Temperature dependent energy gap shifts of single color center in diamond based on modified Varshni equation

Although the diamond has the similar structure (diamond cubic) and symmetry (O-h) as many other conventional semiconductor materials, the extraordinary large Debye temperature and small lattice expansion coefficient make the temperature dependence of energy gaps in diamond to be totally different from those in other semiconductors. Here we propose a modified Varshni formula to describe the temperature dependent zero field splitting and zero phonon line of the nitrogen vacancy center in diamond. The shift of energy gaps shows a T-4 scaling at low temperature and a T-2 scaling at high temperature. The crossover between these two regimes is determined by two positive parameters in the modified formula. This empirical formula can give an excellent prediction of the temperature dependent energy gaps up to 700 K. We experimentally verify this temperature dependent behavior with single negatively charged nitrogen vacancy centers in diamond. These observations demonstrate the leading role of electron-acoustic phonon interaction in the temperature dependent shift of energy gaps in diamond. This empirical equation can benefit the diamond-based applications such as quantum sensing and computing. (C) 2017 Elsevier B.V. All rights reserved.