F4280 Technologie depozice tenkých vrstev a povrchových úprav 4. Deposition Lenka Zajíčková Přírodovědecká fakulta & CEITEC, Masarykova univerzita, Brno lenkaz@physics.muni.cz jarní semestr 2021 Central European Institute of Technology ^ U*U i BRNO | CZECH REPUBLIC ^*$L*^ 4. Deposition 4.1 Introduction to Deposition 4.2 Chemical Reactions - Reaction Rate 4.3 Conversion and Extent of Reaction 4.4 Rate Constant, Order of Reaction 4.5 Complex Reactions 4.6 Arrhenius plot 4.7 Adsorption 4.8 Surface Diffusion 4.9 Nucleation 4.10 Structure Development F4280 Technologie depozice a povrchovych uprav: 4. Deposition Lenka Zajíčková 3/44 4.1 Introduction to Deposition Deposition may be considered as six sequential substeps: 1. Adsorption of arriving atoms and molecules on the surface. 2. Diffusion before becoming incorporated into the film. 3. Reaction of adsorbed species with each other and the surface to form the bonds of the film material. 4. Initial aggregation of the film material - nucleation. 5. Development of a structure (morphology) as the film grows thicker. It includes topography (roughness) and crystallography. 6. Diffusional interactions within the bulk of the film and with the substrate F4280 Technologie depozice a povrchových úprav: 4. Deposition ka Zajíčková 4/44 4.1 Introduction to Deposition Film crystallography may range from amorphous =^ polycrystalline =^ single-crystal. Single-crystalline films are obtained by epitaxy, i.e. replication of the crystalline order of a single-crystal substrate ► homoepitaxy ► heteroepitaxy In this chapter, we will consider that only thermal energy is being supplied to the surface except where energy enhancement is specifically noted. Adding energy by nonthermal means is an important process technique used in energy beams and plasma processes. F4280 Technologie depozice a povrchových úprav: 4. Deposition Lenka Zajíčková 5/44 4.2 Chemical Reactions - Reaction Rate Chemické reakce mohou zahrnovat reakce mezi plyny, kapalinami nebo pevnými látkami. Reakce se nazývá homogenní, pokud jsou reaktanty ve stejném skupenství a heterogenní pokud jsou reaktanty z dvou nebo více různých skupenství. Reakce probíhající na povrchu katalyzátoru jsou také považovány za heterogenní. Tudíž reakce mezi dvěma tekutinami je homogenní, zatímco reakce mezi plynem a pevnou látkou je heterogenní. Uvažujme reakci aA + bB Lze napsat, že A a B reagují rychlostí (1) rk = - úNa dt r'B = - dAfe dř (2) a Q a S se vytvářejí rychlostí r's = dNs d/V Q dř w dt ' kde A/y reprezentuje molární množství reakční složky (v kilomolech) a ŕ je čas. (3) F4280 Technologie depozice a povrchových úprav: 4. Deposition Lenka Zajíčková 6/44 4.2 Chemical Reactions - Reaction Rate Mezi reakčními rychlostmi existují tyto vztahy 1 dNA 1 dNB 1 dNQ 1 dNs a dt b dt q dt s dt (4) Přičemž každou část této rovnice lze považovat za reakční rychlost. Toto lze zobecnit na případ N chemických látek y, které se účastní M nezávislých chemických reakcí /. N rtAi+ai2A2 + '- + aiNAN = 0, tj. 5ľ xb=- N ao N, (10) která nám říká, jak daleko reakce postoupila. F4280 Technologie depozice a povrchových úprav: 4. Deposition Lenka Zajíčková 8/44 Alternativní koncept ke konverzi je stupeň rozvoje reakce, který pro (5) definujeme Ni - Njo OL, (11) Jde o množství, které je stejné pro jakoukoli chemickou látku. A/y0 je počáteční množství A} které se vyskytuje v reakční směsi. Nj = Nj0 + ajŠ (12) Pro vícenásobné reakce / = 1,2,... M pak M Nj = Nj0 + j2aiči- /=1 (13) Rovnice (10) a (12) mohou být zkombinovány a získáme Nj = A/yo + ay — xA. (14) Jestliže látka A je limitující reaktant (zastoupen v nejmenším množství), pak maximální rozsah reakce najdeme pomocí max (15) a relativní konverze definovaná v rovnici (10) přechází na í Xa (16) max F4280 Technologie depozice a povrchových úprav: 4. Deposition ka Zajíčková 9/44 4.4 Rate Constant, Ord er of Reaction Na základě experimentálních pozorování (později vysvětleno pomocí kolizní teorie) bylo zjištěno, že rychlost reakce aA + bB —> qQ + sS lze vyjádřit jako (17) Člen kc se nazývá rychlostní konstanta. Z definice je rychlostní konstanta nezávislá na množství jednotlivých reakčních látek, aleje závislá na jiných proměnných, které ovlivňují reakční rychlost. Pokud je r vyjádřena v kmol m-3 hr_1, pak kc má rozměr (kmol m-3)1-(a+Ď+---) hr_1 Parciální tlaky mohou být také použity k měření množství reakčních látek r = kpM (18) V tomto případě jsou pak rozměry rychlostní konstanty kp (kmol m3) hr_1 pa-(a+Ď+- -) V souladu s rovnicí ideálního plynu Ci = Pí takže RT' kc = kp{RT)a+b+- (19) (20) F4280 Technologie depozice a povrchových úprav: 4. Deposition ka Zajíčková 10/44 Mocniny a, b, ... se nazývají parciální řády reakce (1) aA + bB • • • —> qQ + sS... Součet a + b + ... můžeme nazvat celkovým řádem nebo jen řádem reakce. Ve skutečnosti by měly být řády v předchozích reakcích nahrazeny veličinami á, b', ..., které nejsou nezbytně nutně ve shodě (pouze pro jednoduché procesy) se stechiometrickými koeficienty a, b, ... á, b', ... musí být zjišťovány experimentálně. Pouze u jednoduchých reakcí je řád reakce 1, 2 nebo 3. V případě, že stechiometrická rovnice (1) je pouze obecnou rovnicí procesu, který zahrnuje několik kroků, tak nelze řád reakce určit na základě stechiometrických koeficientů. Pro nevratnou reakci prvního řádu při konstantním objemu A —> Q máme dt Pokud tedy známe rychlostní konstanty k (hr-1), tak z rovnice (21) můžeme spočítat reakční rychlost rA pro jakoukoli koncentraci reakčních složek. A naopak pokud známe funkci změny koncentrace na čase (21), tak můžeme spočítat rychlostní koeficient. Toto je diferenciální metoda pro získání rychlostní konstanty k Integrální metoda využije integrace rovnice (21), což dává (22) a semilogaritmický graf CA0/CA v závislosti na čase t nám také dává k. F4280 Technologie depozice a povrchovych uprav: 4. Deposition Lenka Zajíčková 4.4 Rate Constant, Order of Reaction We showed relations for the rate constant of the irreversible 1st order reaction A —>> Q. Now, think about the expressions for ► reversible 1 st order reaction A ^\ Q ► irreversible 2nd order reaction 2A —>> Q + S ► irreversible 2nd order reaction A + B —>> Q + S F4280 Technologie depozice a povrchových úprav: 4. Deposition Lenka Zajíčková 12/44 We can encounter also with complex reactions: parallel, consequtive, free radical chain reaction (initiation, propagation, termination), free radical addition The rate of reaction depends on the temperature through the variation of the rate coefficient k according to the Arrhenius plot where ► T is the temperature in K, ► E is the activation energy (J/mol), ► R is the gas constant (JK/mol), ► A0 is a constant called the frequency factor. Arrhenius came to this formula by thermodynamic considerations. When In k is plotted versus 1/7", a straight line with the slope —E/R is obtained k = Ao exp(-E/RT) (23) + In i40. (24) F4280 Technologie depozice a povrchových úprav: 4. Deposition ka Zajíčková 14/44 Consider a molecule approaching a surface from the vapor phase. ► A few atomic distances from the surface molecule begins to feel an attraction -interaction with the surface molecules by van der Waals forces (London dispersion forces): ► molecules/atoms without dipole moments (symmetrical or intert) interact due to oscillating dipoles, i.e. induced-dipole interaction ► polar molecules (permanent dipoles) interact more strongly ► The approaching molecule is being attracted into a potential well - accelerates down the curve until it passes the bottom and is repelled by steeply rising potential. 6 2 2 3 4 Distance (a.u.) An illustrative Lennard-Jones potential model for physical adsorption. ► If enough of the molecule's perpendicular component of momentum is dissipated into the surface the molecule cannot escape the well after being repelled =^ physisorption ► fraction of physisorbed molecules - trapping probability S ► reflected 1 — 5 ► S is different from thermal accomodation coefficient 7 introduced previously ► molecule is at least partially accomodated thermally to the surface temperature Ts even when it is reflected ► The physisorbed molecule is mobile on the surface except at cryogenic T - hopping (diffusing) between surface atomic sites. vapor molecule reflection desorption 3 utilization H a incorporation physisorption chemisorption During surface diffusion the molecule ► may desorb after a while by gaining enough energy in the tail of the thermal energy distribution. ► may undergo a further interaction consisting of the formation of chemical bonds with the surface atoms, i.e. chemisorption. The chemisorption reaction probability £ is used in the case of chemisorption on a foreign substrate instead of condensation coefficient ac. ► some of adsorbed species eventually escape back into the vapor phase =^ sticking coefficient Sc - fraction of the arriving vapor that remains adsorbed for the duration of the experiment. vapor molecule reflection desorption 3 utilization H a incorporation physisorption chemisorption F4280 Technologie depozice a povrchových úprav: 4. Deposition Len ka Zajíčková 17/44 Chemisorption ► Sticking coefficient Sc has less fundamental meaning than 5 and £ (or ac) that are determined solely by chemistry and energy. Nevertheless, Sc is very useful in thin film deposition - it is the fraction of arriving vapor incorporated into the film (buried before escaping). ► Utilization fraction 77 of a chemical vapor - fraction of molecules utilized for the deposition =^ r\ can approach unity even when Sc is very low. vapor molecule reflection desorption a * „_, „_^ incorporation physisorption chemisorption F4280 Technologie depozice a povrchových úprav: 4. Deposition ka Zajíčková 18/44 recursor State Chemisorption - sharing electrons, physisorption - dipóle interaction. If both adsorption states exist, the physisorption is called precursor state. The precursor model may also be applied to cases where both the adsorption states involve chemical bonding but one is weaker. The precursor model has long been applied to heterogeneous catalysis, thin-film deposition and condensation of molecular vapors. Recent theory indicates that even the condensation of monoatomic vapor such as Al can involve both adsorption states: the precursor state = AI-AI dimer with limited bonding to bulk Al. ► In most CVD reactions, the feed vapors adsorb as molecules that undergo reaction breaking their molecular bonds and form new bonds to surface SiH4(g) ----y SiH4(a) Si(c) + 2H2(g) (25) ► In deposition of compounds from separate vapor sources of each element, adsorbing vapor bonds much more strongly to surface sites occupied by the other element Zn(g) + Se(a) ZnSe(c) and Se(g) + Zn(a) ZnSe(c) (26) ► Si chemically passivated by H reacts with adsorbates mainly at those few sites that are missing H atom. On the H-passivated sites, adsorbates remain only physisorbed. ► Atomically flat surfaces often bond more strongly with adsorbates at atomic steps. Consider hypothetical diatomic gas-phase molecules chemisorbing as two Y atoms: dissociative chemisorption Y2(q) adsorbing and then dissociative Lifting atomic Y out of its potential well along curve c results in much higher molar potential energy Ep in the gas phase - roughly the heat of formation, AfH, of 2Y(g) from V2(9)- The curve a represents activated chemisorption - there is an activation energy Ea to be overcome for Y2(g) to become dissociatively chemisorbed. For deeper precursor well, curve b, chemisorption is not activated though there is still a barrier Erb. F4280 Technologie depozice a povrchových úprav: 4. Deposition ■ ka Zajíčková 20/44 ► If curve c is followed (Ep is high enough) direct chemisorption (without involving precursor state) =^ Eley-Rideal mechanism, i.e. direct reaction between an incoming species and a surface site ► Reaction among surface species Langmuir-Hinshelwood mechanisms +400 - of Y2(g) -600 | Erb c precursor physisorption dissociative chemisorption Two ways in which vapor can arrive at surface having Ep > 0: ► Gaseous molecules have their Ep raised by becoming dissociated. ► Solids and liquids have it raised by evaporating. Energy-enhanced deposition processes provide enough energy Ep > Ea ► sputter deposition - arriving species have kinetic energy ~ I000kj/mol and Ep > 0. ► plasma-enhanced deposition - vapor molecules are dissociated in plasma F4280 Technologie depozice a povrchových úprav: 4. Deposition nka Zajíčková 21 /44 In evaporation and CVD, the vapors often adsorb first into the precursor state (curve a, b) ► and chemisorb by overcoming the barrier Er(a b) ► or desorb by overcoming the heat of physisorption Ed(a hy these two reactions result in a net rate of chemisorption. First-order chemical reaction Rk = kkns = kkns0Q (27) Rk rate of /cth surface reaction per unit area [m-2s-1] kk rate constant [s_1] ns surface concentration of reactant [m-2] 0 fractional surface coverage by reactant with rate constant following Arrhenius equation: kk = ^exp(-||) (28) vok frequency factor or pre-exponential factor Ek reaction activation energy [kJ/mol] Assumptions: ns is constant over time (steady state), chemisorption reaction occurs only in the forward direction (not valid for too high T at which film begins to decompose), adsorption occurs on free sites mass balance for the physisorbed precursor: ri(5(1 - 0) = Rr + Rd = (kr + kd)ns0Q l~i molecular impingement flux [m_2s_1] Rr reaction (chemisorption) rate and Rd desorption rate (29) F4280 Technologie depozice a povrchových úprav: 4. Deposition Lenka Zajíčková 22/44 Sticking Coefficient Using previous relations we obtain for surface coverage 0 t~iS/nso + kr + kd and substituing into the chemisorption rate expression (27) Vi5kr (30) Rr = krns0Q = t~iS/nso + kr + kd We may now define sticking coefficient Sc more precisely Sc = Rr/\~i In case of small l~i, i.e. small 0 Eq. (31) simplifies to (31) (32) R r = 1 + kd/kr = l~i 1 + u0r eXPV RTS ) (33) where ^ is chemisorption reaction probability. Sc « ^ for 0 < 1 but for larger 0, Sc < 6 For the special case of film deposition from single vapor having the same composition as the film, £ = ac (condensation coefficient). The assumption of 1st order kinetics is not always valid for a more complicated case of compound-film deposition from multicomponent vapors. For more details refer to book of Donald Smith, chapter 7.3.3. F4280 Technologie depozice a povrchových úprav: 4. Deposition Lenka Zajíčková 23/44 Activated adsorption The ► ► chemisorption rate Rr governs the rate of film deposition when kr is the same from site to site along the surface Ts is not so high that decomposition or re-evaporation of the film occur. +400 - of Y2(g) -600 * * h precursor physisorption dissociative chemisorption Rr = l~i 1 + u0r eXPV RTS ) If Er Ed there is an activation energy Ea = Era - Eda for chemisorption (curve a). For high Ea the film fail to deposit unless 7"s is raised to make exp. term smaller => Rr t for T t The activated case is very common in CVD. If Er : Ed (chemisorption is not activated as in curve b) Rr I for T t Example: Si deposits from SiH4 at elevated (not room) Ts. If 7"s becomes too high, the evaporation flux of the Si > Rr and deposition stops. The net deposition flux of Si: V r — Rr — Ty (34) Ts window for deposition. F4280 Technologie depozice a povrchových úprav: 4. Deposition Lenka Zajíčková 24/44 4.8 Surface Diffusion typical U/mol 4M I 4M 400 (a) sit* 1 phyiiaorption transition stat* ■ite 2 chemiaorption Flux of adsorbate rs [m~1s~1] across the Es barrier between 1 and 2 sites in the x direction Rate of barrier crossing Rs = — (35) a a is the distance between the sites. Considering Maxwell-Boltzmann distribution 1 nsv Rs = - — 4 a n _s a kBT_ 2tt/t? (36) nfs - surface concentration of adsorbate residing in the transition state. Relation between n's and r?s? -from statistical physics (next page) F4280 Technologie depozice a povrchových úprav: 4. Deposition ka Zajíčková 25/44 oncentrations in Surface States Relation between n's (concentration in transition states) and ns (concentration in adsorption states)? n>s _ZirZ>Z[ ns ZrZvZt (37) Z - partition function, g, degeneracy of the energy level, r, v, t rotational, vibrational, translation kinetic energies (electronic excitations are neglected at ordinary 7~), The Boltzmann factor accounts for the potential energy difference Es (J/mol) between the adsorption-site state ns and the transition state n's ► rotation of molecules is limited by adsorption =^ Z'r = Zr = 1 ► Zvk derived from quantum mechanics for harmonic oscillator ZVk = 1 1--P(-0) but vibrational modes are mostly in their ground states at ordinary T ► partition function for translation energy V27rm/cB T h (38) (39) n's = nsZ(x exp -(^:) (40) F4280 Technologie depozice a povrchových úprav: 4. Deposition ka Zajíčková 26/44 I ate ot Darner crossing ... using absolute-reaction-rate theory (predicts the absolute reaction rate of a chemical reaction from the quantum mechanical description of the potential energy changes during the interaction; cannot provide a quantitative estimation of the diffusion rate but gives an insight into the determining factors) Rs = ns[ -yj-) exp(--^) fis^osexp(--^:) nsks (41) Arhenius expression for the rate constant ks of "chemical reaction". The rate constant ks (s_1) represents the frequency with which an individual adsorbate molecules "hops" to an adjacent site. Thus, the factor u0s = 1013 - 1016 s_1 is NOT the frequency of any vibrational component vk of the adsorbate. The rate of surface diffusion increases exponentially with t T and I Es (activation energy for surface diffusion). Es < Ed, Ec (desorption activation energy of physisorbed or chemisorbed species, respectively) =^ high rate of surface diffusion at film deposition T approaching the onset of re-evaporation, i. e. when exp(—J^) becoming significant = one of principal ways in which substrate T affects film structure. Es/Ec sometimes referred as corrugation ratio, it is lower for metals than for semiconductors due to absence of bond directionality in metals. F4280 Technologie depozice a povrchových úprav: 4. Deposition ka Zajíčková 27/44 i iTTusion Le Relation between molecular hopping rate ks and the distance which an adsorbate molecule travels during the film deposition: ► classic random-walk problem ► The final locations are more widely dispersed from the starting point with increasing 2 time t. For large number of hops N0, it is Gaussian dispersion exp(—^) characterized by its standard deviation a - here the diffusion length A r is per-hop rms change in the distance from the starting points Two regimes need to be considered separately: ► t is time between adsorption and burial by the next depositing monolayer ► adsorbate is more likely to desorb than to be buried within t Regime 1 - burial time: t = no A = a, ^os^O / Es x -exp (--) rr HV 2RT} where n0 is surface density of adsorption sites (m-^), rr deposition flux (m~^s_1) and ks = ^os exp (-■!§=) F4280 Technologie depozice a povrchových úprav: 4. Deposition Lenka Zajíčková 28/44 Diffusion Length - contin. Regime 2- If T is high enough the film re-evaporation (desorption) becomes significant. =^ t is adsorption lifetime. Considering the desoprtion only from chemisorbed state (negligible concentration of precursor state at high 7~): ŕ- 1 - 1 exp( —) where subscript c denotes the chemisorbed state. Combining both gives A = a Vi OS Voc exp (-———) HV 2RT } (42) E.V2R In a increased Jd IT F4280 Technologie depozice a povrchových úprav: 4. Deposition Lenka Zajíčková 29 / 44 How is the diffusion length A (obtained from the examination of motion of individual adsorbed molecules) related to the macroscopic quantity - diffusion coefficient? Transport equation _ dns rs — ~D~rr rs, ns have surface units m_1s_1 and m-2 Using analogy of 3D case D = \ v^\, in which the mean free path A is the hop distance a and the mean speed i/av is ksa D=-kscř A = av/feř = 2VĎř (43) 4 Thus, we can express D in the Arrhenius form when using this expression for ks: D= l^osa2exp(--^:) = Doexp(--^:) (44) F4280 Technologie depozice a povrchových úprav: 4. Deposition Len ka Zajíčková 30 / 44 4.9 Nucleation Nucleation is a complication that must often be added to the above described model of chemisorption where we expected that kr is the same from site to site. If nucleation is important, the net deposition flux rr = Rr — f~v is Vr > 0 only for certain active substrate-surface sites, nucleation sites or nuclei of film material which have spontaneously accumulated. Various examples: ► Si chemically passivated by H reacts with adsorbates mainly at those few sites that are missing H atom =^ Rr t at unpassivated Si surface atoms because of I Er ► In deposition of compounds from separate vapor sources of each element, adsorbing vapor bonds much more strongly to surface sites occupied by the other element Zn(g) + Se(a) -> ZnSe(c) and Se(g) + Zn(a) -> ZnSe(c) ► atoms of low-reactivity metals often bond much less easily to nonmetallic substrates: Ea of chemical bond of Zn, Cd to glass is very high because of high bond strength between substrate elements =^ Zn, Cd on glass bonds more readily to itself than to the surface =^ formation of nucleus The existence of certain sites which are active in adsorption is common in thin-film processes. Access of precursor to these favored sites can dominate the deposition kinetics. Two types of access ► from vapor phase - Eley-Rideal mechanism ► by surface diffusion - Langmuir-Hinshelwood mechanisms Concept of surface tension 7 has to be introduced to understand nucleation. The force F required to draw a liquid membrane: F = 2^7 (b is circumference, 2 stands for inner and outer surface). Work FAx to create the membrane of area A = 2bAx is stored as surface energy surface energy per unit area FAx/A -- 7 [N/m] =>- For liquids, surface (free) energy per unit area (J/m2) is equal to surface tension 7. For solids at T > 0 K, the surface Gibbs free energy is reduced by entropy factor TS which depends on the degree of surface disorder =^ surf, energy is minimized by surface diffusion. Additionally, in solids, there is an surface energy term A^^a^e^in which ay is surface stress and &e-,j surface strain tensor ^dejjSjj - dA/A. Liquids cannot support such strain because the atoms just rearrange to relax it. F4280 Technologie depozice a povrchových úprav: 4. Deposition Len ka Zajíčková 32 / 44 Thin-film growt h Nature tends to minimize surface energy 7A ► when wire is lifted far enough, the membrane is in the plane of the ring ► in solids, surface energy minimizes by surface diffusion fundamental process to development of structure in thin films In thin-film growth, both A and 7 are varying: ► A depends on surface topography ► 7 depends on many properties of exposed surface (chemical composition, crystallographic orientation, atomic reconstruction, atomic-scale roughness etc.). It is anisotropic for most crystalline solids. For deposition onto a foreign substrate, nucleation behaviour is strongly influenced by surface tension of substrate, 7S. We also need to consider 71 of the substrate-film interface and 7f of film free surface. Two cases for growth modes: ► A > a, i. e. deposition material can rearrange itself to minimize 7, nucleation is not kinetically limited and approaches equilibrium ► A < a atoms sticks where they land and the growth behaviour is "quenched" F4280 Technologie depozice a povrchových úprav: 4. Deposition Lenka Zajíčková 33 / 44 For A > a, there are two nucleation situations on the bare substrate (a) films wets the substrate because 7f + 71 < 7S =>• smooth growth, atomic layer by layer (Frank-van der Merwe growth). It requires strong enough bonding between film and substrate to reduce 71 ► (b) with insufficient substrate bonding film forms 3D islands (Volmer-Weber growth mode). In extreme case of no bonding at all 71 = 7f + 7S, the film spreading across the substrate would increase the total surface energy by 2^. F4280 Technologie depozice a povrchových úprav: 4. Deposition Growth Modes for A > a (contin.) Lenka Zajíčková 34/44 Third growth mode, Stranski-Krastanov, shown in (c) - growth mode changes from layer to island after a monolayer or two due to a change in the energy situation. 77s / V //'iětYi TiYi, (a) (6) (c) 3D nucleation is usually undesirable since it leads to rough, nonuniform films (extreme example being the diamond nuclei) How to manipulated with the growth mode? Film wetting for 7f + 71 < 7S- 7i decreases with film-substrate bonding (covalent, ionic, metallic). In general, interfacial bonding is stronger between materials having the same type of bonding. Examples: ► chemically-active metal, Cr, will bond to glass by breaking Si-0 bond and forming Cr-0 ► Au cannot do this, i.e. does not bond well to glass ► Au forms a strong metallic bond to clean Cr Using intermediate "glue" layer (Cr) which bonds well to both, the film and the substrate, 7/ can be reduced and wetting accomplished. Another good bonding material is Ti. Alternatively, energy-enhanced techniques (plasma treatment, ion bombardment, sputtering) can provide the activation energy for bonding between film and substrate, i.e. reduce7,. Two ways in which 3D nuclei can form ► bonding initiates at active surface sites such as atomic steps, crystal deffects, impurities. At these nucleation sites, the Ea is lower than elsewhere. ► even if there are no active nucleation sites, 3D nuclei can still form at random surface locations because of the interfacial bonding which develops by the spontaneous accumulation of mobile atoms plus arriving vapor into "critical" nuclei which are big enough to be stable (classical nucleation problem) F4280 Technologie depozice a povrchových úprav: 4. Deposition Lenka Zajíčková 37/44 3D nucleation - how 1 o produce smooth & uniform film? ► concentration of critical nuclei n* has to be t ► and their radius r* I, i. e., less coarse nucleation How to achieve it? ► Using very high vapor arrival rate (supersaturation), at least until the nucleation phase is over and the film is continuous. Coarsening will still occur even with one-atom critical nuclei because atoms and nuclei are mobile on the surface migration and coalescence ► Decrease the substrate T to inhibit surface diffusion freezing the nucleation and coalescence. If arriving species do no thave enough energy to desorb or diffuse they remain where they land - quenched growth mentioned earlier. In this case, the nucleation is kinetically inhibited by the surface-diffusion activation-energy barrier Es ructure ueveiopmen Upon coalescence of the surface nuclei to form a continuous film, the nucleation step of the film deposition is complete and 4th step begins - development of the bulk film structure. The form of the structure changes dramatically with ► the amount of thermal motion taking place during film growth: scales with 7"s/7"m (melting point of the film over substrate temperature - in K) - known as homologous or reduced T the amount of additional energy being delivered to the growth surface Fi3nrt £16 Characteristics of the foui basic stractuTal zones and of whiskers, in cro&s section. The ratio of substrate T to film melting T (TyT^") increases in the direction Z1-*ZT-*Z2-*Z3- F4280 Technologie depozice a povrchových úprav: 4. Deposition ka Zajíčková 39/44 ructure ueveiopmen quenched growth for Z1 and ZT: ► Z1 occurs at 7"s/7"m so low that surface diffusion is negligible, i. e. A < a. Z1 consits of columns typically tens of nm in diameter separated by voids a few nm across. The columns have poor crystallinity (many deffects) or are amorphous. In thicker films, an array of cones with wider voids between them become superimposed upon this structure. The cones terminate in domes at the surface, and the size of the domes increases with film thickness. ► ZT also occurs when A < a. It contains defected columns as Z1 but the voids and domes are absent. ZT is usually associated with energy-enhanced processes. H-utíHĽ-FiU: Figure 6,16 Characteristics of the four basic structural zones and of whi^km-a, in croas section. The ratio of substrate T to film melting T (T^T^) increases in the direction F4280 Technologie depozice a povrchových úprav: 4. Deposition ka Zajíčková 40/44 ructure ueveiopmen thermally activated rearrangement on or within the film for Z2 and Z3: ► Z2 occurs for 7"s/7"m > 0.3, diffusion becomes significant. It consits of columns having tight grain boundaries between them and having a characteristic diameter which increases with Ts/Tm. Crystalline columns are less defected than in Z1 and ZT, and are often facetted at the surface. The Z2 structure can also accur in amorphous films. The column boundaries are planes of reduced bonding rather than planes of crystallographic discontinuity. ► Z3 occurs at certain instances at Ts/Tm > 0.5, considerable bulk annealing of the film is taking place during deposition, more isotropic crystallite shapes. nubHľrfitL: Figur* &1S Characteristics of the four basic structural zones and of whiskers, in croas section. The ratio of substrate T to film melting T CT,Tra) increases in the direction F4280 Technologie depozice a povrchových úprav: 4. Deposition Lenka Zajíčková 41 / 44 Simple model of statistical roughnening caused by statistical fluctuation in the vapor arrival flux: each atom is constrained to stick on the site it lands on (even if it is on top of a pillar) For large enough N (average number of atoms per depositing site) the variation in heights is described by Gaussian distribution with standard deviation a = a\/Kl = y/ah where h = aN is average film thickness Note: analogy to dispersion in lateral direction arising from surface diffusion because both are random processes Figure 5.1S Statistical roughening in random ballistic deposition of a 25-atom-thick film. (Pascal solution courtesy of Jansd Smith-Mi ckelson. ) F4280 Technologie depozice a povrchových úprav: 4. Deposition encnea g ka Zajíčková 42/44 (o) Ah Ah j T = 44flK T~460K figura 5.50 Twtj-dimerLFiinna] computer simulation of th* effect af iubitrat* T on void filling by surface diffusion. CSoujtsei Reprinted from Ref. 22 by permission J