1. ECSE-6290 Semiconductor Devices and Models II Lecture 20: Laser Diodes
Shayla M. Sawyer
Bldg. CII, Room 8225
Rensselaer Polytechnic Institute
Troy, NY
Tel. (518)
FAX (518)

2. Lecture Outline Introduction Main Concepts Laser Diode Types
Stimulated Emission
Population Inversion
Optical Gain
Optical Resonator
Threshold Current
Laser Diode Types

3. Concepts: Population Inversion
Switch from two energy levels to two separate continuous bands
Electron concentration as a function of energy, determined by Fermi-Dirac distribution and Density of States
Population Inversion T>0K
Population Inversion T=0K
Equilibrium

4. Concepts: Population Inversion and Optical Gain
Photons above EFn-EFp are absorbed

5. Concepts: Population Inversion and Optical Gain

6. Laser Physics: Population Inversion
Necessary requirements and conditions for lasing
In order for equation below to be positive FC>FV and EFn>EFp (population inversion)
Photon energy must be larger than the bandgap
For current pumped laser diode the quantity (EFn-EFp) is equal to the bias voltage, bias is limited to the built up potential of the junction (ψBn+ ψBp)
Fermi-Dirac
For homojunction: one side must be doped to degeneracy

7. Concepts: Optical Resonator
Need to build up stimulated emissions by a optical resonator
Provided by cleaved and polished ends of the crystal

8. Concepts: Optical Resonator
Requirement is a structure to trap the light and build up intensity inside
Like a Fabry-Perot etalon, two parallel walls perpendicular to the junction
Longitudinal modes: multiple resonant frequencies
Separation of modes in wavelength and frequency
Only multiples of the half wavelength can exist in the cavity
Output spectrum is determined by the optical cavity, and optical gain vs. wavelength characteristics

9. Concepts: Optical Gain
Optical gain (g) due to stimulated emission is compensated by optical loss due to absorption (α)
Net gain/loss as a function of distance
For a given system R1, R2, and α are fixed, the only parameter to vary is overall gain
To keep gain positive
Threshold gain

10. Concepts: Threshold Current
The relationship between optical gain and bias current can be described by the equation
Linear increase of optical gain with bias current
Nominal current density
Threshold value

11. Concepts: Threshold Current
Lasing oscillations occur only when the optical gain in the medium can overcome the photon losses from the cavity
Cavity modes vary with increasing current

12. double heterostructure
Laser Types
single
heterostructure
double heterostructure
homostructure

13. Both Carrier and Optical Confinement!

14. Example: Modes in an optical cavity length
Consider an AlGaAs based heterostructure laser diode which has an optical cavity of length 200 microns. The peak radiation is at 870 nm and the refractive index of GaAs is about 3.7.
a) What is the mode integer m of the peak radiation and the separation between modes of the cavity?
b) If the optical gain vs. wavelength characteristics has a FWHM wavelength width of about 6 nm, how many modes are there within this bandwidth?
c) How many modes are there if the cavity length is 20 μm?

15. Gain guided: optical gain is highest where current density is greatest
Stripe contact increases current density in the active region.
The widths of the active region or the optical gain region is defined by current density from the stripe
Gain guided: optical gain is highest where current density is greatest

16. Index guided: optical power confined to waveguide
Active layer is surrounded by lower index AlGaAs and behaves like a dielectric waveguide
Ensures that photons are confined to the active or optical gain region
Increases rate of stimulated emission
Index guided: optical power confined to waveguide

17. Index guided LD: changes from multiple mode to single mode with increasing optical power
Gain guided: remain multimode even at high diode currents

18. Single Frequency Solid State Lasers: DBR laser
Frequency selective dielectric mirrors a cleaved surfaces.
Only allow a single mode to exist
Periodic corrugated structure that interfere constructively when the wavelength corresponds to twice the corrugation periodicity (Bragg wavelengths)

19. Single Frequency Solid State Lasers: DFB laser
The corrugated layer, called the guiding layer, is now next to the active layer
In the DFB structure traveling wave are reflected partially and periodically as they propogate.

20. Constant 2D density of states means a large concentration of electron can easily occur at E1 (and holes at the minimum valence band energy)
Population inversion occurs quickly without the need for a large current to bring a large number of electrons
Benefits: Threshold current reduced, linewidth is narrower

22. Optical cavity axis along the direction of current flow rather than perpendicular to current flow
Radiation emerges from the surface of the cavity rather than from its edge
Reflectors at the edges of the cavity are dielectric mirrors
20-30 layers for mirror, MQW active region

23. Summary
Laser concepts: Stimulated Emission, Population Inversion, Optical Resonator, Optical Gain, and Laser Threshold Current
Types of laser diodes include
Homostructure
Single heterostructure
Double heterostructure
Gain guided (stripe geometry)
Index guided (buried heterostructure)
Distributed Bragg reflection
Distributed feedback
Quantum well, multiple quantum well
Vertical cavity surface emitting

24. ECSE-6290 Semiconductor Devices and Models II Lecture 21: Photodetectors
Prof. Shayla M. Sawyer
Bldg. CII, Room 8225
Rensselaer Polytechnic Institute
Troy, NY
Tel. (518)
FAX (518)

25. Lecture Outline Introduction to Photodetectors Photodiodes
General
p-i-n and p-n
Metal-Semiconductor
Avalanche
Metal-Semiconductor-Metal Photodetector
Quantum Well Infrared Photodetector
Summary

26. Introduction
Photodetectors are semiconductor devices that can detect optical signals through electronic processes
Three main processes:
Carrier generation by incident light
Carrier transport and/or multiplication by current-gain mechanism
Extraction of carriers as terminal current to provide the output signal
Desired: High sensitivity, high response speed, minimum noise, compact size, low biasing voltage and current

27. Introduction Wavelength relation to transition energy
ΔE is the transition of energy levels
Depending on photodetector type can be:
Energy gap of the semiconductor
Barrier height as in a metal semiconductor photodiode
Transition energy between impurity level and band edge as an extrinsic photoconductor
Often minimum wavelength for detection

28. Introduction Important Factors/Parameters Absorption Coefficient
Response Speed
Quantum Efficiency
Responsivity
Gain
Noise
Detectivity

29. Introduction Absorption coefficient
Determines whether light can be absorbed for photoexcitation
Determines where light is absorbed
High value means near surface
Low value means deeper penetration

30. Introduction Response Speed Quantum Efficiency
Shorter carrier lifetime yields fast response at the expense of higher dark current (noise)
Depletion width should be shortened to reduce transit time at the expense of capacitance
Quantum Efficiency
Number of carriers produced per photon
Iph is the photocurrent, Φ is the photon flux (=Popt/hv) and Popt is the optical power

31. Introduction
Responsivity: Photocurrent generated per incident optical power
Gain and response time for common photodetectors

32. Introduction
Noise ultimately determines minimum detectable signal strength
Sources of noise
Dark current
Thermal noise
Shot noise
Flicker noise
Generation recombination noise
Figure of Merit Noise Equivalent Power
Detectivity A is the Area
B is the Bandwidth
NEP-incident rms optical power required to produce a signal-to-noise ratio of one in a 1 Hz bandwidth (minimum detectable light power)

33. Introduction Detectivity
The signal-to-noise ratio when one watt of light power is incident on a detector of area 1 cm2 measured over 1 Hz bandwidth
Normalized to area, noise is generally proportional to the square root of area
Detectivity depends on
Detector sensitivity
Spectral Response
Noise
Is a function of wavelength, modulation frequency and bandwidth

34. Photodiodes: General
Photodiodes have depleted region with a high electric field that separates photogenerated electron-hole pairs
Tradeoff between speed of response and quantum efficiency (depletion layer: transit time, absorbance area)
Reverse biasing often employed to reduce carrier transit time and lower diode capacitance
All photodiodes except Avalanche has a maximum gain of one
a) p-i-n photodiodes b) pn photodiode c) Metal-i-n photodiode d) Metal-semiconductor photodiode e) Point contact photodiode

35. Photodiodes: General Important characteristics Quantum efficiency
Absorption coefficient strong dependence on wavelength
Long wavelength cutoff given by energy gap of semiconductor
Short wavelength cutoff given by large value of α (surface where recombination is likely)
Response Speed
Limited by
Drift time in the depletion region
Diffusion of carriers
Capacitance of detection region
Optimized when the depletion layer is chosen so the transit time is on the order of one half the modulation period
WD ~ 1/α

36. Photodiodes: General Device Noise Shot noise Thermal noise where
IP average photocurrent, IB background radiation, ID dark current due to thermal generation of electron hole pairs in the depletion region
Thermal noise where
Rj Junction resistance
Ri Input resistance of amplifier
RL External load resistor

37. Photodiodes: General
Signal to Noise for 100% modulated signal with average power Popt
Minimum optical power required to obtain a given signal-to-noise ratio is (setting Ip=0)
Noise equivalent power (S/N=1; B=1 Hz)

38. Photodiodes: p-i-n and p-n
Depletion layer thickness (intrinsic layer) can be tailored to optimize the quantum efficiency and frequency response
Total photocurrent density through reverse biased depletion layer
Total current density is the sum of Idr inside the depletion region and Idiff outside the depletion region

39. Photodiodes: p-i-n and p-n
Drift current equation
For x>WD the minority carrier density (holes) is the bulk semiconductor is determined by the 1D diffusion equation
Solution under boundary conditions pn=pno for x=∞, and pn=0 for x=WD

40. Photodiodes: p-i-n and p-n
Diffusion current density is given by
Total current density is the sum of Idr inside the depletion region and Idiff outside the depletion region

41. Photodiodes: p-i-n and p-n
Quantum efficiency
Reduced from unity from
Reflection R
Light absorbed outside the depletion region
High quantum efficiency, low R and αWD>>1 is desirable
For WD>>1/ α transit time delay may be considerable

42. Photodiodes: p-i-n and p-n
Frequency Response
Phase difference between photon flux and photocurrent will appear when incident light intensity is modulated rapidly
Assume light is absorbed at surface, applied voltage is high enough to ensure saturation velocity
Response time is limited by the carrier transit time through the depletion layer
Compromise for high frequency response and quantum efficiency
Absorption region of thickness 1/α to 2/α
Large portion of light is absorbed within the depletion region

43. Photodiodes: p-i-n and p-n
Frequency Response
3-dB frequency
Illustrates trade off between response speed and quantum efficiency at various wavelengths by adjusting the depletion width
Smaller WD, shorter transit time, higher speed, but reduced η
Shows internal quantum efficiency of the Si p-i-n photodiode as a function of the 3-dB frequency and depletion width

44. Examples: Speed and Responsivity
Operation and speed of a p-i-n photodiode
A Si pin photodiode has an i-Si layer of width 20 μm. The p+ layer on the illumination side is very thin (0.1 μm). The pin is reverse biased by a voltage of 100 V and then illuminated with a very short optical pulse of wavelength 900 nm. What is the duration of the photocurrent if absorption occurs over the whole i-Si layer? 44

45. Examples: Speed and Responsivity
The absorption coefficient at 900 nm ~ 3 x 104 m-1 so that the absorption depth is ~33 μm (from Figure). Assume that the absorption and hence photogeneration occurs over the entire width W of the i-Si layer. The field in the i-Si layer is
At this field the electron drift velocity ve is very near its saturation at 105 m/s, whereas the hole drift velocity vh, is about 7x104 m/s. Holes are slightly slower than the electrons. The transit time th of holes across the i-Si layer is
To improve response time, the width of the i-Si layer has to be narrowed but it decreases the quantity of absorbed photons and reduces responsivity. 45

46. Examples: Speed and Responsivity
Responsivity of a p-i-n photodiode
A Si pin photodiode has an active light receiving area of diameter 0.4mm. When radiation of wavelength 700 nm (red light) and intensity 0.1 mW cm-2 is incident it generates a photocurrent of 56.6 nA. What is the responsivity and QE of the photodiodes at 700 nm?
The incident light intensity 0.1 mW cm-2 means that the incident power for conversion is
The responsivity is QE can be found from 46

47. Photodiodes: p-i-n and p-n
p-n photodiode
Thin depletion layer means some light can be absorbed outside
Light more than a diffusion length outside do not contribute at all to photocurrent
Reduces quantum efficiency
Diffusion process is slow
Time require to diffuse a distance x
Lower response speed than p-i-n
Neutral region contributes to noise

48. Photodiodes: Heterojunction
Advantages
Large bandgap material can be transparent and used as a window for transmission of incoming optical power
Quantum efficiency is not dependent on distance of junction from surface
Unique material combinations so quantum efficiency and response speed can be optimized for a given optical wavelength
Reduced dark current
J.H. Jang et al., Journal of Lightwave Technology, Vol. 20, No. 3, March 2002.

49. Photodiodes: Metal-Semiconductor
Has a threshold of qΦB,
when it gets to the energy gap value the quantum efficiency jumps to a much high value
Operates in two modes
hυ>Eg : radiation produces electron hole pairs (similar to pin photodiode)
hυ<Eg : photoexcited electrons surmount barrier

50. Photodiodes: Metal-Semiconductor
Quantum Efficiency in two modes
hυ>Eg : radiation produces electron hole pairs (similar to p-i-n)
hυ<Eg : photoexcited electrons surmount barrier, internal photoemission
Internal photoemission has typical quantum efficiencies of less than 1%
CF is the Fowler emission coefficient

51. Photodiodes: Metal-Semiconductor
Configurations
Advantageous for band-to-band
Diode illuminated through thin metal contact with antireflection coating
Use low doping i layer similar to p-i-n
Point contact diode reduces active volume, drift time and capacitance are small
Very high modulation frequencies

52. Photodiodes: Metal-Semiconductor
Main advantages
High speed and long wavelength detection capability without having to use a semiconductor with a small energy gap
Not limited by charge storage of minority diffusion current
Ultrafast Schottky barrier photodiodes beyond 100 GHz have been reported
Useful in the visible and UV

53. Photodiodes: Avalanche
Operate at high reverse bias voltages where avalanche multiplication takes place
Creates internal current gain
Can respond to light modulated at microwave frequencies
Current gain-bandwidth product of an APD can be higher than 300 GHz
High gain comes at the price of noise
Low frequency avalanche gain
αn and αp are electron and hole ionization rates

54. Photodiodes: Avalanche
For equal ionization coefficients (α =αn=αp) multiplication takes the simple form
In a practical device, the dc multiplication at high light intensities is limited by series resistance and space-charge effect
Breakdown when αWD=1
I total multiplied current
IP unmultiplied current
ID unmultiplied dark current
IMD multiplied dark current
VR Reverse bias voltage
VB Breakdown voltage

55. Photodiodes: Avalanche
For high light intensity (IP >> ID) and IRs << VB, the maximum value of the photomultiplication is given by
Avalanche multiplication noise
Lower noise factor for electron injection because αn is much larger than αp in Si
max
Noise factor:
Measure of shot noise increase compared to ideal noiseless multiplier

56. Photodiodes: Avalanche
To achieve low noise and wide bandwidth in an APD
Ionization coefficients of the carriers should be as different as possible
Avalanche process should be initiated by the carrier species with a higher ionization rate
Other species with lower ionization rate should be kept to a minimum as primary photogenerated current

57. Photodiodes: Avalanche
Current gain mechanism multiples the signal current, background current and dark current indiscriminately
Signal to noise power ratio

58. Photodiodes: Avalanche
The previous equation can be solved for the minimum optical power Popt required to produce a given S/N with avalanche gain
NEP can be improved by the reduction of Ieq by the gain M

59. Photodiodes: Avalanche
At high light power p-i-n detectors have larger SNR than APD
There is a significant advantage of APDs for low light signals due to multiplication factor
Optimization required for any system depending on optical flux
SNR comparison between 1 mm2 diode detectors with a bandwidth 50Hz

60. Photodiodes: Avalanche
Material comparison
Heterojunction avalanche photodiodes of III-V alloys advantages
Wavelength response can be tuned
High absorption coefficients of direct bandgap III-V alloys makes quantum efficiency high even if a narrow depletion width is used to provide a high speed response
Heterostructure window layer can be grown
Surface recombination loss minimized
High speed performance

61. Photodiodes: Avalanche
Material comparison
AlGaAs/GaAs, AlGaSb/GaSb, InGaAs/InP, and InGaAsP/InP
Shown improvements in speed and quantum efficiency over Si and Ge
Separation absorption and multiplication
Higher bandgap material in the multiplication region
Low bandgap material for light absorption
Breakdown voltage is expected to vary as Eg2/3 so dark current due to tunneling is suppressed

62. Metal-Semiconductor-Metal Photodetectors
Basically two Schottky barriers connected back-to-back on a coplanar surface
Added a thin barrier enhancement layer to reduce dark current
Metal contacts have shape of interdigitated stripes
Light is received at the gap between metal contacts
For more complete light absorption, active layer has a thickness slightly larger than absorption length

63. Metal-Semiconductor-Metal Photodetectors
Typical operation
Photocurrent first rises with voltage then becomes saturated
Increase of photocurrent at low bias is due to expansion of the depletion region in the reverse biased Schottky junction and internal quantum efficiency improves
Voltage at which photocurrent saturates corresponds to flat band condition
Electric field at anode becomes zero
Estimated by 1D depletion equation

64. Metal-Semiconductor-Metal Photodetectors
Main Drawback
High dark current due to Schottky barrier junction
Barrier enhancement layer can be added to reduce dark current of narrow energy gap semiconductor such as InGaAs
Layer thickness ranges from 30 to 100nm
Can be graded in composition to avoid carrier trapping

65. Metal-Semiconductor-Metal Photodetectors
Primary advantages
High speed and compatibility with FET technology
Planar structure easy to integrate on single chip
Very low capacitance per area
Advantageous for detectors requiring large light sensitive areas
Compared to p-i-n capacitance is about half

66. Quantum Well Infrared Photodetectors
Structure of QWIP using GaAs/AlGaAs heterostructure
QW layers 5nm doped to n-type in 1017 range
Barrier layers are undoped and have a thickness 30-50nm
Periods 20 to 50

67. Quantum Well Infrared Photodetectors
Incident light normal to surface has zero absorption
Intersubband transition require electric field have components normal to QW plane
Two methods
Polished facet
Grating to refract light
Figure 716

68. Quantum Well Infrared Photodetectors
Intersubband excitation
Three types of transitions
Bound to bound (escape well by tunneling)
Bound to continuum (escape well because first state is above barrier: easier)
Bound to miniband in superlattice

69. Quantum Well Infrared Photodetectors
I-V of QWIP is similar to photodetectors
Quantum efficiency is different since light absorption and carrier generation occur only in quantum wells
Nop number of optical passes, Nw number of quantum wells, Lw is the length, P is the polarization correction factor
Ep is the escape probability and is a function of bias
Ga is optical gain
Cp is the capture probability
of electron traversing quantum well
tp transit time across single period of structure
tt transit time across entire QWIP active length L

70. Quantum Well Infrared Photodetectors
Dark current is due to thermionic emission over the quantum well barriers and thermionic field emission (thermally assisted tunneling) near the barrier peaks
To limit dark current, the QWIP has to be operated at low temperatures in the range of 4-77 K
Can be applied in focal plane arrays for 2D imaging
High speed capability and fast response
Coupling of light to the photodetector is difficult

71. Summary
Photodiodes have depleted region with a high electric field that separates photogenerated electron-hole pairs
Width of depletion layer determines tradeoff between speed and quantum efficiency
P-n photodiodes have lower response speed and higher noise than a p-i-n photodiode
Heterojunction photodiodes can move light absorption region away from the surface due to transparence of larger bandgap materials
MS photodiodes operate in two modes, used because no minority carriers that increases speed
Avalanche photodiodes have high gain but at the cost of noise, better for signals of low light intensity
MSM photodectors have high speed and large area but have high dark noise
QWIP uses quantum wells and various intersubband transitions for electrons, and are often operated at low temperatures