Nature of the band gap of Ge:C alloys: insights from hybrid functional density functional theory calculations

Kirwan, Amy C.; Schulz, Stefan; O’Reilly, Eoin P.

doi:10.1088/1361-6641/ab23a4

Cited by 8 publications

(18 citation statements)

References 26 publications

(32 reference statements)

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“…As such, we consequently conclude that C incorporation does not drive the formation of a direct band gap in dilute Ge 1−x C x . This conclusion is in direct agreement with the hybrid functional DFT calculations of Kirwan et al 27…”

Section: Resultssupporting

confidence: 91%

“…For small (N ≤ 128) supercells we note that our calculated values of ∆E g and dEg dP are in good quantitative agreement with the hybrid DFT calculations of Ref. 27. Our calculated CB structure for an ordered Ge 127 C 1 supercell is also in good overall agreement with the calculations of Kirwan et al 27 , as well as those of Stephenson et al 25 .…”

Section: B Trends Vs C Composition: Band Mixing and The Ultra-dilutsupporting

confidence: 88%

“…Again, we note that this behaviour is markedly different to that expected on the basis of the BAC model, whereby a direct band gap would be expected to emerge via the transfer of increasing Ge Γ 2 c character to the alloy CB edge with increasing C composition x. In general, the results of our disordered alloy analysis support the conclusions of Kirwan et al, 27 and of our ordered supercell analysis in Sec. III B above: dilute C incorporation in Ge does not give rise to a direct band gap.…”

Section: Impact Of C Incorporation On Conduction Band Edge States supporting

confidence: 75%

“…In addition, as we describe in Sec. III A, the results of our TB supercell calculations for small, ordered Ge 1−x C x supercells are in good quantitative agreement with hybrid functional DFT calculations, 27,73 confirming the validity of our TB model to investigate Ge 1−x C x alloys.…”

Section: B Tight-binding Hamiltoniansupporting

confidence: 69%

“…Indeed, we have recently demonstrated the importance of such effects in determining the nature of the indirect-to direct-gap transition in Ge 1−x Sn x and Ge 1−x Pb x alloys. 23,54,74,75 Our calculations suggest, in agreement with hybrid functional DFT calculations, 24,27 that C incorporation has minimal impact on the VB structure, so we focus our analysis on the alloy CB structure.…”

Section: Resultsmentioning

confidence: 74%

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Electronic structure evolution in dilute carbide Ge1−xCx alloys and implications for device applications

Broderick

Dunne

Tanner

et al. 2019

Journal of Applied Physics

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We present a theoretical analysis of electronic structure evolution in the highly-mismatched dilute carbide group-IV alloy Ge1−xCx. For ordered alloy supercells, we demonstrate that C incorporation strongly perturbs the conduction band (CB) structure by driving hybridisation of A1-symmetric linear combinations of Ge states lying close in energy to the CB edge. This leads, in the ultradilute limit, to the alloy CB edge being formed primarily of an A1-symmetric linear combination of the L-point CB edge states of the Ge host matrix semiconductor. Our calculations describe the emergence of a "quasi-direct" alloy band gap, which retains a significant admixture of indirect Ge L-point CB edge character. We then analyse the evolution of the electronic structure of realistic (large, disordered) Ge1−xCx alloy supercells for C compositions up to x = 2%. We show that short-range alloy disorder introduces a distribution of localised states at energies below the Ge CB edge, with these states acquiring minimal direct (Γ) character. Our calculations demonstrate strong intrinsic inhomogeneous energy broadening of the CB edge Bloch character, driven by hybridisation between Ge host matrix and C-related localised states. The trends identified by our calculations are markedly different to those expected based on a recently proposed interpretation of the CB structure based on the band anti-crossing model. The implications of our findings for device applications are discussed.

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Section: Resultssupporting

confidence: 91%

Section: B Trends Vs C Composition: Band Mixing and The Ultra-dilutsupporting

confidence: 88%

Section: Impact Of C Incorporation On Conduction Band Edge States supporting

confidence: 75%

Section: B Tight-binding Hamiltoniansupporting

confidence: 69%

Section: Resultsmentioning

confidence: 74%

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Electronic structure evolution in dilute carbide Ge1−xCx alloys and implications for device applications

Broderick

Dunne

Tanner

et al. 2019

Journal of Applied Physics

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Challenges for room temperature operation of electrically pumped GeSn lasers

Ellis,

Duffy,

Marko

et al. 2024

Sci Rep

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Recent demonstrations of room-temperature lasing in optically pumped GeSn show promise for future CMOS compatible lasers for Si-photonics applications. However, challenges remain for electrically pumped devices. Investigation of the processes that limit device performance is therefore vital in aiding the production of future commercial devices. In this work, a combined experimental and modelling approach is utilised to explore the dominant loss processes in current devices. By manipulating the band structure of functioning devices using high hydrostatic pressure techniques at low temperature, the dominant carrier recombination pathways are identified. This reveals that 93$$~\pm ~$$ ± 5% of the threshold current is attributable to defect-related recombination at a temperature, T = 85 K. Furthermore, carrier occupation of L-valley states (carrier leakage) is responsible for 1.1$$~\pm ~$$ ± 0.3% of the threshold current, but this sharply increases to 50% with a decrease of just 30 meV in the L-$$\Gamma$$ Γ separation energy. This indicates that thermal broadening of a similar order may reproduce these adverse effects, limiting device performance at higher temperatures. Temperature dependent calculations show that carrier occupation of indirect valley L-states strongly affects the transparency carrier density and is therefore very sensitive to the Sn composition, leading to an effective operational temperature range for given Sn compositions and strain values. Recommendations for future device designs are proposed based on band structure and growth optimisations.

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The carbon state in dilute germanium carbides

Gulyas

Stephenson

Meng

et al. 2021

Journal of Applied Physics

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Conduction and valence band states for the highly mismatched alloy (HMA) Ge:C are projected onto Ge crystal states, Ge vacancy states, and Ge/C atomic orbitals, revealing that substitutional carbon not only creates a direct bandgap, but the new conduction band is optically active. Overlap integrals of the new Ge:C conduction band with bands of pure Ge shows the new band has almost no Ge band character. C sites structurally mimic uncharged vacancies in the Ge lattice, similar to Hjalmarson's model for other HMAs. C perturbs the entire Ge band structure even at the deepest crystal core energy levels. Projection onto atomic sites shows relatively weak localization compared with other HMAs, but does show a strong anisotropy in probability distribution. L-valley conduction band states in Ge are ruled out as major contributors to the carbon state in Ge:C, both by weak inner products between these states and by a negligible effect on optical transition strength when adding C.

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Nature of the band gap of Ge:C alloys: insights from hybrid functional density functional theory calculations

Cited by 8 publications

References 26 publications

Electronic structure evolution in dilute carbide Ge1−xCx alloys and implications for device applications

Electronic structure evolution in dilute carbide Ge1−xCx alloys and implications for device applications

Challenges for room temperature operation of electrically pumped GeSn lasers

The carbon state in dilute germanium carbides

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