Influences of cooling rate on gas sensitive tin oxide thin films and a model of gradient distributed oxygen vacancies in SnO2 crystallites

SnO2 thin films are prepared by sol–gel spin-coating technique and different cooling rates are employed in annealing process. The influences of cooling rate and re-annealing on gas sensing characteristics of thin films are investigated, concluding slow cooling rate benefits gas sensing characteristics. The variation of oxygen vacancies density is found to be responsible for the conclusions. Thus, a model of oxygen vacancy distribution is proposed based on the formation and dynamics of vacancies. The diffusion equation is established on the basis of diffusion and exclusion of vacancies in cooling process and the steady state solution reveals a gradient distribution of oxygen vacancies, which exhibits a trend that vacancies accumulate near the surface. Combining the solution of distribution equation and Schottky model, the quantitative expressions of film resistance (R/R0) and response (S) are formulated. The validity and limitation of the model are also discussed.