layer characterization

Dean P. Neikirk © 1999, last update May 3, 2023 1 Dept. of ECE, Univ. of Texas at Austin

Layer characterization

• need to characterize the layers produced thus far– oxides

• thickness• dielectric constant / index of refraction

– doped layers• junction depth• dopant concentrations• electrical resistance / carrier concentration


Thickness measurements• profilometry

– mechanically measure difference in height across a “step” on the surface

• scanning “needle” traverses surface• Dektak, Tencor Alphastep

– requirements:• must have step on surface• film must be hard enough that needle does not damage it• must be calibrated using known step height

– precision / range• Alphastep specs:• profiling with 10Å (1) or 0.1% repeatability • step height metrology below 50 nm to 300 µm

from http://www.tencor.com/products/metrology/alpha-step500/AlphaStep500.pdf


Transparent layer measurements• ellipsometry

– uses elliptically polarized light incident at an angle on the sample– state of polarization of reflected beam is dependent on

• wavelength of illumination and angle of incidence• optical constants of the “substrate”• optical constants of “covering layer”• thickness of “covering layer”

– precision / range• can measure steps of down to somewhat less than 10 nm• periodicity creates ambiguity for thicknesses over several hundred nm

http://www.afep.cornell.edu/epl/index.html


Transparent layer measurements

• spectroscopic reflectance– measure wavelength dependence of reflectivity

Filmetrics System (figures from http://www.filmetrics.com/technology.html)


silicon

Junction depth measurements

• non-destructive techniques– film thickness gauge

• use refractive index dependence on doping to do ellipsometry– weight gain method for epitaxial films

• junction exposing techniques

stain

optical flat

monochromaticillumination

side view

dark bands stain

top view

– interferometry used to measure gap

destructive interference

– junction lapping– chemical stain used to “electroplate” one side of junction

• when exposed to light p-n junction produces current that can drive chemical reaction on one side or other


Junction groove technique

• grooving tool used to expose p-n junction

– stain used to delineate junction

• “electroplating” reaction used to coat either p or n side

– measure lateral distances W1, W2

RWW

WRWRx j

222

222

22

1

212

222

p-type

n-typeR R

stain

2W22

d2 xj

W1

d1

W2

W1


Sheet resistance• consider a block of uniform conducting material

l

t

wlRt w

• Rs is the “sheet resistance” of the material• for a uniformly doped piece of semiconductor

• if the width and length are the same (i.e., it’s a “square”)

Sl wRt w t

1

orq n p

SR t or

1orS

n pq R t


Sheet resistance measurements

• problem: contact resistance can be VERY large– use “four point”

measurement• inject current through one

pair of contacts, measure voltage across another pair

– what is relation between I, V and resistance?

V

I

a

d

t

s s s


Sheet R from 4-point probe

• assume 2-d problem– geometry of current flow in “thin sheet”

E

J sheetsheet

I sheet2r ˆ r

total current I

perimeter 2πrcurrent density I / 2πr

• electric field/ current density relationship (Ohm’s Law!)– for a single “source” have

– but in our four point geometry have two sources: one in, and one out!


• probe geometry produces “dipole” distribution

4-point probe

xs

IxIJE sheetsheetxx 322

s

s

s

ssheet

s

s sheet

s

s x

xsxI

dxxs

IxIdxEV

22

22

3lnln2

322

V sheetI

22 ln 2

s 2s 3s0 x

+ -

current flow and electric field lines

• along x axis is simple:

• to get voltage integrate along field line


Final result for sheet R

• the relation between the voltage measured across the middle two probes and the current injected through the outer two probes is

sheet RS

ln 2 VI 4.54

VI

A’ B’ C’ D’

conformal map

I

I

B

C D

AVBC RS

ln 2

VBCIAD

• other probe geometries– for any bounded surface with current injected at one point on the

perimeter and removed at another, the measurement of the voltage difference between any other two points on the perimeter is sufficient to determine the sheet resistance

• Van der Pauw geometry: conducting square


Relation between doping profile and resistance

• geometrically

1

01

jxcarriersnet

BS dxNxNNqR

xN(x1)

N(x2)

N(x3)

N(x)

x

(x)

x

– Rs ~ parallel sum of R’s from each layer• R(x) = 1 / [q • (N) • (net carriers) • x]

– resistivity & mobility are functions of ionized impurity concentration


Mobility and resistivity for Si

1x10-5

1x10-4

1x10-3

1x10-2

1x10-1

1x100

1x101

1x102

1x103

1x10141x10151x10161x10171x10181x10191x10201x1021

resi

stiv

ity (o

hm-c

m)

impurity concentration (#/cm3)

Na (#/cm3)

Nd (#/cm3)

0200400600800

100012001400

1x1014 1x1015 1x1016 1x1017 1x1018 1x1019 1x1020

Mob

ility

(cm

2/V-

sec)

Concentration( cm-3)

electronsholes

pornqporn

11

for silicon near room temp:

91.0

17103.11

92136092

DDelectron

NN

76.0

16103.61

7.474957.47

AAhole

NN


Irvin Curves for Si

• note that the average resistivity is given by:

1

1 1

thickness

surface

dxthickness

nnq BD NNn

Sj

x

BDj

Rx

S

dxNNqx

R

j

1

0

1

1 1

• what can we say about the value of average resistivity??

1x

0BD

jSj

j

dxNNxqRx


Irvin Curves for Si

• note that if you specify NS, NB, xj, and the shape you have fully specified the exact doping profile!

2

, exp2

oQ xN x tDt Dt

NS

2

2exp

tDx

NN jSB

BS

j

SB

j

NNx

NNx

tDlnln

222

2

BSjS NNx

xNxNln

exp 2

2

– example: gaussian profile:

– at the junction:

1x

0B

BS2

j

2

SS

j

dxNNNlnx

xexpNqR

• can now do the sheet resistance integral since everything is known:


Irvin Curves for Si

• calculation process– pick shape shape

surf

ace

conc

. NS

xj•Rs

• calculate sheet resistance RS

• find average resistivity = xj•Rs

• graph

– repeat for new value of NB2

NB

– pick NB, xj

• specify NS

• loopNB2


1x1015

1x1016

1x1017

1x1018

1x1019

1x1020

1x1021

1x100 1x101 1x102 1x103 1x104 1x105

Surf

ace

Con

cent

ratio

n (c

m-3

)

Rs xj (Ohm-micron)

Rs Xj Nb=1e17

Rs Xj Nb=1e16

Rs Xj Nb=1e15

Rs Xj Nb=1e14

n-typeGaussian

NB = 1017

NB = 1016

NB = 1015

NB = 1014

Irvin Curves for Si

carrier: electronsshape: gaussian


Irvin Curves for Si

carrier: electronsshape: erfc

1x1015

1x1016

1x1017

1x1018

1x1019

1x1020

1x1021

1x100 1x101 1x102 1x103 1x104 1x105

Surf

ace

Con

cent

ratio

n (c

m-3

)

Rs xj (Ohm-micron)

Rsxj (Nb = 1e17)

Rsxj (Nb = 1e16)

Rsxj (Nb = 1e15)

Rsxj (Nb = 1e14)

n-type Erfc

NB = 1017

NB = 1016

NB = 1015

NB = 1014


Irvin Curves for Si

carrier: holesshape: gaussian

1x1015

1x1016

1x1017

1x1018

1x1019

1x1020

1x1021

1x101 1x102 1x103 1x104 1x105 1x106

Surf

ace

Con

cent

ratio

n (c

m-3

)

Rs xj (Ohm-micron)

Rsxj (Nb = 1e17)

Rsxj (Nb = 1e16)

Rsxj (Nb = 1e15)

Rsxj (Nb = 1e14)

p-typeGaussian

NB = 1017

NB = 1016

NB = 1015

NB = 1014


Irvin Curves for Si

carrier: holesshape: erfc

1x1016

1x1017

1x1018

1x1019

1x1020

1x1021

1x101 1x102 1x103 1x104 1x105

Surf

ace

Con

cent

ratio

n (c

m-3

)

Rs xj (Ohm-micron)

Rsxj (Nb = 1e17)

Rsxj (Nb = 1e16)

Rsxj (Nb = 1e15)

Rsxj (Nb = 1e14)

p-type Erfc

NB = 1017

NB = 1016

NB = 1015

NB = 1014


1x1015

1x1016

1x1017

1x1018

1x1019

1x1020

1x1021

1x100 1x101 1x102 1x103 1x104 1x105

Surf

ace

Con

cent

ratio

n (c

m-3

)

Rs xj (Ohm-micron)

Rs Xj Nb=1e17

Rs Xj Nb=1e16

Rs Xj Nb=1e15

Rs Xj Nb=1e14

n-typeGaussian

NB = 1017

NB = 1016

NB = 1015

NB = 1014

Example: need to know three of: NS, NB, xj, & RS

• n-type dopant, limited source (gaussian), NB = 1016 cm-3

Ns = 4x1018

Rs • xj ~ 2.2 x 102 (ohm-micron) for Ns = 4x1018 & NB = 1016 cm-3

NB = 1016 cm-3


x

y

z

Hall measurements for carrier concentration

• example geometry, electrons as carriers

BvEqF

electronsholes

:

:

yBvq

yBvq

zxBvqBvqF

zx

zx

zx

electronlorentz

ˆ

ˆ

ˆˆ

xareaIj ˆ

xEE x ˆ

zBB z ˆ

xvv x ˆeln

Florentze-

• if apply magnetic field to drifting carriers a Lorentz force is generated

– note Lorentz force is proportional to velocity, direction depends on carrier type (sign of “q”)


x

yz

xareaIj ˆ

xEE x ˆ

zBB z ˆ

xvv x ˆeln

Florentze-• side view again

Lorentz forces

xz

y

F lorentzq velectronB qvx Bz ˆ y

veln B

v x B

|qvxBz|

electron trajectories

current in current out

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

EopposedFeln opposed

xz

y

Fopposed F lorentz q vxBz ˆ y

yBvqFE z

electronx

opposedelectronopposed ˆ

• top view of sample

• but since there are no contacts on the y faces of the sample no current can flow in y direction!


• in summary, application of “transverse” magnetic field induces an electric field in the other transverse direction

Hall effect continued

zxzxy BvBvE

x

x

external

z

external

x

measured

yH j

vBj

ER

holeselectrons

x

holeselectrons

x vpornqj

::

::

pornqvpornqv

Rx

holeselectrons

xH

1

::

HRqpn

typeptheniftypenthenif 1

,,

– - electrons– + holes

• define the Hall coefficient to be

• using a simple “drift” model we have


• for non-uniformly doped layers can still get “sheet” parameters– essentially integral averages of µ and n

Summary of Hall & Rs measurements

RH EyV t

jxI wt

Bzmeasured

VI

wBz

n or p I Bz

qVHall1w

wtl

nqwtlR

1

x

zy jx I wt

Ey Vfronttoback

t

B Bz ˆ z

I tw

• Hall measurement gives the carrier concentration– for rectangular bar, uniform doping

• resistance gives mobility • concentration product• combination of R and RH gives mobility


Other profiling methods

• “beam” techniques– electron

• LEED (low energy electron diffraction): structure• SEM: imaging of topology• AES (Auger spectroscopy): composition (look at energy spectrum

of emitted electrons)– ion

• SIMS (secondary ion mass spectroscopy): bombard sample with ions, look at mass of “sputtered” atoms

• RBS (Rutherford back-scattering): high energy (MeV) He bombardment, look at energy spectrum of back-scattered He

• electrical– spreading resistance, layer stripping

• measure sheet R as function of removed material– capacitance-voltage measurements

• use depletion as function of applied voltage to infer carrier profiles


SIMS• material is “sand-blasted”

– depth information from time and sputtering rate• secondary-ion yields vary with incident ion mass and energy

– standards required to calibrate SIMS measurements• good for measurement of “low” concentrations of impurities

element primary ion detected ion detection limit

B O2+ 11B+ 1015 /cm3

P Cs+ 31P- 1016 /cm3

As Cs+ 75As- 1016 /cm3

Na O2+ 23Na+ 1014 /cm3

Fe O2+ 56Fe+ 1017 /cm3

Cu O2+ 63Cu+ 1016 /cm3

Al O2+ 27Al+ 1015 /cm3

adapted from Sze, 2nd ed., p. 542


– reverse bias produces depletion layer, width function of doping profile and applied bias

– measure capacitance

C-V profiling

• consider p-n junction or Schottky contact

Cunitarea dQdV

sxd

ND xn C3

sqdCdV

1 ND xn

NA xp

np

0-xp xn

xd

ND xn C3

sqdCdV

– solve Poisson’s eq. for applied voltage to get (for p-n junction, assumes n = ND, p = NA):

– for p+-n (“one-sided”) junction simplifies to

• can only profile on lightly-doped side of junction


“Layer stripping” / spreading resistance techniques

• geometrically

jxcarriersnet

BS dxNxNNqR0

1

1

xN(x1)

N(x2)

N(x3)

1/RS

xetch

RS(x)

xetch

– sequentially remove “surface” layer, then measure RS

– slope of 1/Rs curve gives N product

xxRxRxNxNxq etchSetchSBetchetch 11

x

xRxxRq

NxNx etchSetchSBetchetch

111

(x)N(x)

xetch

xxR

qNxNx etchSBetchetch

11


Deposited thin films

• need to be able to add materials “on top” of silicon– both conductors and insulators

• deposition methods– physical vapor deposition (PVD)

• thermal evaporation• sputtering

– chemical vapor deposition (CVD)• general requirements

– good electrical characteristics– free from pin-holes, cracks– low stress– good adhesion– chemical compatibility

• with both layer “below” and “above”• at room temperature and under deposition conditions

layer characterization

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