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Figure 19. Generalized gas concentration profiles within SnO2 thin film, film having straight channel structure, with increasing function of l(k/DK)1/2 (from 'a' to 'e').

Figure 19. Generalized gas concentration profiles within SnO2 thin film, film having straight channel structure, with increasing function of l(k/DK)1/2 (from 'a' to 'e').

The sensitivity (S) defined by this model is given as

where ns is the density of electrons per unit area that are returned to SnO2 particle surface by the oxidation of gas with the surface-adsorbed oxygen ions (O-) and nB is the electron density per unit volume in the film bulk. The model predicts that the gas sensitivity would increase with decrease of the film thickness. In contrast to this behavior, for the film thickness less than ~ 110 nm, a markedly lower gas sensitivity, which decreased with decreasing film thickness, exists. The amount of porosity in the sol-gel derived nanocrystalline SnO2 thin films has also been reported to decrease drastically below the film thickness of 70-200 nm [8, 88]. Very compact films exhibit low surface areas, and as a result, they offer reduced number of the active sites for the oxidation reactions with reducing gases and would decrease the gas sensitivity with decreasing film thickness below the critical thickness range. The decrease in the gas sensitivity with increase in the film thickness can also be explained based on the following model [88].

Consider a porous film having thickness 2l and represented by a straight channel structure as depicted in Figure 18. Each channel is assumed to be a round pore of radius r and length 2l. The gas molecules diffuse into the pores by Knudsen mechanism from both the sides of the film. The Knudsen diffusion coefficient (DK) under these

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