Building Epitaxial Interfaces

Tutorial Created with Software Release: 2026-3
Topics: Energy Capture & Storage, Metals, Alloys & Ceramics, Thin Film Processing
Products Used: MS Maestro

Tutorial files

1 MB
This tutorial is written for use with a 3-button mouse with a scroll wheel.
Words found in the Glossary of Terms are shown like this: Workspacethe 3D display area in the center of the main window, where molecular structures are displayed

 

Tip: You can hover over a glossary term to display its definition. You can click on an image to expand it in the page.
Abstract:

In this tutorial, we will learn how to use the Interface Builder panel to create epitaxial interfaces between two crystalline materials. To do this, we will find compatible crystallographic orientations between the two materials by performing topological matching, then analyze the found matches and identify those with minimal strain and supercell area. We will then generate slab structures containing interfaces with various terminations between layers of various thicknesses.

Tutorial Content

  1. Introduction to Interface Building

  1. Creating Projects and Importing Structures

  1. Performing a Topological Matching Search

  1. Building Interfaces

  1. Conclusion and References

  1. Glossary of Terms

1. Introduction to Interface Building

Interfaces play an important role in materials science, as they dictate how two materials combine and interact in a functional device. They are central to technologies ranging from semiconductor devices and optical coatings to catalytic surfaces and corrosion-resistant barriers. Heteroepitaxial interfaces occur where a crystalline film is in contact with a crystalline substrate of different composition. Grain boundaries are an example of homoepitaxy, where interfaces exist between different crystallographic orientations of the same material.

In order to build an atomistic model of an interfacial system, we have to predict which crystallographic orientations allow coherent matching of the two materials. A supercell of one material (the ‘film’) is strained slightly so as to epitaxially fit an unstrained supercell of the other material (the ‘substrate’). The choice of Miller indices determines the lattice mismatch, the interfacial strain, and ultimately the stability of the heterostructure. Identifying pairs of compatible surface orientations by hand is tedious, particularly when both materials have low-symmetry unit cells or when many orientations must be screened.

The Interface Builder panel constructs heteroepitaxial substrate-film interfaces from the two periodic bulk crystal structures that are inputted. The panel operates in two sequential stages. First, it automates the workflow of finding compatible crystallographic orientations between the two materials by enumerating substrate-film Miller index pairs, generating supercells and assessing the topological match between them. Lattices are matched when the translational symmetry of the two-dimensional interface is compatible (to some precision) with that of both bulk materials on either side of the interface. This is based on the algorithm proposed by Zur and McGill [Zur, A. McGill, T. C. Lattice match: An application to heteroepitaxy. J. Appl. Phys. 55.2, 378–386, (1984)]. The matched Miller index pairs are ranked by match area and von Mises strain. The results are presented as an interactive heatmap from which promising pairs can be selected. Second, for each selected pair the panel builds an atomistic slab interface model with user-defined terminations, slab thicknesses, vacuum spacing, and substrate–film separation, ready for downstream density functional theory (DFT) or molecular dynamics (MD) calculations.

Note that the Surface Energy Calculations panel is available for building slabs of (h k l)-oriented surfaces of individual materials and computing the surface energy of the exposed faces.

This tutorial provides step-by-step instructions for running a topological matching job, interpreting the output heatmap, selecting Miller index pairs (Section 3), and configuring interface parameters to build an atomistic interface model (Section 4). The overall workflow is summarized below:

In this tutorial we construct interfaces between a copper (Cu) substrate and a silicon nitride (Si₃N₄) film. This pairing is relevant to power electronics, where copper serves as a high-thermal-conductivity substrate or metallization layer and silicon nitride acts as a passivating and insulating dielectric film. In power semiconductor packaging, these materials meet at interfaces that must withstand high operating temperatures, large current densities, and repeated thermal cycling – making interfacial adhesion and structural stability critical design considerations. The different crystal systems (FCC metal vs. hexagonal ceramic) produce a rich set of topological matches with a range of strains and match areas, illustrating the value of systematic screening over manual inspection.

2. Creating Projects and Importing Structures

At the start of the session, change the file path to your chosen Working Directorythe location where files are saved in MS Maestro to make file navigation easier. Each session in MS Maestro begins with a default Scratch Projecta temporary project in which work is not saved, closing a scratch project removes all current work and begins a new scratch project, which is not saved. A MS Maestro project stores all your data and has a .prj extension. A project may contain numerous entries corresponding to imported structures, as well as the output of modeling-related tasks. Once a project is saved, the project is automatically saved each time a change is made.

Structures can be built in MS Maestro or can be imported using File > Import Structures (or drag-and-dropped), and are added to the Entry Lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion and Project Tabledisplays the contents of a project and is also an interface for performing operations on selected entries, viewing properties, and organizing structures and data. The Entry Lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion is located to the left of the Workspacethe 3D display area in the center of the main window, where molecular structures are displayed. The Project Tabledisplays the contents of a project and is also an interface for performing operations on selected entries, viewing properties, and organizing structures and data can be accessed by Ctrl+T (Cmd+T) or Window > Project Table if you would like to see an expanded view of your project data.

  1. Double-click the Materials Science icon

Figure 2-1. Change Working Directory option.

  1. Go to File > Change Working Directory
  2. Find your directory, and click Choose
  3. Pre-generated files are included for running jobs or examining output. Download the zip file here: schrodinger.com/sites/default/files/s3/release/current/Tutorials/zip/interface_builder.zip
  4. After downloading the zip file, unzip the contents in your Working Directorythe location where files are saved for ease of access throughout the tutorial

Figure 2-2. Save Project panel.

  1. Go to File > Save Project As
  2. Change the File name to interface_builder_tutorial, click Save
    • The project is now named interface_builder_tutorial.prj

Figure 2-3. Importing the input files.

  1. Go to File > Import Structures
  2. Navigate to where you downloaded the provided tutorial files (presumably in your Working Directorythe location where files are saved), and choose the file copper_silicon-nitride_bulk.maegz
  3. Click Open
    • A new entry group is added to your Entry Lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion named copper_silicon-nitride_bulk (2). It contains two entries, one for copper (Cu) and one for silicon nitride (beta-Si3N4).
    • These bulk structures have been previously optimized and are thus unstrained. See the Electronic Structure Calculations of Bulk Crystals Using Quantum ESPRESSO tutorial to learn more.

3. Performing a Topological Matching Search

In this section, we will perform topological matching of the substrate and film to identify Miller index combinations that minimize strain and area.

Figure 3-1. The interface builder panel.

  1. Go to Tasks > Materials > Structure Builders > Build Interfaces

Let’s get a brief overview of the panel:

The top of the panel is for importing structures and intermediate results. Structures of bulk substrate and film can be specified and imported. The supercell specified as the film is strained slightly so as to epitaxially fit an unstrained supercell of the material specified as the substrate. Optionally, the results of an earlier topological matching search can be imported.

The Select Interfaces section in the middle of the panel will show the results of the topological matching in the form of a heatmap.

The Options For Building Interfaces section at the lower part of the panel contains a parameter table where each row will specify an interface slab that is to be built.

The Run button is at the bottom of the panel.  Please note that this button is context-aware: if no topological matching results are loaded, clicking Run launches a topological matching job. If results are loaded and interface rows are defined in the table, clicking Run launches an interface construction job.

Figure 3-2. Settings and running the topological matches search.

  1. Ensure the entry Cu is includedthe entry is represented in the Workspace, the circle in the In column is blue in the Workspacethe 3D display area in the center of the main window, where molecular structures are displayed
  2. For Substrate, choose Included entry
  3. Click Import
    • The Cu structure is loaded into the panel as the ‘substrate’, i.e. the material that remains unstrained
  4. Includethe entry is represented in the Workspace, the circle in the In column is blue the entry beta-Si3N4 in the Workspacethe 3D display area in the center of the main window, where molecular structures are displayed
  5. For Film, choose Included entry
  6. Click Import
    • The beta-Si3N4 structure is loaded into the panel as the ‘film’, i.e. the material that will be strained
  7. Ensure the Maximum Miller index for topological matches is set to 3
    • This is the upper bound on positive and negative Miller indices of surface planes (h k l) that will be enumerated for both substrate and film, i.e. all combinations of -3≤h≤3, -3≤k≤3, and -3≤l≤3.
    • Low-index surfaces (0, 1, & sometimes 2) are usually the most stable and most likely to form interfaces. Extending the search to a maximum index of 4 would increase the computational time for this step.
  8. Change the Job name to interface_builder_Cu_beta-Si3N4_topological_matches
  9. Adjust the Job Settings () as needed
    • This job can be run on a CPU host and takes less than 5 minutes to complete in serial
  10. If you would like to run the job yourself, click Run. Otherwise, you can proceed and import provided results from the zip file in the next step.

Figure 3-3. Importing the provided results for the topological matching search.

In case you did run the job yourself, upon completion the results are automatically incorporated into the panel and the substrate and film structures are added to the Entry Lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion.

In case you want to proceed with the provided results follow the next steps to import them:

  1. For Topological matches output, click on Import File
    • This option gives us a way to restart building an interface from a previously-run topological match
  2. Browse to the provided files and select Section_03 > interface_builder_Cu_beta-Si3N4_topological-matches > interface_builder_Cu_beta-Si3N4_topological-matches_topological_matches.csv, then click Open

The quality, stability and feasibility of the interfacial matches that we have found can be ranked based on two key properties.

The match area is the minimum supercell area required for lattice coincidence between the surface unit cells of the substrate and film. It reflects the size of the coincidence site lattice. A smaller match area means a smaller periodic repeat at the interface, fewer atoms per cell and therefore more computationally feasible models for subsequent DFT or MD calculations. A smaller match area also means a higher density of coincidence sites, which generally correlates with stronger interface bonding. Very large match areas imply that the two lattices barely match, so that the interface is likely incoherent, and the resulting supercell may be too large for practical atomistic simulations.

Von Mises strain quantifies the amount of geometric distortion (stretching, compression, or shearing) of the film lattice that is required to make it align perfectly with the fixed substrate surface lattice. It reduces the complete 2D strain tensor to a single scalar that encompasses both the normal and shear components. Lower strain results in less elastic energy stored at the interface, a lower driving force for misfit dislocation nucleation, better adhesion and mechanical stability, and more realistic coherent epitaxy. In practice, high-strain matches are unlikely to form coherent interfaces, as the film will either relax through defects or not grow epitaxially at all.

The ideal match has low strain and a small area. The heatmap in the panel allows us to visually identify this sweet spot. In practice, however, we must make trade-offs. For example, a slightly higher strain match with a much smaller supercell may be more useful than a zero-strain match that requires thousands of atoms in the cell.

Figure 3-4. The best topological matches displayed in a heatmap.

The total number of topological matches is displayed in the top right-hand corner, and the Select Interfaces section in the middle of the panel is populated with a heatmap showing the most promising topological matches. These are the ones with the lowest match area (color, Å2) and lowest film von Mises strain (number, %). The horizontal axis shows the Miller indices for the substrate and the vertical axis shows the indices for the film. You can find all matches and their properties in the *_matches.csv file for this job.

  1. Set the option for Plot this number of lowest area matches to 8
  2. Set the option for Plot this number of lowest film von Mises strain matches to 8

In our case, 72 total matches were found. Those with the lowest area and strain are displayed in the heatmap. Because of duplicates, the number of matches displayed may be lower than the numbers specified.

We can now select specific Miller index combinations that are topological matches with low area and low strain. In the next section, we will select the two matches with the lowest area (2 1 0) - (1 1 0) and lowest strain (1 1 1) - (2 1 0), respectively, and specify their terminations, layer thickness and other structural parameters.

Alternatively, in the case of epitaxial film growth, the orientation of the substrate may be predetermined - e.g. Cu(1 1 1) - and the allowed orientations of epitaxial films can be read off that column of the heatmap.

4. Building Interfaces

In this section, we will generate interfaces with different terminations for two of the Miller index pairs we identified in the previous section that minimize strain and area.

Figure 4-1. The reloaded results for the topological matches search displayed in a heatmap.

In case you have closed the Interface Builder panel follow the next steps to reopen the panel and load the results of the topological matching search:

  1. Go to Tasks > Materials > Structure Builders > Build Interfaces
  2. For Topological matches output, click on Import File
    • This option gives us a way to restart building an interface from a previously-run topological match

Either load your own or the provided results. For your own results:

  1. Browse to your Working Directorythe location where files are saved and select interface_builder_Cu_beta-Si3N4_topological-matches > interface_builder_Cu_beta-Si3N4_topological-matches_topological_matches.csv, then click Open

For loading the provided results:

  1. Browse to the provided files and select Section_03 > interface_builder_Cu_beta-Si3N4_topological-matches > interface_builder_Cu_beta-Si3N4_topological-matches_topological_matches.csv, then click Open
  2. Set the option for Plot this number of lowest area matches to 8
  3. Set the option for Plot this number of lowest film von Mises strain matches to 8

We can now select specific Miller index combinations from the heatmap. This will populate the table in the Options For Building Interfaces section of the panel, which we will then build as slabs. We will select the two matches with the lowest area (2 1 0) - (1 1 0) and lowest strain (1 1 1) - (2 1 0), respectively, and specify their terminations, layer thickness and other structural parameters.

Figure 4-2. Selecting the match with the lowest area.

  1. Click on the cell (2 1 0) - (1 1 0) to create a new row for this match in the Options For Building Interfaces table

The table contains the adjustable parameters for building interfaces.

The substrate/film termination defines which atomic plane is exposed at the interface. In some crystals, different terminations are possible for a given (h k l) depending on the location of the cleavage plane. Different terminations expose different atoms at the interface, affecting adhesion, reactivity, and charge transfer.

The substrate/film thickness (n) describes the number of oriented unit cells stacked along the surface normal. Note that this is generally not the same as the number of atomic planes. Additional columns show the resulting slab thickness in Å. The thickness usually needs to be large enough that the interior of each slab behaves in a bulk-like fashion, i.e. atoms at the center should not interact substantially with atoms at the exposed surface or at the interface. 6-10 Å is usually adequate. However, in some applications, the film thickness will be chosen to match that of an experimental thin film. In a production study, we would typically build interfaces at several substrate/film thicknesses and verify that computed properties converge with increasing thickness, ensuring that the slab interior of each slab behaves bulk-like. For this tutorial, we use a fixed value.

The vacuum over film is the vacuum gap above the film, needed to decouple periodic images along the surface normal. It needs to be large enough to prevent spurious interaction between periodic images. 6-10 Å is usually adequate. (To omit any vacuum and build a hetero-stack with two interfaces per cell, this parameter can be set to an appropriate value for substrate-film separation. However, note that the terminations at this interface can not be specified within the panel).

The substrate-film separation specifies the initial distance at the interface between the top of the substrate and the bottom of the film. The choice of this value depends on the expected bonding at the interface and is typically refined during geometry optimization of the built slab, e.g. in subsequent periodic DFT calculations with Quantum ESPRESSO. Trial and error may be needed to find a value for a particular interface that gives reasonable initial bond distances across the interface, with atoms neither too close nor too distant from one another.

Figure 4-3. Settings for building the interfaces of the match with the lowest area.

  1. Click on the cell (2 1 0) - (1 1 0) three more times to create three additional copies of this match in the Options For Building Interfaces table (total of four copies)
  2. Set the Substrate Thickness/n for all four rows to 5 layers
  3. Select a different Film Termination for each of the four rows; there is only one Substrate Termination
  4. Set the Film Thickness/n for all four rows to 2 layers
  5. Set the Substrate-Film Separation for all four rows to 2 Å

If you want to delete any row, just select it in the table and click Remove Selected Rows.

Figure 4-4. Settings for building the interfaces of the match with the lowest strain.

  1. Click on the cell (1 1 1) - (2 1 0) five times to create five copies of this match in the Options For Building Interfaces table
  2. Set the Substrate Thickness/n for all five rows to 4 layers
  3. Select a different Film Termination for each of the five rows
  4. Set the Film Thickness/n for all five rows to 3 layers
  5. Set the Substrate-Film Separation for all five rows to 2 Å

Figure 4-5. Naming and running the job to build the interfaces.

  1. Ensure the option Reduce to primitive cells is checked
    • This option reduces each built interface supercell to its smallest periodic repeat unit (primitive cell), removing redundant translational symmetry. This yields the most compact cell with the fewest atoms. Uncheck this option only if you specifically need the conventional (unreduced) supercell geometry.

There is an additional option to also return substrate and film slab structures, in case you want to separately examine the individual components of an interface.

  1. Change the Job name to interface_builder_Cu_beta-Si3N4_build_interfaces_210-110_111-210
  2. Adjust the Job Settings () as needed
    • This job can be run on a CPU host and takes less than 5 minutes to complete in serial
  3. If you would like to run the job yourself, click Run. Otherwise, you can proceed and import provided results from the zip file in the next step.
  4. Close the Interface Builder panel

Figure 4-6. The resulting entry groups for the generated interface.

In case you did run the job yourself, upon completion the results are automatically incorporated as a new entry group to the Entry Lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion.

In case you want to proceed with the provided results follow the next steps to import them:

  1. Go to File > Import Structures
  2. Navigate to where you downloaded the provided tutorial files (presumably in your Working Directorythe location where files are saved), and choose the file Section_04 > interface_builder_Cu_beta-Si3N4_build_interfaces_210-110_111-210 > interface_builder_Cu_beta-Si3N4_build_interfaces_210-110_111-210_interfaces.mae
  3. Click Open
    • Nine new entries in a series of subgroups are added to your Entry Lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion

One entry for every generated interface in a series of subgroups is added to the Entry List. The hierarchy of subgroups is as follows: (1) orientations of substrate and film in the interface, (2) interface termination of substrate and film, (3) thickness for substrate, film, vacuum, and gap (separation between substrate and film), (4) match area, (5) film von Mises strain.

Figure 4-7. Using the periodic structure tools to improve the visualization of the created interfaces.

The as-generated interface structures can have atoms outside the cells and bonds that are not displayed correctly. This is a visualization issue only, which we can remedy with the Periodic Structure Tools:

  1. Includethe entry is represented in the Workspace, the circle in the In column is blue all 9 interface entries
  2. Open the periodic structure tools from the toolbar at the bottom-right corner of MS Maestro
  3. Click Build Cell
  4. Select Translate to First Unit Cell and Recalculate Connectivity
  5. Check the option to Create new entry
  6. Click APPLY
  7. In the warning popup, click Continue
    • A new entry for every interface is added to the respective subgroup in the Entry Lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion

Figure 4-8. One of the Cu-(2 1 0) and Si3N4-(1 1 0) slabs in the output from the Interface Builder.

Inspect the four structures for the interface between Cu-(2 1 0) and Si3N4-(1 1 0).

In all cases, both Si and N atoms are present at the interface, although bonds to Cu are shown to only some of them at the chosen separation. We can expect more Cu-Si and Cu-N bonds to form at the interface if the structures are subsequently relaxed with DFT or MLFF. When relaxing substrate-film-vacuum structures, the substrate layers far from the interface would typically be constrained.

Some Si and N atoms can be seen to protrude from the exposed topmost surface - a consequence of preserving Si3N4 stoichiometry in the silicon nitride layer - and would probably also relax with DFT. The interface is built so as to be stoichiometric with no compositional defects, but this can either be changed manually by editing atoms or by using the Defect Setup Calculations panel, if desired.

Figure 4-9. One of the output slabs for the Cu-(1 1 1) and Si3N4-(2 1 0) interface.

Qualitatively similar geometries can be seen in the five slabs for the interface between Cu-(1 1 1) and Si3N4-(2 1 0), though here more Cu atoms from the smooth surface are available for bonding to Si or N.

Despite the presence of voids in the silicon nitride layer, the Interface Builder does not propose filling these voids with Cu atoms, or any other form of interfacial mixing.  Subsequent molecular dynamics simulations would be a way to explore interfacial chemistry of this sort.

The Interface Builder panel produces unrelaxed interface structures with an initial guess for the substrate-film separation. Relaxing the atomic positions with periodic DFT (Quantum ESPRESSO) or MLFF finds the equilibrium interfacial geometry, bond lengths, and separation distance. Learn more in the Electronic Structure Calculations of Bulk Crystals Using Quantum ESPRESSO, the Modeling Surfaces, and the Machine Learning Force Field tutorials. To introduce point defects and calculate their defect formation energy, refer to the Defect Formation Energy Calculation tutorial. From the relaxed structure, the adhesion energy can be computed as the difference between the total energy of the interface and the energies of the isolated substrate and film slabs. The adhesion energy is a key quantity for assessing interfacial stability and resistance to delamination.

For applications where operating conditions matter, such as power electronics, MD simulations at elevated temperatures can be used to probe the thermal stability of the interface under realistic thermal cycling conditions. This could be done with the MD Multistage Workflow panel. Please note that we advise using MLFF instead of classical force fields for all MD simulations containing inorganic systems.

5. Conclusion and References

In this tutorial, we learned how to use the Interface Builder panel to create interfaces between two crystalline materials. A supercell of one material (the ‘film’) is strained slightly so as to epitaxially fit an unstrained supercell of the other material (the ‘substrate’). To do this, we performed a topological matching search to identify compatible crystallographic orientations between the two materials, then we analyzed the matches and identified those with minimal strain and supercell area. Finally, we generated slab structures containing interfaces with various terminations between layers of various thicknesses.

For further learning:

For introductory content, focused on navigating the Schrödinger Materials Science interface, an Introduction to Materials Science Maestro tutorial is available. Please visit the materials science content library for access to events, publications, webinars, white papers, and more than 100 tutorials. For scientific inquiries or technical troubleshooting, submit a ticket to our Technical Support Scientists at help@schrodinger.com.

For self-paced, asynchronous, online courses in Materials Science modeling, including access to Schrödinger software, please visit the Schrödinger Online Learning portal on our website.

For some related practice, proceed to explore other relevant tutorials:

6. Glossary of Terms

Entry List - a simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion

Included - the entry is represented in the Workspace, the circle in the In column is blue

Project Table - displays the contents of a project and is also an interface for performing operations on selected entries, viewing properties, and organizing structures and data

Recent actions - This is a list of your recent actions, which you can use to reopen a panel, displayed below the Browse row. (Right-click to delete.)

Scratch Project - a temporary project in which work is not saved, closing a scratch project removes all current work and begins a new scratch project

Selected - (1) the atoms are chosen in the Workspace. These atoms are referred to as "the selection" or "the atom selection". Workspace operations are performed on the selected atoms. (2) The entry is chosen in the Entry List (and Project Table) and the row for the entry is highlighted. Project operations are performed on all selected entries

Working Directory - the location where files are saved

Workspace - the 3D display area in the center of the main window, where molecular structures are displayed