Chapter 8

Optoelectronic Devices (brief introduction)

8.1 Photodiodes8.1.1 Current and Voltage in an Illuminated Junction8.1.2 Solar Cells8.1.3 Photodetectors8.1.4 Gain, Bandwidth, and Signal-to-Noise Ratio of Photodetectors

8.2 Light-Emitting Diodes8.2.1 Light-Emitting Materials8.2.2 Fiber-Optic Communications

8.3 Lasers8.4 Semiconductor Lasers

8.4.1 Population Inversion at a Junction8.4.2 Emission Spectra for p-n Junction Lasers8.4.3 The Basic Semiconductor Laser8.4.4 Heterojunction Lasers8.4.5 Materials for Semiconductor Lasers

Photoconductor

Fig. 4-10

Optically generated current )( WLLqAgI npopop

)-(EHP/ 3 scmgopOptical generation rate

opqV/kT

th IeII 1)(

)(1))(( WLLqAgenL

pL

qAI npopqV/kT

pn

nn

p

p

8.1.1 Current and voltage in an illuminated junction

Optical generation of carriers in a p-n junction

]1[ thopoc /IIq

kTV lnop

qV/kTth IeII 1)(

]1)(

[

op

pn

nn

p

p

npoc g

nL

pL

WLL

q

kTV

ln

)( WLLqAgI npopop

)( pn

nn

p

pth n

Lp

LqAI

Open-circuit Voltage

]1)(

[

op

pn

nn

p

p

npoc g

nL

pL

WLL

q

kTV

ln

For a symmetric junction nppn andnp

Thermal generation rate nnth /pg

Neglecting generation within W biasforwardatW 0

thopth

opoc gfor

gq

kTV g

gln

thopth

opoc gfor

gq

kTV g

gln

• 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)

nnth /pg

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

• 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.

Photodetector Solar cell

For steady state optical excitation, we can write the hole diffusion equation as

opp

p gp

dx

pdD

2

2

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.

Example 8-1

p

popLxn

pppp

op

p

D

LgBexp

DLD

g

L

p

dx

pd

pn

2

22

2

)(

)(

/

oppkTqV

np

pnp

Lx

p

popn

p

p

npnp

Lx

p

popn

pn

p

popLx

p

popkTqVnn

p

popnnn

p

popLxn

pppp

op

p

gqALepL

qADxI

eD

Lgp

L

D

dx

pdqADxIb

eD

Lgp

Ldx

pd

D

Lge

D

Lgepxpa

D

LgpBthusppxAt

D

LgBexp

DLD

g

L

p

dx

pd

pn

pn

pn

pn

)1(0)(

][qA

)()(

][1

])1([)()(

)0(0

)(

)(

2

2

22

2

2

22

2

/

/

/

//

/

,,,

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.

2)-Eq.(8)(1))(( WLLqAgenL

pL

qAI npopqV/kT

pn

nn

p

p

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

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.

1. Large area2. Surface coating3. Junction depth

Solar Cell Characteristics

Open-circuit voltageShort-circuit currentMaximum powerFill factor

scsc

mm

VI

VImmVI

ocV

scI

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 photo-generated carriers out of the depletion region is excessive, leading to low bandwidth.

)62-5( .EqW

AC j

The p-i-n photodetector

One convenient method of controlling the width of the depletion region is to build a p-i-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.

• 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.

)(

)(

hν

Pq

J

op

op

Q Photocurrent densityIncident optical power density

opJ

opP

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.

levelimpurity

intrinsic extrinsic

Chapter 7

Bipolar Junction Transistors

7.1 Fundamentals of BJT Operation7.2 Amplification with BJTs7.3 BJT Fabrication7.4 Minority Carrier Distributions and Terminal Currents7.5 Generalized Biasing7.6 Switching7.7 Other Important Effects7.8 Frequency Limitations of Transistors7.9 Heterojunction Bipolar Transistors

(brief introduction)

7.1 Fundamentals of BJT Operation7.2 Amplification with BJTs7.3 BJT Fabrication7.4 Minority Carrier Distributions and Terminal Currents

7.4.1 Solution of the Diffusion Equation in the Base Region7.4.2 Evaluation of the Termonal Currents7.4.3 Approximations of the Terminal Currents7.4.4 Current Transfer Ratio

7.5 Generalized Biasing7.5.1 The Coupled-Diode Model7.5.2 Charge Control Analysis

7.6 Switching7.6.1 Cutoff7.6.2 Saturation7.6.3 The Switching Cycle7.6.4 Specifications for Switching Transistors

7.7 Other Important Effects7.8 Frequency Limitations of Transistors7.9 Heterojunction Bipolar Transistors

7.1 Fundamentals of BJT Operation7.2 Amplification with BJTs7.3 BJT Fabrication7.4 Minority Carrier Distributions and Terminal Currents

7.4.1 Solution of the Diffusion Equation in the Base Region7.4.2 Evaluation of the Termonal Currents7.4.3 Approximations of the Terminal Currents7.4.4 Current Transfer Ratio

7.5 Generalized Biasing7.5.1 The Coupled-Diode Model7.5.2 Charge Control Analysis

7.6 Switching7.6.1 Cutoff7.6.2 Saturation7.6.3 The Switching Cycle7.6.4 Specifications for Switching Transistors

7.7 Other Important Effects7.8 Frequency Limitations of Transistors7.9 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.