Outline of work - 觀察奈米結構之物理性質: I.自組裝硒化鉛量子點陣列之電荷集體傳輸行為 II.氧化鋅摻雜鈷奈米線之鐵磁性

Chapter 1 Introduction

1.2 Outline of work

The thesis is organized as follows. At first mechanisms of self-assembly of PbSe QDs on a HOPG substrate at different temperatures is investigated and described in chapter 2. Based on the results of chapter 2, we prepared two-dimensional QD arrays with desired sizes on gold substrates by adjusting the self-assembly conditions. We used scanning tunneling microscopy to observe the electron transport in these QD arrays and found the capacitive coupling among QDs resulted in a collective transport behavior. The results are presented in chapter 3. In chapter 4, we switch our samples to ZnO nanowires and study their magnetic properties. After implanting Co ions and

on their size. Magnetic force microscopy was employed to directly observe magnetic domains in individual nanowires at room temperatures. In chapter 5, we give our conclusion.

Chapter 2 Self-assembly of PbSe quantum dot arrays

2.1 Introduction

With the help of the top-down semiconductor technology, lithography, to reduce the lateral dimension of a two-dimensional (2D) electron gas, the quantum dots (QDs) have been experimentally fabricated [55] to demonstrate their atomic-like physical properties which have been introduced in theory for a long time [56]. Later on, a colloidal synthesis strategy [15] has been developed to fabricate QDs (or nanocrystals) which have been examined to show artificial atom features in optical properties [4], magnetic properties due to orbital electrons [58], and electronic structures [17].

Bearing a resemblance to atomic combination of forming a periodic crystal structure in a solid, these colloidal QDs and metal nanoparticles are able to self-organize to form either two- or three-dimensional superlattices [59-61]. Thus, collective physical phenomena were proposed in theory and investigated in the QD-assembled superlattices. Recently, Ge and Brus illuminated that a system of 2D QD self-assembly can be suitably described by a 2D Lennard-Jones model which may

consist of two coexisting phases, resulting in a spinodal phase separation [13]. The same group (Brus’s group) also demonstrated nucleation and growth behaviors [14], and solvent-drying mediated self-assemblies of QDs at room temperature [62]. On the other hand, Jaeger’s group reported their study aimed to a formation of long-range-ordered self-assembly [63] and a highly ordered QD monolayer [7]. More excitingly, binary nanocrystal superlattices [64], coarsening [65], and nanopatterning by moulding [66] in QD formed superlattices have recently been conducted in experiments.

Theoretically, molecular-dynamic calculations of 2D Lennard-Jones model were applied to simulations of physisorbed systems, such as rare gases on graphite, to show interesting snapshots of island morphologies, particle trajectories, or growth patterns [67, 68]. The fruitful phases of this 2D Lennard-Jones system illustrate various kinds of growth behaviors. These phases were commonly presented on the reduced temperature and coverage (ρ^*, T^*) plane. Here ρ*=ρσ² and T* kT= /ε , where ρ is the particle density per unit area, σ is the hard-core diameter, k is the Boltzmann constant, T is the temperature, and ε is the pair bond energy (or the pair interaction energy). At a low coverage (ρ^* ≅ 10%), the critical nucleus size and the small cluster occurrences in thermal equilibrium can be learned and explored on the initial growth stage of a nucleation process [69]. In addition, the scaling function of the cluster size distribution [70, 71] can be studied. With an increase of coverage, e.g. ρ^* up to ~40%, and at a temperature lower than the critical-point temperature of this system, a coexistence of liquid-gas or solid-gas phases should result in a spinodal decomposition of phase separation that could be obtained and recorded on microscopy images. The spinodal patterns have been discovered and observed in several systems such as quenched glass [72] and dried-up colloidal QDs [13, 14, 62] through a rapid

cooling and solvent drying processes, respectively. In these cases, it mainly focuses on diffusion-mediated motion and aggregation of the colloidal QDs.

On the other hand, in the case of colloidal QDs which are normally dispersed in a solvent, the solvent can play another important role in the growth and nucleation processes. The solvent is evaporated quickly when it is heated near its boiling point.

Though the growth temperature is fixed at the boiling point, the rapid evaporation of the solvent shall lead to reduce the QD mobility on substrates and introduce an additional growth mechanism, diffusion-limited aggregation [73]. This effect could be enhanced and dominant especially when the QD assembly takes place on a substrate heated above the solvent boiling point. In previous reports [13, 14, 62], the QD assembly was carries out at a room temperature and the solvent was kept to evaporate very slowly (up to one hour). The slow evaporation rate of the solvent drives a variation of the pair bond energy between QDs and a change of state from a high to a low reduced temperature. Unlike Brus’s experiments [13, 14, 62], we attempt to study the temperature effect on the (ρ^*, T^*) plane. By heating the substrate, the temperature dependence of growth behavior as well as the phase diagram of the colloidal QD system should exhibit. In this work, the solvent was evaporated rapidly (less than one minute) and the growth process can be quenched at such a high temperature. Thus, we can study the growth pattern at a fixed state, rather than transition states at different reduced temperatures. Other than an investigation on long-rang ordered QD film, we concentrated our study on growth mechanisms of the spinodal decomposition and the diffusion-limited aggregation, and their application to syntheses of 2D QD islands.

The QD-assembled 2D islands can be adopted as an approach to study collective properties in mesoscopic physics.

2.2 Theoretical background

In this section, we briefly introduce phase separation, scaling theory, and diffusion- limited aggregation which are applied to analyze our results at different coverages and temperatures.

2.2.1 Phase diagram and phase separation

Two-dimensional Lennard-Jones particle system was investigated for modeling the behavior of rare gas atoms adsorbed on basal planes [80]. The particles in the system interact by the Lennard-Jones potential

where r is the distance between two particles, ε is the pair interaction energy, and σ is the hard-core diameter. Phase diagrams for the two-dimensional Lennard-Jones system were constructed by Monte Carlo simulation. In phase diagrams, the particle system exhibits different phases for specific thermodynamic states, i.e. pressure, density, and temperature. Fig. 2.1(a) shows a phase diagram in the (ρ*, T*) plane, whereρ*=ρσ²is the density (coverage) and T*=k_BT/ε is the reduced temperature, with regions of fluid(F), gas(G), liquid(L), solid(S), and coexistence [67]. With a mediate coverage, the decreasing temperature (T*) gives raise to a phase separation that makes the system transits from the fluid phase to the gas-liquid coexistence phase.

As a homogeneous binary system decomposes into two regions of different

compo

Figure 2.1: (a) The two-dimensional Lennard-Jones phase diagram, reproduced from refs 14 and 67, showing fluid(F), gas(G), liquid(L), solid(S), and coexistence phases.

The dashed line in gas-liquid coexistence phase separates metastable and unstable regions. (b) The free energy versus concentration with ∂²G ∂c² <0. The mean free energy (gray circle) of two compositions (hollow circle) after phase separation is less

compositions by phase separation, there are two possible mechanisms. When the binary system is situated at a state that the secondary derivative of free energy with respect to concentration is minus, i.e.∂²G ∂c² <0, the average free energy of each composition after phase separation will be lower than that before separation, as shown in Fig. 2.1(b). Thus the system is unstable and the phase separation will take place spontaneously to lower down the total free energy. This mechanism of phase separation is called spinodal decomposition [72]. Phase separation by spinodal decomposition is a long-range behavior with an onset of infinitesimal fluctuation. The system eventually forms a labyrinth pattern which possesses a correlation wavelength and the wavelength depends on the temperature. On the other hand, if ∂²G ∂c² >0, the system is situated in a metastable region. The phase separation cannot take place until the fluctuation is large enough to overcome the barrier of free energy. This mechanism is called nucleation and growth. In this mechanism, clusters have a critical size below which the cluster is unstable and cannot exist for long time. The formed clusters must be larger than the critical size.

2.2.2 Scaling theory

In surface physics, the scaling function was studies to understand the nucleation and growth behavior of epitaxial deposition. The critical size i, which is one less than the number of atoms needed to form a stable island, is a dominate parameters for the scaling behavior. Amar and Family have propose a analytic expression of the scaling function by which we can find out the critical size with the known island size distribution [71]. Provided an assumption that the mean island size S(θ) is the only one characteristic size, they derived a general scaling form

N_s(θ)=θS⁻²f_i(s/S), (2.2) where Ns(θ) is the density if island containing s atoms at coverage θ and fi(s/S) is the scaling function which satisfies ( ) ( ) 1

0 =

∫

^∞ ^fⁱ ^u ^du ^∞ ^fⁱ ^u ^udu . Based on the experimental observation, the conjectured the scaling function for i ≥ 1

f_i(u)=C_iuⁱexp(−ia_iu¹^/^aⁱ) (2.3a) matching experimental data to these curves, the critical size i can be decided.

2.2.3 Diffusion-limited aggregation and fractal dimension

Diffusion-limited aggregation (DLA) model was developed by Witten and Sander (WS) to study the formation of dendritic structures [73]. The model is started with a seed particle located at the origin of a two-dimensional lattice. Another particle is put into the lattice and walk randomly from far away until it reaches the site that is adjacent to the seed particle. Then it is stopped and another particle is put into for random walking until it reaches the occupied sites, and so forth. A typical aggregation showing a fractal-like structure is presented in Fig. 2.2(b). The particle number N and the aggregation size have the relation

N ~R_g^D, (2.4) where Rg is the radius of gyration and D is its fractal dimension. The radius of gyration R is the root mean square distance between the particles and the center of

Figure 2.2: (a) Analytic form of Eq. (2.3) for the scaled island-size distribution for i = 1 to 3. (b) A typical aggregation of WS DLA model showing a fractal-like structure.

The black circle represents the seed particle in the origin.

mass of the aggregation. The fractal dimension D can be obtained by log-log plots of Rg as a function of N. By computer simulation, they predicted the fractal dimension D of DLA is ~1.7. On the basis of WS model, subsequent modifications were suggested which allow the formed aggregation to diffusion instead of being static in WS model [78, 79]. When the moving aggregations contact with each other, they merge into a larger aggregation and keep growing. These modified models were referred to cluster-cluster (CLCL) model and the fractal dimension was about 1.4-1.5 which is less than that of WS model. The models mentioned above are mainly focused on the two-dimensional case.

2.3 Experiment

PbSe QDs were prepared using a high-temperature organic solution approach by adopting a method in previous report [15]. To synthesize PbSe QDs, trioctylphosphine-selenium solution (TOP-Se, 1.0 M for Se) was preprepared as Se-source by dissolving 7.90 g of selenium powder (99.99%) into 100 mL of TOP (90%) in a glovebox and stirring for overnight. In a typical experiment, 1.081 g of lead acetate trihydrate (PbAc2 ·3H2O, 99.99%, 2.85 mmol), 3.6 mL of oleic acid (90%), and 15 mL of phenyl ether (>99%) were loaded into a flask and heated to 140°C for 20 min under an argon stream. After the moisture-free solution was cooled to ~40°C, it was transferred into a glovebox and mixed with 5.0 mL of the TOP-Se stock solution in a syringe. This mixed solution was then rapidly injected into vigorously stirred phenyl ether (15 mL) that was preheated to 200°C in a three-neck flask equipped with a condenser under argon atmosphere. After the injection, the

temperature of the mixture dropped to ~160°C because of the addition of the room-temperature reagents. Once the solution temperature increased to ~200°C in ~5 min, the QD growth was terminated by an immediate removal of the heating source.

A size-selective precipitation [74, 75] was subsequently performed by centrifugation using a pair of solvents consisting of anhydrous hexane (98.5%, BDH) and anhydrous ethanol (200 proof, AAPER). Before the size-selection, the QD average size can also be roughly tuned by varying the QD growth temperature [15] after the injection of the reagents into the hot phenyl ether because raising the solution temperature accelerates the QD growth rate. Solution temperature between 150 and 220°C was usually chosen to grow the QDs in the desired range of size. The resultant PbSe QDs were identified using various characterizations including X-ray diffraction study, inductively coupled plasma analysis, transmission electron microscope (TEM, JEOL JEM-2010F) imaging, and energy dispersive spectroscopy evaluation. These PbSe QDs generally present in a spherical shape. However, some cubic particles could be detected when the QDs were grown at a temperature of 200°C or higher. All of the chemicals mentioned above were purchased from Sigma-Aldrich and used as received, except those specified.

The as-synthesized PbSe QDs were stored by dispersing them in toluene. At least three drops of the QD suspension were put on a graphite substrate, which was heated on a hot plate above room temperature. PbSe QDs were deposited on the flat surface of highly oriented pyrolytic graphite (HOPG) substrates after a solvent evaporation. Raising the substrate temperature resulted in agitation of the QDs and varied the distribution of growth pattern coverage on a macroscopic scale. The resultant samples were subsequently studied using a field-emission scanning electron microscope (SEM, JEOL JSM-7000F). All SEM images were taken in a high vacuum at room temperature. The coverage of growth patterns was estimated based on the

SEM images, and usually an area of 5 × 5 μm² was selected for our studies. The coverage was calculated by usingρ*=ρσ², as described in the section 2.1. The windows of SEM imaging areas were varied on a millimeter scale, to broadly sample the coverage in QD growth patterns.

2.4 Results and discussion

The as-synthesized PbSe QDs are capped with TOP and oleic acid to prevent aggregation. As shown in Fig. 2.3(a), the TEM image demonstrates a cluster of PbSe QDs. These QDs exhibit either cubic or spherical shapes. A high resolution TEM image of an individual PbSe QD is given in Fig. 2.3(b). The image confirms a single crystalline structure with a lattice fringe spacing of 3.05 Å which is in agreement with the lattice constant of the rock salt structure in PbSe bulk. The distribution of QD diameters determined in the TEM images is estimated and presented in Fig. 2.3(c).

The size distribution can be fitted with Gaussian distribution, yielding a uniform and average diameter of ∼14.6 nm and a standard deviation of 17%.

Several drops of the PbSe solution were cast on graphite substrates that were preheated above room temperature. After the solvent was evaporated, the QDs formed 2D islands (clusters) with either ordered (solid phase) or disordered (fluid phase) arrangements. After a coverage variation of QD assembly on different places of the substrate, the 2D islands can be imaged using an SEM. Moreover, the difference in coverage and temperature lead to a change of island size and distribution on the growth patterns, and to an observation of various growth mechanisms. The reduced coverage was estimated from the ratio of the island area to the SEM image area and then multiplied by 0.9165 [14].

Figure 2.3: (a) TEM image of PbSe QDs. (b) High-resolution TEM image of an individual PbSe QD. (c) Statistical distribution of QD sizes and a red curve fitted with Gaussian function.

2.4.1 Growth pattern and phase diagram

Various different growth patterns of QD islands on graphite surfaces are displayed in Fig. 2.4. To understand and separate these growth patterns from each other, the following guidelines may be taken into account. The island number, island shape, island size distribution, and voids or holes on islands are important features to categorize the growth patterns. There are several growth mechanisms including diffusion-mediated nucleation [67-72] and diffusion-limited aggregation [73] on the (ρ*, T*) plane. In the nucleation process of the growth, a large fluctuation in island size and a rounded, streamline island shape are important features. On the contrary, the diffusion-limited aggregation results in a growth pattern showing a comparatively uniform size and a dendritic, straight line in shape. In addition, gas, liquid, and solid phases and the spinodal phase decomposition process shall engage to modulate the final morphology of the growth pattern. The gas phase shall show a large number of tiny islands or a complementary pattern containing a large number of voids (smaller holes), whereas the solid phase will exhibit a large area of single islands with few holes and voids. The solid phase should further demonstrate an ordered lattice points on fast-Fourier-transformed images, in comparison with a ring structure existed in the liquid phase. Finally, the spinodal decomposition shall reveal a long-range order and a sinusoidal composition (QD area density) modulation.

Fig. 2.4(a) shows an interconnected network, labyrinthine island pattern extending up to 40 × 25 μm². The growth pattern with ~39% coverage was prepared at 100°C. This pattern indicates undoubtedly a spinodal decomposition behavior scaling up to submillimeter that has never been observed in a room-temperature QD assembly yet. Other growth patterns achieved at the same temperature with varied coverage of

smal

Figure 2.4: SEM images of PbSe QD patterns grown at substrate temperatures of 100°C (a-d), 50°C (e-g), and 180°C (h-j). The QD coverage is (a) 30%, (b) 13%, (c) 66%, (d) 90%, (e) 4%, (f) 41%, (g) 68%, (h) 6%, (i) 20%, and (j) 61%.

small islands and voids illustrated in Fig. 2.4(b) and (c) shows gas- and fluid-like phases, whereas a large island with few big holes, presented in part d of Fig. 2.4, reveals a solid phase at a growth temperature as high as 100°C.

When the substrate temperature was reduced to 50°C, a nucleation behavior was observed in the island pattern change. Fig. 2.4(e)-(g) illustrate a pattern variation with coverages of 4%, 41%, and 68%, respectively. An interconnected labyrinthine characteristic, signifying a spinodal decomposition behavior, can still be determined at such a low temperature (Fig. 2.4(f)). Moreover, a complementary manner of islands and holes in Fig. 2.4(e) and (g) demonstrate a nucleation process that unveils rounded islands or holes, and a large variation of island sizes implies a broadened island size distribution. Comparing Fig. 2.4(e) with Fig. 2.4(b), it can evidently be detected that a considerably large number of small islands with a uniform size appear in Fig. 2.4(b), whereas several area-unequal islands with a rounded shape show up in Fig. 2.4(e), although the coverage in both cases are of the same order. As a result, the gas phase and the nucleation growth behavior can definitely be differentiated from each other.

Furthermore, as the substrate temperature was raised much higher than the boiling point of the solvent, the diffusion length of the QDs becomes shorter which in turn makes a transition from diffusion-mediated to diffusion-limited growth or aggregation.

The shorter diffusion length mainly comes from a shorter time of solvent evaporation.

As shown in Fig. 2.4(h)-(j), the growth patterns were formed at a substrate temperature of 180°C with different coverage areas of 6%, 20%, and 61%. The substrate temperature indicates that the growth temperature shall be no lower than the boiling point of toluene, whereas the elevated substrate temperature must cause rapid evaporation of the solvent, resulting in a diffusion-limited growth behavior. Unlike the gas phase and the nucleation growth patterns, Fig. 2.4(h) demonstrates a few of

formation of chain-like islands or dendritic islands. Further increase of the coverage (refer to Fig. 2.4(j)) shows a dendritic islands as dominant structure and a shape of straight line on the edge of islands. To compare with those prepared at 100 and 50°C (Fig. 2.4(d) and (g)), the growth pattern in Fig. 2.4(j) reveals a thin strip rather than rounded holes.

Unlike the growth at room temperature that a drying process could induce an increase of pair bond energy ε (a decrease of reduced temperature) and change the state from a high to a low reduced temperature [13, 14], the high temperature growth causes a rapid evaporation of the solvent so that the resultant patterns could be quenched. To put all growth patterns (Fig. 2.4) on the (ρ*, T*) plane, we need to determine the pair bond energy. Here, the island number variation as a function of coverage at various temperatures (Fig. 2.5(a)) for the same image size of 5 × 5 μm² is used to determine the pair bond energy, which can be verified further in another analysis in the following paragraphs. We found that the growth pattern at 50°C reveals the lowest island density and a decrease of island density from ~100 to ~10 μm^-2 as the coverage is raised from 10% to 40%. This low island density is mainly due to the nucleation growth and the spinodal decomposition behaviors. As shown in Fig. 2.4(e)-(g), islands can be counted individually only when a coverage is much

在文檔中觀察奈米結構之物理性質: I.自組裝硒化鉛量子點陣列之電荷集體傳輸行為 II.氧化鋅摻雜鈷奈米線之鐵磁性 (頁 19-0)