[Paper Review] Fermi level pinning by defects can explain the large reported carbon 1s binding energy variations in diamond

Michael Walter, Filippo Mangolini+3 more|arXiv (Cornell University)|Feb 8, 2019

Diamond and Carbon-based Materials Research1 references4 citations

TL;DR

This study demonstrates that Fermi level pinning by defects in diamond causes large variations in carbon 1s (C(1s)) binding energy, explaining the long-standing experimental discrepancies in reported values for sp³-bonded carbon. Using density functional theory (DFT) simulations, the authors show that the wide band gap of diamond prevents a well-defined Fermi level reference, leading to strong dependence of C(1s) binding energy on defect and dopant states, with excellent agreement between simulated and experimental data for boron-doped ultrananocrystalline diamond (UNCD).

ABSTRACT

The quantitative evaluation of the carbon hybridization state by X-ray photoelectron spectroscopy (XPS) has been a surface-analysis problem for the last three decades due to the challenges associated with the unambiguous identification of the characteristic binding energy values for sp$^2$ and sp$^3$-bonded carbon. While the sp$^2$ binding energy is well established, there is disagreement for the sp$^3$ value in the literature. Here, we compute the binding energy values for model structures of pure and doped-diamond using density functional theory. The simulation results indicate that the large band-gap of diamond allows defects to pin the Fermi level, which results in large variations of the C(1s) core electron energies for sp$^3$-bonded carbon, in agreement with the broad range of experimental C(1s) binding energy values for sp$^3$ carbon reported in the literature. Fermi level pinning by boron is demonstrated by experimental C(1s) binding energies of highly B-doped ultrananocrystalline diamond that are in good agreement to simulations.

Motivation & Objective

• To resolve the long-standing inconsistency in reported C(1s) binding energy values for sp³-bonded carbon in diamond.
• To investigate how defects and dopants influence the C(1s) core-level binding energy in wide band gap semiconductors.
• To evaluate the validity of using diamond as a reference material in X-ray photoelectron spectroscopy (XPS) due to Fermi level instability.
• To establish a link between experimental C(1s) peak shifts in boron-doped UNCD and defect-induced Fermi level pinning via DFT simulations.
• To demonstrate that the absence of a defined Fermi level in insulating materials like diamond leads to large variations in measured core-level binding energies.

Proposed method

• Density functional theory (DFT) calculations using the GPAW package with the projector augmented wave (PAW) method and PBE exchange-correlation functional.
• Frozen core approximation applied to model C(1s) core holes, enabling accurate binding energy prediction for sp³ and sp² carbon in diamond and graphite.
• Structures of pure and B-doped diamond (C₆₃B) were relaxed until forces on atoms fell below 0.05 eV/Å.
• Simulated C(1s) spectra were convoluted with Gaussian functions (0.82 eV FWHM) to match experimental resolution.
• Experimental XPS measurements on undoped and B-doped ultrananocrystalline diamond (UNCD) were performed using constant-analyzer-energy (CAE) mode with high energy resolution (100 eV pass energy, 0.05 eV step size).
• Spectrometer calibration was performed to ±0.05 eV accuracy using ISO 15472:2001 standards, and data were averaged from at least three independent measurements.

Experimental results

Research questions

• RQ1 Why do experimental C(1s) binding energy values for sp³-bonded carbon in diamond span a wide range (283.25–291.35 eV), despite consistent theoretical expectations?
• RQ2 To what extent do defects and dopants in diamond influence the C(1s) core-level binding energy due to Fermi level pinning?
• RQ3 Can DFT simulations reproduce the experimentally observed C(1s) peak shifts in boron-doped UNCD, particularly the lower binding energy and shoulder on the low-BE side?
• RQ4 Why is diamond an unreliable reference material for XPS when used in insulating or wide band gap systems?
• RQ5 How does the large band gap of diamond prevent a consistent definition of the Fermi level reference, leading to variable C(1s) binding energies?

Key findings

• The C(1s) binding energy for sp³-bonded carbon in diamond is highly sensitive to defects and dopants due to Fermi level pinning, explaining the broad experimental range of 283.25–291.35 eV.
• DFT simulations of B-doped C₆₃B model structures predict a C(1s) binding energy of 284.27 eV, in excellent agreement with experimental measurements of 284.09 ± 0.05 eV for B-doped UNCD.
• The experimental C(1s) spectrum of B-doped UNCD shows a distinct shoulder at lower binding energy, which matches the simulated spectrum and is attributed to defect-induced Fermi level pinning.
• The C(1s) peak for undoped UNCD (284.47 ± 0.05 eV) does not match the pure diamond DFT prediction, confirming the influence of grain boundaries, hydrogen, and sp² carbon defects in real UNCD samples.
• The study demonstrates that Fermi level pinning in wide band gap materials like diamond invalidates the use of diamond as a universal XPS reference due to the absence of a well-defined Fermi level reference.
• The findings extend beyond diamond, indicating that similar C(1s) binding energy variations are expected in other wide band gap materials due to the same fundamental limitation in energy referencing.