Research ArticlePHYSICAL SCIENCES

Microsecond photocapacitance transients observed using a charged microcantilever as a gated mechanical integrator

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Science Advances  09 Jun 2017:
Vol. 3, no. 6, e1602951
DOI: 10.1126/sciadv.1602951
  • Fig. 1 Experimental overview.

    (A) The experimental setup and sample, a spin-coated PFB:F8BT film on indium tin oxide. (B) The cantilever frequency shift δf depends parabolically on the tip voltage Vt. The increased curvature of the δf versus Vt parabola under illumination indicates a light-induced increase in tip-sample capacitance. (C) Photocapacitance charging measured via the cantilever frequency and phase. Data demodulated with a 3-dB bandwidth of 1.92 kHz (blue) and 0.96 kHz (purple). (D) When the light is turned off, but the voltage is still on, light-induced capacitance remains elevated for 10s of seconds to minutes. The dashed line shows the frequency shift before the start of the light pulse. Average of 100 traces shown, each demodulated with a 3-dB bandwidth of 1.92 kHz. Experimental parameters: tip-sample distance, h = 250 nm; tip-sample voltage, Vt = 10 V; light intensity, Ihν = 0.1 kW m–2 in (C) and Ihν = 20 kW m–2 in (D); light pulse time = 50 ms in (C) and 2.5 ms in (D).

  • Fig. 2 Using the pk-EFM experiment to measure a photocapacitance transient.

    For three representative pulse times, we plot (A) cantilever amplitude; (B) cantilever drive voltage, turned off at t = −10 ms; (C) tip voltage, with the pulse time tp indicated; (D) sample illumination intensity, turned on at t = 0; (E) sample capacitance; and (F) cantilever frequency shift. (G) Timing of applied voltages and light pulses. The voltage and light turn off simultaneously at t = tp. After a delay td (typically 5 to 15 ms), the cantilever drive voltage is turned back on. Next, we illustrate how the phase shift Δφ is calculated using the tp = 10.3 ms data. We process the cantilever displacement data using a software lock-in amplifier. (H) The software lock-in amplifier reference frequency changes at t = tp. The software lock-in amplifier outputs (I) the in-phase (solid) and out-of-phase (dashed) components of the cantilever displacement; (J) cantilever amplitude; (K) frequency shift; and (L) phase shift. The total phase shift Δφ is equal to the highlighted area under the cantilever frequency shift curve. (M) The voltage- and light-induced phase shift Δφ is measured as a function of the pulse time tp. We show only every other data point for clarity. The tp = 10.3 ms data point is denoted with a star. Experimental parameters: PFB:F8BT on indium tin oxide (ITO) film, h = 250 nm, Vt = 10 V, Ihν = 0.3 kW m–2, delay time between pulses = 1.5 s.

  • Fig. 3 Phase space and lock-in detector representation of the pk-EFM experiment.

    Top: Sinusoidal cantilever displacement “signal” and square-wave “reference” oscillations versus time, initially (left), under illumination (middle), and with the illumination removed (right). Bottom: Evolution of the signal and reference oscillator as viewed in phase space (X, position; Y, momentum) and at the outputs of a lock-in detector (XLI, in-phase channel; YLI, out-of-phase channel) at short time (middle) and at long time (right).

  • Fig. 4 Comparison of pk-EFM and tr-EFM signals (PFB:F8BT on ITO, h = 250 nm, and Vt = 10 V).

    (A) pk-EFM phase shift versus pulse time data, collected at 100 kW/m2 intensity, overlaid with best-fit pk-EFM and tr-EFM phase shift curves. The control data set (green) shows the observed phase shift with the light off. The gray points show the control data before correcting for the phase shift caused by the abrupt change in tip-sample voltage at the end of the pulse. (B) tr-EFM frequency shift versus time data, overlaid with best-fit tr-EFM and pk-EFM frequency shift curves. (C) Phase shift data collected across a range of light intensities. The photocapacitance transient rises more quickly at higher light intensities. Solid curves are a biexponential fit. The delay time between pulses was at least 87 ms. (D) Time constants for biexponential fits of photocapacitance transients measured using pk-EFM and tr-EFM show a consistent trend.

  • Fig. 5 Direct measurements are insensitive to fast sample dynamics.

    Inferring the charging time via the cantilever frequency and phase (PFB:F8BT on ITO, h = 250 nm, Vt = 10 V). (A) Cantilever tip voltage; (B) sample response function, with charging time constant τc; (C) lock-in amplifier response function; (D) measured cantilever amplitude with modeled, best-fit response for τc = 0.1 ns (orange) and τc = 1000 ns (purple). (E) Fit residuals: 0.1 ns, orange circles; 1000 ns, purple squares. (F) Measured cantilever frequency and (G) measured cantilever phase. Inferring the charging time directly from the cantilever displacement signal. (H) Cantilever tip voltage. (I) Sample response function. (J) Cantilever displacement, with best-fit sinusoid from the data before the voltage step (t < 0). (K) Change in cantilever displacement ΔxV induced by the voltage pulse, along with best-fit responses for τc = 10 ns (orange) and τc = 350 ns (purple). (L) Fit residuals: 10 ns (orange circles) and 350 ns (purple squares).

  • Fig. 6 Experiments and simulations demonstrating subcycle time resolution in pk-EFM.

    (A) Subcycle voltage-pulse control experiment (PFB:F8BT on ITO, h = 250 nm). A voltage pulse of length tp is applied to the cantilever tip (top) at a delay of td relative to the cantilever oscillation (middle) for 100 consecutive cantilever oscillations. (B) The pulses shift the cantilever amplitude by ΔA. (C) Measured frequency shift and (D) phase shift, demodulated with a 3-dB bandwidth of 4.8 kHz (blue) and 1.5 kHz (green). (E) The amplitude shift ΔA versus delay time td for three representative pulse lengths. (F) The normalized response ΔAmax/tp obtained by fitting data in (E) shows the cantilever wiring attenuating the response at short pulse times. The gray line is a fit to a single-exponential cantilever charging transient. (G) Numerically simulated phase shift in microcycles versus tp for a sample with a photocapacitance charging time of 50 ns (blue), 10 ns (green), and 2 ns (red). Solid lines are a fit to a single-exponential risetime model. Simulations include detector noise, thermomechanical cantilever position fluctuations, and sample-related frequency noise at levels comparable to those observed in the experiments of Fig. 4 (text S10). The simulated data assumed 1600 averages per point [16 s/pt = 1600 × (2 ms acq./pt + 8 ms delay/pt); total acquisition time = 30 min].

  • Fig. 7 Frequency noise and phase noise in tr-EFM and pk-EFM.

    (A) Cantilever position versus time data are demodulated using a filter with varying bandwidths (fig. S2). (B) Top: Fourier transform of the filters in (A); middle: experimental power spectral density of frequency fluctuations (PFB:F8BT on ITO, Vt = 0 V, h = 250 nm); bottom: product of top and middle traces, shaded to indicate that the mean-square frequency noise is the integral under this curve. (C) The cantilever phase (calculated by demodulation) is filtered to estimate the phase difference Δφ acquired during the pulse. The filters during the before (t < 0) and after (t > tp) periods are weighted least-squares filters, with exponential weight time constants before τb = 0.67 ms and after τa = 1.2 ms (see text S3). (D) Top: Fourier transform of the filter function in (C); middle: experimental power spectral density of phase fluctuations (PFB:F8BT on ITO, Vt = 0 V, h=250 nm); bottom: product of top and middle traces, shaded to indicate that the mean-square phase noise is the integral under this curve.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/6/e1602951/DC1

    text S1. Tip voltage photocapacitance clearing.

    text S2. Data workup discussion.

    text S3. Weighted best-fit intercept filter.

    text S4. Reference amplitude and phase shift.

    text S5. Biexponential curve fits.

    text S6. Alternative explanations of photocapacitance dynamics.

    text S7. Time domain cantilever oscillation fits.

    text S8. Higher cantilever eigenmodes.

    text S9. Photothermal effects.

    text S10. Numerical simulations.

    text S11. Cantilever characterization.

    text S12. Experimental timing.

    text S13. Curve fitting using PyStan.

    fig. S1. Fast clearing of remnant photocapacitance.

    fig. S2. Cantilever oscillation data workup protocol.

    fig. S3. Power spectral density of cantilever frequency fluctuations.

    fig. S4. Analysis of the amplitude and phase shifts imparted by the abrupt voltage step in the pk-EFM experiment.

    fig. S5. Comparison of single- and biexponential fits to tr-EFM and pk-EFM data.

    fig. S6. Light-induced changes in cantilever displacement.

    fig. S7. Cantilever position power spectral density during tr-EFM.

    fig. S8. Cantilever position power spectral density during pk-EFM.

    fig. S9. Additional comparison of pk-EFM and tr-EFM steady-state photocapacitance.

    fig. S10. Power spectral density of cantilever thermomechanical position fluctuations.

    fig. S11. Photocurrent delay and risetime.

    fig. S12. Block diagram showing the experimental setup and timing circuitry.

    fig. S13. PyStan sampling traces.

    fig. S14. pk-EFM posterior distribution samples.

    fig. S15. tr-EFM posterior distribution samples.

    References (5761)

  • Supplementary Materials

    This PDF file includes:

    • text S1. Tip voltage photocapacitance clearing.
    • text S2. Data workup discussion.
    • text S3. Weighted best-fit intercept filter.
    • text S4. Reference amplitude and phase shift.
    • text S5. Biexponential curve fits.
    • text S6. Alternative explanations of photocapacitance dynamics.
    • text S7. Time domain cantilever oscillation fits.
    • text S8. Higher cantilever eigenmodes.
    • text S9. Photothermal effects.
    • text S10. Numerical simulations.
    • text S11. Cantilever characterization.
    • text S12. Experimental timing.
    • text S13. Curve fitting using PyStan.
    • fig. S1. Fast clearing of remnant photocapacitance.
    • fig. S2. Cantilever oscillation data workup protocol.
    • fig. S3. Power spectral density of cantilever frequency fluctuations.
    • fig. S4. Analysis of the amplitude and phase shifts imparted by the abrupt voltage step in the pk-EFM experiment.
    • fig. S5. Comparison of single- and biexponential fits to tr-EFM and pk-EFM data.
    • fig. S6. Light-induced changes in cantilever displacement.
    • fig. S7. Cantilever position power spectral density during tr-EFM.
    • fig. S8. Cantilever position power spectral density during pk-EFM.
    • fig. S9. Additional comparison of pk-EFM and tr-EFM steady-state photocapacitance.
    • fig. S10. Power spectral density of cantilever thermomechanical position fluctuations.
    • fig. S11. Photocurrent delay and risetime.
    • fig. S12. Block diagram showing the experimental setup and timing circuitry.
    • fig. S13. PyStan sampling traces.
    • fig. S14. pk-EFM posterior distribution samples.
    • fig. S15. tr-EFM posterior distribution samples.
    • References (57–61)

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