We have studied the electrical characteristics of p-GaAs/n-Si heterojunction diodes grown by molecular-beam epitaxy in an effort to investigate the quality of the heterointerface. Both Ga and As prelayers were used to initiate the growth of GaAs epilayers on Si substrates. Current-voltage and capacitance-voltage measurements were made between 300 and 83 K. Ideality factors for heterojunction diodes were as good as n=2.0, despite the 4.1% lattice mismatch between Si and GaAs. At high temperatures the I-V characteristics were dominated by generation-recombination mechanisms that lead to a temperature-independent logarithmic slope with applied bias. By removing a thin layer from the Si surface, the surface leakage current was reduced by more than an order of magnitude. The measured intercept voltages, as determined by capacitance-voltage measurements, have no strong dependence on the type of prelayer used to initiate the growth of the GaAs epilayer on Si substrates. The maximum spread in measured intercept voltages was about 1 V, the absolute value of which depends upon the condition of the interface.