Chapter 32D Carbon Thin Films

§3.1 Scope

This chapter concerns a 2D carbon thin-film programme for hardware security. Its components are a physics-grounded Raman characterisation pipeline, built on the interpretation of Ferrari and Robertson [FR00]; a deterministic synthetic corpus and a verification harness that test the pipeline against spectra of known parameters before it is trusted with measured ones; and an Ed25519-signed provenance ledger into which every acquisition and every fit is written. The programme is moving from modelled to measured data in collaboration with academic characterisation partners. The chapter gives the physical background, describes the pipeline, and states what a measurement must satisfy to count as evidence in the sense of §1.4.

§3.2 Raman spectroscopy of carbon films

Raman scattering measures the vibrational modes of a material through the frequency shift of inelastically scattered light. For sp²-bonded carbon the first-order spectrum is dominated by two features. The G band, near 1580 cm⁻¹ in graphite, is the in-plane stretching mode of sp² pairs and is present in all sp² carbon, whether in rings or chains. The D band, near 1350 cm⁻¹ at 2.41 eV excitation, is a breathing mode of six-fold rings that is forbidden in perfect graphite and becomes active only in the presence of disorder; its intensity relative to G is therefore the principal measure of disorder. A weaker disorder band, D′, appears near 1620 cm⁻¹. The second-order 2D band near 2700 cm⁻¹ is the overtone of D, is active without disorder, and in graphene its shape distinguishes a single layer from a few layers [FCS06], [MPDD09].

The D and 2D bands are dispersive: their positions shift with excitation energy, by about 50 cm⁻¹ per eV for D [FR01] and roughly twice that for 2D. Band positions are therefore never quoted without the excitation wavelength, and a pipeline that compares spectra taken with different lasers must correct for dispersion before comparing anything else.

Ferrari and Robertson organised the evolution of these features into a three-stage amorphisation trajectory that runs from graphite to tetrahedral amorphous carbon [FR00]. In stage 1, graphite becomes nanocrystalline graphite: the G band moves from about 1581 to about 1600 cm⁻¹, the D band appears, and $I(\mathrm{D})/I(\mathrm{G})$ rises in proportion to $1/L_a$, the Tuinstra–Koenig relation [TK70]. In stage 2, nanocrystalline graphite becomes low-sp³ amorphous carbon: the G band falls from about 1600 to about 1510 cm⁻¹, and $I(\mathrm{D})/I(\mathrm{G})$ falls towards zero, now in proportion to $L_a^2$. In stage 3, amorphous carbon becomes tetrahedral amorphous carbon with a high sp³ fraction: the G band rises again from about 1510 to about 1570 cm⁻¹ and the D band is essentially absent. Because G position and $I(\mathrm{D})/I(\mathrm{G})$ are not monotonic across the whole trajectory, the same pair of values can occur in two stages; the width of the G band and the dispersion of its position with excitation energy resolve the ambiguity. Any pipeline that assigns a stage to a spectrum must do so with all of these quantities, not with one.

§3.3 The characterisation pipeline

The pipeline turns a raw spectrum into a small set of quantities with stated uncertainties, and it does so in fixed, recorded steps. Acquisition records the instrument, objective, grating, excitation wavelength, power at the sample, integration time, number of accumulations, and the sample and site identifiers. Calibration references the Raman shift axis to the first-order silicon line at 520.5 cm⁻¹ before and after each session, and records both readings. Baseline correction removes fluorescence and substrate background with a stated model whose parameters are kept. Peak fitting fits the G band with a Breit–Wigner–Fano line and the D band with a Lorentzian, following [FR00], and the 2D band with one or more Lorentzians as the layer count requires; each fit returns position, width, and area with covariances. Derived quantities are the intensity ratio, the dispersion-corrected positions, and, where the regime permits, an estimate of $L_a$. Stage assignment places the spectrum on the Ferrari–Robertson trajectory using G position, G width, $I(\mathrm{D})/I(\mathrm{G})$, and, when two excitation wavelengths are available, the G dispersion. Each step's inputs, parameters, and outputs are serialised and written to the ledger as a receipt.

§3.4 Synthetic corpus and verification harness

A pipeline is not trusted with measured spectra until it has recovered known parameters from synthetic ones. The synthetic corpus is generated deterministically from a seed: for each entry, band positions, widths, intensities, baseline shape, and noise level are drawn from stated distributions covering the three stages, the spectrum is synthesised, and the generating parameters are stored beside it. Because the corpus is deterministic, it can be regenerated exactly by anyone with the seed and the generator, and any change to the generator is a change to the corpus that the ledger records.

The verification harness runs the pipeline over the corpus and compares recovered parameters with generating ones. It reports bias and variance for each quantity as a function of noise level and stage, the rate of correct stage assignment, and the cases in which the pipeline declines to assign a stage. Thresholds for each are fixed in advance; a pipeline version that fails them is not used on measured data. Every harness run is itself written to the ledger, so that the version of the pipeline that produced any measured result can be traced to the harness run that qualified it.

§3.5 Provenance of measurements

Each acquisition, calibration, fit, and harness run is written at the moment it is made as a receipt in the form of §2.2: the actor is the acquisition or analysis software instance, identified by its own key; the digest is that of the serialised record; the sequence number is contiguous per instrument and per analysis host, so that a missing spectrum is detectable as a gap. Where a sample moves between laboratories, the chain head should move with it, so that each side's ledger commits to the state of the other's at the moment of transfer.

Independent repetition is the test that a measurement is evidence rather than observation. A partner laboratory, given a sample, the acquisition protocol, and the pipeline version, acquires and analyses independently; the two ledgers are then compared receipt by receipt. Agreement within the stated tolerance qualifies the result; disagreement is itself recorded and reported as a finding.

§3.6 Electronic-structure background

The security-relevant properties of a carbon thin film follow from its electronic structure, which Raman spectroscopy probes indirectly. For a single graphene layer the nearest-neighbour tight-binding model gives the π-band dispersion of §N, equation N.3, with a linear crossing at the $\mathbf{K}$ points and a Fermi velocity near $10^6$ m s⁻¹ [W47], [CGPNG09]. Disorder of the kind measured by the D band opens scattering channels that this ideal model omits, and the transport properties of a film, such as the on/off ratio of a field-effect device built on it, degrade accordingly. Relating the Raman quantities of §3.3 to device behaviour is the modelling side of the programme. The findings filed under this chapter report that side first, each labelled MODELLED, and will report the measured side as it arrives.