Incomplete Ionization Effects in C–V Characteristics of Radial p–n and p-i-n Junction Structures
Abstract
This work presents a comprehensive numerical investigation of incomplete dopant ionization effects on the capacitance–voltage (C‑V) response of radial p–n and p–i–n junctions fabricated from silicon (Si) and gallium arsenide (GaAs). A self-consistent finite element method (FEM) framework was developed to solve Poisson’s equation while explicitly incorporating temperature-dependent dopant ionization statistics. Simulations were performed for doping concentrations of 2×10¹⁵ cm⁻³ and 2×10¹⁶ cm⁻³ over a wide temperature range of 100–300 K. The results demonstrate a monotonic increase in junction capacitance with both dopant density and temperature, with capacitance variations exceeding 35–60% across the studied temperature interval, depending on material system and geometry. At 100–150 K, incomplete ionization reduces the effective carrier concentration by up to 48% in Si and 41% in GaAs at 2×10¹⁶ cm⁻³, leading to pronounced deviations in the C–V characteristics compared with conventional full-ionization assumptions. In contrast, at 300 K, the ionization efficiency exceeds 97%, rendering incomplete ionization effects negligible. Geometrical dependencies were evaluated for core radii of R = 0.5, 1.0, and 1.5 μm. Furthermore, p–i–n structures with intrinsic layer thicknesses of i = 0.1, 0.3, and 0.5 μm were analyzed at R = 1.5 μm, revealing that increasing the intrinsic region thickness suppresses the impact of incomplete ionization by reducing the space-charge sensitivity to dopant activation, lowering capacitance deviations by more than 30%. Two modeling regimes were systematically compared: (A) full dopant ionization and (B) temperature-dependent incomplete ionization.
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