Electrical Scanning Probe Microscope Measurements Enabling the Acquisition of Nanosecond Conductivity Transients and the Quantification of Charge Density and Electrical Conductivity

I will describe two breakthroughs in the scanning probe characterization of semiconductors.

1. Nanosecond time resolution scanning probe measurements of charge recombination. Prior electrical scanning probe work has demonstrated a time resolution of picoseconds or better, but requires a nonlinear sample response, achieved by using high intensity illumination to saturate the sample’s optical absorption. Time resolved electrostatic force microscopy has demonstrated sub-microsecond time resolution at solar-cell-relevant light intensities, but with a sensitivity dramatically curtailed at timescales below the cantilever period of a few microseconds. We introduced phase-kick electric force microscopy, pk-EFM, to surmount these limitations [1], operating in the linear-response regime of sample excitation and achieving a time resolution limited by the cantilever charging time of a few nanoseconds. Using a nanosecond laser to excite the sample, we have used pk-EFM to record nanosecond photoconductivity transients in both lead-halide perovskite and organic semiconductor thin films. These signals will be compared to time resolved photoluminescence and microwave conductivity measurements. Nanosecond-resolution pk-EFM opens the door to imaging charge recombination and transport at device-relevant illumination intensities in solar-cell films with scanning-probe spatial resolution.

2. Quantitative non-contact measurements of charge density and mobility. Dwyer, Marohn, and coworkers developed a Lagrangian-mechanics description of the tip-sample interaction in electrical scanning probe experiments [2] in which the sample is modeled as a capacitor and resistor in parallel. Their theory predicts a non-linear dependence of cantilever frequency shift and dissipation on light intensity, in agreement with experiments on illuminated inorganic, hybrid, and organic semiconductors. Another successful test of this treatment is the broadband local dielectric spectroscopy experiment, BLDS, in which the cantilever frequency shift is measured versus tip-voltage modulation frequency [3]. The Dwyer treatment leaves unanswered the question of how to convert the inferred sample resistance, an extrinsic quantity depending on tip-sample geometry, to a resistivity or conductivity, an intrinsic sample property.

To address this shortcoming, we turn to the microscopic treatment of the tip-sample interaction introduced by Lekkala and Loring [4]. In their treatment, the sample contains mobile charges and has a complex dielectric constant. The cantilever tip is represented as an oscillating point charge. Cantilever friction and frequency noise is computed, via a fluctuation-dissipation relation, from the sample’s reaction field obtained by solving Maxwell’s equations. In the absence of mobile sample charges, this treatment correctly predicts the dependence of cantilever friction and frequency noise on tip-sample separation and complex dielectric constant in a wide range of polymeric films [5]. We will describe ongoing efforts to (1) test the Lekkala and Loring treatment by measuring friction over lead-halide perovskites and organic semiconductors and (2) extend the treatment to cover the BLDS experiment and transient experiments like phase-kick EFM. This work will enable non-contact electrical scanning probe measurements to quantify local sample charge density and conductivity (i.e., mobility).

[1] R. P. Dwyer et al., Sci. Adv. 2017, DOI: 10.1126/sciadv.1602951
[2] R. P. Dwyer et al., Phys. Rev. Appl. 2019, DOI: 10.1103/physrevapplied.11.064020
[3] A. M. Tirmzi et al., ACS Energy Lett. 2017, DOI: 10.1021/acsenergylett.6b00722
[4] (a) S. Lekkala et al., J. Chem. Phys. 2012, DOI: 10.1063/1.4754602 (b) S. Lekkala et al., J. Chem. Phys. 2013, DOI: 10.1063/1.4828862
[5] S. M. Yazdanian et al., Nano Lett. 2009, DOI: 10.1021/nl9004332