This paper studies the asymptotic behaviour of solutions to the classical semiconductor equations due to Shockley. We will construct not only global solutions but also exponential attractors for the dynamical system determined from the Cauchy problem. Exponential attractors — such a notion was introduced by Eden, Foias, Nicolaenko and Temam — are positively invariant sets which contain the global attractor, have finite fractal dimensions and attract every trajectory in an exponential rate.