Small-polaron barrier: lattice free to relax
electron_barrier_2d held the lattice frozen and found
5.46 eV to move a carrier
between interstitial sites. That is the
vertical barrier — the cost of moving the
charge while the ions stand still — and it is not the quantity that governs transport.
Real hopping is a polaron hop: the carrier sits in a well it has dug itself, the lattice
distorting around it, and it moves together with that distortion. The relevant barrier is the
relaxed one, which is smaller, often by a great deal. This page computes it by letting the
ions move (USER_DYNAMICS) at every point of the scan.
Why this is the semiconductor case. With a relaxed barrier Ea the conductivity is
activated, σ ∝ exp(−Ea/kBT), which is how semiconductors,
oxides and disordered solids conduct. It is not how a metal conducts, and the framework has no
route to that (see the article).
Direct version: add
&free and the carrier is released too — nothing
is held, and one simply watches whether it stays in its pocket or migrates. That is the
illustration; the barrier scan below is the measurement.
URL: ?s=0.5 position along pocket→saddle→pocket,
&a=2.5 spacing, &relax=1 lattice free (default) or
&relax=0 to reproduce the frozen result, &reset clears.
relaxing…