Room Temperature Observation of Quantum Confinement in Single

Dec 11, 2014 - We measure the energy of the sub-bands in nanowires with two different ... as well as in basic phenomena like Majorana Fermion physics...
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Room Temperature Observation of Quantum Confinement in Single InAs Nanowires Eliezer Halpern,†,∥ Alex Henning,†,∥ Hadas Shtrikman,‡ Riccardo Rurali,§ Xavier Cartoixà,⊥ and Yossi Rosenwaks*,† †

Department of Physical Electronics, School of Electrical Engineering, Tel-Aviv University, Ramat-Aviv 69978, Israel Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel § Institut de Ciència de Materiales de Barcelona (ICMAB−CSIC), Campus de Bellaterra, 08193 Bellaterra, Barcelona, Spain ⊥ Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain ‡

S Supporting Information *

ABSTRACT: Quantized conductance in nanowires can be observed at low temperature in transport measurements; however, the observation of sub-bands at room temperature is challenging due to temperature broadening. So far, conduction band splitting at room temperature has not been observed in III−V nanowires mainly due to the small energetic separations between the sub-bands. We report on the measurement of conduction sub-bands at room temperature, in single InAs nanowires, using Kelvin probe force microscopy. This method does not rely on charge transport but rather on measurement of the nanowire Fermi level position as carriers are injected into a single nanowire transistor. As there is no charge transport, electron scattering is no longer an issue, allowing the observation of the sub-bands at room temperature. We measure the energy of the sub-bands in nanowires with two different diameters, and obtain excellent agreement with theoretical calculations based on an empirical tightbinding model. KEYWORDS: InAs nanowires, quantum confinement, KPFM, conduction sub-band, 1-D conductance

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Although the predicted energy splitting of the sub-bands (100 to 200 meV2,9) is larger than the thermal broadening (≈ 26 meV at 300 K), the sub-bands are smeared at room temperature due to phonon, impurity, and surface scattering. Kelvin probe force microscopy (KPFM) was used to determine the surface state distribution in thin films10,11 and NW FETs.12,13 We have used KPFM to demonstrate the observation of the conduction band energy splitting into subbands at room temperature. The energy splitting values were found to be in excellent agreement with theory based on a 20band empirical tight-binding model.14,15 KPFM is an atomic force microscopy (AFM) technique which measures the work function difference, ΔΦ, between the probe tip and the nanowire sample with nanometer spatial resolution and meV

nAs nanowires (NWs) have been studied intensively during the past decade, for potential electronic and optoelectronic applications, as well as in basic phenomena like Majorana Fermion physics. The high electron mobility, typically long coherence length, large spin orbit coupling and Landé g-factor have turned InAs nanowires into key players in mesoscopic physics experiments. Furthermore, InAs possesses a large effective Bohr radius (≈ 34 nm), making it susceptible to quantum confinement at growth-accessible diameters. Recently, conduction band splitting in several diameters below the Bohr radius was demonstrated in InAs NW based field-effect transistors (FETs) at temperatures below 120 K.1−4 Subbands were observed via transport measurements by measuring the conductance, G, or the differential conductance, dG = (dI/ dV), as a function of the gate voltage, VG, of the NW transistor and identified as plateaus in the G−VG curve. NWs of other III−V materials, like InSb and InP, were used to study quantum confinement phenomena,5−8 albeit at low temperature as well. © XXXX American Chemical Society

Received: October 3, 2014 Revised: December 2, 2014

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sensitivity.16 Because the tip work function is constant, ΔΦ is a quantitative measure of the sample Fermi level energy. Results and Discussion. We have studied InAs NWs with diameters of 20 and 27 nm. The NWs are covered by a 2 to 3 nm thick native oxide that was determined by transmission electron microscopy (TEM) and is in agreement with previous reports.17,18 Because the diameter of the measured NWs is smaller than the Bohr radius, quantum confinement occurs and a conduction band energy splitting into discrete one-dimensional (1-D) sub-bands is observable. Using KPFM, we measured the quantum confinement by directly probing the Fermi level energy as a function of the gate voltage while maintaining the drain and source grounded, hence without passing current through the NW. Because surface and other transport related scattering mechanisms are avoided in this particular method, it is possible to observe sub-bands in InAs NWs at room temperature. We note, however, that both thermal fluctuations of electrons (namely, Fermi−Dirac statistics) and lattice vibrations lead to broadening of the subbands at room temperature of about 50 meV. Nevertheless, the sub-band energy spacing is expected to be larger than this value,2,9 and therefore, the sub-bands are resolved. A schematic illustration of the KPFM setup for measurement of single InAs NW FETs in a dry nitrogen atmosphere is illustrated in Figure 1. The NW transistors are fabricated on a 20 nm thin insulator

stacking faults; thus, there is no interfering of structural defects in the measurement. Figure 2a shows a schematic illustration of the NW valence and conduction band edges. When sweeping the NW transistor back gate voltage from negative to positive values while maintaining the drain and source contacts grounded, electrons are injected into the NW shifting the Fermi level energy, EF, from within the band gap into the first conduction mini band, EC1. Consequently, the work function, measured with KPFM, decreases with increasing VG. The conduction sub-bands are expected to appear as plateaus in the measured work function plotted as a function of VG, as schematically illustrated in Figure 2b. The plateaus result from a Fermi level pinning near the conduction sub-band edges where the density of states (DOS) is high (Figure 2c). The NW FET gate voltage-drain−current characteristics, ID− VG, depicted in Figure 3a, indicate a transistor-like behavior. It is evident from the ID−VG curve that the threshold voltage, Vth, is around VG = 0 V, which means that under these conditions EF is in the vicinity of the intrinsic Fermi level, that is, near the middle of the band gap of intrinsic InAs. The drain current− drain voltage characteristics (Figure 3b), ID−VD, show an Ohmic behavior necessary for a quantitative interpretation of the measured energy differences. Ohmic contacts ensure that source and drain are both at exactly the same ground potential in a closed circuit with the AFM probe and minimize the potential drop at the metal−semiconductor junction (NW contacts). Figure 4a and b show the measured change in work function, averaged over a segment in the NW center, as a function of VG, for the 20 and 27 nm diameter NWs. The first plateau at negative VG in both plots, indicated by s, is observed due to the presence of a high concentration of surface states (n = 1.0 ± 0.5 × 1013 eV−1 cm−2), leading to a Fermi level pinning within the band gap.12 The following plateaus for positive VG, indicated with numbers 1 to 5, are attributed to the sub-bands of the Γ valley. According to the measurements, EF lies within the conduction band for VG > 0.25 V. When EF “crosses” one of the sub-band minima, where the DOS is very high, the measured work function change remains constant with increasing VG due to Fermi level pinning. When VG is further increased, EF is in the region between two sub-bands where the DOS is low, and consequently, |ΔΦ| rises more rapidly with increasing VG. The valence band splitting is not detectable at room temperature because the energy spacing between these sub-bands is much smaller. Figure 4c and d show a plot for the measured and calculated energies of the first five conduction sub-bands for the

Figure 1. (a) Schematic illustration of a KPFM setup for the measurement of single InAs NW with evaporated metal (Ni/Au) contacts.

in order to ensure a large dielectric capacitance in series with the NW. Thus, the low NW capacitance is the dominant contribution in the metal-oxide−semiconductor(MOS)-like capacitor structure. This is similar to stating that a high dielectric capacitance gives improved electrostatic control of carrier injection into the NW. The measured NWs are free of

Figure 2. (a) Schematic 1-D band structure plot neglecting trap states located within the NW band gap, Eg. Evac is the local vacuum level and EF is the Fermi level position. EV is the valence band edge and EC1 is the first 1-D conduction band edge of the NW. (b) Illustrated graph of the work function Φ = Evac − EF, multiplied by (−1) as a function of the gate voltage, VG. The plateaus in the curve indicate a high DOS around the conduction sub-band edges. (c) Schematic 1-D diagram of the DOS as a function of energy. B

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Figure 3. (a) Drain current−gate voltage characteristics for an InAs NW based FET is shown in a linear and semilogarithmic plot at 10 mV drain voltage. The threshold voltage, Vth, is just slightly above 0 V. (b) The drain current−drain voltage characteristics shows an ohmic behavior at VG = 1 V.

Figure 4. Measured work function difference, ΔΦ, as a function of the gate bias for (a) a 20 nm and (b) a 27 nm diameter InAs NW. The first plateau, assigned by s, is due to surface states within the band gap the other plateaus correspond to the assigned conduction sub-bands. Comparison of the experimental (red dots) and theoretical (black squares) sub-band energies for (c) a 20 nm and (d) a 27 nm diameter InAs NW.

the confinement energies, thus precluding the use of lighter computational methods such as the effective mass approximation or simpler (e.g., less bands) empirical tight binding models to obtain the positions of the sub-band edges. Due to the large size of the resulting Hamiltonian, Krylov space techniques, as implemented in the SLEPc package,20−22 had to be employed in order to retrieve the lowest lying conduction band eigenvalues. Passivation of the surface bonds was achieved by a fictional zincblende material with a gap chosen such that the wave function decay length within this material would be close to that of an electron confined by vacuum. The lack of detailed information regarding the electronic structure of bulk wurtzite InAs and the theoretically predicted similarity in the conduction band density of states at low energies in bulk wurtzite and zincblende phases23,24 have prompted us to use the parametrization by Jancu et al.,15 which was derived for the zincblende phase. The excellent agreement between the experimental and the ETB model results, without any further adjustment, is strongly in favor of this procedure.

20 and 27 nm diameter NWs. The error bars result from potential variations (±2 mV) of the KPFM measurement and potential fluctuations along a 500 NW segment (±10 mV) for each VG. We have not observed any significant potential gradient along this NW segment. We note that the overall trend of the energy spacing plot is also in agreement with the analytical expression for a quantum-confined long cylinder, Em,n = ((h2/(8πm*r,θr20))ρ2m,n), where r0 is the nanowire radius, m* is the effective mass in the confined coordinates (r, θ), and ρm,n is the nth root of the mth-order Bessel function.19 Moreover, the measured spacing between the sub-bands agrees well with the results on InAs NWs reported by Ford et al.2 Calculations were carried out using a homemade computer code implementing an atomistic 20-band empirical tight binding (ETB) model, as parametrized by Jancu et al.15 for InAs, with the diameters taken as the measured AFM values (20 and 27 nm) subtracting the oxide shell layer (3 nm, determined by TEM). Because of the small band gap of InAs and the small diameter of the NWs investigated, nonparabolicity effects affect C

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measurement was conducted in the dual-frequency mode; in this method, the first resonance is vibrated by a dither piezoelectric crystal (embedded within the tip holder), to acquire the topography image. The KPFM signal is measured during the same scan at the second resonance, with an AC drive of 100 mV; this excitation is extremely small compared to ambient atmosphere KPFM operations,29−32 and resulted in a very small tip−sample distance, which minimizes convolution effects. A tip−sample distance of about 2 nm was determined by force−distance curves using the same cantilever after each measurement.

The quantum confinement, inherent to the NWs investigated in this work, is essentially two-dimensional (2-D), leaving the axial dimension for 1-D conduction; this corresponds to the recent observation of 1-D transport of InAs NWs with diameters below 30 nm where an energy separation between the sub-bands of more than 100 meV was observed by electrical conductance measurements2 and is in accordance with our KPFM measurements. However, due to scattering at the surface as well as possible stacking faults of previously analyzed NWs, to the best of our knowledge such plateaus were so far not observed at room temperature. In this work, we observed the sub-bands and their respective energies at room temperature, because no current was passed through the device, and the Fermi level was directly monitored as a function of VG. This study promotes the basic understanding of the physical characteristics of nanowire-based FETs, which are a potential building block for future electronics devices. Quantum confinement effects at room temperature pave the way for new possibilities in quantum electronics. Material and Methods. The InAs NWs were grown on a (111)B InAs substrate by the gold-assisted vapor−liquid−solid (VLS) technique in a high purity, solid source, molecular beam epitaxy (MBE) system. An extremely thin (≈ 0.1 nm) gold layer was evaporated in situ, in a chamber attached to the MBE system. The wafer was transferred into the growth chamber where it was heated to 500 °C under As4 overpressure to form gold droplets. NWs growth was carried out at 400 °C for an hour using In and As4 at a V/III ratio of ≈ 100, producing pure wurtzite structure NWs25 ≈ 6 μm in length and varying diameters (20−30 nm), with a significantly small diameter distribution (± 0.5 nm) along the NW. The small amount of gold minimizes the diameter of the formed droplets, resulting in a high uniformity. For such diameters, and considering the relatively slow growth rate applied, one expects the NWs to have no stacking faults, as indeed can be seen in typical highresolution TEM images.26,27 To fabricate InAs NW based FETs, the as-grown NWs were suspended in ethanol by sonication, then drop-cast onto a highly n-doped Si substrate with a 10 LPCVD-grown Si3N4 layer on top of a 10 nm thick thermal SiO2 layer. The thin insulator ensures gate control over the NW potential with low bias voltages. Contact regions were defined by electron beam lithography using MMA (EL4)/PMMA (A4) layered resists. The contacts width was 20 μm to minimize convolution effects in KPFM. Thirty seconds, 50 W O2 plasma cleaning of the electrode regions was followed by a 15 min immersion in diluted ammonium polysulfide, in order to passivate the contact area and obtain ohmic contacts.28 Subsequently, the substrates were loaded into an electron beam evaporator for Ni/Au evaporation (10 and 20 nm, respectively). The NW FETs were fabricated with NWs of random diameters in the range of 20 to 30 nm. The KPFM measurements were conducted using the Dimension Edge atomic force microscope (Bruker, Inc.) system, in a controlled N2 environment glovebox (less than 2 ppm of H2O). A CPD image of the NW with contacts was measured at each gate voltage with a scan rate of 0.1 Hz and a lateral resolution of 2.5 nm. The average potential for each VG was obtained from the measured CPD along a 500 nm segment of the NW. The contact regions were neglected due to a potential drop at the metal−semiconductor junction. We have used a Nanosensors Pt/Ir-coated tip, with a first resonance frequency at ≈75 kHz and second resonance at ≈470 kHz. The

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ASSOCIATED CONTENT

S Supporting Information *

Description of KPFM measurements in detail and additional data of measured NWs. This material is available free of charge via the Internet at http://pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions ∥

Contributed equally to this work

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Y.R. and H.S. acknowledge the Israel Science Foundation (grant numbers 498/11 and 532/12) and the Israeli Ministry of Science (grant number 3-66799). R.R. and X.C. acknowledge support under contracts Nos. FEDER-FIS2012-37549-C05-05 and TEC2012-32305 of the Ministerio de Economiá y Competitividad (MINECO) and grants 2014-SGR-301 and 2014-SGR-384 of the Generalitat de Catalunya. R.R. thanks Ilaria Zardo and Luis Ogando for useful discussions.

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