Optical contrast

In plain words

How much a thin stands out from the surface it sits on under a microscope. On the right base – usually silicon coated with a thin layer of glassy oxide – even a of atoms becomes visible through an ordinary optical microscope, thanks to the same effect that paints colours on a soap bubble.

Going deeper

A single layer absorbs only a few percent of light, yet it is visible under an ordinary microscope on the right substrate: light reflected from the flake interferes with light reflected from beneath the oxide, and the flake shifts the balance. Which oxide thickness works depends on the colour of the light.

Interference, not absorption

Graphene absorbs about 2.3% of visible light – far too little to see directly. What makes it visible is interference. Light reflected from the top surface of the flake and light that travels down through the oxide, reflects from the silicon and comes back, meet again with a phase difference set by the oxide thickness and the wavelength. Adding one atomic layer changes both the amplitude and the phase of the first reflection, and near the right thickness that small change alters the total reflected intensity by several percent – enough for the eye.

A Fresnel-law calculation reproduces the measured contrast quantitatively, which is why the effect can be designed rather than discovered by trial.

Choosing the substrate and the light

Because the interference condition depends on both thickness and wavelength, the standard 300 nm oxide gives good contrast for green light but poor contrast at other colours, and a flake that is obvious under one filter can vanish under another. About 100 nm of oxide is better still for visual detection, and with monochromatic illumination almost any oxide thickness can be made to work by choosing the wavelength.

The same reasoning extends beyond graphene: monolayers are found on tuned oxides in the same way, and the contrast against thickness curve is used to count layers, since each added layer changes the reflected intensity in a roughly stepwise manner. On unoptimised – sapphire, glass, thick metal – flakes can be nearly invisible, which is a real obstacle when transferring onto arbitrary targets.

A quick tool, with limits

Optical contrast is the fastest way to find flakes and to guess a layer count: it needs no vacuum, no contact and no damage, and it can be automated, which is how large flake-searching setups scan whole .

It is not a measurement of thickness, though. Contrast depends on illumination spectrum, camera response, objective numerical aperture, oxide thickness tolerance and any residue under the flake, so calibration is per setup rather than universal. The sensible practice is to calibrate against or once on a given microscope and substrate, then use contrast as the routine screen – and to treat any absolute layer assignment from contrast alone as provisional.

For specialists

The difference in reflected intensity between a flake and its substrate, enhanced by thin-film interference in the oxide layer.

Where this comes from

Making graphene visible Blake et al. · Applied Physics Letters 91, 063124 (2007) cited by 1,799
Fine structure constant defines visual transparency of graphene Nair et al. · Science 320, 1308 (2008) cited by 9,117
Visibility of dichalcogenide nanolayers Benameur et al. · Nanotechnology 22, 125706 (2011) cited by 452

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

Wafer and wafer-scale growth

A wafer is the thin, round slice of ultra-pure silicon – today 300 millimetres across – on which computer chips are made, hundreds at a time. Wafer-scale growth means making a 2D material evenly over a whole wafer rather than as scattered flakes, which is what any factory needs. For the best 2D materials that is still hard: a sheet one atom thick has to have the same thickness, quality and orientation from one edge of a dinner-plate-sized disc to the other.

The substrate format of the semiconductor industry – 200 and 300 mm silicon wafers, with sapphire, SiC and glass for particular processes – and the scale at which a material must be grown, transferred and processed to enter manufacturing. Wafer-scale growth of 2D materials uses CVD and MOCVD of TMDCs, CVD of graphene and hBN, and MBE, with targets of uniform layer number, low defect and grain-boundary density and, increasingly, a single orientation on vicinal sapphire or Cu(111). The obstacles are the growth temperature against the thermal budget of a finished wafer (growth on the back end of line needs to stay below about 400 to 450 °C), the transfer from growth substrate to device wafer, and metrology that confirms thickness and quality across the wafer at production speed.

Full explanation