  In this paper, we are interested in the mathematical model of MEMS devices
which is presented by the following equation on $(0,T) \times \Omega:$
\begin{eqnarray*}
  \partial_t u = \Delta u +\displaystyle \frac{\lambda }{ (1-u)^2 \left( 1
+\displaystyle \gamma \int_{\Omega} \frac{1}{1-u} dx \right)^2}, \quad 0 \leq u
<1, \end{eqnarray*} where $\Omega$ is a bounded domain in $\mathbb{R}^n$ and
$\lambda, \gamma > 0$. In this work, we have succeeded to construct a solution
which quenches in finite time T only at one interior point $a \in \Omega$. In
particular, we give a description of the quenching behavior according to the
following final profile $$ 1 - u(x,T) \sim \theta^*\left[
\frac{|x-a|^2}{|\ln|x-a||} \right]^\frac{1}{3} \text{ as } x \to a, \theta^* >
0.$$ The construction relies on some connection between the quenching
phemonenon and the blowup phenomenon. More precisely, we change our problem to
the construction of a blowup solution for a related PDE and describe its
behavior. The proof relies on two main steps: A reduction to a finite
dimensional problem and a topological argument based on Index theory. The
highlight of this work is that we handle the nonlocal integral term in the
above equation. The interpretation of the finite dimensional parameters in
terms of the blowup point and the blowup time allows to derive the stability of
the constructed solution with respect to initial data.
