Recent studies have shown that highly strained InAs/GaAs quantum wells of high crystalline quality can be grown by conventional solid source molecular beam epitaxy. These wells have been optically characterized by photoluminescence and structurally characterized by electron microscopy. We present the first report of the electrical investigation of InAs/GaAs quantum well confined electronic states using capacitance transient spectroscopy and steady state capacitance-voltage profiling techniques. These measurements are combined with high resolution electron microscopy and high-angle annular dark-field (HAADF) imaging to characterize the highly strained ultrathin quantum wells and heterointerfaces. HAADF, in conjunction with nanometer resolution X-ray analysis, gives the compositional distribution of the InAs monolayers. Correlation with photoluminescence is also performed.