第四讲-激子与发光

energy ~ 0.01 eV
binding energy ~ 0.1 -1 eV.
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第四讲 Excitons
•The concept of excitons •Free excitons •Free excitons at high density •Frenkel excitons
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Binding energy and radius of free excitons
•The experimental Rx=4.2 meV is in good agreement with the calculated value.
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第四讲 Excitons
•The concept of excitons •Free excitons •Free excitons at high density •Frenkel excitons
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Rare gas crystals
•Crystallize at cryogenic temperatures. •Large band gap, Neon has the largest band gap in nature. •Exciton transitions all occur in the vacuum ultraviolet spectral range • Binding energies are very large.
•Frenkel激子 （束缚激子）:
Observed in semiconductors; Observed in insulators and molecular
large radius; delocalized crystals; smaller radius; localized
states; move freely; binding states; less mobile and hoping;
•narrow gap semiconductors: RH is so small that exciton effects is hard to observe.
(Eg=1-3eV, free excitons behavior is best observed)
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Exciton absorption
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Density Effects:
1. electron-hole plasma
weakening and broadening of the exciton absorption line is observed (absorption saturation, nonlinear effects).
observe in the absorption spectra of indirect semiconductor)
•At the Brillouim zone centre of direct semiconductor: k=0 and zero gradient.
Eectron-hole pairs created by direct transition and have the same velocities.
Frenkel excitons
•occurring in large band gap materials with small dielectric constants and large effective masses. •small radii and large binding energies, 0.1 eV to several eV, stable at room temperature. •propagating through the crystal by hopping .
Two types of excitons:
Wannier激子（自由激子）
•Stable excitons will only be formed if the attractive energy >>kBT (0.026eV at room temperature) •Free excitons are stable at cryogenic temperature. •Tight bound excitons are stable at room temperature.
•Exciton creation: electron-hole pairs and same velocities. •The group velocity of an electron or hole in a band is given by:
g
1 E k
•Free excitons are typically observed in direct gap semiconductors. (hard to
•The radius of the electron-hole orbit:
rn

m0

r n2aH
n2aX
aX
aH
r m0
aH is the Bohr radius of the hydrogen atom (5.29 10-11m) and ax is the exciton
Bohr radius.
•ground state with n = 1 has the largest binding energy and smallest radius.
n>1: less strong binding energy and larger radius.
•Biding energy tends to decrease and ax to increase as r increase.
2. Biexcitons (exciton molecules)
equivalent process to the formation of an H2 molecule; new feature line can be found.
3. electron- hole droplets
Broad feature line at lower energy than the free exciton
electric field and tend to ionize excitons.
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Experimental data for free excitons in GaAs
•Exciton absorption of ultra pure GaAs at 1.2 K. •hydrogen-like energy spectrum of the exciton in the vicinity of the band gap. •E1=1.5149 eV, E2=1.5180 eV, E3=1.5187 eV •Eg=l.5191 eV, agree with other measurements.
•The energy of the nth level relative to the ionization limit
En


m0 r 2
RH n2
RX n2
RX

(
/
m0
2
r
)
RH
RH is the Rydberg constant of the hydrogen atom (13.6 eV). RX: exciton Rydberg constant.
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The concept of excitons
•In semiconductors and insulators: photon absorption electrons in the conduction band and holes in the valence band. •Exciton: bound electron – hole pair by Coulomb interaction
•Free excitons can only be observed in very pure samples.
Impurities: screening the Coulomb interaction in the exciton
and thereby strongly reduce the binding forces; generating
•Free excitons: weakly bound electron-hole pair; a hydrogenic system
•Applying the Bohr model to the exciton, considering dielectric constant r of the medium and the reduced mass of electron and hole.
Therefore, strong excitons occur in the spectral region close to the fundamental
band gap.
• The energy of exciton absorption is:
En

Eg

RX n2
•Band edge absorption spectrum for a direct gap semiconductor with excitonic effects included. The dashed line shows the expected absorption when the excitonic effects are ignored.
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•Rx tends to increase and ax to decrease as Eg increases.