advsemi_lec01 2013_02_28

7/28/2019 AdvSemi_Lec01 2013_02_28

1/36

Advanced

Semiconductor

Devices

Lecture 1

Advanced

Semiconductor

Devices

Lecture 1

7/28/2019 AdvSemi_Lec01 2013_02_28

2/36

2 V. Ariel 2013 Advanced Semiconductor Devices Lecture 1

Lecture outline

Semiconductor Industry Status

Semiconductor device history

Moore's law

Current industry trends portable devices

Semiconductor physics electron wave properties

Wave properties of matter

Silicon atom, crystal, and doping

Energy bands

Effective mass Mass definition

Relativistic particles

Application to non-parabolic materials

7/28/2019 AdvSemi_Lec01 2013_02_28

3/36


Basic electric switch/amplifier

Vacuum tubes: Radio (1904)

First semiconductor device patent: Julius E. Lilienfeld (1925)

Working transistor:

John Bardeen, Walter Brattain, William Shockley (1947)

Integrated circuit: Jack Kilby (1958)

7/28/2019 AdvSemi_Lec01 2013_02_28

4/36


VLSI device structure

7/28/2019 AdvSemi_Lec01 2013_02_28

5/36

7/28/2019 AdvSemi_Lec01 2013_02_28

6/36


PC to Portable Devices

IBM-PC (1981) vs Galaxy S3 (2012)

Weight 200: 1

Volume 1000:1 Cost 10:1

Clock 1:100

Price/Performance 1:1000

7/28/2019 AdvSemi_Lec01 2013_02_28

7/367 V. Ariel 2013 Advanced Semiconductor Devices Lecture 1

Microprocessor to System-on-a-Chip Consumer demand

Smartphones

Digital cameras GPS devices

Digital televisions

Netbooks and Tablets

Shift to complex semiconductor devices - SOCs

7/28/2019 AdvSemi_Lec01 2013_02_28


Moore's Law (CPU transistor count)

7/28/2019 AdvSemi_Lec01 2013_02_28


Optical Properties of Si

7/28/2019 AdvSemi_Lec01 2013_02_28


CMOS Imager - Camera-on-a-Chip

7/28/2019 AdvSemi_Lec01 2013_02_28


Micro-ElectroMechanical Systems (MEMS)

Pico-projector (2005)

Motor

7/28/2019 AdvSemi_Lec01 2013_02_28


Semiconductor industry leaders

7/28/2019 AdvSemi_Lec01 2013_02_28


Wave properties of matter

Young double slit experiment

wave interference

Particle interference picture wave properties of matter

7/28/2019 AdvSemi_Lec01 2013_02_28


Particle waves

De Broglie hypothesis

/ 2

E

p m k

w

pl

=

= = =v

h

h h

Standing waves quantum states

22

0

, 1, 2, 3.....

2n

nk na

nE

m a

p

p

= =

=

h

Group velocity / /dE dp d dk w= =v

7/28/2019 AdvSemi_Lec01 2013_02_28


Particle waves 3d wave functions

7/28/2019 AdvSemi_Lec01 2013_02_28


Silicon Atom

14 electrons occupying the 1st 3 energy levels:

1s, 2s, 2p orbitals filled by 10 electrons

3s, 3p orbitals filled by 4 electrons To minimize the overall energy, the 3s and 3p orbitals

hybridize to form 4 tetrahedral 3sp orbitals

Each has one electron and is capable of forming a bond

with a neighboring atom

7/28/2019 AdvSemi_Lec01 2013_02_28

17/36


Silicon crystal structure

Diamond Cubic Lattice

Each Si atom has 4 nearest neighbors

Lattice constant = 5.431

Si

Si SiSi

Si

Si

Si Si

Si Si

Si

Si

Si

Si

Si

Si

Si

Si Si

Si Si

Si

Si

Si

Si

Silicon atoms share valence electrons to

form insulator-like bonds.

7/28/2019 AdvSemi_Lec01 2013_02_28

18/36


Silicon crystal doping

7/28/2019 AdvSemi_Lec01 2013_02_28

19/36


Solution of wave equation energy bands

Use parabolic E(k) near band minimum/maximum

Model empty electron states at the top of the valence band

as positive electric charges with positive mass - holes

7/28/2019 AdvSemi_Lec01 2013_02_28

20/36


A problem with effective mass

The following effective mass concepts are often applied to

semiconductor materials and devices Conductivity mass Density-of-states mass Hall mass Optical mass

Cyclotron mass

The traditional theoretical semiconductor effective mass

does not lead to correct theoretical and experimental results for non-parabolic E(k) such as electron mass in HgCdTe and graphene

2

2 2/

mE k

h

7/28/2019 AdvSemi_Lec01 2013_02_28

21/36


Definition of mass

Assume that there is a given dispersion relationship E(k), which has

wave solutions

Assume that waves can form wave-packets with the group velocity

defined as1

v Ek

= h

Here k is the wave-vector, related to the lattice momentum in solid-

state materials

7/28/2019 AdvSemi_Lec01 2013_02_28

22/36


Definition of mass

Lets assume that in semi-classical approximation we can identify

particles with wave-packets satisfying De Broglie relation

This leads to a unified theoretical definition of the effective mass

vp m k= = h

2

/

km

E k=

h

Sometimes, this definition is called the optical effective mass

However, we will demonstrate that this definition is quite general and

can be applied to any parabolic or non-parabolic E(k) relationship

1v

E

k

=

h

7/28/2019 AdvSemi_Lec01 2013_02_28

23/36


Application to relativistic particles

2 2 2 2 4 2 2 2 4

0 0E c m c E c m c= + = +p p

2

2 2 2 4

0

E c

c m c

= = +

p

vp p

2 2 2 4

02

1m c m c

c= = +

pp

v

Assume that a relativistic particle can be described by a

wave packet with group velocity and mass defined as before

,

/

Em

mE

=

=

v p vp

p p

v p

Then using relativistic dispersion relationship for a free particle

Obtain

2 4 2 2 2 4

0m c c m c= +p

7/28/2019 AdvSemi_Lec01 2013_02_28

24/36


This leads to the relativistic mass for a free particle

Application to relativistic particles

Based on the above, obtain standard relativistic equationsfor velocity and mass of the particle

2 2 2 2 2 2

0m c m m c= +v

0

2 2

0

22

,

11

mc mm

cm

= =--

v

v

2E mc=

Note that we derived this result based on the unified mass

definition and E(k) of the free relativistic particles

7/28/2019 AdvSemi_Lec01 2013_02_28

25/36


Application to parabolic materials

Assume that electron energy near conduction band

minimum is described by one-dimensional, parabolic E(k)

Therefore, in parabolic materials (and only in parabolic materials)

mass is constant as a function of energy

with a constant coefficient

2 2

*

02

C

kE E

m= +

h

*

0m

The effective mass is calculated as2

*

0/

km m

E k= =

h

7/28/2019 AdvSemi_Lec01 2013_02_28

26/36


A problem with parabolic mass

Writing Newton's second law

Accounting for variable mass, which potentially depends on

energy and momentum, obtain

dpF

dt=

v vv

dm mF m

dt t t

= = +

7/28/2019 AdvSemi_Lec01 2013_02_28

27/36


A problem with parabolic mass

For a parabolic E(k), the mass is constant and F is approximated as

We obtain the parabolic mass approximation,

which is generally not valid!

2

2 2/

mE k

h

Using the same definition of the group velocity

1v

E

k

=

h

vF m

t

We can approximate

v m E m E k E pF m m

t t k k k t k k t

= = =

h h

7/28/2019 AdvSemi_Lec01 2013_02_28

28/36


Energy bands in real crystals

Detailed E(k) relationship determines material properties

7/28/2019 AdvSemi_Lec01 2013_02_28

29/36



A simplified one-dimensional Kane approximation of electron kinetic

energy in non-parabolic materials, such as HgCdTe, is written as

E

k

2 2 2

02G

E kE

E m

7/28/2019 AdvSemi_Lec01 2013_02_28

30/36



Obtain the effective mass, which is linearly dependent on energy

This result was experimentally confirmed in non-parabolic materials

1

0

11 2

G

E k E

k m Ea

- = = +

vh

h

2

01 2

/ G

k Em m

E k Ea

= = +

h

Derive for the carrier velocity

7/28/2019 AdvSemi_Lec01 2013_02_28

31/36


Electron velocity saturation

Parabolic approximation is valid at low energies

No velocity saturation for parabolic approximation

GE E=

2

2 2

0

0 0

2

1 2

G

EE E

E

kE

m

E k E

k m m

a+

=

v

h

h

h

7/28/2019 AdvSemi_Lec01 2013_02_28

32/36


Electron velocity saturation

At high energies

Electron saturation velocity is a function of bandgap and

carrier effective mass

GE E?

2 2

2 2 2

0

0

0

2

2

1

2

G G

G

G

G

E EE

E E

E k

E m

EE km

EE

k m

a a

a

a

a

+

=

v

h

h

h

7/28/2019 AdvSemi_Lec01 2013_02_28

33/36


Velocity saturation in real crystals

Electron velocity is saturated with high applied voltage /

electric field

7/28/2019 AdvSemi_Lec01 2013_02_28

34/36


Advanced Materials - Graphene

2D honeycomb crystal lattice Energy band structure

7/28/2019 AdvSemi_Lec01 2013_02_28

35/36


Application to graphene

Assume particles with zero rest mass and with linear E(k)

relationship similar to massless fermions in graphene

around Dirac points

- Fermi velocityvFvFE k:

7/28/2019 AdvSemi_Lec01 2013_02_28

36/36

Application to graphene

The definition of the effective mass leads to

The above result was confirmed by cyclotron resonance

mass measurements in graphene

Note that parabolic mass definition is not applicable for linear E(k)

1v vF

E

k

=

:h

Calculate carrier velocity

2

/ vF

kkm

E k=

h:

advsemi_lec01 2013_02_28

Documents