The dynamics of produced excited carriers under the irradiation of Ge crystal is investigated theoretically by using femtosecond laser pulse. A two-temperature model combined with the Drude model is also used to study the nonequilibrium carrier density, carrier and lattice temperatures, and optical properties of the crystal. The properties of the surface plasmon wave when excited are also studied. The influences of non-radiation and radiative recombination process on the photoexcitation of the semiconductor during pulse and the relaxation after the pulse are described in detail. The results show that the effects of Auger recombination on the nonequilibrium carrier density and optical properties of the crystal and the properties of the surface plasmon polariton are great, whereas the effect of radiative recombination is extremely small.
Jia-Qi Ju(居家奇), Zi-Yao Qin(秦子尧), Ju-Kun Liu(刘聚坤), Hong-Wei Zhao(赵宏伟), Yao-Qing Huang(黄耀清), Rong-Rong Hu(胡蓉蓉), and Hua Wu(吴华)$ Effect of recombination process in femtosecond laser-induced modification on Ge crystal 2020 Chin. Phys. B 29 114208
Symbol
Description
Value
Ref.
D0/cm2⋅s−1
ambipolar diffusion coefficient
2.1 × 105Te
γR/cm3⋅s−1
radiative recombination coefficient
1 × 10−9
[28]
γA/cm6⋅s−1
Auger recombination coefficient
2 × 10−31
[29]
θ/m2
free carrier absorption coefficient
5 × 10−22
[30]
τep/fs
electron–phonon relaxation time
300
[31]
Ce/J⋅m−3⋅K−1
electron heat capacity
3NekB
Cl/J⋅m−3⋅K−1
lattice heat capacity
1.7 × (1+Tl/6000)
[32]
κe/eV⋅s−1⋅m−1⋅K−1
electron thermal conductivity
− 3.58 × 1019 + 6.49 × 1016Te
[32]
κl/W⋅m−1⋅K−1
lattice thermal conductivity
675 × Tl−1.23
[32]
τD/fs
Drude damping time
1
[30]
effective optical mass of carriers
0.22
[32]
ε
unexcited dielectric constant
22.08+ i 3.03
[26]
Eg/eV
band gap
0.803-3.9 × 10−4Tl
[32]
Table 1.
Parameters of Ge crystal at 800-nm light.
Fig. 1.
Time-dependent dynamic behaviors of (a) carrier density and (b) carrier temperature on surface of Ge sample irradiated by 50-fs laser pulse of F = 0.1 J/cm2 for different situations with Ip representing laser pulse.
Fig. 2.
Evolutions of (a) lattice temperature, (b) real part, and (c) imaginary part of dielectric constant, and (d) reflectivity on Ge surface, with black dash line in panel (a) denoting melting temperature.
Fig. 3.
Laser fluence-dependent (a) maximum carrier density, (b) carrier temperature, and (c) lattice temperature on surface of a 100-nm-thick Ge sample heated by 50-fs laser pulse for γR = 0, and γA and γR ≠ 0.
Fig. 4.
Calculated time evolutions of (a) surface electron and (b) lattice temperature for different electron–phonon relaxation times, with black dash line in panel (b) representing melting temperature.
Fig. 5.
Calculated relationship between (a) carrier density and real part of dielectric constant, and time evolutions of (b) imaginary part and (c) real part, with a denoting Drude model, and b referring to Drude model with the effect of state renormalization and band filling and band gap renormalization considered.
Fig. 6.
SP wavelength versus (a) carrier density and (b) laser fluence.
Fig. 7.
SP propagation length (a) parallel and (b) perpendicular to surface versus laser fluence.
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