Introductory textbooks in solid state physics usually present the hydrogenic impurity model to calculate the energy of carriers bound to donors or acceptors in semiconductors. This model treats the pure semiconductor as a homogeneous medium and the impurity is represented as a fixed point charge. This approach is only valid for shallow impurities and it also departs from the conventional view in solid state physics, where carriers move in a crystal lattice. As an alternative description of impurities in semiconductors, we present a minimal one-dimensional lattice model within the tight-binding approximation. The lattice model is valid for deep and shallow impurities. In the latter case, the results are in agreement with the predictions of the hydrogenic impurity model. The underlying ideas are simple and knowledge of advanced quantum mechanics is not required. Thus, this alternative model could be suitable for introductory courses in solid state physics and materials science. (Contains 1 figure.)