diffusion [compatibility mode]

24
1 VLSI Process Technology Lecture: DIFFUSION MSc Microelectronics, UKM Prof. Dr. Burhanuddin Yeop Majlis What is Diffusion? Thermally Driven Process statistical net motion of regions of high i l i concentration to low concentration Key Mechanism in Deposition Processes introducing impurities to silicon Used Extensively in IC and MEMS Fabrication control electrical properties of silicon resistors, diodes, BJTs, MOSFETs, … control chemical/mechanical properties p+ etch stop (greatly slows down KOH and EDP etch) piezoresistors (change in stress = change in resistance)

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Page 1: Diffusion [Compatibility Mode]

1

VLSI Process Technology

Lecture:DIFFUSION

MSc Microelectronics, UKM

Prof. Dr. Burhanuddin Yeop Majlis

What is Diffusion?

• Thermally Driven Process – statistical net motion of regions of high

i l iconcentration to low concentration • Key Mechanism in Deposition Processes

– introducing impurities to silicon

• Used Extensively in IC and MEMS Fabrication – control electrical properties of silicon

Prof. Dr. Burhanuddin Yeop Majlis, UKM 2

p p• resistors, diodes, BJTs, MOSFETs, …

– control chemical/mechanical properties • p+ etch stop (greatly slows down KOH and EDP etch) • piezoresistors (change in stress = change in resistance)

Page 2: Diffusion [Compatibility Mode]

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What is Solid-State Diffusion?

• A method of “deposition” by modifying the atomic composition of materials – controlled “contamination”

– high temperature process (700 - 1200ºC) – used extensively in commercial ICs and MEMS

• Typical Dopants (gives or takes an e-) – Donor Atoms (n-type)P, As, …

Prof. Dr. Burhanuddin Yeop Majlis, UKM 3

– Acceptor Atoms (p-type) B, Ga, Al – Unwanted Dopants Au, Fe, Cu, Ni, …

• can ruin solid-state electronic devices • fast diffusers (high diffusivity)

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Vacancy

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Interstitial Diffusion

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Interstitial-Substitutional Diffusion

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Prof. Dr. Burhanuddin Yeop Majlis, UKM 4

Interstitial-Substitutional Diffusion (Kick Out)

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Substitutional Diffusion

Si

Si Si

Si

Si

Si

Si

Si

Si Si

Si

Si

Si

Si

Page 3: Diffusion [Compatibility Mode]

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Flux (atoms/cm2·sec)

Fick’s 1st Law of Diffusion(Concentration Gradient Driven Flux)

NHI J⎟⎠⎞

⎜⎝⎛⋅−=

dxdNDJ

Flux (atoms/cm sec)– diffusivity D, flux J – negative slope cancels with minus

sign and yields a positive flux – dopant concentration N in atoms/cm3

NLO

0 x(surface)

J

Diffusion Coefficient (cm2/sec)

Prof. Dr. Burhanuddin Yeop Majlis, UKM 5

( )– strong function of temperature – Arrhenius relationship – Activation Energy (Ea) – Boltzmann’s constant (1.38×10-23 J/K)

⎟⎠⎞

⎜⎝⎛−

⋅= kTEa

eDD 0

Fick’s 2nd Law of Diffusion(Time Dependence of Concentration and Flux)

Start with Continuity Equation ⎟⎠⎞

⎜⎝⎛−=

dxdJ

dtdN

⎠⎝

Incoming Outgoing

J1

J2

0 x2

Accumulation

positive=dtdN

⎟⎠⎞

⎜⎝⎛⋅−=

dxdNDJ

Prof. Dr. Burhanuddin Yeop Majlis, UKM 6

Combining with Fick’s 1st law yields:

typically ignored -> 0Less true with As due to its

Concentration-dependent diffusivity

Finally: The diff eq. we will solve

2

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅= 2

2

dxNdD

dtdN

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅+⎥⎦

⎤⎢⎣⎡ ⋅=⎥

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛⋅−⋅⎟

⎠⎞

⎜⎝⎛−= 2

2

dxNdD

dxdN

dxdD

dxdND

dxd

dtdN

Page 4: Diffusion [Compatibility Mode]

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Diffusion Coefficients• When temp. increases impurities get more energy

and increase diffusion speed.• Diffusion coefficients, D, is used to represent rate

of diffusion of materials.• D depend on T,

– where D and k is constant T temperature in

D D EkTo

a= −exp( )

Prof. Dr. Burhanuddin Yeop Majlis, UKM 7

– where Do and k is constant , T temperature in Kelvin and Ea activation energy of impurities.

ln ( ) lnDT

Ek

Dao= − +

1

Diffusion Coefficients• Plot ln D vs 1/T is a straight line with negative

gradient.gradient.– This shows that diffusion speed or D very

sensitive to temperature.– A few degree change in T enough to destroy

base transistor– Furnace tem. Must be controlled with ± 0.25 °C.

Prof. Dr. Burhanuddin Yeop Majlis, UKM 8

Page 5: Diffusion [Compatibility Mode]

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⎟⎠⎞

⎜⎝⎛−

⋅= kTEa

eDD 0

Diffusion Coefficients

⎟⎠⎞

⎜⎝⎛−

⋅= kTEa

eDD 0

Diffusion Coefficients

⎟⎠⎞

⎜⎝⎛−

⋅= kTEa

eDD 0 eDD 0 eDD 0 eDD 0

Prof. Dr. Burhanuddin Yeop Majlis, UKM 9

Fast DiffusersTypically Undesirable

Slow Diffusers Fast DiffusersSlow Diffusers (useful)

⎟⎠⎞

⎜⎝⎛−

⋅= kTEa

eDD 0

Prof. Dr. Burhanuddin Yeop Majlis, UKM 10

Over 106 times faster!

Page 6: Diffusion [Compatibility Mode]

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Solving the Diffusion Equations

• Boundary Conditions ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅= 2

2

dxNdD

dtdN

– Constant Source or Supply of Dopants • infinite supply of dopants is provided at the surface to

insure that the concentration of dopants at the surfaceis held constant

• N(x=0,t) = No

• Typical situation with a solid source on the substrate – Constant Dose or Fixed Number of Dopants

Prof. Dr. Burhanuddin Yeop Majlis, UKM 11

– Constant Dose or Fixed Number of Dopants • fixed (finite) amount of dopants in the substrate at all times • Integral of N(x,t) = Q (dose) is constant • Typical situation after an implant or short and shallow

pre-diffusion

Solving Fick’s 2nd Law with the boundary condition: Constant Source:

Case #1: Constant SourceConcentration at Surface is Fixed

( ) 0,0 NtxN ==•Co sta t Sou ce- infinite supply of dopants is provided at the surface to insure that the concentration of dopants at the surface is held constant

yields:

( ) ⎟⎠

⎞⎜⎝

⎛⋅

⋅=tD

xNtxN2

erfc, 0

( ) 0,0 NtxN

Prof. Dr. Burhanuddin Yeop Majlis, UKM 12

erfc is the Complementary Error Function– comes from probability and statistics

– derived by integrating the normal probability function

Page 7: Diffusion [Compatibility Mode]

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Case #1: Constant Source (continued)

Concentration at Surface is Fixed

Prof. Dr. Burhanuddin Yeop Majlis, UKM 13

• Plot on a semi-log graph • Longer time or higher diffusivity D

results in a deeper diffusion

Solid Solubility

• Solid solubility is a maximum concentration of dopant• Solid solubility is a maximum concentration of dopantcan diffuse into solid at certain temp..

• Solid solubility increase with temperature.• Solid solubility is the surface concentration of dopant

for constant source diffusion.

Prof. Dr. Burhanuddin Yeop Majlis, UKM 14

Page 8: Diffusion [Compatibility Mode]

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Solid Solubility

M i t ti

Prof. Dr. Burhanuddin Yeop Majlis, UKM 15

• Maximum concentration without precipitation is the solid solubility – function of temperature – function of dopant

Type of Dopant and SourceDopant Solid solubility Source compound Formula ConditionType nantimony (Sb) 7x1019(1,250 °C) antimony trioxide Sb2O3 solidType nA i (A ) 1 8 1021 (1150°C) i t i id A O lidArsenic (As) 1.8x1021 (1150°C) arsenic trioxide As2O3 solid

arsine AsH3 gasType nPhosphorus (P) 4x1021 (1,150°C) pentoxide P2O5 solid

phosoxychloride POCl3 liquidphosphinen PH3 gassiliconpyrophosphade SiP2O7 solid

Prof. Dr. Burhanuddin Yeop Majlis, UKM 16

Type pboron (B) 5x1020 (1,250°C) boron tryoxida B2O3 solid

boron tribromide BBr3 liquiddiborane B2H6 gasboron trychloride BCl3 gasboron nitride BN solid

Page 9: Diffusion [Compatibility Mode]

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Total Dose (Q)

Q1 Q2 Q3 Q1 < Q2 < Q3

atoms/cm2

Prof. Dr. Burhanuddin Yeop Majlis, UKM 17

• Total Dose is simply the integral of the distribution

( )∫∞ ⋅

⋅⋅=⋅=0

02,π

tDNdxtxNQ

Junction Depth (xj)

xj1 xj2 xj3

Prof. Dr. Burhanuddin Yeop Majlis, UKM 18

• Junction Depth is simply the intersection of the profile N(x,t) with the background concentration NB, thus where N(x,t) = NB

xj1 xj2 xj3

Page 10: Diffusion [Compatibility Mode]

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Junction Depth (xj)

Prof. Dr. Burhanuddin Yeop Majlis, UKM 19

Case #2: Constant DoseTotal Number of Dopants is Fixed

Starting with a mathematical impulse function of dopants (nonphysical, but convenient mathematically):

N Total number of dopants is Q

Depth

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅= 2

2

dxNdD

dtdN

solving:

yields:

Prof. Dr. Burhanuddin Yeop Majlis, UKM 20

( )2

2,⎟⎠

⎞⎜⎝

⎛⋅

⋅⋅⋅

= tDx

etD

QtxNπ

Page 11: Diffusion [Compatibility Mode]

11

Case #2: Constant DoseTotal Number of Dopants is Fixed

• Surface concentration drops with time

• Depth of profile increases with time

Prof. Dr. Burhanuddin Yeop Majlis, UKM 21

Diffusion of Buried Dopants

Prof. Dr. Burhanuddin Yeop Majlis, UKM 22

• Half the dopants diffuse to the left, the other half diffuse to the right – so peak concentration is half

( ) ( )2

2buried 2

,,⎟⎠

⎞⎜⎝

⎛⋅

⋅⋅⋅

== tDx

etD

QtxNtxNπ

Page 12: Diffusion [Compatibility Mode]

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2-D and 3-D DiffusionAn Isotropic Process

• Isotropic diffusion can diffuse under the diffusion mask just

Prof. Dr. Burhanuddin Yeop Majlis, UKM 23

under the diffusion mask just like an isotropic etch does under and etch mask

Sources of Dopants: Gas

Prof. Dr. Burhanuddin Yeop Majlis, UKM 24

• Gas Sources: HAZAROUDS!!! – B2H6 – Diborane – PH3 – Phosphine – AsH3 - Arsine

Page 13: Diffusion [Compatibility Mode]

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Sources of Dopants: Solid

S i O Gl

Prof. Dr. Burhanuddin Yeop Majlis, UKM 25

• Spin-On Glasses – has a volatile solve just like PR

• Previously Deposited Films – deposit at low temp and drive in at high

temperatures (e.g., oxides, polysilicon)

Sheet Resistance⎟⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛=

⋅=

WLR

WL

tALR s

ρρResistance:

I

• Resistance R [Ohm]

W

Lt

I

1 2 3 4 5

L/W = 5 (total # of squares)

I

Prof. Dr. Burhanuddin Yeop Majlis, UKM 26

• Resistance R [Ohm] • Resistivity ρ [Ohm-m] • Resistor Length L, Width W, Thickness t • Sheet Resistance Rs [Ohm/square]

– square is unit less (the aspect ratio of the resistor)

Page 14: Diffusion [Compatibility Mode]

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Sheet Resistance

No

N(x))()()( xNxqx ⋅⋅= μσ

∫==

jxj

s

dxxx

R)(

1

σ

ρ

∫=

jxs

dxxNxqR

)()(

1

μ

xj

NB

• Conductivity σ [ohm-1-m-1] Charge on Electron q [coulombs]

∫ ⋅dxx0

)(σ ∫ ⋅⋅⋅ dxxNxq0

)()(μ

Prof. Dr. Burhanuddin Yeop Majlis, UKM 27

Resistivity ρ [Ohm-m] Free Carrier Mobility µ [cm2v-1s-1]

Sheet Resistance Measurement

ρ F ρ measured.

• 4-Point Probe:

:st >>:ts >>

IVs ⋅⋅⋅= πρ 2 I

Vt⋅

⋅=

)2ln(πρ

IV

tRs ⋅==

)2ln(πρ

Prof. Dr. Burhanuddin Yeop Majlis, UKM 28

– avoids contact resistance – pass current through one pair of

electrodes (contact R and film R) – sense induced voltage with an inner pair

of electrodes across only film R due to high impedance measurement

Page 15: Diffusion [Compatibility Mode]

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Irvin’s Curves (N-Type)Relationship between: Rs, xj, and No

300 K300 K

Prof. Dr. Burhanuddin Yeop Majlis, UKM 29

300

Irvin’s Curves (P-Type)Relationship between: Rs, xj, and No

300 K300 K

Prof. Dr. Burhanuddin Yeop Majlis, UKM 30

300

Page 16: Diffusion [Compatibility Mode]

16

Bulk Resistivity

Prof. Dr. Burhanuddin Yeop Majlis, UKM 31

PROBLEM• Determine the concentration of diffused boron at 1 μm from the

surface. Diffusion was carried out at temperature of 1,100 °C for4 hours where the initial concentration, No equal to 4 × 1018 cm-2., o q

• Diffusion temperature 1,100 °C = 1,373 K

• From Fig 5.7, diffusion coefficient boron 4 × 10-13 cm2.s-1

73.0137310001000

==T

66010 4−x

Prof. Dr. Burhanuddin Yeop Majlis, UKM 32

• From erfc plot at Rajah 5.6, N/No = 0.45• Then N = 0.45 x 4 x 1018 = 1.8 x 1018 cm-2

66.06060410422 13

=××××

=−Dt

Page 17: Diffusion [Compatibility Mode]

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P-Type Doping• Impurities

– Boron(B), gallium(Ga), aluminium(Al), and indium(In).

• boron normally used for p-type doping. • Ga has higher diffusion coefficient in oxide

– Oxide can not be used as an mask.

• In has acceptor level 0.16 eV, while boron only 0.01 eV, as a result not all acceptor level ionised at room temperature.

Prof. Dr. Burhanuddin Yeop Majlis, UKM 33

te pe atu e• Al not suitable because easily react with oxygen in

substrate.

Boron Source

• Boron deposited on Si substrate as boron trioxide (B2O3)– solid boron trioxide (B2O3) also called boron glass– In contact with Si surface, boron trioxide will formed a layer

with boron riched• B2O3 can be obtained by,

– Oxidation of diborane gas (B2H6),,• B2H6 + 3O2 B2O3 + 3H2O

– Or using boron nitride (BN) wafer, put together with Si waferin diffusion furnace

Prof. Dr. Burhanuddin Yeop Majlis, UKM 34

– B2O3 layer can also be formed using polymer material suchPBF coated on Si surface.

• Diborane gas is more popular because flow rate of as can becontrolled and the concentration of boron can be controlled.

Page 18: Diffusion [Compatibility Mode]

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BN Wafer Polymer Materialwafer BN wafer silikon

PBF

Bot kuarza

wafer

PBF

B O B Oresapan

pembakaran

wafer wafer

2 3 2 3

wafer

penyalutan

Prof. Dr. Burhanuddin Yeop Majlis, UKM 35

N-Type Doping• Impurities Type n,

– phosphorous, antimony, and arsenic. • arsenic and antimony have low diffusion

coefficient– To impurities at initial stage of process because.

• Used to formed a burried layer in BJT and n well for CMOS.

arsenic has higher solid solubility can give high

Prof. Dr. Burhanuddin Yeop Majlis, UKM 36

– arsenic has higher solid solubility – can give high surface concentration.

Page 19: Diffusion [Compatibility Mode]

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Source for arsenic and antimony

• Source for arsenic is arsine gas (AsH3) and antimony stibnine gas(SbH3).

• These gases react with oxygen to form an oxide,

2AsH3 + 3O2 →As2O3 + 3H2Oand

2SbH3 + 3O2 →Sb2O3 + 3H2O

Prof. Dr. Burhanuddin Yeop Majlis, UKM 37

3 2 2 3 2

• Both gases are flammable and highly toxic.•

Phosphorous Sources• Source for phosphorous oxide are,

– Phosphine gas (PH3), liquid phosphorous oxychloride (POCl3) and solid SiP Ooxychloride (POCl3), and solid SiP2O7

• Polymer materila used in spin coating techniques is OCD.

• Phosphine gas more porpular, but this as is higher toxic and easily explode.

• Phosphine(PH3) and phosphorous oxychloride(POCl3)react with oxygen form phosphorous oxide

Prof. Dr. Burhanuddin Yeop Majlis, UKM 38

(POCl3)react with oxygen form phosphorous oxide(P2O5),

2PH3 + 4O2 P2O5 + 3H2O2POCl3 + 3O2 P2O5 + 3Cl2

• phosphorous atoms from P2O5 diffuse into silicon.

Page 20: Diffusion [Compatibility Mode]

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Diffusion system for liquid source

Prof. Dr. Burhanuddin Yeop Majlis, UKM 39

EVALUATION OF DIFFUSED LAYER

• There are four parameters,– surface concentration, No,

B k d t ti N– Background concentration, NB, – junction depth, Xj, and– Sheet resistance, Rs.

• Junction depth measurement• colour the n and p type region• There are two technique angle lapping and wafer

Prof. Dr. Burhanuddin Yeop Majlis, UKM 40

• There are two technique, angle lapping, and wafer grooving.

Page 21: Diffusion [Compatibility Mode]

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Angle Lapping• Sample is stick on the block with sloping surface

Xj = d sin θ• Surface cutting at very small angle (0.5°) enable a

distance d at the junction can be measured under

np

d

x j

0

np

optical flat

Prof. Dr. Burhanuddin Yeop Majlis, UKM 41

distance, d, at the junction can be measured under microscope.

• The junction is coloured using stain material, a mixture of hydrofluoric acid and 0.5% nitric acid to darken the p-type material.

Wafer Grooving

• Using cylinder with radius R• Using cylinder with radius R to make groove on the wafer surface.

• The groove will cut and expose the junction.

• Stain material is used to differentiate p-type and n-type

22 aR −

Prof. Dr. Burhanuddin Yeop Majlis, UKM 42

type.

Xj

R

b

an

p

22 bR −

x y

Page 22: Diffusion [Compatibility Mode]

22

Wafer Grooving

In practice, it is easier to measure x

= − − −R bR

aR( ) ( )1 1

22

22

12

12

because a << R and b << R, then

⎥⎥⎦

⎢⎢⎣

⎡−−−= 2

1222122 )()( aRbRX j

p ,and y, where

x = a - b and y = a + b

xy = a2 - b2

X xyRj =

12

Prof. Dr. Burhanuddin Yeop Majlis, UKM 43

X R bR

aRj ≈ − − +( )1 2 1 2

22

22

=−1

2

2 2a bR

R2

Sheet Resistance• If the length of sample, l, width w and thickness, t, then, the

resistance between point A and B is,

l)( l)(w

• Where ρ(t) resistivity as a function of distant t inside the samplefrom surface.

• Ratio between resistivity to layer thickness is called sheetresistance, Rs,

wtltR )(ρ

=wl

tt)(ρ

=

tR )(ρ

l

tArus I

Prof. Dr. Burhanuddin Yeop Majlis, UKM 44

• When length, l, equal to width, w, thenR = Rs

tRs =

Page 23: Diffusion [Compatibility Mode]

23

Four Point Probes

••V

I I

s s s= 4 5324. /V

IΩ square

Prof. Dr. Burhanuddin Yeop Majlis, UKM 45

1 2 3 4t

I

Carier Type Determination• Hot probe will push carrier from the surface and leave only ion

charge, if the semiconductor is n-type then the region is consist of positive ion.

• As a result, the region under the hot probe become more positive compare to the other probe.

• If the semiconductor is p-type, the region is more negative compare with the other probe (cold).

• The deflection direction depends on whether the semiconductor is n or p-type.

+ - +-

Prof. Dr. Burhanuddin Yeop Majlis, UKM 46

coldhot

N-type wafer

Heatingcoil

coldhot

P-type wafer

Heating coil

Page 24: Diffusion [Compatibility Mode]

24

Surface Concentration• Surface concentration, No, can be determined by measuring the

sheet resistance and junction depth.• If we know N diffusion profile can be obtained using GaussIf we know No, diffusion profile can be obtained using Gauss

and erfc relationship.• For diffused layer with background concentration, NB, sheet

resistance is given by,

• A computer calculation had been done by Irvin. [Irvin.1962] to

[ ]R

q x N x N dxs

B

X j=

−∫1

0μ ( ) ( )

Prof. Dr. Burhanuddin Yeop Majlis, UKM 47

p y [ ]get No from the value of Rs and xj for various value of NB

• Irvin produced a plot for relationship of average conductivity andsurface concentration, No, for p-type and n-type materials forboth Gaussian and erfc distribution.

PROBLEM

• A phosphorous dopant is diffused on p-type subtrate with• A phosphorous dopant is diffused on p-type subtrate with doping concentration of 1016 cm3. From four point probe measurement Rs = 5 Ω, and from junction depth measurement, Xj = 0.8 μm. Determine the surface concentration No?

• From Irvin plot (refer Ghandi S.K. 1994) with NB = 1016 cm2,

js XR1

Prof. Dr. Burhanuddin Yeop Majlis, UKM 48

p ( ) B ,then, No = 9 x 1016 cm-3