Band structure calculations of Si Ge Sn alloys: achieving direct band gap materials
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Citations
Progress on germanium-tin nanoscale alloys
Structural and optical characterization of SixGe1−x−ySny alloys grown by molecular beam epitaxy
Investigation of carrier confinement in direct bandgap GeSn/SiGeSn 2D and 0D heterostructures.
Single-crystalline laterally graded GeSn on insulator structures by segregation controlled rapid-melting growth
GeSn-on-insulator substrate formed by direct wafer bonding
References
Self-Consistent Equations Including Exchange and Correlation Effects
Improved tetrahedron method for Brillouin-zone integrations
Electronic Structure: Basic Theory and Practical Methods
Band lineups and deformation potentials in the model-solid theory.
Related Papers (5)
Frequently Asked Questions (10)
Q2. What is the purpose of this work?
The aim of this work is to theoretically explore various possibilities of achieving tunable direct gap semiconductors based on group IV materials, and to investigate the composition dependence of their electronic and optical properties.
Q3. How can bulk alloys with Sn be grown?
With large lattice mismatch between α-Sn (6.489 Å) and Ge (5.646 Å) or Si (5.431 Å), approximately 15% and 17% respectively, and the instability of cubic α-Sn above 13o C, bulk alloys with Sn cannot be readily grown [1].
Q4. What is the corresponding band gap in the alloy?
Band structure calculations show that relaxed Ge1−xSnx alloys have an indirect-to-direct band gap crossover at a Sn content of ≈0.17, with the bowing parameter equal to 2.49 eV.
Q5. How can one evaluate the properties of Si, Ge, and -Sn?
Alloy properties can be evaluated either within the virtual crystal approximation (VCA) with identical, average-composition atoms populating the lattice sites of the minimumvolume crystalline unit cell, or by populating individual lattice sites only with pure element atoms, in proportion to the alloy composition (“mixed atom method”), in which case one has to use a supercell, with increased volume.
Q6. What is the lattice constant of Ge1xySny?
In the electronic structure calculations the lattice constant of Ge1−x−ySixSny alloys was taken to depend on the Si content (x) and Ge content (y) as [35]aGeSiSn(x, y) = aGe +4SiGex + θSiGe(1− x) +4SnGey + θSnGey(1− y), (12)where 4SiGe = aSi − aGe, 4SnGe = aSn − aGe, and θSiGe = −0.026 Å.
Q7. What is the optimum strain for the Ge1xSnx alloy?
This system is currently believed to be of great practical interest, since it offers a direct band gap in Ge at a reasonable level of strain (>1.8%) as well as type-I heterostructure [11] (of importance for realisation of quantum well structures), together with a small thermal expansion mismatch between the two materials [6].
Q8. What is the description of the optical band gap bowing?
According to Chibane et al. [15], who used the model developed by Zunger et al. [16], thecalculated optical band gap gap bowing is in good agreement with experiment for small Sn contents.
Q9. What is the lattice constant of an alloy?
The lattice constant of an alloy can be estimated from Vegard’s law [25]a0(x) AB = (1− x)aA0 + xaB0 , (6)where aA0 and a B 0 are the lattice constants of elemental crystals of atoms A and B respectively, and a more accurate expression (with bowing) was taken where available.
Q10. What is the valence band of the X valley?
The computational method used in this work, and the conditions (strain along the [001] axis), allow meaningful extraction of:: the uniaxial deformation potential b for the valence band at Γ, the sum of valence and conduction band (at Γ) hydrostatic deformation potentials av +ac, and the uniaxial deformation potential Ξ∆u of the X (i.e. ∆) valley of the conduction band.