Merge pull request #304 from Exabyte-io/feature/SOF-7530

feature/SOF 7530

Author: VsevolodX

images/tutorials/materials/heterostructures/heterostructure-silicon-silicon-dioxide-hafnium-dioxide-titanium-nitride/import-standata.webp

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+---
+# YAML header
+render_macros: true
+---
+
+# Creating High-k Metal Gate Stack: Si/SiO2/HfO2/TiN
+
+## Introduction
+
+This tutorial demonstrates how to create a high-k metal gate stack heterostructure consisting of four materials: Si (substrate), SiO2 (gate oxide), HfO2 (high-k dielectric), and TiN (metal gate). The process involves:
+
+1. Creating individual slabs for HfO2 and TiN
+2. Building the Si/SiO2 interface using strain matching
+3. Adding the pre-created slabs sequentially using simple interface builder
+
+We use the [Materials Designer](../../../materials-designer/overview.md) to create the high-k metal gate stack as shown in the figure below.
+
+![High-k Metal Gate Stack](/images/tutorials/materials/heterostructures/heterostructure-silicon-silicon-dioxide-hafnium-dioxide-titanium-nitride/original-figure.webp "High-k Metal Gate Stack")
+
+## 1. Set Up Materials
+
+First, navigate to Materials Designer and import from [Standata](../../../materials-designer/header-menu/input-output/standata-import.md) the following materials:
+
+- Silicon (Si)
+- Silicon dioxide (SiO2)
+- Hafnium dioxide (HfO2)
+- Titanium nitride (TiN)
+
+![Standata Import](/images/tutorials/materials/heterostructures/heterostructure-silicon-silicon-dioxide-hafnium-dioxide-titanium-nitride/import-standata.webp "Standata Import")
+
+## 2. Create HfO2 and TiN Slabs
+
+Before building the stack, we need to create properly terminated slabs for HfO2 and TiN.
+
+### 2.1. Create HfO2 Slab
+
+More detailed instructions on slab creation can be found in the [SrTiO3 Slab](slab-strontium-titanate.md) tutorial.
+
+Open `create_slab_with_termination.ipynb` and set parameters:
+
+```python
+# HfO2 slab parameters
+MILLER_INDICES = (0, 0, 1)
+THICKNESS = 4  # atomic layers
+VACUUM = 0.5  # Angstroms
+XY_SUPERCELL_MATRIX = [[1, 0], [0, 2]]
+USE_ORTHOGONAL_Z = True
+USE_CONVENTIONAL_CELL = True
+
+# Select termination (usually first one is fine)
+TERMINATION_INDEX = 0
+```
+
+Run the notebook to create the HfO2 slab and pass it to Materials Designer.
+
+![HfO2 slab](/images/tutorials/materials/heterostructures/heterostructure-silicon-silicon-dioxide-hafnium-dioxide-titanium-nitride/wave-result-hfo2-slab-wave.webp "HfO2 slab")
+
+### 2.2. Create TiN Slab
+
+Open another instance of `create_slab_with_termination.ipynb` for TiN:
+
+```python
+# TiN slab parameters
+MILLER_INDICES = (0, 0, 1)
+THICKNESS = 3  # atomic layers
+VACUUM = 10.0  # Angstroms - more vacuum for final layer
+XY_SUPERCELL_MATRIX = [[1, 0], [0, 1]]
+USE_ORTHOGONAL_Z = True
+USE_CONVENTIONAL_CELL = True
+
+TERMINATION_INDEX = 0
+```
+
+Run the notebook to create and pass the TiN slab to Materials Designer.
+
+![TiN slab](/images/tutorials/materials/heterostructures/heterostructure-silicon-silicon-dioxide-hafnium-dioxide-titanium-nitride/wave-result-tin-slab.webp "TiN slab")
+
+## 3. Create Si/SiO2 Interface
+
+### 3.1. Launch ZSL Interface Builder
+
+Open `create_interface_with_min_strain_zsl.ipynb` and configure:
+
+```python
+MAX_AREA = 200  # Maximum area for strain matching
+MAX_AREA_RATIO_TOLERANCE = 0.25  # Maximum area ratio tolerance
+MAX_ANGLE_TOLERANCE = 0.15  # Maximum angle tolerance
+MAX_LENGTH_TOLERANCE = 0.15  # Maximum length tolerance
+
+FILM_INDEX = 1  # SiO2
+FILM_MILLER_INDICES = (1, 0, 0)
+FILM_THICKNESS = 3
+FILM_XY_SUPERCELL_MATRIX = [[1, 0], [0, 1]]
+FILM_VACUUM = 0.0
+FILM_USE_ORTHOGONAL_Z = True
+
+SUBSTRATE_INDEX = 0  # Si
+SUBSTRATE_MILLER_INDICES = (1, 0, 0)
+SUBSTRATE_THICKNESS = 4
+SUBSTRATE_XY_SUPERCELL_MATRIX = [[1, 0], [0, 1]]
+SUBSTRATE_VACUUM = 5.0
+SUBSTRATE_USE_ORTHOGONAL_Z = True
+
+INTERFACE_DISTANCE = 2.5  # Angstroms
+INTERFACE_VACUUM = 5.0  # Angstroms
+TERMINATION_PAIR_INDEX = 0
+```
+
+We set a higher tolerances to achieve smaller cell with higher strain of the film (SiO2).
+
+![Interface Setup](/images/tutorials/materials/heterostructures/heterostructure-silicon-silicon-dioxide-hafnium-dioxide-titanium-nitride/jl-setup-notebook-si-sio2.webp "Interface Setup")
+
+### 3.2. Create Initial Interface
+
+Run the notebook to create the Si/SiO2 interface. This is the most critical interface, so we use strain matching to optimize it.
+
+## 4. Add HfO2 Layer
+
+### 4.1. Configure Simple Interface Builder
+
+Open JupyterLite Session again and select the Si/SiO2 interface and HfO2 slab as input materials.
+
+Open `create_interface_with_no_strain.ipynb` and set:
+
+```python
+# Important: Disable slab creation since we're using pre-created slab
+ENABLE_FILM_SCALING = True
+CREATE_SLABS = False  # We already have our HfO2 slab
+
+FILM_INDEX = 1  # Pre-created HfO2 slab
+SUBSTRATE_INDEX = 0  # Si/SiO2 structure
+
+# Interface parameters
+INTERFACE_DISTANCE = 2.5  # Angstroms
+INTERFACE_VACUUM = 0.5  # Angstroms
+```
+
+Film is the material that will be strained (scaled) to match the substrate.
+
+![HfO2 Interface Setup](/images/tutorials/materials/heterostructures/heterostructure-silicon-silicon-dioxide-hafnium-dioxide-titanium-nitride/jl-setup-notebook-si-sio2-hfo2.webp "HfO2 Interface Setup")
+
+### 4.2. Add HfO2
+
+Run the notebook to add the pre-created HfO2 slab to the Si/SiO2 structure.
+
+![Si/SiO2/HfO2](/images/tutorials/materials/heterostructures/heterostructure-silicon-silicon-dioxide-hafnium-dioxide-titanium-nitride/wave-result-si-sio2-hfo2.webp "Si/SiO2/HfO2")
+
+## 5. Add TiN Layer
+
+### 5.1. Configure Final Layer Addition
+
+Similar to steps in Section 4, we add the TiN layer to the Si/SiO2/HfO2 stack.
+
+Use `create_interface_with_no_strain.ipynb` again:
+
+```python
+# Keep slabs disabled
+ENABLE_FILM_SCALING = True
+CREATE_SLABS = False  # Using pre-created TiN slab
+
+FILM_INDEX = 1  # Pre-created TiN slab
+SUBSTRATE_INDEX = 0  # Si/SiO2/HfO2 structure
+
+# Final interface parameters
+INTERFACE_DISTANCE = 2.5  # Angstroms
+INTERFACE_VACUUM = 10.0  # Final vacuum spacing
+```
+
+### 5.2. Complete the Stack
+
+Run the notebook to add the TiN layer and complete the stack.
+
+![Final Stack](/images/tutorials/materials/heterostructures/heterostructure-silicon-silicon-dioxide-hafnium-dioxide-titanium-nitride/wave-result-si-sio2-hfo2-tin.webp "Final Stack")
+
+The user then can [save or download](../../../materials-designer/header-menu/input-output.md) the material in Material JSON format or POSCAR format.
+
+## Interactive JupyterLite Notebook
+
+The following JupyterLite notebook demonstrates the process of creating target material. Select "Run" > "Run All Cells".
+
+{% with origin_url=config.extra.jupyterlite.origin_url %}
+{% with notebooks_path_root=config.extra.jupyterlite.notebooks_path_root %}
+{% with notebook_name='specific_examples/heterostructure_high_k_metal_gate_stack.ipynb' %}
+{% include 'jupyterlite_embed.html' %}
+{% endwith %}
+{% endwith %}
+{% endwith %}
+
+## References
+
+1. [QuantumATK tutorial](https://docs.quantumatk.com/tutorials/hkmg_builder/hkmg_builder.html)
+
+2. **D. A. Muller et al.**
+    "The electronic structure at the atomic scale of ultrathin gate oxides"
+    Nature 399, 758–761 (1999)
+    [DOI: 10.1038/21602](https://doi.org/10.1038/21602)
+
+3. **J. Robertson**
+    "High dielectric constant gate oxides for metal oxide Si transistors"
+    Reports on Progress in Physics 69, 327 (2006)
+    [DOI: 10.1088/0034-4885/69/2/R02](https://doi.org/10.1088/0034-4885/69/2/R02)
+
+## Tags
+
+`slab-creation`, `interfaces`, `high-k`, `metal-gate`, `semiconductor`, `heterostructure`, `strain-matching`, `Si`, `SiO2`, `HfO2`, `TiN`