Self-sustained current oscillations in high-purity n-type GaAs epitaxial layers were investigated for intermittent behavior in the control parameter plane constituted by the constant bias voltage and an external magnetic field. Intermittent windows were observed in a sequence of Hopf bifurcations. Quasiperiodic and frequency-locked oscillations were found to follow an intermittency type-II or type-III route to chaos in the Pomeau-Manneville classification scheme. Additionally, intermittent bursts due to noise were observed at voltages well below the threshold of bifurcation.