Lecture 10 Thin Film Growth 1/76
Announcements Homework: Homework Number 2 is returned today, please pick it up from me at the end of the class. Solutions are online. Homework 3 will be set Thursday (2 nd Nov). Homework 3 is due Thursday 9 th Nov at the start of class. 2/76
Announcements Term Paper: You are expected to produce a 4-5 page term paper on a selected topic (from a list). Term paper contributes 25% of course grade. You should have all been assigned your first-choice topic. The term paper should be handed in at the start of class on Tuesday 21 st November. Details / regulations are on the course website. The term paper will be returned to you in class on Thursday 30 th November. 3/76
Useful Links Wake Forest University: http://users.wfu.edu/ucerkb/nan242/l11- Thin_Film_Growth.pdf University of Basel: https://nanolino.unibas.ch/pdf/surfacephysics/oberflaeche9.p df Max Planck Institute: http://www.imprscs.mpg.de/pdf/vortrag_schmidt_imprs_2013_thin_film_grow th.pdf 4/76
Lecture 10 Overview of Thin-Film Growth Process Adsorption Diffusion Nucleation Film Growth Crystallinity and Epitaxy Thickness Measurment 5/76
CVD Mechanism 1). Bulk transport Reactant molecule Carrier gas (to maintain high pressure & slow reaction rate) 8). Bulk transport of by product 2). Transport across boundary layer J 1 D g C 3). Adsorption 4). Surface diffusion 5). Decomposition 7). Diffusion of gaseous byproduct 6). Reaction with film J 2 k i C i 6/76
Overview of Thin-Film Growth Process Atom arrives: Migration: Collison and Combination: Nucleation: Coalescence: Continuity: 7/76
Adsorption 8/76
Particle Flux We know what the gas impingement rate is from Lecture 3: J A = 1 4 nc Particle number density Mean particle velocity We can show: P = nk B T c = 8k BT πm J A = P 2πmk B T 9/76
Adsorption Adsorption of particles onto the surface is central to the process of film growth. Adsorption is separated in to two categories: Chemisorption. Physisorption. 10/76
Chemisorption A strong chemical bond is formed between the adsorbate atom or molecule. I.e. an ionic or covalent bond In this case, the adsorption energy, E A, of the adatom is likely to be comparable to or even more than the sublimation energy of the substrate (typically a few ev/atom). 11/76
Physisorption Physisorption is weaker, and is often considered as having no chemical interaction involved. The attractive interaction, in this case, is largely due to the van der Waals force. This force is due to fluctuating dipole (and higher order) moments on the interacting adsorbate and substrate, and is present between closed-shell systems. Physisorption energies are of order 100 mev/atom. 12/76
Adsorption Particles are constantly adsorbed and desorbed on a surface: Substrate 13/76
Adsorption Particles are constantly adsorbed and desorbed on a surface: Substrate 14/76
Adsorption Particles are constantly adsorbed and desorbed on a surface: Substrate 15/76
Adsorption Particles are constantly adsorbed and desorbed on a surface: Substrate 16/76
Adsorption Particles are constantly adsorbed and desorbed on a surface: Substrate 17/76
Adsorption Particles are constantly adsorbed and desorbed on a surface: Substrate 18/76
Adsorption Particles are constantly adsorbed and desorbed on a surface: Substrate 19/76
Adsorption Particles are constantly adsorbed and desorbed on a surface: Substrate 20/76
Adsorption The things that determine whether a film forms, and its growth rate, are as follows: The partial pressure of the atoms in the vapor: P. The reaction rate of the adsorption process: k ads. The reaction rate of the desorption process: k des. 21/76
Fractional Coverage The fraction of surface covered is given by: θ = KP 1 + KP 1 exp k des 1 + KP t Where: θ is fractional coverage of the substrate. P is the partial pressure of the atoms in the vapor. k ads is the reaction rate of the adsorption process. k des is the reaction rate of the desorption process. K = k ads k des 22/76
Fractional Coverage θ = KP 1 + KP 1 exp k des 1 + KP t Let s look at this equation s properties. Consider long time scales: lim θ = t KP 1 + KP 1 exp k des 1 + KP e 0 lim θ = t KP 1 + KP K = k ads k des 23/76
Fractional Coverage θ = KP 1 + KP 1 exp k des 1 + KP t Let s look at this equation s properties. Consider long very large k des : If k des then: K = k ads k des 0 exp k des 1 + KP t 0 θ 0 I.e. if the desorption rate is too high the coverage will be zero. 24/76
Fractional Coverage θ = KP 1 + KP 1 exp k des 1 + KP t Let s look at this equation s properties. Consider long very large k ads : If k ads then: KP 1 + KP 1 exp k des 1 + KP t 0 θ 1 I.e. if the adsorption rate is high the coverage will be unity. 25/76
Pressure-Dependence θ = KP 1 + KP 1 exp k des 1 + KP t K = k ads k des k ads = 10-2 s -1 k des = 10-4 s -1 Coverage 1.0 0.8 0.6 0.4 1 Pa 0.1 Pa 0.01 Pa 0.001 Pa 0.2 0.0 0 2 4 6 8 10 Time (hours) 26/76
K-Dependence θ = KP 1 + KP 1 exp k des 1 + KP t K = k ads k des 1.0 100 10 P = 1 Pa Coverage 0.8 0.6 0.4 1 0.1 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 Time (hours) 27/76
Heated Substrate What happens if we heat the substrate? Recall that most reactions can be described as temperature-activated processes: k = k 0 e E A Τ k B T I.e. the reaction is faster at higher temperatures. Let: k abs = k 0 abs e E A abs k B T k des = k 0 des e E A des k B T 28/76
Heated Substrate 1.0 P = 1 Pa k abs 0 = 2 s -1 k des 0 = 1 s -1 E abs A = 0.2 ev E des A = 0.4 ev Coverage 0.8 300 K 0.6 320 K 0.4 340 K 360 K 0.2 380 K 400 K 0.0 0.0 0.2 0.4 0.6 0.8 1.0 Time (hours) 29/76
Diffusion 30/76
Diffusion After the atoms being absorbed on the surface, they become adatoms with an (positive) adsorption energy, E a, relative to zero in the vapor. This sometimes called desorption energy. After particles are adsorbed onto the surface they can hop between surface sites: Substrate 31/76
Diffusion The adatom can diffuse over the surface, with energy E d (migration barrier energy) and the corresponding frequency ν d (order of 10 14 s -1 ). E nu ( v) E d Since E d E a, surface diffusion is far more likely than desorption. l 32/76
Diffusion The probability that during one second the adatom will have enough thermal energy to pass over the barrier is: P d = ν d e E d Τ k B T In one unit of time the adatom will make ν d attempts to pass the barrier, with a probability of e E d Τ k B T of overcoming the barrier. The diffusion coefficient to jump a distance l can then be given by: D = l 2 P d = ν d l 2 e E d Τ k B T 33/76
Diffusion We are interested in a characteristic distance the adatom can move before desorption: L. Recall the activation energy for desorption, is E a. We can quantify the number of attempts to desorb by ν a. This is related to the vibrational energy of the atoms on the surface. We can quantify the probability of desorbing per unit time (or desorption rate) as: P a = ν a e E a Τ k B T 34/76
Diffusion The characteristic time scale for desorption is then: τ a = 1 P a = ν 1 a e E a Τ k B T The length scale of diffusion can then be described by: L = Dτ a Diffusion coefficient of adatoms on surface Timescale for desorption 35/76
Diffusion L = Dτ a This quantifies how far adatoms diffuse on the surface. At low temperatures, the diffusion length increases with temperature. At higher temperatures, the desorption rate also increases and overtakes absorption. Therefore, the diffusion length decreases. Typical diffusion lengths: Physisorption: 300 μm. Chemisorption: 5 nm. 36/76
Nucleation 37/76
Nucleation Single units Monolayer In the course of deposition, the atoms (monomer) arriving from the gas phase with a rate F (units are atoms per surface unit cell, per second, MLs -1 ). For simplicity, we assume the surface temperature is low enough so that only monomers diffuse on the surface and that dimers remain immobile. Two units Substrate 38/76
Nucleation As deposition proceeds, the number of dimers will increase roughly linearly until their concentration n 2 becomes comparable to the density of monomers n 1. n 2 n 1 After n 2 > n 1 the probabilities of a diffusing monomer to encounter one of its own or a dimer become comparable and cluster growth competes with the creation of new stable nuclei. t 39/76
Nucleation After the density of stable nuclei n x (x standing for any size that is stable) has increased sufficiently, any further deposition will exclusively lead to island growth. At this saturation island density, the mean free path of diffusing adatoms is equal to the mean island separation and adatoms will attach themselves with much higher probability to existing islands then to create new ones. Approaching coverage of about half a monolayer, islands eventually coalesce which decreases their density. 40/76
Nucleation Approaching coverage of about half a monolayer, islands eventually coalesce which decreases their density. If the deposition continues the nucleation centers become more numerous and coalescence of 2D islands occurs. As the size of the 2D island is increase and the coverage of the substrate surface gets enlarged. Eventually we may now consider film growth. 41/76
Nucleation STM images showing the transition from the very early nucleation phase to island growth (2D) for Ag deposited (F=1.1 x 10-3 MLs -1 ) onto Pt(111) at 75K. The coverage (θ) and mean island sizes ( തn) are indicated. 42/76
Nucleation If dimers are immobile and no re-evaporation occurs, then the rate equation for the density of monomers: Rate of change of number of monomers The encounter of two diffusing adatoms resulting in the creation of a dimer dn 1 dt = F 2σ 1Dn 1 2 σ x Dn 1 n x κ x F Ft n 1 2κ 1 Fn 1 Deposition flux A monomer is captured by a stable island These two terms denote the decrease caused by direct impingement onto stable island density, n x, due to the creation of dimers, first when two monomers meet by diffusion, and second upon direct deposition onto an adatom. 43/76
Nucleation The rate equation for stable islands is: Rate of change of number of stable islands Diffusion of adatoms resulting in the creation of an island dn x dt = σ 1Dn 1 2 + κ x Fn 1 The time evolution of island and monomer densities can be obtained from integration of these equations (we won t!). 44/76
Island Number Density Numerical solution to previous equations: n1 n x Coverage Four coverage regimes are found. https://journals.aps.org/prb/abstract/10.1103/physrevb.50.8781 45/76
Island Number Density Regime 1: Low coverage. Where n 1 n x. n 1 θ. n x θ 3. Regime 2: Intermediate Coverage. Where n 1 ~n x. Mean island separation ~ mean free path of adatoms 46/76
Island Number Density Regime 3: Aggregation regime θ ~ 0.1 to 0.4. When the islands join together Regime 4: Coalescence and percolation regime θ > 0.4. 47/76
Example Experimental Data Cu on Ni(100): Arrhenius plot of the measured saturation island density of Cu on Ni(100) (flux 1.34 10-3 ML/s, coverage 0.1 ML). https://journals.aps.org/prb/abstract/10.1103/physrevb.54.17858 48/76
Nucleation We are interested in the characteristic length (L) for the nucleation process. L We define it as the mean free path of diffusing adatoms before they create a new nucleus or are captured by existing islands. Can also be interpreted as the mean island distance. D F 1 6 Diffusion coefficient of adatoms on surface Flux onto surface 49/76
Microstructure Higher substrate temperatures favor fewer, larger nuclei. Higher deposition rates favor more, smaller nuclei. To get single crystal or large grained polycrystalline films, you need higher temperatures and slower deposition rates. On the other extreme, you ll get fine grained polycrystalline films. 50/76
Island Shape At low T (slow diffusion), you can get what are called ramified islands: Adatoms stick at islands. Fractal shape. E.g. this is experimental image of Pt on Pt (111): https://journals.aps.org/prl/abstract/10.1103/physrevlett.47.1400 https://journals.aps.org/prl/abstract/10.1103/physrevlett.76.2366 51/76
Island Shape At higher T (faster diffusion), you can get compact islands: Pt on Pt (111) again: 300K 400K 425K + annealing at 700K 52/76
Film Growth 53/76
Classification of Growth Thin film growth can be classified into 3 types: Frank-van der Merwe Growth. Layer-by-layer (2D) growth. Atoms of the deposit material are more strongly attracted to the substrate than they are to themselves. 54/76
Classification of Growth Thin film growth can be classified into 3 types: Volmer-Weber Growth. Island (3D) Growth. The deposit atoms are more strongly bound to each other than they are to the substrate. 55/76
Classification of Growth Thin film growth can be classified into 3 types: Stranski-Krastanov Growth. Layer-plus-Island Growth. Layers form first, but then switches to islands. 56/76
Classification of Growth Volmer-Weber Frank-van der Merwe Stranski- Krastanov Wikipedia 57/76
Factors Affecting Growth: Surface energy (Jm -2 ) is very important in growth. Energy required to create one unit of surface area. Surface energy exists because bonds are broken to create/increase the surface. Surface stress: bonds are elastically strained. https://www.nature.com/articles/srep44213#f3 58/76
Factors Affecting Growth: In thin-film growth there are three relevant surface energies: γ s : substrate free surface. γ f : film free surface. γ i : substrate/film interface. γ f γ s γ i 59/76
Factors Affecting Growth: The relative magnitude of surface energies strongly influence growth: We generally seek layer-by-layer growth. This requires: γ i + γ f < γ s γ i is lower for materials with same type of bonding (metallic/covalent/ionic). γ i is lower if the materials react. γ i increases linearly with the number of strained layers. At some thickness γ i + γ f < γ s SK-Growth 60/76
Crystallinity and Epitaxy 61/76
Types of Film Amorphous films. No long-range order. Polycrystalline films. Randomly orientated grains of crystalline material, separated by boundaries. Single crystal. Complete, long-range order. 62/76
Amorphous films No long-range order. Oxide semiconductors and conductors. Some organic semiconductors. Insulators: glass, SiO 2. Low charge-carrier mobility. Good device-to-device uniformity (compared to poly-crystalline). http://www.sciencedirect.com/science/article/pii/s0010938x13001340 63/76
Polycrystalline films Randomly orientated grains of crystalline material, separated by boundaries. p-si (for solar cells). Some oxides and organics. Transport limited by process across boundaries between grains (grain boundaries). http://onlinelibrary.wiley.com/doi/10.1002/adma.201301622/full 64/76
Single Crystals Complete long range order. Electron wavefunction is coherent and delocalized across crystal: Ψ = Ce i k.rn ωt φ n n c-si (for VLSI electronics). Transport limited by defects and phonons. Can be grown by epitaxy. 65/76
Epitaxy Epitaxy refers to the film growth phenomenon where a relation between the structure of the film and the substrate exists. In particular it commonly denotes a single crystalline layer grown on a single crystal surface. If the single crystalline film and the single crystal substrate are of the same material, we call the growth homoepitaxy. If the film and the substrate are of different materials, we call the growth heteroepitaxy. 66/76
Epitaxy https://www.youtube.com/watch?v=nsgrksv8yh8 67/76
Factors Governing Epitaxy Structural compatibility: Lattice matching crystal structure and lattice constant. Chemical compatibility: Chemical bonding, chemical diffusion. Temperature: Above a substrate temperature T e good epitaxy is obtained. T e depends on the deposition rate, particle energy and the surface contamination. 68/76
Thickness Measurment 69/76
Thickness Measurment There are a number of ways to measure film thickness: A profilometer measures thickness directly with a stylus. A four-point-probe measures thickness by calibrating the relation between thickness and resistance. An ellipsometer measures thickness by calibrating the relation between thickness and refractive index. Thickness Film Substrate 70/76
Profilometer A profilometer is used to measure thickness after a material is deposited. It is made of a diamond tipped stylus that touches the surface. When the profilometer moves across the surface, the stylus moves up and down as the thickness changes. The movement of the stylus is calibrated to read thickness. Stylus Substrate Requires masking, or material to be scratched off. 71/76
Dektak Profilometer https://www.youtube.com/watch?v=wqsymsrq_0q 72/76
Four Point Probe The four point probe is used to measure thickness of conductors which are deposited on insulators. It has four probes which move across the surface. Current flows through the outer two probes. The inner probes measure voltage. The voltage between the two inner probes depends on the resistance of the film, which depends on its 6 thickness. Thin Conducting Layer Insulator Current V Four Point Probe Tip 6 Wafer 0.2 73/76
Ellipsometer The ellipsometer is used to measure the thickness and refractive index of transparent films. It is made of a light source and polarizer on one side and a analyzer and detector on the other side. Light from the source is polarized and reflected off the film. Light Source Detector Light Control Analyzing Polarizer Polarizing Sheet Substrate 74/76
Ellipsometer The analyzer is rotated until no light passes through it. The angle of rotation depends on the thickness of the film. The angle of rotation is calibrated to read thickness. The ellipsometer is used to measure thickness from 20Å to 60,000Å. It is very accurate. 75/76
RHEED Reflection high-energy electron diffraction (RHEED) is used to measure thickness during molecular beam epitaxy. Electrons are fired at surface at very small angle. Electrons are scattered by lattice. Electrons will interfere constructively at certain angles, when a complete monolayer is present. 76/76