Mathematical Modeling of Incomplete Ionization in Radial p-Si/n-GaAs Heterojunctions: Temperature and Doping Effects
摘要
This study investigates the electrophysical behavior of a radial heterojunction (RHJ) based on p-Si/n-GaAs over a wide temperature range (50 K–500 K) and dopant concentrations from 1 × 1014 to 1 × 1016 cm–3. Two modeling scenarios are compared: (A) ionization energy is assumed constant, and (B) ionization energy is treated as temperature dependent. A novel mathematical framework is developed to account for the activation energy’s dependence on both temperature and doping, with explicit incorporation of bandgap narrowing (BGN) effects in both Si and GaAs. The ionization probability P(n,p,T) and space charge density ρ(n,p,T) are evaluated above 300 K, where both scenarios yield P(T) > 98%. At 100 K, donor ionization in n-GaAs reaches 88% (A) and 93% (B), while acceptor ionization in p-Si achieves 22% (A) and 41% (B). The resulting space charge densities at 100 K differ by approximately 6% (n-GaAs donors) and 36% (p-Si acceptors) between the two cases. In addition, the thermal de Broglie wavelength is computed for each carrier type. For electrons: GaAs 30.43 nm (100 K) → 13.61 nm (300 K) → 8.91 nm (500 K); Si 18.64 nm → 9.62 nm → 6.80 nm. For holes: GaAs 15.61 nm → 6.98 nm → 4.57 nm; Si 13.35 nm → 6.80 nm → 4.77 nm. For free electrons: 7.45 nm → 4.30 nm → 3.33 nm. Across the examined temperature span, intrinsic bandgaps shrink by ~80 meV, with heavy doping introducing up to 0.27 eV of additional narrowing. These findings offer detailed quantitative insights into ionization dynamics, electro-neutrality breakdown, BGN effects, and quantum-scale transport behavior providing a rigorous foundation for the design and optimization of p-Si/n-GaAs RHJ devices under diverse thermal and doping conditions.