Thin film

A thin film is a layer of materials ranging from fractions of a

In addition to their applied interest, thin films play an important role in the development and study of materials with new and unique properties. Examples include multiferroic materials, and superlattices that allow the study of quantum phenomena.

Nucleation is an important step in growth that helps determine the final structure of a thin film. Many growth methods rely on nucleation control such as atomic-layer epitaxy (atomic layer deposition). Nucleation can be modeled by characterizing surface process of adsorption, desorption, and surface diffusion.^[2]

Adsorption is the interaction of a vapor atom or molecule with a substrate surface. The interaction is characterized the sticking coefficient, the fraction of incoming species thermally equilibrated with the surface. Desorption reverses adsorption where a previously adsorbed molecule overcomes the bounding energy and leaves the substrate surface.

The two types of adsorptions, physisorption and chemisorption, are distinguished by the strength of atomic interactions. Physisorption describes the van der Waals bonding between a stretched or bent molecule and the surface characterized by adsorption energy ${\displaystyle E_{p}}$. Evaporated molecules rapidly lose kinetic energy and reduces its free energy by bonding with surface atoms. Chemisorption describes the strong electron transfer (ionic or covalent bond) of molecule with substrate atoms characterized by adsorption energy ${\displaystyle E_{c}}$. The process of physic- and chemisorption can be visualized by the potential energy as a function of distance. The equilibrium distance for physisorption is further from the surface than chemisorption. The transition from physisorbed to chemisorbed states are governed by the effective energy barrier ${\displaystyle E_{a}}$.^[2]

Crystal surfaces have specific bonding sites with larger ${\displaystyle E_{a}}$ values that would preferentially be populated by vapor molecules to reduce the overall free energy. These stable sites are often found on step edges, vacancies and screw dislocations. After the most stable sites become filled, the adatom-adatom (vapor molecule) interaction becomes important.^[3]

Nucleation kinetics can be modeled considering only adsorption and desorption. First consider case where there are no mutual adatom interactions, no clustering or interaction with step edges.

The rate of change of adatom surface density ${\displaystyle n}$, where ${\displaystyle J}$ is the net flux, ${\displaystyle \tau _{a}}$ is the mean surface lifetime prior to desorption and ${\displaystyle \sigma }$ is the sticking coefficient:

${\displaystyle {dn \over dt}=J\sigma -{n \over \tau _{a}}}$

${\displaystyle n=J\sigma \tau _{a}\left[1-\exp \left({-t \over \tau _{a}}\right)\right]n=J\sigma \tau _{a}\left[\exp \left({-t \over \tau _{a}}\right)\right]}$

Adsorption can also be modeled by different isotherms such as Langmuir model and BET model. The Langmuir model derives an equilibrium constant ${\displaystyle b}$ based on the adsorption reaction of vapor adatom with vacancy on the substrate surface. The BET model expands further and allows adatoms deposition on previously adsorbed adatoms without interaction between adjacent piles of atoms. The resulting derived surface coverage is in terms of the equilibrium vapor pressure and applied pressure.

Langmuir model where ${\displaystyle P_{A}}$ is the vapor pressure of adsorbed adatoms:

${\displaystyle \theta ={bP_{A} \over (1+bP_{A})}}$

BET model where ${\displaystyle p_{e}}$ is the equilibrium vapor pressure of adsorbed adatoms and ${\displaystyle p}$ is the applied vapor pressure of adsorbed adatoms:

${\displaystyle \theta ={Xp \over (p_{e}-p)\left[1+(X-1){p \over p_{e}}\right]}}$

As an important note, surface crystallography and differ from the bulk to minimize the overall free electronic and bond energies due to the broken bonds at the surface. This can result in a new equilibrium position known as “selvedge”, where the parallel bulk lattice symmetry is preserved. This phenomenon can cause deviations from theoretical calculations of nucleation.^[2]

Surface diffusion describes the lateral motion of adsorbed atoms moving between energy minima on the substrate surface. Diffusion most readily occurs between positions with lowest intervening potential barriers. Surface diffusion can be measured using glancing-angle ion scattering. The average time between events can be describes by:^[2]

${\displaystyle \tau _{d}=(1/v_{1})\exp(E_{d}/kT_{s})}$

In addition to adatom migration, clusters of adatom can coalesce or deplete. Cluster coalescence through processes, such as Ostwald ripening and sintering, occur in response to reduce the total surface energy of the system. Ostwald repining describes the process in which islands of adatoms with various sizes grow into larger ones at the expense of smaller ones. Sintering is the coalescence mechanism when the islands contact and join.^[2]

The act of applying a thin film to a surface is thin-film deposition – any technique for depositing a thin film of material onto a

Deposition techniques fall into two broad categories, depending on whether the process is primarily chemical or physical.^[4]

Here, a fluid

Chemical deposition is further categorized by the phase of the precursor:

Plating relies on liquid precursors, often a solution of water with a salt of the metal to be deposited. Some plating processes are driven entirely by reagents in the solution (usually for noble metals), but by far the most commercially important process is electroplating. In semiconductor manufacturing, an advanced form of electroplating known as electrochemical deposition is now used to create the copper conductive wires in advanced chips, replacing the chemical and physical deposition processes used to previous chip generations for aluminum wires^[5]

The Langmuir–Blodgett method uses molecules floating on top of an aqueous subphase. The packing density of molecules is controlled, and the packed monolayer is transferred on a solid substrate by controlled withdrawal of the solid substrate from the subphase. This allows creating thin films of various molecules such as nanoparticles, polymers and lipids with controlled particle packing density and layer thickness.^[6]

Dip coating is similar to spin coating in that a liquid precursor or sol-gel precursor is deposited on a substrate, but in this case the substrate is completely submerged in the solution and then withdrawn under controlled conditions. By controlling the withdrawal speed, the evaporation conditions (principally the humidity, temperature) and the volatility/viscosity of the solvent, the film thickness, homogeneity and nanoscopic morphology are controlled. There are two evaporation regimes: the capillary zone at very low withdrawal speeds, and the draining zone at faster evaporation speeds.^[8]

Physical deposition uses mechanical, electromechanical or thermodynamic means to produce a thin film of solid. An everyday example is the formation of frost. Since most engineering materials are held together by relatively high energies, and chemical reactions are not used to store these energies, commercial physical deposition systems tend to require a low-pressure vapor environment to function properly; most can be classified as physical vapor deposition.

The material to be deposited is placed in an energetic, entropic environment, so that particles of material escape its surface. Facing this source is a cooler surface which draws energy from these particles as they arrive, allowing them to form a solid layer. The whole system is kept in a vacuum deposition chamber, to allow the particles to travel as freely as possible. Since particles tend to follow a straight path, films deposited by physical means are commonly directional, rather than conformal.

Examples of physical deposition include:

A thermal

An

Sputtering relies on a plasma (usually a noble gas, such as argon) to knock material from a "target" a few atoms at a time. The target can be kept at a relatively low temperature, since the process is not one of evaporation, making this one of the most flexible deposition techniques. It is especially useful for compounds or mixtures, where different components would otherwise tend to evaporate at different rates. Note, sputtering's step coverage is more or less conformal. It is also widely used in optical media. The manufacturing of all formats of CD, DVD, and BD are done with the help of this technique. It is a fast technique and also it provides a good thickness control. Presently, nitrogen and oxygen gases are also being used in sputtering.

Pulsed laser deposition systems work by an ablation process. Pulses of focused laser light vaporize the surface of the target material and convert it to plasma; this plasma usually reverts to a gas before it reaches the substrate.^[10]

Thermal laser epitaxy uses focused light from a continuous-wave laser to thermally evaporate sources of material.^[11] By adjusting the power density of the laser beam, the evaporation of any solid, non-radioactive element is possible.^[12] The resulting atomic vapor is then deposited upon a substrate, which is also heated via a laser beam.^[13][14] The vast range of substrate and deposition temperatures allows of the epitaxial growth of various elements considered challenging by other thin film growth techniques.^[15][16]

) and at the apex of the cone a thin jet emanates which disintegrates into very fine and small positively charged droplets under the influence of Rayleigh charge limit. The droplets keep getting smaller and smaller and ultimately get deposited on the substrate as a uniform thin layer.

Growth modes

It has been suggested that portions of Stranski–Krastanov growth be split from it and merged into this section. (Discuss) (June 2021)

Stranski–Krastanov growth^[20] ("joint islands" or "layer-plus-island"). In this growth mode the adsorbate-surface interactions are stronger than adsorbate-adsorbate interactions.

Volmer–Weber^[21] ("isolated islands"). In this growth mode the adsorbate-adsorbate interactions are stronger than adsorbate-surface interactions, hence "islands" are formed right away.

There are three distinct stages of stress evolution that arise during Volmer-Weber film deposition.^[22] The first stage consists of the nucleation of individual atomic islands. During this first stage, the overall observed stress is very low. The second stage commences as these individual islands coalesce and begin to impinge on each other, resulting in an increase in the overall tensile stress in the film.^[23] This increase in overall tensile stress can be attributed to the formation of grain boundaries upon island coalescence that results in interatomic forces acting over the newly formed grain boundaries. The magnitude of this generated tensile stress depends on the density of the formed grain boundaries, as well as their grain-boundary energies.^[24] During this stage, the thickness of the film is not uniform because of the random nature of the island coalescence but is measured as the average thickness. The third and final stage of the Volmer-Weber film growth begins when the morphology of the film’s surface is unchanging with film thickness. During this stage, the overall stress in the film can remain tensile, or become compressive.  

On a stress-thickness vs. thickness plot, an overall compressive stress is represented by a negative slope, and an overall tensile stress is represented by a positive slope. The overall shape of the stress-thickness vs. thickness curve depends on various processing conditions (such as temperature, growth rate, and material). Koch^[25] states that there are three different modes of Volmer-Weber growth. Zone I behavior is characterized by low grain growth in subsequent film layers and is associated with low atomic mobility. Koch suggests that Zone I behavior can be observed at lower temperatures. The zone I mode typically has small columnar grains in the final film. The second mode of Volmer-Weber growth is classified as Zone T, where the grain size at the surface of the film deposition increases with film thickness, but the grain size in the deposited layers below the surface does not change. Zone T-type films are associated with higher atomic mobilities, higher deposition temperatures, and V-shaped final grains. The final mode of proposed Volmer-Weber growth is Zone II type growth, where the grain boundaries in the bulk of the film at the surface are mobile, resulting in large yet columnar grains. This growth mode is associated with the highest atomic mobility and deposition temperature. There is also a possibility of developing a mixed Zone T/Zone II type structure, where the grains are mostly wide and columnar, but do experience slight growth as their thickness approaches the surface of the film. Although Koch focuses mostly on temperature to suggest a potential zone mode, factors such as deposition rate can also influence the final film microstructure.^[23]

A subset of thin-film deposition processes and applications is focused on the so-called epitaxial growth of materials, the deposition of crystalline thin films that grow following the crystalline structure of the substrate. The term epitaxy comes from the Greek roots epi (ἐπί), meaning "above", and taxis (τάξις), meaning "an ordered manner". It can be translated as "arranging upon".

The term homoepitaxy refers to the specific case in which a film of the same material is grown on a crystalline substrate. This technology is used, for instance, to grow a film which is more pure than the substrate, has a lower density of defects, and to fabricate layers having different doping levels. Heteroepitaxy refers to the case in which the film being deposited is different from the substrate.

Techniques used for epitaxial growth of thin films include

Thin films may be biaxially loaded via

Films may experience a dilatational transformation strain ${\displaystyle e_{T}}$ relative to its substrate due to a volume change in the film. Volume changes that cause dilatational strain may come from changes in temperature, defects, or phase transformations. A temperature change will induce a volume change if the film and substrate thermal expansion coefficients are different. The creation or annihilation of defects such as vacancies, dislocations, and grain boundaries will cause a volume change through densification. Phase transformations and concentration changes will cause volume changes via lattice distortions.^[32][33]

A mismatch of thermal expansion coefficients between the film and substrate will cause thermal strain during a temperature change. The elastic strain of the film relative to the substrate is given by:

${\displaystyle \varepsilon =-(\alpha _{f}-\alpha _{s})(T-T_{0})}$

where ${\displaystyle \varepsilon }$ is the elastic strain, ${\displaystyle \alpha _{f}}$ is the thermal expansion coefficient of the film, ${\displaystyle \alpha _{s}}$ is the thermal expansion coefficient of the substrate, ${\displaystyle T}$ is the temperature, and ${\displaystyle T_{0}}$ is the initial temperature of the film and substrate when it is in a stress-free state. For example, if a film is deposited onto a substrate with a lower thermal expansion coefficient at high temperatures, then cooled to room temperature, a positive elastic strain will be created. In this case, the film will develop tensile stresses.^[32]

A change in density due to the creation or destruction of defects, phase changes, or compositional changes after the film is grown on the substrate will generate a growth strain. Such as in the Stranski–Krastanov mode, where the layer of film is strained to fit the substrate due to an increase in supersaturation and interfacial energy which shifts from island to island.^[34] The elastic strain to accommodate these changes is related to the dilatational strain ${\displaystyle e_{T}}$ by:

${\displaystyle \varepsilon =-e_{T}/3}$

A film experiencing growth strains will be under biaxial tensile strain conditions, generating tensile stresses in biaxial directions in order to match the substrate dimensions.^[32][35]

An epitaxially grown film on a thick substrate will have an inherent elastic strain given by:

${\displaystyle \varepsilon \approx {a_{s}-a_{f} \over a_{f}}}$

where ${\displaystyle a_{s}}$ and ${\displaystyle a_{f}}$ are the lattice parameters of the substrate and film, respectively. It is assumed that the substrate is rigid due to its relative thickness. Therefore, all of the elastic strain occurs in the film to match the substrate.^[32]

The stresses in Films deposited on flat substrates such as wafers can be calculated by measuring the curvature of the wafer due to the strain by the film. Using optical setups, such as those with lasers,^[36] allow for whole wafer characterization pre and post deposition. Lasers are reflected off the wafer in a grid pattern and distortions in the grid are used to calculate the curvature as well as measure the optical constants. Strain in thin films can also be measured by x-ray diffraction or by milling a section of the film using a focused ion beam and monitoring the relaxation via scanning electron microscopy.^[30]

A common method for determining the stress evolution of a film is to measure the wafer curvature during its deposition. Stoney^[37] relates a film’s average stress to its curvature through the following expression:  

${\displaystyle \kappa ={\frac {6\langle \sigma \rangle h_{f}}{M_{s}h_{s}^{2}}}}$

where ${\displaystyle M_{s}={\frac {\mathrm {E} }{1-\upsilon }}}$, where ${\displaystyle \mathrm {E} }$ is the bulk elastic modulus of the material comprising the film, and ${\displaystyle \upsilon }$ is the Poisson’s ratio of the material comprising the film, ${\displaystyle h_{s}}$ is the thickness of the substrate, ${\displaystyle h_{f}}$ is the height of the film, and ${\displaystyle \langle \sigma \rangle }$ is the average stress in the film. The assumptions made regarding the Stoney formula assume that the film and substrate are smaller than the lateral size of the wafer and that the stress is uniform across the surface.^[38] Therefore the average stress thickness of a given film can be determined by integrating the stress over a given film thickness:  

${\displaystyle \langle \sigma \rangle ={\frac {1}{h_{f}}}\int _{0}^{h_{f}}\sigma (z)dz}$

where ${\displaystyle z}$ is the direction normal to the substrate and ${\displaystyle \sigma (z)}$ represents the in-place stress at a particular height of the film. The stress thickness (or force per unit width) is represented by ${\displaystyle \langle \sigma \rangle h_{f}}$ is an important quantity as it is directionally proportional to the curvature by ${\displaystyle {\frac {6}{M_{s}h_{s}^{2}}}}$. Because of this proportionality, measuring the curvature of a film at a given film thickness can directly determine the stress in the film at that thickness. The curvature of a wafer is determined by the average stress of in the film. However, if stress is not uniformly distributed in a film (as it would be for epitaxially grown film layers that have not relaxed so that the intrinsic stress is due to the lattice mismatch of the substrate and the film), it is impossible to determine the stress at a specific film height without continuous curvature measurements. If continuous curvature measurements are taken, the time derivative of the curvature data:^[39] ${\displaystyle {\frac {d\kappa }{dt}}\propto \sigma (h_{f}){\frac {\partial h_{f}}{\partial t}}+\int _{0}^{h_{f}}{\frac {\partial \sigma (z,t)}{\partial t}}dz}$

can show how the intrinsic stress is changing at any given point. Assuming that stress in the underlying layers of a deposited film remains constant during further deposition, we can represent the incremental stress ${\displaystyle \sigma (h_{f})}$ as:^[39]  

${\displaystyle \sigma (h_{f})\propto {\frac {\frac {\partial \kappa }{\partial t}}{\frac {\partial h_{f}}{\partial t}}}={\frac {d\kappa }{dh}}}$

Nanoindentation is a popular method of measuring the mechanical properties of films. Measurements can be used to compare coated and uncoated films to reveal the effects of surface treatment on both elastic and plastic responses of the film. Load-displacement curves may reveal information about cracking, delamination, and plasticity in both the film and substrate.^[40]

The Oliver and Pharr method^[41] can be used to evaluate nanoindentation results for hardness and elastic modulus evaluation by the use of axisymmetric indenter geometries like a spherical indenter. This method assumes that during unloading, only elastic deformations are recovered (where reverse plastic deformation is negligible). The parameter ${\displaystyle P}$ designates the load, ${\displaystyle h}$ is the displacement relative to the undeformed coating surface and ${\displaystyle h_{f}}$ is the final penetration depth after unloading. These are used to approximate the power law relation for unloading curves:

${\displaystyle P=\alpha (h-h_{f})^{m}}$

After the contact area ${\displaystyle A}$ is calculated, the hardness is estimated by:

${\displaystyle H={\frac {P_{max}}{A}}}$

From the relationship of contact area, the unloading stiffness can be expressed by the relation:^[42]

${\displaystyle S=\beta {\frac {2}{\surd \pi }}E_{eff}\surd A}$

Where ${\displaystyle E_{eff}}$ is the effective elastic modulus and takes into account elastic displacements in the specimen and indenter. This relation can also be applied to elastic-plastic contact, which is not affected by pile-up and sink-in during indentation.

${\displaystyle {\frac {1}{E_{eff}}}={\frac {1-\nu ^{2}}{E}}+{\frac {1-\nu ^{2}}{E_{i}}}}$

Due to the low thickness of the films, accidental probing of the substrate is a concern. To avoid indenting beyond the film and into the substrate, penetration depths are often kept to less than 10% of the film thickness.^[43] For a conical or pyramidal indenters, the indentation depth scales as ${\displaystyle a/t}$ where ${\displaystyle a}$ is the radius of the contact circle and ${\displaystyle t}$ is the film thickness. The ratio of penetration depth ${\displaystyle h}$ and film thickness can be used as a scale parameter for soft films.^[40]

Stress and relaxation of stresses in films can influence the materials properties of the film, such as mass transport in microelectronics applications. Therefore precautions are taken to either mitigate or produce such stresses; for example a buffer layer may be deposited between the substrate and film.^[30] Strain engineering is also used to produce various phase and domain structures in thin films such as in the domain structure of the ferroelectric Lead Zirconate Titanate (PZT).^[44]

In the physical sciences, a multilayer or stratified medium is a stack of different thin films. Typically, a multilayer medium is made for a specific purpose. Since layers are thin with respect to some relevant length scale, interface effects are much more important than in bulk materials, giving rise to novel physical properties.^[45]

The term "multilayer" is not an extension of "monolayer" and "bilayer", which describe a single layer that is one or two molecules thick. A multilayer medium rather consists of several thin films.

• An optical coating, as used for instance in a dielectric mirror, is made of several layers that have different refractive indexes.
• Giant magnetoresistance is a macroscopic quantum effect observed in alternating ferromagnetic and non-magnetic conductive layers.

The usage of thin films for decorative coatings probably represents their oldest application. This encompasses ca. 100 nm thin

Thin films are often deposited to protect an underlying work piece from external influences. The protection may operate by minimizing the contact with the exterior medium in order to reduce the diffusion from the medium to the work piece or vice versa. For instance, plastic lemonade bottles are frequently coated by anti-diffusion layers to avoid the out-diffusion of CO₂, into which carbonic acid decomposes that was introduced into the beverage under high pressure. Another example is represented by thin TiN films in microelectronic chips separating electrically conducting aluminum lines from the embedding insulator SiO₂ in order to suppress the formation of Al₂O₃. Often, thin films serve as protection against abrasion between mechanically moving parts. Examples for the latter application are diamond-like carbon layers used in car engines or thin films made of nanocomposites.

Thin layers from elemental metals like copper, aluminum, gold or silver etc. and alloys have found numerous applications in electrical devices. Due to their high

Noble metal thin films are used in plasmonic structures such as surface plasmon resonance (SPR) sensors. Surface plasmon polaritons are surface waves in the optical regime that propagate in between metal-dielectric interfaces; in Kretschmann-Raether configuration for the SPR sensors, a prism is coated with a metallic film through evaporation. Due to the poor adhesive characteristics of metallic films, germanium, titanium or chromium films are used as intermediate layers to promote stronger adhesion.^[49][50][51] Metallic thin films are also used in plasmonic waveguide designs.^[52][53]

Thin-film technologies are also being developed as a means of substantially reducing the cost of

For miniaturising and more precise control of resonance frequency of piezoelectric crystals thin-film bulk acoustic resonators TFBARs/FBARs are developed for oscillators, telecommunication filters and duplexers, and sensor applications.