applying voltage to nearby placed electrode, a back gate for example, allows to realize nanowire-based field-effect transistors (FET). During the last decade substantial efforts have been made to investigate the electron transport in InAs nanowires [37]. In the off-state these transistors have resistances of several hundreds MO while in the on-state the resistance drops to 20-30 kO. Taking into account the possible application of InAs nanowire in electronics strong efforts were made to study the dependence of the mobility of the InAs nanowires on their diameter [6].
At low temperatures the transport in InAs wires is mostly diffusive. Transport measurements performed at He temperatures [3, 5] yielded typical values of the elastic mean free path le in the order of a few tenth of nanometers. In addition at low temperature phase-
coherent transport was investigated, i.e. the temperature dependence of universal conductance fluctuations [4] and the suppression of weak antilocalization were investigated [3,5]. In both cases a good agreement with theoretical predictions based on the dominance of diffusive transport was found. However, in contrast to the relatively small le values reported above, Zhou et al. [8] obtained considerably larger values exceeding 200 nm even at room temperature. So far, scanning gate microscopy (SGM) measurements conducted at T = 4.2 K on InAs nanowire FETs have only been focused on electron transport in the regime close to pinch-off [10, 9]. Here, a number of peculiarities in Coulomb blockade regime were found.
In the current letter we report on SGM measurements in the open FET regime with relatively low nanowire resistance of ~ 30 kO. Standing electron waves are observed in the SGM scans. It is found that the period of the standing electron waves depends on the number of electrons in the wire. We interpret the observation of the standing electron waves as an indication of the presence of ballistic electrons in InAs nanowire.
In our experiment we study a nominally undoped InAs nanowire grown by selective-area metal-organic vapor-phase epitaxy [11]. The diameter of the wire is 100 nm. The wire was placed on an n-type doped Si (100) substrate covered by a 100 nm thick Si02 insulating layer. The Si substrate served as the back-gate electrode. The evaporated Ti/Au contacts to the wire as well as the markers of the search pattern were defined by electron-beam lithography. The distance between the
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contacts is -Lwire = 2.6/¿m. A scanning electron micrograph of the sample under investigation is shown in Fig. la. The source and drain metallic electrodes connected to the wire are marked by "s" and "d".
Fig. 1. (a) - Scanning electron micrograph of the InAs wire. The source and drain contact pads are marked by "s" and "d". The horizontal scale bar corresponds to 1 ¡im. The metallic triangle on the left side of the wire is a marker of the search pattern, (b) - Electrical circuit of the scanning gate microscopy measurements. The back-gate voltage Vbg is applied to the doped Si substrate while the tip voltage Vt is applied to the tungsten tip of the probe microscope. The resistance of the wire is measured using a two terminal circuit by applying a current (Iac) and measuring the voltage (V). Further details are given in the main text
All measurements were performed at T = 4.2 K. The charged tip of a home-built scanning probe microscope [12] is used as a mobile gate during scanning gate imaging measurements. We keep the tip 300 nm above the Si02 surface, in order to eliminate any mechanical or electrical contact of the tip to the InAs wire or metallic contacts. All scanning gate measurements were performed by keeping the potential of the scanning probe microscope tip (Vt) and the back-gate voltage (Vbg) constant. The electrical circuit of the scanning gate imaging measurements is present in Fig. lb. Details of the circuit can be found elsewhere [13].
The conductance of the wire during the scan is measured in a two-terminal circuit by using a standard lock-in technique. Here, a driving AC current with an amplitude of Iac = 1 nA at a frequency of 231 Hz is applied while the voltage is measured by a voltage amplifier.
Figs. 2a-d present a set of the scanning gate measurements performed with a constant tip voltage of V = 0 V and a back-gate voltages of Vbg = 11-8, 10.6, 9.2, and 8.0 V, respectively. It can clearly be seen that the tip position strongly affects the wire resistance. The cross cuts of the SGM scans (Figs. 2a-d) along the wire are present in Figs. 2e-h. The cross-cut in Fig. 2h is obtained after subtracting of smooth background. With the displacement of the tip along the wire a quasi-periodic oscillation of the wire resistance with an amplitude of about
3% of the total resistance are observed. The period of these oscillations increase with decreasing back-gate voltage (Figs. 2a-c,e-g) until it abruptly becomes small again (Figs. 2d, h). As an example, 4, 3, and 2 equidistant minima in the nanowire resistance are marked by arrows in Fig. 2e-g, respectively. An abrupt change of the period is observed between the back-gate voltage 9.2 and 8 V. To make the period change visible we mark in Fig. 2h the equidistant maxima of resistance by arrows.
We argue that the periodic oscillations of wire resistance can be attributed to the presence of the standing electron waves in the nanowire. Let us consider the experimental situation in more details. The number of electrons in our wire at Vbg = 10 V is given by [7]:
(Vbg — ypinch-off)a • 27reeo-lwire/e
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Here, Vbg - Vpinch-off ~ 10 V, a = to—gate/Ctotai ~ 0.3 is the ratio of wire to back-gate and total capacitance of the wire, e = 3.8 is the Si02 permittivity, £o is the permittivity of free space, dox = 100 nm, and r = 50 nm are the thickness of the oxide layer and the wire radius, and e is elementary charge. Knowing the geometrical sizes of the wire it is possible to calculate the mean concentration of the electrons n%D ~ 1-1 • 1017cm-3 [14]. The reciprocal radius of Fermi sphere calculated by considering the InAs nanowire as a 3D structure is 2n/kF,3D = 2n/(Sn2n3D)1//3 ~ 40 nm, and the elastic mean free path in the wire is le = ^/3/8irnlD(h/e2)(l/Rwiie)(Lwiie/irr2) ~ 50nm, with h the Planck constant. Thus, the statement "InAs wire is a 3D structure in diffusive, close to the Ioffe-Regel limit regime kp^oh ~ 1" mentioned previously looks quite reasonable. For these nominally undoped InAs nanowires the main source of scattering is surface scattering, due to irregularities caused by stacking faults or due to surface contaminations [14].
On the other hand, the evaluation of le seems to be too underestimated, because different electron groups in the wire have rather different mean free path. In an ideal one-dimensional wire there are a number of partially filled energy subbands due to the transverse quantization, as it is illustrated in Fig. 3. Because the conductance of the real nanowire is about e2/h and the number of subbands is about 10-20, we have to conclude that the main part of electrons on Fermi level is in the diffusive regime. They are labeled as disordered sea in Fig. 3. Only electrons in the top one or two subbands below the Fermi level (Ep) have a very large wavelength along the wire axis and, correspondingly, a small scattering probability at the smaller scale potential fluctuations caused
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A. A. Zhukov, Ch. Volk, A. Winden et al.
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Fig. 2. (a)-(d) - SGM scans performed at T = 4.2 K with a constant tip voltage of Vt = 0 V and the back-gate voltages of Vbg = 11.8, 10.6, 9.2, and 8.0 V, respectively. The white lines denote the wire axis and the boundaries of
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