Accelerated Dopant Screening in Oxide Semiconductors via Multi-Fidelity Contextual Bandits and a Three-Tier DFT Validation Funnel
Authors: Abhinaba Basu
Organizations: National Institute of Electronics and Information Technology (NIELIT), India · Indian Institute of Information Technology, Allahabad (IIITA), Prayagraj, India
Band gap engineering of oxide semiconductors through doping is critical for photocatalysis and optoelectronics, yet the combinatorial space of dopant elements, substitution sites, and co-doping combinations far exceeds typical density functional theory (DFT) budgets. We screen doped candidates across five oxide hosts (ZnO, TiO2, SrTiO3, SnO2, MgO), culminating in a 529-candidate ZnO co-doping campaign, and identify Cu-containing co-doped ZnO systems as consistently achieving visible-light-range band gaps (1.0-1.8 eV), with Y2Cu2 co-doped ZnO as the optimal candidate (1.84 eV). A three-tier validation funnel (PBE, PBE+U, ionic relaxation) reveals that no single level of theory suffices: V-doped ZnO shifts from near-metallic to wide-gap upon Hubbard U correction, while Cu-doped SrTiO3 enters the visible-light window only after correcting for d-electron localization. To make this screening tractable, we introduce a multi-fidelity screening strategy that replaces 81% of DFT evaluations with computationally inexpensive surrogate predictions, reducing a 529-candidate closed-loop Quantum ESPRESSO campaign from an estimated 440 to 62 CPU-hours while finding the global optimum in 100% of 50 independent trials (p = 5.0e-8 versus random screening, Wilcoxon signed-rank). Cross-host analysis of the dopant-host interaction matrix reveals that dopant performance is governed by just two latent chemical dimensions, enabling prediction of rankings in unseen hosts. All 583 DFT calculations, screening code, and stability proofs are released as an open benchmark.
Figures & tables
Figure 1: Three-tier DFT screening funnel. Tier 1 uses MF-OFUL-guided PBE-SCF for fast initial ranking (245 calculations, 93.9% convergence). Simple flagging criteria—d-electron count >0 and ionic radius mismatch >20% —route candidates to Tier 2 (PBE+U) or Tier 3 (ionic relaxation). The two higher tiers catch orthogonal failure modes: d-electron delocalization (V, Cu, Fe dopants) and geometric distortion (In at the Ti site), respectively.
Benchmark
MF-OFUL
OFUL
TS
Platform
Random
Retroactive benchmarks (both objectives averaged)
Materials Project (20%)
0.000
0.215
—
0.237
0.236
Synthetic (8%)
0.049
0.468
0.464
0.564
0.688
Single-objective validation (target_bandgap_2p0)
MP 500 (8%)
0.017
0.150
0.036
—
0.182
Real QE, ZnO (62.5%)
0.000
0.002
—
—
0.069
Table 1: Screening performance across three benchmark suites. Simple regret (SR): gap between best-found reward and global optimum (lower is better), averaged over 10+ seeds. Parenthetical percentages indicate budget fraction. GP-based methods compared in Supplementary Table 11. Bottom row: Wilcoxon signed-rank p -values for the synthetic benchmark only (paired by seed, n=120 ), which provides the largest sample size for statistical testing. Dashes indicate methods not run on that benchmark.
Figure 2: Simple regret comparison across methods. Mean ± s.d. over 6 hosts × 10 seeds on 1,000-candidate synthetic benchmarks at 8% budget. MF-OFUL achieves 10 × lower simple regret than all other methods. Brackets show Wilcoxon p -values. MF-BO-EI ( n=18 ) uses identical fidelity-switching logic as MF-OFUL but never triggers its surrogate because EI selects high-GP-uncertainty candidates that always exceed the fidelity threshold.
Figure 3: PBE versus PBE+U bandgaps for transition metal dopants. Grouped bar chart showing qualitative reclassifications. Arrows indicate direction and magnitude of shift. Red dashed line: metallic threshold (0.5 eV). Three of five doped systems cross the metallic threshold upon applying the Hubbard U correction, demonstrating that PBE-SCF alone is insufficient for transition metal dopant screening.
Figure 4: HSE06 hybrid functional validation. (a) PBE versus HSE06 bandgaps for 5 systems. PBE misclassifies V-doped ZnO as near-metallic (0.15 eV → 3.87 eV at HSE06) and ZnO:Cu as wide-gap (3.21 eV → 0.09 eV). (b) PBE+U versus HSE06 shows substantially improved agreement for d-electron systems, with mean absolute deviation of 0.15 eV. The dashed line indicates perfect agreement; the shaded band marks the metallic threshold ( < 0.5 eV).
Figure 5: Empirical Lyapunov diagnostics. (a) Lyapunov function decomposition: total L(t) (black), information deficit Φ(t) (blue, saturates), and bias potential μ⋅B(t) (red, grows linearly but bounded). (b) UCB width evolution: OFUL (blue, 80 steps) versus MF-OFUL (red, ∼548 steps). Triangles mark MF-OFUL’s DFT steps. Shaded bands: ±1 s.d. across 5 seeds. The information deficit saturates while the bias potential remains bounded, confirming that surrogate errors do not accumulate.
Figure 6: Collaborative filtering biplot of the host–dopant interaction matrix. SVD decomposition of the (5×16) reward matrix into two latent dimensions. Hosts (stars) cluster by crystal chemistry: MgO–ZnO (Group-II oxides) and TiO 2 –SnO 2 (rutile-type Group-IV oxides), with SrTiO 3 as an outlier. Dopants separate into sp-electron (triangles: Al, Ga, In, Sc, Y) and d-electron (squares: V, Cr, Mn, Fe, Co, Ni, Cu) groups. Cu and In are outliers with strongly host-dependent behavior. PC1 and PC2 together capture 87% of variance.
Single-dopant (16)
Co-doped (120)
OFUL
MF-OFUL
OFUL
Main DFT calls
10
10
18
Surrogate calls
0
0
0
Verification DFT
—
3
3
Best found
Mn (1.85 eV)
Mn (1.85 eV)
Al+Cu (1.28 eV)
Success rate
100%
100%
100%
Table 2: Prospective comparisons on ZnO. Top: single-dopant pool (16 candidates, budget 10). Bottom: co-doped pool (120 candidates, budget 18). Target bandgap: 2.0 eV. Surrogate calls = 0 in these QE campaigns because UCB widths remained above the fidelity threshold at these pool sizes; surrogate activation is confirmed on 500-candidate Materials Project pools (see text).
Figure 7: Bandgap landscape of the 529-candidate ZnO co-doping campaign. Each point represents a DFT-evaluated candidate, sorted by bandgap and colored by reward (green: near 2.0 eV target; red: far from target). Cu-containing systems (diamonds) cluster near the target window (green band), while most other combinations produce wide-gap or near-metallic outcomes. Key Cu co-doped candidates are annotated.
Budget
Method
DFT
Surr.
Cov.
Best reward
SR
Top-5
P(≥0.9)
18 (8%)
MF-OFUL
18
0
8%
0.263
0.723
0.0
0%
OFUL
18
0
8%
0.263
0.723
0.0
0%
Random
18
0
8%
0.678±0.262
0.308
0.4
26%
42 (18%)
MF-OFUL
42
184
98%
0.987±0.000
0.000
5.0
100%
OFUL
42
0
18%
0.452
0.534
0.0
0%
Random
42
0
18%
0.850±0.181
0.136
0.9
58%
Table 3: 50-seed retroactive reanalysis on 230 QE-converged ZnO candidates. The 229 unique QE results from the prospective campaign serve as an oracle. MF-OFUL, OFUL, and Random are each run 50 times. “Cov.” is the fraction of candidates evaluated (DFT + surrogate). “Top-5” is the mean number of true top-5 candidates found. P(≥0.9) is the fraction of seeds achieving reward ≥0.9 . Global optimum: Y 2 Cu 2 ZnO, reward =0.987 .
Figure 8: Simple regret versus DFT budget on real QE data. Mean ± s.d. over 10 seeds on the 223-candidate cross-host QE oracle (5 oxide hosts). MF-OFUL achieves SR =0.000 at 12% budget (annotated), finding the global optimum in every run. The surrogate activation threshold creates a sharp transition between 8% (no surrogate) and 12% (full activation), while DFT-only methods improve gradually.
Appendix figures & tables8 assets
Supplementary material from the paper’s appendix.
Appendix
Objective
Host
MF-OFUL
OFUL
BO-GP-EI †
Platform
Random
target_bandgap_2p0
Al 2 O 3
0.003±0.01
1.230±0.00
0.139±0.17
0.331±0.42
0.560±0.27
MgO
0.282±0.60
1.758±0.00
0.215±0.29
0.951±0.83
1.708±0.62
SnO 2
0.000±0.00
0.000±0.00
0.000±0.00
0.786±0.32
0.512±0.32
SrTiO 3
0.000±0.00
0.000±0.00
0.298±0.42
0.449±0.54
0.768±0.41
TiO 2
0.018±0.06
0.183±0.00
0.000±0.00
0.398±0.36
0.487±0.39
Appendix
Table S1: Synthetic benchmark per-host simple regret (mean ± s.d., 10 seeds). † BO-GP-EI uses budget = 50 from an independent run (not directly comparable to budget-80 methods; see main text Table 3 for budget-matched MF-BO-EI comparison at n=18 ).
Objective
Host
MF-OFUL
OFUL
Platform
Random
target_bandgap_2p0
Al 2 O 3
0.000±0.00
0.264±0.00
0.141±0.10
0.134±0.11
MgO
0.000±0.00
0.025±0.00
0.000±0.00
0.028±0.04
SnO 2
0.000±0.00
0.000±0.00
0.038±0.06
0.055±0.05
SrTiO 3
0.000±0.00
0.000±0.00
0.056±0.05
0.047±0.04
TiO 2
0.000±0.00
0.005±0.00
0.013±0.01
0.015±0.02
Appendix
Table S2: Materials Project benchmark per-host simple regret (mean ± s.d., 10 seeds). Budget = 20% of per-host candidate pool. BO-GP-EI was not run on the MP benchmark. MF-OFUL achieves zero mean simple regret on every host under both objectives.
Dopant Family
Survival Rate
Success Rate
Avg. Budget Allocated
Rare earths (Sc, Y)
84%
42%
22%
Early 3d TM (V, Cr, Mn)
67%
31%
18%
4d/5d TM (Zr, Nb, Mo, W)
58%
28%
15%
Main group (Al, Ga, In)
52%
27%
14%
Late 3d TM (Fe, Co, Ni, Cu)
34%
19%
11%
Alkaline earth (Mg, Sr, Ba)
28%
15%
8%
Appendix
Table S3: Platform trial arm statistics averaged over 120 synthetic benchmark runs (6 hosts × 2 objectives × 10 seeds). Survival rate: fraction of interim analyses where the arm was not dropped. Success rate: fraction of evaluated candidates within the arm that achieved positive reward.
Parameter
Values tested
Best
Default
SR at best
SR at default
SR at worst
Pseudo-weight w
0.0, 0.1, 0.2, 0.4, 0.6, 1.0
0.2
0.2
0.043
0.043
0.312
β (UCB scale)
0.1, 0.5, 1.0, 2.0, 5.0
1.0
1.0
0.043
0.043
0.189
λ (regularization)
0.01, 0.1, 1.0, 10.0
1.0
1.0
0.043
0.043
0.156
Force DFT every N
5, 10, 20, 50
10
10
0.043
0.043
0.098
Bootstrap size
3, 5, 10, 20
5
5
0.043
0.043
0.078
UCB threshold frac.
0.25, 0.5, 0.75, 1.0
0.5
0.5
0.043
0.043
0.267
Appendix
Table S4: MF-OFUL hyperparameter sensitivity on synthetic benchmark (1,000 candidates, budget 80, 10 seeds). Simple regret (SR) reported. The method is robust across a wide range; only extreme values ( w=1.0 , β=0.1 ) cause significant degradation.
Step
Dopant
Family
Bandgap (eV)
Reward
UCB Width
0
Mn
3d TM
1.848
0.747
—
1
In
Main group
3.064
− 1.064
2.41
2
Y
Rare earth
3.252
− 3.252
1.89
3
Al
Main group
3.193
− 1.193
1.52
4
Ga
Main group
3.081
− 1.081
1.23
5
Sc
Rare earth
3.250
− 3.250
1.08
Appendix
Table S5: Step-by-step OFUL selection on ZnO prospective campaign. Target bandgap: 2.0 eV. Mn (step 0, reward 0.747) is the best candidate found. Steps 0–2 explore diverse feature regions (3d TM, main group, rare earth); subsequent steps sample remaining feature regions to reduce uncertainty.
Host
R2 (train)
R2 (5-fold CV)
Best linear feature
ZnO
0.53
0.41
Ionic radius
TiO 2
0.38
0.29
d-electron count
SnO 2
0.35
0.26
Electronegativity
MgO
0.31
0.22
Ionic radius
SrTiO 3
0.21
0.14
Oxidation state
Appendix
Table S6: Ridge regression ( α=1 ) fit quality on DFT bandgap rewards by host. R2 computed on all available DFT data per host. ZnO shows the strongest linear signal, consistent with OFUL’s best performance on this host.
System
Tier 1 (PBE)
Tier 2 (PBE+U)
Tier 3 (relax)
Reclassified?
Flagging criterion
ZnO:V
0.22 eV
3.92 eV
0.25 eV
Yes (Tier 2)
d-electrons >0
ZnO:Cu
3.19 eV
0.36 eV
3.15 eV
Yes (Tier 2)
d-electrons >0
SrTiO 3 :Fe
2.48 eV
0.48 eV
—
Yes (Tier 2)
d-electrons >0
SrTiO 3 :In
0.81 eV
0.79 eV
3.48 eV
Yes (Tier 3)
radius mismatch 31%
ZnO:Al
3.19 eV
—
3.27 eV
No
—
ZnO:Ga
3.08 eV
—
3.16 eV
No
—
Appendix
Table S7: Multi-tier bandgap comparison for systems evaluated at two or more tiers. Four of ten systems are qualitatively reclassified (40%). The two failure modes are strictly orthogonal: d-electron delocalization (Tier 2) and geometric distortion (Tier 3). Simple flagging criteria (rightmost column) correctly identify all reclassified systems.
Step
Co-dopants
Bandgap (eV)
Reward
Phase
0
Al+W
0.298
− 1.702
Main
1
Al+Y
3.734
− 1.734
Main
2
In+Y
3.634
− 1.634
Main
3
Al+V
0.178
− 1.822
Main
4
Cu+In
1.170
− 0.830
Main
5
Nb+Y
0.205
− 1.795
Main
Appendix
Table S8: Step-by-step OFUL selection on ZnO co-doped campaign (120 candidates, budget 18 + 3 verification). Target bandgap: 2.0 eV. Al+Cu (step 6, reward − 0.718) is the best candidate found. Cu-containing pairs (steps 4, 6, 9, 10) consistently produce the narrowest non-metallic gaps, confirming Cu’s role as a p-type acceptor. Verification-phase candidates (steps 18–20) had high surrogate predictions but low actual rewards, demonstrating the importance of DFT verification.
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School of Materials Science and Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798.
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