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Carrier Recombination in Semiconductors

Overview

Within a uniformly doped semiconductor, various recombination mechanisms occur. The carriers in the material bulk can recombine through radiative (band-to-band), Auger, or defect recombination via traps within the energy gap.

Bulk Lifetime Calculation

The lifetime of carriers in the material bulk (τ_b) is the sum of radiative lifetime (τ_rad), Auger lifetime (τ_A), and defect lifetime (τ_defect), as per the equation:

1/τ_b = 1/τ_rad + 1/τ_A + 1/τ_defect

For indirect bandgap semiconductors like silicon, the radiative lifetime is typically large and often ignored in calculations. The Auger lifetime can be determined through theoretical models, while the defect lifetime is more challenging to calculate due to the varying levels of defects in the crystal lattice.

Bulk Lifetime Determination

The bulk lifetime of extrinsic silicon can be estimated using semi-empirical models based on measurements from low-defect float-zone silicon. This lifetime is influenced by the concentrations of excess carriers and doped atoms in the material.

It’s essential to note that most silicon wafers contain higher levels of contaminants, resulting in lower lifetimes compared to ideal calculations. Further information on silicon properties can be found in relevant appendices.

Bulk Lifetime for p-type Silicon

For p-type silicon, the bulk lifetime can be calculated based on the concentrations of excess carriers (Δn) and doped atoms (N_A).

Bulk Lifetime for n-type Silicon

Similarly, for n-type silicon, the bulk lifetime can be determined based on specific parameters related to the material’s properties.

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