Recombination-Generation
Recombination – a process whereby electrons and holes (carriers)
are annihilated or destroyed.
• Band-to-band recombination
• R-G center recombination (Shockley-Read-Hall)
• Auger recombination
Generation – a process whereby electrons and holes are created.
• Band-to-Band generation
• R-G center generation
• Impact ionization
Band-to-Band Recombination & Generation
• Direct annihilation of a conduction band electron and a valence band hole.
• Production of photon (light)
• Does not have to be a “direct bandgap” material, but is typically very slow in
“indirect bandgap” materials.
• Basis for light emission devices such as semiconductor LASER, LED, etc.
• Direct thermal generation or photogeneration : mechanism that results in ni
• Basis for light absorption devices such as semiconductor photodetectors,
solar cells, etc.
R-G Center Recombination & Generation
• R-G centers are lattice defects or special impurity atoms such as Au in Si.
• Allowed electronic levels near the center of the band gap (ET)
• Two step process: Ex. electron trapping at ET ⇒ hole trapping at ET
• Energy loss can result in a photon but more often produces multiple phonons
(lattice vibration) : indirect recombination
• Also known as Shockley-Read-Hall (SRH) recombination
Auger Recombination & Impact Ionization
• Band-to-band recombination with the collision between two like carriers
: requires 3 particles
• e-h pair generation due to the collision between a highly energetic carrier
and the crystal lattice : requires high electric fields (steep band)
Momentum Considerations
• Wave vector k : proportional to the electron crystal momentum (p=ħk)
• E-k plot : the allowed electron energies in the conduction band and valence
bands are plotted versus the allowed momentum.
• Crystal momentum as well as energy must be conserved in any R-G process.
Direct vs. Indirect Semiconductor
• Photon : massless, little momentum ⇒ vertical transition on E-k plot
• Phonon : lattice vibration, small energy (10~50meV), large momentum
⇒ horizontal transition on E-k plot
• Band-to-band recombination ≪ R-G center recombination in Si (indirect)
Photogeneration
• Light on semiconductor surface: partially reflected and partially transmitted.
• Photon with high energy (>Eg) is absorbed and e-h pair is created.
• Intensity of monochromatic light energy in a material;
• Due to one-to-one correspondence between
the absorption of photons and the creation of
e-h pairs, GL exhibits e-αx dependence.
Absorption
Coefficient
(FN)
Indirect Thermal Recombination-Generation Rate
Low Level
Injection:
NT is filled
with
majority
carriers
Almost every traps are filled with electrons.
(FN)
𝜕𝑝
𝜕𝑡
≅
𝑡ℎ𝑒𝑟𝑚𝑎𝑙 𝐺
𝜕𝑝
𝜕𝑡
𝜕𝑝
𝜕𝑡
𝑡ℎ𝑒𝑟𝑚𝑎𝑙 𝐺,
𝐸𝑞𝑢𝑙𝑖𝑏𝑟𝑖𝑢𝑚
= −𝑐𝑝 𝑁𝑇 𝑝
𝑡ℎ𝑒𝑟𝑚𝑎𝑙 𝑅
=−
𝜕𝑝
𝜕𝑡
𝑡ℎ𝑒𝑟𝑚𝑎𝑙 𝑅,
𝐸𝑞𝑢𝑙𝑖𝑏𝑟𝑖𝑢𝑚
= 𝑐𝑝 𝑁𝑇 𝑝0
determined by the number of empty R-G centers
𝜕𝑝
𝜕𝑡
≅
𝑡ℎ𝑒𝑟𝑚𝑎𝑙 𝑅−𝐺
𝜕𝑝
𝜕𝑡
+
𝑡ℎ𝑒𝑟𝑚𝑎𝑙 𝑅
𝜕𝑝
𝜕𝑡
= −𝑐𝑝 𝑁𝑇 𝑝 − 𝑝0
𝑡ℎ𝑒𝑟𝑚𝑎𝑙 𝐺
minority
constant
Sample Problem No. 1
A uniformly donor-doped silicon wafer @300K is suddenly illuminated with light
@ t=0. ND=1015 cm-3, τp=10-6 sec, light-induced creation of 1017 electrons and
holes per cm3-sec throughout the semiconductor, Δpn(t)=? For t>0.
Sample Problem No. 2
The x=0 end of a uniformly doped semi-infinite bar of silicon with ND=1015 cm-3,
is illuminated so as to create Δpn0 =1010 cm-3 excess holes at x=0. The
wavelength of the illumination is such that no light penetrates into the interior
(x>0) of the bar. Δpn(x)=?
Minority Carrier Diffusion Length
HW #4
Exercise 3.4, 3.5
Problems 3.12, 3.19, 3.20, 3.24