semiconductor device and material characterization

ECE 4813 Dr. Alan Doolittle

ECE 4813

Semiconductor Device and Material Characterization

Dr. Alan Doolittle School of Electrical and Computer Engineering

Georgia Institute of Technology

As with all of these lecture slides, I am indebted to Dr. Dieter Schroder from Arizona State University for his generous contributions and freely given resources. Most of (>80%) the figures/slides in this lecture came from Dieter. Some of these figures are copyrighted and can be found within the class text, Semiconductor Device and Materials Characterization. Every serious microelectronics student should have a copy of this book!


Doping Plasma Resonance

Free Carrier Absorption Infrared Spectroscopy

Photoluminescence Hall Measurements Magnetoresistance

Time of Flight


Plasma Resonance and Reflectivity Minimum

Electron/hole plasmas are ensembles of free carriers that can, at certain frequencies, oscillate in concert as a group.

Such a plasma resonance exists whose frequency / wavelength (ν=c/λ) is determined by the free carrier density.

Good for p (or n) > ~1018 cm-3 Since plasma resonances are hard to detect in practice,

most of the time, free carrier densities are determined by empirical reflectivity minimums…

… or free carrier absorption

nmK

qc Os

plasma

*2 επλ =

( )Cplasma BAn += λ


Free Carrier Absorption Free carrier absorption occurs within the conduction or

valance band (not between). For example a conduction electron is absorbs an IR photon and is promoted

into a higher energy state still inside the conduction band

In practice, empirical fitting is used

Generally measured using Fourier Transmission Infrared (FTIR)

Spectrometer Good for p (or n) > ~1017 cm-3

( ) pO

fcmncpq

µεπλα 2*32

23

4=

pAfc2λα =


Infrared Spectroscopy Measures dopant concentrations (low

temperature) and can be used at room temperature to measure free carrier absorption.

Cryogenic temperatures are used to freeze carriers into their dopant ground state

IR (very small energy) light is used to excite electrons/holes into their dopant “excited state” creating sharp absorption lines

Absorption line intensity is calibrated to dopant density

Good for NA (or ND) > ~1011 cm-3


Interferometer Let source be cos2πfx

f: frequency of light x: movable mirror location

L1 = L2 Constructive interference Maximum detector output

L1 = L2 + λ/4 Destructive interference Zero detector output

Source

BeamSplitter

Sample

Detector

Movable Mirror

L1

L2

Fixed Mirror

L1=L2

L1=L2 + λ/4


Fourier Transform Infrared Spectroscopy

Fourier transform infrared spectroscopy (FTIR)

( ) ( )[ ]dfxffBxI f∫ +=0

2cos1 π

( ) ∫ == 1

01

11 2

2sin2cosf

xfxfAfdfxfAxI

πππ

( ) ( ) dxxfxIfB ∫−=

ω

ωπ2cos

( ) ( )[ ]xffBxI π2cos1+=

f f1 f2

Ampl

itude

Spectrum 0

0.2

0.4

0.6

0.8

1

-0.001 -0.0005 0 0.0005 0.001

(sin

y/y)

2

x (cm)

f1=103 cm-1

3x103 cm-1

Interferogram In a Fourier spectrum, frequency bandwidth determines resolution.


Interferogram - Spectrum

Interferogram

www.chem.orst.edu/ch361-464/ch362/irinstrs.htm

Spectrum


FTIR Applications

Determine oxygen and carbon density by transmission dip


Mobilities Conductivity Mobility: µp=1/qpρ

Majority carrier mobility; need carrier concentration and resistivity

Drift Mobility: µp = vd/ε Minority carrier mobility Need drift velocity and electric field (Haynes-Shockley

experiment) Hall Mobility: µH = RH/ρ

Need Hall measurement Hall mobility does not necessarily equal conductivity mobility

MOSFET Mobility: MOSFET mobility lowest, carriers are scattered at the Si-SiO2

interface Interface is microscopically rough


Mobility Electron/hole mobility is a measure of

carrier scattering in the semiconductor Lattice scattering

Silicon atoms Ionized impurity scattering

Dopant atoms Interface scattering

Surface roughness at SiO2/Si interface Polar scattering

Silicon bulk µn ≈ 3 µp

MOSFET mobility (effective mobility) ≈ 0.3 bulk mobility

Courtesy of M.A. Gribelyuk, IBM.

sil µµµµ1111

++=

Vibration

Lattice Scattering:

Ionized Impurity Scattering:

+ Dopant atom

Si


Mobilities For bulk semiconductors,

lattice and ionized impurity scattering dominate the mobility

log T

log µ

µi

µlµ

IncreasingNi

iil N

TT5.1

5.1 ; == − µµ 10

100

1000

1014 1016 1018 1020 1022

Mob

ility

(cm

2 /V·

s)

Doping Density (cm-3)

µn

µp

Silicon

100

1000

1014 1015 1016 1017 1018 1019

µ n (c

m2 /V

·s)

ND (cm-3)

T=200 K250 K

300 K350 K

400 K450 K 500 K

n-Silicon


“Simple” Hall Effect Hall effect is commonly used during the development of new

semiconductor material

Resistivity, carrier concentration AND mobility can all be determined simultaneously

Lorentz Force – deflection of free carriers by an applied magnetic field

Temperature dependent Hall is very powerful and can elucidate scattering mechanisms (plotting mobility vs Ta), and determine dopant activation energies Compensated Dopant Freeze out regime – Arrhenius slope results in EA Uncompensated Dopant Freeze out regime – Arrhenius slope results in EA/2 At moderate temperatures, p~ (NA- ND) At elevated temperatures, p ~ ni


“Simple” Hall Effect

sVρ

VH

Id

w

B

Iε

θ

xy

z

)( BvqF

×+= ε

qwdpBIBv xy ==ε

∫ ∫∫ =−=−==0 0

0 w wyHV

qdpBIdy

qwdpBIdyVdVH ε

BIdVR H

H =

xx qwdpvqApvI ==

Hall coefficient [m3/C or cm3/C]

Lorentz Force

Hall voltage

Voltage induced by current I

In steady state, the magnetic force is balanced by the induced electric field


“Simple” Hall Effect Resistivity is simply found from the voltage drop

along the length (no magnetic field),

Carrier density

Mobility

IV

sdw ρρ =

(r ~ 1 - 2, Hall scattering factor)

HH qRrn

qRrp −== ;

pHH

H

H

H

pp

H

rRRR

rpq

qRrp

µσµ

µµσµ

==

===

=


Detailed Hall Effect The Hall Coefficient for both electrons and holes

present in the same material is in general:

( ) ( )

( ) ( )

−+

+

−+

−

=22

2

2

2

npBnpq

npBnp

rR

np

n

np

n

H

µµµ

µµµ


Detailed Hall Effect The Hall Coefficient is in general:

At low fields (B<<1/µn)…

And at high fields (B>>1/µn)…

( ) ( )

( ) ( )

−+

+

−+

−

=22

2

2

2

npBnpq

npBnp

rR

np

n

np

n

H

µµµ

µµµ

qnror

qpr

npq

npr

R

p

n

p

n

H −≈

+

−

= 2

2

µµ

µµ

( )npqrRH −

=

collisionsbetween mean time theis τwhere2

2

τ

τ=r


Two Layer Hall Effect Sometimes, a semiconductor has two different

conduction layers (surface inversion, fermi-level pinning, substrate layers, n-p junctions or p+/n or n+/n layers)

The Hall coefficient is then a weighted sum of both layers and can be either positive or negative leading to confusion (shown for the low B field limit):

21

22

11

222

2

211

1

tttandtt

ttwhere

ttR

ttRR

total

totaltotal

totalH

totalHH

+=

+

=

+

=

σσσ

σσ

σσ


Two Layer Hall Effect (more detail) The Hall coefficient is then a weighted sum of

both layers and can be either positive or negative leading to confusion:

( ) ( )[ ]( ) ( )

+++

+++=

21221

22

21

22211

21221

222

2112

2221

211

BtRtRttBtRtRRRtRtRtR

HH

HHHHHHtotalH

σσσσσσσσ

Low B Field

High B Field

21

22

11

222

2

211

1

tttandtt

ttwhere

ttR

ttRR

total

totaltotal

totalH

totalHH

+=

+

=

+

=

σσσ

σσ

σσ

+

=1221

21

tRtRtRRR

HH

totalHHH


Two Layer Hall Effect (more detail) The Hall coefficient is then a weighted sum of

both layers and can be either positive or negative leading to confusion (generally):

( ) ( )[ ]( ) ( )

+++

+++=

21221

22

21

22211

21221

222

2112

2221

211

BtRtRttBtRtRRRtRtRtR

HH

HHHHHHtotalH

σσσσσσσσ


Hall Effect Measurements Two approaches:

Hall Bar (5 or 6 contacts)

Van der Pauw configuration Based on Conformal mapping theory Contacts assumed point sources Uniform thickness Cannot contain isolated (interior) holes

1 4 2 3

(6) 5

1

4

2

3


Hall Effect Measurements Van der Pauw configuration

Measure resistivity first by “perimeter measurements”… Example: determine R12,34 where current goes in 1 and leaves 2 and voltage is measured between

terminals 3 and 4. Next determine R23,14 where current goes in 2 and leaves 3 and voltage is measured between terminals 1 and 4.

Use:

…where F is a symmetry term derived from conformal mapping theory F is determined from:

1

4

2

3

Differs some from your text. For details see http://www.nist.gov/pml/semiconductor/hall_resistivity.cfm

FRRt

+

=

2)2ln(14,2334,12πρ

14,23

34,12

)2ln(

1

2cosh

)2ln(11

RR

Rwhere

eFRR

r

F

r

r

=

=

+−

−


Hall Effect Measurements Van der Pauw configuration

Now measure the Hall voltage using “Crossing configurations” Example: Apply the magnetic field and determine V13,24P where current goes in 1 and leaves 3 and

voltage is measured between terminals 2 and 4. Next reverse the field and determine V13,24N again. To find the sheet concentration (#/cm2) use:

…where we have intentionally left out the proportionality constant In reality, 8 resistivity and eight hall voltage measurements are made to reduce contact related offset voltage errors resulting in an equation that is of the form:

See text for important sample geometry considerations (if ignored, significant error can result)

1

4

2

3

( )

+∝

NP VVqIB

24,1324,13

ρ

( )( ) ( ) ( ) ( )[ ]

−+−+−+−=

−

NPNPNPNP VVVVVVVVqIBx

13,2431,2413,4213,4242,3142,3124,1324,13

8108ρ

Differs some from your text. For details see http://www.nist.gov/pml/semiconductor/hall_resistivity.cfm


Haynes - Shockley Experiment Allows mobility, diffusion constant, and minority carrier

lifetime to be determined

Electric field

p Substrate

∆n

d

n Emittern Collector

L

VoutVin

-Vdr

−

−−

=∆ nn

ttD

vtx

n

etD

Ntxn τ

π4

)( 2

4),(

0

0.2

0.4

0.6

0.8

1

0 1 10-6 2 10-6 3 10-6 4 10-6

TheoryExperiment

∆n(

x,t)/

∆n(

x,0)

Time (s)

∆t


Haynes - Shockley Experiment Allows mobility, diffusion constant, and minority carrier

lifetime to be determined

If at least two lengths and two times are measured, the

FWHM of the time plot, ∆t can be used to…

Electric field

p Substrate

∆n

d

n Emittern Collector

L

VoutVin

-Vdr

)/ln(5.0)/ln(;

2ln16)(;;/

1221

123

2

ddoutout

ddn

dn

dndriftd ttVV

ttt

tdDtdvdt

−−

=∆

=== τε

µ

0

0.2

0.4

0.6

0.8

1

0 1 10-6 2 10-6 3 10-6 4 10-6

TheoryExperiment

∆n(

x,t)/

∆n(

x,0)

Time (s)

∆t


Haynes – Shockley Experiment

0

2 1012

4 1012

6 1012

8 1012

1 1013

0 0.4 0.8 1.2∆

n(x,

t) (c

m-3

) d=0.025 cm

Time (µs)

0.05 cm

0.075 cm0.1 cm

0

2 1012

4 1012

6 1012

0.5 0.6 0.7 0.8 0.9 1

∆n(

x,t)

(cm

-3) τn=10 µs

Time (µs)

5 µs2 µs

1 µs

0.5 µs0.2 µs

−

−−=∆

nnn

ttD

vtxtD

Ntxnτπ 4

)(exp4

),(2


MOSFET Effective Mobility Effective mobility determined from drain current – drain

voltage characteristics The MOSFET drain current for small VD (50 - 100 mV) is Determine gd= ∆ ID/∆VD for low VD Solve for µeff

Need gd, QN, VT

DTGoxeffDNeffD VVVCLWVQLWI )()/()/( −≈= µµ

)( TGox

d

N

deff VVWC

LgWQLg

−≈=µ

0

0.005

0.01

0.015

0 1 2 3

Dra

in C

urre

nt (A

)

Drain Voltage (V)

VG=3 VL=0.4 µm, W=25 µmtox=9 nm

2.25 V

1.5 V

0.75 VLinear

Saturated


MOSFET Effective Mobility

ID-VD ⇒ gd; CGC-VG ⇒ QN; ID-VG ⇒ VT

0

1 10-6

2 10-6

0 0.02 0.04 0.06 0.08 0.1

I D (A

)

VD (V)

VG=5 V 4 V4.5 V

3.5 V3 V2.5 V2 V1.5 V

1 V

∫ ∞−= GV

GGCN dVCQ

0

2 10-7

4 10-7

0

1 10-6

2 10-6

0 1 2 3 4 5C

GC (F

/cm

2 ) QN (C

/cm2)

VG (V)


MOSFET Effective Mobility

)(1 TG

oeff VV −+

=θ

µµ

µo = low-field mobility; θ = mobility degradation factor

500

600

700

800

0 1 2 3 4

µ eff

(cm

2 /V·s

)

VG-VT (V)

µo

1

1.1

1.2

1.3

1.4

0 1 2 3 4

µ o/µ

eff

VG-VT (V)

Slope = θ


Review Questions What are the different mobilities? Why is the MOS effective mobility less than the

bulk mobility? How is µeff most commonly determined? Why does the Hall mobility differ from the

conductivity mobility How does a Hall mobility measurement work? How does the Haynes-Shockley experiment

work? What is determined with the Haynes-Shockley

experiment ? For what is the time-of-flight technique used?

semiconductor device and material characterization

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