As suggested by Equation (10), the effective spring constant is a function of zs and becomes harder than the structural spring of the cantilever when zs < z0/p2. Although the equation was derived by a linearization theory supposing a small vibration amplitude, the effective spring constant is modulated by the displacement of the cantilever according to Equation (10); the hardening effect is caused by the electrostatic force rather than the mechanical nonlinearity referred to as the amplitude-stiffened Duffing spring effect [26].