136 of 154: most entries passing one optical-permittivity cut on the Materials Project DFPT set have computed gaps under 1 eV
Gate stacks, capacitors and memory cells need high-k insulators: materials with a large static dielectric constant and a band gap wide enough that charge does not leak through. The Materials Project and JARVIS-DFT report two kinds of permittivity. The electronic, or optical, permittivity counts only how the electrons respond to a field. The total static permittivity, computed with density-functional perturbation theory (DFPT), also counts the ions moving, so it is the quantity a high-k rule should use, though it is still a value for a perfect bulk crystal at zero temperature, not a thin film.
A screen that only has the electronic value to hand may be tempted to use it as a stand-in. We measured what that shortcut does on two public datasets where both values exist.
The test, with the rules fixed first
We fixed the rules, and which quantities each dataset would use, in a note committed to our repository before the run; the note is not published, so that timing rests on our own record. The optical screen passes a material whose electronic permittivity is 10 or more. Our high-k-insulator rule asks for a total static permittivity of 20 or more and a computed band gap of at least 1 eV. That gap floor is lax: a real gate dielectric needs a much wider gap. We then counted two things: how many of the screen's picks fall below the 1 eV floor, and how many entries meeting the rule the screen fails to pick.
The datasets are reported separately: the Materials Project DFPT dielectric set (1,056 entries, using its orientation-averaged electronic and total values) and the 4,496 JARVIS-DFT entries that carry all three fields we need. For JARVIS we used different quantities, its optical permittivity along the x direction of the computed cell as the screen and its reported maximum DFPT static value as the rule, with band gaps from a different functional, so its result is a second look in the same direction, not a repeat of the same test.
Most picks have small gaps; the screen misses most rule-meeting insulators, as a random pick of the same size would
On the Materials Project set, 154 entries pass the optical screen. 136 of them, 88.3%, have a computed band gap under 1 eV, below the insulator floor we fixed in advance. We did not compare that share with the share across the whole dataset. Of the 46 entries that meet our high-k-insulator rule, the screen misses 42, or 91.3%. That sounds damning, but the screen passes few entries at all: a random pick of the same size would be expected to miss 85.4%. On only 46 entries that difference is small, and we ran no significance test, so on this set we do not claim the screen does worse than chance at finding rule-meeting insulators. What it does show is that its picks are dominated by small-gap entries.
JARVIS-DFT, with its own quantities, points the same way, though its picks include entries computed with no gap at all and its screen and rule read different directions, so the two sets are not like for like. 1,435 entries pass the screen and 1,186 of them, 82.6%, have a computed gap under 1 eV; some are computed as metals, where an optical permittivity says little. Of 709 entries meeting the rule, the screen misses 606, or 85.5%, where a random pick of the same size would be expected to miss 68.1%. On this larger set the shortfall against a random pick is large, though we ran no formal test.
At the extreme end, 3 Materials Project entries (orientation-averaged) and 64 JARVIS-DFT entries (x direction) report an optical permittivity above 100. A screen that ranked by this number, rather than using a pass mark as ours does, would put them first, so they are the entries to check before trusting anything else on such a list.
Why it behaves this way
Two standard effects are consistent with the pattern; this run did not test either. First, electrons that respond strongly to a field are usually easy to excite, so a large electronic permittivity tends to come with a small band gap: the screen rewards the property that makes a poor insulator. Second, much of the permittivity in useful high-k insulators comes from the ions moving, which the electronic value does not see, so those materials fall below the cut. The first effect would push the screen below chance; the second would at most make it uninformative; the mismatch between the JARVIS-DFT quantities could also push it below chance; this run does not separate these causes, and on the smaller Materials Project set it cannot separate the result from chance.
What we recommend, as standard practice this run is consistent with but did not test: screen on total static permittivity where a DFPT value exists, apply a band-gap floor in the same step, and check phonon stability, because soft lattice modes can inflate the DFPT total too. We tested one optical cut only, so this says nothing about how a looser optical cut would do as a pre-filter.
What this does not show
The rules are one choice. The 91.3% miss rate on the Materials Project set rests on only 46 entries, which entries clear the bar depends on where the thresholds sit, and we give no confidence intervals or significance test against the random baseline, which we added after the run rather than fixing it in advance. We have not yet published a sweep of the thresholds, so treat the exact percentages as belonging to these rules.
Every value here is computed, not measured. DFT band gaps tend to run low (see our post on DFT band gaps). Correcting them would move some picks above the 1 eV floor and would also add entries to the rule-meeting set, so the miss rate could move either way. Both datasets are the subsets where someone ran DFPT, not whole databases, and the two use different quantities, so we do not pool them.
This grades a screening rule, not any particular material, published screen or candidate of ours. Only the counts are published, not the per-material rows. The run's record names a code revision committed shortly after the run started and notes uncommitted changes, and it does not pin the dataset versions, so the exact inputs behind the counts are not fully identified. No phonon-stability filter was applied to the rule side.