Semiconductors

Lecture 1, Slide # 1 ECE 217 © P.J. Burke, Spring 2002 Last modified 04/08/23 00:31

ECE217B, Spring 2002Advanced Semiconductor Devices II

Graduate Course, 3 units

Professor & Class SchedulePeter Burke

e-mail: [email protected]: EG 2232

Lect. Mo/We 3:00 – 4:20 pm in CS 219Office hours 4:30-5:30 pm

Lecture notes, HWs and solutions online athttp://nano.ece.uci.edu/ece_217b_advanced_semiconductor_devices.htm

and at copy center (ET base) by day of lectureTextbook:

Fundamentals of III-V Devices: HBTs, MESFETs, and HFETs/HEMTsWilliam Liu, Wiley (1999), ISBN 0-471-29700-3

Grade:60% Homework, 40% End-of-term presentation/paper


Reference books:* means on reserve at the science libraryDevice physics:*Physics of Semiconductor Devices, S.M. Sze, Wiley (1981) ISBN 0-471-05661-8*Modern Semiconductor Device Physics, S.M. Sze, Wiley (1998) ISBN 0-471-15237-4*High Speed Semiconductor Devices, S.M. Sze, Wiley (1990) ISBN 0-471-62307-5*Physics of Semiconductor Devices, Michael Shur, Prentice Hall PTR (1996) ISBN 0-13-666496-2*Solid State Electronic Devices, 5th Edition, Ben G. Streetman (2000), ISBN 0-13-025706-0GaAs High-Speed Devices, C.Y. Chang and Francis Kai, Wiley (1994) ISBN 0-471-85641-X*InP-Based Materials and Devices: Physics and Technology, Osamu Wada and Hideki Hasegawa, Wiley (1994) ISBN 0-471-18191-9SiGe, GaAs, and InP Heterojunction Bipolar Transistors, Jiann S. Yuan, Wiley (1999), ISBN 0-471-19746-7*Semiconductor Device Fundamentals, Robert F. Pierret, Addison-Wesley (1995), ISBN 020154393-1*HEMTs and HBTs: Devices, Fabrication, and Circuits, Fazai Ali and Aditya Gupta, Artech House (1991), ISBN 0-89006-401-6InP HBTs: Growth, Processing, and Applications, B. Jalali and S.J. Pearton, Artech House (1994), ISBN 0-89006-724-4*Semiconductor Physics and Devices: Basic Principles, Donald A Neamen, McGraw-Hill (1997) ISBN 0-256-24214-3*Low Dimensional Semiconductor Structures: Fundamentals and Device Applications, Keith Barnham and Dimitri Vvedensky, Cambridge University Press (2001), ISBN 0-521-59103-1.Modern GaAs Processing Methods, Ralph E. Williams, Artech (1990), ISBN 0-89006-343-5, out of printElectrical and Thermal Characterization of MESFETs, HEMTs and HBTs, Robert R H Anholt, Artech House (1994), ISBN 0-89006-749-X*Fundamentals of Semiconductor Theory and Device Physics, Shyh Wang, Prentice Hall (1989), ISBN 0-13-344409-0 (out of print)*Device Electronics for Integrated Circuits, 2nd Edition, Richard S Muller and Theodore I Kamins, Wiley (1986), ISBN 0-471-88758-7, *Compound Semiconductor Device Physics, Sandip Tiwari, Academic Press (1991), ISBN 0-12-691740-X (out of print)High-frequency (microwave, mm-wave) engineering:*Microwave Engineering, 2nd Edition, David Pozar, Wiley (1997), ISBN 0-471-17096-8Microwave and RF Wireless Systems, David Pozar, Wiley (2000), ISBN 0-471-32282-2*Foundations for Microstrip Circuit Design, 2nd Edition, T.C. Edwards, Wiley (1991), ISBN 0-471-93062-8. (out of print)*Fields and Waves in Communications Electronics, 3rd Edition, Simon Ramo, John R. Whinnery, Theodore Van Duzer, Wiley (1994) ISBN 0-471-58551-3 (out of print)*Microstrip Lines and Slotlines, 2nd Edition, K.C. Gupta, Ramesh Garg, Inder Bahl, Prakash Bhartia, Artech House (1996), ISBN 0-89006-766-X*Transmission Line Design Handbook, Brian C. Wadell, Artech House (1991), ISBN 0-89006-436-9*Microwave Transistor Amplifiers: Analysis and Design, 2nd Edition, Guillermo Gonzalez, Prentice Hall (1997), ISBN 0-13-254335-4


ECE217B Advanced Semiconductor Devices II (3) S. Metal-semiconductor field-effect transistors (MESFET), heterojunction bipolar transistors (HBT), microwave semiconductor devices, equivalent circuits, device modeling and fabrication, microwave amplifiers, transmitters, and receivers. Prerequisite: ECE114A.

HW will be hard if you do not meet the prerequisite.


Course Outline1. Review of basic semiconductor physics and III-Vs

2. Two-terminal devices

3. HBT DC properties

4. HBT high frequency properties

5. FET DC properties

6. FET high frequency properties

7. Noise models

8. Quantum devices: resonant tunneling diodes

9. Nano-scale devices: Landauer-Buttiker formalism, single electron transistors, quantum point contacts, quantum dots, carbon nanotubes


Also

As needed by the class:

1. Electromagnetic wave propagation in infinite media

2. Coaxial and microstrip transmission lines

3. S-parameters, reflections, impedances, gains, and Smith chart


III-V vs. Silicon

• Silicon is inexpensive and mature

• Why bother with III-V?– Speed– Power– Noise– Optically active

• These are niche markets, but it’s a big niche


Speed

From Sze, Physics of Semiconductor Devices


Speed



High speed HEMTs:

fT = vmax /(2 L )

Si 0.18 m CMOS @ 30 GHz

InP based @ 362 GHz (fastest)

Endoh et al, 12th Intl. Conf. on InP, 2000 (Fujitsu)

(draw in Si, SiGe)


Noise



Optics

(Adapted from Streetman, Solid State Electronic Devices)

0.01

0.1

1

10

100A

tten

uatio

n (d

B/k

m)

1.81.61.41.21.00.8

Wavelength (m)

RayleighScattering

Infraredaborption


Band gap engineering

• Controlled growth of any structure you can imagine in the z-direction

• Important to LATTICE MATCH

• Dislocations/misfits INCREASE the non-radiative recombination rate, causing higher laser threshold currents

• GaAs, InP typical substrates

• MBE, MOCVD, LPE


MBE

epitaxial growth

GaAs

AlAs

AlAs

1.4 eV2.2 eV

V

z

Also InP, InGaAs, InAlAs, InGaAsP …


MBE

4 atom per layer!

(From Streetman, Solid State Electronic Devices)


Band gaps


Outline• Quantum mechanics• Free electrons in a box (Fermi gas)• Band theory of solids• Fermi/Dirac distribution function• Doping• Electrical conduction in semiconductors

– Drift– Diffusion

• Haynes/Schockley experiment• All bulk this week (discuss)


Free electron theory of solids• Each atom in the solid “gives up” one electron

• Each electron is free to move where-ever it wants, with no scattering

• Amazingly, this simple idea makes predictions that are true!

• Not for semiconductors, but metals

• Still need to understand this for semiconductors


Electrons are waves, too.


Quantum mechanics of free particles:

2),( tr

is probability of finding an electron at point r at time t.

is complex, and both real and imaginary parts are physical.



2),( tr

is probability of finding an electron at point r at time t.

)(~),( trkietr

For a free particle:

kp

m

k

m

pE

2

)(

2

22

Momentum: Energy:

/E is complex, and both real and imaginary parts are physical.


Schrodinger equation:

),(2

),(2

22

txxm

txt

i

(Time dependent)

(1 dimension)



),(2

),(2

22

txxm

txt

i

)(),( tkxieAtx Let

(Time dependent)

A is a (complex) constant.

(1 dimension)



),(2

),(2

22

txxm

txt

i

)(),( tkxieAtx Then

Let

)()( )(),( tkxitkxi eAiieAt

itrt

i

(Time dependent)


(1 dimension)



),(2

),(2

22

txxm

txt

i

)(),( tkxieAtx

),()( txEeAE tkxi

Then

Let


itrt

i

(Time dependent)


(1 dimension)



),(2

),(2

22

txxm

txt

i

)(),( tkxieAtx

),()( txEeAE tkxi

Then

Let

)(22

)(2

22

2

22

22),(

2tkxitkxi eAik

meA

xmtx

xm


itrt

i

(Time dependent)


(1 dimension)



),(2

),(2

22

txxm

txt

i

)(),( tkxieAtx

),()( txEeAE tkxi

Then

Let

)(22

)(2

22

2

22

22),(

2tkxitkxi eAik

meA

xmtx

xm


itrt

i

),(22

2)(

22

txm

peA

m

k tkxi

(Time dependent)


(1 dimension)



),(2

),(2

),(2

2

2

2

2

222

2

trzyxm

trm

trt

i

(3 dimensions)



),(2

),(2

),(2

2

2

2

2

222

2

trzyxm

trm

trt

i

tzkykxkitrki zyxeAeAtr )()(),(Let

(3 dimensions)



),(2

),(2

),(2

2

2

2

2

222

2

trzyxm

trm

trt

i

tzkykxkitrki zyxeAeAtr )()(),(

Then

Let

),(),()(),( trEtriitrt

i

(3 dimensions)

as before.



),(2

),(2

),(2

2

2

2

2

222

2

trzyxm

trm

trt

i


Then

Let

)(2

2

2

2

2

22

2

2

2

2

2

22

2),(

2trkieA

zyxmtr

zyxm


i

(3 dimensions)

as before.

But:



),(2

),(2

),(2

2

2

2

2

222

2

trzyxm

trm

trt

i


Then

Let

)(2

2

2

2

2

22

2

2

2

2

2

22

2),(

2trkieA

zyxmtr

zyxm


i

(3 dimensions)

as before.

But:

),(2

)(

2

2222)(222

2

trm

kkkeAikikik

mzyxtrki

zyx



),(2

),(2

),(2

2

2

2

2

222

2

trzyxm

trm

trt

i


Then

Let

)(2

2

2

2

2

22

2

2

2

2

2

22

2),(

2trkieA

zyxmtr

zyxm


i

),(22

2)(

22

trm

peA

m

k trki

(3 dimensions)

as before.

But:

),(2

)(

2

2222)(222

2

trm

kkkeAikikik

mzyxtrki

zyx



)(~),( trkietr

)()( )(),( tkxi

n

txkin ekAdkeAtr nn

Generally,

is also a possibility.


Time-independent Schrodinger equation

)(),( trkieAtr



)(),( trkieAtr

tizkykxkitzkykxki eeAeA zyxzyx )()(



)(),( trkieAtr


)(rCall this



)(),( trkieAtr


)(rCall this

tiertr )(),(



)(),( trkieAtr


)(rCall this

tiertr )(),(

),(2

),( 22

trm

trt

i

From:



)(),( trkieAtr


)(rCall this

tiertr )(),(

),(2

),( 22

trm

trt

i

titititi erm

trm

erEeriiert

itrt

i

)(2

),(2

)()()(),( 22

22

From:



)(),( trkieAtr


)(rCall this

tiertr )(),(

),(2

),( 22

trm

trt

i

titititi erm

trm

erEeriiert

itrt

i

)(2

),(2

)()()(),( 22

22

From:

)()(2

22

rErm


Confined particles: A box

L

L

L

Goal: find )(r

Similar to electric field inside the box.


L

L

L

z

y

x

Goal: find )(r

0)(2 r

Everywhere outside the box

In particular,

0)(2 r

on the boundaries.

As before, we will consider all six surfaces:


Boundary conditions:

L

L

L

)()( zkykxki zyxeAr

z

y

x

The plane x=0:

Try:



L

L

L

)()( zkykxki zyxeAr

z

y

x

The plane x=0:

Does not solve boundary condition!!!

)()(),,0( zkykizkykxki zyzyx eAeAzyx 0

Try:



L

L

L

)()( zkykxki zyxeAr

z

y

x

The plane x=0:

)( zkykxki zyxeA

Let’s try something:



L

L

L

)()( zkykxki zyxeAr

z

y

x

The plane x=0:

)( zkykxki zyxeA )()( zkykixikxik zyxx eeeAr

baba eee




L

L

L

)()( zkykxki zyxeAr

z

y

x

The plane x=0:


)(),,0( zkykixikxik zyxx eeeAzyx 0 0

baba eee




L

L

L

)()( zkykxki zyxeAr

z

y

x

The plane x=0:



baba eee

0)(00 zkyki zyeeeA




L

L

L

)()( zkykxki zyxeAr

z

y

x

The plane x=0:

Does solve boundary condition!!!



baba eee

0)(00 zkyki zyeeeA




L

L

L

z

y

x

The plane x=L:

)()( zkykixikxik zyxx eeeAr

)()sin(2 zkykix

zyexkiA

?0)sin(2),,( )( zkykix

zyeLkiAzyLx

ii eei

2

1)sin(

Lnkn /

If and only if:



L

L

L

z

y

x

The plane x=L:




L

L

L

z

y

x

The plane x=L:


)()sin(2 zkykix

zyexkiA

ii eei

2

1)sin(



L

L

L

z

y

x

The plane x=L:


)()sin(2 zkykix

zyexkiA


zyeLkiAzyLx

ii eei

2

1)sin(



L

L

L

z

y

x

The plane x=L:


)()sin(2 zkykix

zyexkiA


zyeLkiAzyLx

ii eei

2

1)sin(

Lnkn /

If and only if:



L

L

L

z

y

x

)sin()sin()sin()2()( 3 zkykxkAirzynx nn

Lnk xnx/

We can do the same for y, z:

Lnk yny/Lnk znz

/



L

L

L

z

y

x

)sin()sin()sin()2()( 3 zkykxkAirzynx nn

Lnk xnx/

We can do the same for y, z:

)(2

)/(

2

)( 222222222

zyx

nnnnnn

m

L

m

kkkE zyx

These are the allowed energy levels, or “quantum states”

Lnk yny/Lnk znz

/


Many electrons:

L

L

L

z

y

x

)(2

)/( 22222

zyx nnnm

LE

These are the allowed energy levels, or “quantum states”

Pauli exclusion principle: Each unique combination of nx, ny, nz canonly have two electrons (spin up, spin down).


Energy spectrum of free particles:

nx=1, ny=1, nz=1

energy

nx=2, ny=1, nz=1 nx=1, ny=2, nz=1 nx=1, ny=1, nz=2

Etc.


Density of states:

energy

?dENENumber of states with energy between E and E + dE

E

E+dE

How many states?

If L is large, states are very close together.Approximate as a continuum.

?)( dEENumber of states with energy between E and E + dE per volume.


Density of states:Easier first to think of in k-space:

Density of states in k-space is uniform:

One state per (/L)3:

kx

ky

kz


Density of states:Easier first to think of in k-space:

Density of states in k-space is uniform:

One state per (/L)3:

From Verdeyen


Density of states:

kx

ky

kz

?dkNk

Number of states between k, k+dk:

222zyx kkkk

Lnk xnx/

Lnk yny/Lnk znz

/

From Verdeyen


?dkNkVolume of spherical shell=4k2dk/88 is for upper right quadrant

Number of states in volume=Volume x States/volume

States/volume = 1 / (/L)3:

2

23

32 2

)/(

18/4

dkk

LL

dkkdkNk

2

2

volume dkkdkN

dk kk

HW you will do calculation for 2 dimensional world.


?)( dEE


?)( dEE

dEEdkk )( We use:


?)( dEE

2

2

dkk

dkk

dEEdkk )( We use:


?)( dEE

2

2

dkk

dkk

E

dEmdk

mEk

m

kE

2

22

2 22

22

dEEdkk )( We use:


?)( dEE

2

2

dkk

dkk

E

dEmdk

mEk

m

kE

2

22

2 22

22

dEEdkk )( We use:

dEEm

dEE 2/12/32

2/32/32)(


Fermi gas:

energy

At zero temperature, as we add electrons to thebox, we gradually fill up all the states.(DISCUSS PAULI EXCLUSION PRINCIPLE-IMPORTANT!)

When we are done filling the box, the energyof the last electron is called the “Fermi energy.”

“Gas” means we neglect electron-electron interactions.

All these states are filled with electrons.

E=0

E=EFermi

energy

P(E

)


Fermi energy:

energy


E=0

E=EFermi

ff EE

dEEm

LN0

2/12/32

2/32/13

0 E

2dEelectrons #


Fermi energy:

energy


E=0

E=EFermi

ff EE

dEEm

LN0

2/12/32

2/32/13

0 E

2dEelectrons #

2/32/32

2/32/13

3

22electrons # fE

mL


Fermi energy:

energy


E=0

E=EFermi

ff EE

dEEm

LN0

2/12/32

2/32/13

0 E

2dEelectrons #

2/32/32

2/32/13

3

22electrons # fE

mL

3/2

3

3/43/22 electrons #

2

3

LmE f


Fermi energy:

energy


E=0

E=EFermi

ff EE

dEEm

LN0

2/12/32

2/32/13

0 E

2dEelectrons #

2/32/32

2/32/13

3

22electrons # fE

mL

3/2

3

3/43/22 electrons #

2

3

LmE f

In a typical metal, L ~ 0.1 nm.Ef ~ 10 eV


Occupation probability:

E=EFermi

energy

P(E

)

P(E) = probability of occupying a state with energy E

What about finite temperature?

1

0


Recall Boltzmann factor P():

“The probability for a physical system to be in a state with energy is proportional to .”

Boltzmann:

TkBe /

This is actually not quite true. It is classical.A quantum calculation shows for electrons:

1

1)( /)( kTEE fe

EP

Called Fermi-Dirac distribution function.Boltzman is high-energy limit (discuss!)


Fermi-Dirac:

E=EFermi

energy

P(E

)

1

1)( /)( kTEE fe

EP

kTP=1/2 at Ef for all temperatures.

1

0

Semiconductors

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