## Overcoming Auger recombination in nanocrystal quantum dot laser using spontaneous emission enhancement |

Optics Express, Vol. 22, Issue 3, pp. 3013-3027 (2014)

http://dx.doi.org/10.1364/OE.22.003013

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### Abstract

We propose a method to overcome Auger recombination in nanocrystal quantum dot lasers using cavity-enhanced spontaneous emission. We derive a numerical model for a laser composed of nanocrystal quantum dots coupled to optical nanocavities with small mode-volume. Using this model, we demonstrate that spontaneous emission enhancement of the biexciton transition lowers the lasing threshold by reducing the effect of Auger recombination. We analyze a photonic crystal nanobeam cavity laser as a realistic device structure that implements the proposed approach.

© 2014 Optical Society of America

## 1. Introduction

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## 2. Derivation of numerical model

12. V. I. Klimov, A. A. Mikhailovsky, D. W. McBranch, C. A. Leatherdale, and M. G. Bawendi, “Quantization of multiparticle Auger Rates in semiconductor quantum dots,” Science **287**, 1011–1013 (2000). [CrossRef] [PubMed]

*γ*

_{2}=

*γ*

_{0}+

*γ*/2, where

_{a}*γ*

_{0}is the spontaneous emission rate and

*γ*is the total Auger recombination rate of the biexciton state. We assume the single exciton states decay predominantly by spontaneous emission. We also assume equal spontaneous emission rates for all four allowed transitions, and ignore long-lived trap states that are responsible for blinking behavior [20

_{a}20. M. Nirmal, B. O. Dabbousi, M. G. Bawendi, J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, “Fluorescence intermittency in single cadmium selenide nanocrystals,” Nature **383**, 802–804 (1996). [CrossRef]

21. M. Jones, J. Nedeljkovic, R. J. Ellingson, A. J. Nozik, and G. Rumbles, “Photoenhancement of luminescence in colloidal CdSe quantum dot solutions,” J. Phys. Chem. B **107**, 11346–11352 (2003). [CrossRef]

*R*.

**287**, 1011–1013 (2000). [CrossRef] [PubMed]

*g*(

**r**

_{0}) is the cavity-quantum dot coupling strength given by Here,

*E*(

**r**

_{0}) is the electric field amplitude,

**ê**is the polarization direction of the cavity mode at the quantum dot position

**r**

_{0},

*ω*is the cavity mode resonant frequency,

_{c}*μ*is the quantum dot dipole moment,

*V*= ∫

_{m}*d*

^{3}

**r**

*ε*(

**r**)|

*E*(

**r**)|

^{2}/[|

*E*(

**r**)|

^{2}]

*is the cavity mode-volume [23*

_{max}23. Y. Zhang, I. Bulu, W.-M. Tam, B. Levitt, J. Shah, T. Botto, and M. Loncar, “High-Q/V air-mode photonic crystal cavities at microwave frequencies,” Opt. Express **19**, 9371–9377 (2011). [CrossRef] [PubMed]

*ε*

_{0}is the permittivity of free space and

*ε*(

**r**) is the relative dielectric permittivity. Since

*ε*(

**r**) is dimensionless,

*V*has dimensions of volume. The rate

_{m}*K*= (

_{XX}*γ*

_{0}+ 2

*γ*

_{2}+

*γ*)/2 represents the total linewidth of the biexciton state, which is dominated by the dephasing rate

_{d}*γ*at room-temperature [12

_{d}**287**, 1011–1013 (2000). [CrossRef] [PubMed]

24. W. G. J. H. M. van Sark, P. L. T. M. Frederix, D. J. Van den Heuvel, H. C. Gerritsen, A. A. Bol, J. N. J. van Lingen, C. de Mello Donegá, and A. Meijerink, “Photooxidation and photobleaching of single CdSe/ZnS quantum dots probed by room-temperature time-resolved spectroscopy,” J. Phys. Chem. B **105**, 8281–8284 (2001). [CrossRef]

25. B. Lounis, H. A. Bechtel, D. Gerion, P. Alivisatos, and W. E. Moerner, “Photon antibunching in single CdSe/ZnS quantum dot fluorescence,” Chem. Phys. Lett. **329**, 399–404 (2000). [CrossRef]

*F*that depends on the ratio of the cavity quality factor

*Q*and the cavity mode-volume

*V*[18,22]. This difference occurs because at room temperature the dephasing rate of nanocrystal quantum dots is much larger than the cavity linewidth. The device therefore operates in the bad emitter regime, where

_{m}*F*becomes independent of the cavity

*Q*. By engineering cavities with small mode-volumes, we can achieve large

*F*and enhance the spontaneous emission rate, thereby increasing the radiative efficiency of the quantum dot in the presence of Auger recombination.

*ρ*is the density matrix of the combined cavity-quantum dot system,

**H**is the Hamiltonian, and

**L**is the Liouvillian superoperator that accounts for incoherent damping and excitation processes. The Hamiltonian of the system is given by

**H**+

_{cavity}**H**+

_{NQD}**H**, where In the above equations

_{JC}**a**and

**a**

^{†}are the bosonic annihilation and creation operators of the cavity mode. The summation is carried out over all quantum dots in the cavity, where we denote the total number of quantum dots by

*N*. For the

*m*quantum dot,

^{th}*σ*= |

_{jk,m}*j*〉 〈

*k*| represents the atomic dipole operator when

*j*≠

*k*and the atomic population operator when

*j*=

*k*, for the single exciton states (

*j*= 2, 3) and the biexciton state (

*j*= 4). We set the energy of the quantum dot ground state to zero. We define

*m*quantum dot at position

^{th}**r**

*. At room temperature, the homogenous linewidth of these quantum dots is much larger than the biexcitonic shift [26*

_{m}26. J.-M. Caruge, Y. Chan, V. Sundar, H. Eisler, and M. Bawendi, “Transient photoluminescence and simultaneous amplified spontaneous emission from multiexciton states in CdSe quantum dots,” Phys. Rev. B **70**, 1–7 (2004). [CrossRef]

29. D. Norris and M. Bawendi, “Measurement and assignment of the size-dependent optical spectrum in CdSe quantum dots,” Phys. Rev. B, **53**, 16338–16346 (1996). [CrossRef]

**L**is fully defined in Appendix A.

31. O. Benson and Y. Yamamoto, “Master-equation model of a single-quantum-dot microsphere laser,” Phys. Rev. A **59**, 4756–4763 (1999). [CrossRef]

*p*, and the quantum dot population density,

*V*at location

**r**. We note that

*n*(

_{j}**r**) is a function of the position

**r**inside the cavity because of the non-uniform cavity field distribution. We derive the equations of motion of

*n*(

_{j}**r**) from the master equation (see Appendix B) as

*(*

_{X}**r**) = 2

*g*

^{2}(

**r**)/

*K*and Γ

_{X}*(*

_{XX}**r**) = 2

*g*

^{2}(

**r**)/

*K*are the modified spontaneous emission rates of the single-exciton and biexciton transitions, where

_{XX}*K*= (

_{X}*γ*

_{0}+

*γ*+ 3

_{d}*R*)/2 and

*K*= (

_{XX}*γ*

_{0}+ 2

*γ*

_{2}+

*γ*+

_{d}*R*)/2. Here, we assume equal coupling strength for the single-exciton and biexciton transitions. We also treat the quantum dots in a small volume Δ

*V*of the cavity to be identical, and therefore drop the subscript

*m*from the coupling strength (

*κ*=

*ω*is the cavity energy decay rate. The above equation is coupled to the quantum dot population density rate equations through the cavity gain coefficient and the spontaneous emission rate into the lasing mode where the integral is over all space. We use the notation

_{c}/Q*G*(

*p*) and

*α*(

*p*) to highlight the fact that the above coefficients have a

*p*dependence because the atomic densities

*n*(

_{j}**r**) depend on the cavity photon number. The absorbed pump power of the nanocrystal quantum dot laser is given by where

*ω*is the pump frequency and

_{p}*V*is the optically pumped volume. The output power of the laser is given by

_{p}*β*. This parameter quantifies the fraction of photons spontaneously emitted to the cavity mode. A

*β*approaching unity achieves thresholdless lasing [32

32. G. Bjork and Y. Yamamoto, “Analysis of semiconductor microcavity lasers using rate equations,” IEEE J. Quantum Electron. **27**, 2386–2396 (1991). [CrossRef]

**r**due to the spatially varying cavity field intensity. The rate equations Eqs. (7)–(11) describe the dynamics of a general nanocrystal quantum dot laser. We will use these equations in the remaining sections.

## 3. Lasing analysis under uniform-field approximation

*g*(

**r**). This spatial variation leads to a complex set of coupled differential equations for each position inside the cavity volume. We note that this complexity is not unique to the system we study. It occurs in virtually all laser systems and is responsible for effects such as spatial hole burning [33

33. P. W. Milonni and J. H. Eberly, *Laser Physics* (Wiley, 2010). [CrossRef]

*(*

_{i}**r**) (i = X, XX) in Eqs. (7)– (14) with its spatially averaged value where

*n*(

_{j}**r**) are no longer spatially varying. We can therefore express the equations of motion in terms of the total number of quantum dots in state

*j*given by

*N*=

_{j}*V*where

_{m}n_{j}*V*is the cavity mode volume. These quantum dot populations must satisfy the constraint that ∑

_{m}*=*

_{j}N_{j}*N*, where

*N*is the total number of quantum dots contained in the cavity. With these definitions, the equations of motion become the standard cavity-atom rate equations, given by where and are the gain coefficient and spontaneous emission rate into the lasing mode. The absorbed power is given by The output power of the laser is still given by Eq. (15).

*N*as the total number of quantum dots in the cavity required to achieve a small signal gain equal to the cavity loss (lim

_{th}

_{p}_{→0}

*Ḡ*(

*p*) =

*κ*), and calculate it by using the analytical steady-state solutions to Eqs. (20)–(23) along with the condition ∑

*=*

_{j}N_{j}*N*(see Appendices D, E). To perform calculations, we consider the specific example of colloidal CdSe/ZnS core-shell quantum dots that emit in a wavelength range of 500–700 nm. We perform simulations using a dephasing rate of

*γ*= 4.39×10

_{d}^{4}ns

^{−1}[24

24. W. G. J. H. M. van Sark, P. L. T. M. Frederix, D. J. Van den Heuvel, H. C. Gerritsen, A. A. Bol, J. N. J. van Lingen, C. de Mello Donegá, and A. Meijerink, “Photooxidation and photobleaching of single CdSe/ZnS quantum dots probed by room-temperature time-resolved spectroscopy,” J. Phys. Chem. B **105**, 8281–8284 (2001). [CrossRef]

*γ*

_{0}= 1/18 ns

^{−1}[25

25. B. Lounis, H. A. Bechtel, D. Gerion, P. Alivisatos, and W. E. Moerner, “Photon antibunching in single CdSe/ZnS quantum dot fluorescence,” Chem. Phys. Lett. **329**, 399–404 (2000). [CrossRef]

*γ*= 1/300 ps

_{a}^{−1}[12

**287**, 1011–1013 (2000). [CrossRef] [PubMed]

34. M. Bruchez, M. Moronne, P. Gin, S. Weiss, and A. P. Alivisatos, “Semiconductor nanocrystals as fluorescent biological labels,” Science **281**, 2013–2016 (1998). [CrossRef] [PubMed]

10. B. Min, S. Kim, K. Okamoto, L. Yang, A. Scherer, H. Atwater, and K. Vahala, “Ultralow threshold on-chip microcavity nanocrystal quantum dot lasers,” Appl. Phys. Lett. **89**, 191124 (2006). [CrossRef]

35. R. Bose, X. Yang, R. Chatterjee, J. Gao, and C. W. Wong, “Weak coupling interactions of colloidal lead sulphide nanocrystals with silicon photonic crystal nanocavities near 1.55μm at room temperature,” Appl. Phys. Lett. **90**, 111117 (2007). [CrossRef]

38. M. T. Rakher, R. Bose, C. W. Wong, and K. Srinivasan, “Spectroscopy of 1.55μm PbS quantum dots on Si photonic crystal cavities with a fiber taper waveguide,” Appl. Phys. Lett. **96**, 161108 (2010). [CrossRef]

9. P. T. Snee, Y. Chan, D. G. Nocera, and M. G. Bawendi, “Whispering-gallery-mode lasing from a semiconductor nanocrystal/microsphere resonator composite,” Adv. Mater. **17**, 1131–1136 (2005). [CrossRef]

39. Z. Wu, Z. Mi, P. Bhattacharya, T. Zhu, and J. Xu, “Enhanced spontaneous emission at 1.55μm from colloidal PbSe quantum dots in a Si photonic crystal microcavity,” Appl. Phys. Lett. **90**, 171105 (2007). [CrossRef]

*ε*= 1.

_{eff}*N*as a function of pump rate

_{th}*R*for

*V*= 0.01

_{m}*μm*

^{3}, 1

*μm*

^{3}and 100

*μm*

^{3}and

*γ*= 1/300 ps

_{a}^{−1}. Each mode-volume exhibits an optimum pump rate where the threshold quantum dot number is minimum. We denote this minimum threshold quantum dot number by

*N*. Figure 2(b) plots

_{opt}*N*as a function of

_{opt}*V*. The figure shows that

_{m}*N*scales linearly with mode-volume.

_{opt}*P*as a function of

_{out}*P̄*(also known as the light-in light-out curve), under the uniform-field approximation, for two different mode-volumes of

_{abs}*V*= 0.01

_{m}*μm*

^{3}and 100

*μm*

^{3}, as well as two different Auger recombination rates of

*γ*= 1/300 ps

_{a}^{−1}and 0. We set

*Q*= 20000 and

*N*= 2

*N*(Fig. 2(b)) for each respective mode-volume. We calculate the curves in Fig. 3(a) using the same range of

_{opt}*R*values for both the mode-volumes. We note that the curves for the small mode volume cavity terminate earlier than those of the large mode volume cavity because the number of quantum dots contained inside the cavity mode-volume is much lower, which reduces the maximum output power.

*V*= 100

_{m}*μ*m

^{3}, indicated by the dashed curves in Fig. 3(a), exhibit a pronounced threshold. Near threshold, the light-in light-out curve takes on the well-known S-curve behavior as it transitions from the below-threshold to above-threshold regime. Auger recombination increases the threshold by quenching the gain, which causes the S-curve region to occur at higher absorbed powers. Similar to

*N*, we define the threshold power as the absorbed power where the small signal gain equals the cavity loss. We calculate this value numerically using the steady state solutions to Eqs. (20)– (23), along with Eq. (27). The threshold power for

_{th}*V*= 100

_{m}*μm*

^{3}is 122.7

*μ*W when

*γ*= 1/300 ps

_{a}^{−1}, and 5.9

*μ*W when

*γ*= 0. Auger recombination therefore increases the lasing threshold by a factor of 21. When the mode volume is

_{a}*V*= 0.01

_{m}*μm*

^{3}the light-in light-out curve exhibits a thresholdless lasing behavior. The output power is nearly a linear function of the input power. Using the same definition of threshold, we determine the threshold powers with and without Auger recombination to be 97 nW and 84 nW respectively, corresponding to an increase of only 1.2. Thus, not only does the small mode volume cavity exhibit a much lower overall lasing threshold, but the lasing threshold is also largely unaffected by Auger recombination.

*V*for

_{m}*γ*= 1/300 ps

_{a}^{−1}and 0. We set the total quantum dot number in the cavities to

*N*= 2

*N*for each value of

_{opt}*V*(Fig. 2(b)). Figure 3(c) plots the ratio of absorbed pump powers at threshold for

_{m}*γ*= 1/300 ps

_{a}^{−1}and 0,

*η*, as a function of

*V*. From this curve, we observe that below a mode-volume of 0.1

_{m}*μm*

^{3}the lasing threshold is largely unaffected by Auger recombination. Above this mode volume,

*η*rapidly increases and eventually reaches a saturated value. At large mode-volumes,

*η*becomes independent of the mode volume itself and achieves an asymptotic limit. From the upper and the lower limits of

*η*(21 and 1.2, respectively), we determine that spontaneous emission enhancement can reduce the lasing threshold up to a factor of 17.

*V*. Using the uniform field approximation, we replace Γ

_{m}*(*

_{i}**r**) (i = X, XX) in Eqs. (16)–(17) with its spatially averaged value Γ̄

*which removes the spatial dependence and results in the simplified expressions for the coupling efficiencies given by*

_{i}*β̄*and the biexciton transition

_{X}*β̄*as a function of

_{XX}*V*using

_{m}*γ*= 1/300 ps

_{a}^{−1}. At

*V*= 100

_{m}*μm*

^{3},

*β̄*is more than an order of magnitude smaller than

_{XX}*β̄*. As the mode volume decreases the two efficiencies approach unity. The coupling efficiency of the biexciton transition begins to increase sharply and approach unity around the same mode-volume where

_{X}*η*(Fig. 3(b)) begins to saturate to unity. Thus, at small mode-volumes

*β̄*is insensitive to Auger recombination, and therefore the threshold pump power does not significantly change as indicated in Fig. 3(b).

_{XX}## 4. Cavity device structure for low-threshold laser

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*r*= 0.24

*a*, where

*a*is the lattice constant). The cavity is composed of a defect in the structure created by gradually reducing the radius of the three holes on either side of the hole labelled C to a minimum of

*r*

_{0}= 0.2

*a*. The adiabatic reduction of hole radius creates a smooth confinement for the photon and minimizes scattering due to edge states [52

52. Q. Quan, P. B. Deotare, and M. Loncar, “Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide,” Appl. Phys. Lett. **96**, 203102 (2010). [CrossRef]

*d*= 0.727

*a*and beam width

*b*= 1.163

*a*. The index of refraction of silicon nitride is set to 2.01 [53

53. M. Barth, J. Kouba, J. Stingl, B. Löchel, and O. Benson, “Modification of visible spontaneous emission with silicon nitride photonic crystal nanocavities,” Opt. Express **15**, 17231–17240 (2007). [CrossRef] [PubMed]

*V*= 0.38

_{m}*λ*

^{3}(= 0.11

*μm*

^{3}) and the quality factor is

*Q*= 64, 000.

*ε*= 1.9 for the cavity by numerically integrating Eq. (19) using the computed electric field intensity profile of the simulated cavity structure (Fig. 5). Calculations under the uniform-field approximation follow the same approach as in the section 3.

_{eff}*N*= 60. This number is nearly identical to the value calculated using the uniform-field approximation which is 62. Next, we calculate the light-in light out curve using Eq. (14) and Eq. (15) without the uniform-field approximation. As in the previous section, we set the total number of quantum dots to be

_{opt}*N*= 2

*N*.

_{opt}*P*as a function of

_{out}*P*for the nanobeam photonic crystal cavity with simulated

_{abs}*Q*= 64, 000 using

*γ*= 1/300 ps

_{a}^{−1}and 0, both with and without the uniform-field approximation. The calculations show good agreement between the predicted input-output characteristics of the laser with and without the uniform-field approximation. Without the uniform-field approximation, the absorbed pump power at threshold for the nanobeam laser is 109.8 nW for

*γ*= 1/300 ps

_{a}^{−1}and 29.9 nW for

*γ*= 0, resulting in

_{a}*η*= 3.7. With the uniform-field approximation, the absorbed pump power at threshold for the nanobeam laser is 112.6 nW for

*γ*= 1/300 ps

_{a}^{−1}and 30 nW for

*γ*= 0, resulting in

_{a}*η*= 3.8.

*ε*for the nanobeam cavity, calculated from the cavity-field distribution, is 1.9. This calculated

_{eff}*ε*is higher than the unity assumption in the previous section because in this realistic cavity design a fraction of the cavity field leaks into the dielectric medium (Fig. 5). Figure 6(b) plots

_{eff}*η*as a function of

*V*under the uniform-field approximation for the same parameters used in Fig. 6(a). For a cavity with a mode volume of 100

_{m}*μm*

^{3}, we determine that

*η*= 21.1. This value is 5.6 times larger than the value for the nanobeam cavity. Thus, the nanobeam cavity lasing threshold is much less sensitive to Auger recombination.

## 5. Conclusion

54. J. Zhao, G. Nair, B. R. Fisher, and M. G. Bawendi, “Challenge to the charging model of semiconductor-nanocrystal fluorescence intermittency from off-state quantum yields and multiexciton blinking,” Phys. Rev. Lett. **104**, 1–4 (2010). [CrossRef]

55. M. Kuno, D. Fromm, S. Johnson, A. Gallagher, and D. Nesbitt, “Modeling distributed kinetics in isolated semiconductor quantum dots,” Phys. Rev. B **67**, 1–15 (2003). [CrossRef]

13. H. Htoon, J. Hollingsworth, R. Dickerson, and V. Klimov, “Effect of zero- to one-dimensional transformation on multiparticle Auger recombination in semiconductor quantum rods,” Phys. Rev. Lett. **91**, 1–4 (2003). [CrossRef]

15. M. Kazes, D. Lewis, Y. Ebenstein, T. Mokari, and U. Banin, “Lasing from semiconductor quantum rods in a cylindrical microcavity,” Adv. Mater. **14**, 317 (2002). [CrossRef]

56. J. T. Choy, B. J. M. Hausmann, T. M. Babinec, I. Bulu, M. Khan, P. Maletinsky, A. Yacoby, and M. Lončar, “Enhanced single-photon emission from a diamondsilver aperture,” Nat. Photonics **5**, 738–743 (2011). [CrossRef]

## A. Liouvillian superoperator L

**L**can be expressed as

**L**=

**L**+

_{NQD}**L**+

_{pump}**L**, where

_{cavity}**L**accounts for the spontaneous relaxation of the quantum dot level structure,

_{NQD}**L**accounts for the incoherent pumping of the quantum dot population, and

_{pump}**L**accounts for the cavity decay. These operators are

_{cavity}*κ*=

*ω*.

_{c}/Q## B. Equations of motion: projected on quantum dot levels

*ρ*on the levels (ij) of the

*m*quantum dot and photon states (pp’)

^{th}*p*,

*p′*= 0 to ∞) are obtained using Eq. (3):

*K*= (

_{X}*γ*

_{0}+

*γ*+ 3

_{d}*R*)/2 and

*K*= (

_{XX}*γ*

_{0}+ 2

*γ*

_{2}+

*γ*+

_{d}*R*)/2 are the total relaxation rates of the diagonal terms, and

*γ*is the dephasing rate of the quantum dot (added phenomenologically). We set dephasing rate to be much greater than the cavity decay rate

_{d}*γ*≫

_{d}*κ*, allowing us to drop the cavity decay contributions from the equations of motion of off-diagonal terms (Eqs. (37) – (40)). Large dephasing rate also allows us to adiabatically eliminate the expectation value 〈

*ρ*〉 of the off-diagonal terms (

_{ip,jp′}*i*≠

*j*)from Eqs. (37) – (40), and reduces Eqs. (33) – (36) to

*ρ*=

_{ip,ip}*ρ*, we get

_{ii}ρ_{pp}*p*〉 = ∑

_{p}*pρ*is the mean photon number. We define

_{pp}*lasing level where the sum is carried out over all quantum dots contained in small volume Δ*

^{th}*V*at location

**r**and get Eqs. (7) – (10).

## C. Rate equation for mean cavity photon number

*ρ*=

_{ip,ip}*ρ*, and identifying

_{ii}ρ_{pp}## D. Expression for *N*_{j} under the uniform-field approximation

_{j}

## Acknowledgments

## References and links

1. | M. T. Hill, “Nanophotonics: lasers go beyond diffraction limit,” Nat. Nanotechnol. |

2. | S. Kita, S. Hachuda, S. Otsuka, T. Endo, Y. Imai, Y. Nishijima, H. Misawa, and T. Baba, “Super-sensitivity in label-free protein sensing using a nanoslot nanolaser,” Opt. Express |

3. | P. L. Gourley, J. K. Hendricks, A. E. McDonald, R. G. Copeland, K. E. Barrett, C. R. Gourley, and R. K. Naviaux, “Ultrafast nanolaser flow device for detecting cancer in single cells,” Biomed. Microdevices |

4. | W. J. Parak, D. Gerion, T. Pellegrino, D. Zanchet, C. Micheel, S. C. Williams, R. Boudreau, M. A. Le Gros, C. A. Larabell, and A. P. Alivisatos, “Biological applications of colloidal nanocrystals,” Nanotechnology |

5. | L. Qu and X. Peng, “Control of photoluminescence properties of CdSe nanocrystals in growth,” J. Am. Chem. Soc. |

6. | A. P. Alivisatos, “Semiconductor clusters, nanocrystals, and quantum dots,” Science |

7. | V. I. Klimov, |

8. | H.-J. Eisler, V. C. Sundar, M. G. Bawendi, M. Walsh, H. I. Smith, and V. Klimov, “Color-selective semiconductor nanocrystal laser,” Appl. Phys. Lett. |

9. | P. T. Snee, Y. Chan, D. G. Nocera, and M. G. Bawendi, “Whispering-gallery-mode lasing from a semiconductor nanocrystal/microsphere resonator composite,” Adv. Mater. |

10. | B. Min, S. Kim, K. Okamoto, L. Yang, A. Scherer, H. Atwater, and K. Vahala, “Ultralow threshold on-chip microcavity nanocrystal quantum dot lasers,” Appl. Phys. Lett. |

11. | V. I. Klimov, A. A. Mikhailovsky, S. Xu, A. Malko, J. A. Hollingsworth, C. A. Leatherdale, H.-J. Eisler, and M. G. Bawendi, “Optical gain and stimulated emission in nanocrystal quantum dots,” Science |

12. | V. I. Klimov, A. A. Mikhailovsky, D. W. McBranch, C. A. Leatherdale, and M. G. Bawendi, “Quantization of multiparticle Auger Rates in semiconductor quantum dots,” Science |

13. | H. Htoon, J. Hollingsworth, R. Dickerson, and V. Klimov, “Effect of zero- to one-dimensional transformation on multiparticle Auger recombination in semiconductor quantum rods,” Phys. Rev. Lett. |

14. | H. Htoon, J. A. Hollingworth, A. V. Malko, R. Dickerson, and V. I. Klimov, “Light amplification in semiconductor nanocrystals: quantum rods versus quantum dots,” Appl. Phys. Lett. |

15. | M. Kazes, D. Lewis, Y. Ebenstein, T. Mokari, and U. Banin, “Lasing from semiconductor quantum rods in a cylindrical microcavity,” Adv. Mater. |

16. | S. A. Ivanov, J. Nanda, A. Piryatinski, M. Achermann, L. P. Balet, I. V. Bezel, P. O. Anikeeva, S. Tretiak, and V. I. Klimov, “Light amplification using inverted core/shell nanocrystals: towards lasing in the single-exciton regime,” J. Phys. Chem. B |

17. | J. Nanda, S. A. Ivanov, H. Htoon, I. Bezel, A. Piryatinski, S. Tretiak, and V. I. Klimov, “Absorption cross sections and Auger recombination lifetimes in inverted core-shell nanocrystals: Implications for lasing performance,” J. Appl. Phys. |

18. | E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. |

19. | V. I. Klimov, “From fundamental photophysics to multicolor lasing,” Los Alamos Science |

20. | M. Nirmal, B. O. Dabbousi, M. G. Bawendi, J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, “Fluorescence intermittency in single cadmium selenide nanocrystals,” Nature |

21. | M. Jones, J. Nedeljkovic, R. J. Ellingson, A. J. Nozik, and G. Rumbles, “Photoenhancement of luminescence in colloidal CdSe quantum dot solutions,” J. Phys. Chem. B |

22. | J. Gerard, “Solid-state cavity-quantum electrodynamics with self-assembled quantum dots,” Top. of Appl. Phys. |

23. | Y. Zhang, I. Bulu, W.-M. Tam, B. Levitt, J. Shah, T. Botto, and M. Loncar, “High-Q/V air-mode photonic crystal cavities at microwave frequencies,” Opt. Express |

24. | W. G. J. H. M. van Sark, P. L. T. M. Frederix, D. J. Van den Heuvel, H. C. Gerritsen, A. A. Bol, J. N. J. van Lingen, C. de Mello Donegá, and A. Meijerink, “Photooxidation and photobleaching of single CdSe/ZnS quantum dots probed by room-temperature time-resolved spectroscopy,” J. Phys. Chem. B |

25. | B. Lounis, H. A. Bechtel, D. Gerion, P. Alivisatos, and W. E. Moerner, “Photon antibunching in single CdSe/ZnS quantum dot fluorescence,” Chem. Phys. Lett. |

26. | J.-M. Caruge, Y. Chan, V. Sundar, H. Eisler, and M. Bawendi, “Transient photoluminescence and simultaneous amplified spontaneous emission from multiexciton states in CdSe quantum dots,” Phys. Rev. B |

27. | S. Empedocles, D. Norris, and M. Bawendi, “Photoluminescence spectroscopy of single CdSe nanocrystallite quantum dots,” Phys. Rev. Lett. |

28. | S. A. Empedocles and M. G. Bawendi, “Influence of spectral diffusion on the line shapes of single CdSe nanocrystallite quantum dots,” J. Phys. Chem. B |

29. | D. Norris and M. Bawendi, “Measurement and assignment of the size-dependent optical spectrum in CdSe quantum dots,” Phys. Rev. B, |

30. | D. F. Walls and G. J. Milburn, |

31. | O. Benson and Y. Yamamoto, “Master-equation model of a single-quantum-dot microsphere laser,” Phys. Rev. A |

32. | G. Bjork and Y. Yamamoto, “Analysis of semiconductor microcavity lasers using rate equations,” IEEE J. Quantum Electron. |

33. | P. W. Milonni and J. H. Eberly, |

34. | M. Bruchez, M. Moronne, P. Gin, S. Weiss, and A. P. Alivisatos, “Semiconductor nanocrystals as fluorescent biological labels,” Science |

35. | R. Bose, X. Yang, R. Chatterjee, J. Gao, and C. W. Wong, “Weak coupling interactions of colloidal lead sulphide nanocrystals with silicon photonic crystal nanocavities near 1.55μm at room temperature,” Appl. Phys. Lett. |

36. | I. Fushman, D. Englund, and J. Vuckovic, “Coupling of PbS quantum dots to photonic crystal cavities at room temperature,” Appl. Phys. Lett. |

37. | M. T. Rakher, R. Bose, C. W. Wong, and K. Srinivasan, “Fiber-based cryogenic and time-resolved spectroscopy of PbS quantum dots,” Opt. Express |

38. | M. T. Rakher, R. Bose, C. W. Wong, and K. Srinivasan, “Spectroscopy of 1.55μm PbS quantum dots on Si photonic crystal cavities with a fiber taper waveguide,” Appl. Phys. Lett. |

39. | Z. Wu, Z. Mi, P. Bhattacharya, T. Zhu, and J. Xu, “Enhanced spontaneous emission at 1.55μm from colloidal PbSe quantum dots in a Si photonic crystal microcavity,” Appl. Phys. Lett. |

40. | J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, Henry I. Smith, and E. P. Ippen, “Microcavities in optical waveguides,” Nature |

41. | P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. |

42. | Q. Quan and M. Loncar, “Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities,” Opt. Express |

43. | M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature |

44. | M. Khan, T. Babinec, M. W. McCutcheon, P. Deotare, and M. Loncar, “Fabrication and characterization of high-quality-factor silicon nitride nanobeam cavities,” Opt. Lett. |

45. | S. Gupta and E. Waks, “Spontaneous emission enhancement and saturable absorption of colloidal quantum dots coupled to photonic crystal cavity,” Opt. Express |

46. | P. Velha, E. Picard, T. Charvolin, E. Hadji, J. C. Rodier, P. Lalanne, and D. Peyrade, “Ultra-High Q/V Fabry-Perot microcavity on SOI substrate,” Opt. Express |

47. | A. R. Zain, N. P. Johnson, M. Sorel, and R. M. De La Rue, “Ultra high quality factor one dimensional photonic crystal/photonic wire micro-cavities in silicon-on-insulator (SOI),” Opt. Express |

48. | Y. Gong and J. Vuckovic, “Photonic crystal cavities in silicon dioxide,” Appl. Phys. Lett. |

49. | A. Rundquist, A. Majumdar, and J. Vuckovic, “Off-resonant coupling between a single quantum dot and a nanobeam photonic crystal cavity,” Appl. Phys. Lett. |

50. | K. Rivoire, S. Buckley, and J. Vuckovic, “Multiply resonant high quality photonic crystal nanocavities,” Appl. Phys. Lett. |

51. | J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a zipper photonic crystal optomechanical cavity” Opt. Express |

52. | Q. Quan, P. B. Deotare, and M. Loncar, “Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide,” Appl. Phys. Lett. |

53. | M. Barth, J. Kouba, J. Stingl, B. Löchel, and O. Benson, “Modification of visible spontaneous emission with silicon nitride photonic crystal nanocavities,” Opt. Express |

54. | J. Zhao, G. Nair, B. R. Fisher, and M. G. Bawendi, “Challenge to the charging model of semiconductor-nanocrystal fluorescence intermittency from off-state quantum yields and multiexciton blinking,” Phys. Rev. Lett. |

55. | M. Kuno, D. Fromm, S. Johnson, A. Gallagher, and D. Nesbitt, “Modeling distributed kinetics in isolated semiconductor quantum dots,” Phys. Rev. B |

56. | J. T. Choy, B. J. M. Hausmann, T. M. Babinec, I. Bulu, M. Khan, P. Maletinsky, A. Yacoby, and M. Lončar, “Enhanced single-photon emission from a diamondsilver aperture,” Nat. Photonics |

**OCIS Codes**

(230.5590) Optical devices : Quantum-well, -wire and -dot devices

(270.5580) Quantum optics : Quantum electrodynamics

(230.5298) Optical devices : Photonic crystals

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: October 21, 2013

Revised Manuscript: January 24, 2014

Manuscript Accepted: January 24, 2014

Published: February 3, 2014

**Citation**

Shilpi Gupta and Edo Waks, "Overcoming Auger recombination in nanocrystal quantum dot laser using spontaneous emission enhancement," Opt. Express **22**, 3013-3027 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-3-3013

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### References

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- M. Kuno, D. Fromm, S. Johnson, A. Gallagher, D. Nesbitt, “Modeling distributed kinetics in isolated semiconductor quantum dots,” Phys. Rev. B 67, 1–15 (2003). [CrossRef]
- J. T. Choy, B. J. M. Hausmann, T. M. Babinec, I. Bulu, M. Khan, P. Maletinsky, A. Yacoby, M. Lončar, “Enhanced single-photon emission from a diamondsilver aperture,” Nat. Photonics 5, 738–743 (2011). [CrossRef]

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