Anharmonicity in the Vibrational Modes Associated with H-H, N-H, O-H, and C-H bonds
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Anharmonicity in the Vibrational Modes Associated with H-H, N-H, O-H, and C-H bonds Sukit Limpijumnong School of Physics, Institute of Science, Suranaree University of Technology, Nakhon Ratchasima 30000, Thailand.
ABSTRACT The anharmonic contributions to the vibrational frequency of various H-H, N-H, O-H, and C-H bond configurations are investigated using first principles calculations. While harmonic approximation can be accurately used to calculate the local vibrational mode of most microscopic configurations, the configurations involving strong X-H bond are exceptions because of the exceptionally light mass of the H atom. We will explicitly present the magnitude of the anharmonic contributions to the total frequencies associated with X-H bonds in free molecules as well as in semiconductors defects. INTRODUCTION Hydrogen is one of the most abundant and well-known element in universe. In molecular form[1], it can form strong bond with various elements. It plays an important role as defects in semiconductor [2-4] and in semiconductor alloys [5]. It also plays an important role on semiconductor surfaces [6]. In semiconductors, an interstitial H atom and a H2 molecule are widely studied. As an interstitial atom, it has a tendency to form a strong bond with the host atom or impurity. Infrared spectroscopy, which probes the vibration excitation of local vibrational modes, is a widely used technique to detect H [7-9]. The technique can be used to gain information about hydrogen-related microscopic structures of defects in semiconductors. In calculating the vibration frequency, most of the time the harmonic approximation is used[3][1014]. Under harmonic approximations, the anharmonic part of the vibration is ignored. In a system composed of only heavy atoms, the anharmonic part of the vibration is indeed very small. Even for rather light molecules such as O2 or NO molecules, the anharmonicity of the stretch vibration is reasonably small. For examples, including anharmonic corrections for O2 or NO stretch vibration would result in the reduction of the vibrational frequency by only about 20 cm−1
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out of the total frequency of ~2000 cm−1. However, for systems containing H atom, which is exceptionally light, the anharmonicity of the vibration is sizable. Applying anharmonic corrections to a calculated vibration associated with an X-H bond (in this study X ≡ H, N, O, or C), results in a reduction the total frequency by 150-400 cm−1, or about 10% of the total frequency. Our calculated anharmonic part of the vibration frequency for various X-H bonds in both free molecules form and in defects in semiconductor form are shown in Fig. 1. The plot shows that anharmonic contribution to the vibration frequency is inversely proportional to the bond distance and more enhanced in semiconductors. The large anharmonicity in the vibration of X-H bonds has a root from the fundamental quantum properties of the vibration. Under a harmonic approximation, one must assumes small vibration amplitude such that the potentialdisplace
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