Materials Semiconductor Dopant Types From Config Dim Semiconductor Dopant Cert

The five dopant categories

In semiconductor physics, a dopant is an impurity added to a crystal to change its electrical conductivity. Silicon, the workhorse of electronics, is typically doped with atoms from group V of the periodic table, such as phosphorus, arsenic, or antimony; these donate an extra electron and are called donors. Atoms from group III, such as boron, aluminum, or gallium, accept an electron and are called acceptors. Beyond these shallow dopants, real devices also rely on deep-level impurities, compensating dopants, and transition-metal scattering centers. Together these form the five canonical categories that device engineers use to describe silicon-type semiconductors.

The Recognition Science framework models this classification with a machine-checked library of formal theorems. Its declaration SemiconductorDopantCert is a certificate: a formal object that records the statement that there are exactly five dopant types. The certificate is built from a theorem that establishes, by direct computation, that the number of dopant categories is five. The whole file carries no unproved assumptions and no axioms beyond the standard logical ones. In plain terms, the framework has formally verified the count: five categories, no more, no less.

What the certificate does not do is as important as what it does. It does not assert that these five categories are physically complete or that real silicon devices always fall into exactly one of them. It does not derive the dopant categories from first principles of semiconductor physics. It does not claim that the categories correspond to measurable electrical behavior. The certificate only establishes a combinatorial fact about a formally defined inductive type: the type has five elements. The physical interpretation, the naming of the categories, and the claim that these are the right categories for silicon are all definitional choices made by the framework, not theorems established from physics.

In practice, this means the certificate is a small but solid piece of bookkeeping. It gives a formal guarantee that any code or proof that relies on the five-category classification will not accidentally use a sixth category or miss a fifth. For a reader, the useful takeaway is that the framework has pinned down a counting fact with machine precision, while the physical meaning of the categories remains a modeling decision, not an established law of nature.

structure SemiconductorDopantCert where
  five_types : Fintype.card DopantType = 5

theorem dopantType_count : Fintype.card DopantType = 5 := by decide

def semiconductorDopantCert : SemiconductorDopantCert where
  five_types := dopantType_count

What this page does not claim

The certificate does not assert that the five categories are physically complete or that real devices always fall into exactly one of them. The certificate does not derive the dopant categories from semiconductor physics or from measured material properties. The certificate does not claim that the categories correspond to measurable electrical behavior.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Materials/SemiconductorDopantTypesFromConfigDim.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

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