There is no rigorous theory linking electron/hole capture cross-section with the trap energy. I am not aware of any rigorous theory for the cross-section of a trap for capture of electrons or holes. The capture cross-section represents the probability of the trap capturing the free carrier. It should depend upon the physical/chemical identity of the trap and more importantly upon the charge state of the trap. In general, it is believed that Coulombic attraction between the trap and the carrier increases capture cross-section, while Coulombic repulsion decreases the capture cross-section, by orders of magnitude. For a neutral trap, the capture cross-section is about 10E-14 to 10E-15 cm2, while in the case of Coulomb attraction, it may be as large as 10E-10, and for Coulomb repulsion, it may be as low as 10E-19 cm2. 

Experimental data are meagre in the case of GaAs traps. The main problem is that there are very few reliable techniques for the determination of the capture cross-section of the trap. However, there is substantial data on silicon/silicon-dioxide interface traps, obtained from the MOS admittance technique. Some experimental results indicated the capture cross-section to decrease with the interface trap energy moving towards the band edges.

References:

1. EH Nicollian and JR Brews, MOS Physics and Technology, Wiley, 1982. 

2. A. Rose, Concepts in Photoconductivity and Allied Problems, Wiley, 1963.

There is no rigorous theory linking electron/hole capture cross-section with the trap energy. I am not aware of any rigorous theory for the cross-section of a trap for capture of electrons or holes. The capture cross-section represents the probability of the trap capturing the free carrier. It should depend upon the physical/chemical identity of the trap and more importantly upon the charge state of the trap. In general, it is believed that Coulombic attraction between the trap and the carrier increases capture cross-section, while Coulombic repulsion decreases the capture cross-section, by orders of magnitude. For a neutral trap, the capture cross-section is about 10E-14 to 10E-15 cm2, while in the case of Coulomb attraction, it may be as large as 10E-10, and for Coulomb repulsion, it may be as low as 10E-19 cm2. 

Experimental data are meagre in the case of GaAs traps. The main problem is that there are very few reliable techniques for the determination of the capture cross-section of the trap. However, there is substantial data on silicon/silicon-dioxide interface traps, obtained from the MOS admittance technique. Some experimental results indicated the capture cross-section to decrease with the interface trap energy moving towards the band edges.

References:

1. EH Nicollian and JR Brews, MOS Physics and Technology, Wiley, 1982. 

2. A. Rose, Concepts in Photoconductivity and Allied Problems, Wiley, 1963.

@Samares Kar: Thank you, sir, for giving such detail information. Actually, I am doing some simulation studies where I have to give carrier lifetime and electron capture cross-section value for the different trap energy levels. As the carrier lifetime is dependent on the capture cross-section (SRH recombination), so for particular trap energy level I have to get the details related to electron capture cross-section. I got some papers where they have given data related to the electron capture cross section for GaAs material, but the values are different in papers. So I am not able to figure out which value should I use for my simulations.

Dear Jitendra,

a very systematic investigation/overview on trap characteristics in GaAs, GaP is given by Lang et al. (doi: 10.1103/PhysRevB.15.989). Their main finding is that the capture-cross-section is described by multi-phonon emission theory (see also: Ridley, Quantum processes in semiconductors).

The key parameters are the Huang-Rhys-Factor (S), lattice phonon energy (ħω) and the coupling element (ΔV) - all of which depend on the mechanical properties of the lattice and the trap state. A direct relation between trap depth and cross-section does not follow.

Note: In some systems the 'Meyer-Neldel-Rule' is observed, i.e. a linear, positive correlation between crossection (σ) and activation energy (Ea): log(σ) ∝ Ea. See Fig.4 in  doi: 10.1103/PhysRevB.46.12244.

Best regards

For trapping on shallow defects (

I do not work in this particular field anymore, yet, see, please, my following paper:

http://dx.doi.org/10.1016/0921-5107(96)01596-6

All the best,

JI

As a simple treatment, the capture cross-section for electrons is expressed as:

\sigma = 1/(N*\tau*v)

N= density of localized states(traps)

\tau= trapping lifetime

V= thermal velocity of electron

you may refer to:

1. Hoesterey, D. C., & Letson, G. M. (1963). The trapping of photocarriers in anthracene by anthraquinone, anthrone and naphthacene. Journal of Physics and Chemistry of Solids, 24(12), 1609–1615. https://doi.org/10.1016/0022-3697(63)90104-5

2. Hot-Electron Transport in Semiconductors (1985) Edited by L. Reggiani. (section: 3.2.6 Trapping and Detrapping)

@Jitendra go through the following paper:

1. Physical review B, vol 25, number 6, page 4313-4316, year 1982

2. J. appl. phys. 52(5), 3504-3508, 1981