Research Article  Open Access
Chao Zhang, Jianjun Song, Jie Zhang, Shulin Liu, "Thermophysics Simulation of Laser Recrystallization of HighGeContent SiGe on Si Substrate", Advances in Condensed Matter Physics, vol. 2018, Article ID 5863632, 8 pages, 2018. https://doi.org/10.1155/2018/5863632
Thermophysics Simulation of Laser Recrystallization of HighGeContent SiGe on Si Substrate
Abstract
The highGecontent SiGe material on the Si substrate can be applied not only to electronic devices but also to optical devices and is one of the focuses of research and development in the field. However, due to the 4.2% lattice mismatch between Si and Ge, the epitaxial growth of the highGecontent SiGe epitaxial layer directly on the Si substrate has a high defect density, which will seriously affect the subsequent device performance. Laser recrystallization technique is a fast and lowcost method to effectively reduce threading dislocation density (TDD) in epitaxial highGecontent SiGe films on Si. In this paper, by means of finite element numerical simulation, a 808 nm laser recrystallization thermal physics model of a highGecontent SiGe film (for example, Si_{0.2}Ge_{0.8}) on a Si substrate was established (temperature distribution physical model of Si_{0.2}Ge_{0.8} epitaxial layer under different laser power, Si_{0.2}Ge_{0.8} epitaxial layer thickness, and initial temperature). The results of this paper can provide important technical support for the preparation of highquality highGecontent SiGe epilayers on Si substrates by laser recrystallization.
1. Introduction
In order to improve the performance of MOS devices and continue Moore’s Law, various new materials and new technologies are emerging. HighGecontent SiGe on Si substrate has high carrier mobility, is compatible with Si process, and has better interface characteristics than Ge material on Si substrate and has become one of the semiconductor materials for high speed/high performance MOS device research and application [1, 2]. In addition, the highGecontent SiGe material has an absorption wavelength of up to 1.55 μm in the nearinfrared region, which is suitable for the development of optical devices such as infrared detectors [3, 4]. The development of highGecontent SiGe on Si substrates has become one of the focuses of research and development in the field.
Highquality, highGecontent SiGe alloys on Si substrates are the “material basis" for applications; however, due to a 4.2% lattice mismatch between Si and Ge, it is very difficult to directly heteroepitaxially grow a highquality SiGe alloy on a Si substrate [5]. The higher the Ge composition of the SiGe alloy epitaxial layer, the greater the mismatch rate with the substrate Si. The lattice mismatch on the one hand causes islandlike growth, which increases the surface roughness of the high Ge composition SiGe epitaxial layer [6]. On the other hand, it causes high threading dislocation density (TDD) in the SiGe layer. In the highGecontent SiGe epitaxial layer, either a closed dislocation loop is formed or a pair of screw dislocations extend longitudinally to the outer surface of the highGecontent SiGe epitaxial layer, which decreases the crystal quality of the epitaxial layer and degrades the device performance [7]. Therefore, how to solve the problem of preparing highquality and highcontent SiGe epitaxial layer on Si substrate deserves attention and further research.
From the above, it is difficult to obtain highquality, highcontent SiGe epitaxial layer due to the large lattice mismatch between Si and Ge. Interfacial dislocation defects continuously extend longitudinally to the surface of the epitaxial layer during the gradual thickening of the epitaxial layer, thereby resulting in a decrease in the lattice quality of the epitaxial layer. Laser recrystallization technique (shown in Figure 1) provides an effective method to solve this problem [8]. The highGecontent SiGe epitaxial layer directly prepared on the Si substrate is irradiated by the highenergy laser light and rapidly melted and recrystallized by thermal conduction. The TDD of the SiGe epitaxial layer is reduced by the lateral recrystallization process. The vertical proliferation of the threading dislocations in the SiGe epitaxial layer is suppressed, so that the crystal quality of the highGecontent SiGe epitaxial layer is significantly improved, which provide another effective approach to obtain highquality, highcontent SiGe epitaxial layer on Si substrate.
Compared with the conventional annealing methods, the laser recrystallization technique has the following advantages: minimized thermal diffusion of the dopants; local selective heating of specific regions, and negligible heating of other parts. In addition, this technique has the advantages of fast, simple process steps and low cost. In view of the application advantages of laser recrystallization in the preparation of highGecontent SiGe epitaxial layers, in this paper, a thermal physics model of 808 nm laser recrystallization of highGecontent SiGe film (take Si_{0.2}Ge_{0.8} as an example) on Si substrate is established by finite element numerical simulation. The modeling is based on an approach used for Ge/Si system, which is reported in our previous work [9]. Now the approach is modified in this work to consider the highGecontent SiGe/Si system instead. Physical model of temperature distribution in Si_{0.2}Ge_{0.8} epitaxial layer is obtained under different laser power, Si_{0.2}Ge_{0.8} epitaxial layer thickness, and initial temperature of epitaxial layer. The obtained results of this paper can provide an important technical support for the laser recrystallization assisted preparation of highquality highGecontent SiGe epitaxial layer on Si substrate.
2. Materials and Methods
In this paper, the multiphysics software COMSOL Multiphysics was used to model and analyze the laser recrystallization process of Si_{0.2}Ge_{0.8} thin film on Si substrate. The temperature distribution of Si_{0.2}Ge_{0.8}/Si system under different laser power, different Si_{0.2}Ge_{0.8} layer thickness, and different initial temperatures at 808 nm continuous laser is studied. The obtained results can provide a technical reference for the preparation of highquality Si_{0.2}Ge_{0.8}/Si films for laser recrystallization processes.
The laser heat source used in this paper is a continuous laser with a wavelength of λ=808 nm. The laser is a Gaussian beam along the scanning direction and rectangular shape perpendicular to the scanning direction. The solid heat transfer module was selected in COMSOL Multiphysics to establish a twodimensional steady state model of Si_{0.2}Ge_{0.8} laser recrystallization on Si. Figure 2 shows the laser recrystallization model of the Si_{0.2}Ge_{0.8}/Si system. The numbers indicate the boundaries. The sample absorbs laser energy and performs translational motion along the xaxis.
The process of heating a sample by laser follows the general heat equation [10]: The irradiation of the laser is simulated by the absorption of laser energy and the temperature change in the sample, where ρ, , k, and v represent the density, heat capacity, thermal conductivity, and translational speed of the sample, respectively. The convection term is used to simulate the translational motion of the sample [11]. Since the laser irradiation is continuous and the translational movement speed is constant, the transient change of the laser energy only occurs within a short time from the start of irradiation, so the transient term will be ignored. Therefore, the heat equation is the steady state equation. Heat source Q is produced by the absorption of laser energy by the sample, according to the BeerLambert law:where P, , α, and R are the laser power, the effective laser radius, the absorption coefficient of the material, and the reflectivity of the material surface.
The main parameters that need to be used in the calculations of (1) and (2) are listed in Table 1. Considering the solidliquid change of Si_{0.2}Ge_{0.8} epitaxial layer during laser irradiation, the specific heat capacity of Si_{0.2}Ge_{0.8} should be [10]where is the melting temperature of the Si_{0.2}Ge_{0.8} epitaxial layer, is the latent heat of phase change, and dT is the halftemperature width of the mushy zone (i.e., the solidliquid twophase region), and its value does not normally exceed 5 K. The smooth Heaviside function (flc2hs) in COMSOL is used to describe the abrupt change of temperature and to ensure that the epitaxial layer absorbs heat and changes in the physical properties during the phase transition [12]. Two solidliquid phase transitions are considered during the laser recrystallization of the Si_{0.2}Ge_{0.8} epitaxial layer. The first phase transition occurs when the absorption energy of the laser energy in the epitaxial layer is transformed into the latent heat of phase change, , and the temperature increases. When the temperature of the epitaxial layer reaches the melting point, the solid state changes to the liquid state; the second phase change occurs after the laser irradiation stops. The temperature of the epitaxial layer of Si_{0.2}Ge_{0.8} decreases, and when the temperature reaches the melting point again, the epitaxial layer releases heat. The process of lateral recrystallization occurs. It changes from a liquid state to a solid state again.

COMSOL Multiphysics used the finite element method to solve nonlinear partial differential equations to simulate the laser recrystallization process of Si_{0.2}Ge_{0.8}/Si system. Finite element method is a commonly used highefficiency numerical calculation method. Its principle is to divide the continuous solution domain into a discrete group of unit assemblies and use the hypothesized approximate function in each cell to represent the unknown field function to be solved in the solution domain, so that a continuous infinite degree of freedom problem becomes a discrete finite degree of freedom problem. In the finite element method, optimizing the mesh is very important for obtaining accurate numerical solutions. The number and form of the grids will directly affect the calculation accuracy and the calculation scale. If the number of grids is too small, the calculation results will be inaccurate or the results will not converge, resulting in the inability to obtain ideal results. If the number of grids is too large, it will take a lot of time to make the calculation scale larger, and the calculation efficiency will be low [13]. There are many factors to consider when meshing and optimizing meshes, such as the number of meshes, mesh density, mesh boundaries, and demarcation points. Since the Si_{0.2}Ge_{0.8} epitaxial layer has a high absorption coefficient and we need to study the temperature change in the epitaxial layer, therefore the mesh of the Si_{0.2}Ge_{0.8} epitaxial region needs to be refined to satisfy the rapid spatial change of the absorbed laser power, so that a more accurate numerical solution can be obtained. A coarse mash is employed for the Si substrate area to improve the calculation efficiency. The refined Si_{0.2}Ge_{0.8}/Si system grid is shown in Figure 3. It can be clearly seen from the figure that the epitaxial layer grid is denser than the substrate grid.
Appropriate boundary conditions are crucial for obtaining accurate numerical solutions. Figure 2 shows the various boundaries of the Si_{0.2}Ge_{0.8}/Si model. For the boundaries 1, 2, and 3, the Dirichlet condition holds; i.e., the temperature T is set to a fixed temperature value T_{0}. The adiabatic condition is applied to the Si_{0.2}Ge_{0.8}/Si interface (boundary 4), and the heat flux is specified to 0 to allow the continuity of the thermal field [10]:where n is the outer normal direction vector of the surface and k is the thermal conductivity.
Convection and radiative heat transfer occur at the sides of the upper surface and sample translational motion (boundaries 5, 6, and 7), causing heat loss [14]:where h is the convective heat transfer coefficient, is the external temperature, σ is the StefanBoltzmann constant, is the surface emissivity, and is the ambient temperature. represents the heat flux generated by convection heat transfer, and represents the heat flux generated by radiative heat transfer.
3. Results and Discussion
In the process of laser recrystallization, the parameters of the incident laser and the properties of the sample are two factors that affect the quality of the recrystallized film, including the incident laser output power, epitaxial layer thickness, and the initial temperature of the sample. By changing these parameters and studying the temperature distribution of the Si_{0.2}Ge_{0.8}/Si system, the laser recrystallization process can be optimized. The laser recrystallization technique with optimal process parameters provides theoretical guidance for the preparation of highquality Si_{0.2}Ge_{0.8} epitaxial films.
Figure 4 shows the melting threshold power required for the recrystallization of 400 nm thick Si_{0.2}Ge_{0.8} film on a Si substrate at different initial temperatures. It can be seen from the figure that as the initial temperature increases, the power required for laser recrystallization of the system decreases linearly. The power required for the laser recrystallization of the system at 300 K at room temperature is 165 W, while the power required at 873 K is only about 74 W. Therefore, choosing a reasonable initial preheating temperature can effectively reduce the laser recrystallization power of Si_{0.2}Ge_{0.8}/Si system, which is beneficial to the control of process cost.
There is an important reason why the initial preheating is needed before the Si_{0.2}Ge_{0.8}/Si system is recrystallized. The laser recrystallization is a heat treatment process. If the laser recrystallization is performed directly without preheating the sample, the temperature gradient within the Si_{0.2}Ge_{0.8}/Si system will be steep during the recrystallization temperature rising process and the cooling process after laser irradiation, which is unfavorable to the crystal quality of the epitaxial layer and may even cause cracking phenomenon [16].
Based on the above two points, the preheating process is essential before laser recrystallization of Si_{0.2}Ge_{0.8}/Si system. Considering the two factors of process cost control and recrystallizing quality effect, combined with our experience in the traditional heat treatment of Si_{0.2}Ge_{0.8}/Si system and the simulation results in Figure 4, we propose using 873 K as the preheating temperature of the Si_{0.2}Ge_{0.8}/Si system before laser recrystallization.
The thickness of the Si_{0.2}Ge_{0.8} epitaxial layer is also an important parameter that needs to be considered in the laser recrystallization of the system. When the sample is illuminated by the laser, part of the laser energy is reflected, the other part is absorbed, and the rest is transmitted. The absorption rate is the fraction of absorbed laser light. The 808 nm laser absorption rate is different for different epitaxial layer thicknesses. The laser recrystallization energy should be absorbed by the Si_{0.2}Ge_{0.8} epitaxial layer as much as possible to ensure the melting effect. Figure 5 shows the schematic diagram of the laser reflection, absorption, transmission, and the FDTD simulation results of the absorption rate of 808 nm laser in Si_{0.2}Ge_{0.8} epitaxial layer and Si substrate under different epitaxial layer thickness conditions. It can be seen from the figure that when the epitaxial layer thickness of Si_{0.2}Ge_{0.8} reaches 300 nm or more, the absorption rate of the 808 nm laser in the epitaxial layer exceeds 50%. Moreover, as the thickness of the Si_{0.2}Ge_{0.8} epitaxial layer increases, the absorptivity of the 808 nm laser in the epitaxial layer will further increase. Therefore, in this paper, Si_{0.2}Ge_{0.8} epitaxial layer thickness must reach at least 300 nm in the laser recrystallization process of Si_{0.2}Ge_{0.8}/Si system.
(a)
(b)
Another issue is also worthy of attention. Is the thickness of the Si_{0.2}Ge_{0.8} epitaxial layer thicker the better? If the Si_{0.2}Ge_{0.8} epitaxial layer is too thick, although the absorption rate of the 808 nm laser in the epitaxial layer can be further increased, the temperature difference between the upper and lower layers of the Si_{0.2}Ge_{0.8} epitaxial layer is large, and the full Si_{0.2}Ge_{0.8} epitaxial layer cannot be melted and recrystallized. To achieve melting and recrystallization of the whole Si_{0.2}Ge_{0.8} epitaxial layers, laser power needs to be further increased (see Figure 6).
(a)
(b)
Considering comprehensively, this paper proposes choosing 300 nm~400 nm as the thickness of Si_{0.2}Ge_{0.8} epitaxial layer in laser recrystallization of Si0.2Ge0.8/Si system.
The following further discusses the selection of laser power parameters in the laser recrystallization process. It is known from the foregoing discussion that the laser power is relevant in the selection of two important parameters of the thickness of the epitaxial layer of Si_{0.2}Ge_{0.8} and the preheating temperature. The focus of the laser power parameter discussion here is to study the epitaxial layer thickness (400 nm) and the preheating temperature (873K) of the Si_{0.2}Ge_{0.8} layer that has been determined in this paper. The temperature distribution and the temperature of the upper and lower surfaces of the Si_{0.2}Ge_{0.8} epitaxial layer at different laser powers are examined. According to the temperature values of the upper and lower surfaces of the Si_{0.2}Ge_{0.8} epitaxial layer, it is determined whether the Si_{0.2}Ge_{0.8} epitaxial layer is fully melted to determine the optimal laser power parameter.
Figure 7 shows the simulation results of the internal temperature of Si_{0.2}Ge_{0.8} epitaxial layer/Si substrate and the peak temperatures of Si_{0.2}Ge_{0.8} upper surface and lower surface under different power. The preheating temperature is 873 K and the thickness of the Si_{0.2}Ge_{0.8} epitaxial layer is 400 nm. As can be seen from the figure, the Si_{0.2}Ge_{0.8}/Si sample temperature gradually increases as the incident laser power increases. From the surface of the sample to the inside of the sample, the temperature gradually decreases. The incident laser energy is absorbed by the Si_{0.2}Ge_{0.8}/Si sample after heat conduction and the temperature of the sample increases. When the laser power reaches 70W, the upper surface of the Si_{0.2}Ge_{0.8} epitaxial layer has melted (the melting point of Si_{0.2}Ge_{0.8} is 1268 K). The lower surface is also close to melting; when the laser power is 80 W, the upper and lower surfaces of the Si_{0.2}Ge_{0.8} epitaxial layer have exceeded the melting point, indicating that the Si_{0.2}Ge_{0.8} epitaxial layer achieves full melting. Therefore, it is suggested that the incident power between 70 W and 80 W is selected as the laser recrystallization power of the Si_{0.2}Ge_{0.8}/Si system.
(a)
(b)
Based on the above simulation results of the incident laser output power, epitaxial layer thickness, and sample initial temperature, the proposed laser recrystallization process parameters for the Si_{0.2}Ge_{0.8}/Si substrate system are as follows: System 873 K preheating, Si_{0.2}Ge_{0.8} epitaxial layer 400 nm thick, and 808 nm laser power 74 W. Figure 8 shows the COMSOL Multiphysics simulation results using the laser recrystallization process parameters Si_{0.2}Ge_{0.8}/Si substrate system. Figure 9 shows the surface temperature distribution of Si_{0.2}Ge_{0.8} and the longitudinal temperature distribution of the Si_{0.2}Ge_{0.8}/Si substrate system at x = 0. It can be seen from the figure that the maximum temperature of the Si_{0.2}Ge_{0.8}/Si sample reaches 1352 K, which exceeds the melting point of Si_{0.2}Ge_{0.8}, indicating that the epitaxial layer has melted. It can be clearly seen from Figure 8 that the laser heating area is in the shape of a droplet. The temperature of the sample is highest at the center of the heating area of the laser beam. The laser energy passes through the heat conduction, and the temperature gradually decreases from the surface of the sample to the inside of the sample. When the laser energy reaches the Si substrate, it is already very weak, so that the Si substrate does not melt, thereby realizing the laser recrystallization of the Si_{0.2}Ge_{0.8} epitaxial layer without damaging the substrate material.
(a)
(b)
4. Conclusion
In this paper, a thermal physics model of continuous wave laser recrystallization of highGeContent SiGe (for example, Si_{0.2}Ge_{0.8}) on Si substrate was established using COMSOL Multiphysics finite element analysis software. The effects of different laser and material parameters on the temperature distribution of Si_{0.2}Ge_{0.8}/Si substrate system were simulated in detail, and the optimum process parameters for laser recrystallization of Si_{0.2}Ge_{0.8}/Si substrate system were determined. The numerical simulation results show that the preheating treatment before laser recrystallization in Si_{0.2}Ge_{0.8}/Si system can not only avoid the material damage caused by the large temperature gradients but also reduce the process cost. The thickness of Si_{0.2}Ge_{0.8} epitaxial layer affects the laser absorption rate. Selection of a reasonable epitaxial layer thickness is possible to realize the melting and recrystallization of the whole Si_{0.2}Ge_{0.8} epitaxial layer. The temperature of the Si_{0.2}Ge_{0.8}/Si substrate system increases as the incident laser power increases. Based on the simulation results of the incident laser output power, the thickness of the epitaxial layer, and the initial temperature of the sample, the proposed laser recrystallization process parameters for the Si_{0.2}Ge_{0.8}/Si substrate system are as follows: 873 K preheating, Si_{0.2}Ge_{0.8} epitaxial layer 400 nm thick, and 808 nm laser power 74 W. The process of laser recrystallization can be optimized through reasonable selection of process parameters, which will provide theoretical guidance for the preparation of highquality Si_{0.2}Ge_{0.8} epitaxial films.
Data Availability
The table and graphic data used to support the findings of this study are included within the article. All data of this paper used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant no. 51777167).
References
 F. Isa, M. Salvalaglio, Y. A. R. Dasilva et al., “Highly Mismatched, DislocationFree SiGe/Si Heterostructures,” Advanced Materials, vol. 28, no. 5, pp. 884–888, 2016. View at: Publisher Site  Google Scholar
 T. Ando, P. Hashemi, J. Bruley et al., “High Mobility HighGeContent SiGe PMOSFETs Using Al2O3/HfO2 Stacks with InSitu O3 Treatment,” IEEE Electron Device Letters, vol. 38, no. 3, pp. 303–305, 2017. View at: Publisher Site  Google Scholar
 Z. W. Zhou, “Development of Sibased SiGe, Ge relaxation substrate and its Ge photodetector,” [D], Xiamen: Xiamen University, 2009. View at: Google Scholar
 S. A. Shahahmadi, A. Aizan, B. Bais, M. Akhtaruzzaman, A. R. M. Alamoud, and N. Amin, “Gerich SiGe thin film deposition by cosputtering in insitu and exsitu solid phase crystallization for photovoltaic applications,” Materials Science in Semiconductor Processing, vol. 56, pp. 160–165, 2016. View at: Publisher Site  Google Scholar
 A. M. Hussain, H. M. Fahad, G. A. T. Sevilla, and M. M. Hussain, “Thermal recrystallization of physical vapor deposition based germanium thin films on bulk silicon (100),” Physica Status Solidi  Rapid Research Letters, vol. 7, no. 11, pp. 966–970, 2013. View at: Publisher Site  Google Scholar
 R. R. Lieten, J. C. McCallum, and B. C. Johnson, “Single crystalline SiGe layers on Si by solid phase epitaxy,” Journal of Crystal Growth, vol. 416, pp. 34–40, 2015. View at: Publisher Site  Google Scholar
 D. L. Liu, “Study on RPCVD growth strained Si/Strained SiGe films,” [D] Beijing: Beijing General Research Institute for Nonferrous Metals, 2012. View at: Google Scholar
 Z. Liu, X. Hao, J. Huang, W. Li, A. HoBaillie, and M. A. Green, “Diode laser annealing on Ge/Si (100) epitaxial films grown by magnetron sputtering,” Thin Solid Films, vol. 609, pp. 49–52, 2016. View at: Publisher Site  Google Scholar
 J. Zhang, J. Song, Z. H. Liu et al., “Modeling of continuous wave laser melting of germanium epitaxial films on silicon substrates,” Materials Express, vol. 7, no. 5, pp. 341–350, 2017. View at: Publisher Site  Google Scholar
 Z. SaidBacar, Y. Leroy, F. Antoni, A. Slaoui, and E. Fogarassy, “Modeling of CW laser diode irradiation of amorphous silicon films,” Applied Surface Science, vol. 257, no. 12, pp. 5127–5131, 2011. View at: Publisher Site  Google Scholar
 B. Bourouga, G. L. Meur, B. Garnier, J. F. Michaud, and T. MohammedBrahim, “Heat transfer during a CW laser crystallization process of a silicon thin film on a glass substrate,” in Proceedings of the COMSOL Multiphysics User’s Conference, Paris, France, 2005. View at: Google Scholar
 M. Trifunovic, P. M. Sberna, T. Shimoda, and R. Ishihara, “Analysis of polydihydrosilane crystallization by excimer laser annealing,” Thin Solid Films, vol. 638, pp. 73–80, 2017. View at: Publisher Site  Google Scholar
 F. Yan, C. Hu, X. Zhang et al., “Influence of heat input on HAZ liquation cracking in laser welded GH909 alloy,” Optics & Laser Technology, vol. 92, pp. 44–51, 2017. View at: Publisher Site  Google Scholar
 M. Caninenberg, E. Verheyen, D. Kiesler et al., “Sample temperature profile during the excimer laser annealing of silicon nanoparticles,” Optics & Laser Technology, vol. 74, pp. 132–137, 2015. View at: Publisher Site  Google Scholar
 S. Adachi, Properties of Semiconductor Alloys: GroupIV, III–V and II–VI Semiconductors, John Wiley & Sons Ltd., Chichester, UK, 2009.
 T. Pliewischkies, T. Schmidt, I. Höger et al., “Thermal stresses and cracking behavior during laser crystallization of silicon on glass for thin film solar cells,” Physica Status Solidi (a) – Applications and Materials Science, vol. 212, no. 2, pp. 317–322, 2015. View at: Publisher Site  Google Scholar
Copyright
Copyright © 2018 Chao Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.