  We present measurements of low frequency charge noise and conductance drift
in modulation doped GaAs/AlGaAs heterostructures grown by molecular beam
epitaxy in which the silicon doping density has been varied from $2.4\times
10^{18} cm^{-3}$ (critically doped) to $6.0\times 10^{18} cm^{-3}$ (overdoped).
Quantum point contacts were used to detect charge fluctuations. A clear
reduction of both short time scale telegraphic noise and long time scale
conductance drift with decreased doping density was observed. These
measurements indicate that the {\it neutral} doping region plays a significant
role in charge noise and conductance drift.
