Plasma etching is a critical tool in the fabrication of Si/SiGe heterostructure quantum devices, but it also presents challenges, including damage to etched feature sidewalls that affects device performance. Chemical and structural changes in device feature sidewalls associated with plasma-surface interactions are considered damage, as they affect band structure and electrical conduction in the active region of the device. Here the authors report the results of experiments designed to better understand the mechanisms of plasma-induced sidewall damage in modulation-doped Si/SiGe heterostructures containing a two-dimensional electron gas. Damage to straight wires fabricated in the heterostructure using plasma etching was characterized both by measuring the width of the nonconductive "sidewall depletion" region at the device sidewall and by measuring the noise level factor gamma(H)/N determined from spectra of the low frequency noise. Observed increases in sidewall depletion width with increasing etch depth are tentatively attributed to the increase in total number of sidewall defects with increased plasma exposure time. Excess negative charge trapped on the feature sidewall could be another contributing factor. Defects at the bottom of etched features appear to contribute minimally. The noise level shows a minimum at an ion bombardment energy of similar to 100 eV, while the sidewall depletion width is independent of bias voltage, within experimental uncertainty. A proposed explanation of the noise trend involves two competing effects as ion energy increases: the increase in damage caused by each bombarding ion and the reduction in total number of incident ions due to shorter etch times.