Amorphous semiconductors, such as hydrogenated amorphous silicon (a-Si:H) and chalcogenide glasses, exhibit unique electronic and structural properties due to their disordered atomic arrangements. Unlike crystalline semiconductors, these materials lack long-range order, leading to distinct behaviors in their glass transition temperature (Tg), kinetic fragility, and relaxation dynamics. Understanding these aspects is critical for applications in thin-film electronics, phase-change memory, and photovoltaics.

The glass transition temperature (Tg) marks the transition from a supercooled liquid to a rigid glassy state. For amorphous silicon, Tg is typically around 900 K under standard conditions, though hydrogenation can lower this value due to the introduction of structural flexibility. Chalcogenide glasses, such as Ge-Se or As-Se systems, exhibit lower Tg values, often between 300 K and 600 K, depending on composition. The Tg of Ge2Sb2Te5 (GST), a widely studied phase-change material, lies near 430 K, making it suitable for memory applications where rapid switching between amorphous and crystalline states is required.

Fragility is a measure of how rapidly a material's viscosity changes with temperature near Tg. Strong liquids exhibit Arrhenius-like behavior, while fragile liquids show a non-Arrhenius temperature dependence. Amorphous silicon is considered a strong glass former, with a fragility index (m) close to 20. In contrast, chalcogenide glasses often display higher fragility, with m values ranging from 30 to 80. For example, Se-rich Ge-Se alloys tend to be more fragile than stoichiometric compositions due to the presence of weakly bonded Se chains. The fragility of these materials influences their stability and crystallization kinetics, which is crucial for phase-change memory devices where data retention relies on the amorphous state's persistence.

Relaxation dynamics in amorphous semiconductors are governed by the distribution of atomic bonding environments. The primary (α) relaxation corresponds to large-scale cooperative motion of atoms and is directly linked to the glass transition. Secondary (β) relaxations involve localized atomic rearrangements and can occur below Tg. In a-Si:H, hydrogen diffusion plays a significant role in β relaxations, with activation energies around 1.5 eV. Chalcogenide glasses exhibit pronounced β relaxations due to the flexibility of their covalent networks, with activation energies typically between 0.2 eV and 0.6 eV.

The stretched exponential function, often used to describe relaxation in disordered systems, takes the form:
φ(t) = exp[-(t/τ)^β]
where τ is the relaxation time and β (0 < β ≤ 1) quantifies the deviation from single-exponential decay. For a-Si:H, β values near 0.5 suggest a broad distribution of relaxation times. Chalcogenides like As2Se3 exhibit β values closer to 0.7, indicating a narrower distribution. These differences arise from variations in network connectivity and bond strengths.

Structural relaxation below Tg, known as physical aging, affects the electronic properties of amorphous semiconductors. Prolonged aging can lead to defect state creation in a-Si:H, increasing mid-gap densities and degrading solar cell performance. In chalcogenides, aging induces photostructural changes, altering optical absorption and carrier lifetimes. The kinetics of aging follow a logarithmic time dependence, reflecting the hierarchical nature of energy barriers in disordered systems.

The role of composition in Tg and fragility is evident in ternary chalcogenide systems. Adding Te to Ge-Se glasses reduces Tg due to the weaker Ge-Te bonds compared to Ge-Se. Similarly, introducing Sb into GST increases fragility by disrupting the network rigidity. The following table summarizes key parameters for selected materials:

Material Tg (K) Fragility (m) β-relaxation Ea (eV)
a-Si:H ~900 ~20 1.5
Ge2Sb2Te5 430 60 0.4
As2Se3 460 40 0.5
GeSe2 670 35 0.6

Thermal history also impacts the properties of amorphous semiconductors. Rapid quenching from the melt produces a more disordered structure with higher fictive temperature (Tf), while slow cooling yields a denser, more relaxed network. In a-Si:H, higher Tf correlates with increased defect densities and suboptimal electronic properties. For chalcogenides, quenching rates influence the threshold switching voltage in memory devices, with faster cooling leading to higher thresholds due to greater disorder.

The relationship between viscosity and temperature near Tg is described by the Vogel-Fulcher-Tammann (VFT) equation:
η = η0 exp[B/(T - T0)]
where η0, B, and T0 are material-specific constants. Strong glasses like a-Si:H have large B and T0 values, indicating high resistance to flow. Fragile chalcogenides exhibit smaller B and T0, reflecting their rapid viscosity drop above Tg.

In conclusion, the glass transition behavior of amorphous semiconductors is governed by composition, bonding topology, and thermal history. The interplay between Tg, fragility, and relaxation dynamics determines their stability and functionality in devices. Advances in understanding these properties enable the design of improved materials for optoelectronics, memory technologies, and energy applications. Future research may explore the effects of nanoscale confinement and interfacial interactions on glass transitions in disordered semiconductors.