The authors extend the well accepted two-impurity-level model by including the time-dependent balance equation of the mean electron energy to illustrate the current instability for an n-GaAs semiconductor device with planar-type contacts when an ac bias Eacsin(2πfdt) is added to the applied dc bias E0. To avoid any complications arising from photo-excitation, the authors consider the device in the dark condition. The authors inspect the instability patterns either by keeping the magnitude of dc bias and the frequency of ac current fixed but varying the amplitude of ac bias or by fixing the amplitude and the frequency of ac bias but changing the dc bias. The results of numerical simulations are demonstrated in detail and the system’s bifurcating to chaos via several period-doubling routes can be clearly seen in both cases. The bifurcation maps described as a function of the ac drive amplitude Eac or the dc electric field across the sample Edc preserve the main features of the experimental observations by Aoki (1992 Semicond. Sci. Technol. 7 B474) and Aoki and Yamamoto (1989 Appl. Phys. A 48 111).