Si（硅）晶体的生长方向是一个重要的概念，尤其在半导体工业中。这个概念涉及到晶体在生长过程中原子排列的方向，对晶体的性质和应用有重大影响。让我为您详细解释：
-
晶体生长方向的定义：
- 晶体生长方向指的是晶体在形成过程中，新的原子层沿着特定晶向堆积的方向。
- 这个方向通常用密勒指数来表示，如 <100>、<110>、<111> 等。
-
Si晶体的常见生长方向：
- <100>：沿着立方晶格的边生长
- <110>：沿着立方晶格的面对角线生长
- <111>：沿着立方晶格的体对角线生长
-
生长方向的重要性：
- 影响晶体的物理和电学性质
- 决定了晶体的表面特性和加工性能
- 对半导体器件的性能有直接影响
-
在半导体工业中的应用：
- 不同生长方向的Si晶体用于制造不同类型的半导体器件
- 例如，<100>方向的Si晶片常用于制造CMOS器件
-
生长方向的选择：
- 根据具体应用需求选择合适的生长方向
- 考虑因素包括晶体缺陷、表面平整度、电子迁移率等
-
生长方向的控制：
- 通过控制生长条件（如温度、压力、气氛）来影响生长方向
- 使用特定取向的种子晶体来引导生长
理解Si晶体的生长方向对于半导体材料的研究和应用非常重要，它直接影响了最终器件的性能和制造工艺。在实际应用中，选择适当的生长方向可以优化器件性能，提高产品质量。
100方向
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d.art3d import Line3DCollection
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
def calculate_distance(atom1, atom2):
return np.sqrt(np.sum((np.array(atom1) - np.array(atom2))**2))
def plot_silicon_double_unit_cell():
fig = plt.figure(figsize=(12, 10))
ax = fig.add_subplot(111, projection="3d")
vertices = np.array([
[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0],
[0, 0, 1], [1, 0, 1], [1, 1, 1], [0, 1, 1],
])
face_center_atoms = np.array([
[0.5, 0, 0], [0.5, 1, 0], [0.5, 0, 1], [0.5, 1, 1],
[0, 0.5, 0], [1, 0.5, 0], [0, 0.5, 1], [1, 0.5, 1],
[0, 0, 0.5], [1, 0, 0.5], [1, 1, 0.5], [0, 1, 0.5],
])
internal_atoms = np.array([
[0.25, 0.25, 0.25],
[0.75, 0.75, 0.25],
[0.25, 0.75, 0.75],
[0.75, 0.25, 0.75],
])
all_atoms = np.vstack([vertices, face_center_atoms, internal_atoms])
edges = [
[0, 1], [1, 2], [2, 3], [3, 0],
[4, 5], [5, 6], [6, 7], [7, 4],
[0, 4], [1, 5], [2, 6], [3, 7]
]
direction = [1, 0, 0]
translation_vector = np.array(direction)
vertices2 = vertices + translation_vector
face_center_atoms2 = face_center_atoms + translation_vector
internal_atoms2 = internal_atoms + translation_vector
all_atoms2 = np.vstack([vertices2, face_center_atoms2, internal_atoms2])
edge_lines1 = [[vertices[start], vertices[end]] for start, end in edges]
edge_collection1 = Line3DCollection(edge_lines1, colors='black', linewidths=1)
ax.add_collection3d(edge_collection1)
edge_lines2 = [[vertices2[start], vertices2[end]] for start, end in edges]
edge_collection2 = Line3DCollection(edge_lines2, colors='gray', linewidths=1)
ax.add_collection3d(edge_collection2)
ax.scatter(vertices[:, 0], vertices[:, 1], vertices[:, 2], color='blue', s=100, label="Corner Atom")
ax.scatter(vertices2[:, 0], vertices2[:, 1], vertices2[:, 2], color='blue', s=100)
ax.scatter(face_center_atoms[:, 0], face_center_atoms[:, 1], face_center_atoms[:, 2], color='green', s=100, label="Face Atom")
ax.scatter(face_center_atoms2[:, 0], face_center_atoms2[:, 1], face_center_atoms2[:, 2], color='green', s=100)
ax.scatter(internal_atoms[:, 0], internal_atoms[:, 1], internal_atoms[:, 2], color='red', s=100, label="Internal Atom")
ax.scatter(internal_atoms2[:, 0], internal_atoms2[:, 1], internal_atoms2[:, 2], color='red', s=100)
# 添加内部原子与最近4个原子的连线
for internal_atom in np.vstack([internal_atoms, internal_atoms2]):
distances = [calculate_distance(internal_atom, atom) for atom in np.vstack([all_atoms, all_atoms2])]
nearest_indices = np.argsort(distances)[1:5] # 排除自身
for nearest_index in nearest_indices:
nearest_atom = np.vstack([all_atoms, all_atoms2])[nearest_index]
ax.plot([internal_atom[0], nearest_atom[0]],
[internal_atom[1], nearest_atom[1]],
[internal_atom[2], nearest_atom[2]], color='orange', linewidth=1)
# 添加指定的连线
specified_connections = [
([1.25, 0.25, 0.25], [1, 0, 0.5]),
([1.25, 0.25, 0.25], [1.5, 0, 0]),
([1.25, 0.75, 0.75], [1, 1, 0.5]),
([1.25, 0.75, 0.75], [1.5, 1, 1]),
]
for start, end in specified_connections:
ax.plot([start[0], end[0]],
[start[1], end[1]],
[start[2], end[2]], color='orange', linewidth=2, linestyle='--')
arrow_start = np.array([0, 0, 0])
arrow_end = translation_vector
ax.quiver(arrow_start[0], arrow_start[1], arrow_start[2],
arrow_end[0], arrow_end[1], arrow_end[2],
color='purple', linewidth=2, arrow_length_ratio=0.1)
mid_point = (arrow_start + arrow_end) / 2
ax.text(mid_point[0], mid_point[1], mid_point[2], f"[{direction[0]}{direction[1]}{direction[2]}]", color='purple')
max_range = np.array([vertices2[:, 0].max() - vertices[:, 0].min(),
vertices2[:, 1].max() - vertices[:, 1].min(),
vertices2[:, 2].max() - vertices[:, 2].min()]).max()
mid_x = (vertices2[:, 0].max() + vertices[:, 0].min()) * 0.5
mid_y = (vertices2[:, 1].max() + vertices[:, 1].min()) * 0.5
mid_z = (vertices2[:, 2].max() + vertices[:, 2].min()) * 0.5
ax.set_xlim(mid_x - max_range * 0.5, mid_x + max_range * 0.5)
ax.set_ylim(mid_y - max_range * 0.5, mid_y + max_range * 0.5)
ax.set_zlim(mid_z - max_range * 0.5, mid_z + max_range * 0.5)
ax.set_xlabel("X")
ax.set_ylabel("Y")
ax.set_zlabel("Z")
ax.legend(loc='upper left')
plt.title(f"双晶硅晶胞 (Double Silicon Unit Cell) - [100] Growth Direction")
plt.tight_layout()
plt.show()
plot_silicon_double_unit_cell()
其他方向
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d.art3d import Line3DCollection
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
def calculate_distance(atom1, atom2):
"""计算两点之间的欧几里得距离"""
return np.sqrt(np.sum((np.array(atom1) - np.array(atom2))**2))
def plot_silicon_double_unit_cell(direction):
fig = plt.figure(figsize=(12, 10))
ax = fig.add_subplot(111, projection="3d")
vertices = np.array([
[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0],
[0, 0, 1], [1, 0, 1], [1, 1, 1], [0, 1, 1],
])
face_center_atoms = np.array([
[0.5, 0, 0], [0.5, 1, 0], [0.5, 0, 1], [0.5, 1, 1],
[0, 0.5, 0], [1, 0.5, 0], [0, 0.5, 1], [1, 0.5, 1],
[0, 0, 0.5], [1, 0, 0.5], [1, 1, 0.5], [0, 1, 0.5],
])
internal_atoms = np.array([
[0.25, 0.25, 0.25],
[0.75, 0.75, 0.25],
[0.25, 0.75, 0.75],
[0.75, 0.25, 0.75],
])
all_atoms = np.vstack([vertices, face_center_atoms, internal_atoms])
edges = [
[0, 1], [1, 2], [2, 3], [3, 0],
[4, 5], [5, 6], [6, 7], [7, 4],
[0, 4], [1, 5], [2, 6], [3, 7]
]
if direction == [1, 0, 0]:
translation_vector = np.array([1, 0, 0])
elif direction == [1, 1, 0]:
translation_vector = np.array([1, 1, 0])
elif direction == [1, 1, 1]:
translation_vector = np.array([1, 1, 1])
vertices2 = vertices + translation_vector
face_center_atoms2 = face_center_atoms + translation_vector
internal_atoms2 = internal_atoms + translation_vector
all_atoms2 = all_atoms + translation_vector
edge_lines1 = [[vertices[start], vertices[end]] for start, end in edges]
edge_collection1 = Line3DCollection(edge_lines1, colors='black', linewidths=1)
ax.add_collection3d(edge_collection1)
edge_lines2 = [[vertices2[start], vertices2[end]] for start, end in edges]
edge_collection2 = Line3DCollection(edge_lines2, colors='gray', linewidths=1)
ax.add_collection3d(edge_collection2)
ax.scatter(vertices[:, 0], vertices[:, 1], vertices[:, 2], color='blue', s=100, label="Corner Atom")
ax.scatter(vertices2[:, 0], vertices2[:, 1], vertices2[:, 2], color='blue', s=100)
ax.scatter(face_center_atoms[:, 0], face_center_atoms[:, 1], face_center_atoms[:, 2], color='green', s=100, label="Face Atom")
ax.scatter(face_center_atoms2[:, 0], face_center_atoms2[:, 1], face_center_atoms2[:, 2], color='green', s=100)
ax.scatter(internal_atoms[:, 0], internal_atoms[:, 1], internal_atoms[:, 2], color='red', s=100, label="Internal Atom")
ax.scatter(internal_atoms2[:, 0], internal_atoms2[:, 1], internal_atoms2[:, 2], color='red', s=100)
# 添加内部原子与最近4个原子的连线
for internal_atom in np.vstack([internal_atoms, internal_atoms2]):
distances = [calculate_distance(internal_atom, atom) for atom in np.vstack([all_atoms, all_atoms2])]
nearest_indices = np.argsort(distances)[1:5] # 排除自身
for nearest_index in nearest_indices:
nearest_atom = np.vstack([all_atoms, all_atoms2])[nearest_index]
ax.plot([internal_atom[0], nearest_atom[0]],
[internal_atom[1], nearest_atom[1]],
[internal_atom[2], nearest_atom[2]], color='orange', linewidth=1)
arrow_start = np.array([0, 0, 0])
arrow_end = translation_vector
ax.quiver(arrow_start[0], arrow_start[1], arrow_start[2],
arrow_end[0], arrow_end[1], arrow_end[2],
color='purple', linewidth=2, arrow_length_ratio=0.1)
mid_point = (arrow_start + arrow_end) / 2
ax.text(mid_point[0], mid_point[1], mid_point[2], f"[{direction[0]}{direction[1]}{direction[2]}]", color='purple')
max_range = np.array([vertices2[:, 0].max() - vertices[:, 0].min(),
vertices2[:, 1].max() - vertices[:, 1].min(),
vertices2[:, 2].max() - vertices[:, 2].min()]).max()
mid_x = (vertices2[:, 0].max() + vertices[:, 0].min()) * 0.5
mid_y = (vertices2[:, 1].max() + vertices[:, 1].min()) * 0.5
mid_z = (vertices2[:, 2].max() + vertices[:, 2].min()) * 0.5
ax.set_xlim(mid_x - max_range * 0.5, mid_x + max_range * 0.5)
ax.set_ylim(mid_y - max_range * 0.5, mid_y + max_range * 0.5)
ax.set_zlim(mid_z - max_range * 0.5, mid_z + max_range * 0.5)
ax.set_xlabel("X")
ax.set_ylabel("Y")
ax.set_zlabel("Z")
ax.legend(loc='upper left')
plt.title(f"双晶硅晶胞 (Double Silicon Unit Cell) - [{direction[0]}{direction[1]}{direction[2]}] Growth Direction")
plt.tight_layout()
plt.show()
# 调用函数绘制三种不同晶向的生长情况
directions = [[1, 0, 0], [1, 1, 0], [1, 1, 1]]
for direction in directions:
plot_silicon_double_unit_cell(direction)
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