Due to ir it ir sample greater absorption i t i o

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Unformatted text preview: obability that a photon is absorbed is a constant The number of photons absorbed per increment of distance is propor`onal to the number of incident photons We assume that the propor`onality rela`onship holds for all values of incident photon flux (no satura`on) Differential Equation: dI ( x ) − = α I (x) dx Solution: I (x) = ( Io − Ir ) e −α x I 0e −α x Absorption for sample with thickness "l": I t I o e− α l Note: We've assumed I R is negligible in this analysis I (x) I0 I ( x ) − α I ( x ) Δx I 0 − α I 0 Δx thickness Δx ΔI ( x ) = ( I ( x ) − α I ( x )Δx ) − I ( x ) ΔI ( x ) = −α I ( x )Δx ΔI ( x ) = −α I ( x ) Δx dI ( x ) ⎛ ΔI ⎞ lim ⎜ − ⎟ = − = α I (x) Δx→0 ⎝ Δx ⎠ dx 9 Photon Flux Versus Posi`on •  The photon flux drops exponen`ally in the sample •  The rela`onship for the generated carriers is more complicated due to diffusion 0 I I0 l I ( x ) = I o e− α x x Lower Absorption Difference due to IR αê༎ IT αé༎ IR Sample Greater Absorption I t = I o e− α l 10 Absorp`on Coefficient •  The absorp`on coefficient depends upon the incident wavelength λ •  Below the bandgap there is minimal absorp`on •  The units of absorp`on are typically cm- 1 Useful Relationship: c 1.239 = λ λ (µm) A photon with a wavelength of 1 µm has an energy of 1.239 eV E (eV ) = hv = h 11 Comments on Op`cal Absorp`on •  Semiconductors absorb energies greater than their bandgap, which means wavelengths shorter than the wavelength at their bandgap •  GaAs, Si, and Ge are in the infrared part of the spectra •  GaP is in the visible •  GaN pushes into the UV •  If I want to absorb light emi5ed by one semiconductor, I generally need to use another with a smaller bandgap 12 Bandgap and Layce Constant of Common Semiconductors 13 Terminology Reminder •  Equilibrium: No external perturbing excita`on is present except temperature, and there is no net mo`on of charge. •  Steady State: A non- equilibrium condi`on in which all perturbing processes are constant. In steady state, opposing processes are present that balance perturbing processes. Equilibrium Genera`on Some electrons have sufficient energy to jump to the conduction band (phonon interactions) Generation and recombination are balanced: no(K) Ÿ༉ r g (T ) = gi = ri = α r nopo = α n 2 ri An A...
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