低维半导体材料若干性能的尺寸和界面效应
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摘要
随着低维半导体材料尺寸的减小,表面/体积比急剧增大,表面和界面对半导体材料性能的影响显著增加。本文根据近电子自由理论以及熔化温度的尺寸效应模型,建立了低维半导体能隙的尺寸效应模型。该模型形式简单且无任何可调参数,能预测不同物质、不同维数的低维半导体能隙随尺寸的变化趋势。在此基础上,系统讨论了低维半导体单质以及化合物的尺寸和界面效应、低维半导体固溶体介电常数的尺寸和成分效应以及体等离子能的尺寸效应。此外,根据经典热力学和弹性理论,分别研究了半导体非晶薄膜厚度对晶化动力学的影响,以及半导体外延生长薄膜应变层的临界厚度。以上模型的预测结果与相应的实验以及理论预测结果符合的很好。
In the past 20 years, low dimension semiconductor materials have attracted a great deal of attentions in science studies and technological applications. As the size of low dimension materials approaches to the nanometers scales, they display novel optical, electronic and thermodynamic properties, which are dramatically different from their bulk counterparts. As the promising application, these nanocrystals can be found in many fields, such as solar cells, high energy density (rechargeable) batteries, single-electron transistors and fluorescent biological labels et al. Many of these applications are related to the optical and electronic properties which are usually size dependent. For many semiconductors, since the optical and electronic properties are induced by the edge transitions of the bandgap, Thus, studying the size dependence of the bandgap and the related exciton energy is one of the most important topics in low dimension semiconductor materials research. Besides the size effect, many optical and electronic properties are also influenced by the shape of the corresponding low dimension materials.
Most important chemical and physical processes of low dimension materials occur at the surface and interface and most important chemical and physical phenomenon are related to the surface and interface of materials. When the size of materials is in the nanoscale regime, there will be more surfaces and interfaces. However the energetic states of the atoms at the surfaces and interfaces are different from that within the bulk materials which maybe influence the behaviors of low dimension materials. Thus, the surface or interface situation should be an important object to be considered.
Latterly, in our work, there have some efforts to study the size and interface effect on optical and electronic properties of low dimension semiconductor materials, including bandgap, dielectric constant and volume plasmon energy. The established models without any adjusting parameters, are not only simple, but also proved to be reasonable in the full size range when compared with other experimental and theoretical results. In addition, according to classical thermodynamic and elastic theory, the influence of phase-change layer thickness on the crystallization kinetics and the critical layer number of epitaxial grown ultrathin films on semiconductor substrates, are also studied. The model predictions are confirmed to be valid.
In this thesis, the studies of the size and interface effect on low dimension semiconductor materials are listed as follows:
1. Low dimension semiconductor materials, with the tunable electronic and optical properties have attracted considerable interest as technologically important materials. With the size decreasing, the bandgap increasing is one of the important issue. According to the nearly free electron approach, the bandgap can be considered to be proportional to the cohesive energy, while cohesive energy is also proportional to melting temperature. Based on hereinbefore relationships and the established size effect melting temperature model, we established a simple model to predict the size dependent bandgap. It was found that the bandgap will increase with the dropping of size. When the size of crystal is in several nanometers range, the bandgap will increase dramatically due to increasing of surface/volume ratio (A/V). In addition, for nanocrystals with different shapes, they have different bandgaps even with the same crystal size. The ratio of the bandgap increasing is 3:2:1 for nanoparticles, nanowires and films, respectively. These differences should be attributed to the different surface/volume ratio of A/V = 6/D, 4/D, 2/D for nanoparticles, quasi-dimension nanoparticles or nanowires and thin films with d = 0, 1, 2, respectively. The model prediction results are in good agreement with the corresponding experimental and stimulant result of Si, II-VI and III-V semiconductor nanoparticles and nanowires.
2. Based on the established size dependent bandgap model and relevant relationships between bandgap and dielectric constant, the size and interface effect dielectric constant model can also be obtained. The model suggests that dielectric constant will increase or decrease with the size dropping, relying on the interface situation between crystals and surroundings. If the interaction on the crystal/substance interface is stronger than that within the crystal, the interface effect is dominant and there is an increasing trend for the dielectric constant with size decreasing. By contraries, dielectric constant will decrease with the size dropping when the crystal/substance interface is weak. Moreover, we also established a model to resolve the size and component effect on dielectric constant of solid solutions. For solid solutions, there exists a bowing behavior instead of the linear behavior. When the size is in several nanometers scale, the bowing behavior is weak and the dielectric constant is almost a linear of component x with the size decreasing. However when the size is larger than dozens of nanometers, the size effect is weak and the bowing behavior can be considered as bulk value. This provides an insight for materials design. The validity of the model is confirmed by the corresponding experimental results.
3. The size dependent volume plasmon energy model is established by incorporating the models of size dependent bandgap and lattice contraction model. It predicts that volume plasmon energy increases with the size decreasing. It also implies that the increasing volume plasmon energy is a result of blue shift of bandgap and lattice contraction. The model prediction results are in accordance with the available experimental results of Ge nanopaeticles and nanowires.
4. For the phase-change discs, the crystallization rate of the phase-change materials determines the maximum achievable data transfer rate and thickness dependent crystallization rate is due to a variation of the crystallization speed. According to the equation of crystallization speed, the energy barrier for crystallization is the only thickness dependent parameter. Analysis of the Gibbs free energy of a crystallite embedded in a thin amorphous film indicates that with the reduction of the film thickness, the energy barrier drops firstly, while it will increase steeply when the thickness of the film is further decreased. This is the result of the competition between film/substance and crystal/amorphous interface energy. The obtained results indicate the presence of an optimum film thickness where crystallization rate is maximized. The predicted optimum thickness of Ge2Sb2Te5 phase-change film is consisted with the experimental results.
5. As a critical situation for the stability of the epitaxial grown films on semiconductor substrates, the balance between molar elastic energy and molar interface energy for epitaxial grown films is assumed. The value of the elastic energy and interface energy can be easily determined by the known classic elastic theory and the established interface energy model, respectively. According to the above assumption, the critical thickness of epitaxial grown films on semiconductor substances is obtained. It is found that a smaller strain and a larger melting enthalpy are required to obtain a larger critical thickness. The predicted results are in accordance with the experimental results.
In the past 20 years, low dimension semiconductor materials have attracted a great deal of attentions in science studies and technological applications. As the size of low dimension materials approaches to the nanometers scales, they display novel optical, electronic and thermodynamic properties, which are dramatically different from their bulk counterparts. As the promising application, these nanocrystals can be found in many fields, such as solar cells, high energy density (rechargeable) batteries, single-electron transistors and fluorescent biological labels et al. Many of these applications are related to the optical and electronic properties which are usually size dependent. For many semiconductors, since the optical and electronic properties are induced by the edge transitions of the bandgap, Thus, studying the size dependence of the bandgap and the related exciton energy is one of the most important topics in low dimension semiconductor materials research. Besides the size effect, many optical and electronic properties are also influenced by the shape of the corresponding low dimension materials.
Most important chemical and physical processes of low dimension materials occur at the surface and interface and most important chemical and physical phenomenon are related to the surface and interface of materials. When the size of materials is in the nanoscale regime, there will be more surfaces and interfaces. However the energetic states of the atoms at the surfaces and interfaces are different from that within the bulk materials which maybe influence the behaviors of low dimension materials. Thus, the surface or interface situation should be an important object to be considered.
Latterly, in our work, there have some efforts to study the size and interface effect on optical and electronic properties of low dimension semiconductor materials, including bandgap, dielectric constant and volume plasmon energy. The established models without any adjusting parameters, are not only simple, but also proved to be reasonable in the full size range when compared with other experimental and theoretical results. In addition, according to classical thermodynamic and elastic theory, the influence of phase-change layer thickness on the crystallization kinetics and the critical layer number of epitaxial grown ultrathin films on semiconductor substrates, are also studied. The model predictions are confirmed to be valid.
In this thesis, the studies of the size and interface effect on low dimension semiconductor materials are listed as follows:
1. Low dimension semiconductor materials, with the tunable electronic and optical properties have attracted considerable interest as technologically important materials. With the size decreasing, the bandgap increasing is one of the important issue. According to the nearly free electron approach, the bandgap can be considered to be proportional to the cohesive energy, while cohesive energy is also proportional to melting temperature. Based on hereinbefore relationships and the established size effect melting temperature model, we established a simple model to predict the size dependent bandgap. It was found that the bandgap will increase with the dropping of size. When the size of crystal is in several nanometers range, the bandgap will increase dramatically due to increasing of surface/volume ratio (A/V). In addition, for nanocrystals with different shapes, they have different bandgaps even with the same crystal size. The ratio of the bandgap increasing is 3:2:1 for nanoparticles, nanowires and films, respectively. These differences should be attributed to the different surface/volume ratio of A/V = 6/D, 4/D, 2/D for nanoparticles, quasi-dimension nanoparticles or nanowires and thin films with d = 0, 1, 2, respectively. The model prediction results are in good agreement with the corresponding experimental and stimulant result of Si, II-VI and III-V semiconductor nanoparticles and nanowires.
2. Based on the established size dependent bandgap model and relevant relationships between bandgap and dielectric constant, the size and interface effect dielectric constant model can also be obtained. The model suggests that dielectric constant will increase or decrease with the size dropping, relying on the interface situation between crystals and surroundings. If the interaction on the crystal/substance interface is stronger than that within the crystal, the interface effect is dominant and there is an increasing trend for the dielectric constant with size decreasing. By contraries, dielectric constant will decrease with the size dropping when the crystal/substance interface is weak. Moreover, we also established a model to resolve the size and component effect on dielectric constant of solid solutions. For solid solutions, there exists a bowing behavior instead of the linear behavior. When the size is in several nanometers scale, the bowing behavior is weak and the dielectric constant is almost a linear of component x with the size decreasing. However when the size is larger than dozens of nanometers, the size effect is weak and the bowing behavior can be considered as bulk value. This provides an insight for materials design. The validity of the model is confirmed by the corresponding experimental results.
3. The size dependent volume plasmon energy model is established by incorporating the models of size dependent bandgap and lattice contraction model. It predicts that volume plasmon energy increases with the size decreasing. It also implies that the increasing volume plasmon energy is a result of blue shift of bandgap and lattice contraction. The model prediction results are in accordance with the available experimental results of Ge nanopaeticles and nanowires.
4. For the phase-change discs, the crystallization rate of the phase-change materials determines the maximum achievable data transfer rate and thickness dependent crystallization rate is due to a variation of the crystallization speed. According to the equation of crystallization speed, the energy barrier for crystallization is the only thickness dependent parameter. Analysis of the Gibbs free energy of a crystallite embedded in a thin amorphous film indicates that with the reduction of the film thickness, the energy barrier drops firstly, while it will increase steeply when the thickness of the film is further decreased. This is the result of the competition between film/substance and crystal/amorphous interface energy. The obtained results indicate the presence of an optimum film thickness where crystallization rate is maximized. The predicted optimum thickness of Ge2Sb2Te5 phase-change film is consisted with the experimental results.
5. As a critical situation for the stability of the epitaxial grown films on semiconductor substrates, the balance between molar elastic energy and molar interface energy for epitaxial grown films is assumed. The value of the elastic energy and interface energy can be easily determined by the known classic elastic theory and the established interface energy model, respectively. According to the above assumption, the critical thickness of epitaxial grown films on semiconductor substances is obtained. It is found that a smaller strain and a larger melting enthalpy are required to obtain a larger critical thickness. The predicted results are in accordance with the experimental results.
引文
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