  We present a linear stability analysis of a planar metal electrode during
steady electrodeposition. We extend the previous work of Sundstrom and Bark by
accounting for the extended space-charge density, which develops at the cathode
once the applied voltage exceeds a few thermal voltages. In accordance with
Chazalviel's conjecture, the extended space-charge region is found to greatly
affect the morphological stability of the electrode. To supplement the
numerical solution of the stability problem, we have derived analytical
expressions valid in limit of low and high voltage, respectively.
