Enhancing chaotic behavior at room temperature in GaAs/(Al,Ga)As superlattices

Previous theoretical and experimental work has put forward 50-period semiconductor superlattices as fast, true random number generators at room temperature. Their randomness stems from feedback between nonlinear electronic dynamics and stochastic processes that are intrinsic to quantum transitions. This paper theoretically demonstrates that shorter superlattices with higher potential barriers contain fully chaotic dynamics over several intervals of the applied bias voltage compared to the 50-period device which presented a much weaker chaotic behavior. The chaos arises from deterministic dynamics, hence it persists even in the absence of additional stochastic processes. Moreover, the frequency of the chaotic current oscillations is higher for shorter superlattices. These features should allow for faster and more robust generation of true random numbers.

Figure 1

Simplified image of a semiconductor superlattice. An external voltage is applied between the contacts at the top and bottom of the device, which consists of $N$ periods of GaAs/${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$. The 7-nm GaAs wells are divided into three zones to prevent doping diffusion.

Figure 2

Power spectrum and bifurcation diagram for a ten-period GaAs/${\mathrm{Al}}_{0.45}{\mathrm{Ga}}_{0.55}\mathrm{As}$ SSL, in a voltage region where chaotic behavior is present. Top row: The power spectrum of $J\left(t\right)$ plotted against the bias voltage. Bottom row: The bifurcation diagram, plotting the Poincaré map against the bias voltage.

Figure 3

Power spectrum vs voltage and bifurcation diagrams for a ten-period GaAs/${\mathrm{Al}}_{0.7}{\mathrm{Ga}}_{0.3}\mathrm{As}$ SSL and different voltage regions. Top row: Power spectrum of $J\left(t\right)$ vs voltage. Bottom row: Bifurcation diagram of the Poincaré map vs voltage. The Hopf bifurcation from the steady state is shown in the first column. A period-doubling “bubble” is shown in the second column. A period-doubling cascade is shown in the third column.

Figure 4

Representative phase portraits for the ten-period GaAs/${\mathrm{Al}}_{0.7}{\mathrm{Ga}}_{0.3}\mathrm{As}$ SSL. The first column shows the average current $J$ plotted against time $t$. The second column shows the phase portrait $F_6\left(t\right)$ plotted against $F_4\left(t\right)$. The third column shows the Poincaré map $\mathcal{P}{\dot{F}}_6\left(t^{*}\right)$ plotted against $\mathcal{P}{F}_6\left(t^{*}\right)$. The last column shows the power spectrum of $J\left(t\right)$. A periodic oscillation is shown in the first row. The period-doubling cascade to a chaotic attractor is shown in the bottom four rows.