RAVAN: Why We Built Our Own
Compact Model from First Principles

The Problem with Borrowed Models

When you simulate a new transistor technology, you face an immediate practical problem: there is no SPICE model for your device. It does not exist yet. Nobody has built one because nobody has built the device.

The standard workaround is to borrow a model from a related technology and adjust its parameters. For carbon nanotube FETs, the most commonly used model is the Stanford CNFET model published by Deng and Wong in 2007. It is well-cited, peer-reviewed, and available as a SPICE subcircuit.

There is one problem. It is a Level-1 MOSFET wrapper.

The Stanford model takes the classical MOSFET square-law equations — developed for bulk silicon in the 1960s — and maps CNT parameters onto the MOSFET coefficients. The channel width is set to the tube diameter. The threshold voltage is set to half the bandgap. The transconductance parameter is calibrated to match published CNT measurements. Then the MOSFET equations do the rest.

For many purposes, this works surprisingly well. The IV curves have the right shape. The threshold behaviour is reasonable. The simulation converges quickly. For a provisional patent filing — where the goal is to demonstrate feasibility — it is adequate.

But adequate is not the same as correct.

What the Perfect Symmetry Hides

We used the Stanford model for our provisional SPICE simulations. The results were clean: the ternary inverter transfer curve showed three distinct states, the output swung rail-to-rail, and the current symmetry ratio between the positive and negative trit states was measured at exactly 1.000000.

That last number should have been a warning.

A current symmetry ratio of exactly 1.000000 means the device produces precisely identical current magnitudes for electron conduction and hole conduction at matched gate voltages. In the Stanford model, this happens because the N-type and P-type model cards use identical parameters with opposite signs. The symmetry is a model artefact, not a physical measurement.

No physical device has perfect symmetry. The electron and hole Schottky barriers at the metal-CNT contacts are never identical. The workfunction alignment between gate and channel is never exactly at midgap. A model that claims perfection is a model that is not modelling reality.

Worse: the Stanford model breaks down above approximately 370 K. The Level-1 MOSFET temperature equations — which use empirical polynomial fits calibrated for silicon — produce unphysical results when applied to a 1 nm carbon nanotube at elevated temperatures. Our temperature sweep showed the symmetry ratio collapsing from 1.000 at 300 K to 0.45 at 400 K. That is not a gradual physical degradation. That is a model failure.

For complete patent specifications — where the simulation evidence must be credible and defensible — we needed something better.

Building from First Principles

The RAVAN model — Reconstructed Ambipolar Virtual-source Analytical Nanodevice — replaces the MOSFET wrapper with physics that actually describes what happens inside a carbon nanotube field-effect transistor.

Landauer Transport

In a bulk silicon transistor, current is the result of millions of electrons drifting through a channel, scattering off lattice vibrations and impurities along the way. The drift-diffusion equations that describe this process are the foundation of classical MOSFET models.

In a 20 nm carbon nanotube, the physics is different. The channel is shorter than the electron mean free path. Electrons travel from source to drain without scattering — ballistic transport. The correct description is the Landauer formalism, which treats the channel as a quantum transmission line and the current as the difference in Fermi-Dirac occupation between the source and drain reservoirs.

The Landauer current for a single CNT subband with four conducting modes (two spin, two valley) is:

I = (4e²/h) × V_T × [F⊂0(η_source) − F⊂0(η_drain)]

where F₀(η) = ln(1 + exp(η)) is the Fermi-Dirac integral of order zero, V_T = kT/q is the thermal voltage, and η encodes the energy difference between the carrier reservoir and the channel barrier.

This single equation — derived from quantum mechanics, not fitted to measurements — gives us correct temperature dependence for free. The Fermi-Dirac statistics handle the transition from degenerate to non-degenerate regimes without any empirical temperature coefficients. The model is valid from liquid helium to red-hot carbon.

Virtual Source Saturation

The raw Landauer equation has a subtlety that becomes a problem in circuit simulation: it allows unlimited reverse current injection from the drain terminal when the drain-source voltage is large. In a simple complementary inverter, this means the "off" transistor can inject as much current as the "on" transistor, preventing the output from reaching the supply rails.

The fix comes from the Virtual Source framework developed at MIT. Instead of computing the full source-drain Fermi-Dirac difference, the current is expressed as:

I = (4e²/h) × V_T × F⊂0(η_source) × tanh(V_DS / 2V_dsat)

The tanh function smoothly interpolates between the linear region (small V_DS, current proportional to voltage) and saturation (large V_DS, current limited by the source-side barrier). The saturation voltage V_dsat depends on how strongly the gate has opened the channel: when the gate is off, V_dsat is small and the current saturates almost immediately, preventing drain-side injection.

This is physically correct: in a well-designed FET, the gate controls the channel barrier, and the drain cannot override that control. The tanh saturation captures this physics elegantly.

Realistic Asymmetry

A carbon nanotube is a symmetric object. Its conduction band and valence band are mirror images about the Fermi level (in the nearest-neighbour tight-binding approximation). This is why the Stanford model gives perfect 1.000 symmetry — the underlying band structure genuinely is symmetric.

But a transistor is not just a tube. It has contacts, a gate electrode, and an electrostatic environment. These break the intrinsic symmetry:

• Contact asymmetry: The Schottky barriers at the source and drain contacts have slightly different heights for electrons versus holes, due to Fermi level pinning at the metal-CNT interface.
• Gate workfunction: The gate electrode's work function is never exactly at the CNT midgap. Even a few millielectronvolts of offset shifts the threshold voltage asymmetrically for the two carrier types.

RAVAN captures both effects through two parameters: a workfunction offset (in millivolts) and a hole current scaling factor (a fraction slightly below unity). Together, these produce a current symmetry ratio that is high — comfortably above the thresholds specified in the patent claims — but not trivially perfect.

A reviewer who sees 0.993 thinks: "they modelled the asymmetry and the device still meets spec." A reviewer who sees 1.000 thinks: "they used a symmetric model, so the result is predetermined." The difference matters.

GNR Quantum Capacitance

The THATTE device uses a graphene nanoribbon (GNR) as the gate electrode instead of a conventional metal. This is not merely a materials substitution — it changes the electrostatics of the gate.

A metal gate has effectively infinite quantum capacitance: its density of states is so large that adding or removing a few electrons does not change its Fermi level. A GNR gate, being a quasi-one-dimensional conductor, has a finite quantum capacitance that appears in series with the oxide capacitance.

The total gate capacitance becomes:

1/C_gate = 1/C_oxide + 1/C_quantum

For the dimensions in the THATTE device, the quantum capacitance reduces the effective gate capacitance to approximately 36% of the classical oxide value. This is a significant effect that the Stanford model completely ignores — it treats the gate as a metal with infinite DOS.

In RAVAN, this effect is folded into the gate coupling coefficient α_G, which represents the fraction of the gate voltage that appears as channel potential. With the GNR quantum capacitance included, α_G is measurably lower than the classical estimate, and the subthreshold swing is correspondingly wider.

The Name

In the Puranic tradition, Ravan was not merely a king or a warrior. He was a scholar of extraordinary intellect who, on the orders of Shiva, reconstituted the Vedas — the foundational knowledge of civilisation — and disseminated them for the benefit of all. The act of reconstructing scattered knowledge into a coherent whole and giving it freely is, in the tradition, one of the highest acts of scholarship.

RAVAN — Reconstructed Ambipolar Virtual-source Analytical Nanodevice — reconstructs the physics of the THATTE device from scattered first principles (Landauer transport, Fermi-Dirac statistics, quantum capacitance, Schottky barrier theory) into a coherent compact model. The physics is all published. The constituent theories are all known. What is new is the synthesis: combining these elements to describe a specific device that has not been built before.

Like the scholar Ravan who took existing knowledge and gave it back to humanity in a form they could use — this model takes known physics and assembles it into a tool that anyone can run in an open-source circuit simulator.

What Changes with RAVAN

The most significant change is in the temperature behaviour. The Stanford model uses MOSFET empirical temperature coefficients that were fitted to silicon data. These coefficients have no physical meaning for a carbon nanotube, and they produce nonsensical results outside a narrow range around room temperature. RAVAN uses Fermi-Dirac occupation functions with the actual CNT bandgap, so the temperature dependence is derived from thermodynamics rather than curve fitting.

In verification testing, RAVAN produces stable, physically reasonable results from 77 K (liquid nitrogen) through 500 K (above the boiling point of tin) with no convergence issues, no parameter adjustments, and no model breakdowns. The Stanford model collapses at 400 K.

Impact on the Patent Portfolio

Every claim in the THATTE patent portfolio that references a quantitative measurement — current symmetry ratios, threshold voltage values, noise suppression factors, temperature stability ranges — is backed by SPICE simulation evidence.

With the Stanford model, a patent examiner could reasonably question whether the perfect symmetry result (1.000) is an artefact of the model rather than a property of the device. With RAVAN, the symmetry emerges from physical parameters (Schottky barrier heights, workfunction alignment) that have measurable analogues in real devices. The result is more credible precisely because it is not perfect.

We are now re-running all device-level simulations across Patents P1, P2, and P6 using RAVAN. The complete specification filings will include both sets of results: the Stanford model results from the provisional era, and the RAVAN results that replace them.