Letter pubs.acs.org/NanoLett
Coherently Strained Si−SixGe1−x Core−Shell Nanowire Heterostructures David C. Dillen, Feng Wen, Kyounghwan Kim, and Emanuel Tutuc* Microelectronics Research Center, The University of Texas at Austin, 10100 Burnet Road, Bldg. 160, Austin, Texas 78758, United States S Supporting Information *
ABSTRACT: Coherently strained Si−SixGe1−x core−shell nanowire heterostructures are expected to possess a positive shell-tocore conduction band offset, allowing for quantum confinement of electrons in the Si core. We report the growth of epitaxial, coherently strained Si−SixGe1−x core−shell heterostructures through the vapor−liquid−solid mechanism for the Si core, followed in situ by the epitaxial SixGe1−x shell growth using ultrahigh vacuum chemical vapor deposition. The Raman spectra of individual nanowires reveal peaks associated with the Si−Si optical phonon mode in the Si core and the Si−Si, Si−Ge, and Ge−Ge vibrational modes of the SixGe1−x shell. The core Si−Si mode displays a clear red-shift compared to unstrained, bare Si nanowires thanks to the lattice mismatch-induced tensile strain, in agreement with calculated values using a finite-element continuum elasticity model combined with lattice dynamic theory. N-type field-effect transistors using Si−SixGe1−x core−shell nanowires as channel are demonstrated. KEYWORDS: Nanowire, core−shell, elastic strain, Raman spectroscopy, field-effect transistor, silicon−germanium
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strain-induced shift of conduction band energies, we estimate a minimum shell-to-core conduction band offset of 213 meV in a 30 nm diameter nanowire with 3.9 nm Si0.39Ge0.61 shell (see Supporting Information, sections S1 and S2). While earlier studies have demonstrated the growth of crystalline Si−Ge core−shell nanowires,15,25,26 their epitaxial quality has yet to be established through a systematic study of the elastic strain and a comparison to values expected for a coherent heterostructure. We present here the growth, structural, and electrical characterization of strained Si−SixGe1−x core−shell nanowires. We use Raman spectroscopy to measure the optical phonon frequencies of both core and shell regions combined with calculations using a continuum elasticity model and lattice dynamic theory in order to compare the experimentally measured phonon frequencies to values expected for a fully strained heterostructure. We also demonstrate n-type fieldeffect transistors using Si−SixGe1−x core−shell nanowires as channel material. Our Si−SixGe1−x core−shell nanowires are grown through a sequential combination of vapor−liquid−solid (VLS) and epitaxial chemical vapor deposition (CVD) processes, as shown schematically in Figure 1a. The Si(111) substrate is first prepared using dilute hydrofluoric (HF) acid etching of the native oxide, followed by evaporation of a 7−8 Å Au film. The substrate is then transferred to the cold wall ultrahigh vacuum
ow-dimensional semiconducting materials are expected to play an important role in electronic and optical devices. Examples range from nanowire field-effect transistors (FETs)1−5 to tunnel FETs6 and solar cells7 and include emerging applications such as quantum dot spin qubits.8,9 Semiconductor nanowires are particularly interesting because they provide a one-dimensional quantum confinement route through the use of core−shell heterostructures. Examples of ntype core−shell and core−multishell nanowires using III−V compound semiconductors include GaN-AlN/AlGaN,10 GaN/ InGaN/GaN/AlGaN,11 InAs-InP,12 InGaAs-InP/InAlAs/InGaAs,13 and GaAs-AlGaAs.14 In group IV nanowires, the valence band offset between Ge and Si allows the confinement of holes in the core of Ge−Si and Ge−SixGe1−x core−shell nanowires.15−17 The development of electron-confined systems using group IV nanowire heterostructures has, however, been slower. The interplay between strain and band offset in the Si−Ge system on one hand and the impact of growth conditions on structural coherency on the other are the two main issues. Previous experimental18 and theoretical19 studies using planar materials have revealed electron confinement in the Si layer of coherently strained Si−Si0.5Ge0.5 heterostructures lattice matched to a Si0.75Ge0.25 substrate. Coherently strained Si−SixGe1−x core− shell nanowires represent one possible radial heterostructure where a positive shell-to-core conduction band offset, beneficial for quantum confinement of electrons in the Si core, may be realized. Indeed, by calculating the elastic strain distribution in Si−SixGe1−x core−shell nanowires20−24 and the corresponding © XXXX American Chemical Society
Received: September 29, 2015 Revised: November 14, 2015
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DOI: 10.1021/acs.nanolett.5b03961 Nano Lett. XXXX, XXX, XXX−XXX
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chemical vapor deposition conditions and a combination of SiH4 and GeH4 (20% in He) precursors. For comparison, bare Si nanowires were also grown using the same conditions as the VLS growth of Si cores in Si−SixGe1−x core−shell heterostructures (see Supporting Information, section S3). The bare Si nanowires serve as control to establish the diamond crystal structure, and to obtain a baseline for the optical phonon frequency in nominally unstrained Si nanowires. Transmission electron microscopy (TEM) is used to study the morphology and crystal structure of the Si−SixGe1−x core− shell nanowires. Figure 1b evinces a single-crystal nanowire heterostructure with no obvious surface roughening or sawtooth faceting.27 Electron diffraction analysis indicates a growth axis along [110] for both bare Si nanowires and Si− SixGe1−x core−shell nanowires (see Supporting Information, Section S3). We note that the core−shell interface is hardly discernible in the micrograph of Figure 1b, which in turn testifies to the quality of the epitaxial shell growth. We find that nanowires can grow with either a circular or hexagonal crosssection in the range of diameters we investigate, with the hexagonal structures having four {111} and two {001} type sidewalls. Unless otherwise noted, in the following work we assume all nanowires are cylindrically shaped; a comparison to hexagonal structures is given in Supporting Information, Section S5. To measure the SixGe1−x shell’s thickness (tsh) and relative Si content (x), we use energy-dispersive X-ray spectroscopy (EDX) with a scanning TEM (STEM) electron beam. The inset of Figure 1b plots an EDX linescan perpendicular to the nanowire axis, showing the Kα1 X-ray line counts for Si (red) and Ge (black) with energies of 1.74 and 9.89 keV, respectively, for a heterostructure with tsh = 3.9 nm and x = 0.39. The data is fit using a model which considers the relative numbers of each atom along the beam’s path as a function of beam position.28 We find that the shell thickness and material composition are well controlled by changes to the shell growth time and relative SiH4 and GeH4 source gas flow rates, respectively. Using a gas flow ratio of SiH4/GeH4 = 25, we find a shell content of x = 0.39 and growth rate of 0.65 Å/min, while at SiH4/GeH4 = 36 we find x = 0.56 and 0.40 Å/min growth rate. A fundamental property of a pseudomorphic heterostructure is the elastic strain resulting from the lattice mismatch between individual components. To probe the elastic strain in Si− SixGe1−x core−shell nanowires, we use Raman spectroscopy to
Figure 1. (a) Schematic of Si−SixGe1−x core−shell growth process showing hydrogen annealing, vapor−liquid−solid (VLS) core growth, and chemical vapor deposition (CVD) shell growth. Arrows represent the direction of growth in each regime. (b) High-resolution transmission electron micrograph of a Si−SixGe1−x heterostructure. The inset shows an EDX/STEM linescan, where Si and Ge Kα1 X-ray line counts are plotted with red and black symbols, respectively. EDX fitting results (solid lines: redSi, blackGe) correspond to tsh = 3.9 nm and x = 0.39. The core and shell regions, as determined from the EDX data, are marked using dashed lines in the TEM micrograph.
growth chamber and annealed for 15 min in H2 ambient at 370 °C to produce Au nanoparticles. The Si nanowire cores are grown through the Au-catalyzed VLS mechanism at 430 °C using SiH4 (100%, 100 sccm) source gas at a chamber pressure of 10 Torr. The SixGe1−x shell growth follows in situ at a sample temperature of 390 °C, using ultrahigh vacuum
Figure 2. Comparison of Raman spectra between Si nanowire samples with no shell (black line) and Si−SixGe1−x core−shell samples (red line) with (a) tsh = 3.9 nm, x = 0.39 and (b) tsh = 2.9 nm, x = 0.56. The insets focus on the spectra between 480 and 550 cm−1, corresponding to the Si−Si modes. B
DOI: 10.1021/acs.nanolett.5b03961 Nano Lett. XXXX, XXX, XXX−XXX
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unstrained SixGe1−x has a Raman shift of 477.3 cm−1 for x = 0.39 and 489.2 cm−1 for x = 0.56;29 the Si−Si shell peaks of Figure 2 are shifted to higher frequencies thanks to the compressive strain in the shell. To better understand the dependence of Raman modes with elastic strain, we calculate the strain-induced shift of the Si−Si mode in both core and shell regions. Strain calculations for the Si−SixGe1−x core−shell heterostructure use a finite-element method and are detailed in Supporting Information, Section S1. We find that the Si core is indeed under a tensile strain thanks to the larger lattice constant of the SixGe1−x shell and that all strain components are nearly uniform with position in this region. The shell strain, in comparison, changes appreciably with position and generally has a higher magnitude with both tensile and compressive components. In the presence of elastic strain, the optical phonons modes of a cubic material, which are initially triply degenerate at zone center will shift to lower or higher frequencies, depending on the polarity of the strain (i.e., compressive or tensile), and may split into nondegenerate modes. The strain-induced shift of each Raman mode is found using a linear deformation potential approach, namely, the secular equation of lattice dynamic theory:30,31
measure the optical phonon frequencies of individual nanowires (see Methods). Figure 2 shows the spectra measured from bare Si nanowires (black lines) and Si−SixGe1−x core−shell heterostructures with different shell contents and thicknesses (red lines). The Si nanowire Raman spectra reveal a single peak at 520 cm−1, the expected value for bulk, unstrained Si in the diamond crystal structure. By comparison, the Si−SixGe1−x core−shell heterostructures show a set of additional peaks with frequencies between 290 and 510 cm−1. We associate the low intensity peaks at 292 and 409 cm−1 with the Ge−Ge and Si− Ge modes of the strained SixGe1−x shell, respectively.29 We also observe a peak near 435 cm−1, a local Si−Si vibration in the shell which arises due to a nonuniform local SixGe 1−x composition.29 We attribute the highest intensity peak of the core−shell samples to the Si−Si Raman mode of the Si core, which is redshifted in comparison to bare Si nanowires, as evident from Figure 2 insets, because of the tensile strain applied by the SixGe1−x shell. The full width at half-maximum (fwhm) of this peak averages 6.5 cm−1 compared to 3.7 cm−1 for bare Si nanowires. The additional peak near 505 cm−1 in the core− shell spectra has a wider fwhm and is attributed to the Si−Si mode of the shell. We note that the nominal Si−Si mode in pεxx + q(εyy + εzz) − λ
2rεxy
2rεxz
2rεxy
pεyy + q(εxx + εzz) − λ
2rεyz
2rεxz
2rεyz
pεzz + q(εxx + εyy) − λ
where εuv are the strain tensor components, and p, q, and r are the material’s phonon deformation potential values, given in Table 1 for Si and SixGe1−x alloys. The r values for SixGe1−x
p/ω02
q/ω02
r/ω02
Si Si0.56Ge0.44 Si0.39Ge0.61
−1.84 −1.7432 −1.8232
−2.35 −2.0632 −2.0632
−0.7133 −1.00 −1.00
32
32
(1)
S2 of the Supporting Information), the Si−Si shell modes show a much larger variation with position than those in the core, and the phonon polarization directions are no longer along the nanowire-oriented principle axes. The calculated Raman shift of the three shell modes range between 481 and 496 cm−1. In light of the uncertainty of the r value, we performed the shell calculations using values of the r deformation potential between −0.7 and −1.2; however, we find only 1.4 cm−1 difference in the median Raman shift of mode 1. While the above calculations predict six nondegenerate Si−Si vibrational modes for the strained core−shell heterostructure, only two peaks were actually observed in our experimental Raman data (insets of Figure 2). This apparent discrepancy can be reconciled by examining which Raman modes are active based on selection rules associated with the polarization of the incident (Einc) and scattered (Escat) light, and their corresponding intensities.23,24 To calculate the expected intensity of each Si−Si Raman mode in both strained core and shell regions we use Einc = [110], as the incident polarization is aligned with the nanowire axis during each Raman measurement (see Methods). Furthermore, because of the anisotropic, antennae-like behavior of semiconducting nanowires embedded in a mismatched dielectric, only the light polarized parallel to the nanowire axis will couple into or out of the structure,35,36 requiring that Escat also be along [110]. We have tested this hypothesis by polarizing the scattered beam, finding that Escat is indeed parallel to the nanowire main axis. The calculation results are plotted in Figure 3d−f, for modes 1−3, respectively. In the Si core, we find that only the first mode, with phonon polarization along [001], is expected to be active, while the other two have zero intensity. Similarly, in the SixGe1−x shell we find that mode 3 is inactive across the entire shell, while the other two modes
Table 1. Normalized Phonon Deformation Potentials for Si and SixGe1−x material
=0
have not been reported; we use r/ω02 = −1.0 estimated from the corresponding values in Si and Ge. The eigenvalue solutions λi = ω2i − ω2io express the strain-induced shift of mode i. The initial, unstrained mode frequency, ωio, is 520.0 cm−1 for Si and 477.3 cm−1 (489.2 cm−1) for SixGe1−x with x = 0.39 (0.56).29 The calculated Raman shift of Si−Si modes in a core−shell structure with tsh = 3.9 nm and x = 0.39 are shown in Figure 3a−c. Similar to bulk Si under a tensile uniaxial stress along [110],34 we find that the core’s initially triply degenerate mode at 520 cm−1 shifts to lower frequency and splits into three nondegenerate modes. The average Raman shift is 512.1, 511.5, and 514.1 cm−1 for core modes 1, 2, and 3, respectively, while the eigenvectors indicate phonon polarizations along [001], [110], and [−110] for the same calculated modes. The Raman shift of a given mode changes only slightly across the core, varying by less than 0.5 cm−1. Shell phonons also split into three nondegenerate modes and are blue-shifted in relation to their unstrained frequency. Moreover, because of the spatial dependence of the elastic strain in the shell (see Figures S1 and C
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Figure 3. Calculated (a−c) Raman shift and (d−f) intensity for the three modes of a fully strained Si−SixGe1−x core−shell nanowire with tsh = 3.9 nm, x = 0.39, and d = 30 nm, assuming the incident and scattered light polarizations are parallel to the [110] nanowire growth axis.
Figure 4. Diameter dependence of Si−Si Raman modes for Si−SixGe1−x core−shell nanowires with (a) tsh = 3.9 nm, x = 0.39 and (b) tsh = 2.9 nm, x = 0.56. The black and blue symbols represent the two Raman peaks measured experimentally, while the lines correspond to calculation results using finite-element (black, solid) or analytically (red, dashed) derived strain distributions. The black dotted line marks the position of the Si−Si mode of unstrained Si.
dependence of Figure 4 can be understood by considering the relative volume of core and shell regions. By increasing the nanowire diameter while keeping shell thickness constant, the elastic compliance of the core decreases in relation to that of the shell. This means that a smaller fraction of the total lattice mismatch will be accommodated in the core, resulting in a reduced strain and, hence, smaller strain-induced shift of the core Raman mode. Due to the thinner shell and smaller mismatch in the sample shown in Figure 4b, we find that the strain-induced red shift of the core mode is smaller in comparison to the structure of Figure 4a. In Figure 4, we also plot the diameter dependence of the Raman peaks determined from our experimental data (symbols). We find that the main peak (black symbols) agrees well with the core calculation results, except that a larger straininduced red-shift is expected in a fully strained structure. This finding is most likely a result of partial strain relaxation through defect formation at the core−shell interface. Furthermore, the nanowire tapering is not expected to alter the Raman spectrum significantly. Using Figure 4 data, and a nanowire tapering of ∼1.6 nm per micron of length, a laser spot size of 1 μm, should widen the Raman peak by ∼0.25 cm−1 by comparison to a structure with uniform diameter. The shell calculation results,
have a nonzero, position dependent-intensity, with mode 1 having the highest intensity. The calculated Raman shift and intensity for the second Si−SixGe1−x core−shell heterostructure used in this study (tsh = 2.9 nm and x = 0.56) are qualitatively similar to those described above (see Figure S5 of the Supporting Information). Furthermore, the calculated elastic strain in the Si core and the corresponding Raman shift and intensity for a Si−SixGe1−x core−shell nanowire with hexagonal cross-section are nearly identical to results for cylindrical nanowires of Figure 3 over most of the core cross-section, with differences observed only within a small region near the facet corners (see Supporting Information, Section S5). Figure 4 shows the diameter dependence of the calculated, active Si−Si mode of the core. The solid black line represents an average of the core values found using the anisotropic finiteelement strain results. For comparison, we also include calculation results which use a simplified, analytical strain calculation technique21 which assumes isotropic elastic constants (red dashed line, see Supporting Information, section S1). For this model, we use the Young’s modulus along the nanowire axis E[110] = 169 GPa and the average Poisson ratio in the (110) plane, ν(110) = 0.213,37 and find close agreement between the two strain calculation methods. The diameter D
DOI: 10.1021/acs.nanolett.5b03961 Nano Lett. XXXX, XXX, XXX−XXX
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Figure 5. Si−SixGe1−x core−shell nanowire FETs. (a) SEM image of completed FET with source, gate, and drain contacts labeled and phosphorus doped region shaded in red. (b) Output and (c) transfer characteristics of a device with tsh = 3.9 nm, x = 0.39, d = 32 nm, and LG = 1340 nm. (d) RM versus LG at multiple values of VG − VT (symbols). Linear fits to experimental data are also included.
not shown in Figure 4, lie between 481 and 496 cm−1 in the sample with x = 0.39 and between 493 and 505 cm−1 in the sample with x = 0.56. These values are lower than the frequency of the experimental shell peaks near 505−510 cm−1 (blue symbols), indicating a larger than expected strain-induced blue-shift in this region. While the origin of the discrepancy between the measured shell peaks and theoretical calculations is unclear, we note that the large strain magnitudes in this region, of up to 2.5%, may limit the accuracy of the calculations, as the deformation potential values were determined experimentally using strain values below 1%.33 Next, we address electron transport in Si−SixGe1−x core− shell nanowire heterostructures and demonstrate top-gated ntype field-effect transistors (n-FET) with highly doped source and drain contacts. Details on the device fabrication can be found in the Methods section. For n-FET devices we use core− shell nanowires with tsh = 3.9 nm, x = 0.39, and a shell which is lightly doped with phosphorus by adding PH3 precursor during growth. Figure 5a shows a scanning electron micrograph (SEM) of a typical n-FET with the source, gate, and drain contacts labeled for clarity. In order to realize low resistance contacts, we implant source and drain regions with low-energy phosphorus ions using the gate metal as a self-aligned mask. The energy (5 keV) and dose (5 × 1014 cm−2) are both chosen to minimize implant-induced crystal damage. Four-point conductivity measurements on blanket-implanted control nanowires yield a doped nanowire resistivity of 4.26 × 10−3 Ω·cm and a metal to nanowire specific contact resistance of 1.28 × 10−8 Ω·cm2. For a n-FET using a 32 nm diameter nanowire and 850 nm long source and drain extensions, this corresponds to a total source/drain external series resistance of RSD = 45.7 kΩ. We measure the drain current (ID) vs drain voltage (VD) characteristics at different gate voltages (VG), and the ID−VG
characteristics at various VD for devices of multiple channel lengths (LG). An example is shown in Figure 5b,c for a device with LG = 1340 nm and diameter d = 32 nm. We find that all devices behave as n-type, enhancement mode FETs with a large, positive threshold voltage (VT) over 1.0 V and an increasing ID with increasing VG. To quantify the characteristic device scaling with gate length, in Figure 5d we plot the total device resistance (RM) vs LG at fixed values of gate overdrive voltage, VG − VT. The linear RM vs LG dependence is expected from simple scaling arguments, and indicates the contact resistance does not control the device characteristics. By fitting the RM vs LG data at each VG − VT and extrapolating to their crossover point, we extract an external source/drain series resistance of RSD = 40 kΩ, matching well with the above value calculated from measurements on blanket implanted Si− SixGe1−x nanowires. The electron mobility was extracted from experimental data using μ = LG(RCH·e·p)−1, where RCH = RM − RSD is the intrinsic channel resistance, e is the electron charge, and p is the hole density per unit length calculated as a function of gate voltage using a commercial finite-element software (Sentaurus, Synopsys). We find an average peak electron mobility of 12 cm2·V−1·s−1, which is weakly dependent on temperature. The relatively low mobility value likely stems from fixed charge impurity scattering at the dielectric-nanowire interface due to an unoptimized gate stack, and does not reflect the intrinsic mobility of the nanowire heterostructure. In conclusion, we demonstrate epitaxial, coherently strained Si−SixGe1−x core−shell nanowires as a platform for onedimensional electron confinement in group IV nanowires. Conduction band edge calculations for a strained nanowire heterostructure indicate a minimum shell-to-core conduction band offset of 213 meV in a typical heterostructure. Using a sequence of VLS and CVD growth mechanisms, we demonstrate Si−SixGe1−x nanowire heterostructures, with E
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electrical characterization, with assistance from F.W. and K.K. D.C.D. and E.T. analyzed the data and cowrote the manuscript. All authors have contributed to and approved the final version of the manuscript.
shell thickness and content controlled by the growth conditions. Micro-Raman spectroscopy reveals peaks associated with the Si−Si mode of the Si core, and the Si−Si, Si−Ge, and Ge−Ge modes of the shell. The Si core peak is red-shifted from its unstrained value of 520 cm−1, consistent with a tensile strain in this region and in good agreement with lattice dynamic theory calculations. We also demonstrate enhancement mode n-type FETs with Si−SixGe1−x core−shell nanowires as channel material. Methods. Raman Spectroscopic Measurements. The nanowires were removed from the growth substrate by sonication in ethanol, followed by drop casting onto the target Si/SiO2/Au substrate. The Au film is used to mask Si signal from the underlying substrate and, through comparison to measurements done on a glass substrate, was found to have no effect on the nanowire’s Raman spectrum. All measurements use a Renishaw InVia μ-Raman spectrometer with backscattering geometry, 532 nm incident laser with ∼13 kW·cm−1 power density, and 100× objective lens. To maximize the signal, the incident light is polarized along the nanowire axis in all measurements. If the incident light polarization is aligned at an angle θ with respect to the nanowire main axis, we find a cos2 θ dependence of the signal intensity. Nanowire FET Fabrication. The n-type FETs are prepared using Si−SixGe1−x core−shell nanowires with a shell that was lightly doped with phosphorus during growth. Nanowires are transferred to an oxidized (61 nm) n+2 Si device substrate as described above. The sample is etched in dilute hydrofluoric acid to remove native oxide from the nanowire surface and is followed immediately by atomic layer deposition (ALD) of a 7.9 nm Al2O3 top-gate dielectric at 250 °C, employing trimethylaluminum and deionized water precursors. The metal gate is patterned using electron-beam lithography (EBL) with PMMA resist, followed by sputtering of TaN metal and liftoff in acetone. The samples are then implanted with phosphorus ions at an energy of 5 keV with a total dose of 5 × 1014 cm−2. During implant the sample is tilted by 32° and is rotated in four discrete steps to get uniform coverage. Phosphorus dopants are activated by a rapid thermal annealing process at 550 °C for 10 min in a N2 ambient. To improve device performance, the gate stack is also passivated by annealing at 450 °C for 10 min in a H2 ambient. The device is completed by adding Ni source/drain contacts through EBL, native oxide etching through a brief exposure to dilute HF, electron beam evaporation, and liftoff.
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Funding
This work was supported by the National Science Foundation, grants DMR-0846573 and DMR-1507654. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors would like to thank Chenglin Wu and Rui Huang for assistance with Abaqus finite-element strain calculations.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.5b03961. Additional information is available on calculations of strain, Raman shift, and Raman intensity in both cylindrical and hexagonal structures, as well as conduction band calculations and Si nanowire growth (PDF)
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REFERENCES
AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected]. Author Contributions
D.C.D. performed the nanowire growth, TEM, EDX, Raman measurements, theoretical calculations, FET fabrication, and F
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Nano Letters (26) Fukata, N.; Mitome, M.; Sekiguchi, T.; Bando, Y.; Kirkham, M.; Hong, J.-I.; Wang, Z. L.; Snyder, R. L. ACS Nano 2012, 6 (10), 8887− 8895. (27) Oehler, F.; Gentile, P.; Baron, T.; Ferret, P.; Den Hertog, M.; Rouvière, J. Nano Lett. 2010, 10 (7), 2335−2341. (28) Varahramyan, K. M.; Ferrer, D.; Tutuc, E.; Banerjee, S. K. Appl. Phys. Lett. 2009, 95, 033101. (29) Alonso, M. I.; Winer, K. Phys. Rev. B: Condens. Matter Mater. Phys. 1989, 39 (14), 10056−10062. (30) Anastassakis, E.; Pinczuk, A.; Burstein, E.; Pollak, F. H.; Cardona, M. Solid State Commun. 1970, 8 (2), 133−138. (31) Ganesan, S.; Maradudin, A.; Oitmaa, J. Ann. Phys. 1970, 56 (2), 556−594. (32) Reparaz, J. S.; Bernardi, A.; Goñi, A. R.; Alonso, M. I.; Garriga, M. Appl. Phys. Lett. 2008, 92 (8), 081909. (33) Anastassakis, E.; Cantarero, A.; Cardona, M. Phys. Rev. B: Condens. Matter Mater. Phys. 1990, 41 (11), 7529−7535. (34) Cerdeira, F.; Buchenauer, C. J.; Pollak, F. H.; Cardona, M. Phys. Rev. B 1972, 5 (2), 580−593. (35) Wang, J.; Gudiksen, M. S.; Duan, X.; Cui, Y.; Lieber, C. M. Science 2001, 293 (5534), 1455−1457. (36) Ruda, H. E.; Shik, A. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 72 (11), 115308. (37) Wortman, J. J.; Evans, R. A. J. Appl. Phys. 1965, 36 (1), 153− 156.
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DOI: 10.1021/acs.nanolett.5b03961 Nano Lett. XXXX, XXX, XXX−XXX
Coherently Strained Si−SixGe1−x Core−Shell Nanowire Heterostructures David C. Dillen, Feng Wen, Kyounghwan Kim, and Emanuel Tutuc* Microelectronics Research Center, The University of Texas at Austin, 10100 Burnet Road, Bldg. 160, Austin, Texas 78758, United States S Supporting Information *
ABSTRACT: Coherently strained Si−SixGe1−x core−shell nanowire heterostructures are expected to possess a positive shell-tocore conduction band offset, allowing for quantum confinement of electrons in the Si core. We report the growth of epitaxial, coherently strained Si−SixGe1−x core−shell heterostructures through the vapor−liquid−solid mechanism for the Si core, followed in situ by the epitaxial SixGe1−x shell growth using ultrahigh vacuum chemical vapor deposition. The Raman spectra of individual nanowires reveal peaks associated with the Si−Si optical phonon mode in the Si core and the Si−Si, Si−Ge, and Ge−Ge vibrational modes of the SixGe1−x shell. The core Si−Si mode displays a clear red-shift compared to unstrained, bare Si nanowires thanks to the lattice mismatch-induced tensile strain, in agreement with calculated values using a finite-element continuum elasticity model combined with lattice dynamic theory. N-type field-effect transistors using Si−SixGe1−x core−shell nanowires as channel are demonstrated. KEYWORDS: Nanowire, core−shell, elastic strain, Raman spectroscopy, field-effect transistor, silicon−germanium
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strain-induced shift of conduction band energies, we estimate a minimum shell-to-core conduction band offset of 213 meV in a 30 nm diameter nanowire with 3.9 nm Si0.39Ge0.61 shell (see Supporting Information, sections S1 and S2). While earlier studies have demonstrated the growth of crystalline Si−Ge core−shell nanowires,15,25,26 their epitaxial quality has yet to be established through a systematic study of the elastic strain and a comparison to values expected for a coherent heterostructure. We present here the growth, structural, and electrical characterization of strained Si−SixGe1−x core−shell nanowires. We use Raman spectroscopy to measure the optical phonon frequencies of both core and shell regions combined with calculations using a continuum elasticity model and lattice dynamic theory in order to compare the experimentally measured phonon frequencies to values expected for a fully strained heterostructure. We also demonstrate n-type fieldeffect transistors using Si−SixGe1−x core−shell nanowires as channel material. Our Si−SixGe1−x core−shell nanowires are grown through a sequential combination of vapor−liquid−solid (VLS) and epitaxial chemical vapor deposition (CVD) processes, as shown schematically in Figure 1a. The Si(111) substrate is first prepared using dilute hydrofluoric (HF) acid etching of the native oxide, followed by evaporation of a 7−8 Å Au film. The substrate is then transferred to the cold wall ultrahigh vacuum
ow-dimensional semiconducting materials are expected to play an important role in electronic and optical devices. Examples range from nanowire field-effect transistors (FETs)1−5 to tunnel FETs6 and solar cells7 and include emerging applications such as quantum dot spin qubits.8,9 Semiconductor nanowires are particularly interesting because they provide a one-dimensional quantum confinement route through the use of core−shell heterostructures. Examples of ntype core−shell and core−multishell nanowires using III−V compound semiconductors include GaN-AlN/AlGaN,10 GaN/ InGaN/GaN/AlGaN,11 InAs-InP,12 InGaAs-InP/InAlAs/InGaAs,13 and GaAs-AlGaAs.14 In group IV nanowires, the valence band offset between Ge and Si allows the confinement of holes in the core of Ge−Si and Ge−SixGe1−x core−shell nanowires.15−17 The development of electron-confined systems using group IV nanowire heterostructures has, however, been slower. The interplay between strain and band offset in the Si−Ge system on one hand and the impact of growth conditions on structural coherency on the other are the two main issues. Previous experimental18 and theoretical19 studies using planar materials have revealed electron confinement in the Si layer of coherently strained Si−Si0.5Ge0.5 heterostructures lattice matched to a Si0.75Ge0.25 substrate. Coherently strained Si−SixGe1−x core− shell nanowires represent one possible radial heterostructure where a positive shell-to-core conduction band offset, beneficial for quantum confinement of electrons in the Si core, may be realized. Indeed, by calculating the elastic strain distribution in Si−SixGe1−x core−shell nanowires20−24 and the corresponding © XXXX American Chemical Society
Received: September 29, 2015 Revised: November 14, 2015
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chemical vapor deposition conditions and a combination of SiH4 and GeH4 (20% in He) precursors. For comparison, bare Si nanowires were also grown using the same conditions as the VLS growth of Si cores in Si−SixGe1−x core−shell heterostructures (see Supporting Information, section S3). The bare Si nanowires serve as control to establish the diamond crystal structure, and to obtain a baseline for the optical phonon frequency in nominally unstrained Si nanowires. Transmission electron microscopy (TEM) is used to study the morphology and crystal structure of the Si−SixGe1−x core− shell nanowires. Figure 1b evinces a single-crystal nanowire heterostructure with no obvious surface roughening or sawtooth faceting.27 Electron diffraction analysis indicates a growth axis along [110] for both bare Si nanowires and Si− SixGe1−x core−shell nanowires (see Supporting Information, Section S3). We note that the core−shell interface is hardly discernible in the micrograph of Figure 1b, which in turn testifies to the quality of the epitaxial shell growth. We find that nanowires can grow with either a circular or hexagonal crosssection in the range of diameters we investigate, with the hexagonal structures having four {111} and two {001} type sidewalls. Unless otherwise noted, in the following work we assume all nanowires are cylindrically shaped; a comparison to hexagonal structures is given in Supporting Information, Section S5. To measure the SixGe1−x shell’s thickness (tsh) and relative Si content (x), we use energy-dispersive X-ray spectroscopy (EDX) with a scanning TEM (STEM) electron beam. The inset of Figure 1b plots an EDX linescan perpendicular to the nanowire axis, showing the Kα1 X-ray line counts for Si (red) and Ge (black) with energies of 1.74 and 9.89 keV, respectively, for a heterostructure with tsh = 3.9 nm and x = 0.39. The data is fit using a model which considers the relative numbers of each atom along the beam’s path as a function of beam position.28 We find that the shell thickness and material composition are well controlled by changes to the shell growth time and relative SiH4 and GeH4 source gas flow rates, respectively. Using a gas flow ratio of SiH4/GeH4 = 25, we find a shell content of x = 0.39 and growth rate of 0.65 Å/min, while at SiH4/GeH4 = 36 we find x = 0.56 and 0.40 Å/min growth rate. A fundamental property of a pseudomorphic heterostructure is the elastic strain resulting from the lattice mismatch between individual components. To probe the elastic strain in Si− SixGe1−x core−shell nanowires, we use Raman spectroscopy to
Figure 1. (a) Schematic of Si−SixGe1−x core−shell growth process showing hydrogen annealing, vapor−liquid−solid (VLS) core growth, and chemical vapor deposition (CVD) shell growth. Arrows represent the direction of growth in each regime. (b) High-resolution transmission electron micrograph of a Si−SixGe1−x heterostructure. The inset shows an EDX/STEM linescan, where Si and Ge Kα1 X-ray line counts are plotted with red and black symbols, respectively. EDX fitting results (solid lines: redSi, blackGe) correspond to tsh = 3.9 nm and x = 0.39. The core and shell regions, as determined from the EDX data, are marked using dashed lines in the TEM micrograph.
growth chamber and annealed for 15 min in H2 ambient at 370 °C to produce Au nanoparticles. The Si nanowire cores are grown through the Au-catalyzed VLS mechanism at 430 °C using SiH4 (100%, 100 sccm) source gas at a chamber pressure of 10 Torr. The SixGe1−x shell growth follows in situ at a sample temperature of 390 °C, using ultrahigh vacuum
Figure 2. Comparison of Raman spectra between Si nanowire samples with no shell (black line) and Si−SixGe1−x core−shell samples (red line) with (a) tsh = 3.9 nm, x = 0.39 and (b) tsh = 2.9 nm, x = 0.56. The insets focus on the spectra between 480 and 550 cm−1, corresponding to the Si−Si modes. B
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unstrained SixGe1−x has a Raman shift of 477.3 cm−1 for x = 0.39 and 489.2 cm−1 for x = 0.56;29 the Si−Si shell peaks of Figure 2 are shifted to higher frequencies thanks to the compressive strain in the shell. To better understand the dependence of Raman modes with elastic strain, we calculate the strain-induced shift of the Si−Si mode in both core and shell regions. Strain calculations for the Si−SixGe1−x core−shell heterostructure use a finite-element method and are detailed in Supporting Information, Section S1. We find that the Si core is indeed under a tensile strain thanks to the larger lattice constant of the SixGe1−x shell and that all strain components are nearly uniform with position in this region. The shell strain, in comparison, changes appreciably with position and generally has a higher magnitude with both tensile and compressive components. In the presence of elastic strain, the optical phonons modes of a cubic material, which are initially triply degenerate at zone center will shift to lower or higher frequencies, depending on the polarity of the strain (i.e., compressive or tensile), and may split into nondegenerate modes. The strain-induced shift of each Raman mode is found using a linear deformation potential approach, namely, the secular equation of lattice dynamic theory:30,31
measure the optical phonon frequencies of individual nanowires (see Methods). Figure 2 shows the spectra measured from bare Si nanowires (black lines) and Si−SixGe1−x core−shell heterostructures with different shell contents and thicknesses (red lines). The Si nanowire Raman spectra reveal a single peak at 520 cm−1, the expected value for bulk, unstrained Si in the diamond crystal structure. By comparison, the Si−SixGe1−x core−shell heterostructures show a set of additional peaks with frequencies between 290 and 510 cm−1. We associate the low intensity peaks at 292 and 409 cm−1 with the Ge−Ge and Si− Ge modes of the strained SixGe1−x shell, respectively.29 We also observe a peak near 435 cm−1, a local Si−Si vibration in the shell which arises due to a nonuniform local SixGe 1−x composition.29 We attribute the highest intensity peak of the core−shell samples to the Si−Si Raman mode of the Si core, which is redshifted in comparison to bare Si nanowires, as evident from Figure 2 insets, because of the tensile strain applied by the SixGe1−x shell. The full width at half-maximum (fwhm) of this peak averages 6.5 cm−1 compared to 3.7 cm−1 for bare Si nanowires. The additional peak near 505 cm−1 in the core− shell spectra has a wider fwhm and is attributed to the Si−Si mode of the shell. We note that the nominal Si−Si mode in pεxx + q(εyy + εzz) − λ
2rεxy
2rεxz
2rεxy
pεyy + q(εxx + εzz) − λ
2rεyz
2rεxz
2rεyz
pεzz + q(εxx + εyy) − λ
where εuv are the strain tensor components, and p, q, and r are the material’s phonon deformation potential values, given in Table 1 for Si and SixGe1−x alloys. The r values for SixGe1−x
p/ω02
q/ω02
r/ω02
Si Si0.56Ge0.44 Si0.39Ge0.61
−1.84 −1.7432 −1.8232
−2.35 −2.0632 −2.0632
−0.7133 −1.00 −1.00
32
32
(1)
S2 of the Supporting Information), the Si−Si shell modes show a much larger variation with position than those in the core, and the phonon polarization directions are no longer along the nanowire-oriented principle axes. The calculated Raman shift of the three shell modes range between 481 and 496 cm−1. In light of the uncertainty of the r value, we performed the shell calculations using values of the r deformation potential between −0.7 and −1.2; however, we find only 1.4 cm−1 difference in the median Raman shift of mode 1. While the above calculations predict six nondegenerate Si−Si vibrational modes for the strained core−shell heterostructure, only two peaks were actually observed in our experimental Raman data (insets of Figure 2). This apparent discrepancy can be reconciled by examining which Raman modes are active based on selection rules associated with the polarization of the incident (Einc) and scattered (Escat) light, and their corresponding intensities.23,24 To calculate the expected intensity of each Si−Si Raman mode in both strained core and shell regions we use Einc = [110], as the incident polarization is aligned with the nanowire axis during each Raman measurement (see Methods). Furthermore, because of the anisotropic, antennae-like behavior of semiconducting nanowires embedded in a mismatched dielectric, only the light polarized parallel to the nanowire axis will couple into or out of the structure,35,36 requiring that Escat also be along [110]. We have tested this hypothesis by polarizing the scattered beam, finding that Escat is indeed parallel to the nanowire main axis. The calculation results are plotted in Figure 3d−f, for modes 1−3, respectively. In the Si core, we find that only the first mode, with phonon polarization along [001], is expected to be active, while the other two have zero intensity. Similarly, in the SixGe1−x shell we find that mode 3 is inactive across the entire shell, while the other two modes
Table 1. Normalized Phonon Deformation Potentials for Si and SixGe1−x material
=0
have not been reported; we use r/ω02 = −1.0 estimated from the corresponding values in Si and Ge. The eigenvalue solutions λi = ω2i − ω2io express the strain-induced shift of mode i. The initial, unstrained mode frequency, ωio, is 520.0 cm−1 for Si and 477.3 cm−1 (489.2 cm−1) for SixGe1−x with x = 0.39 (0.56).29 The calculated Raman shift of Si−Si modes in a core−shell structure with tsh = 3.9 nm and x = 0.39 are shown in Figure 3a−c. Similar to bulk Si under a tensile uniaxial stress along [110],34 we find that the core’s initially triply degenerate mode at 520 cm−1 shifts to lower frequency and splits into three nondegenerate modes. The average Raman shift is 512.1, 511.5, and 514.1 cm−1 for core modes 1, 2, and 3, respectively, while the eigenvectors indicate phonon polarizations along [001], [110], and [−110] for the same calculated modes. The Raman shift of a given mode changes only slightly across the core, varying by less than 0.5 cm−1. Shell phonons also split into three nondegenerate modes and are blue-shifted in relation to their unstrained frequency. Moreover, because of the spatial dependence of the elastic strain in the shell (see Figures S1 and C
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Figure 3. Calculated (a−c) Raman shift and (d−f) intensity for the three modes of a fully strained Si−SixGe1−x core−shell nanowire with tsh = 3.9 nm, x = 0.39, and d = 30 nm, assuming the incident and scattered light polarizations are parallel to the [110] nanowire growth axis.
Figure 4. Diameter dependence of Si−Si Raman modes for Si−SixGe1−x core−shell nanowires with (a) tsh = 3.9 nm, x = 0.39 and (b) tsh = 2.9 nm, x = 0.56. The black and blue symbols represent the two Raman peaks measured experimentally, while the lines correspond to calculation results using finite-element (black, solid) or analytically (red, dashed) derived strain distributions. The black dotted line marks the position of the Si−Si mode of unstrained Si.
dependence of Figure 4 can be understood by considering the relative volume of core and shell regions. By increasing the nanowire diameter while keeping shell thickness constant, the elastic compliance of the core decreases in relation to that of the shell. This means that a smaller fraction of the total lattice mismatch will be accommodated in the core, resulting in a reduced strain and, hence, smaller strain-induced shift of the core Raman mode. Due to the thinner shell and smaller mismatch in the sample shown in Figure 4b, we find that the strain-induced red shift of the core mode is smaller in comparison to the structure of Figure 4a. In Figure 4, we also plot the diameter dependence of the Raman peaks determined from our experimental data (symbols). We find that the main peak (black symbols) agrees well with the core calculation results, except that a larger straininduced red-shift is expected in a fully strained structure. This finding is most likely a result of partial strain relaxation through defect formation at the core−shell interface. Furthermore, the nanowire tapering is not expected to alter the Raman spectrum significantly. Using Figure 4 data, and a nanowire tapering of ∼1.6 nm per micron of length, a laser spot size of 1 μm, should widen the Raman peak by ∼0.25 cm−1 by comparison to a structure with uniform diameter. The shell calculation results,
have a nonzero, position dependent-intensity, with mode 1 having the highest intensity. The calculated Raman shift and intensity for the second Si−SixGe1−x core−shell heterostructure used in this study (tsh = 2.9 nm and x = 0.56) are qualitatively similar to those described above (see Figure S5 of the Supporting Information). Furthermore, the calculated elastic strain in the Si core and the corresponding Raman shift and intensity for a Si−SixGe1−x core−shell nanowire with hexagonal cross-section are nearly identical to results for cylindrical nanowires of Figure 3 over most of the core cross-section, with differences observed only within a small region near the facet corners (see Supporting Information, Section S5). Figure 4 shows the diameter dependence of the calculated, active Si−Si mode of the core. The solid black line represents an average of the core values found using the anisotropic finiteelement strain results. For comparison, we also include calculation results which use a simplified, analytical strain calculation technique21 which assumes isotropic elastic constants (red dashed line, see Supporting Information, section S1). For this model, we use the Young’s modulus along the nanowire axis E[110] = 169 GPa and the average Poisson ratio in the (110) plane, ν(110) = 0.213,37 and find close agreement between the two strain calculation methods. The diameter D
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Figure 5. Si−SixGe1−x core−shell nanowire FETs. (a) SEM image of completed FET with source, gate, and drain contacts labeled and phosphorus doped region shaded in red. (b) Output and (c) transfer characteristics of a device with tsh = 3.9 nm, x = 0.39, d = 32 nm, and LG = 1340 nm. (d) RM versus LG at multiple values of VG − VT (symbols). Linear fits to experimental data are also included.
not shown in Figure 4, lie between 481 and 496 cm−1 in the sample with x = 0.39 and between 493 and 505 cm−1 in the sample with x = 0.56. These values are lower than the frequency of the experimental shell peaks near 505−510 cm−1 (blue symbols), indicating a larger than expected strain-induced blue-shift in this region. While the origin of the discrepancy between the measured shell peaks and theoretical calculations is unclear, we note that the large strain magnitudes in this region, of up to 2.5%, may limit the accuracy of the calculations, as the deformation potential values were determined experimentally using strain values below 1%.33 Next, we address electron transport in Si−SixGe1−x core− shell nanowire heterostructures and demonstrate top-gated ntype field-effect transistors (n-FET) with highly doped source and drain contacts. Details on the device fabrication can be found in the Methods section. For n-FET devices we use core− shell nanowires with tsh = 3.9 nm, x = 0.39, and a shell which is lightly doped with phosphorus by adding PH3 precursor during growth. Figure 5a shows a scanning electron micrograph (SEM) of a typical n-FET with the source, gate, and drain contacts labeled for clarity. In order to realize low resistance contacts, we implant source and drain regions with low-energy phosphorus ions using the gate metal as a self-aligned mask. The energy (5 keV) and dose (5 × 1014 cm−2) are both chosen to minimize implant-induced crystal damage. Four-point conductivity measurements on blanket-implanted control nanowires yield a doped nanowire resistivity of 4.26 × 10−3 Ω·cm and a metal to nanowire specific contact resistance of 1.28 × 10−8 Ω·cm2. For a n-FET using a 32 nm diameter nanowire and 850 nm long source and drain extensions, this corresponds to a total source/drain external series resistance of RSD = 45.7 kΩ. We measure the drain current (ID) vs drain voltage (VD) characteristics at different gate voltages (VG), and the ID−VG
characteristics at various VD for devices of multiple channel lengths (LG). An example is shown in Figure 5b,c for a device with LG = 1340 nm and diameter d = 32 nm. We find that all devices behave as n-type, enhancement mode FETs with a large, positive threshold voltage (VT) over 1.0 V and an increasing ID with increasing VG. To quantify the characteristic device scaling with gate length, in Figure 5d we plot the total device resistance (RM) vs LG at fixed values of gate overdrive voltage, VG − VT. The linear RM vs LG dependence is expected from simple scaling arguments, and indicates the contact resistance does not control the device characteristics. By fitting the RM vs LG data at each VG − VT and extrapolating to their crossover point, we extract an external source/drain series resistance of RSD = 40 kΩ, matching well with the above value calculated from measurements on blanket implanted Si− SixGe1−x nanowires. The electron mobility was extracted from experimental data using μ = LG(RCH·e·p)−1, where RCH = RM − RSD is the intrinsic channel resistance, e is the electron charge, and p is the hole density per unit length calculated as a function of gate voltage using a commercial finite-element software (Sentaurus, Synopsys). We find an average peak electron mobility of 12 cm2·V−1·s−1, which is weakly dependent on temperature. The relatively low mobility value likely stems from fixed charge impurity scattering at the dielectric-nanowire interface due to an unoptimized gate stack, and does not reflect the intrinsic mobility of the nanowire heterostructure. In conclusion, we demonstrate epitaxial, coherently strained Si−SixGe1−x core−shell nanowires as a platform for onedimensional electron confinement in group IV nanowires. Conduction band edge calculations for a strained nanowire heterostructure indicate a minimum shell-to-core conduction band offset of 213 meV in a typical heterostructure. Using a sequence of VLS and CVD growth mechanisms, we demonstrate Si−SixGe1−x nanowire heterostructures, with E
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electrical characterization, with assistance from F.W. and K.K. D.C.D. and E.T. analyzed the data and cowrote the manuscript. All authors have contributed to and approved the final version of the manuscript.
shell thickness and content controlled by the growth conditions. Micro-Raman spectroscopy reveals peaks associated with the Si−Si mode of the Si core, and the Si−Si, Si−Ge, and Ge−Ge modes of the shell. The Si core peak is red-shifted from its unstrained value of 520 cm−1, consistent with a tensile strain in this region and in good agreement with lattice dynamic theory calculations. We also demonstrate enhancement mode n-type FETs with Si−SixGe1−x core−shell nanowires as channel material. Methods. Raman Spectroscopic Measurements. The nanowires were removed from the growth substrate by sonication in ethanol, followed by drop casting onto the target Si/SiO2/Au substrate. The Au film is used to mask Si signal from the underlying substrate and, through comparison to measurements done on a glass substrate, was found to have no effect on the nanowire’s Raman spectrum. All measurements use a Renishaw InVia μ-Raman spectrometer with backscattering geometry, 532 nm incident laser with ∼13 kW·cm−1 power density, and 100× objective lens. To maximize the signal, the incident light is polarized along the nanowire axis in all measurements. If the incident light polarization is aligned at an angle θ with respect to the nanowire main axis, we find a cos2 θ dependence of the signal intensity. Nanowire FET Fabrication. The n-type FETs are prepared using Si−SixGe1−x core−shell nanowires with a shell that was lightly doped with phosphorus during growth. Nanowires are transferred to an oxidized (61 nm) n+2 Si device substrate as described above. The sample is etched in dilute hydrofluoric acid to remove native oxide from the nanowire surface and is followed immediately by atomic layer deposition (ALD) of a 7.9 nm Al2O3 top-gate dielectric at 250 °C, employing trimethylaluminum and deionized water precursors. The metal gate is patterned using electron-beam lithography (EBL) with PMMA resist, followed by sputtering of TaN metal and liftoff in acetone. The samples are then implanted with phosphorus ions at an energy of 5 keV with a total dose of 5 × 1014 cm−2. During implant the sample is tilted by 32° and is rotated in four discrete steps to get uniform coverage. Phosphorus dopants are activated by a rapid thermal annealing process at 550 °C for 10 min in a N2 ambient. To improve device performance, the gate stack is also passivated by annealing at 450 °C for 10 min in a H2 ambient. The device is completed by adding Ni source/drain contacts through EBL, native oxide etching through a brief exposure to dilute HF, electron beam evaporation, and liftoff.
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Funding
This work was supported by the National Science Foundation, grants DMR-0846573 and DMR-1507654. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors would like to thank Chenglin Wu and Rui Huang for assistance with Abaqus finite-element strain calculations.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.5b03961. Additional information is available on calculations of strain, Raman shift, and Raman intensity in both cylindrical and hexagonal structures, as well as conduction band calculations and Si nanowire growth (PDF)
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REFERENCES
AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected]. Author Contributions
D.C.D. performed the nanowire growth, TEM, EDX, Raman measurements, theoretical calculations, FET fabrication, and F
DOI: 10.1021/acs.nanolett.5b03961 Nano Lett. XXXX, XXX, XXX−XXX
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DOI: 10.1021/acs.nanolett.5b03961 Nano Lett. XXXX, XXX, XXX−XXX
