{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern