💠 Healgelieder-fab Live model

Basis — it model efter de sifers

Elke relaasje dy't de simulator brûkt, mei de boarne. Konstanten dy't as oanname markearre binne, binne yllustrative kalibraasjes.

Apparatuertastannen folgje SEMI E10: produktyf, standby, yngenieurs, plande en ûnplande stilstân.

Availability = up tools / 8 · Utilization = productive tool-hours / total[1]

Apparaten falle willekeurich út mei in eksponinsjele tiid oant útfal; reparaasjes wachtsje op in frije technikus.

P(fail in Δt) = 1 − e^(−Δt/MTBF), MTBF = 250 h; repair ~ Exp(mean 6 h) once a technician is free[17][1]Oanname: grutteoarders (MTBF, generaasjesifers, k, τ) binne yllustrative kalibraasjes, gjin gegevens fan in echte fab.

De wet fan Little ferbynt wurk yn proses, trochfier en trochrintiid.

CT = WIP / TH = T0 + queue / TH, T0 = 1 h[6][5]

Yn in stabile line is de trochfier gelyk oan it frijjeftempo, dus in waferstart dy’t net frijjûn wurdt, is in wafer dy’t nea derút komt. Wafers dy’t te lang tusken stappen wachtsje, oerskriuwe it queue-time-finster.

TH = release rate while u < 1 ⇒ wafers out ≈ Σ starts; queue wait = CT − T0 = queue / TH ≤ queue-time window (3.5 h CT in semi-tool-crash)[5][16]Oanname: de grins fan 3,5 oere foar de trochrintiid stiet foar in queue-time-finster; echte finsters wurde stap foar stap troch de prosestechnyk fêststeld, en wafers dy’t se oerskriuwe, wurde meastentiids ôfkard.

Kingman-approximaasje: wachttiid groeit as u/(1−u) — se eksplodearret as de benutting de 100 % neist komt.

CTq ≈ ((ca² + ce²)/2) · (u/(1−u)) · te[5]Toand foar yntúsje: de rige fan de simulator komt út willekeurige oankomsten en willekeurige kapasiteit yn stee fan út dizze formule.

ISO 14644-1-klassegrins foar dieltsjes fan grutte D; by 0,1 µm is de klasse de log fan de konsintraasje.

Cn = 10^N · (0.1/D)^2.08 ⇒ N = log10(C≥0.1µm)[2]

Goed mingde romte: konsintraasje = generaasje ÷ (luchtferfarskingen × folume × filtereffisjinsje).

C = G / (ACH · V · η)[13][11]Oanname: grutteoarders (MTBF, generaasjesifers, k, τ) binne yllustrative kalibraasjes, gjin gegevens fan in echte fab.

Fan-affiniteitswet: fermogen nimt ta mei de tredde macht fan de fansnelheid.

P_fan = P_max · (speed)³[10]

Negatyf-binomiale opbringst: defekten klonterje, sadat de opbringst stadiger sakket as it Poisson-model foarsjocht.

Y = (1 + A·D/α)^(−α), α = 2 (α→∞: Y = e^(−A·D))[3][4][15][14]

Opbringstlearen: defektedichtens nimt ôf nei in folwoeksen nivo as yngenieurstiid bestege wurdt.

D(t+Δt) = D∞ + (D − D∞)·e^(−Δt/τ), τ = 120 h · (0.10 / engineering share)[15][18]Oanname: τ is sa'n 100× yn tiid gearparsd yn ferliking mei rapportearre learsifers yn de yndustry (4–6,5 % per moanne, Leachman), sadat in senario fan 14 dagen it effekt toant.

Dieltsjes dy't op wafers delkomme foegje killer-defekten ta yn ferhâlding ta de luchtkonsintraasje.

D_total = D_learn + k · C, k = 4·10⁻⁶ cm⁻² per particle/m³Oanname: in yllustrative konstante — echte fabs kalibrearje killer-defektesifers út har eigen ynspeksjegegevens.

Parametrike opbringst: it diel fan in normaal proses dat binnen de spesifikaasjegrinzen falt; Cpk mjit de marzje.

Y_param = Φ((USL−μ)/σ) − Φ((LSL−μ)/σ), Cpk = min(USL−μ, μ−LSL)/(3σ)[7][8][19]

SPC: gemiddelden fan n stekproeven, mei ±3σ/√n-kontrôlegrinzen en sône-regels.

x̄ ~ N(μ, σ/√n), control limits ±3σ/√n; zone rules (2 of 3 beyond 2σ, 4 of 5 beyond 1σ, 8 on one side)[8][7][12]

Oare wurkkonstanten dy't it model brûkt.

8 scanners × 6 wafer-starts/h · metrology −0.5 % capacity per sampled wafer/h · rollback: 2 h at half capacity + 4 wafer-equivalents reworked · drift 0.25 nm/h · crash repair 18 technician-hours · leak crew +2 people for 3 h · tools 150 kW busy / 60 kW idle, fans 150 kW at 100 %Oanname: grutteoarders (MTBF, generaasjesifers, k, τ) binne yllustrative kalibraasjes, gjin gegevens fan in echte fab.

Brutto dies per wafer fan 300 mm foar in die mei oerflak A.

DPW = π·d²/(4A) − π·d/√(2A), d = 300 mm[9]

Willekeur: in seeded mulberry32-generator; brûkte ferdielingen — unifoarm, eksponinsjeel (omkearde CDF), normaal (Box–Muller), Poisson (Knuth). It seed wurdt toand en is te dielen.

Boarnen

1. SEMI E10 — Specification for Definition and Measurement of Equipment Reliability, Availability, and Maintainability (RAM) and Utilization — SEMI
2. ISO 14644-1:2015 Cleanrooms and associated controlled environments — Part 1: Classification of air cleanliness by particle concentration — ISO, 2015
3. C. H. Stapper, F. M. Armstrong, K. Saji — Integrated circuit yield statistics — Proceedings of the IEEE 71(4), 1983
4. J. A. Cunningham — The use and evaluation of yield models in integrated circuit manufacturing — IEEE Trans. Semiconductor Manufacturing 3(2), 1990
5. W. J. Hopp, M. L. Spearman — Factory Physics (3rd ed.), ch. 7–8: Little’s law, Kingman (VUT) equation — Waveland Press, 2008
6. J. D. C. Little — A Proof for the Queuing Formula L = λW — Operations Research 9(3), 1961
7. D. C. Montgomery — Introduction to Statistical Quality Control (x̄ charts, process capability Cpk) — Wiley, 2019
8. NIST/SEMATECH e-Handbook of Statistical Methods — 6.3 Univariate and Multivariate Control Charts; 6.1.6 Process capability — NIST
9. Dies-per-wafer estimate DPW = πd²/(4S) − πd/√(2S) (de Vries, “Investigation of gross die per wafer formulas”, IEEE TSM 18(1)) — IEEE, 2005
10. Fan affinity laws: flow ∝ speed, pressure ∝ speed², power ∝ speed³ — U.S. DOE — Improving Fan System Performance: A Sourcebook for Industry
11. EN 1822-1:2019 High efficiency air filters (EPA, HEPA and ULPA) — classification (U15 ≥ 99.9995 % at MPPS) — CEN, 2019
12. Western Electric Statistical Quality Control Handbook (1956) — zone rules for control charts — Western Electric / NIST e-Handbook 6.3.2
13. W. Whyte — Cleanroom Technology: Fundamentals of Design, Testing and Operation (2nd ed.), ch. on dispersion of particles from people; well-mixed room dilution equation — Wiley, 2010
14. Yu. I. Bogdanov, N. A. Bogdanova, V. L. Dshkhunyan — Statistical Yield Modeling for IC Manufacture: Hierarchical Fault Distributions (§2 Compound Poisson distribution, after Eq. (17), p. 4 of the arXiv PDF — large-area clustering negative binomial model: the cluster parameter’s “typical values approximately range from 0.3 to 7”) — arXiv physics/0303039, 2003
15. R. C. Leachman — Yield Modeling and Analysis (Poisson, Murphy, Seeds, negative-binomial models; §8: SMLY survey with C. N. Berglund for International SEMATECH, 2002–03 — yield loss fitted as YL(t) = YL(0)·e^(−λt), Table 2 averages 4.4 / 4.0 / 6.5 %/month at 350 / 250 / 180 nm) — UC Berkeley, IEOR 130 course notes (unpublished), 2014
16. A. Klemmt, L. Mönch — Scheduling jobs with time constraints between consecutive process steps in semiconductor manufacturing (time windows set by process engineering against native oxidation and contamination; jobs that violate them are scrapped) — Proceedings of the 2012 Winter Simulation Conference, 2012
17. NIST/SEMATECH e-Handbook of Statistical Methods — 8.1.6.1 Exponential distribution (constant failure rate) — NIST
18. C. Weber — Yield learning and the sources of profitability in semiconductor manufacturing and process development — IEEE Trans. Semiconductor Manufacturing 17(4), 2004
19. M. Abramowitz, I. Stegun — Handbook of Mathematical Functions, 26.2.17 — NBS, 1964