Semiconductor Quantized Voltage Source

We realize and investigate an all-semiconductor quantized voltage source which generates quantized output voltages $V_{\mathrm{out}}=f(h/e)$ linked only to two fundamental constants, the electron’s charge $e$ and Planck’s constant $h$, and to an applied excitation frequency $f$. The device is based on an integrated quantized circuit of a single-electron pump operated at pumping frequency $f$ and a quantum Hall device monolithically integrated in series. Robust output voltages up to several $\mu \mathrm{V}$ are generated, which are expected to be scalable by orders of magnitude using present technology. The device might open a new route towards the closure of the quantum metrology triangle.

Figure 1

(a) Device scheme. Light inner part (gray): semiconductor 2DEG; raised outer parts (orange): ohmic contacts; gates marked $G1–G3$ (yellow). (b) Scanning electron microscope image of a pump. (c) Sketches of pumping operation (i)–(iii). (d) Orange circles: pumped current $I$ vs $V_2$, $f=675\mathrm{MHz}$. $V_1=-0.325\mathrm{V}$, $P_{\mathrm{ac}}=-16\mathrm{dBm}$, $B=4.2\mathrm{T}$, $T=350\mathrm{mK}$. Black line: fit to decay cascade model. (e) $R_{xy}$ (upper orange line) and $R_{xx}$ (lower black line) of Hall bar vs $B$ for $I=1\mu \mathrm{A}$, $T=350\mathrm{mK}$.

Figure 2

Quantized voltage operation. (a) $V_{\mathrm{out}}$ vs $V_2$. (b) Voltage plateau as a function of $V_1$ and $V_2$. Parameters in (a),(b): $\nu =1$, $f=675\mathrm{MHz}$. Data are taken in different cooldown cycles. (c),(d) $V_{\mathrm{out}}$ (symbols) vs $B$ within QHE plateaus at $\nu =1$ (c) and 2 (d). Device $A$. $f=320\mathrm{MHz}$, $P_{\mathrm{ac}}=-6\mathrm{dBm}$. Colors mark different field sweep directions. Solid black lines: $R_{xx}$ in the plateau region. Inset: $V_{\mathrm{out}}$ vs $P_{\mathrm{ac}}$. $f=1.1\mathrm{GHz}$, $\nu =1$, $n=1$ (black squares), $n=2$ (red circles). Data in (a), (b), and the inset are taken on device $B$.

Figure 3

Frequency dependence of $V_{\mathrm{out}}$. Data of various cooldowns and parameters ($V_1$, $V_2$, $P_{\mathrm{ac}}$) of devices $A$ and $B$. Data (symbols) with different slopes correspond to $n=1$, $\nu =1$ (black stars), $n=2$, $\nu =1$ (red triangles), and $n=1$, $\nu =2$ (blue diamonds). Dashed lines are theoretical values. Uncertainty is smaller than symbol size.