Abstract

The piezoresistance effect of silicon¹ has been widely used in mechanical sensors^{2, 3, 4}, and is now being actively explored in order to improve the performance of silicon transistors^{5, 6}. In fact, strain engineering is now considered to be one of the most promising strategies for developing high-performance sub-10-nm silicon devices⁷. Interesting electromechanical properties have been observed in carbon nanotubes^{8, 9}. In this paper we report that Si nanowires possess an unusually large piezoresistance effect compared with bulk. For example, the longitudinal piezoresistance coefficient along the 111 direction increases with decreasing diameter for p-type Si nanowires, reaching as high as -3,550  10^-11 Pa^–1, in comparison with a bulk value of -94  10^-11 Pa^-1. Strain-induced carrier mobility change and surface modifications have been shown to have clear influence on piezoresistance coefficients. This giant piezoresistance effect in Si nanowires may have significant implications in nanowire-based flexible electronics, as well as in nanoelectromechanical systems.

Introduction

Application of strain to a crystal results in a change in electrical conductivity due to the piezoresistance effect. To evaluate the piezoresistance effect (or electromechanical properties) in nanostructures, mechanical manipulations and electrical measurements must be performed simultaneously. Traditionally, this has been carried out by interfacing the nanostructures with lithographically defined electrodes. Such nanostructure–electrode interfaces^{8, 10}, however, inevitably have stability and reliability issues when subject to mechanical forces. To avoid such interface problems, we have recently developed a chemical vapour deposition process to grow suspended nanowires for piezoresistance testing¹¹.

Silicon nanowires with 111 or 110 growth directions were grown in trenches on silicon-on-insulator (SOI) wafers to form bridge structures (Fig. 1; Supplementary Information, Fig. S1). Such bridges are themselves monolithically structured and fully functional devices, enabling direct probing of electromechanical properties. The joints between the nanowires and the trench sidewalls are mechanically robust. As shown in Fig. 1b, the nanowire grew backwards after impinging into the opposite wall, implying a self-welding mechanism. The deflection of these nanowires followed exactly the behaviour of double-clamped beams in our atomic force microscopy experiments¹², confirming the rigidity and equivalence of the two joints. The joints also make reliable electrical connections at the nanowire level. Cross-section transmission electron microscopy images show that there is no catalyst metal at either interface (Fig. 1c and e); hence, the wire–wall junctions are simply Si homojunctions with properties determined primarily by carrier distributions. Ohmic behaviour was readily established at the interfaces for the p-type nanowires studied here. The diameters and resistivities of nanowires can be readily controlled. In this study, the nanowires have diameters ranging from 50 to 350 nm and they were made p-type with resistivities of 0.003–10  cm (see Methods).

Figure 1: 111-oriented Si nanowire bridges on SOI substrates.

a, Single nanowire with the 111 growth direction is bridging a trench confined by vertical {111} faces on a 110-oriented SOI substrate. The parallel lines on the sidewalls with alternating contrast are scallops formed during deep reactive ion etching. b, General morphology of a bridged nanowire, which grew from the left sidewall along the 111 direction and impinged upon the opposite sidewall; it finally grew backwards after self-welding into the sidewall. c,e, Cross-sectional transmission electron microscope images for the two joints between the nanowire and trench sidewalls. d, A high-resolution electron microscopy image confirms the 111 growth direction and reveals a thin oxide layer on the surface of the nanowire. The scale bars in a–e are 2 m, 500 nm, 100 nm, 3 nm and 100 nm, respectively.

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The quantitative relation between conductivity/resistivity and stress/strain is given by the fourth-rank piezoresistance tensor¹. When a uniaxial stress is applied and the electric field and current are along the same direction, the longitudinal piezoresistance coefficient¹³ can be measured and defined as the relative change in conductivity per unit stress:

where ₀ is the conductivity under zero stress and X is the stress. Traditionally, the piezoresistance coefficient was defined with resistivity¹ as _l = (/₀)/X. The conversion is simply _l = -_l for small . Uniaxial stresses were applied on Si nanowires along their lengths by the four-point bending method¹⁴ (Fig. 2a; see Methods); the longitudinal piezoresistance coefficients along the 111 and 110 directions, ₁₁₁ and ₁₁₀, were then examined. The measurements on 111-oriented nanowires will be focused on in the following discussions.

Figure 2: Longitudinal piezoresistance coefficients ₁₁₁ of p-type Si nanowires.

a, Schematic diagram for the four-point bending setup used to apply uniaxial stresses on Si nanowires. b, The conductance of a p-type 111-oriented nanowire (70 nm  1.2 m) increases under compressive stresses and decreases under tensile stresses. c, Relationships between the relative change in conductivity /₀ and stress/longitudinal strain. Four types of nonlinear behaviours of nanowires are shown, labelled with letters I, C, L and Z. The inset shows the overview for L. d, First-order longitudinal piezoresistance coefficient of p-type Si nanowires and its dependence on diameter and resistivity. Different colours represent different nonlinearities: green, I; black, C; blue, L; red, Z. The drop lines are for use as guidelines. The uncertainties for ₁₁₁ in the fittings are typically 2.5% for I, 2.7% for C, 13.5% for L and 7.8% for Z categories.

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Figure 2b illustrates typical data taken from the four-point bending measurements, showing that the conductance increases under compression and decreases under tension for a p-type 111-oriented nanowire. This trend is qualitatively consistent with the longitudinal piezoresistance behaviour of bulk Si along the 111 directions. For further quantitative analyses, the relative change in conductance G/G₀ was converted to the relative change in conductivity /₀ by subtracting the dimensional changes of nanowires (see Supplementary Information). The relationships between /₀ and stress X are shown in Fig. 2c. One of the five curves presented is for the boron-doped SOI-device layer, with resistivity 1  cm, as the representative for bulk Si, and the other four curves represent the typical behaviours of Si nanowires. It can be readily seen that the conductivity of a Si nanowire is much more sensitive to stress than that of bulk Si. For instance, under a compression of 8  10⁷ Pa, /₀ can be as high as 15 for nanowires, but is only 0.08 for bulk Si. Moreover, the piezoresistance effect is generally nonlinear for Si nanowires, but it is essentially linear for bulk Si (refs 1 and 15) in the stress range performed here. The nonlinearities are classified into four categories based on the shape of the (/₀)-X curves. A letter is assigned to each category by the similarity in shape between the letter and curve: 'I' represents a relatively linear curve, 'C' represents a concave curve, 'L' is for curves with greater slope under compression, and a 'Z' curve is convex with compression and concave with tension. Because of these significant nonlinearities, we fitted /₀ as a function of X into the McLaurin series to the third power and took (d/dX)/₀ at zero stress as the first-order piezoresistance coefficient ₁₁₁. The second- and third-order coefficients will not be discussed in detail here; however, it is expected that a large second-order coefficient exists in the C and L curves, and a large third-order coefficient in the Z curves.

Further conclusions can be drawn from the statistical data for ₁₁₁ from nanowires with different diameters and resistivities (Fig. 2d; -₁₁₁ was plotted because ₁₁₁ is negative). Data for bulk Si with different resistivities¹⁶ are also shown in the figure (carrier concentrations were converted to resistivities by adopting the empirical relation¹⁷). It is clear that ₁₁₁ for a nanowire (-35 to -3,550  10^-11 Pa^-1) is generally much higher than that for bulk Si (in the range -17 to -94  10^-11 Pa^-1, depending on resistivities¹⁶). Only those nanowires with diameters larger than 300 nm and resistivities less than 0.004  cm have values close to that of bulk Si. The resistivity dependence of ₁₁₁ for nanowires follows a trend similar to that of bulk: the coefficient increases as the resistivity decreases. In addition, the diameter dependence is particularly interesting: the coefficient increases as the diameter decreases. Furthermore, the nonlinearity of the piezoresistance effect also shows a dependence on diameter and resistivity. From the colour-sorted distribution of the four types of nonlinearities, it can be seen that the nanowires with smaller diameters and higher resistivities have L-shaped (/₀)-X curves, but those with smaller diameters and lower resistivities possess Z curves. Medium-sized nanowires exhibit C shapes, and I curves are quite typical for larger wires with lower resistivities. It is clear that thinner nanowires generally have greater nonlinearities.

For both theoretical considerations and practical applications, it is worth examining whether carrier concentration or mobility plays the dominant role in these remarkable conductivity changes for nanowires. Strained nanowire field-effect transistors (FETs) were made for such a purpose. Solid polyelectrolyte (LiClO₄/poly(ethylene oxide)) was placed over a nanowire to provide surrounding gating¹⁸ and transconductances were measured under varied stresses (Fig. 3a; see Methods). The mobility for the device shown here is estimated to be 30 cm² V^-1 s^-1 at zero stress and the corresponding carrier concentration is 7  10¹⁷ cm^–3. The relative changes in mobility /₀ were compared with the relative changes in conductivity /₀ (Fig. 3b). The close match between them indicates that the large piezoresistance coefficient ₁₁₁ derives mainly from the change in carrier mobility. This mobility origin of the giant piezoresistance effect should have significant implications in strain engineering on the nanometre scale. In the current work, the mobility could be doubled for a nanowire with a diameter of 55 nm under 0.05% compressive strain along the 111 direction.

Figure 3: Strained Si nanowire field-effect transistors.

a, Measurements on transconductances under different stresses. The inset shows the schematic diagram for polyelectrolyte gating. b, Comparison between the relative change in mobility /₀ and the relative change in conductivity /₀. The mobilities are fitted and calculated from V_GS = -2.56 V to -2.9 V and the conductivities are taken at V_GS = -2.74 V. The nanowire measured here is 120 nm thick and 3.5 m long.

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The significant enhancement of the piezoresistance effect is not limited to the 111 direction. Measurements on 110-oriented Si nanowires also show very large longitudinal coefficient ₁₁₀ values. For example, ₁₁₀ was measured to be -660  10^-11 Pa^-1 for a 75-nm-thick nanowire with resistivity 0.3  cm (the bulk value for p-type Si is _110,bulk = -70  10^-11 Pa^-1 for the same resistivity¹⁶). Strained FET experiments also showed the mobility origin for the change in conductance (see Supplementary Information for detailed discussions).

For p-type bulk Si, _111  44 and _110  44/2, where ₄₄ is the shear coefficient. ₄₄ originates from the change in mobility through carrier transfers and effective mass changes when the band structures of Si are modified by strains¹⁹. The mobility origin for ₁₁₁ and ₁₁₀ in Si nanowires suggests that the enhanced piezoresistance effect will be based on modifications on the band structures. The reduced dimensions and increased surface-to-volume ratio should further contribute to the enhancement.

We note that the slightly enhanced piezoresistance effect has been previously reported in Si beams defined by electron-beam lithography²⁰. Some systematic studies on inversion layers of Si metal-oxide-semiconductor devices^{21, 22, 23} have also been carried out. Several anomalous effects, such as sign reversing from bulk to inversion layers (p-type) for ₁₁ and ₁₂, were observed and attributed to the quantization of carriers in the inversion layers. In the case of the nanowires reported here, the quantum confinement simply due to size reduction does not seem evident, given that the diameters of the nanowires are larger than 50 nm. However, the surface effect may contribute significantly here²⁴. This surface effect was tested by a series of surface modifications on the suspended nanowires. The as-grown nanowires generally have 1-nm-thick oxide layers on their surfaces (Fig. 1d). We used HF solution to make the surfaces hydrogen-terminated and used HNO₃ solution to recreate the oxide layers. The conductance of a nanowire was observed to decrease after the treatment with HF or during the immersion in buffered HF; it was brought back by the oxidation in HNO₃ (Fig. 4). The piezoresistance coefficient, however, showed the opposite trend compared with the conductance; that is, it increased after HF treatments and decreased after HNO₃ treatments. These results indicate the importance of surface states in the enhanced piezoresistance effect. Generally, a built-in potential can be readily created near Si surfaces due to Fermi-level pinning at the surface states^{25, 26}, which would mediate the carrier concentrations and induce quantization in the space charge layers²⁷. Different surface states have different energy levels and density of states, which would result in different built-in potentials. So, different carrier concentrations and quantization in the space charge layers are expected for different types of surface states. This influence of carrier concentrations on the piezoresistance coefficients has been experimentally demonstrated in the trend shown in Fig. 2d. The possible effect of quantization needs to be simulated in further theoretical work.

Figure 4: Effects of surface states on the piezoresistance coefficient.

The piezoresistance coefficient varies with surface states but remains large. It shows an opposite trend with respect to the conductance during surface treatments. The dotted lines are used as guidelines. a and b correspond to two different nanowires. The diameters of the nanowires are about 90 nm.

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We have shown that p-type Si nanowires exhibit unusually large longitudinal piezoresistance coefficients. Systematic theoretical calculations are required to reveal the underlying mechanisms for the observations. The enhanced piezoresistance effect could find applications in Si nanotechnology, flexible electronics²⁸, as well as in nanoelectromechanical systems. In particular, intrinsic strains may exist in many nanoscale materials²⁹, and strain sensitivity could be a basic issue affecting the performance of these nanostructure-based electronics.

Acknowledgements

We thank A. San Paulo and Rong Fan for technical assistance, and R. Maboudian and R. T. Howe for helpful discussions. This work was supported by the U.S. National Science Foundation and MARCO MSD Center. We thank the National Center for Electron Microscopy, Lawrence Berkeley National Laboratory, Berkeley, for the use of their facilities.

Competing interests statement:

The authors declare no competing financial interests.

Received 23 June 2006; Accepted 30 August 2006; Published online 4 October 2006.

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1. Department of Chemistry, University of California, Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

Correspondence to: Peidong Yang¹ e-mail: p_yang@berkeley.edu

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