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We study frequency shifts in a piezoelectric quartz resonator induced by asurface mass layer for sensor applications. The scalar differential equationsfor thickness-shear modes in a quartz plate are used. A first-orderperturbation analysis is performed. The frequency shift is obtained and isexpressed by a perturbation integral. It produces the well-known Sauerbreyequation for mass sensitivity in the special case of a uniform mass layer. Asan application of the perturbation integral, frequency shifts due to anonuniform mass layer are calculated.

Frequency perturbation integral for piezoelectric quartz crystal microbalances based on scalar differential equations