semiconductor device and material...

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!


Resistivity Sheet Resistance

Four-point Probe Semiconductor Resistivity

Wafer Mapping van der Pauw Eddy Current

Modulated Photoreflectance Conductivity Type


Graphs and Plots

xxy 17104.6

1−=

10-4

10-2

100

102

1014 1016 1018 1020

y

x

0

50

100

150

200

0 5 1019 1 1020

y

x

When two variables, e.g., resistivity and doping density, vary over many orders of magnitudes (decades) it is best to plot log - log


Graphs and Plots nxy =

nxdydSlope ==)(log)(log

0

2000

4000

6000

8000

10000

0 2 4 6 8 10

y

x

10-410-310-210-1100101102103104

0.1 1 10

y

x

-4-3-2-101234

-1 -0.5 0 0.5 1

logy

logx

What is n?

xnxyxy nn logloglog ==⇒=

Plotted on a Log Scale then Analyzed

Take Log 1st then Plotted and Analyzed

Plotted on a Linear Scale – Cannot be Analyzed


Graphs and Plots: Example 1/ xxKey =

11 3.21

10ln1)(log

xxdxydSlope ===

=→

10lnlnlog yyrecall

1

10

100

0 2 4 6 8 10

y

x

0

20

40

60

80

100

0 2 4 6 8 10

y

x

What are K and x1?

10ln/loglog;/lnln 1

1xxKyxxKy +=+=

Taking Natural Log Scale makes Analysis easier but makes scales hard to read. Data is almost

always presented in a Log10 basis.


Kelvin Measurements Kelvin measurements refer to 4-probe measurements Two probes:

2RProbe+2RContact+2RSpreading

Four probes: RSemicond

VI I

RProbe

RContact

RSpreading

Current

I IV

RSemicond


Four Point Probe The four point probe is

used to determine the resistivity and sheet resistance

s t

I I V


Four Point Probe Derivation of the basic four point probe equation Assumption: Current flows out radially from infinitesimal

probe tip I

P

A=2πr2

∞

∞ ∞r

−=

−=

21

21

112

22

rrIV

rI

rIV

πρ

πρ

πρ

I I

r1 r2

∞

∞ ∞

rIV

rdrIdV

rI

AIJ

drdVJIRV

rV

πρ

πρ

πρε

22

2;;

20

2

=⇒−=

==−===

∫∫∞

Voltage Due to a Single Probe Voltage Due to Two Probes


Four Point Probe For four in-line probes

I I

s s s

1 2 3 4

∞

∞ ∞

cmIVs −Ω= πρ 2

sI

ssssIVVVV

ssIV

ssIV

πρ

πρ

πρ

πρ

21

21

211

2

121

2;

211

2

3223

32

=

+−−=−==

−=

−=


Four Point Probe Since wafers are not infinite

in extent, need to correct for Conducting/non-conducting

bottom boundary Wafer thickness Nearness to wafer edge Wafer size

For non-conducting bottom surface boundary

( ) ( )[ ]stststF

2sinhsinhln21 =

I I

t ρ

V

( )cmIVsF ⋅Ω= πρ 2

0.001

0.01

0.1

1

10

0.01 0.1 1 10

F

t/s

F=F1F2F3 • F1 corrects the sample

thickness • F2 corrects the lateral

dimensions (F2 ~1if wafer size is ~40 times S)

• F3 corrects the probe to edge (d) placement errors (~1 if d>2S)


Resistivity

10-4

10-3

10-2

10-1

100

101

102

10141015101610171018101910201021Res

istiv

ity (Ω

-cm

)Dopant Density (cm-3)

p-Ge

n-Gep-GaAs

n-GaAs

p-GaP

n-GaP

1012 1014 1016 1018 102010-4

10-2

100

102

104

Dopant Density (cm-3)

Res

istiv

ity (Ω

-cm

)

Boron

Phosphorus


Thin Layers Consider a thin film on an insulator

Metal layer on insulator Poly-Si layer on insulator n on p or p on n

Usually t<<s

Recall sinhx ≅ x for x <<1

( )2ln21stF ≈∴

IVt

IVt

IVsts 532.4

2ln2ln2/2 ===

ππρ

( ) ( )[ ]stststF

2sinhsinhln21 =

n

p t


What Is Sheet Resistance? The resistance between the contacts is

L/W has no units ρ/t should have units of ohms But . . . R ≠ ρ/t ! Sheet resistance Rsh = ρ/t (ohms/square)

Resistance independent of the size of the square

ohmsWL

tALR ρρ

==

( ) ( ) [ ]ohmssquaresofnumberxRR sh=

W

L

t

ρ

5 squares

Rsh


Sheet Resistance

Frequently you do not know t. Ion implanted layer Diffused layer Metal film Poly-Si layers

Define sheet resistance Rsh For uniformly-doped layer

IV

ttRsh 2ln

1 πσ

ρ===

IVt

2lnπρ =


Dual Configuration (or Switched Configuration)

Measurement 1: Current in 1 & out 4 and voltage measured on 2 and 3. Directions then reversed.

Measurement 2: Current in 1 & out 3 and voltage measured on 2 and 4. Directions then reversed.

Advantages: Probes can be oriented in any direction (no need to be

parallel or perpendicular to the wafer radius or edges) Lateral dimensions no longer needed Self-correcting for changes in probe spacing

I I

t ρ

V1 2 3 4

+

=2

14

23

14

23

r

r

f

f

a

IV

IV

R

+

=2

13

24

13

24

r

r

f

f

b

IV

IV

R

2

872.7173.25696.14

−+−=

b

a

b

aSH R

RRRR


Wafer Mapping


Wafer Maps Measure sheet resistance; generate and plot

contour maps (lines of equal sheet resistance)

Si-doped Al Rsh,av = 80.6 mΩ/square

1% Contours

Epitaxial Si Rsh,av = 18.5 kΩ/square

1% Contours

B-implanted Si Rsh,av = 98.5 Ω/square

1% Contours


Sheet Resistance For non-uniformly doped layers

∫∫== t

n

tsh

dxnqdxR

00

11

µσ

1013

1015

1017

1019

1021

0 2 10-6 4 10-6 6 10-6 8 10-6

n (c

m-3

)

x (cm)

Rsh=125 Ω/square


Sheet Resistance Sheet resistance Rsh depends on the total number of

implanted or diffused impurities and on the layer thickness

L

W ρ, Rsh

t

squareOhmstqntt

Rn

sh /11µσ

ρ===

squareOhmsdxnq

R t

n

sh /1

0∫

=µ

OhmsW

LRR sh=

Uniformly doped:

Non-uniformly doped:

10-3

10-2

10-1

100

101

102

10-5 10-4 10-3

Rsh

(Ω/s

quar

e)

t (cm)

* Al* Cu

ρ = 10-3 Ω-cm

10-4 Ω-cm

10-5 Ω-cm

10-6 Ω-cm

* Si


van der Pauw Measurements Instead of a four-point probe, one can use an

arbitrarily shaped sample Current flows through two adjacent contacts Voltage is measured across the other two contacts

23

4141,23

12

3434,12

41,2334,12 ;;22ln I

VRIVR

RRFt

==

+=

πρ

1

2

4

3


van der Pauw Measurements

0.2

0.4

0.6

0.8

1

1 10 100 1000

F

Rr

F function is determined from

41,23

34,121

2)2exp(lncosh

2ln11

RR

RFFRR

rr

r =

=

+− −

For symmetrical samples, e.g., circles or squares, F = 1

34,1234,12 2ln;

2lnRRRt

shππρ ==


Precautions For copper metallization barrier layers are used to prevent

Cu from diffusing into SiO2 or Si Barrier layers have negligible effect on sheet resistance Rsh

measurement of thick conductor films Chemical-mechanical polishing (CMP) dishing does affect

Rsh measurements

Copper

Barrier Metal

t

tRsh /ρ=CMP Dishing

T. Turner, “Cu-Linewidth Resistivity Measurements,” Solid State Technol. 43, 89-96, April 2000


Line Width

lineshshlinesh R

LRWWLR

IVR

IVR =⇒===

13

54

65

12 ;)2ln(

π6

1

2

3 4 5

W L

Greek Cross

Cross bridge test structure

12

34

2ln IVRsh

π=

1

2

3

4

Used to determine line width W


Anodic Oxidation / van der Pauw Place wafer into electrolyte Apply constant current, measure voltage Oxide grown anodically at room temperature Oxide growth consumes Si When oxide is etched, Si is removed Measure sheet resistance

n p

SiO2


Anodic Oxidation / van der Pauw

ρσ

σ

1)/1(1−=−=⇒=

∫dx

Rd

dxR sh

t

x

sh

∂∂

−∂∂

=∫b

a caaf

cbbfdxxf

dcd )()()(

1

21

)/1(1)(

−

=−=

dxdR

RdxRdx sh

shsh

ρ

n p

0 t x

103

104

105

106

0 100 2.5 10-5 5 10-5 7.5 10-5 1 10-4

Rsh

(Ω/s

quar

e)

x (cm)

Rsh0

Rsh1

Rsh2

0

0.5

1

1.5

2

0 100 2.5 10-5 5 10-5 7.5 10-5 1 10-4

σ (S

/cm

)

x (cm)

σ2

σ1

σ0

Using Leibniz’s theorem:


Eddy Current - Contactless An oscillating circuit induces time-varying magnetic fields

leading to eddy currents in the wafer ⇒ resulting loss is proportional to the sheet resistance Rsh Sheet resistance Conductor thickness: t = ρmetal/ Rsh, measure metal sheet

resistance Rsh, know metal resistivity ρmetal

t

ρsemicond

ρmetal Drive Coil

Eddy Currents


Four Point Probe / Eddy Current

Rsh,av = 3.024x10-2 Ω/square Std. Dev. = 1.459%

Four Point Probe:

Eddy Current:

Rsh,av = 3.023x10-2 Ω/square

Std. Dev. = 1.413%

Figures courtesy of W. Johnson, KLA-Tencor

1 µm Aluminum

Rsh,av = 62.904 Ω/square Std. Dev. = 2.548%

Rsh,av = 62.560 Ω/square Std. Dev. = 2.94%

200 Å Titanium


Modulated Photoreflectance Pump laser heats semiconductor locally ⇒ small reflectivity

change of the wafer ⇒ measured by the probe beam Ion-implanted samples:

No post-implant annealing required Signal ~ implant dose High spatial resolution (few µm) Can measure implanted patterns Bare and oxidized wafers Non-contact, non-destructive

http://www.thermawave.com

…also known as ThermaWave

Detector

ProbeLaser

PumpLaser

Sample

ThermaWaveSignal

DamagedLayer


Modulated Photoreflectance

B in Si, 30 keV, 8x1010 cm-2, contour intervals: 1%

Courtesy A.M. Tello, Xerox Microelectronics Center

0 20 40 60 80 Distance (mm)

9x1010

8x1010

7x1010

Impl

ant D

ose

(cm

-2)


Conductivity Type Hot Probe

Where vth is the thermal velocity of the carrier Electrons move away from hot probe Positive donor ions left behind For n-type: Vhot > 0 For p-type: Vhot < 0

Thermoelectric power

When you are at ~open circuit (i.e measuring voltage)

dxdTnPqdxndEJ nnFnnn // µµ −=

dxdTqPdxdEJ nFnn //0 =⇒≅

Pn is differential thermoelectric power (<0)

n-type

ColdHot

V

I

ND+

Ec

Ei

Ev

EFn

Vhot

TmkTvth ~

*3

=


Warnings Hot Probe - Warnings:

Works for ~10-3 to ~103 ohm-cm Above ~103 ohm-cm, p-type will likely read as n-type (due to you actually

measuring nµn and pµp not n and p) High resistivity materials need very high input impedance voltmeter

(electrometer type).

Resistivity Warnings: Watch out for surface depletion

Especially serious in compound semiconductors Thermal variations due to drive currents

Follow NIST standards for power levels Fermi-level pinned surfaces (InN for example) Whenever possible, keep drive voltages small (V<kT/q) so contact non-

linearities are not important. Otherwise CHECK CONTACT LINEARITY!

<<

−=

kTqV

kTqVII

eII

O

kTqV

O

Vfor ~

1


Review Questions What is the best way to plot power law data? What is the best way to plot exponential data? Why is a four-point probe better than a two-point probe? Why is resistivity inversely proportional to doping

density? What is an important application of wafer mapping? Why is a four-point probe better than a two-point probe? Why is sheet resistance commonly used to describe thin

films? What is the main advantage of Eddy current

measurements? What are advantages and disadvantages of the modulated

photoreflectance (therma wave) technique?

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