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Effect of Exchange-Correlation Functionals on Schottky Barriers at Si/Metal Interfaces

Viviana Dovale-Farelo, Kamal Choudhary

Abstract

Accurate prediction of Schottky barrier heights (SBHs) at metal-semiconductor (M-SC) interfaces is essential for understanding and optimizing charge injection in electronic and optoelectronic devices. However, first-principles calculations of SBHs remain challenging due to the combined difficulties of semiconductor bandgap underestimation, metal Fermi level placement, lattice-mismatch, relative geometric alignment and electrostatic potential alignment across heterogeneous interfaces. In this work, we present a systematic and physically grounded assessment of computational strategies for SBH prediction using Si(111)/Metal (Al, Cu, Ag, Au) interfaces as representative test cases. We evaluate multiple exchange-correlation (XC) treatments, in combination with three distinct bulk reference protocols: relaxed bulk, relaxed bulk with spin-orbit coupling, and strained bulk references consistent with the interface geometry. By benchmarking against experimental data, we demonstrate that structural and electrostatic consistency between interface and bulk reference calculations is the dominant factor governing SBH accuracy. We show that mixed hybrid-semilocal approaches combined with strained reference protocols yield uniformly positive and significantly improved SBHs, achieving near-experimental accuracy while maintaining a favorable balance between computational cost and predictive performance. Our results establish a clear and transferable methodology for reliable Schottky barrier prediction and provide practical guidance for large-scale screening and interface engineering.

Effect of Exchange-Correlation Functionals on Schottky Barriers at Si/Metal Interfaces

Abstract

Accurate prediction of Schottky barrier heights (SBHs) at metal-semiconductor (M-SC) interfaces is essential for understanding and optimizing charge injection in electronic and optoelectronic devices. However, first-principles calculations of SBHs remain challenging due to the combined difficulties of semiconductor bandgap underestimation, metal Fermi level placement, lattice-mismatch, relative geometric alignment and electrostatic potential alignment across heterogeneous interfaces. In this work, we present a systematic and physically grounded assessment of computational strategies for SBH prediction using Si(111)/Metal (Al, Cu, Ag, Au) interfaces as representative test cases. We evaluate multiple exchange-correlation (XC) treatments, in combination with three distinct bulk reference protocols: relaxed bulk, relaxed bulk with spin-orbit coupling, and strained bulk references consistent with the interface geometry. By benchmarking against experimental data, we demonstrate that structural and electrostatic consistency between interface and bulk reference calculations is the dominant factor governing SBH accuracy. We show that mixed hybrid-semilocal approaches combined with strained reference protocols yield uniformly positive and significantly improved SBHs, achieving near-experimental accuracy while maintaining a favorable balance between computational cost and predictive performance. Our results establish a clear and transferable methodology for reliable Schottky barrier prediction and provide practical guidance for large-scale screening and interface engineering.
Paper Structure (13 sections, 7 equations, 5 figures, 1 table)

This paper contains 13 sections, 7 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methods
  3. Workflow Overview
  4. Interface Construction
  5. Schottky Barrier Formalism
  6. DFT Details
  7. Results and Discussion
  8. Identification of Stable Interface Configurations
  9. Schottky Barrier Calculations
  10. Relaxed bulk reference calculations
  11. Including spin-orbit coupling in bulk references
  12. Strained, vacuum-free bulk references
  13. Conclusion

Figures (5)

  • Figure 1: Schematic overview of the workflow. Based on the JARVIS-DFT repository, the VBM and $E_F$ are calculated for semiconductors (SC) and metals (M), respectively. Interfaces are generated from the bulk counterparts using the Zur algorithm and ALIGNN-FF. The workflow aims to automate Schottky barrier height calculations.
  • Figure 2: Schematic representation of the Schottky barrier at a metal-semiconductor junction.
  • Figure 3: (Top) Electrostatic potential of the Si(111)/Al(111) interface. The reference red line represents the average electrostatic potential. Vertical dashed black lines indicate the positions where the Si and Al layers start and end along the z-axis. Cyan and magenta lines denote the repeat unit layers on the left and right sides, respectively. (Bottom) Atomic structure of the Si(111)/Al(111) interface. Si atoms are shown in blue, and Al atoms in gray.
  • Figure 4: Electrostatic potential isosurface of the Si(111)/Al(111) interface rendered in VESTA (Visualization for Electronic and Structural Analysis) at an isovalue of 9.5 eV Vesta.
  • Figure 5: Local density of states (LDOS) of the Al/Si interface computed with different XC functionals: (a) layer-resolved LDOS along the interface normal (z-axis) using PBE; (b-e) LDOS for the central layers of the Al and Si slabs computed with (b) PBE, (c) OPT, (d) SCAN, and (e) mBJ. In all panels, energies are referenced to the Fermi level ($E_F = 0$).