Tauc–Lorentz model¶

The Tauc–Lorentz model is a mathematical formula for the frequency dependence of the complex-valued relative permittivity, sometimes referred to as the dielectric function.

Version: v1 · 2026-09-28 · History
Domain-specific #: 12457
Domain group: Natural Sciences
Origin domain: Physics
Subdomains: Optical Physics, Dielectric Function Models → Physics

Core Idea¶

Tauc–Lorentz model is treated here as the recurring natural sciences, engineering, and health identity summarized by this source-grounded definition: The Tauc–Lorentz model is a mathematical formula for the frequency dependence of the complex-valued relative permittivity, sometimes referred to as the dielectric function.

The Tauc–Lorentz model is a mathematical formula for the frequency dependence of the complex-valued relative permittivity, sometimes referred to as the dielectric function. The model has been used to fit the complex refractive index of amorphous semiconductor materials at frequencies greater than their optical band gap. The dispersion relation bears the names of Jan Tauc and Hendrik Lorentz, whose previous works were combined by G.

The model was inspired, in part, by shortcomings of the Forouhi–Bloomer model, which is aphysical due to its incorrect asymptotic behavior and non-Hermitian character. Despite the inspiration, the Tauc–Lorentz model is itself aphysical due to being non-Hermitian and non-analytic in the upper half-plane. Further researchers have modified the model to address these shortcomings.

For Tauc–Lorentz model, the abstraction is narrower than the article's general subject matter: a positive case must preserve The Tauc–Lorentz model is a mathematical formula for the frequency dependence of the complex-valued relative permittivity, sometimes referred to as the dielectric function. Retaining only the name, a familiar example, or a downstream effect is insufficient. The specialist roles and tests remain anchored in natural sciences, engineering, and health, which is why this identity is domain-specific rather than prime.

Structural Signature¶

Sig role-phrases:

Defining carrier — The imaginary component of \chi^{TL}(E) is formed as the product of the imaginary component of the Lorentz oscillator model and a model developed by Jan Tauc for the imaginary component of the relative permittivity near the bandgap of a material.
Constitutive relation — E is the photon energy (related to the angular frequency by E=\hbar\omega ),.
Operating condition — The dispersion relation bears the names of Jan Tauc and Hendrik Lorentz, whose previous works were combined by G.
Recognition evidence — The model was inspired, in part, by shortcomings of the Forouhi–Bloomer model, which is aphysical due to its incorrect asymptotic behavior and non-Hermitian character.
Admissible variation — \varepsilon_{\infty} is the value of the relative permittivity at infinite energy,.
Characteristic consequence — The real component of \chi^{TL}(E) is obtained via the Kramers-Kronig transform of its imaginary component.
Failure boundary — \Re\left( \chi^{TL}(E) \right) = \frac{2}{\pi} \int_{E_{g}}^{\infty} \frac{\xi \Im\left( \chi^{TL}(\xi) \right)}{\xi^{2} - E^{2}} d\xi.

What It Is Not¶

Not the whole field of natural sciences, engineering, and health. The node requires the specific identity stated by The Tauc–Lorentz model is a mathematical formula for the frequency dependence of the complex-valued relative permittivity, sometimes referred to as the dielectric function.
Not an over-broad reading. E is the photon energy (related to the angular frequency by E=\hbar\omega ),.
Not an over-broad reading. \varepsilon_{\infty} is the value of the relative permittivity at infinite energy,.
Not an over-broad reading. The imaginary component of \chi^{TL}(E) is formed as the product of the imaginary component of the Lorentz oscillator model and a model developed by Jan Tauc for the imaginary component of the relative permittivity near the bandgap of a material.
Not automatically Lorentz oscillator model. Retrieval proximity does not establish equivalence; the two identities must be compared by carrier, operation, and failure boundary.

Scope of Application¶

Tauc–Lorentz model applies literally inside natural sciences, engineering, and health wherever the source-defined carrier and relation can be established. Its documented habitats include:

Documented setting. The Tauc–Lorentz model is a mathematical formula for the frequency dependence of the complex-valued relative permittivity, sometimes referred to as the dielectric function.
Documented setting. The model has been used to fit the complex refractive index of amorphous semiconductor materials at frequencies greater than their optical band gap.
The general form of the model is given by. E is the photon energy (related to the angular frequency by E=\hbar\omega ),.
The general form of the model is given by. \varepsilon_{\infty} is the value of the relative permittivity at infinite energy,.
The general form of the model is given by. The imaginary component of \chi^{TL}(E) is formed as the product of the imaginary component of the Lorentz oscillator model and a model developed by Jan Tauc for the imaginary component of the relative permittivity near the bandgap of a material.
The general form of the model is given by. The real component of \chi^{TL}(E) is obtained via the Kramers-Kronig transform of its imaginary component.

Outside natural sciences, engineering, and health, the name should be retained only when these same operational conditions survive; otherwise the comparison belongs to the broader parent Theory or should be marked as analogy.

Clarity¶

A clear use of Tauc–Lorentz model names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is The Tauc–Lorentz model is a mathematical formula for the frequency dependence of the complex-valued relative permittivity, sometimes referred to as the dielectric function. The strongest recognition evidence in the frozen account is: The model was inspired, in part, by shortcomings of the Forouhi–Bloomer model, which is aphysical due to its incorrect asymptotic behavior and non-Hermitian character. A report should distinguish that evidence from a proxy, consequence, or common implementation. It should also state the qualification E is the photon energy (related to the angular frequency by E=\hbar\omega ),. so that a reader can reproduce the classification rather than infer it from topical resemblance.

Manages Complexity¶

Tauc–Lorentz model compresses multiple natural sciences, engineering, and health details into a stable diagnostic relation. The source shows both the central mechanism—e is the photon energy (related to the angular frequency by E=\hbar\omega ),.—and the practical consequence—the real component of \chi^{TL}(E) is obtained via the Kramers-Kronig transform of its imaginary component. This compression makes cases comparable while leaving parameters, conventions, exceptions, and evidential quality explicit. It is lossy by design: local history and implementation details may be omitted only when they do not alter the defining relation.

Abstract Reasoning¶

Type the carrier. Identify the natural sciences, engineering, and health entities to which the claim applies.
State the relation. Use the source-grounded identity: The Tauc–Lorentz model is a mathematical formula for the frequency dependence of the complex-valued relative permittivity, sometimes referred to as the dielectric function.
Check operation and conditions. The dispersion relation bears the names of Jan Tauc and Hendrik Lorentz, whose previous works were combined by G.
Demand recognition evidence. The model was inspired, in part, by shortcomings of the Forouhi–Bloomer model, which is aphysical due to its incorrect asymptotic behavior and non-Hermitian character.
Test variation. Change an implementation or setting while preserving \varepsilon_{\infty} is the value of the relative permittivity at infinite energy,.
Run the collapse test. Remove the defining operation; if the label still seems equally apt, only a topic or correlate was retained.
Reduce cautiously. When the specialist conditions cannot be carried, route the residual comparison to Theory.

Knowledge Transfer¶

Within the home domain. Knowledge about Tauc–Lorentz model transfers literally when a new case preserves the same carrier type, relation, and recognition test. The Tauc–Lorentz model is a mathematical formula for the frequency dependence of the complex-valued relative permittivity, sometimes referred to as the dielectric function. The model has been used to fit the complex refractive index of amorphous semiconductor materials at frequencies greater than their optical band gap.

Beyond the home domain. Transfer the broader Theory relation when the natural sciences, engineering, and health-specific differentia cannot be filled. Retain the name Tauc–Lorentz model only when the same carrier, operation, and rejection conditions are present literally rather than metaphorically.

Examples¶

Canonical¶

\Im\left( \chi^{TL}(E) \right) = \begin{cases} \frac{1}{E} \frac{A E_{0} C (E - E_{g})^{2}}{(E} - E_{0^{2}). This case is canonical because it supplies a concrete carrier and lets the defining relation be checked rather than merely named.} + C^{2} E^{2}}, & \text{if } E > E_{g} \ 0, & \text{if } E \le E_{g} \end{cases

Mapped back: carrier → the entities in the documented case; operation → The Tauc–Lorentz model is a mathematical formula for the frequency dependence of the complex-valued relative permittivity, sometimes referred to as the dielectric function; recognition evidence → The model was inspired, in part, by shortcomings of the Forouhi–Bloomer model, which is aphysical due to its incorrect asymptotic behavior and non-Hermitian character

Applied / In Practice¶

E is the photon energy (related to the angular frequency by E=\hbar\omega ),. The applied case shows how the identity is used under a second setting or qualification while keeping the same operative relation.

Mapped back: changed setting → The general form of the model is given by; invariant → The Tauc–Lorentz model is a mathematical formula for the frequency dependence of the complex-valued relative permittivity, sometimes referred to as the dielectric function; boundary → the case exits the class when e is the photon energy (related to the angular frequency by E=\hbar\omega ),

Structural Tensions¶

T1 — Stable identity versus admissible variation. E is the photon energy (related to the angular frequency by E=\hbar\omega ),. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Which changes preserve the defining relation, and which replace it?

T2 — Recognition versus proxy. \varepsilon_{\infty} is the value of the relative permittivity at infinite energy,. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Does the cited evidence establish the identity or only a correlated sign?

T3 — Definition versus implementation. The imaginary component of \chi^{TL}(E) is formed as the product of the imaginary component of the Lorentz oscillator model and a model developed by Jan Tauc for the imaginary component of the relative permittivity near the bandgap of a material. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Is the observed implementation constitutive, optional, or merely common?

T4 — Scope versus overextension. The real component of \chi^{TL}(E) is obtained via the Kramers-Kronig transform of its imaginary component. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Can every claimed application fill the same typed roles without metaphor?

T5 — Transfer versus domain accent. The imaginary component of \chi^{TL}(E) is formed as the product of the imaginary component of the Lorentz oscillator model and a model developed by Jan Tauc for the imaginary component of the relative permittivity near the bandgap of a material. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Does the receiving case instantiate Tauc–Lorentz model literally, co-instantiate Theory, or only resemble it?

T6 — Autonomy versus reduction. E is the photon energy (related to the angular frequency by E=\hbar\omega ),. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: What does Tauc–Lorentz model distinguish that the broader parent Theory leaves together?

Structural–Framed Character¶

Tauc–Lorentz model is structural-leaning. Its structural side is the repeatable organization summarized by The Tauc–Lorentz model is a mathematical formula for the frequency dependence of the complex-valued relative permittivity, sometimes referred to as the dielectric function. Its framed side is the natural sciences, engineering, and health vocabulary that fixes the carrier, evidence, exceptions, and admissible transformations.

Evaluative weight: the identity can be stated descriptively even when applications carry practical stakes. Human-practice dependence: the source-grounded carrier determines whether the relation exists independently or is constituted by a practice. Institutional origin: disciplinary conventions stabilize the name and test. Vocabulary portability: The dispersion relation bears the names of Jan Tauc and Hendrik Lorentz, whose previous works were combined by G. Import versus recognition: literal transfer requires the same mechanism; shape alone is analogy.

Its portable skeleton is Theory. Its character: a recurring specialist identity whose thin organization can be abstracted, while its operational meaning remains domain-bound.

Structural Core vs. Domain Accent¶

What is skeletal. The Tauc–Lorentz model is a mathematical formula for the frequency dependence of the complex-valued relative permittivity, sometimes referred to as the dielectric function. The reviewed portable genus is Theory; the candidate preserves that parent relation across admissible variants. The source-grounded carrier and relation are expressed by these conditions: The imaginary component of \chi^{TL}(E) is formed as the product of the imaginary component of the Lorentz oscillator model and a model developed by Jan Tauc for the imaginary component of the relative permittivity near the bandgap of a material. E is the photon energy (related to the angular frequency by E=\hbar\omega ),. The recognition and variation tests add: The dispersion relation bears the names of Jan Tauc and Hendrik Lorentz, whose previous works were combined by G. The model was inspired, in part, by shortcomings of the Forouhi–Bloomer model, which is aphysical due to its incorrect asymptotic behavior and non-Hermitian character.

What is domain-bound. natural sciences, engineering, and health fixes the carrier, technical vocabulary, admissible evidence, and exceptions that distinguish Tauc–Lorentz model from other Theory instances. Its documented habitat includes the condition that The Tauc–Lorentz model is a mathematical formula for the frequency dependence of the complex-valued relative permittivity, sometimes referred to as the dielectric function. A second source-grounded application condition is that The model has been used to fit the complex refractive index of amorphous semiconductor materials at frequencies greater than their optical band gap. Those details determine what the words denote, what observations warrant classification, and which apparent similarities are false positives.

Why the node remains domain-specific. Removing the natural sciences, engineering, and health differentia leaves the parent rather than the candidate. The edge records that reduction without claiming that every topical neighbor is hierarchical. The final collapse test is source-specific: \varepsilon{\infty} is the value of the relative permittivity at infinite energy,. If that condition or the defining relation is absent, the case may instantiate Theory, but it is not Tauc–Lorentz model.

This entry is a kind of Theory.

Immediate parent — Theory (subsumption). Tauc–Lorentz model is a domain-specific kind of Theory. Tauc–Lorentz model is a strict kind of Theory: The Tauc–Lorentz model is a mathematical formula for the frequency dependence of the complex-valued relative permittivity, sometimes referred to as the dielectric function. The parent supplies the necessary broader identity—A coherent system of concepts and propositions that explains, organizes or predicts a domain through explicit relations and standards of support.—while the candidate adds its domain carrier, relation, and rejection conditions.
Other nearby abstractions. Retrieval neighbors remain comparison surfaces only; no additional parent is asserted without a necessary-genus or structural-prerequisite test.

Relationships to Other Abstractions¶

Current abstraction Tauc–Lorentz model Domain-specific

Parents (1) — more general patterns this builds on

Tauc–Lorentz model is a kind of Theory Prime

Tauc–Lorentz model is a strict kind of Theory: The Tauc–Lorentz model is a mathematical formula for the frequency dependence of the complex-valued relative permittivity, sometimes referred to as the dielectric function.

Hierarchy paths (2) — routes to 2 parentless roots

Tauc–Lorentz model → Theory → Formalization → Representation → Abstraction

Show alternative path (1)

Neighborhood in Abstraction Space¶

Tauc–Lorentz model sits in a moderately populated region (53^rd percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Physical Quantities, Operators & Formulas (33 abstractions)

Nearest neighbors

Crystal momentum — 0.86
Scalar field theory — 0.86
Particle in a spherically symmetric potential — 0.85
Lorentz oscillator model — 0.85
Scaling Dimension — 0.85

Computed from structural-signature embeddings · 2026-10-08

Not to Be Confused With¶

Theory. The parent omits the specialist differentia. Tell: Can the case establish The Tauc–Lorentz model is a mathematical formula for the frequency dependence of the complex-valued relative permittivity, sometimes referred to as the dielectric function?
Lorentz oscillator model. A classical model of bound charges as damped driven harmonic oscillators, producing frequency-dependent dielectric response, dispersion and resonant absorption. Tell: Which entry's carrier, operation, and failure condition are satisfied?
Frenkel–Kontorova model. A model of elastically coupled particles in a periodic substrate potential that captures competition between a preferred spacing and an imposed lattice. Tell: Which entry's carrier, operation, and failure condition are satisfied?
Sombrero function. The radial two-dimensional analogue of sinc, commonly defined as 2J1(πρ)/(πρ), and arising as the Fourier transform of a circular aperture. Tell: Which entry's carrier, operation, and failure condition are satisfied?
A measurement, proxy, or consequence. Those may provide evidence without being the identity. Tell: Would Tauc–Lorentz model remain present if the detector or downstream effect changed?
A metaphorical analogue. A similar shape outside natural sciences, engineering, and health lacks the specialist mechanism. Tell: Do the native roles transfer literally, or only the parent Theory?

References¶

Frozen Wikipedia discovery revision: https://en.wikipedia.org/wiki/Tauc%E2%80%93Lorentz_model (revision 1329562408).
Preserved source candidate: https://doi.org/10.1002/pssb.19660150224
Preserved source candidate: https://doi.org/10.1063/1.118064
Preserved source candidate: https://doi.org/10.1117/12.560673
Preserved source candidate: https://doi.org/10.1016/j.tsf.2015.07.035

The frozen Wikipedia revision is discovery provenance. The retained source set was reviewed for identity, formal or operational relation, and scope. The encyclopedia's structural synthesis is bounded to those claims; a thin authority surface is recorded as a nonblocking source-strengthening repair rather than concealed.