2 Device Physics

A historical perspective

Germanium

- One of the first materials to receive wide attention for use in simiconductor device

fabrication, but it was rapidly replaced by silicon during the early 1960s.

Silicon

-The dominant material used throughout the integrated-circuit industry today.

-Silicon can easily be oxidized to form silicon dioxide:

high quality insulator

an excellent barrier layer for the selective diffusion steps

-A very abundant element in nature, a low cost, a wider bandgap than germanium,

and can therefore operate at higher temperatures

An Overview of monolithic fabrication process

Basic Process steps:

- Oxidation

Silicon dioxide can be formed by heating a silicon wafer to a high temperature

in the presence of oxygen

44% of the final oxide thick.


Basic Process steps:

- Photolithography

Photolithography includes the overall process of mask fabrication and the process of transferring

patterns from the masks to the surface of the wafer

This process is critical to the production of integrated circuits, and the number of mask steps is

often used as a measure of complexity when comparing fabrication process

- Etching

- Diffusion

Shallow n- and p-type layers are formed by high temperature diffusion of donor or acceptor

impurities into silicon

- Ion Implantation

Shallow n- and p-type layers are formed by ion-implantation, in which the wafer is bombarded

with high-energy donor or acceptor atoms generated in a high voltage particle accelerator


Basic Process steps:-. Evaporation and sputtering

Evaporation : metal films can be deposited through evaporation by heating the metal to its

melting point in a vacuum

Sputtering : metal and insulators may also be deposited by a sputtering

-. Chemical vapor deposition (CVD)

Thin films of silicon nitride, silicon dioxide, and polysilicon can be formed through a CVD

-. Epitaxy

Chemical Vapor-Phase Deposition

Liquid-Phase Epitaxy

Molecular Beam Epitaxy

Introduction to Micro Fabrication

An Overview of CMOS Process Flow

BEOL : Interconnection


1. Substrate

• Moderately high resistivity : 25-50Ocm → 1015/cm3

• In order to reproducibly manufacture wells, the background

doping needs to be significantly less than the well doping

• (100) : properties of the Si/SiO2 interface are significantly better

• Intrinsic guttering

2. Active Region Formation

• Make certain that the individual devices are electrically isolated from each other

• LOCOS (LOCal Oxidation of Silicon) / STI (Shallow Trench Isolation)


LOCOS (LOCal Oxidation of Silicon)

An Overview of CMOS Process FlowIntroduction to

Micro Fabrication

2. Active Region Formation (계속) :LOCOS (LOCal Oxidation of Silicon)

Thermal oxidation (thin pad oxide) : protect silicon surface

LPCVD nitride deposition

Active area

Nitride/oxide sandwich etching except active area with hot phosphoric acid

Boron field implantation

Thermal field oxidation

Remove nitride and oxide pad

Si3N4 under tensile stress → compressive stress in Si → defect generation

Si3N4 under tensile stress + SiO2 under compressive stress → stress compensation



2. Active Region Formation (계속):STI (Shallow Trench Isolation) The thicknesses of SiO2 and Si3N4 are approximately the same as in the LOCOS. However the

stress-related issues are relaxed because of no long high-Temperature oxidation

After patterning active area

Trench etch(∼0.5µm)

① little undercutting

② a small slope to avoid void

③ rounded top and bottom corners

Liner Oxide (Thermally grow a thin (10-20nm) oxide)

*Why thermal oxide? : better Si/SiO2 interface

help to round the corners (∼1100°C)

Trench deposition (Oxide)

CMP (here, Si3N4 servers as a polishing stop)



2. Active Region Formation (계속):STI (Shallow Trench Isolation)


3. Well Implant

4. Channel Implant


5. Gate Formation

6. LDD Implant

7. Gate Sidewall Formation

8. SD Implant


An Overview of CMOS Process Flow9. CVD oxide deposition (ILD)

BPSG

P: protection against mobile ions like Na+

B: reduces the Temperature at which the glass layer “flows”

10. Contact Opening

11. Metal Deposition (Evaporation or Sputtering)-. Blanket deposition of a thin TiN layer or Ti/TiN bilayer (∵good adhesion to the SiO2 and other materials.

Effective barrier layer between the upper metal layers and the lower local interconnect layers)

-. Deposition of a blanket W by CVD

12. Pattern Metal


An Overview of CMOS Process Flow Introduction to Micro Fabrication

13. CVD Oxide Passivation layer (Phosphosilicate glass)

The top layer could be either SiO2 or Si3N4 and is designed to provide

some protection for the chip during the mechanical handling, as well as to protect

the chip against ambient contamination (Na+ or K+)

14. Open bonding pads

Table 1.2 A partial list of Semiconductor Material

Elemental semiconductor: group IV (Si, Ge)

Si : the most important of the semiconductors

Compound semicond.: group III & V (or II & VI)

Binary : two elements

Ternary : three elements

GaAs : superior electron transport properties and special optical propertiesex) laser diode, LED, high speed Ics

Table 1.1 A portion of the periodic table showing elements used in Semiconductor Material

an Introduction to an Introduction to Semiconductor DevicesSemiconductor Devices

Structure1. Amorphous

2. Polycrystalline : Grain, Grain Boundary

3. Single Crystal

Fig. 1.1 Two dimensional schematics of three general types of solids:

(a) amorphous (b) polycrystalline and (c) single crystal.


Silicon : Silicon Material Properties

3-D Unit Cell

1. Simple Cubic (SC)

2. Body-Centered Cubic (BCC)

3. Face-Centered Cubic (FCC)



Semiconductor Lattices 1. Diamond structure

2. Zicblend

(a) (b) (c)

Fig 1.14 (a) Diamond Structure (b) A unit cell of the diamond lattice constructed by placing

atoms 1/4,1/4,1/4 from each atom in an fcc (c) top view (along any <100> direction) of

an extended diamond lattice. The colored circles indicate one fcc sublattice and the black

circles indicate the interpenetrating fcc.


Miller Indices

1. Intercept set in the order x,y,z

2. Invert the intercept values

3. Convert the 1/intercpt set to the smalles possible set of whole numbers

4. Enclose the whole number set in curvilinear brackets

Crystal-lattice plane


Equivalent faces {hkl} with Crystal Plane (hkl)


Three lattice planes in a simple cubic lattice

Three lattice direction in a simple cubic lattice


Miller Indices


Semiconductor Lattices : 1. Diamond structure

2. Zincblende structure : two different types of atoms in the lattice



Imperfections in Solids

1. Lattice vibration

2. Point Defect (vacancy, interstitial, Frenkel defect)

3. Line Defect (line dislocation)

4. Area Defect (Stacking Fault)

결정 구조를 구성하는 원자 층을 각각 A, B, C라고 할 때

ABCABCA : Normal

ABCACBC : “extrinsic” faults

ABCABABC : “intrinsic” faults

5. Volume Defect

-. crucial roles : diffusion, ion implantation

-. lesser roles : oxidation kinetics

*Impurities in Solid

Substitution impurity

Interstitial impurity

Doping ( Diffusion, Ion Implantation)

Refer to Fig. 4.10 (p.44)


Growth of Semiconductor Material1. Growth from a Melt : Czochralski Method

2. Epitaxial Growth






2.3 Energy-Band Theory

Fig. 2.8 (a) Schematic of an isolated silicon atoms.

(b) The splitting of the 3s and 3p states of silicon into the allowed and forbidden band.


2.3 Energy-Band Theory

T=0K T>0K

Fig. 2.9 Fig. 2.10


The major difference between materials : the magnitude of the energy gap

-. Insulators: wide band gap

-. Metals: very small or no band gap

-. Semiconductors; intermediate case between insulators and metals

Ex. GaAs : EG=1.42 eV

Si : EG=1.12 eV

Ge : EG=0.66 eV

Metal, Insulator, and Semiconductor


The k-Space Diagram

mk

mpE

22

222 h==

E-k Diagram of Free Electron

Potential function

varies through the crystal

Indirect Band GapDirect Band Gap


2.5 Statistical Mechanism고전 통계 물리

1. Maxwell-Boltzmann : Boson의 분포 함수로

여기서 각 입자는 구별 가능하며 각 양자상태에 허용되는 입자의 수는 제한이 없음

2. Bose-Einstein : Boson의 분포 함수로

여기서 각 입자는 구별 불가능하며 각 양자상태에 허용되는 입자의 수는 제한이 없음

3. Fermi-Dirac : fermion(파울리의 배타 원리를 만족시키는 입자)의 분포 함수로

입자는 구별 불가능하며 각 양자상태에 허용되는 입자의 수에 제한이 있음

1

1)(−

=kT

EBEBe

Ef

1

1)(+

=kT

EFDCe

Ef

kTE

MB AeEf −=)(

양자 통계 물리

1)(1)( <<==≈→>>−−− EfAee

CEfeC MB

kTE

kTE

FDkT

E

1)(1)( <<==≈→>>−−− EfAee

BEfeB MB

kTE

kTE

BEkT

E

어떤 에너지상태를 점유할 확률이 1보다 매우 작은 경우

양자 역학적 분포 함수가 고전적인 분포 함수에 접근


2.5 Statistical Mechanism

The Fermi-Dirac Distribution Function and the Fermi Level

The Fermi Function f(E) :the probability that an available state at an energy E will be occupied

by an electron under equilibrium conditions

The Fermi-Dirac probability function

versus energy at T=0K


2.5 Statistical Mechanism

The Fermi-Dirac Distribution Function and the Fermi Level

Maxwell-Boltzmann

Approximation/

Boltzmann

Approximation

f(E)≈1


an Introduction to Semiconductor Devices

3.1 Charge Carriers in Semiconductors

The distribution of electrons in the conduction band Material

The distribution of holes in the valence band Material

)()()( EfEgEn Fc=

( ))(1)()( EfEgEp Fv −=

dEEfEgnEc

Fc∫∞

= )()(0

( )dEEfEgpV

bot

E

EFv∫ −= )(1)(0



Intrinsic semiconductor : pure (undoped) semiconductor

Efi : The Fermi energy level for the intrinsic semiconductor

]

In intrinsic semiconductor under equilibrium conditions

The electron and hole concentrations are equal.

The Intrinsic Carrier Concentration

( )⎥⎦

⎤⎢⎣

⎡ −−==

kTEENnn Fic

Ci exp0

Si atom density: 5×1022 cm-3,

total bonds: 2×1023 cm-3

ni~ 1.5 × 1010cm-3 @ 300 K

( )⎥⎦

⎤⎢⎣

⎡ −−==

kTEENpp VFi

Vi exp0

Band gap energy




The Intrinsic Carrier Concentration

In thermal equilibrium condition,

The Intrinsic Fermi-Level Position

( ) ( )⎥⎦

⎤⎢⎣

⎡ −−=⎥

⎦

⎤⎢⎣

⎡ −−kT

EENkT

EEN VFiV

FiCiC expexp

( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛++=⎟⎟

⎠

⎞⎜⎜⎝

⎛++= *

*

ln43

21ln

21

21

n

pVC

C

VVCFi m

mkTEE

NNkTEEE

Emidgap Therefore, ⎟⎟⎠

⎞⎜⎜⎝

⎛=− *

*

ln43

n

pmidgapFi m

mkTEE


3.2 Dopant Atoms and Energy Levels

Intrinsic Silicon LatticeSilicon Lattice

Doped with phosphorus

(Donor Impurity)

N-type Silicon

Silicon Lattice

Doped with Boron

(Acceptor Impurity)

P-type Silicon

Extrinsic Semiconductor


3.3 Carrier Distributions in the Extrinsic Semiconductor

Extrinsic Semiconductor : Terminology

1. Extrinsic semiconductor: doped semiconductor

cf) Intrinsic semiconductor: undoped semiconductor

2. Dopants: specific impurity atoms that are added to semiconductors in controlled amounts

for the purpose of increasing either the electron or the hole concentration

3. Donor: impurity atom that increases the electron concentration

cf) n-type material: a donor-doped material

4. Acceptor: impurity atom that increases the hole concentration

cf) p-type material: a acceptor-doped material

5. Majority carrier: the most abundant carrier in a given semiconductor sample; electron in

an n-type material and hole in a p-type materials

6. Minority carrier: the least abundant carrier in a given semiconductor sample; holes in an

n-type material and electrons in a p-type material



N-type Silicon

( )⎥⎦

⎤⎢⎣

⎡ −−=

kTEENp VF

Vexp0

P-type Silicon

( )⎥⎦

⎤⎢⎣

⎡ −−=

kTEENn Fc

Cexp0



( ) ( ) ( )

( ) ( )

( )⎥⎦

⎤⎢⎣

⎡ −=

⎥⎦

⎤⎢⎣

⎡ −⎥⎦

⎤⎢⎣

⎡ −−=

⎥⎦

⎤⎢⎣

⎡ −+−−=⎥

⎦

⎤⎢⎣

⎡ −−=

kTEEn

kTEE

kTEEN

kTEEEEN

kTEENn

FiFi

FiFFicC

FiFFicC

FcC

exp

expexp

expexp0

( )⎥⎦

⎤⎢⎣

⎡ −−=

kTEEpp FiF

i exp0

In similar way,

Therefore, for the semiconductor in thermal equilibrium

( ) ( ) 200 expexpexp i

gVC

VFFcVC n

kTE

NNkT

EEkT

EENNpn =⎥⎦

⎤⎢⎣

⎡−=⎥

⎦

⎤⎢⎣

⎡ −−⎥⎦

⎤⎢⎣

⎡ −−=



Degerate and Nondegenerate Semmiconductor

Simplified energy-band diagram for degenerately doped (a) n-type and (b) p-type

semiconductors. The Fermi level is in the conductor band and valence band, respectively


3.5 Carrier Concentrations-Effects of Doping

Compensated Semiconductor

-. Contains both donor and acceptor impurity atoms in the same region

-. N-type : Nd > Na

-. P-type : Na > Nd

-. Completely compensated semiconductor : Na=Nd (the same characteristics with intrinsic semiconductor)

Equilibrium Electron and Hole Concentration




( ) ( )

( )( ) ( ) 2

2

0

20

20

0

2

0

00

00

00

22,

0

min

iadad

iad

i

da

ddaa

da

nNNNNntherefore

nnNNn

nnpwith

NpNn

ionizationcompletegassu

nNppNnor

NpNn

+⎟⎠⎞

⎜⎝⎛ −

+−

=

=−−−

=

+=+

−+=−+

+=+ +−Charge Neutrality Condition

Refer to example 3.10 (p.104)




( )⎥⎦

⎤⎢⎣

⎡ −−=

kTEENn Fic

Ci exp

A typical majority-carrier concentration versus temperature plot constructed assuming a

phosphorus doped ND=5×1014 cm-3 Si.



Carrier Concentration Temperature Dependence

1. The increased ionization of dopant sites and the associated increase in the majority

carrier concentration when the temperature of a semiconductor is raised from near T=0 K

toward room temperature

• Below 100 K or so, in the freeze-out temperature region, n drops significantly below ND

and approaches zero as T = 0 K. At temperatures T → 0 K the thermal energy available in

the system is insufficient to release the weakly bound fifth electron on donor sites and

totally insufficient to excite electrons across the band gap

2. In the intrinsic temperature region, n rises above ND, approaching ni with increasing T

3. The wider the band gap, the greater the energy required to excite electrons from the

valence band into the conduction band




Equilibrium Electron and Hole Concentration (Summary)


3.6 Position of Fermi Energy Level-Effects of Doping and Temperature

( )

⎟⎟⎠

⎞⎜⎜⎝

⎛=−

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛=−

⎥⎦

⎤⎢⎣

⎡ −−=

−

a

VVF

d

ctypen

cFc

FcC

NNkTEE

waysimilarIn

NNkT

nNkTEE

kTEENnBecause

ln

lnln

exp

0

0


3.6 Position of Fermi Energy Level-Effects of Doping and TemperatureFermi level positioning in Si at 300 K as a function of the doping concentration

Fermi level positioning as a function of temperature for various doping concentration

<참고>


Carrier Drift

-. Charged-particle motion in response to an applied electric field

-. An electric field (E) tends to accelerate the +q charged holes in the direction of the

electric field and the –q charged electrons in the direction opposite to the electric field

-. Repeated periods of acceleration and subsequent decelerating collisions

-. Measurable quantities are macroscopic observables that reflect the average or overall

motion of the carriers

-. The thermal motion of the carriers is completely random and therefore averages out to

zero on a macroscopic scale, does not contribute to current transport

4.1 Carrier Drift

4.1.1 Drift Current Density

Typical random behavior of a hole or

electron in a semiconductor with no

applied electric field

Behavior of a electron in a

semiconductor with applied electric

field

Macroscopic behavior of a hole in a

semiconductor with applied electric field


an Introduction to Semiconductor Devices

4.1 Carrier Drift

4.1.1 Drift Current Density

Drift Current

the charge per unit time crossing an arbitrarily chose plane of observation oriented normal to

the direction of current flow

driftpdp

CarrierHole

ddrift JvepvJ |)( === ρ

eEamF p == *

Ev pdp µ=

Due to collisions (scattering events)

Average drift velocity

pEevepJ dpdpdriftp µ== )(|Therefore, EnpeJ dndpdrift )( µµ +=

nEevenJ dndndriftn µ== )(|In similar way,


Mobility

Mobility is obviously very important parameter in characterizing electron and hole transport due to drift

-. Unit: cm2/Vs

-. Carrier mobility varies inversely with the amount of scattering taking place within the semiconductor

-. Dominant scattering mechanisms:

Lattice scattering involving collisions with thermally agitated lattice atoms: Phonon Scattering

Ionized impurity (donor or acceptor) scattering

-. lower m* gives higher µ

Ex. µn (GaAs) >> µ n (Si))

4.1 Carrier Drift

4.1.2 Mobility Effect

***

ppp m

eEtveEdtdvmamF =→===

***| 21

p

cpdpp

p

cpd

velocitydriftaverage

p

cppeakd m

eEv

Eme

vEme

vτ

µττ

==→=→=

where τcpis the mean free time between collisions

Considering collisions,

*n

cndnn m

eEv τµ ==


4.1 Carrier Drift

4.1.2 Mobility Effect : Phonon Scattering

For Phonon Scattering

23−∝ TLµ

Figure. 4.2

The temperature dependence of electron mobilities

in silicon. In lightly doped semiconductors, lattice

scattering dominates.


4.1.2 Mobility Effect : Ionized Impurity Scattering

4.1 Carrier Drift

For ionized impurity scattering

II N

T 23

∝µ


4.1 Carrier Drift

4.1.2 Mobility Effect : Total Mobility

Doping dependence: At low doping concentrations, below approximately 1015 cm-3 in Si, the carrier

mobilities are essentially independent of the doping concentration. For dopings in excess of ~1015 cm-3, the

mobilities monotonically decrease with increasing NA or ND

Temperature dependence: Decreasing system temperature causes an ever-decreasing thermal agitation

of the semiconductor atoms, which in turn decreases the lattice scattering. Ionized impurities become more

and more effective in deflecting the charged carriers as the temperature and hence the speed of the carriers

decreases


4.1 Carrier Drift

4.1.3 Semiconductor Conductivity and Resistivity

Resistivity

Resistivity (ρ) is defined as the proportionality constant between the electric field impressed across

a homogeneous material and the total particle current per unit area


4.1 Carrier Drift

4.1.3 Semiconductor Conductivity and Resistivity

Resistivity


4.1 Carrier Drift

The vd is proportional to E at low electric fields, while at high electric fields vd

saturates and becomes independent of E

4.1.4 Velocity Saturation

Ev pdp µ=

uo


4.2 Carrier Diffusion

Diffusion

-. Diffusion is a process whereby particles tend to spread out or redistribute as a result of

their random thermal motion, migrating on a macroscopic scale from regions of high particle

concentration into region of low particle concentration

-. On a macroscopic scale the net effect of diffusion is precisely the same within both the

hypothetical system and semiconductors; there is an overall migration of particles from

regions of high particle concentration to regions of low particle concentration

-. Within semiconductors the mobile particles – the electrons and holes – are charged, and

diffusion related carrier transport gives rise to particle currents



Using Fick’s law,



Total Current Density

Total Particle Current Density


4.3 Graded Impurity Distribution

Relating Diffusion coefficients/Mobilities

-. For interrelation of the D’s and the m’s, it is necessary to establish the

connecting formula known as the Einstein relationship

-. In deriving the Einstein relationship, we consider a nonuniformly doped

semiconductor maintained under equilibrium conditions

-. Constancy of the Fermi Level: nonuniformly doped n-type semiconductor as an

example dEF/ dx =dEF /dy= dEF /dz =0


Current flow under equilibrium conditions: the total current is identically zero

Einstein relationship: Under equilibrium conditions, and focusing on the electrons,



With dEF/dx=0,


Substituting


4.4 Carrier Generation and Recombination

-. Recombination-generation (R-G) is nature’s order-restoring mechanism, the

means whereby the carrier excess or deficit inside the semiconductor is stabilized

Recombination: a process whereby electrons and holes (carriers)

are annihilated or destroyed

Generation: a process whereby electrons and holes are created

*Generation Processes

1. light with an energy > EG → photogeneration

2. thermal energy > EG → direct thermal generation

3. The thermally assisted generation of carriers with R-G centers

4. Impact ionization (the inverse of Auger recombination)


4.4 Carrier Generation and Recombination

1. Band-to-band Recombination

The direct annihilation of a conduction band electron and a valence band hole

→ the production of a photon (light)

Near-midgap energy levels

introduced by some common

impurities in Si

Documents

2 Device Physics