Transport properties of high-mobility semiconductors are governed by the interplay of charge carrier dynamics and scattering mechanisms. These properties determine how efficiently electrons and holes move through the material under an applied electric field. High-mobility semiconductors, such as gallium arsenide (GaAs) and silicon-germanium (SiGe), exhibit superior performance due to their low effective masses and reduced scattering rates. Understanding these mechanisms is critical for optimizing material performance in advanced electronic and optoelectronic systems.

The mobility of charge carriers in semiconductors is a key parameter that quantifies how easily they move under an electric field. Mobility is inversely proportional to the scattering rate, which arises from interactions with phonons, impurities, defects, and other carriers. In high-purity materials, phonon scattering often dominates at room temperature, while impurity and defect scattering become significant at lower temperatures or in less pure samples. The temperature dependence of mobility provides insights into the dominant scattering mechanisms.

Phonon scattering is intrinsic to all semiconductors and arises from lattice vibrations. It can be categorized into acoustic and optical phonon scattering. Acoustic phonon scattering is typically more significant at lower temperatures, where long-wavelength vibrations dominate. Optical phonon scattering becomes important at higher temperatures due to the increased population of high-energy phonons. In GaAs, for example, the mobility at room temperature is primarily limited by polar optical phonon scattering, which is strong due to the polar nature of the material. The mobility-temperature relationship in GaAs follows a power law, with mobility decreasing as temperature increases due to enhanced phonon interactions.

Impurity scattering occurs when charge carriers interact with ionized or neutral impurities in the material. Ionized impurity scattering is particularly significant at low temperatures, where phonon scattering is reduced. The Coulombic interaction between carriers and ionized impurities leads to a scattering rate proportional to the impurity concentration. In high-purity GaAs, impurity concentrations below 10^14 cm^-3 can result in mobilities exceeding 10,000 cm²/Vs at low temperatures. Neutral impurity scattering, though less impactful, still contributes to the overall scattering rate, particularly in materials with high defect densities.

Defect scattering includes interactions with dislocations, grain boundaries, and point defects. These defects act as localized scattering centers, disrupting the periodic potential of the crystal lattice. In SiGe alloys, for instance, alloy disorder scattering arises due to the random distribution of silicon and germanium atoms, introducing local variations in the potential experienced by carriers. This mechanism is particularly relevant in strained SiGe layers, where the mismatch in lattice constants between silicon and germanium can introduce additional defects. The mobility in SiGe alloys is thus strongly influenced by the germanium fraction and the quality of the epitaxial growth, even though growth techniques are not the focus here.

Material purity plays a crucial role in determining transport properties. High-purity semiconductors exhibit significantly higher mobilities due to reduced impurity and defect scattering. For example, ultra-pure GaAs grown by molecular beam epitaxy can achieve electron mobilities exceeding 200,000 cm²/Vs at low temperatures, where phonon scattering is minimized. In contrast, commercially available GaAs wafers with higher impurity concentrations typically exhibit mobilities an order of magnitude lower. Similarly, in SiGe alloys, increasing the germanium content can enhance mobility due to the reduced effective mass of holes, but this benefit may be offset by increased alloy disorder scattering if the material is not grown under optimal conditions.

The temperature dependence of mobility provides a fingerprint of the dominant scattering mechanisms. At very low temperatures, impurity and defect scattering dominate, leading to a mobility that is relatively temperature-independent. As temperature increases, phonon scattering becomes more significant, and mobility decreases following a T^(-n) relationship, where n depends on the specific phonon mechanism. In GaAs, n is typically around 1.5 to 2 for acoustic phonon scattering and higher for optical phonon scattering. In SiGe alloys, the temperature dependence is more complex due to the interplay of alloy disorder and phonon scattering, but a similar trend is observed.

The effective mass of charge carriers also influences mobility. Materials with lower effective masses, such as GaAs, generally exhibit higher mobilities because carriers accelerate more readily under an electric field. In GaAs, the electron effective mass is approximately 0.067 times the free electron mass, contributing to its high mobility. In SiGe alloys, the hole effective mass decreases with increasing germanium content, leading to improved hole mobility in germanium-rich compositions. However, this benefit must be balanced against the increased scattering from alloy disorder.

High-mobility semiconductors are also sensitive to external perturbations such as strain and electric fields. Strain can modify the band structure, altering the effective mass and scattering rates. In SiGe, compressive strain can enhance hole mobility by reducing the effective mass and suppressing intervalley scattering. Electric fields, particularly at high intensities, can cause carrier heating, leading to non-ohmic behavior and reduced mobility due to increased phonon emission.

The impact of material purity on transport properties cannot be overstated. Even trace amounts of impurities or defects can drastically reduce mobility by introducing additional scattering centers. High-purity materials are therefore essential for achieving the highest mobilities. Advanced purification techniques and careful control of growth conditions are necessary to minimize these extrinsic scattering sources. For instance, in GaAs, residual carbon and silicon impurities must be kept below parts-per-billion levels to achieve ultra-high mobilities.

In summary, the transport properties of high-mobility semiconductors like GaAs and SiGe are governed by a complex interplay of scattering mechanisms, material purity, and temperature. Phonon scattering dominates at high temperatures, while impurity and defect scattering are more significant at low temperatures or in less pure materials. The mobility-temperature relationship provides valuable insights into these mechanisms, and material purity is a critical factor in achieving optimal performance. Understanding these principles is essential for the development of next-generation semiconductor technologies.