NE 353: Nanoprobing and Lithography

Estimated study time: 10 minutes

Table of contents

Sources and References

Bhushan (ed.), Springer Handbook of Nanotechnology
Wiesendanger, Scanning Probe Microscopy and Spectroscopy: Methods and Applications (Cambridge)
Madou, Fundamentals of Microfabrication and Nanotechnology (CRC Press)
Wagner and Harned, Lithography Gets Extreme, review articles in Nature Photonics
Online: Bruker AFM University, AIST-NT tutorials, nanoHUB metrology modules

Chapter 1: Foundations of Scanning Probe Microscopy

1.1 The Tunneling Phenomenon

Scanning tunneling microscopy (STM) exploits the exponential sensitivity of quantum tunneling current to gap width. For a vacuum barrier of height \( \phi \) and width \( d \), the tunneling probability is

\[ T \propto \exp\!\left( -2\kappa d \right), \qquad \kappa = \frac{\sqrt{2 m_e \phi}}{\hbar}. \]

With typical work functions \( \phi \approx 4 \) eV, a gap change of 1 Å modulates the current by roughly one order of magnitude, giving the STM its sub-Ångström vertical resolution. In the constant-current mode, a feedback loop moves a piezoelectric scanner to hold tunneling current fixed as the tip rasters the surface, and the vertical displacement provides the topographic image. In the constant-height mode, only the current is recorded while the tip moves at fixed \( z \), enabling faster scans on atomically flat samples.

1.2 Spectroscopy Modes

Scanning tunneling spectroscopy measures \( dI/dV \) at fixed tip position to probe the local density of states (LDOS):

\[ \frac{dI}{dV}(V) \propto \rho_s(E_F + eV)\,\rho_t(E_F). \]

Lock-in amplification at a small modulation voltage extracts \( dI/dV \) with low noise. This resolves individual molecular orbitals, superconducting gaps, Kondo resonances, and dopant states.

Chapter 2: Atomic Force Microscopy

2.1 Tip-Sample Forces

Atomic force microscopy (AFM) senses the force between a sharp tip and a surface through a compliant cantilever. Forces include van der Waals (attractive at long range), short-range Pauli repulsion, capillary menisci in ambient conditions, and electrostatic or magnetic forces when relevant.

The Lennard-Jones potential

\[ U(r) = 4\varepsilon\!\left[\left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6}\right] \]

captures the transition from attraction to repulsion. A cantilever of stiffness \( k \) deflects by \( \Delta z = F/k \); for \( k \sim 0.1 \) N/m and \( F \sim 100 \) pN, deflections are order of a nanometre, easily resolved by laser beam-bounce detection.

Contact mode rasters the tip in the repulsive regime with constant force; non-contact stays in attraction; tapping (intermittent contact) oscillates the cantilever near resonance and samples both regimes briefly, minimising lateral forces on soft samples.

2.2 Dynamic Imaging

In tapping mode the cantilever oscillates near its resonant frequency \( \omega_0 \) with quality factor \( Q \). The phase shift relative to drive reflects energy dissipation and encodes contrast between materials of different viscoelastic response. Frequency-modulation AFM locks the drive at the tip’s instantaneous resonance, which shifts with tip-sample force gradient

\[ \Delta f = -\frac{f_0}{2k}\frac{\partial F}{\partial z}. \]

Under ultra-high vacuum with qPlus or tuning-fork sensors, FM-AFM resolves individual bonds of adsorbed molecules.

Chapter 3: Scanning Near-Field Optical Microscopy

3.1 Breaking the Diffraction Limit

Conventional far-field optics are constrained by Abbe’s limit \( \approx \lambda/2 \). Scanning near-field optical microscopy (SNOM/NSOM) overcomes this by confining light within a subwavelength aperture (tapered fibre with metal coating) or at the apex of a sharp metallic tip (apertureless SNOM). The evanescent field decays on the scale of the aperture, and by holding the tip within that distance — maintained by shear-force feedback — resolutions of 20–50 nm are routine and tens of nanometres attainable with plasmonic enhancement.

3.2 Tip-Enhanced Spectroscopy

Tip-enhanced Raman spectroscopy (TERS) combines a gold or silver AFM tip with confocal Raman excitation. Localised surface plasmons at the apex enhance both excitation and scattering, boosting signal by \( |E_{loc}/E_0|^{4} \), approaching factors of \( 10^{6}-10^{8} \) that permit vibrational imaging of single molecules.

Chapter 4: Photon-Based Lithography at the Extreme

4.1 Deep-UV and Immersion

Optical lithography resolution from the Rayleigh criterion is

\[ R = k_1 \frac{\lambda}{\mathrm{NA}}, \]

with \( k_1 \) a process-dependent constant floored at 0.25. Immersion lithography fills the space between final lens and wafer with a liquid of index \( n > 1 \), raising the effective numerical aperture to 1.35 and shrinking features below 40 nm at \( \lambda = 193 \) nm. Multiple patterning (litho-etch-litho-etch, self-aligned double patterning) effectively divides pitch by two or four but multiplies process cost and overlay budget.

4.2 Extreme Ultraviolet Lithography

Extreme-UV (EUV) lithography uses \( \lambda = 13.5 \) nm generated by laser-produced tin plasmas. At such wavelengths, all materials absorb, so reflective optics (molybdenum/silicon multilayer mirrors) replace refractive lenses, and vacuum chambers replace the ambient air path. Masks are reflective with patterned absorber. Source power at intermediate focus now exceeds 250 W, enabling commercial 5 nm and 3 nm logic nodes.

The depth of focus scales as \( \mathrm{DOF} = k_2 \lambda / \mathrm{NA}^{2} \), so aggressive resolution comes at the cost of wafer flatness and focus control specifications measured in nanometres.

Chapter 5: Particle-Beam Lithographies

5.1 Electron-Beam Lithography

Electron-beam lithography writes patterns serially by deflecting a focused electron beam through a resist such as PMMA or HSQ. Resolution is limited by beam diameter, resist contrast, and proximity effects from backscattered electrons producing a forward-scattered core and a broader backscatter halo, modelled by a double-Gaussian point-spread function. Proximity correction adjusts local dose so that the convolution of PSF and dose gives the intended pattern.

E-beam throughput is low (centimetre-scale pattern times in hours), limiting use to mask making and research. Multiple-beam systems multiplex throughput.

5.2 X-Ray and Focused Ion Beam

X-ray lithography uses soft X-rays (0.4–5 nm) through a 1:1 mask in close proximity, achieving sub-50 nm resolution without complex optics. Its adoption is limited by mask fabrication difficulty and source brightness.

Focused ion beam (FIB) systems, usually gallium, image and mill simultaneously. FIB is indispensable for site-specific cross-sectioning, prototype modification, and TEM sample preparation. Ion species such as helium and neon from gas field sources yield sub-nanometre beams for lithography and imaging.

Chapter 6: Imprint and Soft Lithographies

6.1 Nanoimprint Lithography

Nanoimprint lithography (NIL) replicates a rigid master (silicon or quartz, patterned by e-beam) by mechanical deformation of a polymer: thermal NIL heats a thermoplastic above its glass transition \( T_g \) and cools under pressure, while UV-NIL uses a liquid photopolymer cured by ultraviolet light through a transparent template. Feature fidelity below 10 nm is demonstrated, and throughput via step-and-repeat or roll-to-roll is attractive for patterned media, optical films, and biochips.

A UV-NIL process might pattern 40 nm half-pitch lines across a 300 mm wafer in under a minute per exposure, compared to far slower e-beam writing of the same total area.

6.2 Soft Lithography

Soft lithography casts an elastomer (commonly polydimethylsiloxane, PDMS) against a master to produce stamps used for microcontact printing, replica moulding, or microfluidic channel formation. Microcontact printing transfers self-assembled monolayers — for example, alkanethiols onto gold — with micrometre-to-submicrometre resolution, enabling patterned surface chemistry on curved or flexible substrates without need for photoresist.

PDMS is gas permeable, biocompatible, and transparent in the visible, making it the workhorse for lab-on-chip devices. Its low modulus limits aspect ratios and feature sizes to about 100 nm before pattern collapse or elastic deformation dominates.

6.3 Choosing Among Techniques

Each lithography has a trade-off triangle of resolution, throughput, and cost. Optical lithography dominates volume manufacturing. EUV enables the smallest commercial features at very high capital cost. E-beam and FIB are the metrology and mask-making tools as well as research workhorses. Nanoimprint and soft lithography offer nanoscale patterning at low capital cost for niche high-volume products and for research.

Every nanolithographic technique ultimately transfers information from a pattern generator (beam, mask, stamp) to a material through an energy-matter interaction whose range and linearity determine the achievable resolution, fidelity, and defectivity.

Coupling these lithographic techniques with scanning probe metrology closes the process-measurement loop: probes visualise what the lithography writes, while lithography patterns the very tips and circuits that probing requires.