Film Formation   1. Introduction Thin film growth modes

(1)  Island (Volmer-Weber) Growth Mode - Atoms in the film are more strongly bound to each other than to the substrate. - metal/insulator, alkali halide, graphite, mica   (2) Layer (Frank – van der Merwe) Growth Mode - Atoms are more strongly bound to the substrate than to each other. layer by layer growth (3)  Layer + Island ( Stranski - Krastanow) Growth Mode - Intermediate (1) & (2) - eq. strain energy due to lattice mismatch trigger island formation metal / metal, metal / semiconductor - Capillarity Theory - Atomistic Nucleation Processes - Cluster Coalescence and Depletion - Experimental Studies of Nucleation & Growth - Grain Structures - Amorphous thin films

2. Capillarity Theory Simple qualitative thermodynamic theory  lack of atomistic process However, connections of T, deposition rate, critical nucleus size can be obtained.   2-1. Homogeneous nucleation of a spherical solid phase of radius  from a prior supersaturated vapor  Nucleation occurs during the very early stages of phase change Gas-to-solid transformation results in decrease of G : Where, Gv : change in free energy per unit volume W    : atomic volume Ps : vapor pressure above solid Pv : pressure of supersaturated vapor

Vapor supersaturation without vapor supersaturation (S = 0), Gv = 0  no nucleation with Pv > Ps, Gv < 0  nucleation New surfaces and interfaces form : G: total free energy change in forming the nucleus : surface free energy per unit area

G* : energy barrier to the nucleus process If r < r* : cluster is unstable and shrink r > r* : cluster is stable and grow larger while lowering the energy of system

Nucleation rate

Where, Nucleation rate is also S dependent in the gas phase. S=0 : no nucleation S>0 : nucleation is possible  troublesome in CVD

a3 r3 =  ( 2 - 3cos + cos3 ) / 3 r3 : volume 2.2 Heterogeneous nucleation of solid film on a planar substrate a3 r3 =  ( 2 - 3cos + cos3 ) / 3 r3 : volume a2 r2 =  sin2 r2 : projected circular area a1 r2 = 2  ( 1 - cos ) r2 : curved surface area

Young’s equation: mechanical equilibrium among the interfacial tensions sv = fs + vf cos    island growth :  > 0  sv < fs + vf  layer growth :  = 0  sv = fs + vf If fs = 0 (no interface )  homo- or autoepitaxy  S.K growth : sv > fs + vf The strain energy of film overgrowth is large with respect to vf , permitting nuclei to form above the layer. The critical nucleus size r*,

see < Fig. 1-19> homogeneous nucleation Wetting(layer) : wetting factor = 0 at  = 0 Dewetting(sphere) : w. f. =1, at  = 180

2.3 Nucleation Rate The rate at which critical nuclei grow depends on the rate at which adsorbed adatoms attach to it in the earliest stage of film growth. a0 : atomic dimension The impingement rate onto area A* = jump frequency  na adatom surface density

adatom diffusive jumps :  e -Es/kT Es is the activation energy for surface diffusion. * Random walk for a time t over a mean square distance <X2> : <X2> = 2DSt DS = D0 exp (-Es/kT)   * Residence time S of adatoms

During the residence time, adatoms diffuse a mean distance X : surface diffusion coefficient DS :

high nucleation rate fine grained, amorphous low nucleation rate coarse-grained, single crystal steep dependence of on the vapor supersaturation ratio. 2.4. Nucleation dependence on substrate temperature and deposition rate ( : atoms /cm2•sec)

Assuming an insert substrate, fs = vf Assuming typical values,

Large r* and G*  large crystallites, monocrystal hi substrate temp. low deposition rate Small r* and G*  polycrystallites

Time to consider an atomistic model instead of thermodynamic capillarity model. Let’s estimate r* ;  = 20  10-20 cm3  = 1000 ergs / cm2 PV = 10-3 Torr PS = 10-10 Torr For example Then r* = 6  10 –8 cm Size is too small for continuous concepts like surface tension and nucleus radius. An atomistic model for heterogeneous nucleation will be more realistic.

3. Atomistic Nucleation Processes 3.1 The Walton-Rhodin Theory   The critical concentration of clusters of size i, Ei* : critical dissociation energy which is required to disintegrate a critical cluster containing i atoms into i separate atoms n0 : total density of adsorption sites N1 : monomer density

Critical monomer supply rate = (vapor impingement rate)  (area by surface diffusion before desorbing) Then, Therefore, the critical nucleation rate ( cm-2  sec-1 ) Measuring i* and Ei* is better than G*, ,  for small nuclei.

One of the applications of this theory is the subject of epitaxy At hi supersaturations & low temp.;  i* = 1 (single adatom is the critical nucleus)

At hi temperature, 2~3 atom nuclei are possible Epitaxy : stable nuclei (clusters) + adatoms  same as original surface structure.   There exist the critical temperatures where the nucleus size and orientation change. T12 : transition temperature from one to two atom nucleus.

From Fig 5-4  Edes + Es = 1.48ev at 1Å/sec  obtain epitaxial transition temperature for a given Ŕ T=577K for Ŕ= 8.5x1014 atoms/cm2-sec   There is another way to estimate epitaxial growth temperature based on surface-diffusion. For layer-by-layer growth, ledge terrace 100-1000 atoms

A typical terrace width of 100-1000 atoms During the monolayer growth time of 0.1 ~ 1 sec This means different critical epitaxial growth temperatures exist For different materials. (TE)

At Ds = 10-8 cm2/sec : TE ~ 0.5 TM for layer growth on group IV semiconductors  TE ~ 0.3TM for metals TE ~ 0.1 TM alkali hilides These epitaxial growth temperature agree qualitatively with Experimental values.   From RHEED intensity oscillations, TEs of 0.2 TM, 0.12TM, 0.03 TM are also observed.