ZnO·DefectLab — Native Point-Defect Workbench

The user wants me to create an impressive HTML software for a professor studying Zinc Oxide (ZnO) defects. This should be a comprehensive, educational, and scientifically accurate tool. Let me think about what would be useful for a professor in academia studying ZnO defects: 1. **ZnO Crystal Structure Visualization** - Wurtzite structure (most common), zinc blende, rocksalt 2. **Point Defects in ZnO:** - Oxygen vacancies (V_O) - deep donor, green luminescence - Zinc vacancies (V_Zn) - acceptor - Zinc interstitials (Zn_i) - shallow donor - Oxygen interstitials (O_i) - Antisites (Zn_O, O_Zn) - Hydrogen impurities 3. **Defect formation energies** - depends on Fermi level, chemical potential (O-rich vs Zn-rich conditions) 4. **Charge states** - q = -2, -1, 0, +1, +2 5. **Band structure** - bandgap ~3.37 eV, exciton binding energy ~60 meV 6. **Optical properties** - PL emissions (UV near-band-edge ~3.3 eV, green ~2.4-2.5 eV, yellow, red) 7. **Formation energy diagrams** - like the famous Janotti & Van de Walle diagrams Key features to include: 1. **Interactive 3D crystal structure viewer** (wurtzite ZnO) with clickable defects - I could use Three.js or canvas-based rendering 2. **Defect formation energy calculator** - E_f = E_tot(defect) - E_tot(bulk) - Σn_i μ_i + q(E_VBM + E_F) + E_corr 3. **Formation energy vs Fermi level plotter** (interactive chart) - switch between O-rich and Zn-rich conditions 4. **Photoluminescence / defect level diagram** - energy level positions in the bandgap 5. **Charge transition level calculator/viewer** 6. **Kroger-Vink notation reference** 7. **Defect concentration calculator** - N = N_sites exp(-E_f/kT) 8. **Literature data tables** with references (Janotti & Van de Walle papers) Let me design this as a professional academic tool: **Tabs/Sections:** 1. Dashboard/Overview - intro to ZnO 2. 3D Structure Explorer - wurtzite lattice with defect placement 3. Formation Energy Lab - interactive plot of formation energies vs Fermi level, with chemical potential conditions 4. Energy Levels / Band diagram - defect transition levels in the gap 5. Optical Signatures - PL/DLTS signatures 6. Concentration Calculator - Boltzmann statistics 7. Reference Library - Kroger-Vink notation, key papers For the 3D visualization, I'll use Three.js from CDN to render wurtzite ZnO. The wurtzite structure: - Hexagonal, space group P6_3mc - Lattice constants: a = 3.25 Å, c = 5.21 Å - Zn at (1/3, 2/3, 0) and (2/3, 1/3, 1/2) - O at (1/3, 2/3, u) and (2/3, 1/3, u+1/2) with u ≈ 0.382 Let me build the wurtzite unit cell properly: - Lattice vectors: a1 = a(1, 0, 0), a2 = a(-1/2, √3/2, 0), a3 = c(0, 0, 1) - Basis: Zn: (0,0,0), (1/3, 2/3... wait let me get this right. Wurtzite conventional cell: - Zn at: (1/3, 2/3, 0), (2/3, 1/3, 1/2) - O at: (1/3, 2/3, u), (2/3, 1/3, 1/2 + u) with u = 3/8 = 0.375 ideal, actual 0.382 For the formation energy diagram, I'll use data based on Janotti & Van de Walle (Rep. Prog. Phys. 2009, Phys. Rev. B 2007). Key charge transition levels (approximate, LDA+U/HSE values vary): For O-rich conditions (approximate values at E_F = 0 for VBM): - V_O: (2+/0) deep at ~1.5-2 eV; formation energy at E_F=0 in O-rich ~ 1-2 eV? Actually let me recall the famous figure. From Janotti & Van de Walle PRB 76, 165202 (2007), O-rich (using their GGA+U approach, μ_O = O-rich limit): - V_O: at E_F=0, formation energy ~2.5 eV (2+ charge state), slopes... (2+/0) transition around 2.1 eV above VBM? Actually V_O is a deep donor with ε(2+/0) around 1.7-2.5 eV depending on the method. - V_Zn: acceptor, (0/1-) ~0.2-0.5 eV? V_Zn has ε(0/-) around 0.2 eV and ε(-/2-) around 0.9-1 eV. In O-rich conditions, V_Zn has low formation energy and is the dominant compensating acceptor. - Zn_i: shallow donor, (2+/0) very deep or negative-U... Zn_i is a shallow donor with low formation energy in Zn-rich. ε(2+/0) is deep, around 2.3 eV? Actually Zn_i 2+ is stable for most of the gap, (2+/0) around 1.5 eV? - O_i: in O-rich, octahedral O_i is low energy, (0/2-) transitions... O_i is a deep acceptor, ε(0/2-) around 1 eV? - Zn_O antisite: donor, high energy in O-rich - O_Zn antisite: high energy Let me use representative numbers (HSE06-like or the classic Janotti-VdW values). I'll present them as "representative values from hybrid DFT literature" and let the user edit the chemical potentials. Actually, to make this interactive and educational, I can let users: - Toggle O-rich / Zn-rich conditions - See formation energy lines E_f(E_F) = E_0 + q*E_F for each charge state - The lowest envelope determines stability - Charge transition levels marked where slope changes Data (representative, e.g., from Janotti & Van de Walle 2007 GGA+U, gap corrected; or Oba et al.): Let me construct line segments. For each defect, give charge-state formation energies at E_F = 0 (in eV) and the relevant ranges: O-rich limit (μ_O = ½E(O2), μ_Zn determined by equilibrium): From Janotti-VdW PRB 76 165202 (2007), Fig. 2 (O-rich): - V_O^2+: ~0.5 eV at E_F=0? Hmm. Actually in their figure O-rich, V_O 2+ starts around 2.3 eV at E_F=0? Let me think again. I remember the O-rich diagram: V_Zn is lowest near the CBM (compensating acceptor for n-type). V_Zn 2- at E_F = E_g is around 0.5-1 eV. V_O near VBM is ~1 eV or so... Rather than chase exact published values, I'll use a well-known dataset approximately matching Janotti & Van de Walle's classic results, and clearly label it as representative values with references. Since the user is a professor, they'd appreciate editability — I could allow adjusting μ_O via a slider from O-rich to Zn-rich! That's a killer feature: slider for oxygen chemical potential, and the formation energies of O-containing defects shift accordingly. ΔE for V_O = +μ_O... wait: E_f(V_O) = E(V_O) - E(bulk) + μ_O + qE_F. So removing an O costs +μ_O; when μ_O is high (O-rich), V_O formation energy is high. When Zn-rich (μ_O low), V_O formation energy is low. Similarly V_Zn: E_f = E - E_bulk + μ_Zn + qE_F. In Zn-rich (μ_Zn high), V_Zn is expensive; O-rich, cheap. Constraint: μ_Zn + μ_O = μ_ZnO ≈ ΔH_f(ZnO) = -3.6 eV (formation enthalpy ~ -3.6 eV, actually -3.63 eV). With references: ΔH_f(ZnO) = -3.6 eV. Define Δμ_O = μ_O - ½μ_O2 (range: ΔH_f ≤ Δμ_O ≤ 0). O-rich: Δμ_O = 0. Zn-rich: Δμ_O = ΔH_f = -3.6 eV. And Δμ_Zn = ΔH_f - Δμ_O. So a slider for Δμ_O from -3.6 to 0 eV lets the user sweep growth conditions continuously. For each defect with charge q, E_f(E_F) = E_form^0 + q·E_F + n_O·(−Δμ_O)... let me define: E_f(D^q) = E0^q(D) + q·E_F + Σ n_i Δμ_i where n_i is the number of atoms of species i ADDED to the system (negative for vacancies). For V_O: n_O = -1, so E_f shifts by -Δμ_O. O-rich (Δμ_O=0): E_f = E0. Zn-rich (Δμ_O = -3.6): E_f = E0 + 3.6 → wait that's wrong direction. Hmm: E_f(V_O) = E_tot(V_O) − E_tot(bulk) + μ_O + q(E_V + E_F) + ... The μ_O here is the absolute chemical potential. If we parametrize by Δμ: E_f = E0^q + q E_F − n_O Δμ_O... Let me be careful: E_f = [E_tot(defect) − E_tot(bulk) + q E_VBM + E_corr] + q E_F − Σ n_i μ_i where n_i = number of atoms added (defect − bulk). For V_O: one O removed → n_O = −1. So term = −n_O μ_O = +μ_O. Using μ_O = μ_O^ref + Δμ_O: E_f = const + Δμ_O (since −n_O = +1... wait −Σn_iμ_i = −(−1)(μ_O) = +μ_O). So E_f(V_O) = E0 + Δμ_O + qE_F, where E0 is the value in the reference state (O-rich limit if we fold μ_O^ref into E0). O-rich: Δμ_O = 0 → E_f(V_O) = E0 (highest). Zn-rich: Δμ_O = −3.6 → E_f(V_O) = E0 − 3.6 (lower). ✓ Correct: O vacancies are easier to form under Zn-poor... wait, V_O is easier to form under O-poor = Zn-rich conditions. ✓ Yes. V_Zn: n_Zn = −1 → E_f = E0 + Δμ_Zn + qE_F = E0 + (ΔH_f − Δμ_O) + qE_F. O-rich: Δμ_O = 0 → Δμ_Zn = −3.6 → lower. ✓ Zn vacancies are easier under O-rich (Zn-poor) conditions. ✓ Zn_i: n_Zn = +1 → E_f = E0 − Δμ_Zn + qE_F = E0 + Δμ_O − ΔH_f + qE_F. Zn-rich: Δμ_Zn = 0 → E_f = E0. O-rich: Δμ_Zn = −3.6 → E_f = E0 + 3.6 (high). ✓ O_i: n_O = +1 → E_f = E0 − Δμ_O + qE_F. O-rich: Δμ_O=0 → E0. Zn-rich: higher by 3.6. ✓ Zn_O antisite: n_Zn = +1, n_O = −1 → E_f = E0 − Δμ_Zn + Δμ_O = E0 + 2Δμ_O − ΔH_f... Zn-rich favored. ✓ O_Zn: n_O = +1, n_Zn = −1 → E_f = E0 − Δμ_O + Δμ_Zn = E0 + ΔH_f − 2Δμ_O. O-rich favored. ✓ Great, the chemistry works out with a single slider. Now I need reference E0 values (at the respective reference states) and charge transition levels. I'll adopt values inspired by Janotti & Van de Walle (2007) and standard review values. Let me set (E0 defined as formation energy at E_F = 0 with Δμ_O = 0, i.e., O-rich reference; for species where the reference state differs, I'll just bake into E0 consistently using the formulas above with O-rich as reference): Charge transition levels (ε, eV above VBM), representative hybrid-DFT/LDA+U values: - V_O: (2+/0) at ~2.0 eV (deep donor, negative-U, +1 not stable). Actually HSE gives ε(2+/0) around 1.5-2.4 eV; I'll use 2.0. - V_Zn: (0/−) ~0.3 eV? Reports: ε(0/−) ≈ 0.2-0.5 eV? V_Zn transitions: (0/−) at ~0.3 eV, (−/2−) at ~1.0 eV? Hmm, Janotti-VdW got (0/−) at 0.18? and (−/2−) at 0.87? There are also (−2/−3)? Some say V_Zn is (2−) stable in n-type. I'll use (0/−) = 0.3, (−/2−) = 0.9. - Zn_i: shallow donor; (2+/0) at ~2.3 eV? In Janotti-VdW, Zn_i is (2+) throughout most of gap, (2+/0) around 1.5? Hmm. Actually I recall ε(2+/0) for Zn_i ~ 2.3 eV (deep negative-U). I'll use 2.3. - O_i (octahedral): deep acceptor (0/−)? O_i is an acceptor with (0/−) around 1.3? Actually O_i: charge states 0, −, 2−... ε(0/−)?? I recall O_i has (0/2−) around ~1 eV? Let me just use (0/−) at 0.7 eV, (−/2−) at 1.3 eV? Hmm. Janotti-VdW: O_i split-interstitial/octahedral, ε(0/−) ≈ 0.7? I'll go with transitions at 1.0 (0/−)? I need to be careful not to present wrong physics to a professor. Best approach: label clearly "Representative values (see references: Janotti & Van de Walle 2007; Oba et al. 2008; Lyons et al. 2017)". The tool is for studying/teaching — interactive exploration. I'll also make the dataset editable? That might be too much. But maybe a small "Edit dataset" JSON in a modal would be a killer feature for a professor. Could do a textarea where they can tweak numbers. Let me include it — makes it genuinely useful. Let me define the dataset as JS objects: defects = [ { name: "V_O", label: "V_O (oxygen vacancy)", type: donor, color, states: [ {q:+2, E0: 2.3, from 0 to 2.0}, {q:0, E0: ...} ] } Better: represent each defect by list of (q, E0_q) where E0_q is formation energy at E_F=0 at reference chemical potential (Δμ_O=0). Then the envelope picks min over states at each E_F. Charge transition levels emerge automatically at intersections — elegant and physically correct! Then I don't need to separately specify ε values; they're computed. I can display them. So for each defect, give E_f(q, E_F=0, O-rich) for all relevant q. Values (inspired by literature, e.g., Janotti-VdW PRB 76 165202 Fig. 2): O-rich, at E_F=0: - V_O: q=+2: 2.4 eV; q=0: 6.4 eV? For negative-U with ε(2+/0) at ~2.0 eV: E(0) = E(2+) at E_F=2.0 → E0(0) = E0(2+) + 2·2.0 = 2.4+4.0 = 6.4. Hmm that gives ε(2+/0)=2.0. But also need q=+1 higher than both (negative U). E0(+1) should be above line: ε(2+/+) < ε(+/0). For teaching, I can include q=+1 as metastable with E0 = 4.6 say → ε(2+/+)=2.2, ε(+/0)=1.8 → negative U ordering (+/0 below 2+/+) means +1 never stable. Nice teaching moment. Under Zn-rich, V_O 2+ at E_F=0 → 2.4−3.6 = −1.2 eV. Negative formation energy! That matches the literature statement that V_O is cheap in Zn-rich near VBM but still high for n-type (E_F near CBM adds +2·3.2). At E_F=3.2: −1.2+6.4=5.2 eV → explains "V_O cannot cause n-type conductivity". - V_Zn: q=0: 4.2?; q=−1: E0; q=−2: E0. With O-rich reference: E0(0) such that lines work: E0(−1) = E0(0) − ε(0/−)... wait E_f(−1) = E0(−1) − E_F. At ε(0/−): E0(0) = E0(−1) − ε → E0(−1) = E0(0) + ε(0/−). With ε(0/−)=0.3, ε(−/2−)=0.9: E0(−2) = E0(−1) + 0.9·2? No: at ε(−/2−): E0(−1) − ε = E0(−2) − 2ε → E0(−2) = E0(−1) + ε = E0(−1) + 0.9. Set E0(0, O-rich) = 3.5 → E0(−1) = 3.8, E0(−2) = 4.7. At E_F = 3.2 (n-type): E_f(−2) = 4.7 − 6.4 = −1.7 eV → strongly negative, compensating acceptor in n-type under O-rich. ✓ Matches "V_Zn is a killer of n-type doping... compensating acceptor". Good pedagogy. - Zn_i: q=+2: O-rich E0 = 2.8? Under Zn-rich reference... my formulas use O-rich as reference (Δμ_O=0). Zn_i: E_f = E0 + (Δμ_O − ΔH_f)... wait: E_f = E0 − Δμ_Zn where Δμ_Zn = ΔH_f − Δμ_O → E_f = E0 − ΔH_f + Δμ_O = E0 + 3.6 + Δμ_O. Hmm wait ΔH_f = −3.6. E_f = E0 − Δμ_Zn = E0 − (ΔH_f − Δμ_O) = E0 + 3.6 + Δμ_O. O-rich: Δμ_O=0 → E_f = E0 + 3.6?? That means E0 as I defined ("O-rich reference") isn't the O-rich value for interstitials. Simpler: define E0 as the formation energy at E_F=0 under O-rich conditions, and apply ΔE = −Σ n_i Δμ_i shifts. For Zn_i: n_Zn=+1 → shift = −Δμ_Zn = −(ΔH_f − Δμ_O) = Δμ_O − ΔH_f = Δμ_O + 3.6. O-rich: shift 0 ✓. Zn-rich: shift = −3.6+3.6 = 0?? That's wrong — Zn_i should become cheaper in Zn-rich... wait no. In Zn-rich, Δμ_Zn = 0 → Zn_i cheap? Zn-rich means μ_Zn high (metallic Zn reservoir) → Zn interstitial formation energy = E0' − μ_Zn... yes cheaper. Under O-rich, μ_Zn = ΔH_f = −3.6 → expensive. My E0(O-rich) for Zn_i should be high, and at Zn-rich it drops by 3.6. Shift = Δμ_O + 3.6: Zn-rich → Δμ_O = −3.6 → shift 0; O-rich → shift +3.6?? No! Shift should be 0 at O-rich if E0 is defined at O-rich. Shift relative to O-rich = −Δμ_Zn − (−Δμ_Zn^O-rich) = −(ΔH_f−Δμ_O) + ΔH_f = Δμ_O. So shift(Zn_i) = Δμ_O (0 at O-rich, −3.6 at Zn-rich). ✓ General: shift = −Σ_i n_i Δμ_i with Δμ values relative to the O-rich reference state where Δμ_O=0, Δμ_Zn=ΔH_f. Check V_O: shift = +Δμ_O: O-rich 0, Zn-rich −3.6 (cheaper ✓). V_Zn: shift = +Δμ_Zn = ΔH_f − Δμ_O → O-rich: −3.6?? But E0 was defined at O-rich, so shift must be 0 there. ✗. Because Δμ_Zn at O-rich = ΔH_f ≠ 0. The issue: "shift relative to O-rich reference" = −Σ n_i (Δμ_i − Δμ_i^ref) with Δμ_O^ref=0, Δμ_Zn^ref=ΔH_f. So: shift = −Σn_iΔμ_i − [−Σn_iΔμ_i^ref]. For V_Zn: −(−1)(Δμ_Zn − ΔH_f) = Δμ_Zn − ΔH_f = (ΔH_f−Δμ_O) − ΔH_f = −Δμ_O: O-rich 0 ✓, Zn-rich +3.6 (more expensive ✓). For Zn_i: −(+1)(Δμ_Zn − ΔH_f) = −Δμ_O: O-rich 0 ✓, Zn-rich −3.6? wait −Δμ_O at Zn-rich = +3.6?? Δμ_O=−3.6 → −(−3.6)=+3.6. Hmm that says Zn_i more expensive in Zn-rich — wrong sign? Let's recheck: Δμ_Zn − ΔH_f where Δμ_Zn = ΔH_f − Δμ_O. At Zn-rich Δμ_O = ΔH_f → Δμ_Zn = 0 → Δμ_Zn − ΔH_f = +3.6. Shift for Zn_i = −(+1)(+3.6) = −3.6. ✓ cheaper. I made an arithmetic error: −Δμ_O... −(Δμ_Zn − ΔH_f) = −(−Δμ_O) = Δμ_O. Zn-rich: Δμ_O = −3.6 → shift −3.6 ✓. O-rich: 0 ✓. Good: shift(Zn_i) = Δμ_O. V_Zn shift = +(Δμ_Zn − ΔH_f) = −Δμ_O ✓ (O-rich 0, Zn-rich +3.6, more expensive ✓). O_i: −(+1)(Δμ_O − 0) = −Δμ_O: Zn-rich +3.6 more expensive ✓. V_O: −(−1)(Δμ_O) = Δμ_O: Zn-rich −3.6 ✓. Zn_O: n_Zn=+1, n_O=−1 → shift = −(Δμ_Zn−ΔH_f) + (Δμ_O) = Δμ_O + Δμ_O = 2Δμ_O: Zn-rich −7.2 (much cheaper) ✓ makes sense (antisite = adding Zn, removing O; strongly favored Zn-rich). O_Zn: n_O=+1, n_Zn=−1 → shift = −Δμ_O + (Δμ_Zn − ΔH_f)... = −Δμ_O + (−Δμ_O) = −2Δμ_O: O-rich cheaper ✓. Nice: shift = −(Δn_Zn)(Δμ_Zn−ΔH_f) − (Δn_O)(Δμ_O) with Δμ_O ∈ [ΔH_f, 0], Δμ_Zn − ΔH_f = −Δμ_O. So shift = Δn_Zn·Δμ_O − Δn_O·Δμ_O = (Δn_Zn − Δn_O)·Δμ_O. Beautiful: shift = (n_Zn − n_O)·Δμ_O. Check V_O: n_Zn=0, n_O=−1 → shift = +Δμ_O ✓. V_Zn: n_Zn=−1, n_O=0 → shift = −Δμ_O ✓. Zn_O: n_Zn=+1,n_O=−1 → 2Δμ_O ✓. So in code: E_f(defect, q, E_F, Δμ_O) = E0_q + q·E_F + (n_Zn − n_O)·Δμ_O. Clean! Now choose E0 values (O-rich, E_F=0), consistent with typical literature transition levels. Let me pick values so the O-rich diagram resembles Janotti-VdW Fig. 2(a) reasonably: - V_O: q=+2: 2.3; q=+1: 4.5 (metastable); q=0: 6.3. → ε(2+/0) = (6.3−2.3)/2 = 2.0 eV. ε(2+/+) = 2.2, ε(+/0) = 1.8 → +1 metastable (negative-U). Good. - V_Zn: q=0: 3.4; q=−1: 3.7; q=−2: 4.6. → ε(0/−)=0.3, ε(−/2−)=0.9. - Zn_i: q=+2: 4.2? Under O-rich Zn_i is expensive. Hmm, but with shift formula, Zn-rich E0 becomes 4.2−3.6=0.6 eV → low formation energy in Zn-rich near VBM ✓ (known result). ε(2+/0) around 2.2: E0(0) = 4.2 + 2·2.2 = 8.6. q=+1 metastable ~6.5. - O_i (octahedral): q=0: 2.6; q=−1: 3.3; q=−2: 4.6 → ε(0/−)=0.7, ε(−/2−)=1.3. O-rich: O_i is lowish near VBM? Under O-rich, O_i is the lowest-energy intrinsic defect for p-type... Actually yes, O_i is the dominant compensating defect in p-type ZnO (acceptor? no—O_i in p-type would be neutral or 2−? Hmm, O_i is a deep acceptor; in p-type material (E_F near VBM), O_i would be neutral with formation ~2.6 eV. In n-type, 2− with E_f = 4.6−6.4 = −1.8? That would make O_i strongly compensating in O-rich n-type. Hmm, that matches Janotti-VdW? In their O-rich figure, O_i 2− at E_F=E_g has E_f ≈ −1 eV? I think theirs was around −1 eV, yes-ish (O_i and V_Zn both negative in n-type O-rich → equilibrium favors strongly compensated material; the point is p-type is hard). Fine for a teaching tool. Hmm wait, actually I want to double check ε values for O_i. Janotti-VdW 2007: O_i(oct) ε(0/−)? They found O_i is stable as 2− throughout much of the gap? I recall O_i (0/−) ~ 1 eV and (−/2−) ~ 1.6 eV? Not sure. I'll pick (0/−)=1.0, (−/2−)=1.7, E0(0)=2.6 → E0(−1)=3.6, E0(−2)=5.3 → at E_F=3.2: 5.3−6.4=−1.1 eV. OK. - Zn_O antisite: q=+2: 5.5 (O-rich); Zn-rich: 5.5−7.2 = −1.7?? Too low. Janotti-VdW: Zn_O is a shallow donor but high energy ~ always high. Let me set O-rich E0(+2) = 6.5, ε(2+/0) ~ 1.7? Actually Zn_O (2+/0) around 1.7 eV? I recall Zn_O is negative-U with ε(2+/0) ≈ 1.7 eV above VBM? Hmm. Set E0(+2)=6.5, E0(0)=6.5+3.4=9.9. Zn-rich: 6.5−7.2=−0.7 → negative at VBM, meaning antisites form spontaneously?? In reality Zn_O in Zn-rich at E_F=0 is ~ −0.5? Hmm, actually I don't think Zn_O goes negative even Zn-rich; Janotti-VdW Fig shows Zn-rich Zn_O 2+ around 0 eV at VBM? I believe in their Fig. 2(b) Zn-rich, Zn_O^2+ starts near ~0.5 eV at E_F=0. So O-rich ≈ 0.5+7.2 = 7.7. Set 7.5. - O_Zn antisite: q=0 mostly? O_Zn is a deep acceptor? Actually O_Zn is high energy always; neutral or 2−? I'll include q=0: 5.0, q=−2: 7.0? Hmm. O_Zn (0/2−)? To keep it simple and not misinform, maybe exclude O_Zn or include with high energies. O_Zn under O-rich: shift = −2Δμ_O → Zn-rich +7.2 → 12.2, O-rich 5.0. In n-type O-rich: E_f(2−) = 7.0 − 6.4 = 0.6 eV? Hmm that would make O_Zn relevant... I think literature says O_Zn is high in energy in all conditions. Let me set E0(0) = 5.4, E0(−2) = 9.2 → ε(0/2−) = 1.9, at E_F=3.2: 9.2−6.4=2.8. OK that's high-ish. Fine. Also could add H interstitial (H_i^+, shallow donor, μ_H conditions) — adds complexity; maybe include as optional with fixed Δμ reference? I'll skip H in the plot but mention in library. Or include with a fixed H chemical potential choice noted. Hmm, keep scope tight: 6 defects is plenty. Defect concentrations: c = N_sites · g · exp(−E_f/kT) with temperature slider (300–1300 K). Show bar chart or per-defect concentration at given T and E_F, μ conditions. Also compute net charge/neutrality? Full self-consistent Fermi level would be fancy but requires DOS. Maybe simpler: given E_F slider, show concentrations and note charge. Could add "freeze-in" concept: anneal at T, quench. Keep it as an explorer. Band diagram tab: draw bandgap 3.37 eV, VBM=0, CBM, plot transition levels as horizontal lines with labels ε(q/q'), color-coded by defect, toggle O-rich/Zn-rich (levels don't depend on μ, but stability ranges do). Also show optical signatures: V_O → green PL ~2.5 eV (debated! Actually green luminescence historically assigned to V_O but hybrid DFT says V_O has deep levels inconsistent... The green emission ~2.4 eV was assigned to V_O, later to V_Zn or Cu. This is a nice nuance for a professor tool!). I'll include a "PL signatures" section with the caveat notes. 3D structure: Three.js wurtzite supercell (2x2x2 or 3x3x2), Zn atoms (blue-gray), O (red), click an atom to create vacancy (it disappears), or click "add interstitial"/"antisite" mode. Show selected defect info panel with formation energy at current conditions, Kroger-Vink notation. Controls: rotate, reset, cell outline, bond display. This is the "wow" centerpiece. Implementation plan (single HTML file): - CDNs: Tailwind (script), Three.js (use r128 or newer via unpkg; use global build to avoid module issues: https://cdnjs.cloudflare.com/ajax/libs/three.js/r128/three.min.js), OrbitControls from a compatible source... OrbitControls for r128 non-module: https://cdn.jsdelivr.net/npm/three@0.128.0/examples/js/controls/OrbitControls.js. That works with global THREE. Chart.js for charts (https://cdn.jsdelivr.net/npm/chart.js). GSAP maybe unnecessary. Use Chart.js for formation energy diagram and concentration bars. Actually, I could hand-roll the formation-energy plot with SVG for full control (kinks, markers, envelopes, hover tooltips). Chart.js can do line charts with tooltips easily. But envelope + crossing markers + custom labels is easier custom SVG/Canvas. Let me hand-roll an SVG plotter — more control, academic style (axis labels, eV ticks, dashed metastable lines, shaded stability regions, transition-level markers). It'll look like a real publication figure, which will impress a professor. Structure of the app: - Header: title "ZnO Defect Workbench" / "defect-lab", subtitle. - Tab nav: Structure Explorer | Formation Energies | Transition Levels | Concentration & T | Optical Signatures | Reference Library - Sidebar within Formation tab: Δμ_O slider (O-rich ↔ Zn-rich), E_F handled by x-axis, defect toggles, temperature for concentration, export PNG/SVG button, dataset editor. Let me think about the SVG formation energy plot: - x-axis: E_F from 0 to 3.37 eV (label "Fermi level (eV)", VBM=0, CBM=3.37) - y-axis: Formation energy (eV), 0 to maybe 8, auto-scale. - For each defect: for each charge state q: line E = E0_q + q·E_F + shift. But only draw the state where it's the minimum among that defect's states (bold solid), other segments faint dashed. Transition levels: circles at kinks with tooltip "ε(2+/0) = 2.00 eV". - Shade conduction band region beyond 3.37. - Hover crosshair showing E_F and values of all defects? Maybe tooltip on nearest line. - Toggle defects via legend checkboxes. - Buttons: "O-rich", "Intermediate", "Zn-rich" presets + slider. - Readout panel: at current Δμ and a chosen E_F (draggable vertical line!), list formation energies sorted, highlight lowest → "dominant defect". Draggable E_F line is a great interactive feature. - Export: SVG download (serialize node). Concentration tab: given E_F (linked), T slider, compute c for each defect = N_sites exp(−E_f/kT) (use N_sites ~ 4.2×10^22 cm⁻³ for Zn sites; degeneracy factors optional). Bar chart (custom SVG or Chart.js) log scale. Include "quench/freeze-in" note. Maybe also show net doping estimate? Skip net neutrality—too much. Wait — could actually do charge-neutrality solver: solve for E_F such that Σ q·c_q = 0 (only intrinsic defects). That's very doable: concentrations as function of E_F are sums of exponentials; bisection on E_F in gap. With freeze-in at T_freeze then recompute at T_op? That's sophisticated but maybe just do equilibrium at T. That's a genuinely impressive "research-grade" feature: "Equilibrium Fermi level solver". Let me include it in Concentration tab: given T and Δμ, find E_F where neutrality holds (include electrons/holes? Without DOS carriers, charge balance among defects only — at high T defects dominate... hmm, actually free carriers matter: n = N_C exp(−(E_C−E_F)/kT) etc. I can include N_C = 2.9×10^18? ZnO m_e* = 0.24, N_C = 2.5e19·(m*/m0)^1.5·(T/300)^1.5 ≈ 2.9e18 at 300K; N_V with m_h* = 0.59 → ~1.1e19. Include carriers → real self-consistent Fermi level! That's a proper mini defect-equilibrium engine (like a tiny py-sc-fermi). This would blow a professor's mind in a one-shot HTML. Let's do it. Neutrality: n + Σ q_neg·c = p + Σ q_pos·c. Solve via bisection over E_F ∈ [−0.5, 3.9]. Defect concentration: for each defect, total concentration over charge states using formation energies at that E_F: c_D(E_F) = N_site · Σ_q g_q exp(−E_f(q,E_F)/kT). Charge contribution = Σ_q q·N_site·g_q exp(−E_f/kT). Site counts: vacancies/interstitial sites ~ 2 per unit cell volume... N_Zn sites = 4.15e22 cm⁻³ (ZnO density 5.61 g/cm³, M=81.38 → 4.15e22 formula units/cm³). Interstitial site count ~ 2×? Just use N = 4.15e22 for all, with degeneracy g=1, note approximation. Actually V_O uses O sites (same count), Zn_i octahedral sites = 4.15e22 too (2 per cell). Fine. Show: solved E_F, carrier concentrations n, p, defect concentrations chart, "quench to RT" button (freeze defects at T_eq, resolve E_F at 300K with fixed total defect counts — that's more advanced: at quench, total defect concentrations fixed, charge states re-equilibrate → solve neutrality again with fixed totals and Fermi-dirac... that requires distribution over charge states via ratios from E_f differences: ratio c_q'/c_q = exp(−(E_f(q')−E_f(q))/kT) — that works with fixed totals! Nice: implement freeze-in: fix c_total(D) = c at T_eq; at T_op, for each defect distribute charge states by Boltzmann ratios of formation energies (which depend on E_F), then solve neutrality. This is legitimately what researchers do. I'll implement it — it's maybe 30 lines.) Optical signatures tab: interactive PL spectrum! Show synthesized PL spectrum (Gaussian peaks: NBE 3.26 eV at RT / 3.37 at low T, green 2.45, yellow 2.2, red 1.8) with toggles per band, wavelength axis, assignments and controversy notes. Draw with canvas/SVG, convert eV ↔ nm. Maybe a fun "spectrum painter". Include DLTS/EPR notes. Reference library: Kröger–Vink notation builder! Interactive: pick defect (V/Zn/O/Zn_i...), site, charge (•, ′, ×) → renders proper notation with Unicode: e.g., V_O^•• → V$_O^{••}$. Kröger-Vink: V_O•• (oxygen vacancy, +2 effective), Zn_i••, V_Zn′′. Rendered with superscript dots/primes. Also key equations (formation energy, neutrality), key references list (Janotti & VdW 2007 & 2009, McCluskey, Özgür 2005, Look, Lyons 2017 HSE, Oba 2008, Kohan 2000, Van de Walle H-doping 2000). Structure explorer details (Three.js): - Build wurtzite lattice: a=3.25, c=5.206 Å. Generate supercell 3×3×2 by default. - Atoms: Zn spheres color #7f9fcf? Classic: Zn gray/blue (like CPK Zn = brownish?), Jmol Zn color is #7a80a6? Oxygen red #d33. Use nice materials: MeshPhongMaterial, O red, Zn slate blue-gray. - Bonds: connect Zn–O < 2.1 Å (tetrahedral). Creating bonds for supercell — compute pairs within cutoff. Fine for ~100 atoms. - Interaction: raycast click on atom → depending on mode: "Vacancy" (remove atom with puff?), "Antisite" (swap species), "Inspect" (show site info). Add interstitial: click empty space? Place at octahedral site of clicked tetrahedron... simpler: buttons "Add Zn_i at octahedral site" places at fixed known octahedral position; user can click it to remove. Keep: modes [Inspect, Vacancy, Antisite, Zn interstitial, O interstitial]. For interstitial mode, click a Zn/O atom to insert nearby octahedral site? Octahedral holes in wurtzite: e.g., (2/3, 1/3, ~0.66)? Known octahedral interstitial site in wurtzite at (1/3, 2/3, 0.56)? For Zn_i, octahedral site. Simplest robust: clicking any atom in "Zn_i" mode adds a Zn at the nearest octahedral hole from a precomputed list of holes in the supercell. I'll precompute octahedral holes: in wurtzite, octahedral holes at (2/3, 1/3, 1/8) type positions? Hmm. The octahedral hole in wurtzite: coordinates (2/3, 1/3, 0.13)? Let me just pick holes at positions like (2/3,1/3, u−1/4)? To avoid wrong crystallography, I could compute holes geometrically: find centers of octahedra of O atoms... Simpler and safe: use the known site: octahedral hole at fractional (2/3, 1/3, 0.125)? Hmm, let me think. Wurtzite = hexagonal close packing of O with Zn in half the tetrahedral holes. Octahedral holes in hcp lattice at (1/3, 2/3, 1/4) and (1/3, 2/3, 3/4)? In hcp, octahedral holes are at (1/3, 2/3, 1/4) & (1/3, 2/3, 3/4) relative to the hcp cell. For wurtzite O sublattice approximating hcp: O atoms at (1/3,2/3,u)≈(1/3,2/3,0.375) and (2/3,1/3,0.875). The octahedral hole between layers: (0, 0, ~0.25)? Hmm. Known from literature (Janotti-VdW): Zn octahedral interstitial site. In wurtzite, octahedral site at fractional (0, 0, ~0.25)? Let me just compute: O at A layer (1/3,2/3,0.375) and B layer (2/3,1/3,0.875) i.e., (2/3,1/3,−0.125). Octahedral hole coordinated by 3 O from each layer: position (0,0, 0.125)? An octahedron center at (0,0,z) with 3 O at (1/3,2/3,0.375) above and 3 O at (2/3,1/3,−0.125) below → center z = (0.375 + (−0.125))/2 = 0.125. ✓ So octahedral hole at (0, 0, 0.125) (and equivalents + (1/3,2/3,?)...). Also (0,0,0.625). Good: octa holes at (0,0,0.125) and (0,0,0.625) in fractional coords of wurtzite cell. I'll use these for interstitial placement (nearest to click point). That's crystallographically defensible. - Info panel shows: site type, fractional coords, if defected: formation energy at current Δμ_O/E_F, charge state, Kröger-Vink. - Visual polish: fog, soft lighting, unit cell outline, atom labels toggle, animation (slow rotation), "explode vacancy" animation (scale down + fade). Maybe glow on hover. Also nice: ambient page design — dark academia theme: deep navy/ink background, brass/gold accents, serif headings (Cormorant Garamond / EB Garamond), mono for data (JetBrains Mono / IBM Plex Mono). Tailwind + custom CSS. Loading screen with title? Keep quick. Tabs as SPA with show/hide. Ensure Three.js only initializes when structure tab active (or on load hidden container issue — init lazily on first open). Let me also add a "Defect Card" library: click defect in any context → modal with details: description, diffusion, relevant experiments, references. Maybe fold into Reference tab as cards. Time to define precise dataset (O-rich E0 at E_F=0). Let me sanity-check each against memory of Janotti & Van de Walle PRB 76, 165202 (2007), Fig. 2 (values approximate from figure): O-rich (Fig. 2a) at E_F=0 (approx): V_O^2+ ≈ 2.0; O_i^0 ≈ 2.7 (oct); V_Zn^0 ≈ 3.6; Zn_i^2+ ≈ 4.2; Zn_O^2+ ≈ 5.5; O_Zn^0 ≈ 6.5. At E_F = Eg (3.4 in their corrected): V_Zn^2− ≈ 3.6+?... with ε(0/−)=0.2? Their V_Zn: (0/−)=0.18? (–/2–)=0.87? At Eg: E_f(2−)=3.6+0.2+0.87... hold on: E0(−2) = E0(0)+ε(0/−)+ε(−/2−) = 3.6+1.07 = 4.67 → at 3.4: 4.67−6.8 = −2.1 eV. Their figure shows V_Zn 2− at Eg ≈ −2 eV O-rich? I believe ~ −2. ✓ plausible. Zn-rich (Fig 2b): V_O^2+ at 0 → 2.0−3.6 = −1.6 ✓ (theirs ~ −1.5). Zn_i^2+ at 0 → 4.2−3.6 = 0.6 ✓ (theirs ~0.5). V_Zn^0 → 3.6+3.6=7.2 (theirs ~7) ✓. O_i^0 → 2.7+3.6=6.3 ✓. Zn_O^2+ → 5.5−7.2 = −1.7 (theirs ~ −1?? I recall Zn_O 2+ slightly negative Zn-rich? hmm maybe ~0.2). Adjust Zn_O E0(+2)=6.5 → Zn-rich −0.7... Let me set 6.8 → −0.4. Eh. Set 7.0 → −0.2. Fine ≈0. Transition levels to encode: - V_O: (2+/0) = 2.0; +1 metastable between 1.8/2.2. - V_Zn: (0/−)=0.3? Use 0.2 to match J-VdW? Theirs: ε(0/−) = 0.18, ε(−/2−) = 0.87? Hmm hybrid HSE: (0/−)=0.5? (−/2−)=1.1? I'll use 0.3 and 1.0 as compromise, label "representative". - Zn_i: (2+/0) = 2.3? J-VdW got Zn_i (2+/0) ~ 2.3? I recall Zn_i ε(2+/0) ≈ 2.3 eV. OK. - O_i: (0/−)=1.0, (−/2−)=1.7? J-VdW: O_i oct transitions around 1.0 and 1.7? I don't remember exactly; plausible. Actually for O_i(oct) I recall (0/−) ≈ 1.3 eV? I'll go 1.0/1.7. - Zn_O: (2+/0)=1.7: E0(0) = 7.0 + 3.4 = 10.4. - O_Zn: keep only q=0 at 6.5 and maybe (−2) 10.9? Actually O_Zn: acceptor (0/−)? I'll include 0 and −2 with ε(0/2−)=2.2: E0(−2) = 6.5+2·2.2=10.9. At Eg O-rich: 10.9−6.8 = 4.1 high ✓. E0 table (O-rich, E_F=0): V_O: {+2: 2.0, +1: 4.2, 0: 6.0} → check: ε(2+/+)= E0(+1)−E0(+2) = 2.2; ε(+/0) = E0(0)−E0(+1) = 1.8. Since (2+/0)=2.0 < midpoint consistency: +1 stable only if ε(+/0) > ε(2+/+); here 1.8<2.2 → metastable ✓. V_Zn: {0: 3.6, −1: 3.9, −2: 4.9} → ε(0/−)=0.3, ε(−/2−)=1.0. Zn_i: {+2: 4.2, +1: 6.7, 0: 8.8} → ε(2+/+)=2.5, ε(+/0)=2.1, (2+/0)=2.3 ✓ negative-U. O_i: {0: 2.7, −1: 3.7, −2: 5.4} → ε(0/−)=1.0, ε(−/2−)=1.7. Zn_O: {+2: 7.0, 0: 10.4} → (2+/0)=1.7. (skip +1, note negative-U) O_Zn: {0: 6.5, −2: 10.9}. Colors: V_O green (#22c55e?) — thematic: green luminescence. V_Zn amber. Zn_i sky blue. O_i violet. Zn_O orange. O_Zn rose. Now the "impressive" factor: I want this to feel like premium software ("VANTA" / "ZINCWORKS"). Name: "ZnO Defect Workbench" or "VURTZITE" — let me go with "Wurtzite Lab — ZnO Defect Workbench"? Or "DEFECTA: ZnO Point-Defect Laboratory". I'll call it "ZnO·DefectLab" hmm. Maybe "VANTA: Virtual Analysis of Native defects in ZnO"? Cheesy. Keep classy: "ZINCWORKS — a computational workbench for native point defects in ZnO". Or simply "ZnO Defect Workbench". I'll go with "DefectLab·ZnO" branding in header with version badge "v1.0 · for research & teaching". Design: dark theme (#0a0f1e base), glassmorphism cards, gold accent (#d4af6a) + teal (#5eead4) accents, Garamond display font. Tabs with smooth transitions. Subtle grain/noise background. Loading overlay fade. Let me now carefully write the code. It's long; be systematic. Sections: 1. : fonts (Google Fonts: Cormorant Garamond, Inter, JetBrains Mono), Tailwind CDN, custom CSS (scrollbars, tab styles, sliders, tooltips, kbd, etc.) 2. Body: - Loading overlay - Header with logo mark (SVG hexagon), title, small nav - Tab bar - Panels: A. Overview (hero + stats + quick intro + mini band diagram teaser + "launch" buttons) B. Structure (Three.js canvas + toolbar + inspector panel) C. Formation (SVG plot + controls: Δμ slider, presets, E_F draggable cursor, defect toggles, results table, export SVG/CSV, edit dataset) D. Levels (band diagram SVG: levels per defect, animate with Δμ? levels don't shift; show stability ranges + negative-U badges; also side table) E. Equilibrium (concentration engine: T slider, Δμ slider (shared global state), solve button / auto, results: E_F*, n, p, defect table + log bar chart, quench to 300K toggle) F. Optical (PL spectrum canvas/SVG with bands toggles, NBE, green/yellow/red, eV↔nm, temperature effect note; controversy notes) G. Library (Kröger–Vink builder, equations with nice typography, defect cards, references) - Footer 3. Scripts: state object, dataset, formation energy functions, SVG plot renderers, neutrality solver, Three.js scene, tab router, dataset editor (JSON modal with validation), export functions. Shared state: { dmu: 0 (O-rich), EF: 1.6, T: 1000, toggles: {...} }. Components subscribe & re-render. Let me make sure physics formulas displayed correctly: Formation energy (Kröger-style display): E_f[D^q] = E_tot[D^q] − E_tot[bulk] − Σ_i n_i μ_i + q(E_V + E_F) + E_corr Concentration: c[D^q] = N_sites g exp(−E_f/k_B T) Charge transition: ε(q/q′) = (E_f^q − E_f^q′)/(q′ − q) at crossing. Neutrality: p + Σ q⁺c = n + Σ |q⁻|c. Band diagram tab design: vertical energy axis 0–3.37 eV, VBM at bottom, CBM top (hatched), each defect a vertical column showing its transition levels as ticks with labels; negative-U defects get special marker (double-tick). Color-coded. Plus a table of ε values computed from dataset (auto-generated!). Auto-generating from dataset ensures consistency when professor edits dataset. Also compute and show in Formation tab the "dominant defect at cursor" and charge state. CSV export: E_F, E_f per defect (min envelope) — easy. SVG export of formation plot: serialize SVG element with inline styles → blob download. Since I hand-roll SVG with attributes (stroke etc.), serialization works. Need xmlns. OK. Now, wurtzite supercell generation code: ```js const a = 3.25, c = 5.206, u = 0.382; const A1 = new THREE.Vector3(a,0,0); const A2 = new THREE.Vector3(-a/2, a*Math.sqrt(3)/2, 0); const A3 = new THREE.Vector3(0,0,c); basis = [ {el:'Zn', f:[1/3,2/3,0]}, {el:'Zn', f:[2/3,1/3,0.5]}, {el:'O', f:[1/3,2/3,u]}, {el:'O', f:[2/3,1/3,0.5+u]}, ] ``` Supercell nx=3, ny=3, nz=2 → 2*2*27? atoms = 4 per cell × 18 cells = 72. Good. Bonds: distance < 2.2 Å between Zn-O. With 72 atoms, pairwise ~2500 checks fine. Bond as cylinders — could be many (~72×4/2=144). Use cylinders with low radial segments (6). OK. Octa holes: fractional (0,0,0.125), (0,0,0.625) per cell → supercell list. Click handling: raycaster against atom meshes. Modes: - inspect: show info - vacancy: remove (store defect record, animate shrink then hide) - antisite: swap element color/radius - Zn_i / O_i: add atom at nearest octa hole (mark as interstitial) Reset button restores. Defect info panel: shows current defects list with KV notation: V_O^•• using charge from current E_F/Δμ (the stable state) — computed from dataset! Nice integration: same physics engine feeds structure view. E.g., "V_O^{2+} → V_O^••, E_f = 1.24 eV at current conditions." KV notation rendering: V with subscript O, superscript ••. Use HTML: V_O^••. Charges: + → •, − → ′ (prime ′). e.g., V_Zn′′. Also in structure view: show cell edges (LineSegments), axes helper optional. Lighting: hemisphere + directional + rim. Background transparent over CSS gradient. Slow auto-rotate toggle. Now the PL spectrum tab: canvas plot, x from 1.5 to 3.6 eV (and nm top axis 827→344). Bands (Gaussian, σ): - NBE exciton: 3.26 eV (RT), σ=0.03, intensity 1 - Green band: 2.45 eV, σ=0.18, intensity var (assign: V_Zn/Cu debate; historically V_O) - Yellow: 2.15 eV, σ=0.15 (Li/O_i related) - Red: 1.85 eV, σ=0.12 (O_i?/V_O-related transitions debated) Each with toggle + intensity slider? Keep toggles + one "defect density" slider per band maybe overkill. Toggles + hover tooltip with assignment notes. Sum curve drawn + filled. Also a "10 K vs 300 K" toggle shifting NBE (3.37 vs 3.26) — nice touch. Add phonon replica? Skip. Also mention techniques: PL, DLTS, EPR/ODMR, positron annihilation (PAS) for V_Zn — nice table "which probe sees which defect". Library references (real): - Janotti & Van de Walle, Phys. Rev. B 76, 165202 (2007) - Janotti & Van de Walle, Rep. Prog. Phys. 72, 126501 (2009) - Özgür et al., J. Appl. Phys. 98, 041301 (2005) - McCluskey & Jokela, J. Appl. Phys. 106, 071101 (2009) - Look et al., Phys. Rev. Lett. 82, 2552 (1999) - Van de Walle, Phys. Rev. Lett. 85, 1012 (2000) (H in ZnO) - Lyons, Alkauskas, Janotti, Van de Walle, Phys. Status Solidi B (2017) - Oba et al., Phys. Rev. B 77, 245202 (2008) - Kohan, Ceder, Morgan, Van de Walle, Phys. Rev. B 61, 15019 (2000) - Vanheusden et al. green luminescence V_O, J. Appl. Phys. 79, 7983 (1996) Kröger–Vink builder: dropdowns: species [V, Zn, O], site [Zn, O, i], charge [2+, +, 0, −, 2−] → render + example reaction equations (e.g., incorporation of O2: ½O2 → O_O^× + V_Zn′′ + 2h•? hmm need correct: ½O2(g) + 2e′... let me write classic: ½O₂(g) ⇌ O_O^× + V_Zn″ + 2h•? Charge balance: LHS 0; RHS: 0 + (−2) + 2(+1) = 0 ✓. Mass: O ✓. That's the p-type oxidation reaction creating zinc vacancies. And Zn-rich: ZnO ⇌ Zn_i^•• + 2e′ + ½O2? LHS 0; RHS: +2 −2 +0 = 0 ✓ mass: Zn ✓ O ✓ (O_O removed to gas). Good teaching. I must be careful: quotes/primes in JS strings fine. Now write the formation-energy SVG plot function carefully: ``` function renderFormationPlot(){ const W=860,H=520, margins... x: 0..Eg(3.37); y: ymin..ymax auto from visible lines clipped to [-3, 9]. For each enabled defect: states sorted; envelope segments: compute intersections between consecutive q lines within [0,Eg]; For robustness: sample or compute properly. ``` Better: compute for each defect the lower envelope of its q-lines over [0,Eg] → list of segments (E_Fstart, E_Fend, q). Since lines are linear, envelope computed by scanning candidate breakpoints: all pairwise intersections within range, plus endpoints; evaluate min state at midpoint of each sub-interval. Robust and simple. Also draw faint dashed full lines for all states (dimmed) optionally toggle "show all charge states". Transition markers at envelope kinks: circle + small label ε(2+/0). Cursor line at state.EF draggable (pointer events on overlay rect). Side readout table: for each defect at cursor E_F & dmu: min E_f, q*, concentration at T. Sorted ascending. Highlight top row "lowest". Also show computed transition levels list under plot maybe as chips. Y-axis domain: compute min over all enabled at endpoints minus margin; clamp to [−4, 10]. Auto. Grid lines + labels. Title: "Native defect formation energies — {O-rich / Zn-rich / intermediate} (Δμ_O = x eV)". Footnote: "Representative hybrid-DFT dataset; editable in ⚙ Dataset." Concentration & Fermi solver tab: - Controls: T (300–1500 K) slider, Δμ slider (mirrors global), "Solve equilibrium" auto on change, quench toggle: T_quench shown when enabled: freeze totals at T_anneal, solve charge redistribution + E_F at T_op=300K (T_op slider too? keep 300 fixed with small slider). - Output: big E_F readout, n/p, per-defect c chart (horizontal log bars), neutrality residual, warnings (e.g., "negative formation energy — supersaturation, model breaks down"). - Note about validity (dilute limit, no complexes). Solver: ```js function defectCharge(EF,T,dmu){ sum q*N*exp(-Ef/kT), sum N*exp(-Ef/kT) per defect} function carriers(EF,T){ n=Nc(T) exp(-(Eg-EF)/kT), p=Nv(T) exp(-EF/kT) } (non-degenerate; warn if EF within 2kT of band edges) neutrality f(EF) = p + pos - n - neg; bisection. ``` Nc(T)=2.9e18*(T/300)^1.5? m_e=0.24: Nc=2(2π m* kT/h²)^{3/2} → 2.5e19*(0.24)^1.5*(T/300)^1.5 = 2.5e19*0.1176=2.94e18 ✓. Nv: m_h=0.59 → 2.5e19*0.453=1.13e19 ✓. Quench: totals frozen: for defect D, c_tot fixed; charge state fractions: w_q = exp(−E_f(q,EF)/kT_op)/Σ; charge = c_tot·Σ q w_q. Solve again. Show both panels: "At anneal T" and "After quench to 300 K". This is really slick. Degeneracy g: skip (g=1) but mention. Also I should double check: with O-rich at T=1200K, solver should yield p-ish or compensated? Whatever comes out comes out; it's exploratory. Edge: E_f very negative → exp overflow: clamp exponent to [−100, 100]; concentrations cap ~1e23. Levels tab: render band diagram: for each defect column x position, draw horizontal tick at each ε(q/q′) computed from dataset (auto), label "ε(2+/0)=2.00". Add green-arrow annotation "green PL ~2.4 eV historically linked to V_O". Add CBM/VBM labels, shaded gap. Also donor/acceptor classification chips. Optical tab: implement with canvas 2D, devicePixelRatio aware. Draw axes, eV bottom, nm top, curves. Bands toggle chips. Vertical hover line showing λ, E, and band assignment tooltip. Dataset editor modal: textarea with JSON (pretty), "Apply", "Reset defaults", validation (numeric). This elevates it for real research use (prof can plug their own HSE numbers!). Overview tab: hero with animated mini 3D? Too heavy; instead: animated SVG of wurtzite (rotating 2D projection?) Keep: big title, key facts grid (bandgap 3.37 eV, exciton 60 meV, wurtzite P6₃mc, a/c lattice, n-type tendency), "why defects matter" blurb, and buttons jumping to tabs. Plus a small live formation-energy sparkline? Could render mini version — reuse renderer with small size. Nice touch: the overview shows live plot thumbnail that reflects global Δμ. Maybe skip to control size. Simple quick-stat cards + "open workbench" buttons. Also a periodic-style element card for ZnO? Cute. Alright, code size is big but manageable. Let me write carefully with consistent IDs. Key implementation details to nail: - Tailwind CDN: https://cdn.tailwindcss.com - Three.js: use r128 global + OrbitControls from jsdelivr examples/js (works for r128). - No Chart.js needed (custom SVG/Canvas everywhere) — fewer deps, more control. Actually skip Chart.js entirely. - Fonts: Cormorant Garamond (display), Inter (UI), JetBrains Mono (data). Custom CSS: glass cards, gold slider thumbs, tab underline animation, scrollbar, noise overlay, tooltip, modal. Tab switching: nav buttons with data-tab; sections with hidden class; on switch, trigger resize handlers (Three init lazily). Let me write the neutrality solver and formation functions first mentally: ```js const KB = 8.617333262e-5; // eV/K const EG = 3.37; // eV const DHF = -3.63; // formation enthalpy ZnO eV (μ_Zn+μ_O) let DEFECTS = [ {id:'VO', name:'Oxygen vacancy', kv:'V', site:'O', color:'#34d399', nZn:0, nO:-1, states:[{q:2,e0:2.0},{q:1,e0:4.2},{q:0,e0:6.0}], note:'Deep donor...'}, ... ]; function efLine(d, st, EF, dmu){ return st.e0 + st.q*EF + (d.nZn - d.nO)*dmu; } ``` Check shift formula: shift = (n_Zn − n_O)·Δμ_O ✓ derived above. Wait let me recheck V_O: n_Zn−n_O = 0−(−1)=1 → shift=Δμ_O ✓ (Zn-rich −3.6 ✓). V_Zn: −1−0=−1 → shift=−Δμ_O → Zn-rich +3.6 ✓. Zn_i: +1−0 → Δμ_O → Zn-rich −3.6 ✓. O_i: 0−1 → −Δμ_O → Zn-rich +3.6 ✓. Zn_O: 1−(−1)=2 → 2Δμ_O ✓. O_Zn: −1−1=−2 → −2Δμ_O ✓. Envelope per defect: given EF range, find min-state segments. ```js function envelope(d, dmu, EFmin=0, EFmax=EG){ // gather candidate points const pts=[EFmin,EFmax]; for(i0 q·c) − (n + Σq<0 |q|·c). f increasing in EF? p decreases with EF, positive defect charge decreases with EF (higher EF favors negative states), n increases... so f decreases with EF. Bisect: f(lo)>0, f(hi)<0. Quench: freeze totals per defect from anneal; at T_op distribute: c_q = c_tot * w_q where w_q ∝ exp(−ef/kT_op) (normalized). Charge from defect = c_tot Σ q w_q. Edge: if any ef < 0 at anneal → totals huge (~N) → physically supersaturated; warn banner "negative formation energy: precipitates/extended defects would form; treat qualitatively". Good honest touch. Now the levels diagram: for each defect, transitions from envelope boundaries (O-rich doesn't matter; levels independent of dmu? Lines shift by same amount for all q of a given defect (same n), so intersections independent of dmu ✓ — nice teaching point: "transition levels are μ-independent"). Compute transitions per defect: from envelope over [−1, EG+1] to capture levels slightly outside? Keep within [0,EG]; list ε values. Draw: SVG width ~ container; columns per defect (6) → x spacing; vertical axis eV. CBM shaded top. Each tick: line + label right. Legend chips. Also classification: donor (q decreases with EF? donors: positive states at low EF) vs acceptor. Auto from states: has positive q → donor; negative → acceptor. Optical PL canvas: bands data: ``` bands = [ {id:'nbe', name:'Near-band-edge (free/bound exciton)', center_RT:3.26, center_LT:3.36, sigma:0.03, color:'#a78bfa', amp:1.0, note:'FX/DBE...'}, {id:'green', center:2.45, sigma:0.18, color:'#4ade80', amp:0.55, note:'Historically V_O (Vanheusden 1996); hybrid DFT & PAS link to V_Zn/Cu — still debated'}, {id:'yellow', 2.15, 0.16, '#facc15', 0.3, 'O_i / Li-related'}, {id:'red', 1.78, 0.13, '#f87171', 0.28, 'Possibly O_i / V_O-related deep emission'}, ] ``` Temperature toggle shifts NBE and changes its amplitude (exciton stronger at LT). Draw sum fill with gradient. Hover: crosshair + readout eV/nm/intensity + nearest band within tolerance → note tooltip. Structure tab toolbar: mode buttons (Inspect 🔍, Vacancy ✕, Antisite ⇄, Zn interstitial, O interstitial), toggles (bonds, labels, cell, spin), Reset, supercell size select (2×2×1, 3×3×2). Inspector: selected site info + defects made list with live E_f (using global EF & dmu) + KV. Given the shared state, structure info uses state.dmu & state.EF — set via the formation tab cursor; add note "conditions synced with Formation tab". Or add mini sliders in structure panel too. Add small Δμ & EF sliders in the inspector — syncs globally. Header nav + footer with references mini + "single-file · no backend". Loading overlay: fade out on window load. Now let me also plan the dataset JSON editor: default JSON string from DEFECTS; modal with textarea; on apply: JSON.parse, validate fields, replace, re-render all (plot, levels, tables). Provide "Copy" and "Reset". Also CSV export: rows EF 0..3.37 step 0.01? That's 337 rows fine. Columns: EF, then per defect min Ef. Download blob. PNG export for PL canvas: toDataURL → download. For SVG plots: serialize. Also print stylesheet? Skip. Accessibility: buttons with aria-labels, decent contrast. Given the huge scope, I must be efficient in writing but complete. Let me start drafting the full HTML. Header design: ```

[hexagon ZnO logo] ZnO·DefectLab — Native point-defect workbench for wurtzite ZnO ... [badges: single-file, v1.0] ``` Nav tabs: Overview, 3D Structure, Formation Energies, Transition Levels, Defect Equilibria, Optical Signatures, Library. Overview content: - Left: big serif headline "A virtual laboratory for native defects in zinc oxide." paragraph, buttons: "Open 3D structure", "Explore formation energies". - Right: card with crystal quick facts + animated sparkline plot (mini formation plot auto-updating with dmu slider? include small dmu slider here too — cute: "growth conditions" slider that syncs everywhere). Yes! Put global Δμ slider in header? No — in overview card and in formation tab; keep one source of truth. Let me consolidate global controls into a sticky "Conditions bar"? That's elegant: a slim bar under header with: Δμ_O slider (with O-rich/Zn-rich endpoints), E_F readout (from cursor/solver), T. Synced everywhere. Nice software feel. I'll add a conditions bar shown on all tabs (except maybe overview). Show current values + quick sliders for dmu and T and EF. EF is draggable cursor on plot and slider here; solver can "adopt" solved EF → button "Use solved E_F in cursor". OK writing time. I'll write compact but readable JS. Use helper `el(id)`, `fmt(x,d)`. Let me write SVG builders with template strings, using a helper `svgEl`. Simpler: build innerHTML strings for SVG content — easiest. Formation plot renderer: ```js function renderFormation(){ const svg = $('#formPlot'); const W=920,H=540, ml=64, mr=18, mt=18, mb=48; // compute y-domain ... const x = EF => ml + (EF/EG)*(W-ml-mr); const y = E => mt + (ymax - E)/(ymax-ymin)*(H-mt-mb); build grid: y ticks every 1 eV; x ticks every 0.5. for each defect enabled: allStates dashed faint polylines (if showAll) envelope segments → path with stroke color, width 2.5 kink markers circles + ε labels cursor line at state.EF (draggable), label. defect labels at right end of envelope (name at last segment end) — nice publication style. Position at x=EG, y=E_f(EG) with clamping & collision adjust simple. } ``` Drag: pointerdown on svg → if near cursor x or anywhere? Drag cursor anywhere on click in plot area: set EF. That's intuitive (click anywhere moves cursor). Also hover tooltip showing values at hover EF? Click-to-set is enough + readout table. Readout table rows sorted by E_f at cursor: name chip, q*, E_f, c (cm⁻³) at T. Highlight min. Transition chips under plot: per defect computed ε list. Levels diagram renderer similar SVG. Concentration bars: simple divs with log-scaled widths — easier than SVG. Show value labels. PL canvas: straightforward. Three.js scene: ~150 lines. Watch pitfalls: OrbitControls CDN compatibility. Use: ``` ``` This combo is known to work (global THREE.OrbitControls). Structure building: store atoms array {mesh, el, frac, siteType}. Bonds via cylinder between points. Labels: sprites with canvas text (Zn/O) — maybe heavy; use small canvas sprites only when labels toggle on; fine. Vacancy animation: tween scale to 0.01 over ~300ms then remove from scene (keep record for reset → simplest reset = rebuild entire scene). Antisite: change material color & scale to other species. Interstitial: add mesh at nearest octa hole (convert frac→cart), smaller radius? same radius, distinct emissive. Inspector default text: prompt to click. Show unit cell: LineSegments of hexagonal prism edges. Hex prism vertices: corners at combinations? Conventional hex cell is a hexagonal prism; easier: draw the orthorhombic bounding? Proper: hexagonal prism with vertices at (0,0), a1, a2, a1+a2... The conventional cell in (a1,a2,a3) basis is a parallelepiped (rhombic prism). I'll draw the parallelepiped defined by a1,a2,a3 at origin offset — clean and correct for the supercell extents: corners 0, nx*a1, ny*a2, nz*a3 combos. Draw 12 edges. Good. Center the supercell at origin for controls: compute bounding center, shift all meshes. Raycast: on click, intersect atom meshes. Also hover cursor pointer. Lighting: ambient 0.4, dir light (1,1,1), point rim. Background: transparent (renderer alpha) over CSS radial gradient. Auto-rotate: controls.autoRotate = true, speed 0.6, toggle. Handle resize. Init lazily when tab first shown (canvas size 0 when hidden → must init after visible; call on tab click). Now numbers formatting and Kröger-Vink helper: ```js function kv(species, site, q){ // species: 'V','Zn','O'; site 'Zn','O','i'; q number let sup = q>0? '•'.repeat(q) : q<0? '′'.repeat(-q) : '×'; return `${species}_${site}^${sup}`; } ``` For defects: V_O → species V site O. Zn_i → species Zn site i. Zn_O → species Zn site O (antisite). O_Zn → O on Zn. O_i. Map from dataset: add kv fields {sp, site}. Also add chemical notation ZnO with subs: ZnO plain. Alright, also a small detail: the neutrality solver needs degenerate stats? Non-degenerate fine with warning when E_F within 3kT of edges. Write the neutrality display: E_F* value, n, p (cm⁻³), ionized defect counts, compensation ratio Σacceptors/Σdonors. Also compute "carrier type" label: n-type / p-type / compensated / intrinsic. Quench panel: after solve at anneal T_a, button "Quench to T_op" → shows second card: frozen totals, new E_F, n/p at 300K. This demonstrates "defects frozen, carriers re-equilibrate" — textbook. Potential issue: at high T with O-rich, E_F may sit midgap with tiny n,p — fine. Now — writing everything. I'll aim for clean, organized code with comments. It'll be long (~1300-1600 lines). Let's go. CSS theme variables: ``` --ink:#0b1020; --panel: rgba(255,255,255,.04); --line: rgba(148,163,184,.18); --gold:#d8b26e; --teal:#5eead4; text slate-200. ``` Headings font: 'Cormorant Garamond', serif. UI: Inter. Mono: JetBrains Mono. Tailwind config inline: extend colors maybe not needed; use arbitrary values. Slider styling: accent-color or custom webkit thumb. Custom: appearance none, track gradient gold, thumb circle. Tab styles: uppercase tracking, gold underline for active. Cards: rounded-2xl border white/10 bg-white/[0.03] backdrop-blur. Noise: SVG feTurbulence data-URI overlay at low opacity. Buttons: gold gradient for primary. Let me now write the actual file mentally with all IDs: - #loading - header #topbar - #condBar (dmu slider #dmuSlider, #dmuVal, EF #efSlider #efVal, T #tSlider #tVal, button #adoptEF hidden unless solved) - nav #tabs buttons data-tab - sections: #tab-overview, #tab-structure, #tab-formation, #tab-levels, #tab-equil, #tab-optical, #tab-library Formation tab elements: #formPlot (svg), #defToggles (chips), #formTable tbody, #transChips, buttons #btnO #btnMid #btnZn (presets), #btnCSV, #btnSVG, #btnDataset, #showAllStates checkbox. Dataset modal: #dsModal, #dsText, #dsApply, #dsReset, #dsClose, #dsMsg. Structure: #gl container, toolbar buttons .modeBtn data-mode, toggles #tgBonds #tgLabels #tgCell #tgSpin, #btnResetStruct, #cellSize select, #inspector content, #defectList. Levels: #levelsPlot svg, #levelsTable. Equil: #eqT slider, #eqDmu slider (sync global), #eqResults: #eqEF #eqN #eqP #eqType #compTable #concBars, #quenchChk #quenchPanel #qResults. warnings #eqWarn. Optical: #plCanvas, chips .bandChk, temp select #plTemp, #plTip tooltip div, #plNote, export #btnPLPNG. Library: KV builder selects #kvSp #kvSite #kvQ → #kvOut; reaction examples; equations list; references

lo+1e-9&&xa-b); const segs=[]; for(let k=0;k{ let pos=0,neg=0; const kT=KB*T; if(quenchTotals){ for(const dt of quenchTotals){ // {d, ctot} let Z=0, qc=0; for(const st of dt.d.states){const e=efLine(st,dt.d,EF,dmu); const w=Math.exp(clamp(-e/kT,-60,60)); Z+=w; qc+=st.q*w;} const qavg=qc/Z; const c=dt.ctot; if(qavg>0)pos+=qavg*c; else neg+=-qavg*c; } } else { for(const d of DEFECTS){ if(!state.toggles[d.id])continue; for(const st of d.states){const e=efLine(st,d,EF,dmu); const c=NSITES*Math.exp(clamp(-e/kT,-60,60)); if(st.q>0)pos+=st.q*c; else if(st.q<0)neg+=-st.q*c;} } } const Nc=2.94e18*Math.pow(T/300,1.5), Nv=1.13e19*Math.pow(T/300,1.5); const n=Nc*Math.exp(clamp(-(EG-EF)/kT,-60,60)); const p=Nv*Math.exp(clamp(-(EF)/kT,-60,60)); return (p+pos)-(n+neg); }; let lo=-0.4, hi=EG+0.4, flo=f(lo), fhi=f(hi); // f decreasing; find sign change; expand if needed for(let it=0;it<80;it++){const mid=(lo+hi)/2; const fm=f(mid); if(fm>0)lo=mid;else hi=mid;} return (lo+hi)/2; } ``` Check monotonic decreasing: p decreases with EF ✓, pos: higher EF → defect charge states more negative → pos decreases ✓; n increases ✓; neg increases ✓. So f decreasing ✓. f(lo): at EF=−0.4, p huge? p=Nv exp(0.4/kT): at 300K kT=0.0258 → e^{15.5}~5e6 ×1e19 = overflow → clamp exponent 60 → 1e19*1e26=1e45 fine as float. OK bisection robust. But with clamp at 60, f saturates — still sign-correct. Also defect pos at EF=−0.4: donors fully positive, c=N exp(−e/kT) with e possibly very negative (e0+q EF+shift... e.g., V_O 2+ Zn-rich at EF=−0.4: −1.6−0.8=−2.4 → exp(93) clamped 60 → 1e26×4e22=4e48 — big but finite. Sign fine. Bisection converges. Good. Guard monotonic: clamping may create flat regions — bisection still OK. Warnings: if min ef < 0 → show supersaturation warning. If solved EF within 3kT of 0 or EG → non-degenerate warning (carrier stats). Show "degeneracy may matter". Quench: totals from solve at T_a using equilibrium distribution: c_tot(d)=Σ c_q at (EF_a,T_a). Then solveEF(T_op,dmu, totals). Show both. Also show per-defect bars for both. Bars: log10 scale from 1e8 to 1e22 mapped 0–100% width; value text. PL draw code ~120 lines. Fine. Now KV builder: selects; render output + also render "formation reaction" hint? Keep builder + static examples. Dataset modal JSON: pretty JSON of DEFECTS minus note? Keep note fields. On apply, validate: array, each has id,name,color,nZn,nO,states[{q,e0}] with q in −3..3. Then DEFECTS=parsed; rebuild toggles; render all. Reset restores DEFAULT_DEFECTS (deep copy stored at load). Edge: toggles keyed by id — rebuild state.toggles all true. Colors allowed any string; validate /^#[0-9a-fA-F]{6}$/ else fallback palette. OK also "showAllStates" checkbox draws faint lines for every state across full range. Header badges: "Single-file app", "Wurtzite · P6₃mc", "v1.0". Footer: disclaimers: "Representative dataset inspired by hybrid-DFT/GGA+U literature (see Library). For teaching & exploration; verify with your own calculations." Now — write it all. I'll now produce the final file. Careful with unicode: − (minus U+2212) vs hyphen; primes ′; bullets •; subscripts via _{. In SVG text, use tspan baseline-shift for sub/sup? SVG supports baseline-shift in most browsers: O. Use for labels in plots (defect labels like V_O). baseline-shift="sub" works in Chrome/FF. OK.

For SVG labels of defects, use tspan: VO. Or simpler plain "VO". I'll use tspans for polish.

Escape in template strings: fine.

Let me also add keyboard: arrow keys move EF cursor? minor, add left/right on formation tab. Skip for brevity... include simple: document keydown when formation visible. Eh, skip.

Write loading overlay fade: on load add class opacity-0 pointer-events-none then remove after 500ms.

Also small "sparkline" mini formation plot on overview re-render on dmu change.

Alright — also make sure the condBar EF slider and formation cursor are same state.EF; and "Use equilibrium E_F" button copies eqResult to state.EF.

Number formatting: fmt(x,d=2).

Write concisely but completely. Begin final answer.

Let me also double check V_Zn transition ordering with my E0s: lines: 0: 3.6; −1: 3.9−E; −2: 4.9−2E. Crossings: 0/−1 at 0.3 ✓; −1/−2: 3.9−E=4.9−2E → E=1.0 ✓. Envelope: EF<0.3: 0; 0.3–1.0: −1; >1.0: −2 ✓.

O_i: 0:2.7; −1:3.7−E; −2:5.4−2E: crossings 1.0 and 1.7 ✓.

O_Zn: 0:6.5; −2:10.9−2E: crossing at 2.2 ✓.

Zn_O: +2:7.0+2E; 0:10.4: crossing 1.7 ✓.

At Zn-rich, V_O 2+ at EF=0: 2.0−3.63=−1.63 ✓ nice.

Default ΔH_f: use −3.63 eV. Slider min −3.63.

Also display μ_Zn implied: μ_Zn = ΔH_f − Δμ_O shown in condBar. Nice.

Write the code now. Also remember: no external file references besides CDNs; everything inline.

For Tailwind config, set darkMode not needed (all dark). Add tailwind config extend fontFamily maybe skip — use inline styles/classes with arbitrary font-[...] or custom CSS classes .font-display etc. I'll define CSS classes: .disp{font-family:'Cormorant Garamond',serif} .mono{font-family:'JetBrains Mono',monospace}. Body font Inter.

Potential pitfall: Tailwind CDN + custom classes coexist fine.

Three.js: verify OrbitControls path for 0.128.0 exists on jsdelivr: https://cdn.jsdelivr.net/npm/three@0.128.0/examples/js/controls/OrbitControls.js ✓ exists (examples/js removed after r147; r128 fine).

Renderer alpha:true, setClearColor 0x000000,0.

Supercell select: rebuild.

Bond geometry: cylinder between p1,p2:
```js
function bond(p1,p2){const d=p2.clone().sub(p1);const len=d.length();const g=new THREE.CylinderGeometry(0.055,0.055,len,6);const m=new THREE.Mesh(g,bondMat);m.position.copy(p1).addScaledVector(d,0.5);m.quaternion.setFromUnitVectors(new THREE.Vector3(0,1,0),d.normalize());return m;}
```

Raycaster on pointerdown (click) — distinguish from orbit drag: use 'click' event and check small movement: record pointerdown pos, on pointerup if moved <5px treat as click.

Auto-rotate: controls.autoRotate.

Now, inspector: default shows instructions + global condition readout + defect count. On click atom: show element, fractional coords, coordination (number of bonds), suggestion: "click Vacancy mode then click atom".

Defects list panel: each created defect chip with KV (using stable charge at current EF/dmu for that defect type mapping: vacancy on O→V_O dataset id VO; vacancy on Zn→VZ; antisite Zn→O? clicking O atom in antisite mode → O replaced by Zn = Zn_O (ZNO); clicking Zn → O_Zn (OZN). Interstitial Zn→ZNI, O→OI.) Show E_f(min over q) and q*.

Mapping object: defectFromSite(el, mode).

Good. Also allow deleting a created interstitial via vacancy mode click on it → just remove.

Reset clears arrays, rebuilds.

Structure header note: "Conditions synced with global Δμ_O & E_F".

Also color Zn #8fa3c7? Use #93a7cf-ish slate blue; O #ef4444-ish red (#e5484d). Interstitial emissive tint.

Now writing final answer HTML. I'll include comments. Ensure no stray unescaped `<` in JS strings (e.g., '→' fine; '<' in comparisons fine; in template strings building HTML, careful with `_{` etc. — fine as strings). In " sequence inside strings — none.

Also the "superscript minus" using U+2212 in JS: fine.

Length check — this will be big; go.

One more design flourish: header background subtle radial glow; tab content fade-in animation (CSS keyframes on section activate). Add small "kbd" hints. And a top-left "hex" logo SVG: hexagon with Zn/O dots.

For the formation plot: also shade region EF>EG? x-range ends at EG; add CB label at right edge "CBM". Add VBM/CBM labels on x-axis ends. Y-axis label rotated "Formation energy (eV)". X label "Fermi level E_F (eV) — VBM = 0, CBM = 3.37".

Include zero line bold.

Plot height ~ 480.

Alright, code:

I'll write it as one big artifact-style code block. Ensure every referenced element exists. Let me carefully list all element IDs as I write and keep consistent.

Also handle: switching to equil tab triggers solve; switching to optical triggers drawPL (canvas needs visible size). Use requestAnimationFrame after tab show.

Resize handler: redraw PL, re-render SVGs (they're viewBox-based, so they scale — set width 100% via viewBox; then no resize needed for SVG). For canvas PL, resize redraw. For three, resize.

Set SVGs with viewBox and class w-full h-auto — responsive.

Let me now also prepare the "dataset JSON" default pretty string generation at runtime: JSON.stringify(DEFECTS,null,2).

Edge: JSON uses standard chars; my notes contain unicode — fine.

For CSV: BOM not needed.

Let me write final code. I'll structure script into sections:
1. Constants & dataset
2. State
3. Utilities (fmt, kv, clamp, download)
4. Tab router
5. Conditions bar sync
6. Formation plot + readouts + transitions chips
7. Levels diagram + table
8. Equilibrium solver UI
9. Optical PL
10. Library (KV builder, cards)
11. Three.js structure
12. Dataset modal
13. Init

Also overview mini-plot uses formation renderer compact mode.

Write now, thorough and careful. Given the size, I'll keep prose in the answer minimal: brief intro + the code + short feature list & how to use. The user said "one-shot" — deliver the file. I'll include concise usage notes after the code.

Let me draft the trickiest render function fully in my head once more, then write.

renderFormation(svg, {compact}):
- sizes: full: W=940,H=520, ml=66,mr=150 (room for right-side labels), mt=16, mb=52. compact: W=460,H=240, ml=40,mr=8,mt=8,mb=26, no right labels.
- enabled defects list.
- compute envelopes; gather E values at seg endpoints for domain: vals = segs endpoints ef. ymin=Math.min(-0.2, minV-0.3); ymax=Math.max(3, maxV+0.5); clamp ymin>=-5, ymax<=12.
- scales x(EF), y(E).
- gridlines: for gy=Math.ceil(ymin); gy<=ymax; gy++ → line + label; x ticks 0..3.37 step 0.5 labels (compact: 0,1,2,3 + CBM).
- zero axis darker.
- right boundary line at EG with label CBM (text rotated? just top "CBM").
- dashed faint lines if showAll && !compact: for each defect each state: line from (0, ef(0)) to (EG, ef(EG)) clipped: compute endpoints clamp to y range; only draw if within extended range; stroke color opacity .18 dash 3 4. Clip via svg clipPath rect plot area — simpler: clipPath.
- envelope: path per defect: M x(from),y(ef(from)) L ... stroke width 2.6, color, no fill, linejoin round.
- kink circles r=3.5 fill panel-bg stroke color; plus label group: ε(q/q') value — position above point alternate offsets to reduce overlap; keep simple: text at (x+4, y−8) font 10 mono fill color.
- end labels (full only): defect KV at x=EG+6, y=ef_min(EG) adjusted for collisions: collect label positions, sort, enforce min gap 14px: simple pass.
- cursor: vertical line at state.EF, gold, dash; circle handle at top; text EF value.
- transparent rect on top capturing pointer events to set EF.

pointer→EF: rect bounds → EF = (clientX-rect.left)/rect.width*(W) ... account viewBox scaling: EF = ( (clientX-bb.left) * (W/bb.width) - ml ) / (W-ml-mr) * EG; clamp 0..EG.

Set svg style touch-action none.

Readout: table with rows; each row: color dot, KV name (stable state), q*, E_f, log10 c at T, and role donor/acceptor (sign of q*). Highlight min row with gold left border.

Transitions chips: per defect: `V_O: ε(2+/0)=2.00` chips; negative-U note if any state never on envelope over extended range.

Levels renderer similar; skip hover complexity.

Equil UI update function `runEquil()` reading state.eqT etc.

Optical drawPL.

KV builder change handler.

Three init function initStruct() once.

syncAll(): renderFormation main + mini + readouts + structure inspector update + condBar labels.

On load: build toggles, presets, render all, show overview tab, fade loader.

Preset buttons: set dmu via setDmu(v) updating sliders.

Okay. Writing final output now. Must remember not to mention iframe. Provide the single HTML file in one code block, then short notes.

Also careful: in HTML, characters like ′ and • and − are fine UTF-8.

For the PL nm top axis: compute tick positions: nm→E=1240/nm→x. Ticks: 350,400,450,500,550,600,650,700,750,800,850 within E range.

Bands toggles as styled checkboxes (chips). Hover tooltip: absolute positioned div.

Green band note tooltip text with controversy.

Include "phonon replicas" faint? skip.

Include intensity sliders? Keep toggles only + temp select.

Fine. Write!

Also include a tiny "About / methods" accordion in formation tab explaining equations used (formation energy formula, concentration formula) — professor will appreciate transparency. Short.

Now produce final answer. Watch total length but completeness matters more. Let me write.

(While writing, keep variable names consistent!)

Additional check — OrbitControls with r128: THREE.OrbitControls global ✓.

Tailwind arbitrary values used sparingly.

Let me write the code.

After writing, double-check IDs referenced in JS all exist in HTML.

I'll write the file in the answer directly, carefully.

Structure (Three) fractional→cartesian:
```js
function frac2cart(f){ // f = [f1,f2,f3] in lattice-vector coords
return new THREE.Vector3(
f[0]*A1.x + f[1]*A2.x + f[2]*A3.x,
f[1]*A2.y,
f[2]*A3.z
);
}
```
A2 = (−a/2, +a√3/2, 0). ✓

Supercell loops i

Here's a complete, single-file research workbench for ZnO point-defect studies — interactive wurtzite crystal builder, formation-energy diagrams with a continuous O-rich↔Zn-rich chemical potential slider, charge-transition level maps, a self-consistent equilibrium/quench Fermi-level solver, photoluminescence signatures, and a Kröger–Vink reference library. All physics is computed live from an editable dataset.

```html

ZnO·DefectLab — Native Point-Defect Workbench

ZnO · DefectLab
initialising wurtzite lattice…

ZnO · DefectLab
native point-defect workbench · wurtzite ZnO

P6₃mc
E_g 3.37 eV
single-file · v1.0

Δμ_O growth
Zn-rich

O-rich
0.00 eV

E_F

1.60 eV

T

1200 K

A virtual laboratory for
native point defects in zinc oxide.

Zinc oxide's technological promise — UV optoelectronics, transparent conductors, spintronics — is governed by its native defect chemistry.
This workbench lets you build defects in a 3D wurtzite lattice, compute formation energies across growth conditions,
map charge-transition levels, solve defect equilibria with freeze-in, and connect each defect to its experimental fingerprint.

The central dogma
Hybrid-DFT shows V_O is a deep, negative-U donor — it cannot explain unintentional n-type conductivity (Janotti & Van de Walle 2007). Hydrogen and complexes are the usual suspects.

The p-type wall
As E_F approaches the VBM, V_Zn formation energy plunges — but it is an acceptor. Reliable p-type ZnO remains one of the great open problems of oxide electronics.

live preview · formation energies
O-rich

Drag the Δμ_O slider above — every view in the lab responds.

structure
wurtzite, P6₃mc
lattice
a 3.250 · c 5.206 Å
band gap
3.37 eV (10 K)
exciton BE
60 meV
ΔH_f(ZnO)
−3.63 eV
site density
4.2×10²² cm⁻³
m_e* / m_h*
0.24 / 0.59 m₀
nature
n-type prone

mode

bonds
cell
spin

Zn O
drag to orbit · scroll to zoom · click an atom to apply mode
defect energetics sync with global Δμ_O & E_F

site inspector
Click any atom in the lattice to inspect its site, coordination and crystallographic position.

defects in this crystal
Pristine wurtzite. Introduce defects with the toolbar modes.

crystallography notes
Wurtzite = hcp anion sublattice, Zn in half the tetrahedral holes, internal parameter u = 0.382.
Octahedral interstitial holes at (0, 0, ⅛) & (0, 0, ⅝) — the preferred Zn_i site (Janotti & Van de Walle 2007).

Formation energy vs Fermi level

all charge states

click / drag in the plot to move the E_F cursor · slope of each segment = charge state q · kinks = thermodynamic transition levels ε(q/q′)

defects

at cursor

export & dataset

method & equations

E_f[D^q] = E_tot[D^q] − E_tot[bulk] − Σ n_iμ_i + q(E_VBM + E_F) + E_corr
Chemical-potential window: μ_Zn + μ_O = ΔH_f(ZnO) = −3.63 eV, referenced to O₂ / metallic Zn reservoirs. Slider spans Δμ_O ∈ [ΔH_f, 0].
c[D^q] = N_sites · g · exp(−E_f/k_BT)
Default E₀ values are representative of GGA+U / hybrid-DFT literature (see Library). Replace them with your own calculations via ⚙ edit dataset — all plots, levels and the solver update consistently.

Charge-transition levels in the gap

transition levels are μ_i-independent — growth conditions change which defect dominates, not where levels sit · negative-U defects show a single (q/q−2) level

equilibrium solver
Self-consistent charge neutrality over all enabled defects + free carriers (non-degenerate statistics). Uses global Δμ_O.
anneal temperature
1200 K
simulate quench → 300 K (freeze defect totals, re-equilibrate charge states & carriers)

what this emulates
A minimal py-sc-fermi-style engine: defect concentrations from formation energies, carriers from N_C,V(T) with m_e*=0.24, m_h*=0.59. Quench mode freezes stoichiometry at T_anneal and re-solves at 300 K — the standard picture for as-grown vs measured material.

equilibrium @ —

E_F*
—
n
—
p
—
character
—

after quench → 300 K (defect totals frozen)

E_F(300 K)
—
n(300 K)
—
p(300 K)
—
character
—

Photoluminescence signature builder

the green-band controversy
The ~2.4–2.5 eV green band was assigned to V_O for decades (Vanheusden 1996). Hybrid DFT places V_O's level too deep for this transition; positron annihilation correlates green PL with V_Zn, and Cu contamination is a classic impostor. A cautionary tale in defect identification.

who sees what

PL / CL radiative levels, green/yellow/red bands
DLTS majority-carrier traps, activation energies
EPR / ODMR paramagnetic states: V_O⁺ (S=½, photoinduced)
PAS open-volume: V_Zn & vacancy clusters
Hall net carriers — blind to compensation
μSR / IR hydrogen impurities & complexes

Kröger–Vink notation builder

V_O^××
• = +1 effective charge · ′ = −1 · × = neutral

canonical defect reactions

½O₂(g) ⇌ O_O^× + V_Zn″ + 2h• oxidation · acceptor incorporation
O_O^× ⇌ V_O•• + 2e′ + ½O₂(g) reduction · oxygen loss
ZnO(s) ⇌ Zn_i•• + 2e′ + ½O₂(g) Zn-rich limit
nil ⇌ e′ + h• band excitation

defect dossiers

essential references

Janotti & Van de Walle, Native point defects in ZnO, Phys. Rev. B 76, 165202 (2007) — doi:10.1103/PhysRevB.76.165202
Janotti & Van de Walle, Fundamentals of zinc oxide as a semiconductor, Rep. Prog. Phys. 72, 126501 (2009)
Kohan, Ceder, Morgan & Van de Walle, Phys. Rev. B 61, 15019 (2000)
Oba et al., Energetics of native defects in ZnO, Phys. Rev. B 77, 245202 (2008)
Van de Walle, Hydrogen as a cause of n-type conductivity, Phys. Rev. Lett. 85, 1012 (2000)
Look et al., Evidence for native-defect donors in n-type ZnO, Phys. Rev. Lett. 82, 2552 (1999)
McCluskey & Jokela, Defects in ZnO, J. Appl. Phys. 106, 071101 (2009)
Lyons, Alkauskas, Janotti & Van de Walle, First-principles theory of acceptors in nitride and oxide semiconductors, Phys. Status Solidi B (2017)
Vanheusden et al., Green luminescence and V_O, J. Appl. Phys. 79, 7983 (1996)
Özgür et al., A comprehensive review of ZnO, J. Appl. Phys. 98, 041301 (2005)

Disclaimer: default energetics are representative literature values for teaching & exploration — substitute your own hybrid-DFT data via ⚙ edit dataset before drawing quantitative conclusions.

ZnO·DefectLab — single-file HTML · no backend · all physics computed client-side
built for research & teaching

Formation-energy dataset
JSON array. e0 = formation energy (eV) at E_F=0 under O-rich conditions; μ-shifts are applied automatically as (n_Zn−n_O)·Δμ_O.

```

**What's inside & how to use it:**

- **3D Structure** — orbit a real wurtzite supercell (a=3.25 Å, c=5.21 Å, u=0.382); click atoms to introduce vacancies, antisites, or octahedral interstitials. Every defect reports its *live* formation energy and Kröger–Vink charge state under the current global conditions.
- **Formation Energies** — publication-style E_f vs E_F diagram. The **Δμ_O slider** sweeps continuously from O-rich to Zn-rich (μ_Zn + μ_O = ΔH_f enforced); slopes = charge states, kinks = ε(q/q′). Negative-U behavior (V_O, Zn_i, Zn_O) emerges automatically from the line geometry. Export as SVG/CSV.
- **⚙ Edit dataset** — paste your own HSE/GGA+U numbers as JSON; every plot, level diagram, and the solver recompute consistently.
- **Defect Equilibria** — bisection solver for charge neutrality including free carriers (N_C, N_V from m*), with a **quench mode** that freezes defect totals at T_anneal and re-equilibrates at 300 K.
- **Optical Signatures** — synthetic PL spectrum (NBE, green/yellow/red bands) with the V_O/V_Zn green-band controversy documented.
- **Library** — Kröger–Vink builder, canonical defect reactions, and the essential Janotti–Van de Walle literature trail.}}

A virtual laboratory fornative point defects in zinc oxide.

A virtual laboratory for
native point defects in zinc oxide.

One-shot an impressive html software that a professor in aca...