Impact of carrier transport on the performance of QD lasers on silicon: a drift-diffusion approach

Marco Saldutti; Alberto Tibaldi; Federica Cappelluti; Mariangela Gioannini

doi:doi:10.1364/PRJ.394076

Photonics Research, 2020, 8 (8): 08001388, Published Online: Jul. 31, 2020

Impact of carrier transport on the performance of QD lasers on silicon: a drift-diffusion approach Download： 626次

Marco Saldutti ^*Alberto Tibaldi Federica Cappelluti Mariangela Gioannini

Author Affiliations

Department of Electronics and Telecommunications, Politecnico di Torino, Turin 10129, Italy

Figures & Tables

Fig. 1. Schematic representation of the epitaxial structure of the studied QD lasers, similar to those in Refs. [24,25]. The growth direction is from the bottom to the top.

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Fig. 2. Band diagram at thermodynamic equilibrium, with the conduction band (blue), the valence band (red), and the Fermi level (dashed, black). The dotted, vertical lines delimit the SCH region.

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Fig. 3. Schematic representation of the QD energy states and intersubband transitions.

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Fig. 4. Calculated GS modal gain versus current density for different levels of TDD and experimental gain (circles) from Ref. [24].

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Fig. 5. (a) GS threshold current density and (c) optical power as a function of TDDbulk, for fixed DWELL SRH lifetime corresponding to TDDWL=105 cm−2. The solid lines are almost overlapped. (b) GS threshold current density and slope efficiency and (d) optical power as a function of TDD in the barrier and DWELL layers (TDDWL=TDDbulk).

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Fig. 6. GS (solid) and ES (dotted) optical power with (a) μn=8500 cm2/(V·s) and μp=350 cm2/(V·s) and (b) μn=μp=8500 cm2/(V·s) in the SCH region.

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Fig. 7. Net capture rate from the bulk states to the WL with (a) μn=8500 cm2/(V·s) and μp=350 cm2/(V·s) and (b) μn=μp=8500 cm2/(V·s) in the SCH region. Layer 1 (5) is the closest to the p-contact (n-contact).

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Fig. 8. Contribution of (a) electrons and (b) holes to the GS modal gain: solid line is the overall contribution, whereas colored dashed lines are the contribution of the different layers (color legend is the same as in Fig. 6). Vertical lines indicate GS and ES threshold currents. (c) GS electrons and (d) holes occupation probability. The mobility of electrons and holes in the SCH region is μn=8500 cm2/(V·s) and μp=350 cm2/(V·s). Layer 1 (5) is the closest to the p-contact (n-contact).

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Fig. 9. GS (solid) and ES (dotted) optical power with (a) no p-type modulation doping and a p-type modulation doping of (b) 5×1017 cm−3 and (c) 30×1017 cm−3.

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Fig. 10. (a) GS (blue) and ES (red) threshold current density as functions of the p-type modulation doping density. (b) Total radiative and SRH recombination rates as functions of p-type modulation doping density calculated at the JthGS values in (a).

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Fig. 11. (a) GS modal gain versus current density and (b) holes (GGSmod,p, dashed) and electrons (GGSmod,n, solid) contributions to the modal gain.

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Fig. 12. (a) Contribution of electrons (blue) and holes (red) to the GS modal gain at J=580 A/cm2 versus p-doping density and (b) corresponding GS modal gain.

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Fig. 13. (a) Conduction band (solid) and electron quasi-Fermi level (dashed) for the bulk states of the SCH region at J=580 A/cm2. (b) Valence band (solid) and hole quasi-Fermi level (dashed) for the bulk states of the SCH region at J=580 A/cm2.

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Fig. 14. Net capture rate from the bulk states to the WL at J=580 A/cm2 for each layer of QDs.

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Fig. 15. Total SRH recombination rate versus voltage at three different doping levels. The vertical dashed lines indicate the voltage value corresponding to the lasing threshold.

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Table1. Simulation Parameters

Parameters	Values
$Δ E_{n}^{k}$ , $k = WL, ES, GS$ [meV]	177.7, 30, 41.1 [14]
$Δ E_{p}^{k}$ , $k = WL, ES, GS$ [meV]	166.3, 25, 25 [14]
$τ_{n, CAP}^{B \to WL}$ , $τ_{n, CAP}^{WL \to ES}$ , $τ_{n, CAP}^{ES \to GS}$ [ps]	0.1, 1, 1 [26]
$τ_{p, CAP}^{B \to WL}$ , $τ_{p, CAP}^{WL \to ES}$ , $τ_{p, CAP}^{ES \to GS}$ [ps]	0.1, 0.1, 0.1 [26]
$τ_{rad}^{k}$ , $k = WL, ES, GS$ [ns]	1, 1, 1 [11,22]
$τ_{n, SRH}^{k}$ , $k = ES, GS$ [ns]	1, 1 [11,22]
$τ_{p, SRH}^{k}$ , $k = ES, GS$ [ns]	1, 1 [11,22]
QD sheet density $N_{QD, i}$ [ ${cm}^{- 2}$ ]	$4.9 \times 10^{10}$
GS (ES) degeneracy $μ_{GS}$ ( $μ_{ES}$ )	2 (4)
Gain coefficient $G_{0}^{GS}$ ( $G_{0}^{ES}$ ) [ ${cm}^{- 1}$ ]	433 (779.4)
Electron (hole) effective mass $m_{n}^{}$ ( $m_{p}^{}$ ) [ $m_{0}$ ]	0.054 (0.49)
Optical confinement factor $Γ_{i}$	$\sim 2 %$
Intrinsic loss $α_{i}$ [ ${cm}^{- 1}$ ]	5
Waveguide width [μm]	3.5
Facet reflection coefficient	0.32
Spontaneous emission factor $β_{sp}$	$10^{- 4}$
Group index	3.56
GaAs $D_{n}$ , $D_{p}$ [ ${cm}^{2} \cdot s^{- 1}$ ]	221, 10
${In}_{0.15} {Ga}_{0.85} As$ $D_{n}$ , $D_{p}$ [ ${cm}^{2} \cdot s^{- 1}$ ]	181, 10
Temperature [K]	300

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Marco Saldutti, Alberto Tibaldi, Federica Cappelluti, Mariangela Gioannini. Impact of carrier transport on the performance of QD lasers on silicon: a drift-diffusion approach[J]. Photonics Research, 2020, 8(8): 08001388.

Impact of carrier transport on the performance of QD lasers on silicon: a drift-diffusion approach Download： 626次

Fig. 1. Schematic representation of the epitaxial structure of the studied QD lasers, similar to those in Refs. [24,25]. The growth direction is from the bottom to the top.

Fig. 2. Band diagram at thermodynamic equilibrium, with the conduction band (blue), the valence band (red), and the Fermi level (dashed, black). The dotted, vertical lines delimit the SCH region.

Fig. 3. Schematic representation of the QD energy states and intersubband transitions.

Fig. 4. Calculated GS modal gain versus current density for different levels of TDD and experimental gain (circles) from Ref. [24].

Fig. 6. GS (solid) and ES (dotted) optical power with (a) μn=8500 cm2/(V·s) and μp=350 cm2/(V·s) and (b) μn=μp=8500 cm2/(V·s) in the SCH region.

Fig. 7. Net capture rate from the bulk states to the WL with (a) μn=8500 cm2/(V·s) and μp=350 cm2/(V·s) and (b) μn=μp=8500 cm2/(V·s) in the SCH region. Layer 1 (5) is the closest to the p-contact (n-contact).

Fig. 9. GS (solid) and ES (dotted) optical power with (a) no p-type modulation doping and a p-type modulation doping of (b) 5×1017 cm−3 and (c) 30×1017 cm−3.

Fig. 10. (a) GS (blue) and ES (red) threshold current density as functions of the p-type modulation doping density. (b) Total radiative and SRH recombination rates as functions of p-type modulation doping density calculated at the JthGS values in (a).

Fig. 11. (a) GS modal gain versus current density and (b) holes (GGSmod,p, dashed) and electrons (GGSmod,n, solid) contributions to the modal gain.

Fig. 12. (a) Contribution of electrons (blue) and holes (red) to the GS modal gain at J=580 A/cm2 versus p-doping density and (b) corresponding GS modal gain.

Fig. 13. (a) Conduction band (solid) and electron quasi-Fermi level (dashed) for the bulk states of the SCH region at J=580 A/cm2. (b) Valence band (solid) and hole quasi-Fermi level (dashed) for the bulk states of the SCH region at J=580 A/cm2.

Fig. 14. Net capture rate from the bulk states to the WL at J=580 A/cm2 for each layer of QDs.

Fig. 15. Total SRH recombination rate versus voltage at three different doping levels. The vertical dashed lines indicate the voltage value corresponding to the lasing threshold.

Table1. Simulation Parameters

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Impact of carrier transport on the performance of QD lasers on silicon: a drift-diffusion approach Download： 626次

Fig. 1. Schematic representation of the epitaxial structure of the studied QD lasers, similar to those in Refs. [24,25]. The growth direction is from the bottom to the top.

Fig. 2. Band diagram at thermodynamic equilibrium, with the conduction band (blue), the valence band (red), and the Fermi level (dashed, black). The dotted, vertical lines delimit the SCH region.

Fig. 3. Schematic representation of the QD energy states and intersubband transitions.

Fig. 4. Calculated GS modal gain versus current density for different levels of TDD and experimental gain (circles) from Ref. [24].

Fig. 6. GS (solid) and ES (dotted) optical power with (a) μn=8500 cm2/(V·s) and μp=350 cm2/(V·s) and (b) μn=μp=8500 cm2/(V·s) in the SCH region.

Fig. 7. Net capture rate from the bulk states to the WL with (a) μn=8500 cm2/(V·s) and μp=350 cm2/(V·s) and (b) μn=μp=8500 cm2/(V·s) in the SCH region. Layer 1 (5) is the closest to the p-contact (n-contact).

Fig. 9. GS (solid) and ES (dotted) optical power with (a) no p-type modulation doping and a p-type modulation doping of (b) 5×1017 cm−3 and (c) 30×1017 cm−3.

Fig. 10. (a) GS (blue) and ES (red) threshold current density as functions of the p-type modulation doping density. (b) Total radiative and SRH recombination rates as functions of p-type modulation doping density calculated at the JthGS values in (a).

Fig. 11. (a) GS modal gain versus current density and (b) holes (GGSmod,p, dashed) and electrons (GGSmod,n, solid) contributions to the modal gain.

Fig. 12. (a) Contribution of electrons (blue) and holes (red) to the GS modal gain at J=580 A/cm2 versus p-doping density and (b) corresponding GS modal gain.

Fig. 13. (a) Conduction band (solid) and electron quasi-Fermi level (dashed) for the bulk states of the SCH region at J=580 A/cm2. (b) Valence band (solid) and hole quasi-Fermi level (dashed) for the bulk states of the SCH region at J=580 A/cm2.

Fig. 14. Net capture rate from the bulk states to the WL at J=580 A/cm2 for each layer of QDs.

Fig. 15. Total SRH recombination rate versus voltage at three different doping levels. The vertical dashed lines indicate the voltage value corresponding to the lasing threshold.

Table1. Simulation Parameters

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