Internal friction in semiconductors arises from various microstructural mechanisms that dissipate mechanical energy under cyclic stress. These mechanisms include dislocation motion, point-defect relaxation, and grain-boundary sliding, each contributing uniquely to the material's mechanical response. Understanding these processes is critical for optimizing semiconductor performance in applications requiring mechanical stability, such as MEMS, power electronics, and flexible devices.
Dislocation damping is a dominant source of internal friction in crystalline semiconductors. Dislocations are line defects that move under applied stress, leading to energy dissipation through phonon scattering and interactions with other defects. The Granato-Lücke model describes this behavior, where dislocation segments pinned by point defects bow under stress and break free at critical strains, causing hysteresis. The damping coefficient due to dislocations depends on their density, mobility, and interaction with impurities. For example, in silicon, dislocation densities above 10^4 cm^-2 significantly increase internal friction, with activation energies for unpinning ranging from 0.1 to 1.0 eV depending on the defect type.
Point defects, such as vacancies, interstitials, and impurity atoms, contribute to internal friction through stress-induced reorientation or diffusion. The Snoek effect is a well-known mechanism in which interstitial atoms jump between equivalent lattice sites under cyclic loading, relaxing the strain field. In diamond cubic semiconductors like silicon, oxygen interstitials exhibit Snoek-type relaxation peaks at specific temperatures and frequencies. For instance, oxygen in silicon produces a relaxation peak near 300°C at 1 Hz, with an activation energy of approximately 2.5 eV. Similarly, carbon-vacancy complexes in silicon carbide show relaxation peaks around 500°C, influencing the material's mechanical loss spectrum.
Grain boundaries in polycrystalline semiconductors introduce additional friction mechanisms. These interfaces act as barriers to dislocation motion but also slide or rotate under stress, dissipating energy through viscous flow or localized atomic rearrangements. The Zener model describes grain-boundary sliding as a thermally activated process, with relaxation strength proportional to the boundary area and inversely proportional to grain size. In nanocrystalline materials, such as ultrafine-grained germanium, grain-boundary sliding dominates internal friction at temperatures above half the melting point, with activation energies close to those of grain-boundary diffusion.
Measurement techniques for internal friction must isolate these mechanisms while minimizing extrinsic effects. Resonant ultrasound spectroscopy (RUS) is a powerful method for probing mechanical losses in semiconductors. RUS measures the decay of free vibrations in a sample at resonant frequencies, providing data on the damping coefficient (Q^-1) and elastic moduli. The technique operates over a wide frequency range (kHz to MHz) and can resolve distinct relaxation peaks associated with different defects. For example, RUS studies on gallium arsenide have identified dislocation-related damping peaks near 200 K, while point-defect relaxations appear at higher temperatures.
Other complementary techniques include dynamic mechanical analysis (DMA) and torsion pendulum methods. DMA applies oscillatory stress at controlled frequencies and temperatures, mapping the viscoelastic response. In cadmium telluride, DMA reveals grain-boundary sliding peaks above 400°C, correlating with RUS data. Torsion pendulums offer high sensitivity at low frequencies (0.01–10 Hz), useful for studying slow relaxation processes like impurity drag on dislocations.
The interplay between these mechanisms complicates the interpretation of internal friction spectra. For instance, in heavily doped silicon, dislocation damping may overlap with point-defect relaxations, requiring deconvolution of the loss spectrum. Analytical models, such as the Debye relaxation function, help separate contributions by fitting peaks to Arrhenius relations. Empirical rules, like the Barton-Dominquez-Nava relation, link relaxation strength to defect concentration, aiding quantitative analysis.
Practical implications arise from controlling internal friction in semiconductor devices. In MEMS resonators, excessive damping reduces quality factors, degrading performance. Engineering solutions include annealing to reduce dislocation densities, passivating grain boundaries with hydrogen, or optimizing doping levels to minimize point-defect mobility. For power electronics, low internal friction materials like single-crystal silicon carbide are preferred to avoid mechanical fatigue under thermal cycling.
Future research directions include exploring defect dynamics in emerging materials, such as 2D semiconductors and hybrid perovskites, where confined geometries alter traditional friction mechanisms. Advanced characterization tools, like in situ TEM with mechanical loading, could provide atomic-scale insights into dislocation-defect interactions. Multiscale modeling combining density functional theory with dislocation dynamics simulations will further refine predictive capabilities.
In summary, internal friction in semiconductors is governed by dislocation motion, point-defect relaxations, and grain-boundary effects, each with distinct thermal and frequency dependencies. Accurate measurement and analysis of these mechanisms enable tailored material design for applications demanding precise mechanical control. Techniques like RUS, DMA, and torsion pendulums provide critical data, while theoretical models guide the interpretation of complex loss spectra. Continued advances in characterization and modeling will deepen understanding of these phenomena, supporting the development of next-generation semiconductor technologies.