Microscale and nanoscale silicon structures form essential parts of current semiconductor processors, sensors, and MEMS devices. Microscale and nanoscale structures are typically no larger than a millimeter in any dimension, and typically include components no larger than 100 micrometers in size. Microscale and nanoscale structures described herein include MEMS (Micro-Electro-Mechanical Systems), which are typically made up of components between 1 to 100 micrometers in size (i.e. 0.001 to 0.1 mm), and generally range in overall size from 20 micrometers to a millimeter (i.e. 0.02 to 1.0 mm). Devices of this size are frequently characterized by having a relatively large surface area for its mass (sometimes referred to as having a large surface area to volume ratio), resulting in the surface effects of the device (e.g., electrostatic interaction and wetting) frequently dominating over the mass effects (e.g., inertia and thermal conductivity). The functioning of such devices has been found to be highly affected by their operating temperature. Such densely packaged devices generate considerable heat density during operation, which leads to temperature increase of device components. Associated differential thermal expansion leads to thermal stresses and, ultimately, device failure due to thermal stress induced fatigue induced by temperature cycling. The passage of heat in such structures depends upon thermal conductivity. At the microscale, it has been revealed using experiments and simulations that the thermal conductivity of silicon structures changes as a function of mechanical stress. Fundamentally, such analyses have shed new insights regarding the effect of atomic vibrations (thermal properties) on atomic displacements (stress/strain). Results suggest that the influence of stress related thermal property change can lead to a reduction in the passage of heat out of devices and, ultimately, accelerated device failure. Analyses so far have measured thermal properties at a fixed constant applied stress. However, analyses so far have not measured the effect of thermal property change while stress is being applied simultaneously in situ, and, vice versa. Such measurements can reveal new insights regarding the mechanism of thermal stress development as a function of temperature and the corresponding changes in thermal properties. It is useful to be able to measure thermal and mechanical properties simultaneously. Various embodiments of the present disclosure include to simultaneously measuring thermal shift and mechanical shift components in a microscale silicon cantilever structure using Raman spectroscopy.
There are numerous experimental methods available to measure stress distribution inside silicon micro-structures, such as X-ray diffraction (XRD) and cross-sectional transmission electron microscopy (XTEM). These methods have been used to investigate stress distributions in silicon devices. In silicon, the mechanical stress or strain affects Raman shift by changing the frequency of Raman modes. Compared with other available methods for thermal conductivity measurement, Raman spectroscopy is a non-destructive technique, requires minimal sample preparation, and has spatial resolution of less than 1 μm. This method is also suitable for the measurement of temperature distribution and thermal conductivity of silicon structures.
In Raman spectroscopy measurements, a focused laser spot on the sample surface creates localized temperature increase, which can be detected by the Raman spectroscopy system by knowing the temperature dependence of the Raman peak position. Using the corresponding heat transfer models, the Raman spectra can be related to the thermal conductivity. This approach is called Raman thermometry. This method can be applied to thin films deposited onto a thick substrate, with the thickness of the film at least one magnitude higher than the laser spot size. Besides being used for thin films with substrates, the micro-Raman method has also been used for suspended nanowires, suspended membranes, or membranes with support.
As discussed above, the Raman shift of silicon is affected by both applied mechanical stress and temperature. The measured Raman shift is a combination of these two, which creates difficulty for investigation of the relationship between mechanical stress and thermal conductivity. One method that may be used of investigate this relationship is based on Raman Stokes peak position and line width broadening. Using this method, the surface temperature of a polysilicon sample can be measured irrespective of stress state, but with a certain extent of uncertainty. Raman Stokes peak position has better accuracy than Stokes line width when used for temperature measurement.
Microscale silicon structures have been essential parts in micro-electromechanical systems (MEMS). In such applications, the silicon structures are commonly subject to temperatures ranging from 25° C. to 100° C. and stress levels of tens to hundreds of MPa. Various embodiments pertain to measurements of in-situ creep properties of silicon micro-cantilevers in this temperature range under uniaxial compressive stress. Several embodiments have been experimentally verified with a microscale mechanical loading platform and localized heating module. The results reveal that in the stress range of 50 MPa to 150 MPa, the strain rate of the silicon cantilever increases linearly as a function of applied stress. The strain rate also increases as a function of temperature increase. However, the strain rate increase slows down with increase in temperature. The strain rate of the microscale silicon cantilever (0.2˜2.5×10−6 s−1) was comparable to literature values for bulk silicon reported in temperature range 1100° C.˜1300° C. but with one tenth of the applied stress level. However, the sensitivity of the strain rate change with respect to change in temperature or stress was found to be lower, compared with the literature values. It has been earlier revealed by different experiments that the near-surface atoms of the microscale silicon exhibit a relaxed state signified by lower surface stress values than bulk, especially at high temperature. The relaxation of the near-surface atoms also contributes to the creep of the material. As the temperature increases, the relaxation involves atoms deeper into the material surface, which contributes to the higher creep rate at higher temperature. However, the increase rate in the atomic volume with respect to temperature increase reduces, contributing to reduction in the rate of strain rate increase with increase in creep temperature. The present experiments quantify the extent by measuring surface stress values during uniaxial temperature dependent creep.
The thermal conductivity of many solids and liquids is affected by mechanical stress/strain at small length scales of nanometer and micrometer. At the bulk scale, mechanical strain is mediated by line or point defects (such as dislocations and vacancies). The role of diffusion (motion of grain boundaries, interfaces) is negligible unless the temperature is comparable to the melting point. Since dislocations are sparse enough to not influence the mean free path and velocities of electrons and phonons, strain dependence of electrical and thermal transport at bulk scale is insignificant. However, at the nanoscale, the predominant mechanism becomes surface and interface (i.e., diffusion) mediated deformation. For example strain rate at nano- and microscale scales with the inverse cubic (d−3) dependence of length-scale (d) using the following expression:
                              ɛ          .                =                  C          ⁢                                                    D                gb                            ⁢              Gb                                                      k                B                            ⁢              T                                ⁢                                    (                              b                d                            )                        3                    ⁢                                    (                              σ                G                            )                        .                                              (                  3          ⁢                      -                    ⁢          1                )            
Here, C is a constant; Dgb is interface diffusion coefficient; G is the shear modulus; b is the Burger's vector; kB is the Boltzmann's constant; T is the absolute temperature; and a is the applied stress. The inverse cubic (d−3) dependence of length-scale may induce diffusion even at the room temperature at the nanoscale. However diffusion mainly influences electric transport, not the thermal transport. Unlike dislocations (1D defects), surface and interfaces (2D defects) strongly scatter phonons and electrons at all temperatures. Because of the change in defect dimensionality (1D to 2D), the influence of strain on thermal scattering at the nanoscale and microscale can be expected to be 10 times higher than that at the bulk scale. The same conclusion can be drawn for thermal transport in super-lattices or hetero-structures. Even stronger influence is expected because of the exponentially increasing surface to volume fraction at the nanoscale. Also, strain-induced phase transformation (improbable at bulk scale) may drastically change thermal conductivity. Various embodiments described herein use a nanomechanical Raman spectroscopy approach to analyze thermal conductivity of microscale Si cantilevers as a function of temperature.
Controlling the thermal conductivity of Si at the micro/nano-scale opens up opportunities for on-chip heat management and energy conservation of electronic devices. In silicon, phonons are the main energy carrier. Any constraint to the mean free path of the phonons will subsequently affect the thermal conductivity. Some examples of such a constraint are temperature change, grain boundary scattering, mechanical stress, and dopant atom scattering. In the case of bulk silicon, the thermal conductivity increases in the temperature range of 3 K to 30 K, then decreases as a function of temperature. In the temperature range of 300 K to 400 K, which covers the working temperature of most semiconductor devices, the thermal conductivity of bulk silicon is 150 w/m·K at 300 K and 110 w/m·K at 400 K.
Size effect can also significantly affect the thermal conductivity of silicon. At room temperature, it has been found that thermal conductivity of silicon films with the thickness of 1 μm is 10% less than that of bulk silicon; while for the silicon films with the thickness of 100 nm, the thermal conductivity is about half of the value for bulk silicon. The scale of the silicon structures in semiconductor devices is usually in microns or nanometers. This scale constraint brings challenge to the experimental measurement of thermal conductivity of silicon micro-structures. The experimental methods of thermal conductivity measurement at microscale include steady state method, 3ω method, photoacoustic/photothermal method, thermal microscopy method, time-domain thermal reflectance method, and micro-Raman method. Compared with other thermal conductivity measurement methods listed above, the micro-Raman setup discussed herein is open-path with high spatial resolution. It provides the space to the microscale loading module, which applies mechanical stress to the sample.
In Raman spectroscopy measurements, the focused laser spot on the sample surface creates localized temperature increase, which can be detected by the Raman spectroscopy system by knowing the temperature dependence of the Raman peak position. With corresponding heat transfer models, the Raman spectra can be related to the thermal conductivity of the material. This is the principle of the Raman thermometry. This method can be applied to thin films deposited onto a thick substrate, where the thickness of the film should be at least one magnitude higher than the laser spot size. In this way, the effect of the substrate can be neglected.
Drawbacks to prior systems/methods (e.g., prior AFM-Raman testing systems) include load ranges that are too low (e.g., a maximum load range approximately one mN (micro-Newton)) and the absence of uniaxial loading. Drawbacks to other prior systems (e.g., SEM-Raman testing systems) require specific testing conditions (e.g., generating a vacuum, generating an electron field, and destructive sample preparation), and do not provide uniaxial loading. Drawbacks to still other prior systems (e.g., TEM-Raman testing systems) require onerous sample preparation procedures, which frequently involve destructive sample preparation.