The purpose of the present paper is the investigation of the importance of exchange in the dielectric response of a semiconductor. It is shown that within the framework of the linearized Thomas-Fermi-Dirac theory the spatial dielectric function of a semiconductor can be obtained in a very simple analytical form that differs from the form obtainable from the linearized Thomas-Fermi (TF) theory only by different values of the constants appearing in it. The main conclusion is that introduction of exchange results in a contraction of the TF screening radius beyond which the screening of a positive point charge by the valence electrons is complete.