Introduction to Semiconductor Band Structures
The electronic properties of semiconductors are fundamentally determined by their band structures, which define the permissible energy states for electrons. Crystalline semiconductors, such as silicon (c-Si) and gallium arsenide (GaAs), possess long-range atomic order, resulting in well-defined band structures with distinct valence and conduction bands separated by a sharp bandgap. In contrast, amorphous semiconductors, like hydrogenated amorphous silicon (a-Si:H), lack this long-range order, leading to significant alterations in their electronic band structure.
Crystalline Semiconductor Band Structure
In crystalline materials, the periodic atomic arrangement creates a potential landscape that permits electrons to occupy delocalized states, described by Bloch waves. This periodicity results in:
- Extended states forming continuous energy bands
- A clear separation between the valence band (occupied by electrons) and the conduction band (unoccupied at 0 K)
- A sharp, well-defined bandgap
For example, crystalline silicon has an indirect bandgap of approximately 1.1 eV, while gallium arsenide has a direct bandgap of about 1.4 eV. The absence of disorder enables high carrier mobility, with electron mobility in c-Si exceeding 1000 cm²/V·s and reaching up to 8000 cm²/V·s in GaAs.
Amorphous Semiconductor Band Structure
The lack of translational symmetry in amorphous semiconductors introduces disorder that profoundly modifies the band structure. Key features include:
- Localized states within the bandgap arising from defects and structural variations
- Mobility edges separating extended from localized states
- Tail states extending into the bandgap
The concept of mobility edges, as proposed by Mott and Davis, is central to understanding carrier transport in these materials. In a-Si:H, mobility edges for electrons and holes lie near the conduction and valence bands, respectively. The energy region between them is termed the mobility gap.
Tail States and Defect States
Tail states result from statistical fluctuations in bond lengths and angles, creating an exponential decay of the density of states (DOS) into the bandgap, known as Urbach tails. The Urbach energy, typically ranging from 50 to 100 meV in a-Si:H, quantifies the degree of disorder. These tail states act as traps, reducing carrier mobility and influencing phenomena like stretched-exponential recombination.
Localized states are primarily caused by defects such as dangling bonds, which introduce deep-level traps within the mobility gap. Hydrogen passivation in a-Si:H reduces dangling bond density, but residual defects remain significant. The density of these mid-gap states can range from 10¹⁵ to 10¹⁷ cm⁻³eV⁻¹, acting as recombination centers that limit carrier lifetime and affect device performance.
Comparative Implications
The differences in band structure between crystalline and amorphous semiconductors have direct consequences for electronic and optical properties. Crystalline materials offer high carrier mobility and efficient transport, making them suitable for high-performance electronics. Amorphous semiconductors, while exhibiting lower mobilities, provide advantages in large-area applications and flexibility, with their properties highly dependent on deposition conditions and defect management.