F4280 Technologie depozice tenkých vrstev a povrchových úprav 4. Deposition Lenka Zajíčková Přírodovědecká fakulta & CEITEC, Masarykova univerzita, Brno lenkaz@physics.muni.cz jarní semestr 2017 Central European Institute of Technology ^ U*U j BRNO | CZECH REPUBLIC ^*$L*^ 4.1 Introduction to Deposition 4.2 Chemical Reactions - Reaction Rate 4.3 Conversion and Extent of Reaction 4.4 Order of Reaction, Rate Constant 4.5 Adsorption 4.6 Surface Diffusion 4.7 Nucleation 4.8 Structure Development F4280 Technologie depozice a povrchových úprav: 4.1 Introduction to Deposition Len ka Zajíčková 3/40 4.1 Introduction to De position 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: 4.1 Introduction to Deposition ka Zajíčková 4/40 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: 4.2 Chemical Reactions - Reaction Rate ka Zajíčková 5/40 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) r'A = - áNA r'B = - dAfe dř ° dř a Q a S se vytvářejí rychlostí (2) r's = áNs d/V, Q dř w dř ' kde Nj reprezentuje molární množství reakční složky (v kilomolech) a ř je čas. (3) F4280 Technologie depozice a povrchových úprav: 4.2 Chemical Reactions - Reaction Rate Lenka Zajíčková 6/40 4.2 Chemical Reactions - Reaction Rate Mezi reakčními rychlostmi existují tyto vztahy 1 dNA 1 dNB 1 úNq 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, které se účastní M nezávislých chemických reakcí. a/i /\i + a/2/42 + ... + qljnAn = 0 (5) nebo n 7=1 M (6) Používáme konvenci, že stechiometrické koeficienty a,y bereme jako kladné pro produkty a jako záporné pro reaktanty. Reakční rychlost je obecně vztažena k nějakému množství, například objemu, pak když V reprezentuje objem, který zabírá reakční směs, pak 1 1 n = — V OL\l dNj (7) Pokud se objem reakční směsi nemění n = 1 d C j ay dt (8) V tomto prípade by pro získání reakční rychlosti stačilo měření koncentrace. F4280 Technologie depozice a povrchovych uprav: 4.3 Conversion and Extent of Reaction Lenka Zajíčková 7/40 4.3 Conversion and Extent of Reaction Často se místo koncentrací v rovnicích užívá pojem konverze a vyjadřuje se jako x'A = NA0-NA x'B = NBQ-NB (9) nebo pro konstantní objem, xÄ = Cao — CA x'd = Cbo — C, b- (10) Dolní index 0 označuje počáteční množství chemické látky. Nejčastěji se setkáváme s pojmem relativní konverze xA = NAo - N a x b = NB0 - N b NAo Afeo která nám říká, jak daleko reakce postoupila. (11) F4280 Technologie depozice a povrchových úprav: 4.3 Conversion and Extent of Reaction Lenka Zajíčková 8/40 Alternativní koncept ke konverzi je stupeň rozvoje reakce (6), který definujeme jako ľ_Nj- typ S OL \ (12) Jde o množství, které je stejné pro jakoukoli chemickou látku. Také, Nj = Nj0 + ajÍ, (13) kde Njo je počáteční množství Aj které se vyskytuje v reakční směsi. Pro vícenásobné reakce pak M (14) /=1 Rovnice (11) a (13) mohou být zkombinovány a získáme Nj = A/yo + ay— xA. (15) Jestliže látka A je limitující reaktant (zastoupen v nejmenším množství), pak maximální rozsah reakce najdeme pomocí 0 = NA0 + CM^max (16) a relativní konverze definovaný v rovnici (11) přechází na (17) max F4280 Technologie depozice a povrchových úprav: 4.4 Order of Reaction, Rate Constant ka Zajíčková 9/40 4.4 Order of Reaction, Rate Constanl Na základě experimentálních pozorování (později vysvětleno pomocí kolizní teorie) bylo zjištěno, že rychlost reakce v rovnici (1) lze vyjádřit jako r — kcCßCß. (18) 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 r je vyjádřena v kmol m-3 hr_1, pak kc má rozměr (kmolm-3)1-(a+Ď+-)hr-1 Fyzikální rozměr rychlostní konstanty používaný v konverzi je stejný jako ten, co se používá při práci s koncentracemi. Parciální tlaky mohou být také použity k měření množství reakčních látek r = kpp%pbB. V tomto případě jsou pak rozměry rychlostní konstanty kp (kmol m3)hr-1Pa"(a+Ď+-) V souladu s rovnicí ideálního plynu Pí Ci = RT takže kc = kp{RT)a+b+- (19) (20) (21) (22) (23) F4280 Technologie depozice a povrchových úprav: 4.4 Order of Reaction, Rate Constant ka Zajíčková 10/40 4.4 Order of Reaction, Rate Constanl Mocniny a, b, ... se nazývají "parciální řády" reakce ve vztahu k A, B.... Součet a + b + ... můžeme nazvat "celkovým řádem" nebo jen "řádem" reakce. Ve skutečnosti by měly být řády v předchozích reakcích nahrazeny veličinami a', b\ ..., které nejsou nezbytně nutně ve shodě (pouze pro jednoduché procesy) se stechiometrickými koeficienty a, b, ... a 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 máme rA = -**=kCA. A dt A (24) Pokud tedy známe rychlostní konstanty k (hr-1), tak z rovnice (24) můžeme spočítat reakční rychlost rA pro jakoukoli koncentraci reakčních složek. A naopak pokud známe funkci změny koncentrace na čase (24), tak můžeme spočítat rychlostní koeficient. Tato metoda pro získání koeficientu k je známá jako diferenciální. Integrací rovnice (24) získáme, kt = In C ao C (25) a a semilogaritmický graf CA0/CA v závislosti na čase t nám také dává k. 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 F4280 Technologie depozice a povrchových úprav: 4.5 Adsorption Len ka Zajíčková 13/40 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 a * «_, „_^ incorporation physisorption chemisorption F4280 Technologie depozice a povrchových úprav: 4.5 Adsorption Len ka Zajíčková 14/40 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 Chemisorption - sharing electrons, physisorption - dipole 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 ► 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 ► 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. SiH4(g) SiH4(a) Si(c) + 2H2(g) (26) Zn(g) + Se(a) —)• ZnSe(c) and Se(g) + Zn(a) —)• ZnSe(c) (27) F4280 Technologie depozice a povrchových úprav: 4.5 Adsorption ka Zajíčková 16/40 +400 - of Y2(g) Consider hypothetical diatomic gas-phase molecules Y2(g) adsorbing and then dissociative chemisorbing as two Y atoms: 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. * * „ ■ ■ precursor physisorption -600 dissociative chemisorption F4280 Technologie depozice a povrchových úprav: 4.5 Adsorption Lenka Zajíčková 17/40 ► 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 J 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 ~ 1000kJ/mol and Ep > 0. ► plasma-enhanced deposition - vapor molecules are dissociated in plasma F4280 Technologie depozice a povrchových úprav: 4.5 Adsorption Lenka Zajíčková 18/40 Thermally controlled deposition process 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?b). these two reactions result in a net rate of chemisorption. First-order chemical reaction (28) Rk rate of /cth surface reaction per unit area [m~^s_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 = uokexp(-^) (29) uok 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: r^O - 0) = Rr + Rd = {kr + kd)ns0Q l~i molecular impingement flux [m_2s_1] Rr reaction (chemisorption) rate and Rd desorption rate (30) F4280 Technologie depozice a povrchových úprav: 4.5 Adsorption Lenka Zajíčková 19/40 Sticking Coefficient Using previous relations we obtain for surface coverage 0 0 ^jS/ns0 t~iS/nso + kr + kd and substituing into the chemisorption rate expression (28) ^ ri£/cr Rr = krns0O =-. ^iS/ns0 + kr + kd We may now define sticking coefficient Sc more precisely Sc = Rr/V{ In case of small ri5 i.e. small 0 Eq. (32) simplifies to V{5 _ 6 Rr = 1 + kd/kr = l~i 1 + ^exp(^ ) (31) (32) (33) (34) where £ is chemisorption reaction probability. Sc « £ for 0 < 1 but for larger 0, Sc < £. 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: 4.5 Adsorption Lenka Zajíčková 20/40 Activated adsorption The ► ► +400 - 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. Rr = l~i of Y2(g) -600 * * h precursor physisorption dissociative chemisorption 1 + "Od "Or exp( Er Ed RTa ) If Er ■ Ed > 0 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: Vr = Rr — Vv (35) =^ Ts window for deposition. F4280 Technologie depozice a povrchových úprav: 4.6 Surface Diffusion ka Zajíčková 21/40 m m urtace ÜITTUSIOn typical kJ/mol 4M I 4 0 only for certain active substrate-surface sites called nucleation sites or on 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 ^ X)/y °"/yd£:/y in which cr,y is surface stress and cte,y surface strain tensor dejjSjj = dA/A. Liquids cannot support such strain because the atoms just rearrange to relax it. F4280 Technologie depozice a povrchovych uprav: 4.7 Nucleation Len ka Zajickova 29 / 40 Thin-film growt h Nature tends to minimize (surface) energy: ► 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 7 of substrate, 7S. We also need to consider 71 of the substrate-film interface and 7f of film free surface. Two cases ► 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" 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, i.e. spreading of the film across the substrate would increase the total surface energy by 2^. (a) (6) (O F4280 Technologie depozice a povrchových úprav: 4.7 Nucleation es ka Zajíčková 31 /40 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. 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? 71 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: 4.7 Nucleation ka Zajíčková 34/40 ciea For objective to produce a smooth and 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 - quneched growth mentioned earlier. In this case, the nucleation is kinetically inhibited by the surface-diffusion activation-energy barrier Es F4280 Technologie depozice a povrchovych uprav: 4.8 Structure Development Lenka Zajíčková 35/40 4.8 Structure Development 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"m/Ts (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 flgur* £16 Characteristics cf the foui basic structural zones and of whiskers, in cross section. The ratio of substrate T to film melting T GVTpi) increases in the direction Z1-*ET-*Z2-*Z3. F4280 Technologie depozice a povrchovych uprav: 4.8 Structure Development Lenka Zajíčková 36/40 4.8 Structure Development ► Z1 occurs at 7"m/7s so low that surface diffusion is negligible, i. e. A < a ► 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 ► Z2 occurs for 7"m/Ts > 0.3, diffusion becomes significant ► Z3 pccurs at certain instances at 7"m/Ts > 0.5, considerable bulk annealing of the film is taking place during deposition quenched growth for Z1 and ZT, thermally activated rearrangement on or within film for Z2 and Z3 figure 6,16 Characteristics of the four basic structural zones and of whiskers,, in croaa section. The ratio of substrate T to film melting T iTVTpJ increases in the direction 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 = \fah where h = aN is average film thickness Note: analogy to dispersion in lateral direction arising from surface diffusion because both are random processes Rguru 5.16 Statistical roughening in random ballistic deposition of a 25-atom-thick film. (Pascal solution courtesy of Jared Smith-Mkkdson.) F4280 Technologie depozice a povrchových úprav: 4.8 Structure Development Lenka Zajíčková 38/40 Quenched growth Ai (o) Kl Aí|Ah| (b) to Atomistic processes in quenched-growth structure development (more realistic model): ► (a) ballistic aggregation (arriving atoms cannot perch on top of each other but rather settle sideways) ► (b) effect of atoms finite size (shadowing low areas) ► (c) sideways attraction (development of columns) (d) oblique shadowing (self-shadowing, incidence over range of 0 occurs for fluid-flow regime Kn