Turgay,

I see that you are getting some excellent answers, but I think we are still a bit "defocused". (At least, I am.)

[see disclaimer after] What material(s) are you sputter depositing? Approx. what substrate temperature? What sort of atmosphere is ambient in the deposition chamber? Especially what is the pressure of the atmosphere and the distance from sputter target to substrate? Disclaimer: I know that all research is somewhat secret until it is ready for publication; perhaps you can give us the general families of materials or a specific case that is similar to the actual case on which you work?

I believe we could comment more effectively if we knew the materials and energetics of your process. You said that you are interested in thin film growth i.e. nucleation, island growth, coalescence etc. All of these microscopic or nano-scale processes differ depending upon a) the nature/type of chemical bonding being formed in the new material and b) the strength of these chemical bonds relative to the kB*T energy (temperature). This is merely the grossest scale of phenomena. Many other molecular-scale steps may actually be rate-limiting and/or structure-determining, as you can imagine.

You said that someone suggested that you look at thin film growth nucleation, island growth, coalescence etc. as a Stefan problem. In fact, you mentioned that R. Ghez describes the nucleation as a Stefan problem. Could you give us the full citation?

The Stefan problem originated in the study of phase transitions in matter, but I think I it may have more general mathematical applicability. See http://www.encyclopediaofmath.org/index.php/Stefan_problem . I would be interested to see how Ghez applies phase transitions to nucleation.

Myself, I suspect that, rigorously, thin film growth in the moving 2-dimensional "slab" of the growing surface is hardly amenable to traditional phase transformational description. Traditionally, this mathematics deals with two phases (states, forms, compositions, etc.) are in equilibrium at some temperature and pressure, or, if conditions are changing, mass conversion from one phase to the other. Strictly speaking, I do not think there are any definable "phases" in the extremely disordered, highly energetic and rapidly quenched environment of a growing surface under vapor deposition. Nevertheless, I will try to be open-minded. Sometimes the mathematical form of a solution fits the problem, even if the initial definition of variables does not seem to fit or needs to be re-interpreted somehow. I will be interested to hear if ultimately choose a Stefan problem formalism.

Turgay,

Could you be a little more specific with your question?

If your question relates to the process for thin film deposition, rather than relate to growth of the material itself, then please say what type of process. For example, sputter deposition is very common. Within the field of sputter processes, you might look at the works of S. Berg's group, his collaborators and his follow-on group members in the present day. Have a look at 25-year-old work by Berg et al:

S.Berg, H-O. Blom, T. Larsson and C. Nender, "Modeling of reactive sputtering of compound materials", J. Vac. Sci. Technol. A 5(2), 202–207 (1987). [for TiN]

And some more recent work by his present-day colleagues:

T. Kubart, D.H. Trinh, L. Liljeholm, L. Hultman, H. Högberg, T. Nyberg and S. Berg, "Experiments and modeling of dual reactive magnetron sputtering using two reactive gases", J. Vac. Sci. Technol. A 26(4), 565-570 (2008). [for Al-ZrOxNy]

These are very complex cases with reactive gases. This field is fairly far-advanced. You should be able to find what you are looking for.

Hi,

I am interested in thin film growth i.e. nucleation, islands growth, coalescent etc. For example, one author describe nucleation as a Stefan problem. As I know, Stefan dealts with phase transitions and I do not know how to implement it. I am using magnetron sputtering with Ar for deposition. I want to study the dynamics of thin film growth.

The dynamics of film growth in terms of elementary steps and processes has been studied in quite some depth, especially since the availability of tunneling microscopes.

A relevant review of an experimentalist is the following:

H. Brune: "Microscopic view of epitaxial metal growth: nucleation and aggregation", Surface Science Reports 31, 121 (1998)

Concerning surface diffusion, nucleation and growth modelling I recall J.A. Venables as one of the relevant authors, but there may (and will) be quite a few others, I guess.

In your case, using sputtering, is there also high energy impact of deposited atoms? This may create defects which can strongly influence the diffusion and growth dynamics. (This is why in our experiments, using electron beam evaporators, we usually block the ions by electrostatic means. In some applications, their presence and influence might be desirable, though.)

Edit: You will find, that there is not one single equation for all of growth but that there are (critical) parameters some of which which depend on temperature and flow of adsorbing atoms, which ultimately control and determine the growth mode.

Hi Turgay,

Have you come across the 1986 paper by Thornton (see attached file). It does an excellent job of explaining film growth by sputtering, taking into account microstructure. He conceptually divides films into "zones" where the microstructure varies as a result of substrate temperature and considers growth dynamics in each case.

Thank you very much for your comments and paper suggestions. As I understood, it is very complex area.

1-) There are 3 growth modes: Volmer-Weber, Frank-van der Merve and Stranski-Krastanov. How can understand which mode my samples grows accordingly? By AFM?

2-) R. Ghez describe the nucleation as a Stefan problem. How can I decide initial and boundary value problems for it?

@Mr. Fauth: I am not sure whether there is a high energy impact of atoms.

@Mr. Frantz: Many publications including Thornton'86 cite Thornton's 1976 paper, where the zone model is introduced, which I have not had it. If you have it, would you send it to me?

I have seen some articles about using Monte-Carlo.

Turgay,

I see that you are getting some excellent answers, but I think we are still a bit "defocused". (At least, I am.)

[see disclaimer after] What material(s) are you sputter depositing? Approx. what substrate temperature? What sort of atmosphere is ambient in the deposition chamber? Especially what is the pressure of the atmosphere and the distance from sputter target to substrate? Disclaimer: I know that all research is somewhat secret until it is ready for publication; perhaps you can give us the general families of materials or a specific case that is similar to the actual case on which you work?

I believe we could comment more effectively if we knew the materials and energetics of your process. You said that you are interested in thin film growth i.e. nucleation, island growth, coalescence etc. All of these microscopic or nano-scale processes differ depending upon a) the nature/type of chemical bonding being formed in the new material and b) the strength of these chemical bonds relative to the kB*T energy (temperature). This is merely the grossest scale of phenomena. Many other molecular-scale steps may actually be rate-limiting and/or structure-determining, as you can imagine.

You said that someone suggested that you look at thin film growth nucleation, island growth, coalescence etc. as a Stefan problem. In fact, you mentioned that R. Ghez describes the nucleation as a Stefan problem. Could you give us the full citation?

The Stefan problem originated in the study of phase transitions in matter, but I think I it may have more general mathematical applicability. See http://www.encyclopediaofmath.org/index.php/Stefan_problem . I would be interested to see how Ghez applies phase transitions to nucleation.

Myself, I suspect that, rigorously, thin film growth in the moving 2-dimensional "slab" of the growing surface is hardly amenable to traditional phase transformational description. Traditionally, this mathematics deals with two phases (states, forms, compositions, etc.) are in equilibrium at some temperature and pressure, or, if conditions are changing, mass conversion from one phase to the other. Strictly speaking, I do not think there are any definable "phases" in the extremely disordered, highly energetic and rapidly quenched environment of a growing surface under vapor deposition. Nevertheless, I will try to be open-minded. Sometimes the mathematical form of a solution fits the problem, even if the initial definition of variables does not seem to fit or needs to be re-interpreted somehow. I will be interested to hear if ultimately choose a Stefan problem formalism.

suitability of AFM: it is a possibility, but most probably only if applied in the vacuum environment. Taking such an ultrathin film out of vacuum will irreversibly modify the film in most cases.

Monte Carlo simulations: of course you need an adequate physical model prior to simulating it with MC. Setting up this model properly for the materials combination of your case may be quite demanding (unless models and parameters are already available).

@David:in my opinion it is rather the lateral corrugation of the interaction (diffusion barriers) than the bonding strength itself which determines nucleation and growth behavior. In relation with thermal energy, it yilds the mobility of the adatoms and islands.

@David: Yes, it is difficult to know from where we start. Concerning about your questions:

1-) Our target materials are Copper, Silver, Titanium and Indium Tin Oxide (ITO) and mostly ı have worked on ITO.

2-) I have no idea about substrate temperature.

3-) Working pressure is 10 mTorr.

4-) Distance to target is 5 or 8 cm.

5-) Working power is 60 Watt (tolerance limit of 2” diameter ITO -Kurt Lesker Company advised after one target was broken.

http://www.lesker.com/newweb/deposition_materials/RampProcedure_CeramicTarget_Materials.cfm?pgid=0

6-) I have seen Richard Ghez’s course syllabus of Nucleation and Crystal Growth and says “Nucleation as a Stefan Problem”. If so, my master advisors have 2 publications about Stefan. I think we can apply it to nucleation if possible. Therefore, I am trying to understand thin film growth and modelling.

Article about stefan

The other

Turgay, Great! Thank you for the information on sputtering details and for the papers. (I have not studied the papers in detail.)

You may benefit from finding out what phase of ITO is desired or is being deposited in your machine now. Unless you have strong reason to know or believe otherwise, it is most probable that the ITO is depositing as polycrystalline, or, if temperature is cool enough, as nanocrystalline or amorphous with nanocrystalline inclusions. To get epitaxial single crystalline ITO, you would need to provide very specific substrate surface crystalline geometry, substrate temperature and growth rate. There are other possibilities: e.g., non-epitaxial single crystal and oriented (textured) polycrystal. X-ray diffraction (XRD) will get you some of the answers, but most assuredly not all the answers. Electron diffraction and transmission electron microscopy (TEM) may be needed to uncover more structural details. This is expensive and may not be worth while on every sample variant.

ITO may not be fully oxidized. ITOx may be sub-stoichiometric in O. The sputtering process may result in loss of O. Oxygen atoms liberated from the ITO target can bind to the walls or be pumped away as O2. Are you adding O2 gas into the (argon?) sputtering gas atmosphere? This may add back some O to replace what would otherwise be lost. Rutherford backscattering (RBS) or maybe X-ray photoelectron or Auger electron spectroscopy (XPS and AES) can give O/Sn and O/In composition ratios valid to +/- 2%, though this accuracy may not be good enough. Measurement of absolute O concentration is a huge problem. Other measurements of electrical or optical properties dependent upon O concentration may be much cheaper and quicker, though subject to "aliasing" from other effects.

The papers by Sinsoysal seem excellent. Have you asked him about your present application? He realizes that "it is necessary to obtain the moving unknown boundary together with the solution of a differential problem". This sounds promising. Ghez also said to "...give attention to the processes that occur at phase boundaries and to the structure of real crystal surfaces. It is emphasized that crystal growth, by its very nature, is a dynamic process..." My question is/was: What are the phases? If one of the phases is the population of mobile, pre-bound adatoms, then these are in intimate physical contact with the other phase(s), by virtue of the pseudo-2-dimensional nature of the growth slab or moving growth region. Not a simple problem, to me.

@ Kai: Yes, absolutely. The various diffusion energy barriers in relation to thermal activation energy determines atom mobility etc. Of course you understand that these barriers are somewhat, at least, dependent upon the chemical bonding that will/would form, and also that the chemical bonding becomes kind of a "sink" that sweeps diffusing atoms out of the population of mobile atoms (thereby releasing even more thermal energy, in the exothermic rxn case). I am also thinking ahead to the portion of the process in which the substrate is completely covered, and now the diffusing atoms are mostly choosing between possible "permanent" sites in the soon-to-be-buried growth slab.