Direct measurement of surface photovoltage by AC bias Kelvin probe force microscopy

General concept

KPFM measures the CPD by compensating the electrostatic forces between the tip and the sample. When an AC bias VAC·cos(ωmt) with modulation frequency ωm between the tip and the sample is applied, the electrostatic force Fele in darkness is described as

[2190-4286-13-63-i1](1)

where ∂C/∂z is the capacitance gradient of the tip–sample system and VCPD is the CPD in darkness. Applying a modulated laser power with a sinusoidal waveform of frequency ωm, which is synchronized with the AC bias (Figure 1b), induces the SPV with the peak-to-peak amplitude VSPV:

[2190-4286-13-63-i2](2)

Therefore, the electrostatic force [Graphic 1] under modulated laser irradiation is described as

[2190-4286-13-63-i3](3)

This equation can be divided into three parts:

[2190-4286-13-63-i4](4) [2190-4286-13-63-i5](5) [2190-4286-13-63-i6](6)

[Graphic 2] (Equation 5) is measured to determine the SPV by controlling VAC and nullifying the modulated force [Graphic 3] where the SPV is derived as

[2190-4286-13-63-i7](7)

Thus, AC-KPFM controls the AC bias VAC to directly measure the SPV, unlike classical KPFM, in which the DC bias VDC is controlled to determine the CPD or SPV. It is noted that when the SPV is negative, VAC yields a negative amplitude, where the phase of the AC bias is in phase opposition. It is also noted that it would be useful to measure the signal of the second harmonic component [Graphic 4] (Equation 6) since zero amplitude of [Graphic 5] indicates that the SPV is correctly compensated by the VAC control.

[2190-4286-13-63-1]

Figure 1: Schematics of AC-KPFM for direct SPV measurements. (a) Block diagram of AC-KPFM in FM mode. FG is a function generator. (b, c) Scheme of the AC bias nullifying method by laser power modulation with (b) sinusoidal and (c) square waveforms, which are synchronized to VAC.

Next, when the laser power is modulated with a square waveform of frequency ωm using, for example, a chopper synchronized to the AC bias (Figure 1c), the SPV with a peak-to-peak amplitude VSPV is expressed as a Fourier series,

[2190-4286-13-63-i8](8)

Therefore, the electrostatic force [Graphic 6] under square-waveform illumination is described as

[2190-4286-13-63-i9](9)

The modulated force with frequency ωm is described as

[2190-4286-13-63-i10](10)

In the same manner as before, the SPV is determined by controlling VAC and nullifying the modulated force [Graphic 7]

[2190-4286-13-63-i11](11)

Thus, AC-KPFM can directly and quantitatively measure the SPV by laser power modulation with either sinusoidal or square waveforms.

AC-KPFM in AM mode

In the AM mode, AC-KPFM measures the oscillation amplitude with frequency ωm, which is driven by the modulated electrostatic force [Graphic 8] This signal is measured with a lock-in amplifier and compensated by VAC control, yielding the SPV value. To improve the sensitivity, ωm is usually tuned to the second (first) resonance frequency of the cantilever, while the first (second) resonance frequency is assigned to the AFM measurement [29]. Since these resonance frequencies are commonly in the kilohertz to megahertz range, the time scale of the measured SPV is from microseconds to milliseconds, which is much faster than that measured by classical KPFM, which measures the slow SPV response of the order of seconds to hours because of the long image acquisition time [31] and the need for consecutive experiments in darkness and under illumination. Here, ωm should be set slower than the intrinsic SPV response, which we aim to observe, otherwise the SPV response cannot follow the modulated laser and yields zero amplitude. The spatial and energy resolutions and the image acquisition time of AC-KPFM in the AM mode are comparable to those of the classical KPFM in the AM mode, because both methods detect the electrostatic force, [Graphic 9] and the response time of the bias feedback τ limits the image acquisition time. To reach sufficient sensitivity, the [Graphic 10] value should typically be larger than 100 mV.

AC-KPFM in FM mode

In the FM mode, AC-KPFM measures the modulated frequency shift [Graphic 11] with frequency ωm, which is driven by the modulated electrostatic force [Graphic 12] For a small oscillation amplitude, [Graphic 13] under a modulated laser can be approximately expressed as

[2190-4286-13-63-i12](12)

where

[2190-4286-13-63-i13](13)

This signal is measured by a lock-in amplifier and compensated by controlling VAC, yielding the SPV value:

[2190-4286-13-63-i14](14)

Since ωm is usually set in a range from a few tens of hertz to several kilohertz, the time scale of the measured SPV is of the order of milliseconds, which is faster than that measured by classical KPFM. The spatial and energy resolutions and the image acquisition time of AC-KPFM in the FM mode are comparable to those of the classical KPFM in the FM mode, because both methods detect the electrostatic force gradient [Graphic 14] and the response time of the bias feedback τ limits their image acquisition time [31]. To reach sufficient sensitivity, the [Graphic 15] value should typically be larger than 1 V.

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