Charge collection efficiency measurements in silicon detectors at low temperature (T<0.5 K) and low applied electric field (E=0.1-100 V/cm) were performed using a variety of high-purity, p-type silicon samples with room-temperature resistivity in the range 2-40 k Ohm cm. Good charge collection under these conditions of low temperature and low electric field is necessary for background suppression, through the simultaneous measurement of phonons and ionization, in a very low event rate dark matter search or neutrino physics experiment. Charge loss due to trapping during drift is present in some samples, but the data suggest that another charge-loss mechanism is also important. We present results which indicate that, for 60 keV energy depositions, a significant fraction of the total charge loss by trapping occurs in the initial electron-hole cloud near the event location which may briefly act as a shielded, field-free region. In addition, measurements of the lateral size, transverse to the applied electric field, of the initial electron-hole cloud indicate large transverse diffusion lengths. At the lowest fields a lateral diameter on the order of 1 mm is found in a detector similar to 5 mm thick. (C) 1996 American Institute of Physics.