Carbon nanotubes as a tip calibration standard for electrostatic scanning probe microscopies

Abstract

Scanning Surface Potential Microscopy (SSPM) is one of the most widely used techniques for the characterization of electrical properties at small dimensions.Applicability of SSPM and related electrostatic scanning probe microscopies for imaging of potential distributions in active micro-and nanoelectronic devices requires quantitative knowledge of tip-surface contrast transfer. Here we demonstrate the utility of carbonnanotube-based circuits to characterize geometric properties of the tip in the electrostatic scanning probe microscopies (SPM). Based on experimental observations, an analytical form for the differential tip-surface capacitance is obtained. For small tip-surface separations tip geometry can be accounted for using the spherical tip approximation and the corresponding geometric parameters can be obtained from electrostatic force-or force gradient distance and bias dependences.[5,6] Such a calibration process is often tedious and tip parameters tend to change with time due to mechanical tip instabilities. [7] Alternatively, the tip contribution to measured surface properties can be quantified directly using an appropriate calibration method.[8] If known, a tip-surface transfer function can be used to deconvolute the tip contribution from experimental data and obtain the exact surface potential distribution. Recently, systems with well defined metal-semiconductor interfaces have been considered as a "potential step" standard.[9] However, the presence of surface states and mobile charges significantly affects potential distributions of even grounded surfaces. In addition, such a standard is expected to be sensitive to environmental conditions (humidity, temperature, etc). [10] Well defined geometry and stability of carbon nanotubes enabled their successful application as SPM probes. [11,12,13,14] Here we propose a carbon nanotube based standard for tip calibration in electrostatic SPM. An ac voltage bias is applied to the nanotube resulting in the oscillation of the SPM tip due to the capacitive force. [15,16] 3 Taking into account that the typical lateral size of the nanotube is significantly smaller than the tip radius of curvature, the nanotube effectively probes the tip geometry. (Fig. 1a). The tip acquires surface topography in the intermittent contact mode and then retraces the surface profile maintaining constant tip-surface separation. Measurements were performed using CoCr coated tips (Metal coated etched silicon probe, Digital Instruments, l ≈ 225 µm, resonant frequency ~ 62 kHz) and Pt coated tips (NCSC-12 F, Micromasch, l ≈ 250 µm, resonant frequency ~ 41 kHz), further referred to as tip 1 and tip 2. A lock-in amplifier is used to determine the magnitude and phase of cantilever response. The output amplitude, R, and phase shift, θ, are recorded by the AFM electronics (Nanoscope-IIIA, Digital Instruments). To avoid cross-talk between the sample modulation signal and topographic imaging, the frequency of ac voltage applied to the nanotube (50 kHz) was selected to be far from the canti...

Tip-Modulation Scanned Gate Microscopy

“…The EFM signal from a nanotube on an insulator is known to be well described, empirically, by a Lorentzian function of the distance x perpendicular to the nanotube. 16,17 We find that tmSGM peaks such as that in Figure 3 are also accurately fit by Lorentzians, consistent with the parallel between tmSGM and EFM. The narrower linewidth for tmSGM compared with SGM can then be quantified as follows.…”

“…16 (~ μm) decay back to steady state, which is not evident in the tmSGM signal. The better signal to noise ratio is a result of the lock-in detection scheme, as has been employed for SGM before.…”

Quantitative Kelvin probe force microscopy of current-carrying devices

“…SWNT devices are an excellent test case that have proven to be quite complex in past research. 12,13,[16][17][18][19][20][21][22][23] Because of their extremely small diameters (1 nm) and low carrier densities (1 to 100 lm À1 ), SWNT channels couple very weakly to KPFM probe tips 12 and some researchers have concluded that SWNT potential gradients are too small to image reliably. 13,16,22 Devices in our study consisted of dilute SWNTs synthesized by chemical vapor deposition directly on 4 00 p þþ silicon wafers with 250 nm backgate oxides.…”

Electrostatic Force Microscopy and Kelvin Force Microscopy as a Probe of the Electrostatic and Electronic Properties of Carbon Nanotubes

“…The crucial issue to understand KFM experiments on transistors is to derive quantitative information from KFM images, even though the role of side capacitances has been pointed out earlier [15,43]. We here present a KFM study performed on Pd-contacted CNTFETs fabricated on an ∼ 320 nm-thick SiO 2 layer, which addresses this issue [48].…”