[Paper Review] Superconductivity in doped cubic silicon: an ab initio study

Emmanuel Bourgeois, Xavier Blase|arXiv (Cornell University)|Jan 10, 2007

Physics of Superconductivity and Magnetism4 citations

TL;DR

This ab initio study investigates superconductivity in heavily doped cubic silicon, demonstrating that boron-doped c-Si exhibits phonon-mediated superconductivity consistent with BCS theory. The key finding is that aluminum doping could increase the critical temperature (T_C) by an order of magnitude due to favorable electron-phonon coupling and reduced lattice compression effects, as revealed by density functional theory and electron-phonon coupling calculations in a supercell framework.

ABSTRACT

We study within a first-principle approach the band structure, vibrational modes and electron-phonon coupling in boron, aluminum and phosphorus doped silicon in the diamond phase. Our results provide evidences that the recently discovered superconducting transition in boron doped cubic silicon can be explained within a standard phonon-mediated mechanism. The importance of lattice compression and dopant related stretching modes are emphasized. We find that T$_C$ can be increased by one order of magnitude by adopting aluminum doping instead of boron.

Motivation & Objective

• To determine the microscopic origin of superconductivity in boron-doped cubic silicon, recently observed experimentally.
• To investigate whether electron-phonon coupling can explain the observed superconducting transition temperature (T_C) in doped c-Si.
• To compare the electron-phonon coupling strength and predicted T_C across different dopants—boron, aluminum, and phosphorus—within a first-principles framework.
• To assess the impact of lattice compression and localized vibrational modes on T_C, particularly in boron-doped systems.
• To predict the potential for higher T_C in aluminum-doped c-Si compared to boron-doped c-Si, and evaluate the feasibility of such doping.

Proposed method

• Employed density functional theory (DFT) with the PBE exchange-correlation functional and ultrasoft pseudopotentials.
• Used a (2×2×2) supercell with 16 atoms to model 6.25% doping concentration, replacing one Si atom with B, Al, or P.
• Calculated electronic band structures, phonon density of states (ph-DOS), and Eliashberg functions α²F(ω) to analyze electron-phonon coupling.
• Applied a (10×10×10) k-point grid for accurate q-dependent electron-phonon coupling constants λ(q), with tetrahedron integration for convergence.
• Used the McMillan formula and modified relations to estimate T_C, with μ* set between 0.08 and 0.12.
• Performed computational experiments by imposing lattice contraction (2.1%) on Al-doped c-Si to isolate the effect of pressure on λ and T_C.

Experimental results

Research questions

• RQ1 Can a phonon-mediated BCS mechanism explain the superconducting transition in boron-doped cubic silicon?
• RQ2 How does lattice compression due to doping affect the electron-phonon coupling strength and critical temperature T_C?
• RQ3 What is the predicted T_C for aluminum-doped cubic silicon compared to boron-doped c-Si, and what physical factors drive this difference?
• RQ4 How do localized vibrational modes, such as B-Si or Al-Si stretching modes, contribute to electron-phonon coupling?
• RQ5 Why does phosphorus n-doping fail to significantly enhance T_C despite theoretical expectations for multi-valley semiconductors?

Key findings

• The superconducting transition in boron-doped cubic silicon is well explained by a standard phonon-mediated BCS mechanism, with calculated T_C values ranging from 0.06 K to 0.24 K for μ* in 0.08–0.12, consistent with experimental observations (up to 0.34 K).
• Aluminum doping is predicted to increase T_C by approximately one order of magnitude, yielding values between 0.6 K and 2.8 K, due to enhanced electron-phonon coupling and reduced lattice compression effects.
• Lattice compression in B:Si reduces the electron-phonon coupling strength by ~10% and shifts high-energy phonon modes to higher frequencies, decreasing their contribution to λ by ~0.03–0.04.
• The Eliashberg function α²F(ω) shows a significant contribution from modes near 50 cm⁻¹ below the softened optical modes in Al:Si, indicating strong coupling involving Al-Si vibrational modes.
• The 10% reduction in λ under 2.1% lattice contraction in Al:Si is attributed to a 6.5% decrease in the density of states at the Fermi level, highlighting the detrimental effect of compression on T_C.
• Phosphorus n-doping yields a λ value of 0.30, similar to boron-doped c-Si, indicating no significant enhancement in electron-phonon coupling despite strong band splitting and multi-valley effects.