Reduced-order non-self-consistent Monte Carlo simulation of a planar magnetron discharge: electron heating, recapture and racetrack formation

Franz F. Locker; Georg Strau{\ss}

REVIEW 2 major objections 4 minor 34 references

Reduced-order non-self-consistent Monte Carlo simulation of a planar magnetron discharge: electron heating, recapture and racetrack formation

T0 review · 2 major / 4 minor · reviewed 2026-08-01 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Resolving finite permanent-magnet geometry, not dipole approximations, is the dominant modeling choice for predicting racetrack erosion width in a reduced-order magnetron model.

desk verdict A candid, clearly-scoped reduced-order magnetron simulation whose headline claim—finite-magnet field predicts a sharper racetrack than dipole—is plausible but not yet statistically demonstrated; the paper itself defers the needed convergence study. read the letter →

arxiv 2607.19930 v1 pith:I2VF5KBD submitted 2026-07-22 physics.plasm-ph physics.comp-ph

Franz F. Locker , Georg Strau{ss} This is my paper · ORCID

classification physics.plasm-phphysics.comp-ph

keywords magnetronsputteringMonteCarlosimulationracetrackerosionmagnetic-fieldrepresentationelectronheatingcathoderecapturereduced-ordermodelplanar

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that in a reduced-order, non-self-consistent Monte Carlo model of a planar magnetron, the way the magnetic field is represented—point dipoles versus numerical integration over the finite magnet volumes—is the first-order determinant of where the erosion racetrack forms and how wide it is. If correct, this means that cheap test-particle simulations can rank magnet designs for racetrack localization without full particle-in-cell simulations, provided they resolve the actual magnet shape. The model also reproduces a qualitative two-temperature electron population (hot near the cathode, cold away from it) and shows that the cathode reflection probability controls electron multiplication. Because the collision module overestimates absolute drift velocities by roughly a factor of 1.5, the paper frames its predictions as semi-quantitative trend studies rather than absolute discharge predictions.

What carries the argument

The central mechanism is the comparison between two magnetic-field representations: a superposition of point dipoles versus a numerically integrated field from the finite permanent-magnet volumes via the magnetic vector potential. This is embedded in a reduced-order Monte Carlo framework with a prescribed one-dimensional Gaussian-plus-cosh sheath–bulk potential, adaptive fourth-order Runge–Kutta orbit integration, a null-collision Monte Carlo collision operator, and a generation-cycle bookkeeping scheme that treats cathode-return events through a reflection probability RC. The geometric racetrack-width estimate ωRT ≈ 2√(2 r_e L R_c), based on the electron Larmor radius and magnetic-field-lin

What would settle it

Run the same racetrack calculation with an order of magnitude more seed electrons (e.g., 2×10^5 or 2×10^6) for both field representations; if the finite-magnet FWHM no longer stays close to the geometric estimate while the dipole profile broadens, the claim fails. Additionally, if a measured magnetic-field map for the experimental geometry becomes available and the finite-magnet simulation no longer matches the observed trench width, the inference about the magnetization would be overturned.

Watch

Extended reading notes

Core claim

For racetrack calculations initiated with at least 2×10^4 cathode-emitted electrons and a reflection probability RC = 0.5, the finite-magnet field produces a more sharply localized erosion profile whose full width at half maximum is close to the geometric estimate ωRT ≈ 2√(2 r_e L R_c). The dipole approximation yields a broader profile. This identifies magnetic-field geometry, not the prescribed sheath potential or collision details, as the dominant modeling requirement for the predicted racetrack localization. Additionally, the reduced model demonstrates that a prescribed one-dimensional sheath–bulk potential, combined with the finite-magnet field, is sufficient to produce a hot near-cathod

Load-bearing premise

The racetrack comparison assumes that ensembles of at least 2×10^4 seed electrons yield statistically converged radial erosion profiles, but the paper contains no convergence study or variance analysis, so the claimed FWHM difference between dipole and finite-magnet fields could be Monte Carlo noise.

Editorial extensions

If this is right

If the central claim holds, reduced-order magnetron models should resolve the finite magnet geometry rather than rely on point-dipole approximations when predicting racetrack width and localization.
The finite-magnet calculation yields a racetrack FWHM close to the geometric estimate ωRT, suggesting that a simple geometric formula can serve as a rapid benchmark for erosion width once the field is resolved.
The cathode reflection probability RC is a sensitive control on electron availability for ionizing collisions; conclusions derived from a single RC value should be read as sensitivity results, not as material constants.
Because the drift velocity is overestimated by a factor of about 1.5, absolute transport predictions are not quantitative; the model's utility lies in comparative magnetic-configuration studies and mechanism identification.
The model is not a replacement for self-consistent PIC-MCC simulations, but its low computational cost makes it suitable for scanning magnet designs and exploring cathode-interaction parameters.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the finite-magnet versus dipole difference persists under rigorous statistical convergence checks, then common dipole-based test-particle studies may systematically overestimate racetrack width, with direct consequences for target-utilization predictions in sputtering applications.
The same reduced-order setup could be extended to test unbalanced or moving magnet configurations as a design sweep, because the finite-magnet integration cost remains workstation-scale and the model already isolates magnetic-field effects from sheath nonlinearity.
The claim is conditional on the prescribed 1D sheath–bulk potential; a self-consistent or hybrid potential could alter radial confinement, so the identified dominance of magnetic-field geometry might be partly an artifact of freezing the potential.
A testable extension would be to replace the inferred magnetization (from nominal remanence) with a measured field map for the experimental source; this would separate the error from magnetization uncertainty from the error due to the magnetic-field representation itself.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Honest, clearly-scoped reduced-order simulation. The genuinely new thing here is the head-to-head comparison of two magnetic-field representations (dipole superposition vs numerical integration over finite magnet volumes) inside a single non-self-consistent electron Monte Carlo, with the finding that the field representation is the dominant modelling choice for predicted racetrack width: finite-magnet fields give a sharper trench, dipole fields broaden it. That is practically useful if true, and the authors are appropriately modest about the rest of the model.

What earns credit: the paper is remarkably candid about its own limits. The factor-1.5 drift-velocity overestimate is disclosed in the abstract and Section 3.2, not hidden. The temperature results are explicitly qualitative. The racetrack result is framed as a discrimination test, not a prediction. No parameters are fitted to make the racetrack or temperature curves come out right. The authors also flag that no measured field map was available, so magnetisation is inferred from nominal remanence (Section 3.4).

The soft spots are concentrated in the headline claim. Section 3.7 reports that the finite-magnet FWHM is "close to" the geometric estimate from Eq. (5) and that the dipole profile is "broader," but gives no FWHM numbers, no confidence intervals, and no particle-number convergence study. The paper's own Section 4 lists convergence studies as required for quantitative extension. That is an explicit admission that 2e4 seed electrons may not be enough, and with an energy-weighted erosion statistic the variance could be large. Eq. (5) is also introduced without derivation and compared only qualitatively. The concluding statement that resolving the finite magnet geometry is "necessary to obtain the observed degree of racetrack localisation" overreaches; "necessary" is too strong for a qualitative comparison to a published surface image. No code or data are shipped, only available on request.

These are real gaps, but they are not load-bearing flaws in the sense that the qualitative trend is almost certainly right. The model is computationally light, the collision physics is standard, and the comparison logic is sound. The central weak point is statistical evidence: the paper needs a convergence study and some estimate of uncertainty before the dipole-broadening claim can be taken as established. That is fixable.

The paper deserves peer review—a serious referee could push on the convergence issue. It is for magnetron modellers and experimentalists who want a cheap way to compare magnet configurations. I would not cite the central result in its current form, but I would follow the revision.

Recommendation: send to peer review, with a request for convergence analysis and quantitative FWHM comparison.

Referee Report

2 major / 4 minor

Summary. F. F. Locker and G. Strauß present a reduced-order, non-self-consistent Monte Carlo model of a circular planar magnetron discharge in argon. The model combines two magnetic-field representations (point-dipole superposition and numerically integrated finite-magnet fields) with a prescribed one-dimensional sheath–bulk potential, adaptive fourth-order Runge–Kutta orbit integration, and a null-collision treatment of electron–argon collisions. The collision module reproduces the reduced-field dependence of the electron drift velocity but overestimates its absolute value by about a factor of 1.5. Applied to a published magnetron geometry, the simulations yield a qualitatively two-temperature electron population and a racetrack erosion calculation in which the finite-magnet field produces a more sharply localised profile whose FWHM is 'close to' a geometric estimate, while the dipole approximation is broader. The paper explicitly frames results as semi-quantitative and lists convergence studies, measured field maps, and constrained cathode-interaction models as prerequisites for quantitative extension.

Significance. If substantiated, the paper would be a useful, computationally light tool for comparing magnetic-field representations in magnetron discharges. Its main potential contribution is identifying finite-magnet field resolution as the dominant modelling choice for racetrack localisation and showing that the dipole approximation broadens the predicted erosion profile. Strengths are the transparent disclosure of the failed drift test (§3.2), the clear discrimination-test framing, and the repeated, explicit caveats about the model's scope. The central racetrack claim, however, is not yet supported statistically: no FWHM values, confidence intervals, or particle-number convergence study are reported, and Eq. (5) is neither derived nor quantified. The paper is honest about these gaps, which makes the claims promising but not yet established.

major comments (2)

[§3.7 and §4] The central claim—that the finite-magnet field yields an erosion FWHM close to Eq. (5) while the dipole approximation is broader—is not backed by statistical evidence. 'At least 2×10^4 seed electrons' is a floor, not a convergence criterion; no FWHM values, error bars, or multiple-seed variances are reported. Section 4 explicitly lists 'particle-number convergence studies' as a future requirement, an admission that the sufficiency of N_e was not established. Since the erosion profile is an energy-weighted sum of rare high-energy impacts, Monte Carlo noise could plausibly account for the reported broadening. Please add a convergence study (e.g., N_e from 2×10^4 upward, several independent seeds) and quantify the FWHM difference with confidence intervals.
[§3.7, Eq. (5)] Equation (5), ω_RT ≈ 2√(2 r_L^e R_c), is introduced without derivation and without specifying how r_L^e and R_c are evaluated. No numerical value of ω_RT is given, and the comparison is only qualitative ('close to'). Because the geometric estimate is computed from the same nominal B_r ≈ 1.37 T field used in the simulation, it is not an independent check of the absolute width. Please state the definitions of all quantities, give the numerical value of ω_RT, and compare it quantitatively to the simulated FWHM for both field representations. Otherwise the 'close to' claim cannot be assessed.

minor comments (4)

[§3.4] The temperature calculation uses only 1200 seed and approximately 1400 ionisation-born electrons; no statistical uncertainty is reported. This is acceptable for the qualitative two-temperature claim, but a sentence quantifying the bin-to-bin variance would strengthen the comparison.
[§2.5 / §3.2] The initial seed-electron energy interval (4.36–4.95 eV) is stated as a numerical assumption, and the drift test overestimates the absolute drift velocity by a factor of 1.5. A brief sentence relating the emission-spectrum assumption to the drift overestimate would help readers judge whether the two issues are coupled.
[Figure 9] The geometric racetrack-width estimate ω_RT is plotted or indicated, but the caption does not define the plotted quantity or specify units. Please add axis labels, units, and a short definition of the geometric estimate in the caption.
[Abstract and §3.7] There are minor typographical inconsistencies: '2 × 10^4' appears without superscript formatting in the abstract, and R_C/RC is used inconsistently. These should be normalised.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the simulation predictions are not constructed from the quantities they purport to predict.

full rationale

The derivation chain is self-contained. The two magnetic-field representations are inputs; the erosion profile is accumulated from Monte Carlo trajectories using standard LXCat cross-sections and a Yamamura yield, with no parameter fitted to the racetrack or temperature outputs. The prescribed potential is selected by comparison with published sheath solutions (§2.2), not by fitting the two-temperature electron measurements used later as a qualitative check (§3.4), so the 'reproduction' is an independent validation rather than a tautology. The drift-velocity comparison is an external benchmark that overestimates by a factor 1.5 and is disclosed, which weakens precision but not circularity. The finite-magnet versus dipole comparison is computed from the same collision and potential model with only B changed; no term in Eq. (5) is adjusted to match the simulated FWHM. The only self-citation, Raggl et al. [9], supplies the experimental geometry and a qualitative IFM image; it is evidence, not a load-bearing argument. The outstanding limitations—missing particle-number convergence study, inferred magnetisation, qualitative FWHM comparison—are correctness/uncertainty concerns, not circular-construction concerns. No step in the paper defines an output in terms of its target or renames an empirical pattern as prediction.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

The model introduces no new physical entities — no new particles, forces, or ledgers — but its central claims rest on several hand-chosen inputs (RC, seed emission energies, potential coefficients, nominal remanence) and external data sets (Biagi cross-sections, Yamamura sputter yields). The most exposed item is the geometric racetrack formula Eq. (5), stated without derivation or citation and used as the benchmark for the headline FWHM agreement. The paper is transparent about most inputs, which is why the ledger is mostly about unexamined external validity rather than hidden fitting.

free parameters (4)

RC (cathode reflection probability) = 0.5
Cathode reflection probability used for the racetrack runs (§3.7); not measured or derived. The paper treats it as a sensitivity parameter combining unresolved surface physics (§3.6).
Seed electron initial energies = 4.36–4.95 eV
Initial kinetic energy of cathode-emitted electrons chosen from the molybdenum work-function range; the paper calls it 'a numerical emission assumption rather than a microscopic secondary-electron spectrum' (§2.5).
Sheath–bulk potential coefficients (Gaussian + cosh join) = not stated
Coefficients of the 1D potential are chosen by hand, 'tested against the qualitative form of published self-consistent and analytic magnetron-sheath solutions' (§2.2); exact values are not reported.
Br (nominal remanence) = ≈ 1.37 T
Magnetisation inferred from nominal remanence because no measured field map was available for the experimental source (§3.4); uncertainty propagates into both the simulated fields and the geometric benchmark ωRT.

assumptions (7)

standard math Null-collision Monte Carlo treatment (Vahedi–Surendra) correctly samples electron–neutral collisions in argon
Established MC technique cited as [28] and applied in §2.4; assumed reliable for the energy range of interest.
domain assumption Biagi LXCat argon cross-section data set is accurate for the simulated energy range
External experimental data set cited as [29] (§2.4); the acknowledged factor-1.5 drift overestimate (§3.2) suggests at least one ingredient in the collision chain is imperfect.
domain assumption A prescribed 1D sheath–bulk potential with no radial structure is adequate for electron-heating and ionisation-localisation studies
Explicitly called 'a strong approximation' in §2.2; radial potential variation documented across magnetron cathodes (§1, refs [25–27]) is omitted.
domain assumption Ions can be treated as unmagnetised with negligible ion–neutral collisions for the erosion mapping
Stated in §2.1; the erosion result is a reduced mapping from ion-production statistics to sputter yield without kinetic ion transport.
domain assumption Yamamura empirical sputter-yield formula applies to this target/gas combination
Cited as [31] and used in §2.5 to weight cathode ion impacts; no uncertainty from the empirical fit is propagated.
ad hoc to paper Geometric racetrack-width estimate ωRT ≈ 2√(2 r_L R_c) governs the erosion width
Introduced without derivation or citation in Eq. (5), §2.5, and used as the benchmark for the headline FWHM result (§3.7); if this formula is not the correct racetrack-width model the claimed agreement is unsupported.
domain assumption Termination rules (energy below 15.7596 eV, domain exit, removal at the z = 40 mm measurement plane) do not bias the reported distributions
Rules stated in §2.5 and §3.4; removal at the virtual measurement plane could distort temperature statistics near that plane.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Reduced-order non-self-consistent Monte Carlo simulation of a planar magnetron discharge: electron heating, recapture and racetrack formation." pith.science (2026). https://pith.science/paper/I2VF5KBD

@misc{pith2026260719930,
  author       = {Pith},
  title        = {Pith review of: Reduced-order non-self-consistent Monte Carlo simulation of a planar magnetron discharge: electron heating, recapture and racetrack formation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/I2VF5KBD}},
  note         = {Machine review of arXiv:2607.19930}
}

read the original abstract

A reduced-order non-self-consistent Monte Carlo model is presented for a circular planar magnetron discharge in argon. The model combines two magnetic-field representations, namely a superposition of magnetic dipoles and a numerically integrated field of the finite permanent magnets, with a prescribed one-dimensional sheath-bulk potential, adaptive fourth-order Runge-Kutta orbit integration, and a null-collision treatment of electron-argon collisions. The collision module reproduces the dependence of the electron drift velocity on the reduced electric field, but overestimates its absolute value by approximately a factor of 1.5. The resulting transport predictions are therefore interpreted semi-quantitatively. Applied to a magnetron geometry based on published Langmuir-probe measurements, the simulations reproduce the qualitative emergence of a cold electron population away from the cathode while retaining a hotter near-cathode component. Electrons returning to the cathode are reflected with a prescribed probability RC, which controls their availability for further ionising collisions. For racetrack calculations initiated with at least 2 x 10^4 cathode-emitted electrons and RC = 0.5, the finite-magnet field produces a more sharply localised erosion profile whose full width at half maximum is close to a geometric racetrack-width estimate. The dipole approximation yields a broader profile. The model is not a replacement for self-consistent PIC-MCC simulations, but is a computationally light tool for comparing magnetic-field representations and analysing electron heating, ionisation localisation, and racetrack formation.

Figures

Figures reproduced from arXiv: 2607.19930 by the authors.

**Figure 2.** Internal bookkeeping diagnostic illustrat [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 5.** Generation-counting diagnostic for effective [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

Figures from the paper (4 more)

**Figure 6.** Figure 6: Simulated radial mean electron-temperature [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]

**Figure 7.** Figure 7: Simulated axial trend of the electron temper [PITH_FULL_IMAGE:figures/full_fig_p005_7.png]

**Figure 8.** Figure 8: Normalised axial dependence of ionisation [PITH_FULL_IMAGE:figures/full_fig_p006_8.png]

**Figure 9.** Figure 9: Simulated radial erosion profiles including the [PITH_FULL_IMAGE:figures/full_fig_p006_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

34 extracted references

[1]

Joseph E. Greene. Review article: Tracing the recorded history of thin-film sputter deposition: Fromthe1800sto2017.Journal of Vacuum Science & Technology A, 35(5):05C204, 2017

2017
[2]

Magnetron sputtering— milestones of 30 years.Vacuum, 84(12):1354–1359, 2010

Günter Bräuer, Bernd Szyszka, Michael Vergöhl, and Rainer Bandorf. Magnetron sputtering— milestones of 30 years.Vacuum, 84(12):1354–1359, 2010

2010
[3]

Khan.Handbook of Thin-Film Technology

Hartmut Frey and Hamid R. Khan.Handbook of Thin-Film Technology. Springer, Berlin, 2015

2015
[4]

Thornton

John A. Thornton. Magnetron sputtering: Ba- sic physics and application to cylindrical mag- netrons.Journal of Vacuum Science and Tech- nology, 15(2):171–177, 1978

1978
[5]

J. T. Gudmundsson. Physics and technology of magnetron sputtering discharges.Plasma Sources Science and Technology, 29(11):113001, 2020

2020
[6]

Czekaj, E

D. Czekaj, E. K. Hollmann, A. B. Kozirev, V. A. Volpyas, and A. G. Zaytsev. Ion energies at the cathode of the DC planar magnetron sputtering discharge.Applied Physics A: Solids and Surfaces, 49(3):269–272, 1989

1989
[7]

Rossnagel and Harold R

Stephen M. Rossnagel and Harold R. Kaufman. Langmuir probe characterization of magnetron op- eration.Journal of Vacuum Science & Technology A, 4(3):1822–1825, 1986

1986
[8]

Flat erosion magnetron sputter- ing with a moving unbalanced magnet.Vacuum, 80(7):662–666, 2006

Takayuki Iseki. Flat erosion magnetron sputter- ing with a moving unbalanced magnet.Vacuum, 80(7):662–666, 2006

2006

Show all 34 references

[9]

Raggl, J

S. Raggl, J. Postler, J. Winkler, G. Strauß, C. Feist, A. Plankensteiner, M. Eidenberger-Schober, and P. Scheier. Correlation of target properties and plasma parameters in DC magnetron sputtering with Langmuir probe measurements.Journal of Vacuum Science & Technology A, 35(6):...

2017
[10]

Evolution mechanism of sputtered film uni- formity with the erosion groove size: Integrated simulation and experiment.Molecules, 28(22):7660, 2023

Guo Zhu, Yutong Yang, Baijun Xiao, and Zhiyin Gan. Evolution mechanism of sputtered film uni- formity with the erosion groove size: Integrated simulation and experiment.Molecules, 28(22):7660, 2023

2023
[11]

Kondo and K

S. Kondo and K. Nanbu. A self-consistent numeri- cal analysis of a planar DC magnetron discharge by the particle-in-cell/Monte Carlo method.Journal of Physics D: Applied Physics, 32(10):1142–1152, 1999

1999
[12]

PIC–MCC numerical simulation of a DC planar magnetron

Ivan Kolev and Annemie Bogaerts. PIC–MCC numerical simulation of a DC planar magnetron. Plasma Processes and Polymers, 3(2):127–134, 2006

2006
[13]

Detailed nu- merical investigation of a DC sputter magnetron

Ivan Kolev and Annemie Bogaerts. Detailed nu- merical investigation of a DC sputter magnetron. IEEE Transactions on Plasma Science, 34(3):886– 894, 2006

2006
[14]

Computer modelling of mag- netron discharges.Journal of Physics D: Applied Physics, 42(19):194018, 2009

Annemie Bogaerts, Evi Bultinck, Ivan Kolev, Lau- rent Schwaederlé, Koen Van Aeken, Guy Buyle, and Diederik Depla. Computer modelling of mag- netron discharges.Journal of Physics D: Applied Physics, 42(19):194018, 2009

2009
[15]

Particle-in- cell simulations for the improvement of the target 7 erosion uniformity by the permanent magnet con- figuration of DC magnetron sputtering systems

Young Hyun Jo, Cheongbin Cheon, Heesung Park, Min Young Hur, and Hae June Lee. Particle-in- cell simulations for the improvement of the target 7 erosion uniformity by the permanent magnet con- figuration of DC magnetron sputtering systems. Coatings, 13(4):749, 2023

2023
[16]

Computer simulation of mag- netron sputtering—experience from the industry

Stanislav Kadlec. Computer simulation of mag- netron sputtering—experience from the industry. Surface and Coatings Technology, 202(4–7):895– 903, 2007

2007
[17]

Jimenez, Steven K

Francisco J. Jimenez, Steven K. Dew, and David J. Field. Comprehensive computer model for mag- netron sputtering. II. Charged particle trans- port.Journal of Vacuum Science & Technology A, 32(6):061301, 2014

2014
[18]

Theory and molecular simulations of plasma sputtering, transport and deposition pro- cesses.The European Physical Journal D, 77:19, 2023

Pascal Brault, Anne-Lise Thomann, and Marjorie Cavarroc. Theory and molecular simulations of plasma sputtering, transport and deposition pro- cesses.The European Physical Journal D, 77:19, 2023

2023
[19]

Biersack and L

Jochen P. Biersack and L. G. Haggmark. A Monte Carlo computer program for the transport of en- ergetic ions in amorphous targets.Nuclear Instru- ments and Methods, 174(1–2):257–269, 1980

1980
[20]

Modeling target erosion during reactive sputtering.Applied Surface Science, 331:185–192, 2015

Koen Strijckmans and Diederik Depla. Modeling target erosion during reactive sputtering.Applied Surface Science, 331:185–192, 2015

2015
[21]

Modeling reactive magnetron sputtering: Opportunities and challenges.Thin Solid Films, 688:137326, 2019

Diederik Depla, Koen Strijckmans, Dulmaa Altan- gerel, Florian Cougnon, Robin Dedoncker, Roeland Schelfhout, Isabella Schramm, Filip Moens, and Roger De Gryse. Modeling reactive magnetron sputtering: Opportunities and challenges.Thin Solid Films, 688:137326, 2019

2019
[22]

The characteristics of electrical dis- charges in magnetic fields

David Bohm. The characteristics of electrical dis- charges in magnetic fields. In A. Guthrie and R. K. Wakerling, editors,The Characteristics of Elec- trical Discharges in Magnetic Fields, pages 77–86. McGraw-Hill, New York, 1949

1949
[23]

R. Chodura. Plasma–wall transition in an oblique magnetic field.The Physics of Fluids, 25(9):1628– 1633, 1982

1982
[24]

Moritz, M

J. Moritz, M. Lesur, E. Faudot, S. Devaux, S. Heuraux, and J. Ledig. The plasma-wall transi- tion with collisions and an oblique magnetic field: Reversal of potential drops at grazing incidences. Physics of Plasmas, 26(1):013507, 2019

2019
[25]

J. W. Bradley and G. G. Lister. Model of the cath- ode fall region in magnetron discharges.Plasma Sources Science and Technology, 6(4):524–532, 1997

1997
[26]

The effect of the magnetic field strength on the sheath region of a DC magnetron discharge.Journal of Physics D: Applied Physics, 41(20):202007, 2008

Evi Bultinck and Annemie Bogaerts. The effect of the magnetic field strength on the sheath region of a DC magnetron discharge.Journal of Physics D: Applied Physics, 41(20):202007, 2008

2008
[27]

T. E. Sheridan and J. Goree. Analytic expres- sion for the electric potential in the plasma sheath. IEEE Transactions on Plasma Science, 17(6):884– 888, 1989

1989
[28]

Vahedi and M

V. Vahedi and M. Surendra. A Monte Carlo colli- sion model for the particle-in-cell method: Appli- cations to argon and oxygen discharges.Computer Physics Communications, 87(1–2):179–198, 1995

1995
[29]

Biagi-v7.1 electron collision cross sections for argon

Biagi database. Biagi-v7.1 electron collision cross sections for argon. LXCat database, 2020. Accessed 9 July 2020

2020
[30]

C. B. Opal, W. K. Peterson, and E. C. Beaty. Measurements of secondary-electron spectra pro- duced by electron impact ionization of a number of simple gases.The Journal of Chemical Physics, 55(8):4100–4106, 1971

1971
[31]

Yamamura, S

Y. Yamamura, S. Nakagawa, and S. Enoki. Empiri- cal formula for sputtering yield andZ2 dependence of its Q values. In A. Benninghoven, J. Okano, R. Shimizu, and H. W. Werner, editors,Secondary Ion Mass Spectrometry SIMS IV: Proceedings of the Fourth International Conference, O...

1983
[32]

Study electron transport coefficients for Ar, O2 and their mixtures by using an EEDF program.Journal of Physics: Conference Series, 1003:012116, 2018

Dhuha Sadi Abdul Majeed, Bushra Joudah Hus- sein, and Mustafa Kamel Jassim. Study electron transport coefficients for Ar, O2 and their mixtures by using an EEDF program.Journal of Physics: Conference Series, 1003:012116, 2018

2018
[33]

T. E. Sheridan, M. J. Goeckner, and J. Goree. Ob- servation of two-temperature electrons in a sputter- ing magnetron plasma.Journal of Vacuum Science & Technology A, 9(3):688–690, 1991

1991
[34]

Influence of electron recapture by the cathode upon the discharge characteristics in DC planar mag- netrons.Physical Review E, 72(5):056402, 2005

Ivan Kolev, Annemie Bogaerts, and Renaat Gijbels. Influence of electron recapture by the cathode upon the discharge characteristics in DC planar mag- netrons.Physical Review E, 72(5):056402, 2005. 8

2005

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.

[1] [1]

Joseph E. Greene. Review article: Tracing the recorded history of thin-film sputter deposition: Fromthe1800sto2017.Journal of Vacuum Science & Technology A, 35(5):05C204, 2017

2017

[2] [2]

Magnetron sputtering— milestones of 30 years.Vacuum, 84(12):1354–1359, 2010

Günter Bräuer, Bernd Szyszka, Michael Vergöhl, and Rainer Bandorf. Magnetron sputtering— milestones of 30 years.Vacuum, 84(12):1354–1359, 2010

2010

[3] [3]

Khan.Handbook of Thin-Film Technology

Hartmut Frey and Hamid R. Khan.Handbook of Thin-Film Technology. Springer, Berlin, 2015

2015

[4] [4]

Thornton

John A. Thornton. Magnetron sputtering: Ba- sic physics and application to cylindrical mag- netrons.Journal of Vacuum Science and Tech- nology, 15(2):171–177, 1978

1978

[5] [5]

J. T. Gudmundsson. Physics and technology of magnetron sputtering discharges.Plasma Sources Science and Technology, 29(11):113001, 2020

2020

[6] [6]

Czekaj, E

D. Czekaj, E. K. Hollmann, A. B. Kozirev, V. A. Volpyas, and A. G. Zaytsev. Ion energies at the cathode of the DC planar magnetron sputtering discharge.Applied Physics A: Solids and Surfaces, 49(3):269–272, 1989

1989

[7] [7]

Rossnagel and Harold R

Stephen M. Rossnagel and Harold R. Kaufman. Langmuir probe characterization of magnetron op- eration.Journal of Vacuum Science & Technology A, 4(3):1822–1825, 1986

1986

[8] [8]

Flat erosion magnetron sputter- ing with a moving unbalanced magnet.Vacuum, 80(7):662–666, 2006

Takayuki Iseki. Flat erosion magnetron sputter- ing with a moving unbalanced magnet.Vacuum, 80(7):662–666, 2006

2006