1. Frank-van der Merwe (Layer-by-Layer) Growth

  • Condition: The film wets the substrate completely, , so the spreading coefficient is zero or positive and the wetting angle is zero (Kiel; Tuebingen; my reading for ).
  • Energy test: In the cluster-energy form, layer growth corresponds to (BME).
  • Picture: Each layer is completed before the next begins, the layer-by-layer mode of metals in SNU’s description (SNU; Kiel).
  • Nucleation: The heterogeneous barrier is the homogeneous one times , which falls to zero as (Sakrani et al.; computed).
  • Kinetics: Monolayer filling follows Langmuir kinetics, , and layer-by-layer growth gives the RHEED oscillations used in MBE (Tuebingen; BME; Molecular Beam Epitaxy (MBE) System page).

2. Volmer-Weber (Island) Growth

  • Condition: The film does not wet, , so and the wetting angle is finite, (Kiel; Tuebingen).
  • Energy test: gives three-dimensional islands (BME).
  • Picture: Islands form from the very start of deposition and later coalesce into a closed but bumpy layer (SNU; Kiel).
  • Nucleus density: Higher substrate temperature gives fewer, larger nuclei, and faster deposition more, smaller ones (Semnan).

3. Stranski-Krastanov (Layer-plus-Island) Growth

  • Condition: The film first wets and grows layer by layer, then switches to islands once strain builds up (Kiel; SNU).
  • Cause: Lattice misfit ; islands form when the elastic strain range exceeds the adhesion range (Tuebingen; BME).
  • Threshold: Above about 1 to 2 per cent misfit for InGaAs on GaAs; Ge on Si has a misfit of 0.042 (BME; SNU).
  • Critical thickness: Balancing strain energy against dislocation energy gives (BME).
  • Caveat: All three energy criteria are equilibrium limits; real growth is kinetic, so diffusion and flux can override them (Tuebingen).

4. Diffusion-Limited and Reaction-Limited Regimes

  • Two steps in series: In chemical vapour deposition, reactants first diffuse through a boundary layer, with , then react at the surface, (KTH; MIT 3.155J).
  • Growth rate: Equating the fluxes gives , so the slower step controls (MIT 3.155J; KTH).
  • Diffusion (mass-transport) limited: When , , which varies only about as ; supply, flow and boundary-layer thickness set the rate (MIT 3.155J). In MOCVD this is the normal regime, from about 550 to 800 C for GaAs from TMGa, with the rate proportional to the group III partial pressure (Stringfellow; MOCVD Reactor page).
  • Reaction (surface-kinetics) limited: When , and follows an Arrhenius law, with an activation energy of 1.7 eV for silane polysilicon; below about 550 C TMGa growth enters this regime (KTH; Stringfellow).
  • Role of pressure: Gas diffusivity scales as , so low pressure raises and keeps growth reaction-limited, which is why LPCVD furnaces need even temperature rather than careful flow (MIT 3.155J; LPCVD Furnace page; my reading for the furnace consequence).

Wetting and Growth Modes

NameFormulaRelated FormulaeVariables/Constants
Young’s equation



Spreading coefficient
Stranski-Krastanov

Nucleation

NameFormulaRelated FormulaeVariables/Constants
Homogeneous nucleus
Supersaturation
Heterogeneous nucleus

Kinetics, Strain and Microstructure

NameFormulaRelated FormulaeVariables/Constants
Nucleation rate
Surface diffusion
Critical thickness and zones

Diffusion-Limited and Reaction-Limited Growth

NameFormulaRelated FormulaeVariables/Constants
Grove fluxes in series


Diffusion (mass-transport) limited
Reaction (surface-kinetics) limited

Important Questions

Ques: How do surface energies decide the growth mode?

Through the balance at the edge of a nucleus. Kiel and Tuebingen write Young’s equation as , linking the substrate surface energy, the film-substrate interface energy and the film surface energy through the wetting angle. If , the film wets fully and grows layer by layer (Frank-van der Merwe); if not, it forms islands (Volmer-Weber). The spreading coefficient is this test rearranged, positive for layers (my reading). For assumed values of 1.0, 1.2 and 0.5 , is 65 degrees and , so islands form (computed). Tuebingen warns that these equilibrium criteria are only a guide to non-equilibrium growth. Reference: [1] H. Foell, “Semiconductor technology,” hyperscript, section 3.3.2, “Nucleation and growth modes,” University of Kiel; [2] F. Schreiber group, “Nanoscience, section 4: growth,” lecture notes, University of Tuebingen, 2012.

Ques: Why does Stranski-Krastanov growth switch from layers to islands?

Because strain builds up in the wetting layers. Kiel describes Stranski-Krastanov growth as layer-plus-island growth driven by strain, and Tuebingen attributes it to lattice mismatch: islands form once the range of the elastic strain field exceeds the range of adhesion. BME defines the misfit as and places the transition above about 1 to 2 per cent for InGaAs on GaAs. It balances the strain energy against the dislocation energy , giving a critical thickness , so larger misfit means thinner wetting layers. In my reading, islands relieve the stored strain without dislocations, which is why they are used as quantum dots. Reference: [1] H. Foell, “Semiconductor technology,” hyperscript, section 3.3.2, “Nucleation and growth modes,” University of Kiel; [2] F. Schreiber group, “Nanoscience, section 4: growth,” lecture notes, University of Tuebingen, 2012; [3] “Thin film nucleation and structure,” Lecture 21, Nanoscale Science and Engineering course slides, 2007 (hosted by BME Budapest).

Ques: What sets the size of a stable nucleus?

The balance between surface energy and the volume energy gained. Tuebingen writes , with a critical radius . SNU gives the driving term through supersaturation, per volume, and the barrier . For assumed values of , , 600 K and , . That gives and a barrier of 79 (computed). Sakrani et al. state that larger supersaturation gives a smaller critical radius and barrier. Kiel makes the same point in words: surface energy grows with the square of the radius and the volume gain with its cube, so growth pays only beyond a critical size. In my reading, raising the arrival rate or cooling the substrate raises the supersaturation, which is why fast, cold deposition gives a fine-grained film with many small nuclei. Reference: [2] F. Schreiber group, “Nanoscience, section 4: growth,” lecture notes, University of Tuebingen, 2012; [4] Seoul National University OpenCourseWare, “Application to nanoscience,” Lecture Note 8, Spring 2020; [5] S. Sakrani, L. Q. Jie and Y. Wahab, “The formation of nanoscale clusters - nanofilms/quantum dots predicted using a capillary model of nucleation,” Journal of Fundamental Sciences, vol. 1, pp. 23-33, 2005; [1] H. Foell, “Semiconductor technology,” hyperscript, section 3.3.2, “Nucleation and growth modes,” University of Kiel.

Ques: How does the substrate lower the nucleation barrier?

By replacing part of the nucleus surface with a cheaper interface. Sakrani et al. treat the nucleus as a spherical cap with wetting angle and geometric constants , and . Their critical radius is the same as for homogeneous nucleation, but the barrier is multiplied by the wetting factor . That factor is 0.5 at 90 degrees, 0.156 at 60 degrees and 0.013 at 30 degrees (computed). A well-wetting substrate therefore makes nucleation far easier (my reading). Kiel adds that the cluster removes an area of substrate surface, which is the origin of the terms. At complete wetting the barrier vanishes and growth proceeds layer by layer, the Frank-van der Merwe case of the first Q/A (my reading). Reference: [5] S. Sakrani, L. Q. Jie and Y. Wahab, “The formation of nanoscale clusters - nanofilms/quantum dots predicted using a capillary model of nucleation,” Journal of Fundamental Sciences, vol. 1, pp. 23-33, 2005; [1] H. Foell, “Semiconductor technology,” hyperscript, section 3.3.2, “Nucleation and growth modes,” University of Kiel.

Ques: How do substrate temperature and deposition rate change film growth?

Temperature lengthens diffusion; rate shortens the time available. The Semnan notes state that the critical nucleus size increases with temperature and decreases with deposition rate, so hot substrates give fewer, larger nuclei and fast deposition gives more, smaller ones. They give the nucleation rate as , with . BME gives the adatom hop time , with and for GaAs. At an assumed 853 K that is 4.8 (computed). Diffusion length follows , where falls with rate R. Tuebingen adds the Ehrlich-Schwoebel barrier, 0.14 for Pt/Pt(111), which hinders hops down steps. The arrival flux itself is the Hertz-Knudsen flux of the Thermal Evaporator page, and the 1.3 value came from RHEED oscillations, as used on the RHEED and Molecular Beam Epitaxy (MBE) System pages. Reference: [6] “Thin film growth and evolution,” Thin Film Techniques lecture notes, Semnan University; [3] “Thin film nucleation and structure,” Lecture 21, Nanoscale Science and Engineering course slides, 2007 (hosted by BME Budapest); [2] F. Schreiber group, “Nanoscience, section 4: growth,” lecture notes, University of Tuebingen, 2012; [13] Thermal Evaporator page of this vault; [16] Reflection High-Energy Electron Diffraction (RHEED) page of this vault; [14] Molecular Beam Epitaxy (MBE) System page of this vault.

Ques: What are the structure zones, and which boundaries are more likely right?

Zone 1 is porous, zone T dense fibrous, zone 2 columnar and zone 3 recrystallized. The Semnan notes give, for evaporation, zone 1 below 0.3 of the melting temperature, zone 2 from 0.3 to 0.5 and zone 3 above 0.5. For sputtering they give zone 1 below 0.1 to 0.4 depending on pressure, with zone T between. Valente-Feliciano, citing Thornton (1974), writes zone 2 as below about 0.3 and zone 3 above about 0.45. Zone 2 below 0.3 contradicts zone 1 being the low-temperature zone in the same slides. It is more likely a transcription slip for above 0.3, matching Semnan (my reading). Assuming 933 K for aluminium, zone 2 then spans about 7 to 193 (computed). Ion energy also matters, as on the DC and RF Magnetron Sputter System page. Reference: [6] “Thin film growth and evolution,” Thin Film Techniques lecture notes, Semnan University; [7] A.-M. Valente-Feliciano, “Energetic condensation review,” TFSRF 2012 workshop slides, Jefferson Lab, 2012; [15] DC and RF Magnetron Sputter System page of this vault.

Ques: What is the misfit of Ge on Si, and which value is more likely?

About 4.2 per cent; the two figures agree to rounding. SNU gives a misfit of 0.042 for Ge on Si and 0.0726x for on GaAs. BME gives for on Si(001), which for pure Ge, x = 1, is 0.040. The difference is about 5 per cent of the value (computed). SNU’s 0.042 is more likely the precise figure, because it is quoted to three digits for the pure-Ge case, while BME’s linear form is a rounded rule of thumb for alloys (my reading). Both lie well above the 1 to 2 per cent at which BME places the Stranski-Krastanov transition, so Ge on Si grows in that mode. Reference: [4] Seoul National University OpenCourseWare, “Application to nanoscience,” Lecture Note 8, Spring 2020; [3] “Thin film nucleation and structure,” Lecture 21, Nanoscale Science and Engineering course slides, 2007 (hosted by BME Budapest).

Ques: How do the diffusion-limited and reaction-limited regimes differ?

In which step controls the rate, and so in what the engineer must control. MIT 3.155J and KTH describe CVD as gas transport, with , in series with surface reaction, , giving . When transport is slower, growth is diffusion (mass-transport) limited and varies only about as (MIT). When reaction is slower, growth follows an Arrhenius law; KTH gives 1.7 for silane polysilicon, so the rate rises 1.66 times from 600 to 620 (computed). Stringfellow finds MOCVD of GaAs diffusion-limited from about 550 to 800 and kinetic below. In my reading, flow uniformity matters in the first regime and temperature uniformity in the second, as on the LPCVD Furnace and MOCVD Reactor pages. Reference: [9] MIT 3.155J/6.152J Micro/Nano Processing Technology, “CVD,” lecture slides, 12 October 2005, MIT OpenCourseWare; [8] KTH Royal Institute of Technology, “Lecture 8: CVD and ALD,” course slides; [10] G. B. Stringfellow, “Fundamentals of vapor phase epitaxial growth processes,” AIP Conference Proceedings CP916, 2007; [11] LPCVD Furnace page of this vault; [12] MOCVD Reactor page of this vault.

References

  1. H. Foell, “Semiconductor technology,” hyperscript, section 3.3.2, “Nucleation and growth modes,” University of Kiel. Available: https://www.tf.uni-kiel.de/matwis/amat/semitech_en/kap_3/backbone/r3_3_2.html
  2. F. Schreiber group, “Nanoscience, section 4: growth,” lecture notes, University of Tuebingen, 2012. Available: https://www.soft-matter.uni-tuebingen.de/teaching/FSchreiberNanoScience_Sec-4-Growth2012.pdf
  3. “Thin film nucleation and structure,” Lecture 21, Nanoscale Science and Engineering course slides, 2007 (hosted by BME Budapest). Available: https://www.eet.bme.hu/~mizsei/Nanoelektronika,%20nanotechnol%c3%b3gia/Nanoelektronika/__2007-Nanoscale_Science_and_Engineering-course/Lecture21-Thin_Film_Nucl_n_Struct.pdf
  4. Seoul National University OpenCourseWare, “Application to nanoscience,” Lecture Note 8, Spring 2020. Available: https://ocw.snu.ac.kr/sites/default/files/NOTE/ASS-8-2020%2815week%29.pdf
  5. S. Sakrani, L. Q. Jie and Y. Wahab, “The formation of nanoscale clusters - nanofilms/quantum dots predicted using a capillary model of nucleation,” Journal of Fundamental Sciences, vol. 1, pp. 23-33, 2005. Available: https://mjfas.utm.my/index.php/mjfas/article/download/12/606/1707
  6. “Thin film growth and evolution,” Thin Film Techniques lecture notes, Semnan University. Available: https://mmousavi.profile.semnan.ac.ir/downloads/file/9591
  7. A.-M. Valente-Feliciano, “Energetic condensation review,” TFSRF 2012 workshop slides, Jefferson Lab, 2012. Available: https://indico.jlab.org/event/22/contributions/2233/attachments/1871/2362/TFSRF12-EnergeticCondensationReview-AMVF.pdf
  8. KTH Royal Institute of Technology, “Lecture 8: CVD and ALD,” course slides. Available: https://www.kth.se/social/upload/510bc6e8f276547a4fe3c222/Lecture%208.pdf
  9. MIT 3.155J/6.152J Micro/Nano Processing Technology, “CVD,” lecture slides, 12 October 2005, MIT OpenCourseWare. Available: https://www.ocw.mit.edu/courses/6-152j-micro-nano-processing-technology-fall-2005/cad5227ddbdf120be10a0c372f2ccedd_cvd.pdf
  10. G. B. Stringfellow, “Fundamentals of vapor phase epitaxial growth processes,” AIP Conference Proceedings CP916, 2007. Available: https://collections.lib.utah.edu/dl_files/b4/04/b404dc111a8a9725bd80fb776b124dbb568e3cf7.pdf
  11. LPCVD Furnace page of this vault.
  12. MOCVD Reactor page of this vault.
  13. Thermal Evaporator page of this vault.
  14. Molecular Beam Epitaxy (MBE) System page of this vault.
  15. DC and RF Magnetron Sputter System page of this vault.
  16. Reflection High-Energy Electron Diffraction (RHEED) page of this vault.

Related pages in this vault: Thermal Evaporator, Electron-Beam Evaporator, DC and RF Magnetron Sputter System, LPCVD Furnace, PECVD Reactor, Atomic Layer Deposition (ALD) Reactor, MOCVD Reactor, Molecular Beam Epitaxy (MBE) System, Electroplating (ECD) Cell, Reflection High-Energy Electron Diffraction (RHEED), Wafer Curvature Stress Gauge.