Abstract

A robust, computationally efficient modeling method describing multi-pulse femtosecond laser-material interaction is required to determine the optimal laser parameters to control and differentiate non-thermal ablation and heat accumulation processes for surface structuring and laser welding applications. We establish a three-dimensional, two-temperature model (TTM) and a heat-accumulation model based on classical heat generation and conduction equations to evaluate their efficacy and efficiency in simulating non-thermal ablation and heat accumulation during multi-pulse femtosecond laser processing of silicon. Only the TTM is capable of accurately predicting the laser fluences required to achieve non-thermal ablation, which is experimentally validated. Both the TTM and the classical heat accumulation model can predict heat accumulation. The TTM can accurately predict heat accumulation, but requires lengthy simulation times on the order of several hours. The classical heat accumulation model consistently predicts heat accumulation with the TTM and is time efficient, but is case specific to interaction parameters, requiring input of an experimentally-determined absorption coefficient. For the first time to our knowledge, an integrated modeling method is devised to accurately and efficiently simulate laser-processing-induced heat accumulation by using the TTM to determine an absorption coefficient to feed back to the heat accumulation model to extend it to the general case. This integrated modeling method enables the accurate prediction of heat accumulation with simulation times on the order of a minute per pulse, defining a path to determine laser parameters to control heat accumulation for specific processing applications.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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2016 (4)

D. R. Austin, K. R. P. Kafka, Y. H. Lai, Z. Wang, K. Zhang, H. Li, C. I. Blaga, A. Y. Yi, L. F. DiMauro, and E. A. Chowdhury, “High Spatial Frequency Laser Induced Periodic Surface Structure Formation in Germanium under Strong Mid-IR Fields,” J. Appl. Phys. 120(14), 143103 (2016).
[Crossref]

L. L. Taylor, J. Qiao, and J. Qiao, “Optimization of Femtosecond Laser Processing of Silicon via Numerical Modeling,” Opt. Mater. Express 6(9), 2745–2758 (2016).
[Crossref]

B. Neuenschwander, B. Jaeggi, M. Zimmermannn, V. Markovic, B. Resan, K. Weingarten, R. de Loor, and L. Penning, “Laser Surface Structuring with 100 W of Average Power and Sub-ps Pulses,” J. Laser Appl. 28(2), 022506 (2016).
[Crossref]

M. V. Shugaev, C. Wu, O. Armbruster, A. Naghilou, N. Brouwer, D. S. Ivanov, T. J.-Y. Derrien, N. M. Bulgakova, W. Kautek, B. Rethfeld, and L. V. Zhigilei, “Fundamentals of Ultrafast Laser–Material Interaction,” MRS Bull. 41(12), 960–968 (2016).
[Crossref]

2015 (3)

2014 (3)

A. M. K. Hafiz, E. V. Bordatchev, and R. O. Tutunea-Fatan, “Experimental Analysis of Applicability of a Picosecond Laser for Micro-Polishing of Micromilled Inconel 718 Superalloy,” Int. J. Adv. Manuf. Technol. 70(9–12), 1963–1978 (2014).
[Crossref]

H. L. An, A. Arriola, S. Gross, A. Fuerbach, M. J. Withford, and S. Fleming, “Creating Large Second-Order Optical Nonlinearity in Optical Waveguides Written by Femtosecond Laser Pulses in Boro-Aluminosilicate Glass,” Appl. Phys. Lett. 104(2), 021113 (2014).
[Crossref]

C. Wu and L. V. Zhigilei, “Microscopic mechanisms of laser spallation and ablation of metal targets from large-scale molecular dynamics simulations,” Appl. Phys., A Mater. Sci. Process. 114(1), 11–32 (2014).
[Crossref]

2013 (1)

2012 (1)

J. Thorstensen and S. E. Foss, “Temperature Dependent Ablation Threshold in Silicon Using Ultrashort Laser Pulses,” J. Appl. Phys. 112(10), 103514 (2012).
[Crossref]

2011 (1)

2008 (1)

2005 (2)

J. K. Chen, D. Y. Tzou, and J. E. Beraun, “Numerical Investigation of Ultrashort Laser Damage in Semiconductors,” Int. J. Heat Mass Transf. 48(3–4), 501–509 (2005).

A. Y. Vorobyev and C. Guo, “Direct Observation of Enhanced Residual Thermal Energy Coupling to Solids in Femtosecond Laser Ablation,” Appl. Phys. Lett. 86(1), 011916 (2005).
[Crossref]

2002 (1)

S. K. Sundaram and E. Mazur, “Inducing and Probing Non-Thermal Transitions in Semiconductors Using Femtosecond Laser Pulses,” Nat. Mater. 1(4), 217–224 (2002).
[Crossref] [PubMed]

1987 (1)

H. M. Van Driel, “Kinetics of High-Density Plasmas Generated in Si by 1.06- and 0.53- µm Picosecond Laser Pulses,” Phys. Rev. B Condens. Matter 35(15), 8166–8176 (1987).
[Crossref] [PubMed]

1982 (1)

1965 (1)

B. E. Deal and A. S. Grove, “General Relationship for the Thermal Oxidation of Silicon,” J. Appl. Phys. 36(12), 3770–3778 (1965).
[Crossref]

An, H. L.

H. L. An, A. Arriola, S. Gross, A. Fuerbach, M. J. Withford, and S. Fleming, “Creating Large Second-Order Optical Nonlinearity in Optical Waveguides Written by Femtosecond Laser Pulses in Boro-Aluminosilicate Glass,” Appl. Phys. Lett. 104(2), 021113 (2014).
[Crossref]

Armbruster, O.

M. V. Shugaev, C. Wu, O. Armbruster, A. Naghilou, N. Brouwer, D. S. Ivanov, T. J.-Y. Derrien, N. M. Bulgakova, W. Kautek, B. Rethfeld, and L. V. Zhigilei, “Fundamentals of Ultrafast Laser–Material Interaction,” MRS Bull. 41(12), 960–968 (2016).
[Crossref]

Arriola, A.

H. L. An, A. Arriola, S. Gross, A. Fuerbach, M. J. Withford, and S. Fleming, “Creating Large Second-Order Optical Nonlinearity in Optical Waveguides Written by Femtosecond Laser Pulses in Boro-Aluminosilicate Glass,” Appl. Phys. Lett. 104(2), 021113 (2014).
[Crossref]

Austin, D. R.

D. R. Austin, K. R. P. Kafka, Y. H. Lai, Z. Wang, K. Zhang, H. Li, C. I. Blaga, A. Y. Yi, L. F. DiMauro, and E. A. Chowdhury, “High Spatial Frequency Laser Induced Periodic Surface Structure Formation in Germanium under Strong Mid-IR Fields,” J. Appl. Phys. 120(14), 143103 (2016).
[Crossref]

Bauer, F.

Beraun, J. E.

J. K. Chen, D. Y. Tzou, and J. E. Beraun, “Numerical Investigation of Ultrashort Laser Damage in Semiconductors,” Int. J. Heat Mass Transf. 48(3–4), 501–509 (2005).

Bian, H.

Blaga, C. I.

D. R. Austin, K. R. P. Kafka, Y. H. Lai, Z. Wang, K. Zhang, H. Li, C. I. Blaga, A. Y. Yi, L. F. DiMauro, and E. A. Chowdhury, “High Spatial Frequency Laser Induced Periodic Surface Structure Formation in Germanium under Strong Mid-IR Fields,” J. Appl. Phys. 120(14), 143103 (2016).
[Crossref]

Bordatchev, E. V.

A. M. K. Hafiz, E. V. Bordatchev, and R. O. Tutunea-Fatan, “Experimental Analysis of Applicability of a Picosecond Laser for Micro-Polishing of Micromilled Inconel 718 Superalloy,” Int. J. Adv. Manuf. Technol. 70(9–12), 1963–1978 (2014).
[Crossref]

Brouwer, N.

M. V. Shugaev, C. Wu, O. Armbruster, A. Naghilou, N. Brouwer, D. S. Ivanov, T. J.-Y. Derrien, N. M. Bulgakova, W. Kautek, B. Rethfeld, and L. V. Zhigilei, “Fundamentals of Ultrafast Laser–Material Interaction,” MRS Bull. 41(12), 960–968 (2016).
[Crossref]

Bulgakova, N. M.

M. V. Shugaev, C. Wu, O. Armbruster, A. Naghilou, N. Brouwer, D. S. Ivanov, T. J.-Y. Derrien, N. M. Bulgakova, W. Kautek, B. Rethfeld, and L. V. Zhigilei, “Fundamentals of Ultrafast Laser–Material Interaction,” MRS Bull. 41(12), 960–968 (2016).
[Crossref]

Carter, R. M.

Chen, F.

Chen, J.

Chen, J. K.

J. K. Chen, D. Y. Tzou, and J. E. Beraun, “Numerical Investigation of Ultrashort Laser Damage in Semiconductors,” Int. J. Heat Mass Transf. 48(3–4), 501–509 (2005).

Chen, W.-J.

Chowdhury, E. A.

D. R. Austin, K. R. P. Kafka, Y. H. Lai, Z. Wang, K. Zhang, H. Li, C. I. Blaga, A. Y. Yi, L. F. DiMauro, and E. A. Chowdhury, “High Spatial Frequency Laser Induced Periodic Surface Structure Formation in Germanium under Strong Mid-IR Fields,” J. Appl. Phys. 120(14), 143103 (2016).
[Crossref]

Cvecek, K.

de Loor, R.

B. Neuenschwander, B. Jaeggi, M. Zimmermannn, V. Markovic, B. Resan, K. Weingarten, R. de Loor, and L. Penning, “Laser Surface Structuring with 100 W of Average Power and Sub-ps Pulses,” J. Laser Appl. 28(2), 022506 (2016).
[Crossref]

Deal, B. E.

B. E. Deal and A. S. Grove, “General Relationship for the Thermal Oxidation of Silicon,” J. Appl. Phys. 36(12), 3770–3778 (1965).
[Crossref]

Deng, Z.

Derrien, T. J.-Y.

M. V. Shugaev, C. Wu, O. Armbruster, A. Naghilou, N. Brouwer, D. S. Ivanov, T. J.-Y. Derrien, N. M. Bulgakova, W. Kautek, B. Rethfeld, and L. V. Zhigilei, “Fundamentals of Ultrafast Laser–Material Interaction,” MRS Bull. 41(12), 960–968 (2016).
[Crossref]

DiMauro, L. F.

D. R. Austin, K. R. P. Kafka, Y. H. Lai, Z. Wang, K. Zhang, H. Li, C. I. Blaga, A. Y. Yi, L. F. DiMauro, and E. A. Chowdhury, “High Spatial Frequency Laser Induced Periodic Surface Structure Formation in Germanium under Strong Mid-IR Fields,” J. Appl. Phys. 120(14), 143103 (2016).
[Crossref]

Eaton, S. M.

Eppelt, U.

Fleming, S.

H. L. An, A. Arriola, S. Gross, A. Fuerbach, M. J. Withford, and S. Fleming, “Creating Large Second-Order Optical Nonlinearity in Optical Waveguides Written by Femtosecond Laser Pulses in Boro-Aluminosilicate Glass,” Appl. Phys. Lett. 104(2), 021113 (2014).
[Crossref]

Foss, S. E.

J. Thorstensen and S. E. Foss, “Temperature Dependent Ablation Threshold in Silicon Using Ultrashort Laser Pulses,” J. Appl. Phys. 112(10), 103514 (2012).
[Crossref]

Fuerbach, A.

H. L. An, A. Arriola, S. Gross, A. Fuerbach, M. J. Withford, and S. Fleming, “Creating Large Second-Order Optical Nonlinearity in Optical Waveguides Written by Femtosecond Laser Pulses in Boro-Aluminosilicate Glass,” Appl. Phys. Lett. 104(2), 021113 (2014).
[Crossref]

Gross, S.

H. L. An, A. Arriola, S. Gross, A. Fuerbach, M. J. Withford, and S. Fleming, “Creating Large Second-Order Optical Nonlinearity in Optical Waveguides Written by Femtosecond Laser Pulses in Boro-Aluminosilicate Glass,” Appl. Phys. Lett. 104(2), 021113 (2014).
[Crossref]

Grove, A. S.

B. E. Deal and A. S. Grove, “General Relationship for the Thermal Oxidation of Silicon,” J. Appl. Phys. 36(12), 3770–3778 (1965).
[Crossref]

Guo, C.

A. Y. Vorobyev and C. Guo, “Direct Observation of Enhanced Residual Thermal Energy Coupling to Solids in Femtosecond Laser Ablation,” Appl. Phys. Lett. 86(1), 011916 (2005).
[Crossref]

Hafiz, A. M. K.

A. M. K. Hafiz, E. V. Bordatchev, and R. O. Tutunea-Fatan, “Experimental Analysis of Applicability of a Picosecond Laser for Micro-Polishing of Micromilled Inconel 718 Superalloy,” Int. J. Adv. Manuf. Technol. 70(9–12), 1963–1978 (2014).
[Crossref]

Hand, D. P.

Hartmann, C.

Herman, P. R.

Ho, S.

Hou, X.

Ivanov, D. S.

M. V. Shugaev, C. Wu, O. Armbruster, A. Naghilou, N. Brouwer, D. S. Ivanov, T. J.-Y. Derrien, N. M. Bulgakova, W. Kautek, B. Rethfeld, and L. V. Zhigilei, “Fundamentals of Ultrafast Laser–Material Interaction,” MRS Bull. 41(12), 960–968 (2016).
[Crossref]

Jaeggi, B.

B. Neuenschwander, B. Jaeggi, M. Zimmermannn, V. Markovic, B. Resan, K. Weingarten, R. de Loor, and L. Penning, “Laser Surface Structuring with 100 W of Average Power and Sub-ps Pulses,” J. Laser Appl. 28(2), 022506 (2016).
[Crossref]

Kafka, K. R. P.

D. R. Austin, K. R. P. Kafka, Y. H. Lai, Z. Wang, K. Zhang, H. Li, C. I. Blaga, A. Y. Yi, L. F. DiMauro, and E. A. Chowdhury, “High Spatial Frequency Laser Induced Periodic Surface Structure Formation in Germanium under Strong Mid-IR Fields,” J. Appl. Phys. 120(14), 143103 (2016).
[Crossref]

Kautek, W.

M. V. Shugaev, C. Wu, O. Armbruster, A. Naghilou, N. Brouwer, D. S. Ivanov, T. J.-Y. Derrien, N. M. Bulgakova, W. Kautek, B. Rethfeld, and L. V. Zhigilei, “Fundamentals of Ultrafast Laser–Material Interaction,” MRS Bull. 41(12), 960–968 (2016).
[Crossref]

Kiedrowski, T.

Lai, Y. H.

D. R. Austin, K. R. P. Kafka, Y. H. Lai, Z. Wang, K. Zhang, H. Li, C. I. Blaga, A. Y. Yi, L. F. DiMauro, and E. A. Chowdhury, “High Spatial Frequency Laser Induced Periodic Surface Structure Formation in Germanium under Strong Mid-IR Fields,” J. Appl. Phys. 120(14), 143103 (2016).
[Crossref]

Li, H.

D. R. Austin, K. R. P. Kafka, Y. H. Lai, Z. Wang, K. Zhang, H. Li, C. I. Blaga, A. Y. Yi, L. F. DiMauro, and E. A. Chowdhury, “High Spatial Frequency Laser Induced Periodic Surface Structure Formation in Germanium under Strong Mid-IR Fields,” J. Appl. Phys. 120(14), 143103 (2016).
[Crossref]

Li, J.

Liu, J. M.

Markovic, V.

B. Neuenschwander, B. Jaeggi, M. Zimmermannn, V. Markovic, B. Resan, K. Weingarten, R. de Loor, and L. Penning, “Laser Surface Structuring with 100 W of Average Power and Sub-ps Pulses,” J. Laser Appl. 28(2), 022506 (2016).
[Crossref]

Mazur, E.

S. K. Sundaram and E. Mazur, “Inducing and Probing Non-Thermal Transitions in Semiconductors Using Femtosecond Laser Pulses,” Nat. Mater. 1(4), 217–224 (2002).
[Crossref] [PubMed]

Meng, X.

Michalowski, A.

Miyamoto, I.

Naghilou, A.

M. V. Shugaev, C. Wu, O. Armbruster, A. Naghilou, N. Brouwer, D. S. Ivanov, T. J.-Y. Derrien, N. M. Bulgakova, W. Kautek, B. Rethfeld, and L. V. Zhigilei, “Fundamentals of Ultrafast Laser–Material Interaction,” MRS Bull. 41(12), 960–968 (2016).
[Crossref]

Neuenschwander, B.

B. Neuenschwander, B. Jaeggi, M. Zimmermannn, V. Markovic, B. Resan, K. Weingarten, R. de Loor, and L. Penning, “Laser Surface Structuring with 100 W of Average Power and Sub-ps Pulses,” J. Laser Appl. 28(2), 022506 (2016).
[Crossref]

Ng, M. L.

Nolte, S.

Penning, L.

B. Neuenschwander, B. Jaeggi, M. Zimmermannn, V. Markovic, B. Resan, K. Weingarten, R. de Loor, and L. Penning, “Laser Surface Structuring with 100 W of Average Power and Sub-ps Pulses,” J. Laser Appl. 28(2), 022506 (2016).
[Crossref]

Qiao, J.

Resan, B.

B. Neuenschwander, B. Jaeggi, M. Zimmermannn, V. Markovic, B. Resan, K. Weingarten, R. de Loor, and L. Penning, “Laser Surface Structuring with 100 W of Average Power and Sub-ps Pulses,” J. Laser Appl. 28(2), 022506 (2016).
[Crossref]

Rethfeld, B.

M. V. Shugaev, C. Wu, O. Armbruster, A. Naghilou, N. Brouwer, D. S. Ivanov, T. J.-Y. Derrien, N. M. Bulgakova, W. Kautek, B. Rethfeld, and L. V. Zhigilei, “Fundamentals of Ultrafast Laser–Material Interaction,” MRS Bull. 41(12), 960–968 (2016).
[Crossref]

Russ, S.

Schmidt, M.

Schulz, W.

Shan, C.

Shugaev, M. V.

M. V. Shugaev, C. Wu, O. Armbruster, A. Naghilou, N. Brouwer, D. S. Ivanov, T. J.-Y. Derrien, N. M. Bulgakova, W. Kautek, B. Rethfeld, and L. V. Zhigilei, “Fundamentals of Ultrafast Laser–Material Interaction,” MRS Bull. 41(12), 960–968 (2016).
[Crossref]

Siebert, C.

Sun, M.

Sundaram, S. K.

S. K. Sundaram and E. Mazur, “Inducing and Probing Non-Thermal Transitions in Semiconductors Using Femtosecond Laser Pulses,” Nat. Mater. 1(4), 217–224 (2002).
[Crossref] [PubMed]

Taylor, L. L.

Thomson, R. R.

Thorstensen, J.

J. Thorstensen and S. E. Foss, “Temperature Dependent Ablation Threshold in Silicon Using Ultrashort Laser Pulses,” J. Appl. Phys. 112(10), 103514 (2012).
[Crossref]

Tutunea-Fatan, R. O.

A. M. K. Hafiz, E. V. Bordatchev, and R. O. Tutunea-Fatan, “Experimental Analysis of Applicability of a Picosecond Laser for Micro-Polishing of Micromilled Inconel 718 Superalloy,” Int. J. Adv. Manuf. Technol. 70(9–12), 1963–1978 (2014).
[Crossref]

Tzou, D. Y.

J. K. Chen, D. Y. Tzou, and J. E. Beraun, “Numerical Investigation of Ultrashort Laser Damage in Semiconductors,” Int. J. Heat Mass Transf. 48(3–4), 501–509 (2005).

Van Driel, H. M.

H. M. Van Driel, “Kinetics of High-Density Plasmas Generated in Si by 1.06- and 0.53- µm Picosecond Laser Pulses,” Phys. Rev. B Condens. Matter 35(15), 8166–8176 (1987).
[Crossref] [PubMed]

Vorobyev, A. Y.

A. Y. Vorobyev and C. Guo, “Direct Observation of Enhanced Residual Thermal Energy Coupling to Solids in Femtosecond Laser Ablation,” Appl. Phys. Lett. 86(1), 011916 (2005).
[Crossref]

Wang, Z.

D. R. Austin, K. R. P. Kafka, Y. H. Lai, Z. Wang, K. Zhang, H. Li, C. I. Blaga, A. Y. Yi, L. F. DiMauro, and E. A. Chowdhury, “High Spatial Frequency Laser Induced Periodic Surface Structure Formation in Germanium under Strong Mid-IR Fields,” J. Appl. Phys. 120(14), 143103 (2016).
[Crossref]

Weingarten, K.

B. Neuenschwander, B. Jaeggi, M. Zimmermannn, V. Markovic, B. Resan, K. Weingarten, R. de Loor, and L. Penning, “Laser Surface Structuring with 100 W of Average Power and Sub-ps Pulses,” J. Laser Appl. 28(2), 022506 (2016).
[Crossref]

Withford, M. J.

H. L. An, A. Arriola, S. Gross, A. Fuerbach, M. J. Withford, and S. Fleming, “Creating Large Second-Order Optical Nonlinearity in Optical Waveguides Written by Femtosecond Laser Pulses in Boro-Aluminosilicate Glass,” Appl. Phys. Lett. 104(2), 021113 (2014).
[Crossref]

Wu, C.

M. V. Shugaev, C. Wu, O. Armbruster, A. Naghilou, N. Brouwer, D. S. Ivanov, T. J.-Y. Derrien, N. M. Bulgakova, W. Kautek, B. Rethfeld, and L. V. Zhigilei, “Fundamentals of Ultrafast Laser–Material Interaction,” MRS Bull. 41(12), 960–968 (2016).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 (a) TTM-simulated maximum electron number density versus laser fluence for laser-silicon interaction (300-fs pulse width, 1030-nm wavelength). The dashed line marks the critical density above which ablation occurs (6.9 × 1020 cm−3 [17]). (b) Predicted carrier number density, carrier temperature, and lattice temperature with respective maxima of 9.3 × 1020 cm−3, 2.1 × 104 K, and 847 K for a TTM simulation at the laser fluence of 0.53 J/cm2. The vertical line marks the time of peak pulse intensity at 0 ps.
Fig. 2
Fig. 2 (a) Ablated crater area on silicon versus laser pulse fluence. The ablation threshold was determined to be 0.43 J/cm2, corresponding to the x-intercept of the regression. (b) Surface height map of single-shot laser ablation of silicon at 0.65 J/cm2 fluence with depth and width on the orders of 10 nm and 35 µm, respectively.
Fig. 3
Fig. 3 3D-TTM prediction of maximum surface temperature versus time for multi-pulse laser processing of silicon using a 350-fs pulse width, a 515-nm wavelength, a 0.52 J/cm2 peak laser fluence (~0.2 J/cm2 ablation threshold for 515-nm silicon processing [17]), a 500-kHz repetition rate, and a 4 m/s scanning speed. The two horizontal lines mark the melting point (Tm = 1687 K) and the temperature at which oxidation becomes significant (To = 973 K) for silicon.
Fig. 4
Fig. 4 Surface temperature versus time/arrival of different pulses predicted by the classical heat accumulation model (dotted line) and 3D-TTM (solid line; from Fig. 3). Models consistently predict settling temperatures for the same set of simulation parameters (515-nm wavelength, 350-fs pulse width, 0.52 J/cm2 peak fluence, 500 kHz repetition rate, and 4 m/s laser scanning speed).
Fig. 5
Fig. 5 Comparison of the integrated modeling method (dashed line) and 3D-TTM (solid line) prediction of heat accumulation using the same laser parameters as in Fig. 4 (0.52-J/cm2 laser fluence, 500-kHz repetition rate, 4-m/s scanning speed, 350-fs pulse width, and 515-nm wavelength). The models consistently predict the rise and settling of surface temperatures.

Equations (11)

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N c t = G c D c J ¯
C e h T c t = S [ Γ ( T c T l ) + W ¯ + N c t ( E g + 3 k b T c ) + E g t N c ]  
ρ C l T l t = Γ ( T c T l ) + ( κ l T l )
A a b l a t e d = π w o 2 2 ln [ F l a s e r F t h r e s h o l d ]
ρ C l T l t = ( κ l T l )
E l = 2 A E p π w o 2 e 2 ( ( x x c ) 2 + ( y y c ) 2 ) w o 2 Δ x Δ y   +   E i
T l = E l ρ V C l ( T l )
η = E a E p
N c t = G c D c J ¯
C e h T c t = S [ Γ ( T c T l ) + W ¯ + N c t ( E g + 3 k b T c ) + E g t N c ]
ρ C l T l t = Γ ( T c T l ) + ( κ l T l )

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