Quantum confined materials

Transcription

1 Quantum confined materials Quantum Wells Quantum wells structures can be fabricated by seeral methods in semiconductors alloys. A quantum well is fabricated by depositing ery thin layers of different materials (with thickness equialent to few atomic layers) between other thicker layers of semiconductor materials. The carriers (electrons or holes) located in the thin crystal will experience a potential well that will keep them confined in a plane allowing only free moement in two dimensions and forcing them to occupy a planar region. The effects of quantum confinement take place when the quantum well thickness becomes comparable at the de Broglie waelength of the carriers ( λ = h ), leading to energy leels called "energy p sub-bands", i.e., the carriers can only hae discrete energy alues instead of the energy bands allowed in the case that they are located in the bulk material. The fabrication of these D structures is achieed by thin film deposition. The technology of thin film deposition has been a subject of intense study for almost a century, an many methods hae been deeloped and improed. Thin film growth methods can be diided in two main groups: apor-phase deposition and liquid-phase deposition. The former includes eaporation, molecular beam epitaxy (MBE), sputtering, chemical apor deposition (CVD) and atomic layer deposition (ALD). Examples of the latter are electrochemical deposition, chemical solution deposition (CSD), Langmiur-Blodgett films and self-assembled monolayers (SAMs). The growth of thin films inoles the process of nucleation and growth on the substrate surface or growth surfaces. This nucleation process plays an important role in the determination of the crystallinity and microstructure of the resultant films. In the case of deposition of layers with nanometer thickness, the initial nucleation process plays an een more important role. Experimental obserations reealed that there are three basic nucleation modes: 1- Island or Volmer-Weber growth - Layer or Frank-an der Merwe growth and - Island-layer or Stranski-Krastono growth. Island growth occurs when the growth species are more bounded to each other than to the substrate. Many metals on insulator substrates, alkali halides, graphite and mica substrates display this type of nucleation during the initial film deposition stages. Subsequent growth generates islands that coalescence to form a continuous film. Layer growth is the opposite. The growth species are more likely to bound to the substrate than to each other. In this case a first monolayer is formed before the deposition of a second layer. The most important examples of this type of nucleation is the epitaxial growth of single crystal layers. The island-layer growth is an intermediate situation. Such type of growth usually inoles the stress which is deeloped during the formation of the nuclei or films. Fundamentals of homogeneous nucleation If the concentration of a solute in a solent exceeds its equilibrium solubility or the temperature decreases below the phase transformation point, a new phase appears. For example a solution with the solute exceeding the solubility has a high Gibbs free energy.

2 The Gibbs free energy is a thermodynamic potential which measures the "useful" work obtainable from an isothermal, isobaric thermodynamic system. It is the maximum amount of non-expansion work which can be extracted from a closed system in a completely reersible process. When a system changes from one state to a final state, the Gibbs free energy G is the work exchanged by the system with its surroundings, less the work of the pressure forces, during a reersible transformation of the system from the same initial state to the same final state. Gibbs energy is also the chemical potential that is minimized when a system reaches equilibrium at constant pressure. The supersaturated solution decreases its Gibbs energy by forming a solid phase and maintaining an equilibrium concentration in the rest of the solution. This reduction in the Gibbs free energy is the driing force for nucleation and growth. The change of the Gibbs free energy depends on the concentration of the solute: kt C kt G = ln = ln ( 1+ σ ) Ω C0 Ω In this expression k is the Boltzman constant, T is the temperature, Ω is the atomic olume, C the concentration, C 0 the equilibrium concentration and σ = (C-C 0 )/C 0 is the supersaturation. Without supersaturation, this is σ = 0, G = 0 and no nucleation would occur. When C > C 0 G < 0 and nucleation occurs spontaneously. Assuming an spherical nucleus with a radius r, the change of the olume energy is 4 µ = πr G This energy reduction is counterbalanced by the surface energy accompanied with the formation of a new phase. The increase in the surface energy is µ s = 4πr γ where γ is the surface energy per unit area. The total change in the Gibbs free energy is 4 G = µ + µ s = πr G + 4πr γ This equation is schematically shown in figure 1. From this figure one can see that the newly formed nucleus is stable only if the radius exceeds a critical size r *. A nucleus smaller than this alue will dissole into the solution to reduce the oerall Gibbs free energy, whereas the nucleus larger than r * is stable and continuos to grow bigger. At the critical size r = r * d, ( G) = 0 and the dr critical size r * and critical energy G * are defined by: r γ = G = G * * 16πγ ( G ) The aboe discussion is alid for a supersaturated solution, but all the concepts can be generalized for a supersaturated apor and a supercooled gas or liquid.

3 For the synthesis of nanoparticles by nucleation this critical size represents a limit. To reduce this limit one needs to increase the change of the Gibbs free energy G and reduce the surface energy of the new phase γ. The alue of G can be significantly increased by increasing the supersaturation σ, which increases with decreasing the temperature. The rate of nucleation per unit olume and per unit time R N is proportional to: i) the probability of a thermodicamical fluctuation of the critical free energy G * *, gien by P = exp G ( kt ). ii) the number of growth species per unit olume that can be used as nucleation centers (in homogeneous nucleation this is proportional to the concentration). iii) the successful jump frequency of growth species which is gien by Γ= kt, where λ is the diameter of the growth species and η is the πλη iscosity of the solution. So the rate of nucleation can be described by * CkT 0 G RN = npγ= exp πλ η kt This equation indicates that a high initial concentration or supersaturation, a low iscosity and low critical energy barrier will faor the formation of a large number of nuclei, which for gien concentration of solute a large number of nuclei means a smaller size nuclei. The nucleation occurs when the supersaturation reaches a certain alue aboe the solubility corresponding to the barrier energy G * defined before. After the nucleation, the concentration decreases. When the concentration decreases below this specific leel, no nucleation will take place, howeer, the growth continues till the concentration has attained its equilibrium. Nuclei growth The growth process of the nuclei inoles seeral steps: a) generation of growth species b) diffusion of the growth species from the bulk solution to the surface of the growth nuclei c) adsorption of the growth species onto the growth surface d) surface growth due to irreersible incorporation of the growth species onto the solid surface. Growth controlled by diffusion: If the concentration of the growth species in the solution (or saturated apor) reduces below the minimum concentration for nucleation, the nucleation stops howeer the growth continues. If this growth is controlled by diffusion the growth rate is gien by dr Vm = D( C C dt s ), where r is r the radius of the spherical nucleous, D is the diffusion coefficient of the growth species, C is the bulk concentration, C s is the concentration in the surface, V m the molar olume of the nuclei.

4 Soling the differential equation, for an initial size of the nucleus r 0 and assuming that the concentration in the bulk remains constant we obtain: r = D( C Cs) Vmt+ r0 This expression indicates that the radius of the particles tends to be equal. For two particles with an initial radius difference δr 0 the radius difference δr decreases as r0 δ r0 δ r = r This is the radius difference decreases with time. The diffusion controlled growth promotes the formation of uniformly sized particles. Growth controlled by surface process: When the diffusion of the growth species to the growth surface is sufficiently fast, the concentration of the growth species in the surface is the same as the concentration in the bulk. In this case the growth process is controlled by surface process. For the surface process there are two possible mechanisms: mononuclear growth and polynuclear growth. In the first case the growth proceeds layer by layer. The growth species are incorporated into de layer and proceeds to another layer only after the growth of the preious layer is completed. The growth rate is thus proportional to the area of the growth surface: dr km r dt = The constant k m depends on the concentration of the growth species. The growth rate is gien by 1 1 = kt m r r0 and the radius difference increases with an increasing radius of the nuclei δ r0 δ r = r r0 that can be also written as δ r0 δ r = ( 1 kmr0 t) This indicates that this mechanism does not faor the generation of monosized particles. In the case of polynuclear growth, the surface concentration is so high that a second layer starts to grow before the first layer is complete. In this case the growth rate is constant and independent of particle size or time dr k p dt = The particles grow linearly with time: r = kpt+ r0. In this case the relatie radius difference remains constant regardless of the growth time and the absolute particle size. As the radius difference remains constant, as the particle grows in size the radius relatie

5 radius difference becomes smaller and consequently this process leads to the synthesis of monosized particles. Heterogeneous nucleation When a new phase is formed on the surface of another material, the process is called heterogeneous nucleation. Consider a planar substrate. Assuming that the growth species in the apor phase impinges in the surface, these growth species diffuse and aggregate to form a nucleus with a cal shape as shown in figure. The total change in the free energy G associated with the formation of this nucleus is gien by G = a r µ ν + a1 r γf + a r γ fs a r γs where r is the mean dimension of the nucleus, µ is the change in the free Gibbs energy per unit of olume, γ f, γ fs, γ s are surface energies of apor-nucleus, nucleus-substrate and substrate-apor interfaces. The respectie geometrical constants are 1 ( θ) a = π 1 cos a a = π sin θ ( ) = π cosθ + cos θ The angle θ is the contact angle and depends only on the surface properties of the interfaces inoled. The relation between these coefficients is defined by the Young s equation γ = γ + γ cosθ s fs f In a similar way as homogeneous nucleation, the formation of a new phase results in a reduction of the Gibbs free energy, and an increase in the total surface energy. The nucleus will be stable only when its size is larger than the critical size r * : ( a * 1γ f + a γ fs a γs ) r = a G and the critical energy barrier G * is gien by 4( a ) * 1γf + aγ fs aγs G = 7 a G

6 Substituting the geometrical constants πγ * f sin θ cosθ + cosθ r = G cosθ + cos θ 16πγ * f cosθ + cos θ G = ( G ) 4 Comparing this equation with the case of homogeneous nucleation, the first term represents the critical energy barrier while the second term is the wetting factor. When the contact angle θ is 180 o, this is the new phase does not wet the surface at all, the wetting factor equals 1 and the critical energy barrier equals the one obtained in homogeneous nucleation. For angles smaller than 180 o the energy barrier for heterogeneous nucleation is always smaller than the energy barrier for homogeneous nucleation. This explains why heterogeneous nucleation is easier than homogeneous nucleation in most cases. When the contact angle is zero, the wetting factor is zero and there is no barrier for the formation of the new phase. This occurs for example when the deposit is the same as the substrate. For the formation of nanoparticles on quantum dots on substrates θ > 0 is required and the Young s equation becomes γ s < γ fs + γf Synthesis of nanoparticles Various methods hae been proposed to generate homogeneous surface defects that act as nucleation centers for the growth of nanoparticles. Eaporated metals as Ag and Au tend to form small metal nanoparticles associated with surface defects. When edges are the only defects on the substrate surfaces, the particles are concentrated only around the edges. Howeer for other defects as pit holes the nanoparticles are found distributed oer the substrate surface. For example gold clusters were produced by condensing eaporated gold in nanometersized preformed pits on the surface of highly oriented pyrolytic graphite (HOPG). The height of the clusters was 6.7 f 0.7 nm as measured with scanning tunneling microscopy in ultrahigh acuum, the lateral width was 10.1 f 1.9 nm as determined with transmission electron microscopy (TEM). The figure shows these gold nanoparticles grown selectiely on the pit holes generated in the surface of a crystalline graphite

7 Kinetically confined synthesis of nanoparticles Kinetically controlled growth is to spatially confine the growth so that it stops when a gien amount of material is consumed or the aailable space is filled up. Spatial confinement is diided into seeral groups: i) liquid droplets in gas phase, ii) liquid droplets in liquids such as micelles, iii) template based synthesis and i) self terminating synthesis. Synthesis inside micelles Synthesis of nanoparticles is achieed by confining the reaction in a restricted space. An example is the synthesis in micelles or in microemulsions. In micelles, reaction proceeds among the reactants that are only aailable inside the micelle olume and the synthesis stops when the reactants are consumed. When surfactants or polymers typically consisting of two parts, one hydrophilic and another hydrophobic are dissoled in a solent they preferentially self assemble at air/aqueous solution or hydrocarbon/aqueous solution interfaces. The hydrophilic part is turned towards the aqueous solution. When the concentration of the surfactants or polymers exceeds a critical leel they self assemble in such a way to form micelles. The following figure indicates this self arrangement of the polymers in the surface of the dispersed droplets on the solent. A microemulsion is a dispersion of droplets of an organic solution in an aqueous media. The chemical reactions in these systems takes place either at the interfaces between the organic droplets and the aqueous media or inside the droplets. Various monodispersed polymers can be prepared by carefully controlled emulsion polymerization. Typically a water soluble polymerization initiator and a surfactant are added into a mixture of water and the monomer. The hydrophobic monomer molecules form large droplets typically 5 to 10 microns in diameter which are stabilized by the surfactant whose hydrophilic ends point outwards and the hydrophobic end inwards towards the monomer droplet. The typical concentration of micelles is per ml. The monomer droplets typical concentration is to pel ml, much lower than the concentration of micelles. The polymerization initiators enter both the monomer droplets and the micelles and polymerization proceeds both in the droplets and the micelles with monomers transferred from monomer droplets. The resulting polymer particles are typically between 50 nm and 00 m with a remarkable narrow distribution in size. Aerosol synthesis In this method a liquid precursor is prepared. The precursor can be a simple mixture solution of desired constituents elements or a colloidal dispersion. The precursor is mystified to produce an aerosol, this is a uniform dispersion of liquid droplets in gas which may simply solidify by eaporation or further reach with some reactant in the gas phase. The resulting particles are spheres and their size is determined by the size of the

8 initial liquid droplets. Depending on the especial procedure the size distribution, morphology, and homogeneity of the nanoparticles can ary. The following figure shows few examples of nano particles of polyestirene, ffabricated by the aerosol phase method. Growth termination This method uses a suitable element to stop or control the growth in size of the nanoparticels. For example particles of CdS can be controlled in size by terminating the growth by capping the surface of the crystallites with thiophenol. The thyophenol attaches to the surface of the growing CdS crystal coering the surface, quenching the chemical reaction and canceling the crystal growth. One simple way to control the size of the nanoparticles is changing the concentration of thiophenol in the solution. With this method and a control of the reactants concentrations it is possible to accurately control the size of the nanoparticles that can be as small a.5 nm. Under these conditions the crystals undergo a strong structural change and the energy leels shift due to the quantum confinement prooked by the small size. The characterization of these nanoparticels can be done studying the spectral composition of the photoluminescence. Due to the quantum confinement, the photoluminesce of the crystal aries with the article size and measuring the peak waelength of the light emission it is possible to estimate the size of the nanoparticles dispersed in a liquid. The figure below shows different containers with nanoparticles of CdSeS of different sizes showing the different colors of the photoluminescence.

9 Spray pyrolysis The process can be described as conerting microsize liquid droplets of a precursor or precursors mixture into solid particles through heating. In practice spray pyrolysis inole seeral steps: i) generating microsized droplets of liquid precursor, ii) eaporation of the solent, iii) condensation of solute, i) decomposition and reaction of solute and ) sintering of solid particles.