A scanning probe microscopy approach for identifying defects in aluminum oxide

TL;DR

This study demonstrates cryogenic electrostatic force microscopy as a chemically specific tool to identify defects in ALD-grown Al$_2$O$_3$ on Si, linking local charging transitions to defect chemistry. By integrating precise tip geometry modeling, COMSOL-based electrostatics, and DFT defect energetics, the authors map charging voltages to defect energies and identify candidate species (e.g., V$_ ext{Al}$-H, C$_ ext{O}$-H, V$_ ext{O}$) for 20 surface-proximal defects. The work introduces robust pipelines for defect identification, combining large-scale maps with high-resolution hysteresis analyses, and demonstrates the necessity of 3D device simulations over 1D capacitor models for thick dielectrics. The results establish EFM as a powerful, spectroscopically selective approach to characterize defect structures in solid-state qubits, informing materials processing and surface preparation to mitigate charge noise.

Abstract

The coherence of quantum dot qubits fabricated in semiconductors is often limited by charge noise from defects in gate dielectrics, which are material- and process-dependent. Characterizing these defects is an important step towards reducing their impact and improving qubit coherence. The identification of individual defects requires atomic-scale spatial resolution, however, and sufficient spectral sensitivity to determine their electronic structure. Electrostatic force microscopy (EFM) provides highly resolved maps of the surface potential of dielectrics, and importantly, is also sensitive to single-electron charging processes that reflect the spectral structure of underlying defects. In this work, we use cryogenic EFM to characterize aluminum oxide grown by atomic layer deposition (ALD) on bulk silicon. These measurements reveal defects close to the surface that exchange electrons with the EFM tip as they transition through different charge states. Detailed electrostatic modeling opens the door to powerful techniques for mapping tip-backgate charging voltages onto defect transition energies, allowing defects such as aluminum vacancies, and carbon, oxygen, or hydrogen impurities to be identified, by comparing to density functional theory (DFT). These results point towards EFM as a powerful tool for exploring defect structures in solid-state qubits.

Figures (44)

• Figure 1: Experimental setup. (A) Schematic of a typical electrostatic force microscope (EFM) experiment: an oscillating tip is raster-scanned in vacuum across a sample comprised of Al$_2$O$_3$ grown atop a silicon substrate with a backgate. Interactions between the tip and charged defects in the oxide cause a change in the tip resonant frequency $\Delta f$ as a function of the tip-backgate bias voltage $V_b$. The color-scale plot shows a spatial map of the measured contact potential (CPD) difference, $V_b=V_\text{CPD}$, that maximizes $\Delta f$ at a given location. Variations in $V_\text{CPD}$ are caused by charged defects near the sample surface. (B) Electrostatic simulations are used to compute the electrostatic potential at the location of the defect $\phi(V_{b},{\mathbf r}_d)$. (Here, $V_{b}$ = 1 V.) The inset shows a linecut directly below the tip, corresponding to the dashed line in the main figure. Note that the oxide layer is not labeled here, because its much smaller thickness (60 nm) is not visible on the larger scale of the image. (C) Schematic variations of the resonant frequency as a function of bias (an $f$-$V$ curve). Jumps indicate discrete charging events, as electrons tunnel between the tip and the defect. (Defect charge states are indicated.) (D) A corresponding energy diagram, with matching colors, as a function of the chemical potential of the defect. The lowest-energy states are indicated by thick lines. (E) A corresponding charge-occupancy-chemical-potential diagram, which we use to identify the chemical species of the defect by comparing to density functional theory (DFT) calculations.
• Figure 2: EFM results. Note that all scale bars in this figure are 5 nm. (A) Topography map of the oxide-on-silicon sample studied in this work, obtained via nc-AFM. (B) $f$-$V$ curves are obtained for every pixel in a CPD map; several examples are shown here. Special features include maxima, corresponding to $V_b=V_\text{CPD,a(b)}$ (left-hand side), and charging transitions, corresponding to $V_b=V_\text{transition}$ (right-hand side), with charging states identified by different colored regions (see SI Appendix, section S11). Here, a, b, 2, and 8 refer to distinct pixels, whose locations are shown in the maps of panels C-E. In particular, pixels 2 and 8 coincide with the centers of Defects 2 and 8, as identified in F. Following procedures described in the main text, only one charging transition was considered for Defects 2 and 8. (C) A $V_\text{CPD}$ map describing the same scan region as A. (D,E) Maps of $V_\text{transition}$ for the same scan region, within the voltage range indicated by color bars. (White pixels indicate that no transitions are observed in this range.) (F) Colored regions indicate the pixels assigned to different defects, as determined by the clustering algorithm, for 15 different defects. (Five other defects were identified using high-resolution scans.) The color bar indicates our best guesses for defect species, according to the "single-defect analysis" described below, based on comparison with DFT. Hatched regions indicate overlapping defects, whose charging transitions can still be uniquely identified. Defects whose chemical species could not be identified are also shown in color, and fall into three main categories: (i) charging transitions in the forward and backward bias sweeps that cannot be matched ('Uncertain matches'); (ii) defects that are too irregular in shape ('Noncompact'); or (iii) that have too few pixels assigned to them by the combined clustering and Gaussian-mixture algorithms ('Too few pixels').
• Figure 3: Device and sample parameters. The experimental set-up, including (A) vertical profiles of the tip and sample, and (B) the lateral tip geometry, in which a fine tip (left) is attached to the apex of a big tip (right). The work function of gold ($W_\text{Au}$) is well known, while the work functions of tungsten and molybdenum ($W_\text{W}$ and $W_\text{Mo}$) are determined in SI Appendix, section \ref{['AuMeasurements:simulations']}. Unknown parameters are listed in the table and illustrated above it. These parameters are determined as described in Fig. \ref{['fig:tip_characterization']} through a series of experiments, including EFM scans as a function of tip height, above either the bare oxide surface or a gold-coated sample. The local electrostatic potential depends on the tip height, the voltage bias $V_b$ between tip and back gate, and the presence of charged defects in the sample. The reference vacuum energy level (solid purple line) is obtained at the special bias $V_b=\overline V_\text{CPD}$ for which interactions between the tip and sample vanish. (We define the reference with respect to the globally averaged CPD potential.) Local shifts in the electrostatic potential $\Delta \phi$ (dashed purple line) are computed via electrostatics simulations. A charging transition occurs when a defect's chemical potential crosses the Fermi energy of the tip $E_F$, as a function of $V_b$. DFT calculations also provide the chemical potential for these transitions, $\Delta$, relative to the valance-band edge. Combining experimental measurments, DFT calculations, and electrostatics simulations allow us to identify the chemical species of a defect.
• Figure 4: Identifying the chemical species of defects in Al$_2$O$_3$ by comparing EFM measurements and DFT analyses. (A) Wide bars show DFT predictions for the chemical potentials ($\Delta$) of multiple charging transitions, for seven different defect species, with charge states indicated by colors (inset). Here, $\Delta$ is referenced to the valence-band edge of Al$_2$O$_3$ and the gray dashed line represents the Fermi level for the case where the vacuum potentials of the tungsten portion of the EFM tip and the molybdenum backgate are aligned ($V_b=V_{\Delta\Phi}$, see main text). The small bars to the right of the wide bars define the color coding used to identify the defects, below, and the length of the bar indicates the theoretical energy uncertainty $\sigma_i$ for a given transition $i$. (B) Top: the measured $f$-$V$ curve for Defect 5. The vertical dashed line shows our best match (V$_\text{O}$) to a theoretically predicted transition, based on the single-defect analysis. The vertical dotted lines (including one behind the dashed line) show our best theoretical matches (C$_\text{Al}$-H, C$_\text{O}$, and V$_\text{O}$), based on the multi-defect analysis. Bottom: pie charts showing the relative assignment probabilities for different defect species, based on the single-defect analysis (left) and the multi-defect analysis (right). Here, the notation (1) indicates that one transition was ignored in the analysis, because it was an edge case, while (2) indicates that all transitions were included in the analysis. (C) For Defects 1-5, we show our best matches between theoretical predictions (left column) and experimentally measured charging transitions, based on the single-defect analysis (middle column) and the multi-defect analysis (right column). Here, black lines represent the experimental transition voltages, converted to chemical potentials (see main text), the gray bars represent the experimental uncertainties for the transition ($\rho_i$), the black boxes represent the experimental measurement range, a red background indicates a negatively charged defect, and a blue background indicates a positively charged defect. Colored boxes are reproduced from A, with boxes removed if they fall outside the experimental range. The defects are ordered from left to right in decreasing order of assignment probabilities, based on the single-defect analysis.
• Figure 5: An overview of the methods used to characterize the geometrical parameters of the two-section EFM tip. (Full details are presented in SI Appendix, section \ref{['sec:Tip_Geometry']}.) (A)-(C) Measurements above a gold sample. (A) The capacitance curvature $\partial^2C/\partial z^2$ is measured as a function of tip-sample separation $h_\text{ts}$. Two types of behavior are observed: for small $h_\text{ts}$, tip-sample interactions are affected by both the coarse and fine-tip sections (red data), while for $h_\text{ts}>12.5$ nm, interactions are dominated by just the coarse ("big") tungsten portion of the tip (purple data). (B) First, COMSOL simulations are used to characterize the tungsten portion of the tip. For the purple data in (A), simulations are performed as a function of the tip-sample separation and the big-tip radius $R$. Minimizing the RMS difference between $\partial^2C/\partial z^2$ values from the experiments and simulations (red circle) provides a two-parameter fit, yielding $R=1800$ nm. Additional knowledge of the tip-sample separation $h_\text{ts}$ from SI Appendix, section \ref{['sec:tip-sample_separation']}, gives the optimal value for the fine-tip height $h_\text{tip}=h_\text{big tip}-h_\text{ts}=23$ nm. (C) Fine-tip parameters are obtained similarly, by comparing experimental data to COMSOL simulations, which now include the full two-section tip geometry. A fitting procedure gives the optimal relation between the length of the gold coating on the fine tip $h_\text{Au}$ and the fine-tip radius $r_\text{apex}$. However, since these two parameters have a similar effect on $\partial^2C/\partial z^2$, we are not able to determine a globally optimized pair of values $(h_\text{Au},r_\text{apex})$ from experiments above a gold sample. (D)-(E) Measurements above an oxide-on-Si sample. Here, we choose an isolated defect with a well-defined charging transition and track this transition voltage $V_b=V_\text{transition}$ as the tip is scanned both vertically and laterally. (D) Data points (pink markers) show $V_\text{transition}$ as a function of $h_\text{ts}$ when the tip is placed directly above the defect and scanned vertically. Simulation results (blue curve) are obtained for a fixed set of parameters $(h_\text{Au},r_\text{apex},d)$, where $d$ is the unknown depth of the defect below the sample surface, and the correlated parameters $h_\text{Au}$ and $r_\text{apex}$ are taken from (C). $d$ is used as a fitting parameter, here, to provide the best match between simulations and experiments. The figure shows simulations results for the case $r_\text{apex}=1$ nm. (E) The same procedure is used for lateral scans passing directly over the defect. Simulations results are again shown for $r_\text{apex}=1$ nm. (F) Results of the fitting procedure in (D, orange) and (E, blue) showing the best-fit results for $d$. Since the optimal $d$ value should be consistent between these two cases, we settle on $d=(0.65\pm 0.30)$ nm as our final optimized result, with corresponding values for $h_\text{Au}$ and $r_\text{apex}$. Based on these parameter characterizations, the inset shows the resulting conversion between an experimentally measured charging-transition voltage $V_\text{transition}$ for a given defect, to its corresponding chemical potential $\Delta$, as discussed in SI Appendix, section \ref{['sec:converting_Vtransion']}. Here, the shading indicates the uncertainty.