Kelvin probe force microscopy (KPFM) is a well-known variant of AFM that allows probing at the nanoscale the electrostatic landscape on the surface of a sample by measuring the so-called contact potential difference (CPD). If one considers a simple junction formed by a metallic AFM tip and a metallic sample, the CPD originates from the tip–sample work function difference. More generally, the CPD stems from the existence of electric charges and/or dipoles in the system under consideration. As a result, the applications of KPFM are extremely broad. It is now used by physicists, chemists, and biologists to characterize the nanoscale electronic/electrostatic properties of an ever-expanding range of materials, interfaces, and devices, in ambient conditions, under ultrahigh vacuum, or at the liquid–substrate interface.

Since the early 90’s, a variety of approaches have been implemented to improve KPFM performances in terms of spatial, potentiometric, and temporal resolution. Several research teams continue to work in this direction and KPFM is still an evolving technique in many aspects. In particular, the development of KPFM-based approaches specifically designed to investigate photogeneration mechanisms and charge dynamics at the nanoscale in photovoltaic and optoelectronic materials is an active research area.

In photoassisted KPFM, the idea is to probe the surface photovoltage (SPV), which is the illumination-induced change in the surface electrostatic potential (i.e., the opposite of the CPD shift under illumination). To map the SPV, the most basic approach consists in performing a dual-pass experiment. Two CPD maps are recorded, the first in the “dark state” and the second under continuous wave (cw) illumination. An SPV image can eventually be recalculated as the difference between both sets of data . The inherent drawback of this dual-pass method is that the source images used for the SPV calculation may feature misalignments, which is especially unavoidable at room temperature (RT) due to thermal drift . Another issue is that some of the SPV components – related to dynamical processes – can remain hidden to this “conventional” SPV imaging .

To mitigate the effects of thermal drift, a first alternative consists in performing a data cube acquisition of CPD curves synchronously recorded with the application of a light pulse (i.e., a curve is recorded at each point of the surface along a 2D grid). Again, a differential SPV image can be reconstructed from the matrix of spectroscopic curves . However, this approach is not free from artefacts, in particular the cantilever photothermal bending can significantly modify (depending on the optical power) the tip–surface distance during the spectroscopic measurement (which has to be performed in open z-loop).

Whenever possible, it is preferable to investigate the photoresponse of the sample under modulated or pulsed illumination. Provided that the modulation frequency of the light source is set high enough, it becomes possible to “stabilize” the static bending in a steady state, and photothermal cantilever excitation can be avoided (by setting the optical modulation at a frequency that differs from the cantilever resonance eigenmodes).

Working under modulated illumination also allows direct SPV measurements using special modulation/demodulation schemes, such as the one recently proposed by Miyazaki and co-workers for ac-bias KPFM . In addition, most time-resolved KPFM modes developed so far rely on the use of a pulsed/modulated illumination chain. This is for instance the case of intensity-modulated KPFM , pump-probe KPFM , or G-mode KPFM , to name a few (we refer the readers to review articles for a more comprehensive introduction to AFM-based time-resolved potentiometric and electrostatic modes ).

Each of these approaches have advantages and disadvantages. Intensity-modulated KPFM implementation is straightforward, since it simply consists in analysing the frequency response of the time-average CPD under modulated illumination. Nevertheless, it is prone to capacitive artefacts . Accurate quantitative measurements can be performed by pump-probe KPFM (pp-KPFM), with a time-resolution down to the sub-nanosecond scale . However, pp-KPFM features a severely limited bandwidth. In the case of our last implementation of pp-KPFM , several tens of seconds (to minutes) are needed to record a single spectroscopic curve, and tens of hours to several days are needed to map a 2D matrix of data. Last, G-mode KPFM requires analysis of large datasets acquired with high-speed data capture .

A few years ago, Borgani and Haviland presented an interesting alternative for time-resolved SPV measurements , which consists in analysing the intermodulation products between the mechanical oscillation of the cantilever and the photogenerated surface potential. In short, intermodulation spectroscopy allows working in the frequency domain (instead of the time domain) by extracting, during a single measurement, quantities that are directly proportional to the Fourier coefficients of the time-periodic surface photovoltage. Unfortunately, the translation of this promising technique from ambient conditions – where it has proven its worth – to ultra-high vacuum poses significant challenges. This is mainly due to the enhanced quality factors under vacuum, which severely limits the frequency window available to increase the amplitude of the intermodulation products (for a more detailed discussion, see ).

In this work, we propose to approach the measurement of intermodulation products with non-contact AFM under ultra-high vacuum in a slightly different way. We demonstrate that the Fourier spectrum (modulus and phase coefficients) of the time-periodic electrostatic surface potential generated under optical (or electrical) pumping can be probed, by exploiting a double heterodyne frequency mixing effect between the cantilever mechanical oscillation, the surface photovoltage harmonics, and an ac bias modulation signal. The frequency of the modulated bias can be set so that any given spectral component of the surface potential (or intermodulation product) can be “transferred” to the second cantilever eigenmode. This transfer or rejection (i.e., a measurement of a Fourier harmonic at the pump frequency through a demodulation at the second eigenmode frequency) is achieved by using two numerical lock-in amplifiers in cascade, which allows the generation of proper phase-coherent combination of reference signals.

Dual-heterodyne KPFM (DHe-KPFM) dramatically enhances the sensitivity to “weak” (i.e., a few mV) surface photovoltage signals, thanks to the amplification by the second resonance mode. Time-resolved measurements can be performed in data-cube mode, by recording spectra of the SPV Fourier components (modulus and phase) onto a 2D grid. The validity of DHe-KPFM implementation is first demonstrated by carrying out measurements on a conducting reference substrate under electrical pumping. The results confirm that – thanks to the constant transfer function over the entire spectrum provided by the signal demodulation at the second cantilever eigenmode – a quantitative measurement of the Fourier spectrum can be performed. In the case of the amplitude spectrum, that measurement is done within a scalar factor related to the capacitance gradient. Furthermore, 2D images of time constant that characterize the surface photovoltage dynamics are acquired on a photovoltaic organic bulk-heterojunction (BHJ) thin film. The time-constant values are shown to be fully consistent with the results of pump-probe KPFM. Last, the ability of DHe-KPFM to detect weak SPV signals is illustrated by investigating optoelectronic interfaces formed between caesium lead bromide perovskite nanosheets and highly oriented pyrolytic graphite.

Many KPFM modes rely on the detection of a modulated component of the electrostatic force proportional to the CPD, using a lock-in amplifier. The attractive electrostatic force between the tip and the surface can be expressed as:

In the above equation, C'z stands for the tip–sample capacitive gradient. Vbias represents the external bias voltage applied to the system (including both a dc and an ac component, see hereafter). The plus or minus sign applies if Vbias is applied to the tip (+ sign) or to the sample (− sign), respectively.

The lock-in output provides a modulated ac bias voltage (Vac, amplitude Uac, and angular frequency ωac) that is added to the static dc voltage applied to the tip (or sample), Vbias = Vac + Vdc. The electrostatic force displays modulated components, and some are directly proportional to the dc electrostatic potential term (i.e., Vdc ± VCPD). The idea is to demodulate such a component, and feed it into a loop which controls the dc bias. The KPFM controller (with a zero set point), will eventually adjusts the dc bias to minimize its input, yielding a measurement of the CPD (Vdc = ±VCPD depending on the setup geometry). In the following, the dc compensation bias provided to the tip by the KPFM controller (in our setup Vdc = −CPD) will be referred to as either Vdc or KPFM potential. To avoid repetition, this quantity is sometimes also referred to as "surface potential". This is obviously a misuse of language, as KPFM gives a relative measurement of the surface electrostatic potential with respect to that of the tip. However, it is partly justified because in our setup the compensation bias is applied to the tip. Then, provided that the effective work function of the tip remains constant during the measurement, any change in the KPFM compensation potential will strictly follow the change in the surface electrostatic potential without sign inversion (a local positive surface charging corresponds to a positive Vdc change).

Actually, there are many ways to perform the signal demodulation. Amplitude heterodyne KPFM, introduced in 2012 by Sugawara et al. , is a very elegant approach. It combines the advantages of frequency-modulated KPFM (FM-KPFM) and amplitude-modulated KPFM (in terms of lateral resolution and sensitivity, respectively). This mode takes advantage of heterodyning effects (frequency mixing) between the electrical bias modulation and the cantilever mechanical oscillation (usually performed at the first eigenmode, angular frequency ω0). These effects result in the existence of additional modulated component of the electrostatic force (or sidebands) at frequencies ω0 ± ωac. They stem from higher harmonic components in the capacitance term :

If we restrict ourselves to the first harmonic (n = 1), electrostatic force components emerge (we just describe the first set of sidebands, other exist at ω0 ± 2ωac) which are:

It can be shown , that the Fourier coefficient at n = 1 is proportional to the second z-derivative of the capacitance (K1 ≡ C''z). Consequently, demodulating the amplitude of the sidebands gives access at a term that is proportional to the dc potential difference, and one works (like in frequency-modulation KPFM) on a signal that is proportional to the electrostatic force gradient (through C''z). For that reason, this “side-band” KPFM is often referred to as a variant of FM-KPFM.

Amplitude-modulated heterodyne KPFM further improves this approach. The idea is to set the modulated bias angular frequency so that the first right sideband (ω0 + ωac) is “rejected” at the second mechanical resonance eigenmode (frequency ω1) of the cantilever. Implementing this modulation/demodulation scheme is nowadays greatly facilitated by the flexibility offered by last-generation digital lock-in amplifiers, which allow generating (and demodulating) phase-coherent combinations of multiple oscillators (i.e., an excitation at ωac = ω1 − ω0 and a demodulation at ω1).

Here, it is mandatory to stress a very important point. In all strictness, in the above, we should have written that ωac = ω1 − (ω0 + Δω0), where Δω0 stands for the cantilever frequency shift due to the tip–surface interaction. In heterodyne KPFM, the reference sideband that drives the modulated bias is indeed generated as follows. The frequency of the first source signal (or lock-in internal oscillator) is set to ω1, ultimately it will be used for signal demodulation. The second source signal is obtained by tracking the cantilever resonance frequency at its first eigenmode (ω0 + Δω0) with a second oscillator configured as a phase-locked loop (PLL). This tracking is necessary because the first mode is used by the main AFM controller for topographic control (in frequency modulation mode in the case of non-contact AFM under UHV). In other words, it is the AFM controller which generates the source signal at ω0 + Δω0 which “excites” the mechanical oscillation of the cantilever. The frequency mixing effect will effectively generate a modulated electrostatic component at ω1 – phase-coherent with the demodulation chain – only and if only the frequency shift that the cantilever (at its first resonance mode) experiences in the tip–surface interaction is taken into account. In FM-AFM, it is impossible to perform a heterodyne-KPFM measurement by setting a “fixed” value for ω0.

To understand how dual-heterodyne KPFM works, consider the case of a sample subjected to a time-periodic pump that generates a (time-)periodic electrostatic potential. Within the framework of investigations on photoactive materials, of course, the pump will consist of light pulses (in which case one generates a periodic SPV), but DHe KPFM experiments (as shown below) can also be performed under electrical pumping (by applying bias pulses directly to the sample with an arbitrary waveform generator).

The time-periodic electrostatic potential Vmod (or photopotential) generated at the sample under modulated illumination can be described by a Fourier series:

As in other KPFM modes, a combination of dc (Vdc) and ac (Vac) bias is applied to the AFM tip. The total electrostatic force between the tip and the sample is now:

This can be rewritten as:

Finally, the other frequency mixing process (multiplication by the capacitive term, first harmonic) results in the appearance of additional spectral components in the oscillating electrostatic force, but this time there are 4 × n of them (instead of two sidebands for conventional AM-heterodyne KPFM):

To avoid any confusion, in the following, the sidebands will be labelled as follow:

As with conventional AM-heterodyne KPFM, the idea is to use the second mechanical resonance eigenmode of the cantilever to "boost" a selected sideband. For example, the ac value can be adjusted so that the n_4 sideband frequency is rejected at the second eigenmode (i.e., ωac = ω1 – ω0 + nωmod). Note that depending on the frequency range of the harmonics, other bands can be used for rejection (such as the n_1 one, with ωac = ω1 – ω0 – nωmod).

Figure 1: The implementation of DHe-KPFM. The real geometry of the sample stage (backside or front side illumination depending on the nature of the substrate) and the external optics differ from that of the simplified scheme. The cantilever is mechanically excited by the AFM control unit at its first eigenmode resonance frequency ω0, shifted by Δω0 in the tip-surface interaction. The first lock-in unit performs a combination (or sideband generation) to generate a reference sine at ω1 − (ω0 + Δω0). The "intermediate" reference signal at ω1 − (ω0 + Δω0) is subsequently fed to the external input of a second digital lock-in. The second lock-in combines it with another reference sine signal generated by the arbitrary waveform generator (AWG, channel 2) at nωmod. Then, a modulated bias Vac with an angular frequency ωac = ω1 – (ω0 + Δω0) + nωmod is generated at the lock-in output and applied to the AFM cantilever. NB: the configuration can be switched (software-controlled toggle of the modulation unit) between DHe-KPFM (DHe) and standard AM-heterodyne-KPFM (He). The AWG also generates the pump source signal (channel 1, i.e.; a square-waved modulation with period 2π/ωmod, duty ratio fixed at the user convenience). The time-periodic SPV displays multispectral components at the frequencies nωmod which stem from the dynamics of photoexcited states. Demodulating the normal force at ω1 yields access to the SPV n-th Fourier coefficients (amplitude and phase). Curves of the SPV Fourier spectrum are acquired by sequentially sweeping the output signal from the second channel of the AWG (i.e., nωmod with n = 1, n = 2, n = 3, etc.). This is achieved by playing a pre-programmed list of waveforms, triggered by TTL pulses generated by the AFM controller.

As with AM-heterodyne KPFM, the first lock-in unit performs a combination of two signals to generate a reference at the frequency ωref = ω1 − (ω0 + Δω0). The frequency of the first source signal (or internal oscillator) is set to ω1, ultimately it will be used for signal demodulation. The second source signal is obtained by tracking the cantilever resonance frequency at its first eigenmode (ω0 + Δω0) with a second oscillator configured in a PLL configuration.

Non-contact AFM (nc-AFM) and KPFM experiments are performed with a VT-beam AFM system (Scienta-Omicron) at room temperature (RT) under ultra-high vacuum (UHV), driven by a Mimea scanning probe microscope (SPM) controller (SPECS-Nanonis). Topographic imaging is performed in FM mode (FM-AFM) in the attractive regime, with negative frequency shifts of a few Hz and vibration amplitudes of a few tens of nm. All experiments were performed with Pt/Ir coated silicon cantilevers (PPP-EFM, Nanosensors, resonance frequency in the range 45–115 kHz), annealed in situ to remove atmospheric contaminants.

The dual-heterodyne KPFM mode was implemented by combining the SPM unit with two digital lock-ins from Zurich Instruments (lock-in 1: MFLI, lock-in 2: HF2LI). Both are equipped with multiple oscillators, control loops, PLLs, and modulation modules (2 for the HF2LI). The MFLI modulation module is used to generate the intermediate reference signal with an angular frequency of ω1 – (ω0 + Δω0). The reference sidebands for the electrical excitation (Vac, ωac) are generated by the HF2LI modulation module. As aforementioned, different series of sidebands can be used to probe the signal Fourier spectrum. In this regard, it should be noted that a 180 phase shift is added by the HF2LI to its output (Vac) if one uses the left sideband (with respect to the carrier, as defined in the HF2LI modulation module) instead of the right one. In our case, this additional 180 phase shift is taken into account when the n_1 sidebands are used instead of the n_4 ones.

The pump (modulated square wave with an adjustable duty ratio and period 2π/ωmod) and the harmonic reference (sine, angular freq. n × ωmod) are generated by a Keysight 33600 A arbitrary waveform generator. The maximum frequency for the sine signal is 120 MHz, 50 MHz for a square wave with a duty ratio of 25%. On its part, the HF2LI unit can handle signals up to 50 MHz. In principle, these combined features allow up to approximately 10 harmonics to be sampled with a base pump period as small as 200 ns (10 × ωmod/2π ~ 50 MHz). It should be noted, however, that other factors may limit measurements at high frequencies (e.g., attenuation of the ac signals transmitted to the cantilever).

Time-resolved measurements are performed by recording curves of the demodulated Fourier components of the time-periodic surface potential (Vn,Φn) as a function of the harmonic number (n). This is done by sequentially sweeping the output signal from the second channel of the AWG (i.e., nωmod with n = 1, n = 2, n = 3, etc.). To that end, a pre-programmed list of waveforms is played, and the triggering is done by TTL pulses generated by the AFM controller. The AWG waveform playlist is programmed by using the Keysight benchlink pro software, and the TTL pulses are generated during the course of the spectroscopic ramp by using a user-available high speed digital output of the Mimea unit.

Figure 2: Benchmarking of DHe-KPFM under electrical pumping. Plots of the demodulated amplitude and phase (lock-in outputs) at the second cantilever eigenmode as a function of time, recorded on an HOPG sample under electrical pumping (pump period T = 100 µs and peak-to-peak amplitude of 1 V for all spectra). ω0/2π ≈ 83.3 kHz, ω1/2π ≈ 519.3 kHz, Δω0/2π = −25 Hz, ωmod/2π = 10 kHz, Uac = 0.5 V. The first 20 harmonics have been recorded (n = 1 to 20, 1 s per harmonic). a) Square-wave pump with a 50% duty ratio. b) Saw-tooth ramp. c,d) Square-wave pump with a 10% duty ratio. a,b,c) Rejection at ω1 of the n_4 sidebands, ωac = ω1 – (ω0 + Δω0) + nωmod. d) Rejection at ω1 of the n_1 sidebands, (ωac = ω1 – (ω0 + Δω0) − nωmod). The controller configuration is switched in standard AM-heterodyne KPFM (ωac = ω1 – (ω0 + Δω0)) during the 20 s < t < 21 s time window (highlighted by a semi-transparent pink area). This allows setting a reference phase level (zero or 180° depending on the set of sidebands used to probe the intermodulation products, see main text).

To further validate the DHe-KPFM implementation, a second set of measurements was performed under optical pumping on an organic photovoltaic donor–acceptor blend. As in our previous works, we used the PTB7:PC71BM tandem. We refer the reader to our former reports and review articles for a detailed introduction to KPFM on organic heterojunctions , and to the specificities of the PTB7:PC71BM blend.

We limit ourselves here to recall that in these organic blends, charge photogeneration can be understood, in a first approach, as the result of exciton dissociation into Coulomb bound charge transfer (CT) states at the donor–acceptor interfaces. This event is finally followed by the dissociation of the CT states into delocalized carriers of opposite sign on both sides of the D–A interface.

In the context of this work, it is also worth recalling that KPFM investigations are carried out in an "open circuit voltage" configuration. In such a geometry, the surface photovoltage probed under continuous-wave illumination results from a balance between the processes of photogeneration and carrier annihilation (by electron–hole recombination). In addition, from the venture of time-resolved KPFM under pulsed illumination, the SPV dynamics are mainly governed by the effective carrier mobility and trapping mechanisms. The main factor limiting the photocharging dynamics is indeed the effective mobility of holes and electrons (under the effect of drift diffusion) in the donor and acceptor networks. After the application of a light pulse – and during the duration of the pulse – the charge mobility limits the rate at which an electrostatic equilibrium can be reached in the sample. Clearly, this parameter also has an impact on the SPV decay dynamics. However, in the latter case, the slower trap release processes are actually the limiting factor. In particular, in the case of the PTB7:PC71BM system, it is now well-established that isolated PC71BM clusters act as electron trapping centres. The blend morphology, phase composition and concentration gradients of the donor and acceptor species (through the film thickness) can therefore have a dramatic impact on the SPV decay dynamics probed by KPFM.

Figure 3: The SPV imaging of an organic solar cell by DHe-KPFM. Topographic (a) and DHe-KPFM (b,c) images (500 × 500 nm, 256 × 256 pixels) of a PTB7:PC71BM blend acquired under pulsed illumination (λ = 515 nm, Popt = 300 mW·cm−2, illumination in backside geometry). ω0/2π ≈ 83.3 kHz, ω1/2π ≈ 519.3 kHz, Δω0/2π = −30 Hz, Uac = 1 V. ωac = ω1 – (ω0 + Δω0) + nωmod with n = 1. The optical pump consists in a square-shaped signal with a base period of 5 ms (ωmod/2π = 200 Hz) and a duty ratio of 20 percent (optical pulse duration: 1 ms). The DHe-KPFM data have been acquired by demodulating (n_4 sideband) the amplitude V1 (b) and the phase Φ1 (c) of the first (n = 1) harmonic of the time-periodic SPV. The scan rate was set to 5 s/line. d) Histogram of the phase values.