Low-frequency charge noise in Si/SiGe quantum dots

Electron spins in silicon have long coherence times and are a promising qubit platform. However, electric field noise in semiconductors poses a challenge for most single- and multiqubit operations in quantum-dot spin qubits. We investigate the dependence of low-frequency charge noise spectra on temperature and aluminum-oxide gate dielectric thickness in Si/SiGe quantum dots with overlapping gates. We find that charge noise increases with aluminum-oxide thickness. We also find strong dot-to-dot variations in the temperature dependence of the noise magnitude and spectrum. These findings suggest that each quantum dot experiences noise caused by a distinct ensemble of two-level systems, each of which has a nonuniform distribution of thermal activation energies. Taken together, our results suggest that charge noise in Si/SiGe quantum dots originates at least in part from a nonuniform distribution of two-level systems near the surface of the semiconductor.

Figure 1

Experimental setup. (a) False color scanning electron microscope image of an overlapping-gate quantum-dot device identical to those measured. Dots are formed under plunger gates (blue) using screening gates (dark gray) and tunneling gates (yellow) to confine the electrons in the underlying two-dimensional electron gas (2DEG). A source drain bias $V_{\text{SD}}$ is applied to the 2DEG to drive a current (dashed white arrow) through the dot. Current is measured with a current preamplifier and a spectrum analyzer (SA). (b) Cross section of the device along the current path. The gate oxide consists of ${\mathrm{Al}}_2{\mathrm{O}}_3$ grown by atomic layer deposition. (c) Differential conductance $\partial I/\partial V_{\text{SD}}$ showing representative Coulomb blockade diamonds.

Figure 2

Noise spectrum measurement. (a) Current noise power spectral density measurement. Charge noise is measured by acquiring current noise spectra with the plunger gate $V_P$ set on both sides of a transport peak where $\left|dI/d{V}_P\right|$ is large, as shown in the inset. Additional spectra are measured with $V_P$ set within the Coulomb blockade region for a baseline measurement of our experimental setup, and with $V_P$ set on top of the peak where $\left|dI/d{V}_P\right|$ is small as a check to ensure that the measurement is sensitive to charge noise. A dashed trendline proportional to $f^{-1}$ is shown. (b) Measured current noise spectrum showing non-power-law behavior (magenta). The green line is a fit of the measured data to a function of the form $\frac{A}{f^{\beta }}+\frac{B}{f^2/f_0^2+1}$, where $A, B, \beta$, and $f_0$ are fit parameters. Dashed lines proportional to $f^0$ and $f^{-2}$ are shown.

Figure 3

Temperature dependence of the charge noise. (a) Plot of the averaged $S_{\epsilon }\left(1\text{Hz}\right)$ vs temperature across three different samples with 0, 15, and 46 nm of gate oxide. Measurements of $S_{\epsilon }(1\text{Hz},T)$ were made on three quantum dots on device 1, two quantum dots on device 2, and one quantum dot on device 3. The inset shows the same data near the base temperature of the dilution refrigerator. The data show a clear trend of increasing noise with gate-oxide thickness, especially at high temperature. Error bars are included on every third point and represent the standard error in the mean. (b) Plot of the spread of $\gamma (\text{1}\text{Hz},T)$ of all measured samples. The colored shadow represents the distribution of $\gamma \left(\text{1}\text{Hz}\right)$ at a given temperature, and is centered about the mean value. The dashed lines indicate one standard deviation above and below the mean.

Figure 4

Measured temperature dependence of the noise magnitude and exponent. (a) $S_{\epsilon }\left(\text{1}\text{Hz}\right)$ vs temperature on the left side of a transport peak for quantum dot L1 on device 1. (b) $S_{\epsilon }\left(\text{1}\text{Hz}\right)$ vs temperature on the left side of a transport peak for dot R1 on device 2. (c) $S_{\epsilon }\left(\text{1}\text{Hz}\right)$ vs temperature on the right side of a transport peak for dot R1 on device 2. (d) Averaged measurements of $\gamma \left(\text{1}\text{Hz}\right)$ vs temperature on the left side of the transport peak for dot L1 on device 1. (e) Averaged measurements of $\gamma \left(\text{1}\text{Hz}\right)$ vs temperature on the left side of the transport peak for dot R1 on device 2. (f) Averaged measurements of $\gamma \left(\text{1}\text{Hz}\right)$ vs temperature on the right side of the transport peak for dot R1 on device 2. The smooth yellow lines are generated by taking a moving average of the data. The black lines in (a), (b), and (c) are the estimates for $S_{\epsilon }(\text{1}\text{Hz},T)$ using Eq. (6) of the Dutta-Horn model and the data in (d), (e), and (f), respectively. Error bars in (d), (e), and (f) represent the standard error associated with averaging the data over temperature ranges of 25 mK. The solid lines in (d), (e), and (f) are estimates for $\gamma (\text{1}\text{Hz},T)$ using Eq. (6) of the Dutta-Horn model and the smoothed yellow lines in (a), (b), and (c), respectively.