An exciton scattering model for carrier multiplication in semiconductor nanocrystals: Theory

Journal of Chemical Physics

Volumn 133, Issue 8, 2010, Pages

  Piryatinski, Andrei ^a   Velizhanin, Kirill A ^a  

^a CENTER FOR NONLINEAR STUDIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIEXCITON; BIEXCITON STATE; CARRIER MULTIPLICATION; CLOSED SET; COULOMB COUPLINGS; INTERBAND; INTERBAND SCATTERING; LIMITING CASE; MULTIEXCITONS; NUMERICAL CALCULATION; PHOTOGENERATION; POPULATION RELAXATION; PROJECTION OPERATOR; PUMP PULSE; SCATTERING MATRIX ELEMENTS; SCATTERING MODEL; SEMICONDUCTOR NANOCRYSTALS; THEORETICAL MODELS; TIME-DEPENDENT DENSITY MATRIX;

DYNAMICS; EXCITONS; MATHEMATICAL OPERATORS; NANOCRYSTALS;

SCATTERING;

EID: 77956313293     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3474576     Document Type: Article

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69. B T.
70. The poles are assumed to be of the first order which is the general situation for arbitrary Coulomb coupling. Two poles can coincide if we use the second-order expansion of Eq.. This results in the renormalization of the energy in the exponential but the form of Eq. will still be the same.
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77. This follows from the observation that for Vx,xx →0, +x = - xx =1/2 and -x = + xx =0.
78. 2 /2 τ pm 2 ≈ 2π τ E pm (0) δ (t) and further substituted into Eqs. to get the pulse self-convolution functions.
79. α (ω) is a constant for ω varying within the range defined by Vx,xx.
80. 1) ∼ τpm E pm (0) 2.
81. The self-energy contributions to the energy are dropped because they correspond to fourth-order corrections.