Nanomechanical Raman Spectroscopy
Investigating In-situ Surface Stress Variation in Materials
- Fig. 1: (a–c) Diagrams of the combined mechanical loading and Raman spectroscopy setup: (a) overview; (b) detailed view; (c) schematic showing the directions of load application and Raman laser focus. (d) SEM image of a silicon cantilever sample.
- Fig. 2: Applied stress, stress calculated from the strain, and stress measured from Raman spectroscopy at (a) room temperature, (b) 50 °C, and (c) 100 °C.
- Fig. 3: (a) The effect of creep on Raman spectroscopy measurement; (b) comparison of near-surface stress and applied stress to the silicon cantilever
- Fig. 4: (a) strain rate of the silicon cantilever as a function of applied stress at 25 °C, 50 °C and 100 °C; (b) comparison with literature values [6-8].
Surface stress has been shown to affect the mechanical properties of materials at or below the microscale. The change in surface stress in a material in response to externally applied stress as a function of temperature has not been explored experimentally. Such measurements have been performed recently for the first time using a new analytical technology: Nanomechanical Raman Spectroscopy.
In-situ nondestructive measurements of the applied compressive stress and the corresponding microscale surface stress were performed using the technology from room temperature to 100 °C. Based on the measured values and observed trends, an exponential Gaussian function is proposed to describe the stress as a function of surface depth. In-situ creep property measurements of silicon micro-cantilevers at temperatures ranging from 25 °C to 100 °C under uniaxial compressive stress were also performed.
With short-wavelength ultraviolet light and tip enhancement technology, the spatial resolution of Raman spectroscopy can be as high as 100 nm. For a laser wavelength of 244 nm, the penetration depth into silicon is about 6 nm. This implies that Raman spectroscopy can be used to measure the depth-sensitive stress distribution in silicon at the nanoscale. First in-situ measurements of the surface stress as a function of applied stress and as a function of temperature have only been recently reported by Tomar and co-workers [1-5], in the case of silicon via development of Nanomechanical Raman Spectroscopy. The surface stress as a function of depth was determined. Microscale creep behavior of silicon cantilevers is investigated from room temperature to 100 °C.
The Nanomechanical Raman Spectroscopy experiments were carried out using an integrated nanomechanical loading Raman spectroscopy platform (Fig. 1(a) and (b)). The mechanical load was applied in the uniaxial direction [Fig. 1(a)] and the Raman spectroscopy apparatus approached the sample from the lateral direction [Fig.
1(b)]. The sample used in this research was an AFM cantilever CT170 (Nanoscience Instruments, Inc., AZ), as shown in Figure 1(d). The size of the cantilever was 225 µm × 40 µm × 6.5 µm. The sample was highly-doped single-crystalline silicon, with the top surface having a  orientation. The laser used for Raman spectroscopy was a 514.5-nm Ar+ laser (Modu-Laser Inc., UT) with a maximum output of 50 mW. The laser was focused and collected using a 40× objective. The Raman signals were sent to a spectrometer (Acton SP2500; Princeton Instruments Inc., NJ).
Surface Stress as a Function of Applied Compressive Stress
The stress inside the silicon cantilever specimens during measurements can be expressed in three different ways: σA, the applied stress (the applied force divided by the cross-sectional area); σS, the stress calculated from the measured strain and the compliance matrix; σR, the stress measured by Raman spectroscopy. The laser spot size in the Raman spectroscopy method used in the present work is on the micrometer length scale. Therefore, the stress obtained from Raman spectroscopy is the localized stress near the surface, which is in the vicinity of 4 µm. A comparison of σS and σR can validate the Raman deformation potentials. The comparison between the global stress (σA, σS) and the localized stress (σR) reveals the difference between the stress near the surface at the microscale and the applied Cauchy stress. All three stress measurements at the different temperatures are shown in Figure 2 as a function of strain.
Relationship between Surface Stress and Applied Stress
As pointed out in reference to Figure 2, the surface stress is invariably lower than the applied stress. Based on this observation, a relationship between the two stresses can be obtained, which can be used to predict the stress at the surface, and to predict the bulk and applied stress as a function of distance from the surface as:
Here, σS is the bulk stress (applied stress); d is the distance to the free surface; d0 is the characteristic depth (constant for a given material and a fitting constant in this work), at which the stress approaches σS α is a constant dependent on the geometry of the material; T is the absolute temperature in Kelvin at which the stress is being predicted; and T0 is the room temperature. At a specific temperature, the stress at the surface is zero (d=0). With increasing distance from the free surface, the stress increases rapidly to σS. The constant d0 is taken as half the cross-section thickness.
Correlation of Surface Stress and Creep Deformation
The Raman shift from a single time interval of 200 s is shown in Figure 3 (a). Considering the strain rate of the silicon cantilever is only 2.5 x 10-7s-1, for the time interval of 200 s, the strain change is 5 x 10-5, or 0.005%, which is at least one order of magnitude lower than the strain level in the Raman spectroscopy measurement of this research. Therefore, in the temperature range of 25 °C to 100 °C, and the stress level of tens to hundreds of MPa, the effect of creep on the Raman spectroscopy measurement is very limited during the exposure time of 200 s. The strain rate of the silicon sample measured in earlier research works was in the range of the 3 x 10-7s-1 to 3 x 10-6s-1, which is comparable to the strain rate observed in this research (Fig. 4).
A new analytical technology, Nanomechanical Raman Spectroscopy, has been developed to measure in-situ surface stress evolution at microscale and nanoscale in materials undergoing deformation as a function of temperature. Results are demonstrated in the case of silicon at microscale. Analyses show correlation between the surface stress and applied stress as a function of deformation at temperatures upto 100 °C.
Authors acknowledge support provided by Purdue Birck Nanotechnology Center. This work was supported by the United States National Science Foundation (US-NSF) Grant No. CMMI1 131121131112 (Program Manager: Dr. Dennis Carter).
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Authors: Yang Zhang, Ming Gan, Devendra Verma, Jonathan Marsh and Vikas Tomar
School of Aeronautics and Astronautics,
Assoc. Prof. Vikas Tomar
West Lafayette, IN 47907, USA