The technique and some applications of a graded‐thickness sample deposition method for molecular‐beam epitaxy (MBE) are described. We discuss the use of this method for the growth of GaAs on Si and related materials systems. In this method the substrate is translated during growth relative to a fixed, near‐sample‐plane shutter so that a wedge shaped growth thickness profile is obtained. We have found this method to be especially useful in conjunction with bothexsituandinsituanalytical techniques for probing the continuous evolution of thin film growth. The technique offers several advantages over the traditional method of preparing a series of samples of different thicknesses. We have also found it useful for the direct comparison of the evolution of growth of two different surface preparations. We describe the use of Auger forinsitumeasurement of the composition and structure of the film at various stages of the growth with near monolayer resolution. Rutherford backscattering (RBS) has been used as anexsituprobe of the evolution of the deposited film. In an attempt to understand and control the atomic scale processes during the initiation of growth at the GaAs–Si interface we have used this method to grow graded‐thickness samples with total thickness 3.5–10 nm. Analysis of these films has led us to develop a model for the nucleation and initial stages of growth of GaAs‐on‐Si. We also report on possible device applications of this technique.