125 lines
7.0 KiB
XML
125 lines
7.0 KiB
XML
= Method
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== 4H-SiC wafer details and Raman experiments setup
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外延片的厚度、掺杂浓度、生长 C/Si 比，斜切角度。
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5 个 6 寸的 p 型外延片被使用，我们将它们称为 W#sub[i]。
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使用的衬底都是 n 型，前四个外延片的厚度为 1 微米，第五个外延片的厚度为 2 微米。
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外延层的 Al 掺杂浓度分别为 0.1 3.8 5.1 6.4 10 E18 cm#super[-3]，使用 SIMS 测试。
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生长时 Si/C 比分别为 0.7 1.2 1.6 2.4 2.0。、
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所有外延片都有 4 度斜切。
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Five 6-inch p-type epitaxial wafers (W#sub[1]–W#sub[5]) were fabricated on n-type substrates
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using the step-flow growth method with a 4° offcut angle.
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The Al doping concentrations, determined by SIMS,
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were 0.1, 3.8, 5.1, 6.4, and 10 #sym.times 10 cm#super[-3] for W#sub[1]–W#sub[5], respectively.
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W#sub[1]–W#sub[4] had an epitaxial layer thickness of 1 μm, while W#sub[5] had a thickness of 2 μm.
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The Si/C ratios during growth were 0.7, 1.2, 1.6, 2.4, and 2.0 for the five wafers, respectively.
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拉曼设备的型号。激光的波长，背散射。共焦针孔。
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拉曼设备的型号是 LabRAM HR Evolution，使用背散射。
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大部分实验中，我们使用 532 nm 的激光，少部分实验中使用 325 nm 的激光以观测紫外拉曼。
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有三个不同的入射配置，包括正入射、掠入射、边入射。
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考虑到 4 度斜切和 4H-SiC 几乎各向同性的折射率（2.73） @shaffer_refractive_1971 ，掠入射的入射角大约为 25 度。
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在正散射过程中，我们使用 100 微米的共焦针孔，以尽可能提高 z 方向的分辨率 @song_depth_2020；其它情况使用常用的 200 微米针孔以提高信噪比。
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此外，在正入射和边入射时，拉曼散射信号较强，因此我们使用较短的积分时间（约 60 秒），
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而在掠入射时，拉曼信号较弱，因此使用较长的积分时间（约 300 秒）。
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All Raman experiments were conducted using a LabRAM HR Evolution system in a back-scattering configuration,
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where the collected scattered light propagates in the opposite direction to the incident laser.
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A 532 nm laser served as the primary excitation source,
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while a 325 nm laser was employed for only ultraviolet Raman measurements.
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Three distinct incidence configurations were utilized, as illustrated in @figure-incidence:
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(i) normal incidence, where the laser incident perpendicularly to the epitaxial surface;
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(ii) grazing incidence, where the laser incident nearly parallelly to the epitaxial surface;
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and (iii) edge incidence, where the laser is incident at the wafer edge and perpendicularly to the edge surface.
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Considering the 4° offcut angle and the nearly isotropic refractive index of 2.73 for 4H-SiC @shaffer_refractive_1971,
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the refracted laser in 4H-SiC during grazing incidence forms an angle of approximately 25° with the c axis.
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A 100 μm confocal pinhole was used for normal incidence to enhance axial (z-direction) resolution @song_depth_2020,
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while a 200 μm pinhole was employed for the other configurations to improve the signal-to-noise ratio.
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Besides, the integration time was set to 60 seconds for normal and edge incidence,
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while it was extended to 300 seconds for grazing incidence due to the weaker Raman signal.
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#include "figure-incidence.typ"
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== Simulation details
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我们建立了三类模型：无缺陷、点缺陷和面缺陷。
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Three types of models were established: defect-free models, point defect models, and surface defect models.
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无缺陷和点缺陷的模型
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无缺陷和点缺陷的模型尺寸为 xxA x xxA x xxA。
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我们认为是足够大的，因为无缺陷模型的结果与实验差距在一定范围内，且继续扩大模型对准确程度没有提升。
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对于点缺陷模型，我们考虑了 Si 空位、C 空位、N 替位、Al 替位。
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分别记为 V#sub[Si]、V#sub[C]、N#sub[Si] 和 Al#sub[C]。
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考虑到 SiC 的对称性 p63mc （引用），有两个不同的位点，记为 k 和 h，
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根据局部环境近似为立方（k）还是六角（h）。
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此外，还有人提出，N 替换 C、C 替换 Si 的模型（引用），
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此结构除了 h 位与 k 位的区别以外，还需要考虑发生替换的两个原子位于面内还是面外（将会导致对称性的不同）。
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The defect-free and point defect models were established with a size of xxA x xxA x xxA.
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This size should be large enough to calculate phonon properties for defect-free and point defect 4H-SiC,
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since the defect-free results obtained with these models were within 5% errors of the experimental data,
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and further increasing the model size did not improve the accuracy.
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Twelve point defect models were considered, including Si vacancies (V#sub[Si]),
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C vacancies (V#sub[C]), nitrogen substitutions (N#sub[Si]), and aluminum substitutions (Al#sub[C]).
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Considering the symmetry of 4H-SiC, which is p63mc (cite),
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there are two different sites, k and h,
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which can be approximated as cubic (k) or hexagonal (h) based on the local environment.
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For point defect models, we considered five different structures,
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including Si vacancies (V#sub[Si]), C vacancies (V#sub[C]),
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nitrogen substitutions (N#sub[Si]), aluminum substitutions (Al#sub[C]),
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and the structure of a nitrogen substitute carbon and carbon substitute silicon (N#sub[C]C#sub[Si])
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which is proposed by xxx (ref) to be a possible structure of nitrogen doping.
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Besides,
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For surface defect models, larger models where used to ensure the accuracy of the phonon properties.
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（图：a k 位与 h 位对比 b 面内与面外对比）
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因此对于无缺陷和点缺陷的模型，我们使用 xxA x xxA x xxA 的模型大小。
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对于面缺陷，一个更大的 xxA x xxA x xxA 的模型被使用。
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点缺陷模型考虑了哪些结构
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面缺陷模型考虑了哪些结构
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对于面缺陷模型，我们主要考虑了三类 BPD（引用自己的文章），这些缺陷在室温下被认为是可以稳定存在的。
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对于每类BPD，我们考虑两个模型，一个将两个 PD 包括在内，为了模拟 PBD 未分解或分解后边缘处的信号；
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另一类则仅仅包含一个贯穿的层错，为了模拟 BPD 分解后在层错处的信号。
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计算工具和参数
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第一性原理计算使用 VASP，使用 PBE PAW，平面波截断能在弛豫时使用 xx，在计算声子时提高到 xx。
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K 点网格根据模型大小不同，分别使用 xxx 和 xxx。
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涂抹使用 xxx 以统一比较点缺陷和无缺陷的模型。
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弛豫的精度为 xxx。
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声子计算使用 phonopy phono3py ufo，BEC 修正使用 xxx 的算法。（引用）
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First-principles calculations were performed using Vienna Ab-initio Simulation Package (VASP) @kresse_efficiency_1996.
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The Perdew–Burke–Ernzerhof (PBE) exchange energy @ernzerhof_assessment_1999
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and projector-augmented wave (PAW) representation @kresse_ultrasoft_1999
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were used along with a cutoff energy of 400 eV,
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a Gamma-centered k-point mesh of 3 #sym.times 3 #sym.times 1,
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and a self-consistent convergence criterion of $1 times 10^(-3)$ eV.
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The ionic relaxation was performed until the energies converged to $1 times 10^(-2)$ eV.
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