Thermal Expansion Characteristics of Planar and Radial Si/GaAs p–n Heterojunctions

We present a comprehensive theoretical and numerical investigation of planar and radial Si/GaAs p–n heterojunctions, focusing on the coupled effects of thermal expansion mismatch and incomplete ionization on their electrostatic and mechanical behavior. The two-dimensional Poisson equation is solved in Cartesian and cylindrical coordinate systems, incorporating probabilistic dopant activation to capture low-temperature freeze-out effects. At 100 K, incomplete ionization reduces the built-in potential by up to 40% and expands the depletion width by over 50%, with radial junctions showing 15–25% higher potential due to curvature-induced field enhancement. Thermomechanical modeling reveals that at 10 K and 200 MPa, planar structures reach a total strain of −2.8 × 10⁻³ and stress of ≈280 MPa, whereas radial designs sustain −3.9 × 10⁻³ strain but lower stress (≈234 MPa) due to their reduced elastic modulus. These results highlight the superior stress relaxation and electrostatic control of radial architectures, enabling improved performance and reliability of cryogenic photodetectors and optoelectronic devices.