Experimental Realization of a Quantum Dot Energy Harvester

We demonstrate experimentally an autonomous nanoscale energy harvester that utilizes the physics of resonant tunneling quantum dots. Gate-defined quantum dots on $\mathrm{GaAs}/\mathrm{AlGaAs}$ high-electron-mobility transistors are placed on either side of a hot-electron reservoir. The discrete energy levels of the quantum dots are tuned to be aligned with low energy electrons on one side and high energy electrons on the other side of the hot reservoir. The quantum dots thus act as energy filters and allow for the conversion of heat from the cavity into electrical power. Our energy harvester, measured at an estimated base temperature of 75 mK in a $\mathrm{H}{\mathrm{e}}^3/\mathrm{H}{\mathrm{e}}^4$ dilution refrigerator, can generate a thermal power of 0.13 fW for a temperature difference across each dot of about 67 mK.

Figure 1

Resonant tunneling energy harvester. (a) Two quantum dots connect two electronic leads (at temperature $T_0=T_L=T_R$) to a hot cavity at $T_C$. A heat current $\dot{Q}$ at frequency $f$ is absorbed by the flowing electrons to generate a heat current $I$ at frequency $2f$. (b) Relative energy diagram of the heat engine. Tuning the resonant level positions filters tunneling transitions with an energy gain $\mathrm{\Delta }E$. (c) False color SEM image of the device with the electrical circuit used for the thermopower measurement. (d) Enlarged false-color-SEM image of the right quantum dot.

Figure 2

(a) The thermal voltage ${\mathrm{V}}_{\mathrm{th}}$, across the device, as a function of left and right plunger gates measured while an ac current, ${\mathrm{I}}_{\mathrm{heat}}=100\mathrm{n}\mathrm{A}$, is applied to the heating channel. The applied ${\mathrm{I}}_{\mathrm{heat}}$ results in an estimated temperature difference of $\mathrm{\Delta }T=T_C-T_L\approx 47\mathrm{m}\mathrm{K}$ across the dots. (b) and (c) Line graphs through (a) at $V_{\mathrm{LD}}=-1.924$ and $V_{\mathrm{RD}}=-0.805\mathrm{V}$, respectively. (d) Estimated power output of the device showing the two expected operational points and a third (highlighted by the box with a mark star $*$) due to external circuit impedance. The power is given by $P=V_{\mathrm{th}}^2/R_{\text{Load}}$, where $R_{\text{Load}}$ is the resistance loading on the circuit. (e) and (f) Conductance peaks of the two dots as a function of the respective gate voltage.

Figure 3

Engine characteristics. The points of black circles, red stars, and blue triangles show results of experimental measurements. Panel (a) depicts the maximum thermal power from the measurements with different loading resistance, while applying ac current 60 (black circles), 80 (red stars), and 100 nA (blue triangles) on the heating channel. Panel (b) shows the thermal power and its relative thermal voltage, which is also the bias voltage between $A-B$ in Fig. 1. Panel (c) depicts the ratio of the estimated efficiency through Eq. (2) with the Carnot efficiency while changing the resistance. The solid lines show the relative theoretical modeling for different heating currents leading to different cavity temperatures, $T_C$. The theoretical efficiency in (c) is computed from Eq. (6), with resonances of ${\mathrm{\Gamma }}_L={\mathrm{\Gamma }}_R=3.5\mu \mathrm{e}\mathrm{V}$ and the energy level difference of $\mathrm{\Delta }E=45\mu \mathrm{e}\mathrm{V}$ of the two dots. Parameter $A_1=0.8$ is related to the quantum dot barriers. The base temperature in the theoretical model is 85 mK.

Figure 4

Theoretical calculation of (a) the thermovoltage and (b) the generated power with parameters of $A_L=A_{\mathrm{R}}=1,{\mathrm{\Gamma }}_L=0.2\mathrm{m}\mathrm{e}\mathrm{V},{\mathrm{\Gamma }}_R=0.1\mathrm{m}\mathrm{e}\mathrm{V}$, ${\alpha }_L=0.026$ and ${\alpha }_{\mathrm{R}}=0.014$, the base temperature of $T_0=85\mathrm{m}\mathrm{K}$ and the cavity temperature of $T_C=170\mathrm{m}\mathrm{K}$. The influence of the external load resistance is taken into account.