theory and practice of materials analysis for

ICNMTA2012

Lisbon, 23 July 2012 Ettore Vittone 1

Theory and practice of Materials

Analysis for Microelectronics with a

nuclear microprobe

Ettore Vittone

Physics Department

University of Torino, Italy

TUTORIAL

ICNMTA2012


IBIC for the

functional characterization of

semiconductor materials and devices

Measurement of the their electronic properties and performances

Main physical observable: current

Current = F(carrier density; carrier transport)

Free carriers (electron/hole) transport

Two mechanisms: Drift and Diffusion

Drift: by the electrical force v=μ·E Diffusion: by a concentration gradient

Recombination/trapping

Carrier lifetime

ICNMTA2012


Principles of radiation detection techniques

Deposited Energy

Moving charge q

Induced charge Q

Output Signal Vout

Transport)Carrier Free Energy, Deposited(FVout

Nuclear spectroscopy Material characterisation

Incoming radiation

V

Q

Incoming radiation

V

Vout

ICNMTA2012


Electrode energy loss very small ( 1%)

SRIM (Stopping and Range of Ion in Matter)

Using MeV ions to probe

the electronic features of semiconductors

analysis through

thick surface layers

charge pulses

height spectra

almost independent

on topography .

profiling

long range

low lateral scattering

a wide choice of ion

range and electronic

energy losses

0 5 10 15 20 25 30 0

1x10 7

2x10 7

3x10 7

0

50

100

150

200

3 keV Photon current: 5*10 7 photons/s

XBIC

X-r

ay e

ne

rgy l

os

s r

ate

(ke

V\(

mm

s -1

)

Depth ( m m )

IBIC H+ ion energy (MeV)

1.7 1.5 1.3 1.1 0.9 0.7

Sto

pp

ing

po

wer

(ke

V m

m -1

)

ICNMTA2012


Electron/Hole pair generation

eh

ioneh

EN

A. Lo Giudice et al. Applied Physics Letters 87, 22210 (2005)

1 MeV in diamond

generates about

77000 e/h pairs

Each high energy ion

creates large numbers of

charge carriers to be

measured above the

noise level.

ICNMTA2012


d

vq)t(I

Shockley-Ramo Theorem

Induced current

Ev mThe current is induced by

the motion of charges in

presence of an electric field

Physical Observable:

Induced current/charge

ICNMTA2012


-2 0 2 4 6 8 10 12 14

0.000

0.025

0.050

0.075

0.0

0.2

0.4

0.6

0.8

1.0

I

Time

Q

Physical Observable:

Induced current/charge

d

vq)t(I

T

0

dt)t(I)t(Q

W. Shockley, J. Appl. Phys. 9 (1938) 635.

S. Ramo, Proc. I.R.E. 27 (1939) 584.

ICNMTA2012


-2 0 2 4 6 8 10 12 14 16

0.000

0.025

0.050

0.075

0.0

0.2

0.4

0.6

0.8

1.0

I

Time

Q

Induced current

CARRIER LIFETIME

texp

d

vq)t(I

-2 0 2 4 6 8 10 12 14

0.000

0.025

0.050

0.075

0.0

0.2

0.4

0.6

0.8

1.0

I

Time

Q

Drift time=d/v

ICNMTA2012


C. Canali, E. Gatti, S.F. Koslov, P.F. Manfredi,

C. Manfredotti, F. Nava, A. Quirini

Nucl. Instr. Meth. 160 (1979) 73-77

400 mm thick natural diamond,

biased at 40 V @ RT

IIa diamond; resistivity about 1015 Ω·cm; dielectric constant

=0.5 pF/cm; Dielectric relaxation time = 500 s.

Charge neutrality not maintained

ICNMTA2012


V

Vout

d

v

Generation at the anode -> Hole collection

Generation at the cathode -> Electron collection

E

d

d

ECCE

e

e

m

mexp1 K. Hecht, Z. Physik 77, (1932) 23

ICNMTA2012


C. Canali, E. Gatti, S.F. Koslov, P.F. Manfredi,

C. Manfredotti, F. Nava, A. Quirini

Nucl. Instr. Meth. 160 (1979) 73-77

400 mm thick natural diamond,

biased at 40 V @ RT

Electrons:

Drift velocity; v mE d/TR

Mobility; md2/(TR *VBias)

ICNMTA2012


d

vq)t(I

Shockley-Ramo Theorem

Induced current

Ev mThe current is induced by

the motion of charges in

presence of an electric field

ICNMTA2012


50 mm thick N-type epitaxial 4H-SiC layer Schottky electrode

Frontal ion

Irradiation

Dep

leti

on

Reg

ion

FAST DRIFT

COMPLETE COLLECTION DIFFUSION

0 5 10 15 20 25 30 350

20

40

60

80

100

120

140

160

180

0

20

40

60

80

100

120

140

En

erg

y L

oss (

ke

V/m

m-1)

Depth (mm)

2 MeV

1.5 MeV

Bragg.opj

Ap

plie

d B

ias

Vo

ltag

e (V

)

ICNMTA2012


Frontal ion

Irradiation

0 5 10 15 20 25 30 350

20

40

60

80

100

120

140

160

180

0

20

40

60

80

100

120

140

Energ

y L

oss (

keV

/mm

-1)

Depth (mm)

2 MeV

1.5 MeV

Bragg.opj

Ap

plie

d B

ias V

olta

ge (V

)

4H-SiC Schottky diode

ICNMTA2012


Frontal ion

Irradiation

0 5 10 15 20 25 30 350

20

40

60

80

100

120

140

160

180

0

20

40

60

80

100

120

140

Energ

y L

oss (

keV

/mm

-1)

Depth (mm)

2 MeV

1.5 MeV

Bragg.opj

Ap

plie

d B

ias V

olta

ge (V

)


ICNMTA2012


Lp=(9.0

0.3) mm

Dp = 3 cm2/s

p = 270 ns

minority carrier

diffusion length

1.5 MeV

CC

E

2 MeV

0 20 40 60 80 100 120 140 0,0

0,2

0,4

0,6

0,8

1,0

Applied Bias Voltage (V)


Active region

width

ICNMTA2012


4

5

6

7

8

9

10

100 150 200 250 300 350 4000,010

0,015

0,020

0,025

0,030

0,035

0,040

0,045

0,050 (b)

(a)

Lp (

mm

)

L-2 p(

mm

-2 )

T (K)

Temperature dependent IBIC (TIBIC)

TTDTL ppp

Two trapping levels

SRH recombination model 2 0.5

0.5p p p B Bt

D B

1 1 1 1 1 1 1 1A

L D D (T) T EBT T exp

N k T

The fitting procedure provides a trapping level of about

0.163 eV which is close to the value found in similar

4H SiC Schottky diodes by DLTS technique (S1 level).

ICNMTA2012


From Spectroscopy to micro-spectroscopy

Use of focused ion beams

ICNMTA2012

Lisbon, 23 July 2012 Ettore Vittone 21 20 m

m

20 mm

Electrons

10 keV

Electrons

40 keV

2 MeV H+ in Si 3 MeV H+ in Si

4 MeV H+ in Si

2 mm

4 mm

6 mm

47

mm

90

mm

14

7 m

m

Trajectories One advantage of IBIC over other forms of charge collection microscopy is that

it provides high spatial resolution analysis in thick layers since the focused

MeV ion beam tends to stay ‘focused’ through many micrometers of material.

Abs#151-F. Watt: nuclear microprobe, towards nanometer spost sizes

ICNMTA2012


MeV Ions

Frontal IBIC

Vout

Vb

ICNMTA2012


Frontal IBIC

M.B.H.Breese et al. NIM-B 181 (2001), 219-224; P.Sellin et al. NIM-B 260 (2007), 293-294

Intra-crystallite charge transport

Single grain IBIC line scan

Position (nm)

0 50 100 150 200 250

Counts

0

1000

2000

3000

4000

5000 200 V

370 V

IBIC imaging with 2 MeV protons

IBIC maps of polycrystalline diamond inter-digitated detectors show ‘hot

spots’ at electrode tips due to concentration of the electric field

ICNMTA2012


Poster Session I (23/07/2012) h. 17.30-18.40

Poster #75

Aleksandr Ponomarev

Investigation of Cd1-xMnxTe Polycrystalline Thin Films

Using Nuclear Microprobe Techniques

ICNMTA2012


LATERAL IBIC-TRIBIC

ICNMTA2012


Monocrystalline Diamond Schottky diode

ICNMTA2012


Plateaux:

Depletion region

(active region)

Vs.

Bias voltage

30 35 40 45 50

5

10

15

20

25

30

30 35 40 45 50

5

10

15

20

25

30

30 35 40 45 50

5

10

15

20

25

30

30 35 40 45 50

5

10

15

20

25

30

30 35 40 45 50

5

10

15

20

25

30

30 35 40 45 50

5

10

15

20

25

30

30 35 40 45 50

5

10

15

20

25

30

60

50

40

2515

5

Ind

uc

ed

ch

arg

e (

fC)

X axis (mm)

Vbias

=0

Exponential-like decay

outside the highly efficient

depletion region

2

ee

eee

cm/V)3.057.2( : lifetimeMobility

m)17.057.2(DL :lengthdiffusion Electron

m

m

ICNMTA2012


A high-speed imaging system for Time

Resolved digital IBIC at Surrey

Lateral TRIBIC

d

vq)t(I

Induced current

Ev m

CdZnTe

radiation detector

ICNMTA2012


Poster Session III (26/07/2012) h. 16.15-18.00

Poster #171

Natko Skukan

CVD diamond as a position sensitive detector

using charge carrier transition time

ICNMTA2012


Gunn’s theorem

Pulse shapes calculation

V-qI

Ev

Shockley-Ramo theorem

d

1-qI v

Weighting field

ICNMTA2012


dt

drv Equation of motion:

Weighting potential:

VVwww

E

AB

B

A

B

A

B

A

VVq)()(q

dEqdtEqIdtQ

AwBw

w

t

t

w

t

t

rr

r

r

rr

rv

The induced charge Q

into the sensing electrode

w-qV

-qI EvE

v

is given by the difference in the weighting potentials between any

two positions (rA and rB) of the moving charge

Weighting field

Induced current into the sensing electrode

ICNMTA2012


To evaluate the total induced charge

Magnetic effects are negligible;

Electric field propagates instantaneously

Free carrier velocities much smaller than

the light speed

Excess charge does not significantly

perturb the electric field

equation sPoisson’ thesolvingby

potential actual theEvaluate

equations y)(continuit

rt transpo theSolve

electrode sensitive at the potential bias theis V

V

potential weightingsGunn' theEvaluate

AB rr VVqQ

The induced charge Q into the sensing electrode is

given by the difference in the weighting potentials

between any two positions (rA and rB) of the moving

charge

ICNMTA2012


Depth Weig

hting

pote

ntial 1

0

Weig

hting

field

E

lectr

ic

Fie

ld

Vw

E

E

Vw

Depth

Depth

Neutral

n-type

Schottky

barrier

Depletion

Region

Vbias

ICNMTA2012


Weig

htin

g

po

ten

tia

l

1

0

Vw

Electric field

h+

e-

position

initial

position

final VVqQ

Electrons/holes

Electrostatics

Transport

properties

Induced charge

Depth

ICNMTA2012


Weig

htin

g

po

ten

tia

l

Vw

1

0

h+

Depth x0

e-

Electric field

ICNMTA2012


Weig

htin

g

po

ten

tia

l

Vw

1

0

h+ e-

Electric field

ICNMTA2012


Weig

htin

g

po

ten

tia

l

Vw

1

0 Depth x0

e-

w

x

electrons ofNumber Totalq

VVq

Q

QCCE

electronsposition

initial

position

final

Generated

collected 01

Electric field

h+

ICNMTA2012


Weig

htin

g

po

ten

tia

l

Vw

1

0 Depth x0

Electric field

h+

ICNMTA2012


Weig

htin

g

po

ten

tia

l

Vw

1

0

h+

Electric field

w

x

holes ofNumber Totalq

VVq

Q

QCCE

holesposition

initial

position

final

Generated

collected 0

11 00

w

x

w

x

holes

holes

electrons

electronsCCE

Generated

collected

Generated

collectedToT

ICNMTA2012


Vacancy profiles

generated by

11 MeV Cl,

4 MeV O,

2.15 MeV Li

1.4 MeV He 1 2 3 4 5 6

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

1

10

100

1000

En

erg

y l

oss (

keV

/mm

)

He

Li

Cl

Depth (mm)

Vacan

cy/Io

n/m

m

O

ionization profile of the 1.4 MeV He ion probe

ICNMTA2012


Weig

htin

g

po

ten

tia

l

Vw

1

0

h+

Depth x0

Traps

Recombination Centers

e-

Electric field

Effects of localized recombination centres

ICNMTA2012


Weig

htin

g

po

ten

tia

l

Vw

1

0

h+

Depth x0

Traps


e-

Electric field

ICNMTA2012


Weig

htin

g

po

ten

tia

l

Vw

1

0

h+

Depth x0

Traps


e-

w

x

electrons ofNumber Totalq

VVq

Q

QCCE

electronsposition

initial

position

final

Generated

collected 01

Electric field

ICNMTA2012


Weig

htin

g

po

ten

tia

l

Vw

1

0

h+

Depth x0

Traps


Electric field

ICNMTA2012


Weig

htin

g

po

ten

tia

l

Vw

1

0

h+

Depth x0

Electric field

w

x

holes ofNumber Totalq

VVq

Q

QCCE

holesposition

initial

position

final

Generated

collected 0

w

Traps


ICNMTA2012


Radiation Damage in 4H-SiC

Vb = 10 V

20 MeV 4+C Vout

x

z

y

ICNMTA2012


Low Level of damage

Shockley-Read-Hall

Recombination/trapping

model

Vacancy profille

(from SRIM; PAS)

Electrostatics of the

device (TCAD)

Trap cross section

(DLTS)

Trap/vacancy ratio

Radiation hardness

Transport equations

Shockley-Ramo-Gunn Theorem

ICNMTA2012


Oral Session 25/07/2012, h 9:00-10.30

#250: Milko Jaksic (invited) : Review of nuclear microprobe applications in

material science

Oral Session 25/07/2012, h 11:00-12.30

#198: Gyorgy Vizkelethy: Investigation of ion beam induced radiation damage in

Si and GaAs diodes

#92: Zeljko Pastuovic: Overview of radiation damage studies in silicon diodes

exposed to focused ion beam irradiation-Proposed template for further research

of radiation damage studies in semiconducting materials and devices by IBIC


Poster #141: Veljko Grilj: Comparison of scCVD diamond and silicon SB detectors

irradiated by low energy protons

ICNMTA2012


CHARGE SHARING IN MULTIELECTRODE DEVICES

positioninitial

positionfinal VV

qQ

The induced charge Q into the sensing

electrode is given by the difference in the

weighting potentials between any two

positions (rA and rB) of the moving charge

ICNMTA2012


Actual potential Weighting potential

ICNMTA2012


Actual potential

Weighting potential

0

2

4

6

8

10

12

14

16

0,0

0,5

1,0

1,5

2,0

2,5

CH

AR

GE

time

CU

RR

EN

T

time

positioninitial

positionfinal VV

qQ

ICNMTA2012


Actual potential

Weighting potential

positioninitial

positionfinal VV

qQ0

2

4

6

8

10

12

0.00

0.05

0.10

0.15

0.20

0.25

CH

AR

GE

time

CU

RR

EN

Ttime

ICNMTA2012


Actual potential

Weighting potential

positioninitial

positionfinal VV

qQ-4

-3

-2

-1

0

1

-0,5

-0,4

-0,3

-0,2

-0,1

0,0

0,1

CH

AR

GE time

CU

RR

EN

T

time

ICNMTA2012


Actual potential

Weighting potential

positioninitial

positionfinal VV

qQ-1,0

-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

-0,04

-0,02

0,00

0,02

0,04

CH

AR

GE

time C

UR

RE

NT

time

ICNMTA2012



Poster #123: Jacopo Forneris: IBIC characterization of an ion beam

micromachined multi electrode diamond detector

Poster Session III (26/07/2012) h. 16.15-18.00

Poster #160: Laura Grassi: Charge collection study in the interstrip

region of DSSSD using proton microbeam

ICNMTA2012


Horizontal electric field

positioninitial

positionfinal VV

qQ

ICNMTA2012


A SUB-MICROMETER

POSITION SENSITIVE

DETECTOR

-6 -4 -2 0 2 4 6

0,0

0,2

0,4

0,6

0,8

1,0

RIGHT ELECTRODE

CC

E

Position (mm)

LEFT ELECTRODE

2 MeV He+

ICNMTA2012


Oral Session 25/07/2012, h 11:00-12.30

#133: David Jamieson (invited): Addressing roadmap challenges: adapting

nuclear microprobe technology to build engineered atom devices

#124: Jacopo Forneris: Modeling of ion beam induced charge sharing

experiments for design of high resolution position sensitive detectors.

ICNMTA2012


I HOPE YOU

ENJOY YOUR TIME

AT THE ICNMTA2012

ICNMTA2012


SOLUTION OF THE EQUATIONS OF MOTION

= TRAJECTORIES OF CHARGES

Initial point (rA) ; final point (rB)

)()(qQ AwBw rr

w-qV

-qI EvE

v

ICNMTA2012


0

2

4

6

8

10

12

14

16

0,0

0,5

1,0

1,5

2,0

2,5

CH

AR

GE

time C

UR

RE

NT

time

Ew

Ew




)()(qQ AwBw rr

w-qV

-qI EvE

v

ICNMTA2012





)()(qQ AwBw rr

w-qV

-qI EvE

v

0

2

4

6

8

10

12

0.00

0.05

0.10

0.15

0.20

0.25

CH

AR

GE

time

CU

RR

EN

T

time

ICNMTA2012





)()(qQ AwBw rr

w-qV

-qI EvE

v

-4

-3

-2

-1

0

1

-0,5

-0,4

-0,3

-0,2

-0,1

0,0

0,1

CH

AR

GE time

CU

RR

EN

T

time

ICNMTA2012





)()(qQ AwBw rr

w-qV

-qI EvE

v

-1,0

-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

-0,04

-0,02

0,00

0,02

0,04

CH

AR

GE

time

CU

RR

EN

T

time

Ew

Ew

Ew

Ew

ICNMTA2012


IBIC

(Ion Beam Induced Charge Collection)

Control of in-depth generation profile

Suitable for finished devices (bulk analysis).

Micrometer resolution

CCE profiles: Active layer extension; Diffusion length

In-situ analysis of radiation damage

Analytical technique suitable for the measurement of transport properties in

semiconductor materials and devices

ICNMTA2012


4

5

6

7

8

9

10

100 150 200 250 300 350 4000,010

0,015

0,020

0,025

0,030

0,035

0,040

0,045

0,050 (b)

(a)

Lp (

mm

)

L-2 p(

mm

-2 )

T (K)

Temperature dependent IBIC (TIBIC)

Two trapping levels

SRH recombination model

2 0.5

0.5p p p B Bt

D B

1 1 1 1 1 1 1 1A

L D D (T) T EBT T exp

N k T

The fitting procedure provides a trapping level of about

0.163 eV which is close to the value found in similar

4H SiC Schottky diodes by DLTS technique (S1 level).

E. Vittone et al., NIM-B 231 (2005) 491.

ICNMTA2012


0 1 2 3 40.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

50 V

100 V

Experiment

Theory

CC

E

200 V

Time (ms)

Time resolved IBIC (TRIBIC)

Silicon Power diode Mesa Rectifier

lifetime

0 = (5 1) ms

V

Charge sensitive

preamplifier

ADC

Proton beam

(2-3-4 MeV)

n p+

W

C

n+

IBIC

Digital

oscilloscope TRIBIC

Shaping

amplifier

Mesa Rectifier 168

Ballistic deficit

p+

n

n+

Electrodes

(Ag-Ni-Cr)

30 mm

160 mm

110 mm

Passivation

“Mesa Glass”

ICNMTA2012


68 μm

170 μm

145 μm

Fluences (cm-2)

Area 1: ……..

Area 2: 1,8 E10

Area 3: 6,1 E9

Area 4: 2,0 E9

Area 5: 6,1 E8

Area 6: 2,0 E8

Good Reproducibility

Radiation Damage

ICNMTA2012


Lateral IBIC

Vb = 50 V

Area 5 Area 6 Area 1 Area 2 Area 3 Area 4

CCE profiles

• Lifetime reduction

• Depletion region shrinking

ICNMTA2012


5.000

7.500

10.00

12.50

15.00

17.50

20.00

22.50

25.00

27.50

30.00

CCE

Under

illumination

Dark

conditions

Polycrystalline CVD diamond Frontal IBIC

ICNMTA2012


i

N

1j

2

j,i

iN

ss

s

11s

i

= overall average signal evaluated over the total scanned area ATOT

Ni = Number of pixel of area ai : ATOT = ai · Ni

si,j = signal from the j-th pixel of area ai

a16

Ni=16

ATOT

Ni=4

a4

Ni=32

a32

iN

1j

j,i

i

sN

1s

Uniformity (D.Meier, PhD thesis 1999, C.Manfredotti 2000)

ICNMTA2012


100 150

20

40

60

80

100

120

100 150

20

40

60

80

100

120

100 150

20

40

60

80

100

120

100 150

20

40

60

80

100

120

100 150

20

40

60

80

100

120

100 150

20

40

60

80

100

120

720 mm

0

2.000

4.000

6.000

8.000

10.00

12.00

14.00

16.00

18.00

20.00

22.00

24.00

26.00

28.00

30.00

32.00

IBIC maps with different pixel dimension

10 100 1000

0.2

0.4

0.6

0.8

1.0

Un

ifo

rmity

pixel dimension (mm)

The uniformity is between 80% and 100% on the length scale above 200 mm;

at 100 mm the uniformity is 69%

i

N

1j

2

j,i

iN

ss

s

11s

i

ICNMTA2012


Frontal ion

Irradiation

Schottky electrode 50 mm thick N-type epitaxial 4H-SiC layer

0 5 10 15 20 25 30 35 40 45 500

20

40

60

80

100

120

140

160

180

1.71.51.3

1.10.9

Ene

rgy

Loss

(keV

/mm

-1)

Depth (mm)

0.7 Neutral region

Diffusion transport

Incomplete collection

Depletion region

Fast drift transport

Complete collection

0,20000,25000,30000,35000,40000,45000,50000,55000,60000,65000,70000,75000,80000,85000,90000,95001,000

0 1

CCE

1 mm

0.7 MeV 0.9 MeV0.9 MeV 1.1 MeV1.1 MeV 1.3 MeV1.3 MeV 1.5 MeV1.5 MeV 1.7 MeV

M. Jaksic et al.NIM-B, 188 (2002), 130-134

ICNMTA2012


Numerical Simulations

nsp 80

30 V 50 V 70 V

Vb

m, ,(Lp m)3094

ICNMTA2012


Diamond Schottky diode structure:

homoepitaxial growth on HPHT

substrates

(type Ib, 440.4 mm3) slightly B

doped (Acceptor concentration

1013-1014 cm-3)

heavily B-doped buffer layer as

back contact (Acceptor

concentration 1018-1019 cm-3)

25 μm thick intrinsic layer as

active volume

Schottky contact: frontal Al circular

contact ( = 2 mm, 200 nm thick) on

intrinsic layer

back contact on B-doped layer ohmic

contact

sample cleaved in order to expose its

cross section for IBIC characterization

S. Almaviva et al. “Synthetic single crystal diamond dosimeters for conformal radiation therapy application”

Diamond & Related Materials 19 (2010) 217–220

ideality factor: n = (1.51 0.04)

series resistance: Rs = (5.1 1.6) kΩ

back B-doped contact

shunt resistance: Rsh = (900 6) GΩ

@ 50 V -> I<50 pA

Lateral IBIC of a diamond Schottky diode

ICNMTA2012


Si-face

Starting Material: 360 mm n-type 4H-SiC by CREE (USA) Epitaxial layer from Institute of Crystal Growth (IKZ), Berlin, Germany

Devices from Alenia Marconi System


ICNMTA2012


ion species and energy: H+ @ 2 MeV

ion current: 103 ions s-1 no pile up

or charging effects

ion beam spot on the sample:

FWHM = 3 μm

raster-scanned area: S = 6262 μm2

charge sensitive electronic chain

and synchronous signal

acquistition with microbeam

scanning

Lateral IBIC measurements performed at the ion

microbeam line of the AN2000 accelerator of the

National Laboratories of Legnaro (LNL-INFN)

ICNMTA2012


4 MeV Protons (100 mm range)

4H SiC Schottky barrier

theory and practice of materials analysis for

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