Size effect and comprehensive mathematical model for gas-sensing mechanism of SnO2 thin film gas sensors

Tin oxide (SnO2) is widely used in metal-oxide-semiconductor for gas-sensing materials due to its unique physical and chemical properties. The grain size is one of the major influencing factors that determine the gas-sensing characteristics. In this work, a facile hydrolysis-oxidation-hydrothermal method is used to prepare the size-controllable SnO2 quantum dots (QDs) of 4.7–8.9 nm, and the gas-sensing characteristics of the SnO2 QDs sensors are evaluated by C4H10, H2 and C2H5OH at room temperature. The experimental results show that the resistance has a negative correlation with hydrothermal time, and the maximum response is obtained when the grain radius is comparable to the depletion layer width. A comprehensive model is proposed by considering all gas-sensing procedures of the receptor function, the transducer function and the utility factor. The sensor properties are formulated as functions of grain size, depletion layer width, film thickness, oxygen vacancy density, gas concentration, pore size as well as operating temperature. The present model provides a comprehensive mathematical interpretation of the size effects of SnO2 from partial depletion to volume depletion.