Scanning Impedance Microscopy (SIM) is a novel SPM technique based on the on the detection of the phase change of cantilever oscillations induced by a lateral ac bias applied to the sample. The bias induces oscillations in surface potential and, therefore, results in the periodic force acting on the dc biased tip. The lock-in system detects phase and amplitude of tip vibration as shown on the image below. The phase and amplitude of the cantilever oscillation is comprised of SIM phase and amplitude images. The phase of the surface potential oscillations is related to the local transport properties. For example, phase and amplitude change abruptly at the electroactive interfaces such as metal-semiconductor interfaces or grain boundaries. For the measurements performed far (>5kHz) from the resonant frequency of the cantilever (60-70kHz) the phase lag between the surface potential oscillations and cantilever oscillations is constant (albeit frequency dependent). Therefore, variation of measured cantilever oscillation phase is equal to voltage phase angle variation across the surface.
This technique bears certain similarity to Scanning Surface Potential Microscopy (SSPM) under lateral bias, but the former allows to study dc transport properties of complex microstructures while SIM directly addresses ac transport properties. Currently we are able to perform SIM imaging in the frequency range from 300 Hz to 100kHz and obtain quantitative information on the transport properties of the electroactive interfaces. The lower limit is imposed by the pixel acquisition time, while the upper is given by lock-in range. Spectroscopic variants of SIM can be extended to dc frequency limit, while the high frequency limit is limited by cantilever dynamic properties (the response amplitude is small above the resonant frequency, hence phase and amplitude error increases). Shown below is the example of SSPM and SIM imaging of metal-semiconductor interface (Schottky diode).
Reconstruction of dc and ac transport properties from SSPM and SIM data requires the overall circuit topology. In experimental setup, R is known current limiting resistors in the circuit. Variation of R allows correctness of the chosen equivalent circuit to be verified (e.g. presence of additional resistive or capacitive elements can be detected) and parameters of the interface can be reconstructed. Measured in SSPM under lateral bias is potential drop at the interface as a function of external lateral bias (voltage characteristic of the interface). Measured in SIM is phase shift across the interface and ratio of oscillation amplitudes across the interface. Both these quantities are independent of the cantilever and tip properties and are dependent solely by frequency dependent impedance of the interface and the circuit. Shown below is surface topography (left) and surface potential (right) of the Schottky diode under slow (~2mHz) triangular voltage ramp. Note that under forward bias conditions there is no potential drop at the interface, which however develops under reverse bias. Also shown is potential profiles across the interface for low (R = 500 Ohm) and high (R = 100kOhm) resistivity circuit terminations.
Note that onset of reverse bias condition shifts to the negative voltages for high-resistivity terminations. Voltage characteristic of the interface are shown below. Analysis of these characteristic allows to obtain both saturation current density and leakage resistivity of the diode under reverse bias.
Note that these values are extremely close to saturation current density from conventional I-V measurements and leakage resistance (600 kOhm). On the next step, SIM phase and amplitude images were acquired in the frequency range from 3 to 100 kHz. Shown below is phase (left) and amplitude (right) of cantilever oscillations to the left and right of the interface for two different circuit terminations.
phase (left) and amplitude (right) of cantilever oscillations to the left and right of the interface for two different circuit terminations
Note that absolute values of measured phase and amplitude are the convolution of tip dynamics (harmonic oscillator) and lateral surface transport. However, phase shift cross the interface and ratio of the oscillation amplitudes are independent on the cantilever properties and interface capacitance can be calculated from SIM phase data as shown below.