110 lines
6.9 KiB
XML
110 lines
6.9 KiB
XML
= Method
|
||
|
||
== 4H-SiC wafer details
|
||
|
||
外延片的厚度、掺杂浓度、生长 C/Si 比，斜切角度。
|
||
|
||
5 个 6 寸的 p 型外延片被使用，我们将它们称为 W#sub[i]。
|
||
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。
|
||
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。
|
||
生长时 Si/C 比分别为 0.7 1.2 1.6 2.4 2.0。、
|
||
所有外延片都有 4 度斜切。
|
||
|
||
Five 6-inch p-type epitaxial wafers (W#sub[1]–W#sub[5]) were fabricated on n-type substrates
|
||
using the step-flow growth method with a 4° offcut angle.
|
||
The Al doping concentrations, determined by SIMS,
|
||
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.
|
||
W#sub[1]–W#sub[4] had an epitaxial layer thickness of 1 μm, while W#sub[5] had a thickness of 2 μm.
|
||
The Si/C ratios during growth were 0.7, 1.2, 1.6, 2.4, and 2.0 for the five wafers, respectively.
|
||
|
||
== Raman experiments setup
|
||
|
||
拉曼设备的型号。激光的波长，背散射。共焦针孔。
|
||
|
||
拉曼设备的型号是 LabRAM HR Evolution，使用背散射。
|
||
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。
|
||
有三个不同的入射配置，包括正入射、掠入射、边入射。
|
||
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。
|
||
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。
|
||
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），
|
||
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）。
|
||
|
||
All Raman experiments were conducted using a LabRAM HR Evolution system in a back-scattering configuration,
|
||
where the scattered light was collected in the direction opposite to the incident laser.
|
||
A 532 nm laser was primarily used as the excitation source,
|
||
while a 325 nm laser was employed for only ultraviolet Raman measurements.
|
||
Three distinct incidence configurations were utilized, as illustrated in @figure-incidence:
|
||
(i) normal incidence, where the laser incident perpendicularly to the epitaxial surface;
|
||
(ii) grazing incidence, where the laser incident nearly parallelly to the epitaxial surface;
|
||
and (iii) edge incidence, where the laser is incident at the wafer edge and perpendicularly to the edge surface.
|
||
Considering the 4° offcut angle and the nearly isotropic refractive index of 2.73 for 4H-SiC @shaffer_refractive_1971,
|
||
the refracted laser in grazing incidence forms an angle of approximately 25° with the c axis.
|
||
A 100 μm confocal pinhole was used for normal incidence to enhance axial (z-direction) resolution @song_depth_2020,
|
||
while a 200 μm pinhole was employed for the other configurations to improve the signal-to-noise ratio.
|
||
The integration time was set to 60 seconds for normal and edge incidence,
|
||
while it was extended to 300 seconds for grazing incidence due to the weaker Raman signal.
|
||
|
||
#include "figure-incidence.typ"
|
||
|
||
== Atomic model establishment
|
||
|
||
我们建立了三类模型：无缺陷、点缺陷和面缺陷。
|
||
|
||
Three types of models were established: defect-free models, point defect models, and surface defect models.
|
||
|
||
无缺陷和点缺陷的模型
|
||
|
||
无缺陷和点缺陷的模型尺寸约为 $12.4 angstrom times 10.7 #sym.angstrom times 10.1 #sym.angstrom$，包含了大约 128 个原子。
|
||
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。
|
||
对于点缺陷模型，我们考虑了 Si 空位、C 空位、N 替位、Al 替位。
|
||
分别记为 V#sub[Si]、V#sub[C]、N#sub[Si] 和 Al#sub[C]。
|
||
考虑到 SiC 的对称性 p63mc （引用），有两个不同的位点，记为 k 和 h，
|
||
根据局部环境近似为立方（k）还是六角（h）。
|
||
此外，还有人提出，N 替换 C、C 替换 Si 的模型（引用），
|
||
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）。
|
||
|
||
The defect-free and point defect models were established using supercells
|
||
with dimensions of $12.4 #sym.angstrom times 10.7 #sym.angstrom times 10.1 #sym.angstrom$,
|
||
containing approximately 128 atoms.
|
||
This supercell size was found sufficient for accurately capturing the phonon properties
|
||
of both defect-free and point-defect-containing 4H-SiC,
|
||
as the calculated phonon frequencies for the defect-free model deviated by less than 5% from experimental values,
|
||
and further enlargement of the supercell yielded negligible changes.
|
||
Twelve point defect models were constructed,
|
||
including Si vacancies (V#sub[Si]-h and V#sub[Si]-k), C vacancies (V#sub[C]-h and V#sub[C]-k),
|
||
N substitutions at C sites (N#sub[C]-h and N#sub[C]-k),
|
||
Al substitutions at Si sites (Al#sub[Si]-h and Al#sub[Si]-k),
|
||
and complex defects involving N substitution at a C site followed by C substitution at a Si site
|
||
@gerstmann_formation_2003
|
||
(N#sub[C]C#sub[Si]-i-h, N#sub[C]C#sub[Si]-i-k, N#sub[C]C#sub[Si]-o-h and N#sub[C]C#sub[Si]-o-k).
|
||
Here, the suffixes -h and -k denote the quasi-hexagonal and quasi-cubic sites, respectively,
|
||
while -i and -o denote the in-plane and out-of-plane configurations.
|
||
|
||
（图：a hk 位置 b 复杂缺陷 强调在复杂缺陷中，h k 根据 N 原子而定）
|
||
|
||
面缺陷的模型
|
||
|
||
对于面缺陷模型，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。
|
||
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；
|
||
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。
|
||
|
||
== Simulation details
|
||
|
||
计算工具和参数
|
||
|
||
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。
|
||
K 点网格根据模型大小不同，分别使用 xxx 和 xxx。
|
||
涂抹使用 xxx 以统一比较点缺陷和无缺陷的模型。
|
||
弛豫的精度为 xxx。
|
||
声子计算使用 phonopy phono3py ufo，BEC 修正使用 xxx 的算法。（引用）
|
||
|
||
First-principles calculations were performed using Vienna Ab-initio Simulation Package (VASP) @kresse_efficiency_1996.
|
||
The Perdew–Burke–Ernzerhof (PBE) exchange energy @ernzerhof_assessment_1999
|
||
and projector-augmented wave (PAW) representation @kresse_ultrasoft_1999
|
||
were used along with a cutoff energy of 400 eV,
|
||
a Gamma-centered k-point mesh of 3 #sym.times 3 #sym.times 1,
|
||
and a self-consistent convergence criterion of $1 times 10^(-3)$ eV.
|
||
The ionic relaxation was performed until the energies converged to $1 times 10^(-2)$ eV.
|
||
|
||
|