Analyze lattice fit for layered crystals. Estimate strain, relaxation risk, and temperature corrected mismatch values. Use practical inputs for reliable thin film comparisons now.
| Film | Substrate | Film Constant (Å) | Substrate Constant (Å) | Mismatch (%) |
|---|---|---|---|---|
| GaAs | Si | 5.6533 | 5.4310 | 4.0932 |
| Ge | Si | 5.6580 | 5.4310 | 4.1797 |
| InP | GaAs | 5.8687 | 5.6533 | 3.8103 |
| Sample A | Sample B | 4.1200 | 4.1000 | 0.4878 |
Temperature corrected film constant: af,T = af,0 × film factor × [1 + αf × 10-6 × (Ttarget - Tref)]
Temperature corrected substrate constant: as,T = as,0 × substrate factor × [1 + αs × 10-6 × (Ttarget - Tref)]
Raw lattice mismatch: f = [(af,T - as,T) / as,T] × 100
Residual mismatch: fresidual = f × (1 - relaxation / 100)
In-plane strain: ε = fresidual / 100
Approximate dislocation spacing: D = b / |ε|
Approximate critical thickness: hc = b / [8π|ε|(1 + ν)]
These last two outputs are simplified engineering estimates. They are useful for quick screening.
Lattice mismatch measures the difference between a film crystal and a substrate crystal. It matters in epitaxy, semiconductor growth, and thin film design. A small mismatch often supports coherent growth. A large mismatch increases defects, dislocations, and stress. This calculator gives a quick way to estimate that difference.
A simple mismatch value is helpful, but advanced work usually needs more context. Temperature can shift lattice constants. Orientation can change the effective in-plane spacing. Partial relaxation can reduce stored strain after growth. Burgers vector and Poisson ratio can also support rough screening for dislocation spacing and critical thickness.
The calculator first corrects film and substrate constants for temperature. It then compares the corrected values to produce raw mismatch. After that, it applies the selected relaxation percentage. The remaining difference becomes residual mismatch. That value is converted into in-plane strain for easier interpretation.
A positive mismatch usually suggests a tensile film relative to the substrate. A negative mismatch usually suggests a compressive film. Both cases can change band structure, reliability, and interface quality. Designers often compare several material pairs before choosing a growth stack or process temperature.
Use the mismatch result for first-pass material screening. Use the residual value when you expect partial relaxation. Use the strain estimate when discussing film stress or coherence. Use the approximate dislocation spacing and critical thickness only as fast engineering checks. They do not replace detailed elasticity or growth models.
This page is useful for semiconductor wafers, oxide films, layered crystals, and research notes. It supports fast comparison work. It also helps students understand how lattice constants, thermal expansion, and relaxation interact. That makes the lattice mismatch calculator practical for both learning and pre-design evaluation.
Lattice mismatch is the percentage difference between the in-plane lattice constant of a film and that of its substrate. It helps predict strain, coherence, and possible defect formation in thin films.
Lattice constants change with temperature because materials expand or contract. Even small thermal differences can shift mismatch enough to alter strain, growth quality, and interface stability.
Relaxation describes how much strain is released after a film grows thicker or forms defects. A fully coherent film has zero relaxation. A fully relaxed film has little residual strain.
The orientation factor lets you adjust the effective lattice spacing when your comparison depends on crystal direction or plane selection. It is useful for more advanced in-plane matching studies.
No. The critical thickness shown here is a simplified estimate. Real values depend on full elasticity, interface quality, growth kinetics, and material specific defect behavior.
A positive mismatch usually means the film lattice constant is larger than the substrate value after corrections. That often points to tensile behavior when the film is forced to fit the substrate.
Yes. The mismatch formula is unitless, so any consistent unit works. Keep film constant, substrate constant, and Burgers vector in the same unit for correct spacing and thickness outputs.
Export when you want to document a material pair, compare process cases, or save screening results for a report. CSV is useful for data logs. PDF is useful for sharing.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.