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(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` diff --git a/mkdocs.yml b/mkdocs.yml index 0a00fdd7..5159fdeb 100644 --- a/mkdocs.yml +++ b/mkdocs.yml @@ -232,6 +232,7 @@ nav: - Interface between Graphene and hBN: tutorials/materials/specific/interface-2d-2d-graphene-boron-nitride.md - Interface between Copper and SiO2 (Cristobalite): tutorials/materials/specific/interface-3d-3d-copper-silicon-dioxide.md - Interface between Graphene and SiO2 (alpha-quartz): tutorials/materials/specific/interface-2d-3d-graphene-silicon-dioxide.md + - High-k Metal Gate Stack (Si/SiO2/HfO2/TiN): tutorials/materials/specific/heterostructure-silicon-silicon-dioxide-hafnium-dioxide-titanium-nitride.md # COMMON UI COMPONENTS - Interface Components: