Temperature effect on surface roughening of thin films

The effect of the deposition temperature on the surface roughness and the growth exponent of thin films in the early growth time regime has been studied using a linear continuum model. Surface diffusion and three commonly observed roughening mechanisms, namely, shot noise, the Ehrlich–Schwobel (ES) effect, and the stress-induced instability, are step-by-step incorporated into the model to analyze the temperature effect in different cases. It has been revealed that when the thermal activated surface diffusion is operative, the surface roughness of the films without the stress effect will decrease with deposition temperature. In addition, a rougher film surface caused by the ES effect can also be observed at low temperatures. If stress exists due to a lattice mismatch at the film/substrate interface, however, high deposition temperatures may result in an unstable growth with the roughness increasing with temperature. Our analyses have also found that the growth exponent is strongly temperature dependent, and the film growth may fall into three or four temperature regions depending on whether the stress effect is present or not: (1) low-temperature region with a fixed growth exponent of 0.5 or slightly larger than 0.5 due to the ES effect; (2) a middle crossover temperature region with the growth exponent decreasing with temperature from 0.5 (or slightly larger than 0.5) to 0.25; (3) high-temperature region characterizing by noisy Mullins diffusion equation with a constant growth exponent of 0.25; and (4) if stress exists during film growth, at the high-temperature region where the stress-induced morphology instability begins to operate the growth exponent will be larger than 0.25 and increase with temperature.