Non-linearity in the compositional dependence the GeSn band gap can be described by,
𝐸𝑔𝑎𝑙𝑙𝑜𝑦(𝑥) = 𝑥𝐸𝑔𝐴+ (1 − 𝑥)𝐸𝑔𝐵+ 𝑏0 𝑎𝑙𝑙𝑜𝑦
𝑥(1 − 𝑥) (J.1)
Where 𝐸𝑔 is the critical point bandgap, 𝑥 is the Sn fraction and 𝑏0 is the critical point bowing parameter
(𝑏0= 0 in the case of linear interpolation).
Reported bowing parameters vary between 1.94-2.8 eV (Table J.1) with indirect-direct crossover values ranging between ~6-10% Sn. Several groups have also suggested (from both theory [473] and experiment [481]) a compositional dependent bowing parameter, although the exact dependence is difficult to access at present given the scarcity and scatter of data, especially at high Sn content.
BOWING PARAMETER b0 METHOD YEAR REF. 1.94 VASE 2006 [479] 2.2 VASE 2002 [546] 2.3±0.1 Transmittance 2007 [547] 2.8 Absorption 1997 [477] 2.42±0.04 PR 2012 [502] 2.46±0.06 PL 2014 [442] 2.1 PL 2011 [480] 2.92±0.11 Absorption 2016 [548]
Table J.1: Summary of the room temperature bowing parameters reported in the literature for GeSn. VASE =
APPENDIX J
171
GeSn Lasers
The first GeSn laser, reported in 2015, was an edge emitting Fabry-Perot cavity laser comprising a 560 nm Ge0.874Sn0.126 layer grown on a strained relaxed Ge buffer and on-axis Si substrate [482]. The maximum lasing temperature was 90 K, with a threshold excitation density and lasing wavelength of 325 kW/cm2 and 2.3 µm respectively at 20 K. Subsequent years have seen rapid improvements in every metric with lasing reported with bulk DHS, graded and MQW active regions integrated within a diverse range of device structures, including Fabry-Perot [494], [549]–[551], micro-disk [492], [552]–[554] and photonic crystal membrane lasers [555]. Currently the highest lasing temperature published in the literature is 230 K with DHS micro-disk lasers [492]. Over successive generations the threshold excitation density has also been dramatically reduced. As an indication of the progress than has been made, optically pumped lasing using GeSn/SiGeSn MQWs report a threshold excitation density of 35 kW/cm2 at 20 K [164], amounting to an order of magnitude reduction in less than three years. The highest Sn content lasers use compositional graded layer up to 22.3% Sn, grown using CVD. However, since crystal quality tends to degrade with increasing Sn concentration [556] most GeSn devices reported at present typically have around 15% Sn or less.
GESN LASER PROPERTIES AVAILABLE IN THE LITERATURE
STRUCTURE MAX TEMP. THRESHOLD (kW/cm2) %SN λ µm YEAR GROUP REF. FP 90 K 325 (20 K) 12.6 % 2.3 µm (20 K) 2015 PGI [482] FP 110 K 68 (10 K), 166 (90 K) 10.9% 2.50 µm (90 K) 2016 UoAr [557] MD 130 K 130 (20 K) 12.5% 2.48 µm 2016 PGI [552] MD 180 K 377 (25 K) 16% 3.1 µm 2017 UGA [553] FP 180 K 138 (77 K) 14.4% 2.63 µm 2018 UoAr [549] MD† 120 K 300 (20 K) 14.5% 2.65 µm (20 K) 2018 PGI [164], [554] MD-MQW† 120 K 35 (20 K) 13.3% 2.45 µm (20 K) PC 60 K 227 (15 K) 16% 2.88 µm (60 K) 2018 UGA [555] FP-MQW 90 K 25 (10 K), 62 (77 K) 14.4% 2.52 µm (77 K) 2018 UoAr [550] Graded-FP 180 K 137 (77 K) 22.3% 2.98 µm (180 K) 2018 UoAr [551] MD 230 K 134 (15 K) 16% 2.8 µm (15 K) 3.2 µm (230 K) 2018 UGA [492] FP-MQW 270 K 2019 UoAr [558]
Table J.2: Summary of GeSn lasers reported in the literature. †The maximum lasing temperature and lowest threshold densities were obtained with 1550 nm and 1064 nm pump sources respectively. FP = Fabry Perot Cavity, MD = Micro-Disk Cavity, MQW = Multiple Quantum Wells, PC = Photonics Crystal. PGI = Peter Grünberg Institute, UoAr = University of Arkansas, UGA = Université Grenoble Alpes.
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