Atomic force microscopy (AFM)

In plain words

A tip on a tiny springy arm is moved across a surface and its bending is measured, mapping height point by point – much as a fingertip reads Braille. It works on anything, conducting or not, which is why it is the routine way to check how thick a is.

Going deeper

AFM measures height by feeling the surface with a tip, so it works on insulators and conductors alike. The apparent height of a monolayer is not its crystallographic thickness: in tapping mode, poorly chosen settings can add up to about a nanometre to a graphene step.

How it measures

The atomic force microscope, introduced by Binnig, Quate and Gerber in 1986, scans a sharp tip on a flexible cantilever across a surface. A laser reflected from the back of the cantilever onto a segmented detects tiny deflections, and a feedback loop moves the sample or tip to keep the interaction constant, recording height at every point.

In contact mode the tip touches the surface continuously. In tapping, or intermittent-contact, mode the cantilever oscillates near resonance and the feedback holds its amplitude constant, which is gentler on soft samples and loose flakes. Vertical noise can be well below an ångström, while lateral resolution is limited by the tip radius, typically several nanometres. Unlike tunnelling microscopy, AFM needs no electrical conduction.

Why a monolayer rarely measures its true thickness

Graphene layers are 0.34 nm apart, yet on silicon oxide are routinely reported between about 0.4 and 1 nm. The tip interacts differently with the flake and with the , water and adsorbates can sit underneath the flake, and in tapping mode the chosen free amplitude and set-point change how hard the tip presses on each surface. A systematic study found that poorly chosen amplitudes can add as much as a nanometre to the measured height.

The reliable part of a measurement is the step between terraces within the same flake, where tip and material are unchanged. Layer counts are best confirmed with an independent method such as or , and the mode and settings reported with any thickness.

More than height

Variants of AFM map far more than topography. Kelvin probe force microscopy measures surface potential, revealing , differences and layer number. Conductive AFM maps local current through a flake. Piezoresponse force microscopy images and domains. Lateral force microscopy shows contrast that can distinguish crystal orientations and stacking domains, and phase images separate materials by how they dissipate energy.

The tip is also a tool. Pressing on suspended measures stiffness and breaking strength, and scanning in contact mode can sweep from a device surface. Tips wear and pick up contamination, and a blunt tip broadens narrow features, so sharp edges and small particles always look wider than they are.

For specialists

Force microscopy in contact, tapping or non-contact mode, used for thickness, roughness, bubbles and polymer residue, with variants for surface potential (KPFM) and local conductivity (c-AFM). Apparent height is not the crystallographic thickness: the tip interacts differently with flake and substrate, so a monolayer commonly reads between 0.4 and 1 nm. Quote the mode, and calibrate against a step of known height.

Where this comes from

Atomic force microscope Binnig et al. · Physical Review Letters 56, 930 (1986) cited by 14,730
Anomalies in thickness measurements of graphene and few layer graphite crystals by tapping mode atomic force microscopy Nemes-Incze et al. · Carbon 46, 1435 (2008) cited by 609

Substrate

The base a thin film or flake sits on – often a polished slice of silicon, glass or sapphire. For a crystal one atom thick, the substrate is not just a table: its bumps, stray charges and vibrations reach right into the sheet and change how it conducts and glows. That is why the same material can behave differently on two substrates, and why the flattest, cleanest one – boron nitride – gives the best results.

The material beneath a 2D layer. It acts on the layer through surface roughness, charged impurities, surface optical phonons, dielectric screening, strain and charge transfer, and during growth it sets orientation through epitaxy. Replacing SiO₂ with hexagonal boron nitride, which is atomically flat and nearly free of dangling bonds and charge traps, improved the mobility and charge homogeneity of graphene by close to an order of magnitude.

Full explanation

Ferroelectricity

A material that holds an electric polarisation – one side slightly positive, the other slightly negative – with no voltage applied, and that can be flipped by a field and stay flipped. That memory of the last field applied is what makes it useful for storing data.

A spontaneous, switchable electric polarisation produced by a structural distortion that breaks inversion symmetry. In 2D the usual obstacle – depolarising fields destroying the polarisation as a film thins – is sidestepped in three ways: in-plane polarisation, layered compounds whose dipoles survive to the monolayer such as CuInP₂S₆ and In₂Se₃, and sliding ferroelectricity, where the polarisation belongs to the interface between layers rather than to the layers themselves.

Full explanation

Solid lubricant

A powder or coating that makes surfaces slide over each other easily without oil. Layered crystals such as graphite, MoS₂, WS₂ and hBN are natural lubricants: their layers are strongly bonded inside but only weakly stuck to each other, so they shear apart and coat the rubbing surfaces with slippery sheets. They work where oil cannot – in a vacuum, in space or at high temperatures – and are among the oldest uses of layered materials.

Lamellar solids whose weak interlayer bonding allows easy shear: graphite (which needs adsorbed water or vapour to lubricate well), MoS₂ and WS₂ (best in vacuum and dry gas, oxidising in humid air), and hBN (stable to high temperature in air). Used as burnished or sputtered films, bonded coatings and additives in oils and greases, they reach friction coefficients of a few hundredths, and in space mechanisms MoS₂ is a standard. At the nanoscale, incommensurate contact between layers can make friction nearly vanish – structural superlubricity, seen when graphite flakes are rotated out of register and in MoS₂ – while friction on atomically thin sheets rises as they get thinner because the sheet puckers ahead of the tip.

Full explanation

2D membrane

A sheet that lets some molecules through and holds others back. A perfect layer of graphene is so tight that not even helium gets through, so useful membranes need openings: tiny holes made in a single layer, or the narrow gaps between flakes stacked like a pack of cards. Because such a membrane is only atoms thick, water or gas can pass far faster than through today’s plastic membranes, which could make filtering, purifying water or separating gases cheaper.

Separation membranes made from 2D materials, in two designs: nanoporous single layers (graphene, hBN, MoS₂ with pores opened by ion irradiation, oxidative etching or defects), whose pore size sets the selectivity, and laminates of stacked flakes (graphene oxide, MXenes, COF and MOF nanosheets), whose interlayer channels – often swelling in water – act as sieves. Pristine graphene is impermeable to gases including helium, yet transmits protons; atomic thickness promises high permeance, and restraining the laminate spacing can exclude hydrated ions. Against mature polyamide reverse-osmosis membranes the obstacles are large defect-free areas, swelling and stability in water, fouling and cost. The word also names any freestanding thin film, as in oxide membranes lifted off a sacrificial layer.

Full explanation

Layer transfer

Moving an atomically thin layer from where it was made to where it is needed – from the copper foil it grew on to a silicon wafer, or from a flake on tape onto another flake. The layer is too thin to pick up on its own, so it is carried on a polymer film or a soft stamp, put down, and the carrier removed. Each step risks tears, wrinkles, trapped bubbles and a film of leftover polymer, which is why transfer is often the dirtiest step in making a 2D device.

The step that moves a 2D layer from its growth substrate or exfoliation source to a target substrate or stack. Wet transfer coats the layer with a supporting polymer, usually PMMA, detaches it by etching the growth substrate or by electrochemical bubbling, and floats it onto the target before the polymer is dissolved. Dry transfer picks layers up with a viscoelastic PDMS stamp or a polymer film such as polycarbonate, often using the van der Waals adhesion of a top flake, and releases them by heating. The costs are cracks and wrinkles, trapped water, hydrocarbons and polymer residue, strain and doping, and – at wafer scale – yield that compounds with every transfer, which is why growth directly on the target and transfer-free routes are pursued.

Full explanation