1. Region of possible oscillations
Review Problem
Find the photon lifetime of the passive cavity; that is, with 0() = 0.
What is the passive cavity Q?
What is the free spectral range of the cavity?
What is the minimum gain coefficient 0(0) necessary to sustain oscillations in this cavity?
If the gain coefficient 0(0) were 2 x 10-2 cm-1 (at line center) and the line shape of the transition was approximated by a Lorentzian with h = 1.5 GHz, then how many TEM0,0,q modes are above the threshold?
What is the stimulated emission cross section (at line center)?
What is the absorption cross section?
The characteristic beam parameter z0 is related to the dimensions of the cavity and the focal length of the lens by
Where is z = 0 in the cavity?
Find a formula for the resonant frequency of the TEMm,p,q mode.
What is the difference in resonant frequencies (in MHz) of the TEM 0,0,q and the TEM1,0,q modes?
allowed modes B
Region of possible oscillations

2. Introduction to Optical Electronics
Quantum (Photon) Optics (Ch 12)
Resonators (Ch 10)
Electromagnetic Optics (Ch 5)
Wave Optics (Ch 2 & 3)
Ray Optics (Ch 1)
Photons & Atoms (Ch 13)
Laser Amplifiers (Ch 14)
Lasers (Ch 15)
Photons in Semiconductors (Ch 16)
Semiconductor Photon Detectors (Ch 18)
Semiconductor Photon Sources (Ch 17)
Optics
Physics
Optoelectronics

3. Semiconductors k Photons & Atoms Distinct Energy Levels
Probability: Boltzmann
Gain: Population Inversion E2 1 2 h E1 E
Photons in Semiconductors
Energy Bands
Probability: Fermi-Dirac
Gain: Quasi-Fermi Energies Efc – Efv > Eg E2 Ec h Ev E1 k

4. Review of Quantum Mechanics
Free Electron Theory of Solids
Free Electrons are Waves, (r,t)
Obey Schrodingers’ Equation
Time-Independent Schrodinger’s Equation

5. Free-Electron’s Energy Spectrum

6. Fermi Gas

7. Fermi Gas

8. Band Theory of Solids 1 Hydrogen Atom 2 Hydrogen Atoms
N Hydrogen Atoms

9. Energy Bands Conduction & Valence
Bandgap Energy
Eg=1.11 eV (Si)
Eg=1.42 eV (GaAs)
Conduction Band
Valence Band
Electron Energy E
Conduction
Band
Valence
Bandgap
energy Eg
Electron
Hole

10. Direct & Indirect Semiconductor BandgapsEv
Eg=1.11 eV
Silicon (Si)
Eg=1.42 eV
[111]
[100] k E
Gallium Arsenide (GaAs) k E

11. Semiconducting MaterialsII
III IV V VI
Aluminum (Al)
Silicon (Si)
Phosphorus (P)
Sulfur (S)
Zinc (Zn)
Gallium (Ga)
Germanium (Ge)
Arsenic (As)
Selenium (Se)
Cadmium (Cd)
Indium (In)
Antimony (Sb)
Tellurium (Te)
Mercury (Hg)
Elemental
Binary
Ternary
Quaternary Al Ga In P As Sb Si x Al Ga As Ga In P As y x
1-y Ga
1-x
1-x

12. Lattice Constants

13. Density of States near the band edgesk E Ec Ev Eg
Allowed energy levels (at all k)
Density of states E

14. Semiconductor’s Density of States
Electrons
Heavy Hole
Light Hole

15. Fermi-Dirac Distribution f(E)
T > 0 K E
T = 0 K E
f(E) Ec Ec Ec Ef Eg Ef Ef Ev Ev Ev
1-f(E)
0.5 1
0.5 1
f(E)

16. Carrier Concentration (n & p)Ec Ef Eg Ev

17. n- and p-type SemiconductorsED Ec E
Donor level Ef Ev
Carrier
concentration 1
f(E) Ec E
Acceptor level EA Ef Ev
Carrier
concentration 1
f(E)

18. Exercise 16.1-2 Exponential Approximation of the Fermi Function

19. Semiconductors Law of Mass Action: Density of States
Probability of Occupation
Concentration of Carriers
Concentration of Carriers (Approximation)
Law of Mass Action:

20. Quasi-Equilibrium Carrier Concentrations
Efc Ec Ec Eg Ev Ev
Efv
Efv

21. Exercise 16.1-3 Determination of the Quasi-Fermi Levels Given the Electron and Hole Concentrations

22. Electron-Hole Generation & RecombinationEv
Generation
Recombination Ec Ev
Trap

23. Exercise 16.1-4 Electron-Hole Pair Injection in GaAs

24. How to Handle an Inverted Semiconductor Verdeyen’s Approach
Setting:

25. Inverted Semiconductor Example: GaAs

26. Semiconductors Density of States Probability of Occupancy
Carrier Concentrations
Law of Mass Action

27. Generation, Recombination & Injection
Rate of Recombination
Recombination Lifetime, 
Internal Quantum Number (low concentrations)

28. Semiconductor Fermi Energy Levelsp n
Concentration
Carrier
Electron Energy
Before Contact
Position E0
Neutral p
Neutral n
After Contact
Depletion
Layer
eV0
Concentration
Carrier
Electron Energy
p(x)
n(x) x

29. Forward-Biased p-n Junction
Neutral p
Neutral n
Neutral
eV0
Concentration
Carrier
Electron Energy
p(x)
n(x) x Ef
Forward Bias
E0 - E
Neutral p
Neutral n eV
Concentration
Carrier
Electron Energy
p(x)
Excess electrons
n(x)
Excess holes x + _
e(V0-V) V
Efc
Efv n p

30. Current-Voltage Characteristics of an ideal p-n Junction Diode_ + V p n is i V

31. PIN Diode in Thermal Equilibrium
Depletion layer
Electric Field Ec
Electron
energy - + x
Fixed-charge
density
Electric-
field magnitude

32. Photon Absorption & Emission Mechanics
Eg=1.42 eV Ec Ev
Band-to-Band
Transitions
EA = eV
Eg=0.66 eV
Acceptor-Level
Transition
Free-Carrier

33. Absorption
Intensity

34. Stimulated Emission

35. Absorption Phenomenon

36. Band-To-Band Photon InteractionsEc Ev E1 E2 k h k h k h
Absorption
Spontaneous
Emission
Stimulated
Emission

37. Optical Joint Density of StatesEg

38. Band-To-Band Photon Interactions
Photon Emission
Indirect-gap Semiconductor k
Photon
Phonon k
Thermalization
Photon
Absorption h
Photon Absorption
Indirect-gap Semiconductor

39. Exercise 16.2-1 Requirement for the Photon Emission Rate to Exceed the Absorption Rate

40. Spontaneous Emission Spectral Density in Thermal EquilibriumEg
rsp()
kBT

41. Absorption Coefficient in Thermal Equilibrium
() (cm-1)
h- Eg

42. Exercise 16.2-2 Wavelength of Maximum Band-to-Band Absorption