Chapter 8
Optoelectronic Devices (brief introduction)
8.1 Photodiodes
8.1.1 Current and Voltage in an Illuminated Junction
8.1.2 Solar Cells
8.1.3 Photodetectors
8.1.4 Gain, Bandwidth, and Signal-to-Noise Ratio of Photodetectors
8.2 Light-Emitting Diodes
8.2.1 Light-Emitting Materials
8.2.2 Fiber-Optic Communications
8.3 Lasers
8.4 Semiconductor Lasers
8.4.1 Population Inversion at a Junction
8.4.2 Emission Spectra for p-n Junction Lasers
8.4.3 The Basic Semiconductor Laser
8.4.4 Heterojunction Lasers
8.4.5 Materials for Semiconductor Lasers
Photoconductor
Fig. 4-10
8.1.1 Current and voltage in an illuminated junction
Optical generation rate
gop (EHP/cm3 - s)
Optically generated current
I op  qAgop ( Lp  Ln  W )
I  Ith (eqV/kT  1)  I op
I  qA(
Lp
p
pn 
Ln
n
n p )(eqV/kT  1)  qAgop ( Lp  Ln  W )
Optical generation of carriers in a p-n junction
Open-circuit Voltage
I  Ith (eqV/kT  1)  I op
Voc 
kT
ln [ I op /I th  1]
q
I op  qAgop ( Lp  Ln  W )
I th  qA(
Lp
p
Lp  Ln  W
kT
Voc 
ln [
g op  1]
Lp
Ln
q
( pn  n p )
p
n
pn 
Ln
n
np )
Lp  Ln  W
kT
Voc 
ln [
g op  1]
L
L
q
( p pn  n n p )
p
n
For a symmetric junction
pn  np and  p   n
Thermal generation rate
gth  pn / n
Neglecting generation within W
kT g op
Voc 
ln
q
gth
W 0
at forward bias
for g op  gth
kT g op
Voc 
ln
q
gth
for g op  gth
gth  pn / n
• pn is fixed, for a given Nd and T.
• As minority carrier concentration is increased by optical generation of EHPs, the
lifetime n becomes shorter, and pn/n becomes larger.
• Therefore, Voc cannot increase indefinitely with increased generation rate.
• In fact, the limit on Voc is the equilibrium contact potential Vo. (see next page)
The appearance of a forward voltage across an illuminated junction is known as the
photovoltaic effect.
The limit on Voc
The contact potential Vo is the maximum forward bias that can appear across a junction.
Photodiode operation at different quadrants
Photodetector
Solar cell
• The photodiode can be operated in either the third or fourth quarters of its I-V
characteristic.
• Power is delivered to the device from the external circuit when the current and
junction voltage are both positive or both negative (first or third quadrants).
• In the fourth quadrant, the junction voltage is positive and the current is negative.
Power is delivered from the junction to the external circuit.
• Notice that in the fourth quadrant the current flows from the negative side of V to the
positive side, as in a battery.
Example 8-1
For steady state optical excitation, we can write the hole diffusion equation as
d 2p p
Dp

 gop
2
dx
p
Assume that a long p+-n diode is uniformly illuminated by an optical signal, resulting
in gop EHP/cm3-s. Calculate the hole diffusion current Ip(xn) and evaluate it at xn = 0.
Compare the result with Eq. (8-2) evaluated for a p+-n junction.
d 2p p g op
 2 
2
dx
Lp Dp
( Lp 
 xn / L p
g op L2p
p( xn )  Be

Dp
D p p )
d 2p p g op
 2 
2
dx
Lp Dp
 xn / L p
p( xn )  Be
( L p  D p p )

g op L2p
Dp
At xn  0, p(0)  pn , thus, B  pn 
(a) p( xn )  [ pn (e
qV / kT
 1) 
g op L2p
Dp
]e
g op L2p
Dp
 xn / L p

g op L2p
Dp
g op L2p  xn / L p
dp
1
  [pn 
]e
dxn
Lp
Dp
g op L2p  xn / L p
dp qAD p
(b) I p ( xn )  qADp

[pn 
]e
dxn
Lp
Dp
I p ( xn  0) 
qADp
Lp
pn (e qV / kT  1)  qALp g op
The last equation corresponds to Eq. (8-2) for np<<pn, except that the component due
to generation on the p side is not included.
I  qA(
Lp
p
pn 
Ln
n
n p )(eqV/kT  1)  qAgop ( Lp  Ln  W )
Eq.(8 - 2)
8.1.2 Solar cells
The voltage is restricted to values less than the contact potential, which is in turn is
generally less than the band gap voltage Eg/q.
For Si the voltage Voc is less than about 1 V. The current generated depends on the
illuminated area, but typically Iop is in the 10-100 mA range for a junction with an area
of about 1 cm2.
Arrays of solar cells are used.
Design consideration of a solar cells
1. Large area
2. Surface coating
3. Junction depth
Compromises
1. The junction depth
• The junction depth d must be less than Lp.
• The thickness of p region must be such that electrons generated in this region
can diffuse to the junction before recombination takes place.
• A proper match between Ln, dp-region, and .
2. Doping
• Desirable large contact potential Vo.
- Heavy doping is required.
• Long lifetimes are desirable.
- Reduced by doping too heavy.
3. Large area
• Large area for light harvest.
• Series resistance be small to reduce ohmic losses.
• Contacts to the thin n region require special design.
- Add small contact fingers.
Solar Cell Characteristics
Open-circuit voltage
Short-circuit current
Maximum power
Fill factor
Voc
I mVm
I sc
I mVm
I scVsc
8.1.3 Photodetectors
When the photodiode is operated in the third quadrant of its I-V characteristic, the
current is essentially independent of voltage but is proportional to the optical generate
rate.
• Measure the illumination levels
• Convert time-varying optical signal into electrical signals
Bandwidth
The bandwidth is how fast the photodiode is to respond to a series of light pulses.
To increase the bandwidth
• The carrier diffusion step in this process should be eliminated.
• Large depletion width (Depletion layer photodiode)
• Most of the photons are absorbed in W rather than in the neutral regions
• When EHP is created in the depletion region, the carriers are swept by the
electric field.
• Fast response.
•Dope at least one side of the junction lightly so that W can be made large.
The appropriate width for W
The appropriate width for W is chosen as a compromise between sensitivity and speed
of response.
• If W is wide, most of the incident photons will be absorbed in the depletion region,
leading to high sensitivity.
• A wide W results in a small junction capacitance (see Eq.(5-62)), thereby reducing
the RC time constant of the detector circuit.
• On the other hand, W must not be so wide that the time required for drift of photogenerated carriers out of the depletion region is excessive, leading to low bandwidth.
Cj 
A
W
( Eq.5 - 62)
The p-i-n photodetector
One convenient method of controlling the width of the depletion region is to build a pi-n photodetector.
• When the device is reverse biased, the applied voltage appears almost entirely across
the i region.
• The carrier lifetime within i region is long.
• Low recombination, low loss.
External quantum efficiency
An important figure of merit for a photodetector is the external quantum efficiency Q.
- The number of carriers that are collected for every photon impinging on the
detector.
(
J op
)
q
Q 
Pop
( )
hν
J op
Photocurrent density
Incident optical power density
Pop
• For a photodiode that has no current gain, the maximum Q is unity.
• If low-level optical signals are to be detected, it is often desirable to operate the
photodiode in the avalanche region of its characteristic.
• In this mode each photogenerated carrier results in a significant change in the
current because of avalanche multiplication, leading to gain and quantum
efficiencies of greater than 100%.
• Avalanche photodiodes (APDs) are useful as detectors in fiber-optic systems.
Intrinsic and extrinsic detectors
1. The intrinsic detector is the type of photodiode sensitive to photons with energies
near the band gap energy.
• If h is less than Eg, the photons will not be absorbed.
• If the photons are much more energetic than Eg, they will be absorbed very
near the surface, where the recombination rate is high.
2. Detectors sensitive to longer wavelengths can be designed such that photons can
excite electrons into or out of impurity levels (extrinsic detectors).
• However, the sensitivity of such extrinsic detectors is much less than intrinsic
detectors.
im purity level
intrinsic
extrinsic
Chapter 7
Bipolar Junction Transistors
7.1 Fundamentals of BJT Operation
7.2 Amplification with BJTs
7.3 BJT Fabrication
7.4 Minority Carrier Distributions and Terminal Currents
7.5 Generalized Biasing
7.6 Switching
7.7 Other Important Effects
7.8 Frequency Limitations of Transistors
7.9 Heterojunction Bipolar Transistors
(brief introduction)
7.1 Fundamentals of BJT Operation
7.2 Amplification with BJTs
7.3 BJT Fabrication
7.4 Minority Carrier Distributions and Terminal Currents
7.4.1 Solution of the Diffusion Equation in the Base Region
7.4.2 Evaluation of the Termonal Currents
7.4.3 Approximations of the Terminal Currents
7.4.4 Current Transfer Ratio
7.5 Generalized Biasing
7.5.1 The Coupled-Diode Model
7.5.2 Charge Control Analysis
7.6 Switching
7.6.1 Cutoff
7.6.2 Saturation
7.6.3 The Switching Cycle
7.6.4 Specifications for Switching Transistors
7.7 Other Important Effects
7.8 Frequency Limitations of Transistors
7.9 Heterojunction Bipolar Transistors
7.1 Fundamentals of BJT Operation
7.2 Amplification with BJTs
7.3 BJT Fabrication
7.4 Minority Carrier Distributions and Terminal Currents
7.4.1 Solution of the Diffusion Equation in the Base Region
7.4.2 Evaluation of the Termonal Currents
7.4.3 Approximations of the Terminal Currents
7.4.4 Current Transfer Ratio
7.5 Generalized Biasing
7.5.1 The Coupled-Diode Model
7.5.2 Charge Control Analysis
7.6 Switching
7.6.1 Cutoff
7.6.2 Saturation
7.6.3 The Switching Cycle
7.6.4 Specifications for Switching Transistors
7.7 Other Important Effects
7.8 Frequency Limitations of Transistors
7.9 Heterojunction Bipolar Transistors
• For simplicity, we shall assume (a) unity emitter injection efficiency and (b) negligible
collector saturation current.
• The average excess hole spends a time t, defined as the transit time from emitter to
collector.
• The hole lifetime in the base is p.
• An average excess electron supplied from the base contact spends p in the base.
• The average electron waits p for recombination with hole.
• While recombination with electrons, many individual holes can enter and leave the base
region, each with an average transit time t.