Determination of the Fermi Energy of Diamond using Photoluminescence Spectral Analysis

Yifan Song; Sina Ilkhani; Leah Webb; Derrick Lin; Gem Nakamura; Helen Highland; Stephen B. Cronin; Susumu Takahashi

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arXiv · 2604.25097

Determination of the Fermi Energy of Diamond using Photoluminescence Spectral Analysis

Yifan Song·Sina Ilkhani·Leah Webb·Derrick Lin·Gem Nakamura·Helen Highland·Stephen B. Cronin·Susumu Takahashi

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Abstract

Electronic band structures and the Fermi energy provide essential information for understanding the electronic properties of solids. In semiconductors, the Fermi energy is determined by the donor and acceptor concentrations. For diamond, the relationship between the Fermi energy and the donor-acceptor concentrations is highly nonlinear; therefore, experimental determination of the Fermi energy is important. Here, we report a method to determine the Fermi energy of diamond based on photoluminescence (PL) measurements. The density-functional-theory (DFT) study by Deák et al.~\cite{deak2014formation} showed the relationship between the Fermi energy and the formation energies of nitrogen-vacancy centers in the negatively charged (NV$^-$) and neutrally charged (NV$^0$) charge states. In the present method, we measure the relative populations of the NV$^-$ and NV$^0$ centers from PL spectral analysis and determine the Fermi energy using these populations and the DFT result. Moreover, we show the application of the method by extracting the Fermi energies of several diamond samples and discuss the spin coherence times of their NV centers and their stability against the charge state conversion. The PL-based method is advantageous for determining the Fermi energy with high spatial and fast time resolutions, even in extreme environments, and can be extended to determine various wide bandgap semiconductors.

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Yifan Song, Sina Ilkhani, Leah Webb, Derrick Lin, Gem Nakamura, Helen Highland, Stephen B. Cronin, Susumu Takahashi. 2026-08-09. Determination of the Fermi Energy of Diamond using Photoluminescence Spectral Analysis. https://arxiv.org/abs/2604.25097

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