半导体纳米材料生长机制及成核理论研究
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摘要
传统的薄膜异质外延技术,由于不同材料晶格常数的失配,会在接触表面产生位错,从而导致薄膜光学和电学性能的显著下降。纳米线解决了长期困扰薄膜异质外延领域的技术问题。由于弹性能量在纳米线侧壁上的弛豫,使得纳米线可以在晶格失配衬底上无位错生长,因此纳米异质外延技术被认为是减少位错缺陷产生的有效途径。同时,为制备出高晶体质量的纳米材料,去除催化物对纳米材料造成的污染,世界上很多实验小组都在尝试用无催化方法制备纳米材料。因此,理解半导体纳米材料的生长机制及成核理论,将为制备出高质量纳米材料打下坚实的理论基础。
本论文研究工作主要围绕任晓敏教授担任首席科学家的国家重点基础研究发展规划(973计划)项目(No:2010CB314900)以及课题组承担的国家自然科学基金重大国际(地区)合作研究项目(No：90201035)、高等学校学科创新引智计划项目(No：B07005)、国家863计划项目(No:2007AA03Z418)杜布罗夫斯基教授承担的俄罗斯联邦科学创新项目(No：02.740.11.0383)、俄罗斯基础研究项目(No：11-02-00727-a)、俄罗斯科学院科学研究项目(No：10-02-93107-a)展开。
针对倾斜纳米线在MBE沉积条件下的理论和实验,异质生长纳米结构弹性应变能及塑性应变能模型,三维纳米结构应力驱动成核理论,以及量子点在台阶衬底的成核理论进行了研究。取得了以下主要研究成果：
1.首次推导出倾斜纳米线在MBE沉积条件下的生长速率模型。分析了纳米线生长速率对纳米线半径和沉积条件的函数关系。用MBE沉积法分别制备出在GaAs(211)A和GaAs(111)B衬底上的GaAs纳米线。实验表明,由于入射粒子对倾斜纳米线侧壁有着更大碰撞率,倾角为20°的倾斜纳米线平均长度大约是垂直生长纳米线长度的两倍。通过理论模型与实验结果对比分析,估算出吸附粒子在衬底和纳米线侧壁的超饱和度和扩散长度,认为在MBE生长条件下粒子在纳米线侧壁的扩散效应对其生长速率有着重要影响。
2.首次用解析的方法推导出在大高宽比和失配生长条件下不同形状纳米结构的弹性应变能弛豫函数。比较了柱状纳米结构分别在刚性衬底和弹性衬底上弹性弛豫函数的异同。通过对比不同形状纳米结构在有位错以及无位错条件下总能量之间的差异,得到了产生位错的临界直径和临界厚度。研究表明：弹性能量弛豫与纳米结构的形状以及侧壁衬底之间夹角相关,夹角越大,弹性能量随着高宽比的增加弛豫得越迅速。上述结论得到了已发表实验数据及有限元仿真结果的验证。
3.首次提出三维纳米结构在晶格失配衬底上的应力驱动成核模型。得到了二维和三维纳米结构的成核势垒和最有利成核高宽比。通过分析二维和三维纳米结构成核势垒之间的差异,得到了纳米结构的三维成核条件。将上述分析结果与实验数据进行对照后发现：对于多种材料系三维纳米结构最有利成核高宽比均随晶格失配度的增大而变大。理论分析预测了三维纳米结构在应力驱动成核条件下为纤锌矿晶体结构,这与实验得到的在蓝宝石衬底上无催化自组织GaAs纳米针的晶体结构一致。总之,应力驱动成核为实验制备出无催化高质量纳米材料提供了一种新的生长机制。
4.首次提出了在失配台阶衬底上按照Stranski-Krastanov(SK)生长模式生长三维纳米结构时的成核理论模型,并基于此模型分析得出了不同材料系纳米结构的成核势垒、最有利成核高宽比以及该比值随衬底取向偏角的变化关系。结果表明,纳米结构的最小成核势垒随着台阶衬底取向偏角的增大而减小,这说明相对于平面衬底,纳米结构在台阶衬底更容易成核,此结论与实验结果一致。通过选取不同衬底取向偏角的台阶衬底,可以控制纳米结构自组织成核过程。
5.在考虑浸润层表面能随厚度变化的条件下,提出了Ge量子点在Si台阶衬底上按照SK生长模式成核的模型。拟合出量子点形状系数和弹性能量密度随衬底取向偏角的变化关系,分析了衬底取向偏角、浸润层厚度和量子点密度对量子点成核的影响。得出量子点成核势垒和临界体积均随衬底取向偏角和浸润层厚度的增大而减小,而量子点密度对量子点成核势垒的影响较小。
The conventional film technologies have run into interfacial lattice mismatch issues that often result in highly defective optical materials. The unique one-dimensionality inherent to nanowires has already solved some of the long-standing technical problems that have plagued the thin film community. In this regard, nanowires growth provides a natural mechanism for relaxing the lattice strain at the interface and enables dislocation-free semiconductor growth on lattice mismatched substrates. The unwanted Au contamination has led to many attempts to develop catalyst-free growth procedures by a lot of research groups in the world. Understanding their growth mechanism as well as nucleation theory is crucial for the fabrication of high-quality materials.
The research in this dissertation is supported by grants from The National Basic Research Program of China (No:2010CB314900), which professor Xiaomin Ren is responsible for as a chief scientist, Key Program Project of the National Natural Science Foundation of China(No:90201035), The111Project(No:B07005), The National High Technology Research and Development Program of China(No:2007AA03Z418)。The Russian Federal Agency for Science and Innovation(No:02.740.11.0383), The Russian Foundation for Basic Research(No:11-02-00727-a), The Scientific Programs of Russian Academy of Sciences(No:10-02-93107-a), which professor Dubrovskii is responsible for them.
In this dissertation, a great deal of research work can be described as follow:theoretical and experimental studies on the growth of inclined nanowires by Molecular Beam Epitaxy, study of elastic energy relaxation and plastic deformation in nanostructures on lattice mismatched substrates, stress-driven nucleation theory of three-dimensional nanostructures, the nucleation theory of quantum dots on the vicinal substrates. The main achievements are listed as follows.
1. Theoretical model for the growth of inclined semiconductor nanowires via Molecular Beam Epitaxy deposition is developed. General expression for the nanowires growth as function of its radius and the growth condition is obtained and analyzed. Growth experiments are carried out on the GaAs(211)A and GaAs(111)B substrates. It is found out that20°inclined nanowires are two times longer in average, which is explained by a larger impingment rate on their sidewalls. Supersaturations and diffusion lengths of surface and sidewall adatoms are also estimated by fitting the theoretical model to the experimental data. The obtained results show the importance of sidewall adatoms in the MBE growth of nanowires.
2. An analytical expression of elastic strain energy relaxation in nanostructures of different isotropic geometries grown on lattice mismatched substrates is obtained. The results are derived from large aspect ratio condition. The differences of the elastic strain energy relaxation in cylindrical nanostrucuture on the rigid and elastic substrate are compared. A dislocation model is considered to analyze the competition between the elastic and dislocation energies. We calculate out the critical diameter and critical thickness below which the plastic deformation is energetically suppressed. Our data indicate that the elastic energy is highly depended on the island shape, with the relaxation becoming faster as the contact angle increases. The analytical model is compared with experimental and numerical results.
3. The model of stress-driven nucleation of three-dimensional nanostructures in lattice mismatched systems is proposed. The nucleation barrier and the energetically preferred aspect ratio are obtained. The comparison between the two-dimensional and three-dimensional nucleation barrier is carried in order to get the three-dimensional nucleation conditions. The fitting curve is plotted according to the experimental results, and the curve shows the tendency for an increase in the preferred aspect ratio with regard to different material systems. The nucleation theory expects the wurzite crystal structure of nanocrystals under the stress-driven nucleation process, which is consistent with the case of GaAs nanoneedles on sapphire. Overall, the stress-driven nucleation of islands may offer a new growth mechanism for the fabrication of catalyst-free high quality nanomaterials.
4. A model of the nanoislands nucleation in Stranski-Krastanov growth mechanism on lattice-mismatched vicinal substrate is proposed. The nucleation barrier and energetically favorable aspect ratio are obtained on different material systems. The favorable aspect ratio as a function of miscut angle is also demonstrated. The theoretical analysis shows the minimum nucleation barrier of island is on the decrease with increment of substrate misorientation, which means the nucleation of nanoislands on vicinal substrate is more favorable than that on singular substrate. This result is consistent with experimental observation. It is suggested that the vicinal substrate can be explored further as an effective way to direct nanoislands nucleation and self-assembly. With regard to miscut, it offers an additional degree of control over the nucleation process of nanoislands.
5. A nucleation model of Ge quantum dots on Si vicinal substrate in Stranski-Krastanov growth mechanism is proposed. The variation of shape factor and elastic energy densities of quantum dots with miscut angles is fitted. The influence of miscut angles, the thickness of wetting layers and the densities of quantum dots on the nucleation process is analyzed. The conclusion shows the tendency for a decrease in the nucleation barrier and critical volume of quantum dots with miscut angle and the thickness of wetting layers. The variation of densities of quantum dots is trivial to the nucleatin barrier.
本论文研究工作主要围绕任晓敏教授担任首席科学家的国家重点基础研究发展规划(973计划)项目(No:2010CB314900)以及课题组承担的国家自然科学基金重大国际(地区)合作研究项目(No：90201035)、高等学校学科创新引智计划项目(No：B07005)、国家863计划项目(No:2007AA03Z418)杜布罗夫斯基教授承担的俄罗斯联邦科学创新项目(No：02.740.11.0383)、俄罗斯基础研究项目(No：11-02-00727-a)、俄罗斯科学院科学研究项目(No：10-02-93107-a)展开。
针对倾斜纳米线在MBE沉积条件下的理论和实验,异质生长纳米结构弹性应变能及塑性应变能模型,三维纳米结构应力驱动成核理论,以及量子点在台阶衬底的成核理论进行了研究。取得了以下主要研究成果：
1.首次推导出倾斜纳米线在MBE沉积条件下的生长速率模型。分析了纳米线生长速率对纳米线半径和沉积条件的函数关系。用MBE沉积法分别制备出在GaAs(211)A和GaAs(111)B衬底上的GaAs纳米线。实验表明,由于入射粒子对倾斜纳米线侧壁有着更大碰撞率,倾角为20°的倾斜纳米线平均长度大约是垂直生长纳米线长度的两倍。通过理论模型与实验结果对比分析,估算出吸附粒子在衬底和纳米线侧壁的超饱和度和扩散长度,认为在MBE生长条件下粒子在纳米线侧壁的扩散效应对其生长速率有着重要影响。
2.首次用解析的方法推导出在大高宽比和失配生长条件下不同形状纳米结构的弹性应变能弛豫函数。比较了柱状纳米结构分别在刚性衬底和弹性衬底上弹性弛豫函数的异同。通过对比不同形状纳米结构在有位错以及无位错条件下总能量之间的差异,得到了产生位错的临界直径和临界厚度。研究表明：弹性能量弛豫与纳米结构的形状以及侧壁衬底之间夹角相关,夹角越大,弹性能量随着高宽比的增加弛豫得越迅速。上述结论得到了已发表实验数据及有限元仿真结果的验证。
3.首次提出三维纳米结构在晶格失配衬底上的应力驱动成核模型。得到了二维和三维纳米结构的成核势垒和最有利成核高宽比。通过分析二维和三维纳米结构成核势垒之间的差异,得到了纳米结构的三维成核条件。将上述分析结果与实验数据进行对照后发现：对于多种材料系三维纳米结构最有利成核高宽比均随晶格失配度的增大而变大。理论分析预测了三维纳米结构在应力驱动成核条件下为纤锌矿晶体结构,这与实验得到的在蓝宝石衬底上无催化自组织GaAs纳米针的晶体结构一致。总之,应力驱动成核为实验制备出无催化高质量纳米材料提供了一种新的生长机制。
4.首次提出了在失配台阶衬底上按照Stranski-Krastanov(SK)生长模式生长三维纳米结构时的成核理论模型,并基于此模型分析得出了不同材料系纳米结构的成核势垒、最有利成核高宽比以及该比值随衬底取向偏角的变化关系。结果表明,纳米结构的最小成核势垒随着台阶衬底取向偏角的增大而减小,这说明相对于平面衬底,纳米结构在台阶衬底更容易成核,此结论与实验结果一致。通过选取不同衬底取向偏角的台阶衬底,可以控制纳米结构自组织成核过程。
5.在考虑浸润层表面能随厚度变化的条件下,提出了Ge量子点在Si台阶衬底上按照SK生长模式成核的模型。拟合出量子点形状系数和弹性能量密度随衬底取向偏角的变化关系,分析了衬底取向偏角、浸润层厚度和量子点密度对量子点成核的影响。得出量子点成核势垒和临界体积均随衬底取向偏角和浸润层厚度的增大而减小,而量子点密度对量子点成核势垒的影响较小。
The conventional film technologies have run into interfacial lattice mismatch issues that often result in highly defective optical materials. The unique one-dimensionality inherent to nanowires has already solved some of the long-standing technical problems that have plagued the thin film community. In this regard, nanowires growth provides a natural mechanism for relaxing the lattice strain at the interface and enables dislocation-free semiconductor growth on lattice mismatched substrates. The unwanted Au contamination has led to many attempts to develop catalyst-free growth procedures by a lot of research groups in the world. Understanding their growth mechanism as well as nucleation theory is crucial for the fabrication of high-quality materials.
The research in this dissertation is supported by grants from The National Basic Research Program of China (No:2010CB314900), which professor Xiaomin Ren is responsible for as a chief scientist, Key Program Project of the National Natural Science Foundation of China(No:90201035), The111Project(No:B07005), The National High Technology Research and Development Program of China(No:2007AA03Z418)。The Russian Federal Agency for Science and Innovation(No:02.740.11.0383), The Russian Foundation for Basic Research(No:11-02-00727-a), The Scientific Programs of Russian Academy of Sciences(No:10-02-93107-a), which professor Dubrovskii is responsible for them.
In this dissertation, a great deal of research work can be described as follow:theoretical and experimental studies on the growth of inclined nanowires by Molecular Beam Epitaxy, study of elastic energy relaxation and plastic deformation in nanostructures on lattice mismatched substrates, stress-driven nucleation theory of three-dimensional nanostructures, the nucleation theory of quantum dots on the vicinal substrates. The main achievements are listed as follows.
1. Theoretical model for the growth of inclined semiconductor nanowires via Molecular Beam Epitaxy deposition is developed. General expression for the nanowires growth as function of its radius and the growth condition is obtained and analyzed. Growth experiments are carried out on the GaAs(211)A and GaAs(111)B substrates. It is found out that20°inclined nanowires are two times longer in average, which is explained by a larger impingment rate on their sidewalls. Supersaturations and diffusion lengths of surface and sidewall adatoms are also estimated by fitting the theoretical model to the experimental data. The obtained results show the importance of sidewall adatoms in the MBE growth of nanowires.
2. An analytical expression of elastic strain energy relaxation in nanostructures of different isotropic geometries grown on lattice mismatched substrates is obtained. The results are derived from large aspect ratio condition. The differences of the elastic strain energy relaxation in cylindrical nanostrucuture on the rigid and elastic substrate are compared. A dislocation model is considered to analyze the competition between the elastic and dislocation energies. We calculate out the critical diameter and critical thickness below which the plastic deformation is energetically suppressed. Our data indicate that the elastic energy is highly depended on the island shape, with the relaxation becoming faster as the contact angle increases. The analytical model is compared with experimental and numerical results.
3. The model of stress-driven nucleation of three-dimensional nanostructures in lattice mismatched systems is proposed. The nucleation barrier and the energetically preferred aspect ratio are obtained. The comparison between the two-dimensional and three-dimensional nucleation barrier is carried in order to get the three-dimensional nucleation conditions. The fitting curve is plotted according to the experimental results, and the curve shows the tendency for an increase in the preferred aspect ratio with regard to different material systems. The nucleation theory expects the wurzite crystal structure of nanocrystals under the stress-driven nucleation process, which is consistent with the case of GaAs nanoneedles on sapphire. Overall, the stress-driven nucleation of islands may offer a new growth mechanism for the fabrication of catalyst-free high quality nanomaterials.
4. A model of the nanoislands nucleation in Stranski-Krastanov growth mechanism on lattice-mismatched vicinal substrate is proposed. The nucleation barrier and energetically favorable aspect ratio are obtained on different material systems. The favorable aspect ratio as a function of miscut angle is also demonstrated. The theoretical analysis shows the minimum nucleation barrier of island is on the decrease with increment of substrate misorientation, which means the nucleation of nanoislands on vicinal substrate is more favorable than that on singular substrate. This result is consistent with experimental observation. It is suggested that the vicinal substrate can be explored further as an effective way to direct nanoislands nucleation and self-assembly. With regard to miscut, it offers an additional degree of control over the nucleation process of nanoislands.
5. A nucleation model of Ge quantum dots on Si vicinal substrate in Stranski-Krastanov growth mechanism is proposed. The variation of shape factor and elastic energy densities of quantum dots with miscut angles is fitted. The influence of miscut angles, the thickness of wetting layers and the densities of quantum dots on the nucleation process is analyzed. The conclusion shows the tendency for a decrease in the nucleation barrier and critical volume of quantum dots with miscut angle and the thickness of wetting layers. The variation of densities of quantum dots is trivial to the nucleatin barrier.
引文
[1]任晓敏,国家重点基础研究发展计划(973计划)项目“新型光电子器件中的异质兼容集成与功能微结构体系基础研究”申请书,2010.
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