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The oxygen vacancies (VO) play an essential role in the gas-sensing mechanism of semiconductor devices. A diffusion equation is established to describe the VO behaviors during a cooling process based on the model of gradient-distributed oxygen vacancies. Numerical solutions of the diffusion equation are found to illustrate the VO distribution in grains. The gradient of VO distribution is of negative dependence on the cooling rate, which also influences the average VO density in the depletion layer. The migration of oxygen vacancies in cooling process could be interrupted by quenching and it is restarted by the re-annealing process. The VO distributing process is illustrated by three stages from initial uniform distribution to final gradient profile via a transient stage. The influence of VO distribution on gas-sensing characteristics of semiconductor grains is discussed. Potential opportunities are found to control the gas sensor characteristics by a designed annealing process.

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Numerical Analysis of Oxygen Vacancy Distribution in Semiconductor Gas Sensors in the Cooling Process Based on the Model of Gradient-Distributed Oxygen Vacancies