Diffusion in Silicon

Diffusion in SiliconWritten by: Scotten W. Jones

iPreface

The following document was written in 2000 as a chapter on Diffusion in Silicon for inclu-sion in a highly technical - text book on Silicon Integrated Circuit Process Technology. For marketing reasons we abandoned the book without completing it but this was one of several chapters that are complete. We have recently been posting chapters from this book for free download, we hope you find it useful. This particular chapter is an update of the previous diffu-sion chapter post and now includes the appendix with the properties of the error function.

Please note that this material was written back when we planned to publish it as a hard cover book in black and white and is not in color the way all of the current IC Knowledge reports are.

Scotten W JonesPresidentIC Knowledge LLCApril 25, 2008

ii

Contents

1.1. Introduction 11.2. Basic concepts 11.3. Atomic mechanisms of diffusion 21.4. Mathematics of diffusion 41.5. Diffusion equations 71.6. Diffusivity 151.7. Solid solubility 371.8. Deviations from simple diffusion theory 411.9. Diffusion Equipment 561.10. Metrology 561.11. Properties of the error function 67

Copyright 2000 IC Knowledge LLC, all rights reserved 1

Diffus

1.1. In1.2. Ba1.3. At1.4. M1.5. Di1.6. Di1.7. So1.8. De1.9. Di1.10. M

1.1. IntIC fab

through thintegrated lowed by required trequired juthe desireddiffusion hprocesses sstate-of-thIn this reposion will blated.

1.2. BaThrou

junction de Impur Backg

rity prion in Silicon

troductionsic conceptsomic mechanisms of diffusionathematics of diffusionffusion equationsffusivitylid solubilityviations from simple diffusion theory

ffusion Equipmentetrology

roductionrication is accomplished by selectively changing the electrical properties of silicon e introduction of impurities commonly referred to as dopants. In the early years of circuit fabrication, deep semiconductor junctions required doping processes fol-a drive-in step to diffuse the dopants to the desired depth, i.e. diffusion was o successfully fabricated devices. In modern state-of-the-art IC fabrication the nction depths have become so shallow that dopants are introduced into the silicon at depth by ion implantation and any diffusion of the dopants is unwanted, therefore as become a problem as opposed to an asset. There are many non state-of-the-art till in use throughout that industry where doping and diffusion are still in use and for

e-art processes diffusion must be understood in order to minimize undesired effects. rt the physical mechanisms of diffusion will be reviewed, the mathematics of diffu-

e presented and diffusion data will be provided to allow diffusion effects to be calcu-

sic conceptsghout this report the concepts of impurity profile, background concentration and pth will be used.

ity profile - the concentration of an impurity versus depth into the silicon. round concentration - an impurity concentration existing in the silicon that an impu-ofile is formed into.


Junction depth - the depth at which the impurity profile concentration is equal to the back-ground concentration.Figure 1.1 illustrates the preceding three concepts. The impurity profile, C(x) varies with

depth into junction de

Fig

1.3. AtImpur

(see figurearsenic (Atrons or honot occupycessing imbution of ihigh tempe

Diffusmediuthe silicon, x, the background concentration CB is shown at a constant level and the pth, xj is the depth at which C(x) = CB.

ure 1.1: Impurity profile, background concentration and junction depth.

omic mechanisms of diffusionity atoms may occupy either substitutional or interstitial positions in the Si lattice 1.2). Impurity atoms utilized as dopants such as boron (B), phosphorus (P) and s) occupy substitutional positions where the dopant atoms can contribute free elec-les to the silicon lattice (dopant atoms introduced to silicon by ion implantation may substitutional positions until the dopant is activated). During high temperature pro-purity profiles are redistributed through a process known as diffusion. The redistri-mpurities may be intentional as in a drive-in step or unintentional as a result of rature oxidation, deposition or annealing processes.

Figure 1.2: Substitutional and interstitial impurities in silicon.

ion - the redistribution of an initially localized substance throughout a background m due to random thermal motion.

Impu

rity

conc

entra

tion

-C

(atom

s/cm

)3Impurityprofile C(x)

Backgroundconcentration - CB

C

x

C(x) = CB

Junctiondepth, xj

Depth - x ( m)

a) Substitutional b) Interstitial


The movement of a substance due to diffusion is driven by the slope of the concentration profile.

Impurity atom diffusion may be vacancy, interstitial or a combination mechanism known as interstit

Fi

Vacanvacancy - atom jumpinterstitialsof silicon sself-interstphorus, arsis closely l

Whethsilicon, theprobabilityincreasing

In ordtrated in fition to jumjump to thareas of hitime the nefigure 1.5aform throuialcy - see figure 1.3.

gure 1.3: Vacancy, interstitial and interstitialcy diffusion mechanisms.

cy diffusion occurs when a substitutional atom exchanges lattice positions with a requires the presence of a vacancy. Interstitial diffusion occurs when an interstitial s to another interstitial position. Interstitialcy diffusion results from silicon self- displacing substitutional impurities to an interstitial position - requires the presence elf-interstitials, the impurity interstitial may then knock a silicon lattice atom into a itial position. It is important to observe here that since dopant atoms such as phos-enic and boron occupancy substitutional positions once activated, dopant diffusion inked to and controlled by the presence of vacancy and interstitial point defects.er an impurity atom occupies a substitutional or interstitial position in single crystal atom is trapped in a periodic potential defined by the lattice - see figure 1.4. The of an atom jumping from one position to the next increases exponentially with

temperature.

Figure 1.4: Impurity atom diffusing along a periodic potential.

er to understand diffusion, consider the highly concentrated impurity profile illus-gure 1.5a, time = 0. If random thermal motion causes 20% of the atoms in each posi-p to a new position in each unit of time, 10% of the atoms would be expected to

e left and 10% of the atoms would be expected to jump to the right at time = 1. The gher concentration would have more atoms jump out of the area than jump in. Over t result of the random thermal motion would be a gradual spreading of the profile - , time = 0 to 1.5e, time = 4. At infinite time the impurity distribution would be uni-ghout the background medium

a) Vacancy b) Interstitial c) Interstitialcy


Figur

1.4. MaFrom t

derived as

1.4.1. FiConsid

slice 2 hav

and

and, N1 ancross secti

Atomsperature eaprobabilitythe next inatoms acroe 1.5: Impurity profile spreading due to random thermal motion - diffusion.

thematics of diffusionhe basic principles outlined in the preceding section, the diffusion equations may be

follows [1],[2].

cks first lawer the two equal thickness slices of a solid illustrated in figure 1.6 where slice 1 and e different impurity concentrations, C1 and C2 given by

(1.1)

(1.2)

d N2 are the number of impurity atoms in slice 1 and slice 2 respectively, A is the onal area of the slices and is the thickness of the slices. throughout the solid are constantly vibrating from thermal energy. At a given tem-ch atom in the slice has a frequency of jumps to the adjacent slice, , with equal of jumping in either direction, therefore the frequency of jumps from one slice to a particular direction is /2. For the plane separating slice 1 from slice 2, the flow of ss the boundary is

(1.3)

a) time=0 b) time=1 c) time=2 d) time=3 e) time=4

C1N1A-------=

C2N2A-------=

+N1->2t--------------------

N12

---------=


and

(1.4)

where t is direction o

Comb

and substit

Since

equation 1

-N2->1------------------ N2---------=time. Note that left to right is the positive direction and right to left is the negative f motion.

Figure 1.6: Diffusion from a concentration gradient.

ining equations 1.3 and 1.4 yields the net flow across the boundary

(1.5)

uting concentration from equations 1.1 and 1.2 into equation 1.5, gives

(1.6)

the concentration gradient is given by

(1.7)

.6 and 1.7 can be combined to give

(1.8)

t 2

Slice 1

Area A

Slice 2 Slice 3

N atoms1 N atoms2 N atoms3

Nt--------

2--- N1 N2( )=

Ct--------

C1 C2( )A2

----------------------------------=

Cx--------

C2 C1------------------=

Ct--------

-A22

----------------Cx--------=


By now introducing flux, j, defined as Flux - the number of units passing through a boundary area per unit time.and dividing equation 1.8 by area, the expression for flux may be found as

The di

Comb

which in p

Ficksand from Frapidly tha

1.4.2. FiFicks

calculated,function o

Considcentration slice 2 to s

Which

and

therefore(1.9)

ffusion constant D, is now introduced and defined as

(1.10)

ining equations 1.9 and 1.10 results in

(1.11)

artial differential terms is known as Ficks first law

(1.12)

first law relates the flux of atoms across a boundary to the concentration gradient icks law it can be seen that regions with a large concentration gradient diffuse more n regions with a small concentration gradient.

cks second law first law allows the diffusive flux as a function of the concentration gradient to be Ficks second law allows the concentration function, C(x), to be calculated as a f time. er the second slice in figure 1.5. Since matter is conserved the time change in con-in slice 2 must be the sum of the fluxes across the slice 1 to slice 2 boundary and the lice 3 boundary. results in

(1.13)

(1.14)

(1.15)

j 1A---Ct-------- -

22

---------Cx--------= =

D 22

---------

j -DCx--------=

j -D Cx------=

Ct-------- j1 j2=

j1 j2--------------

jx------=

Ct-------- -

jx------=


In differential terms, equation 1.15 is the transport equation

(1.16)

Substi

Ficksfor heat coheat flow c

1.5. DiFicks

previously

1.5.1. InEarly

ing was acdesired imdopant wadopant at tble in silireduced thgas containsuch as P2impurity sis orders otical interebility at anCS - see fi

To sol1.17, mustgiven by

and the ini

C------ - j-----=tuting Ficks first law - equation 1.12 into equation 1.16 gives Ficks second law

(1.17)

second law as derived in the preceding sections is identical in form to the equation nduction differing only in the constant D, and therefore the large body of work on an be applied to the problems of impurity atom diffusion in silicon.

ffusion equations laws can now be applied to solve diffusion problems of interest. As was the case the solutions presented here assume a constant diffusivity.

finite source diffusion into a semi-infinite body - single step diffusionin the development of integrated circuit fabrication technology, semiconductor dop-complished by exposing semiconductor substrates to a high concentration of the

purity. In order to maintain good process control, the concentration of the impurity s maintained at a level in excess of the level required to achieve solid solubility of the he semiconductor surface (solid solubility is the maximum doping level that is solu-con at a given temperature - see section 1.7). The high concentration of dopant e process control requirements to time and temperature. The doping source may be a ing the dopant of interest such as arsine - AsH3 - an arsenic source, or a glass layer

O5 as a phosphorus source. The dopant in these cases may be considered an infinite ource in contact with a semi-infinite medium (the semiconductor substrate thickness f magnitude greater than the diffusion depth of the dopant for most instances of prac-st). The surface concentration of the semiconductor will be CS set by the solid solu-y time during the diffusion process and the dopant concentration in the gas CG is >

gure 1.7ve for the impurity profile in the silicon versus time, Fick's second law - equation be solved for the boundary and initial conditions, where the boundary conditions are

(1.18)

tial conditions are

(1.19)

t x

Ct------ D

2Cx2

----------=

C C0, x = 0, t > 0=

C 0, x > 0, t = 0=


.

The soLaplace tralized to rea

Laplace traStartin

respect to

Assumjustified fo

Integra

Since 1.19 and a

CFigure 1.7: Single step diffusion - initial conditions.

lution to Ficks law for single step diffusion that will be derived here will apply nsforms after reference [4]. There are several alternate methods that can also be uti-ch the same result. The laplace transform for a known function of t, for t > 0, is

(1.20)

nsforms of common functions may be constructed by integrating equation 1.20.g with Ficks law - equation 1.17, multiplying both sides by e-pt and integrating with t from zero to infinity results in

(1.21)

ing that the orders of differentiation and integration can be interchanged (this can be r the functions of interest [4]), then

(1.22)

ting by parts

(1.23)

the term in the square brackets vanishes at t = 0 for the initial conditions - equation t t = infinity through the exponential factor - equation 1.17 reduces to

CGCS

+x-x

x = 0

gas silicon

f p( ) e-ptf t( ) td0

=

e-pt 2Cx2

---------- t d 1D---- e-pt C t------ td

0

0

0=

e-pt 2Cx2

---------- td0

x2

2

Ce-pt

0

dt 2Cx2

----------= =

e-pt C t------ td0

Ce-pt[ ]0 p Ce-pt td0

+ pC= =


(1.24)

By tre

Thus tnary differ

The soas x appro

where, b2

where, erfsion theory

The cois plotted aand as a lo

The to

Integra

If a sidopants, eqQ will also

The gr

D 2Cx2

---------- pC=ating the boundary conditions - equation 1.18 in the same way

(1.25)

he Laplace transform reduces from the partial differential equation 7.17 to an ordi-ential equation 1.24.lution of equation 1.24 that satisfies equation 1.25 and for which C bar remains finite aches infinity is

(1.26)

= p/D. The Laplace transform for equation 1.26 is [4]

(1.27)

c is the complementary error function, one of the most important functions in diffu-. Error function properties are presented in appendix F.ncentration of impurities versus depth into the silicon calculated using equation 7.27 s a linear plot versus 2 multiplied by the square root of DT in the top of figure 7.8 g plot versus 2 root DT in the bottom of figure 1.8.tal number of impurity atoms Q which enter a 1 cm2 section of silicon is defined by

(1.28)

ting equation 1.28 results in

(1.29)

ngle step diffusion as outlined above is used to introduce impurities into silicon as uation 1.29 can be utilized to calculate the total number of dopant atoms introduced. be used later to calculate profiles resulting from two step diffusion processes.adient or slope of the impurity profile can be calculated by

(1.30)

C C0e-pt td

0

CSp------ , x = 0= =

CCSp

------e-bx=

C x t,( ) CS erfc x2 Dt-------------=

Q t( ) C x t,( ) xd0

Q t( ) 2------- DtCS=

Cx------ x t,( )

CSDt--------------e

x 2/4Dt=


Fig

Using F, equation

0.91.0ure 1.8: Complementary error function profile evolution versus time [5].

the asymptotic approximation for the complementary error function from appendix 1.31 results that is valid for most practical situations [5].

(1.31)

0.00

01x10-5

1x10-4

1x10-3

1x10-2

1x10-1

1x100

1.0

1.0

x( )

x( )

2.0

2.0

3.0

3.0

0.10.20.30.40.50.6

C/C S

C/C S

0.70.8

0.1 m 0.5 m 2 Dt = 1.0 m

1.0 m0.5 m2 Dt = 0.1 m

Cx------ x t,( )

x2Dt---------C x t,( )


1.5.2. Plane source - two step diffusionWhen a single step diffusion is used to introduce dopant into a semiconductor, a follow-on

second drive-in diffusion is also frequently used. During deposition an oxide-masking layer maybe useis performloss of thedesired Q etch back without fetion and dr

Followthe diffusi

and

The soinitial conequation 1cult probled to mask the dopant from some areas of the semiconductor. If single step diffusion ed with a long cycle, the dopant can diffuse through the masking oxide resulting in a desired pattern. Alternately a short single step diffusion can be used to introduce the or total dopant into the semiconductor. The single step diffusion is followed by an to remove the doped portion of the oxide and then a long drive-in cycle can be used ar of the dopant penetrating the masking oxide. Figure 1.9 illustrates the pre-deposi-ive in doping process.

Figure 1.9: Pre-deposition and drive-in process.

ing the pre-deposition step the impurity distribution can be determined by solving on equation which satisfies the boundary conditions

(1.32)

(1.33)

lution must also provide for a constant Q to be maintained in the semiconductor. The dition is given by equation 1.27 using the Dt for the pre-deposition step. Solving .27 with the boundary condition given by equation 1.32 and equation 1.33 is a diffi-m. In practice the Dt from the drive-in step is much greater than the Dt for the pre-

Mask and etchSilicon

Dopant

Oxide

Pre-deposition

Oxide etch-back

Drive-in andgrow oxide

Cx------ 0 t,( )

0=

C t,( ) 0=


deposition step. A practical approximation is to assume that the total dopant Q is located in a sheet at the interface.

By differentiation it may be shown that

is a solutiabout x, teishes every

The tosection is g

If the c

and

Equatithe amounequation 1

In the cates one sdirections)

Whichknown gauprofile wit(1.34)

on to equation 1.17 where A is an arbitrary constant. Equation 1.34 is symmetric nds to zero as x approaches infinity positively or negatively for t>0, and at t=0 van-where but x=0, where it becomes infinite.tal amount of impurities Q, diffusing in a cylinder of infinite length and unit cross iven by

(1.35)

oncentration distribution is given by equation 1.34, then

(1.36)

(1.37)

on 1.37 shows that amount of impurity diffusing remains a constant and is equal to t in the interface sheet at x=0. Therefore, substituting for A from equation 1.37 into .34 results in

(1.38)

actual pre-deposition - drive-in case being considered the gas-silicon interface trun-ide of the distribution, (equation 1.35 assumes the distribution is continuous in both . Equation 1.38 becomes

(1.39)

is the drive-in concentration following pre-deposition. Equation 1.39 is the well ssian distribution. The top of figure 1.10 illustrates the progression of the impurity

h time as a linear plot and the bottom of figure 1.10 illustrates a log plot.

C At

-----e x2/4Dt=

Q C xd

=

x2 4Dt 2 dx = 2 Dt d,=

Q 2A D e 2

d

2A D= =

C x t,( ) Q2 Dt-----------------e

x 2/4Dt=

C x t,( ) QDt--------------ex 2/4Dt=


Since decrease - tion 1.39, t

1.2Figure 1.10: Gaussian distribution normalized concentration versus distance for successive times [5].

Q is fixed, as the impurities diffuse into the silicon the surface concentration CS must this is in contrast to the single step diffusion case where CS is a constant. From equa-he surface concentration may be calculated by

0.00

01x10-3

1x10-2

1x10-1

1x100

1x101

1.0

1.0

x( )

x( )

2.0

2.0

3.0

3.0

0.2

0.4

0.6C/

Q (cm

)-1

C/Q

(cm)

-1

0.8

1.0

1.0 m

0.5 m

2 Dt = 0.1 m

1.0 m0.5 m2 Dt = 0.1 m


(1.40)

Thus t

The gr1.41 and is

Figurewhere

CS t( ) QDt--------------=he concentration distribution can also be represented by

(1.41)

adient of the concentration distribution can be obtained by differentiating equation given by

(1.42)

1.11 presents some values of the error function and Gaussian function versus z

(1.43)

Figure 1.11: Gaussian and error function values versus z.

C x t,( ) CS t( )e x2/4Dt=

Cx------ x t,( )

x2Dt---------C x t,( )=

z x2 Dt-------------=

01x10-8

1x10-7

1x10-6

1x10-5

1x10-4

1x10-3

1x10-2

1x10-1

1x100

1.0

Erfc Gaussian

z( )2.0 3.0 4.0

C/C

BS


As will be seen in the problem section, figure 1.11 is very useful for performing diffusion calculations.

1.6. DiIn equ

section thewill be pre

In ordsilicon atofrom one iand a relatvacancy ormation areseen later excess of and substit

The diis the enering to anowhich the approximathe barrierconstant aposition is

Each anumber ofFor the int

For sua vacancy stitials forexpression

Experi0.5eV andffusivityation 1.10 the concept of a diffusion constant - the diffusivity was introduced. In this physical basis of diffusivity will be reviewed and some data on diffusivity values sented.er for an impurity to diffuse through silicon, the impurity must either move around ms or displace silicon atoms. During interstitial diffusion the diffusing atom jumps nterstitial position to another interstitial position, with relatively low barrier energy ively high number of interstitial sites. Substitutional atoms require the presence of a an interstitial to diffuse and must break lattice bonds. Vacancy and interstitial for- relatively high-energy processes and so are relatively rare in equilibrium (as will be certain processes can result in concentrations of interstitials and or vacancies well in equilibrium). Breaking bonds to the lattice is also a relatively high-energy process utional atoms tend to diffuse at a much lower rate than interstitial atoms.ffusion process can be characterized by a barrier with activation energy Ea, where Eagy required to jump from one site to the next site. The probability of an atom jump-ther site is given by the product of two terms. The first term is the frequency with atom collides with the barrier 0 (the frequency of atomic oscillation in silicon is tely 1013 to 1014 /sec.). The second term is the probability the atom will surmount during a collision (given by the boltzman factor exp(-Ea/kT)) where k is boltzmans nd T is the temperature in degrees Kelvin. The rate at which atoms jump to a new given by

(1.44)

tom can move to any adjacent site, so equation 1.44 should be multiplied by the adjacent sites which is four for silicon for both the interstitial and substitutional case. erstitial case equation 1.44 becomes

(1.45)

bstitutional atoms an additional term must be added to account for the probability of or interstitial existing in the adjacent site (vacancies for vacancy diffusion and inter- interstitialcy diffusion). If Ed is the energy for point defect formation, the resulting is

(1.46)

mentally determined activation energies for interstitial atoms are approximately for substitutional atoms are approximately 3eV (including defect formation) [3]. It is

0eE a/kT=

inst 40eE a/kT=

vsubst 40eEa Ed+( ) /kT=


now possible to rewrite the diffusion constant equation 1.10 in terms of the physical properties of the materials.

Substituting equation 1.45 into equation 1.10 and taking into account that the spacing between atsivity is gi

Substiing gives t

Equatiand the difields, impplicate act

From that vacanature, and interstitialction whichIC fabricat1.1 summaindicates i

Ion imlattice posilying silicobination siinto accoudependingact as an inoms is d divided by the square root of 3 for a diamond structure, interstitial diffu-ven by

(1.47)

tuting equation 1.46 into equation 1.10 and taking into account the inter-atomic spac-he diffusivity for substitutional atoms of

(1.48)

ons 1.47 and 1.48 imply that the diffusivity for all interstitial atoms will be the same ffusivity for all substitutional atoms will be the same, this is not the case. Electric urity - lattice size mis-match induced strain and multiple diffusion mechanisms com-ual diffusivity values. the discussion of diffusion mechanisms presented in section 1.2 one would expect cy diffusion would depend on vacancy concentration, which is a function of temper-any non-equilibrium vacancy generation or annihilation mechanisms. Conversely, y diffusion would be expected to be sensitive to silicon self-interstitial concentra-, also depend on temperature and non-equilibrium processes. There are a number of ion processes which can generate non-equilibrium point defect concentrations. Table rizes process effects on point defects where V indicates vacancy generation and I

nterstitial generation.

plantation generates interstitial vacancy pairs by knocking lattice atoms from their tion, oxidation is a partially complete reaction and injects interstitials into the under-n, nitridation and silicide formation inject vacancies. Silicon surfaces act as recom-tes for point defect concentrations so that the proximity of a surface must be taken nt. Interstitials may also cluster together to form defects which grow and shrink on time, temperature and interstitial concentrations with the result that defects may terstitial sink or source. Interstitials and vacancies may also recombine in the bulk.

Table 1.1: Process generated point defects

Process step Point defects

Ion implantation I-V pairs

Oxidation I

Nitridation V

Salicidation V

D40d2

6--------------e

E a/kT=

D40d2

6--------------e

Ea Ed+( ) /kT=


In order to accurately calculate diffusivity it is therefore important to understand the atomic mechanism by which each dopant diffuses as well as the local point defect concentrations. Effective diffusivities in the presence of point defects can be expressed as

where, Deffusion duerium intervacancy co

Equatithe presen

One otherefore tbegins witdeposited cient thickSi3N4 opeatoms are uicon self-iregion whbeing meainterstitialsvacancy sucenter sect(1.49)

f is the effective diffusivity, D* is the equilibrium diffusivity, fI is the fraction of dif- to an interstitialcy mechanism, CI is the interstitial concentration, C*I is the equilib-stitial concentration, CV is the vacancy concentration and C*V is the equilibrium ncentration.on 1.49 allows vacancy, interstitialcy or mixed vacancy-interstitialcy diffusivity in ce of point defects to be modeled.f the classic experiments for determining the effect of interstitials on diffusivity and he interstitialcy component of diffusion is illustrated in figure 7.12. The experiment h the formation of a uniform doped layer. A layer of silicon nitride (Si3N4) is then and patterned to leave an opening where oxidation is to take place - Si3N4 of suffi-ness can block thermal oxidation. A silicon dioxide (SiO2) layer is then grown in the ning. Oxidation is usually incomplete and approximately 1 in every 1,000 silicon n-reacted. The un-reacted silicon atoms breaks free of the interface and becomes sil-

nterstitials. The concentration of silicon self-interstitials is higher under the center ere oxidation is occurring and if interstitials increase the diffusivity of the dopant sured then the dopant will diffuse deeper under the center section. Conversely if retard diffusion, for example if interstitials recombine with vacancies limiting the pply for vacancy diffusion, the dopant will diffuse to a shallower depth under the ion.

Figure 1.12: Experiment to measure oxidation enhanced diffusion.

DeffD--------- fI

CICI-------- 1 fI( )

CVCV---------+=

Form uniform doped layer

Deposit and pattern siliconnitride layer (blocks oxidation)

SiliconDoped layer

Silicon nitride

Silicon dioxide Grow oxide - dopant diffusesduring oxidation

Degree ofenhancement


It is important to note here that the oxidation reaction is consuming silicon in the center section. Without diffusivity enhancement the distance between the SiO2 - Si interface and dif-fusion boundary under the center section would be smaller than the distance between the Si3N4 - Si interfa

Many the intersti

From componenments of thsingle equthe ratios ce and the diffusion boundary out at either side. researchers have investigated the mechanisms of diffusion. Table 1.2 summarizes tialcy component

table 1.2 it is clear that there is a great deal of disagreement about the interstitialcy t of diffusion. Recently Grossman [67] has pointed out that experimental measure-e interstitialcy component of diffusion for a single species require the solution to a

ation, equation 1.49 with three unknowns, the percent of interstitialcy diffusion and of interstitial and vacancy concentrations to equilibrium. If however, two different

Table 1.2: Interstitialcy component of diffusion [20].

ElementTemperature (oC)

Reference950 1,000 1,050 1,100

Aluminum 0.6-0.7 11

Antimony 0.02

0.02

9

11

Arsenic 0.10

0.22

0.09

0.25

0.12

0.25

0.09

0.30

0.15

0.30

0.09

0.35

0.19

0.2-0.4

0.35

0.09

0.42

0.2-0.5

12

9

19

8

10

11

Boron 0.16

0.22

0.17

0.38

0.17

0.24-

0.34

0.32

0.17

0.45

0.18

0.42

0.17

0.60

0.19

0.52

0.17

0.80

0.8-1.0

12

9

19

8

10

11

Gallium 0.6-0.7 11

Indium 0.30 9

Phosphorus 0.14

0.27

0.12

0.30

0.16

0.38

0.34

0.12

0.35

0.19

0.42

0.12

0.45

0.23

0.55

0.51

0.12

0.55

0.5-1.0

12

9

19

8

10

11


diffusing species are measured under identical conditions a system of two equation in two unknowns can be formulated and solved without resulting to assumptions about the vacancy and interstitial ratios. Grossman has performed this experiment for boron and antimony and found

and

Or in Sb diffuseany substitstitialcy m

A coming speciesfor boron w

A neut

An int

An intinterstitial

A negboron - intelectron an

A negneutral borinto a nega

A neustitial pair charged boncy.(1.50)

(1.51)

other words, B diffuses through an almost exclusively interstitialcy mechanism and s through an almost exclusively vacancy mechanism. Grossman further suggests that utional dopant in silicon should diffuse through either a pure vacancy or a pure inter-echanism.plete diffusion model needs to account for point defect interactions with the diffus- and also formations of defect clusters. For example, a complete set of interactions ould need to account for the following eight interactions [68]:

ral interstitial interacts with a cluster to either grow or shrink the cluster

(1.52)

erstitial and vacancy either annihilate each other or are generated as a Frenkel pair

(1.53)

erstitial and a hole interact to create a positively charged interstitial from a neutral or a positively charged interstitial releases a hole and becomes neutral.

(1.54)

atively charged boron atom combines with a neutral interstitial to form a neutral erstitial pair and release an electron or a neutral boron - interstitial pair captures an d breaks up into a negatively charged boron atom and a neutral interstitial.

(1.55)

atively charged boron atom combines with a neutral interstitial and a hole to form a on - interstitial pair or a natural boron - interstitial pair releases a hole and breaks up tively charged boron atom and a neutral interstitial.

(1.56)

tral boron - interstitial pair combine with a vacancy annihilating the vacancy - inter-and releasing a negatively charged boron atom and a hole or a hole and a negatively ron atom combine and generate a neutral boron - interstitial pair and release a vac-

fB 860oC( ) 0.98 0.01+

fSb 790oC( ) 0.01 0.01+

I0 C C+

I0 V0 0+

I0 h+ I++

B- I0 BI0 e-++

B- I0 h+ BI+ +


(1.57)

A positively charged boron - interstitial pair combine with a vacancy annihilating the vacancy - holes and interstitial

A negato form a nboron atom

The eform [69]:

This syto evaluatebecome avexpect that

In orddiffusivityfusivity bagood fit toof the indi

The in

where: Di positively rity diffusithe intrinsi

For ex

where, Dximpurity c

BI0 V0 B- h+++

CBI0

t-------------interstitial pair and releasing a negatively charged boron atom and two holes or two a negatively charged boron atom combine and generate a positively charged boron - pair and release a vacancy.

(1.58)

tively charged boron atom and a positively charged boron - interstitial pair combine eutral boron cluster or a neutral boron cluster breaks apart into a negatively charged and a positively charged boron - interstitial pair.

(1.59)

quation set can be implemented through a set of reaction diffusion equations of the

(1.60)

stem of equation contains a large number of parameters that must be know in order the model predictions. Recently general purpose differential equation solvers have ailable which allows systems like this to be evaluated [80]. It seems reasonable to commercial process simulators will include such models in the future. er to enable the reader to make diffusion calculations of reasonable accuracy Fairs model will be presented in the next few sections. Fair has developed a model for dif-sed on impurity interactions with charged vacancy states that provides a reasonably most observed diffusion results [6],[7]. Fair's model calculates diffusivity as the sum vidual charged vacancy - impurity diffusivities.trinsic model is given by

(1.61)

is the intrinsic diffusivity, D0 is the neutral vacancy - impurity diffusion, D+ is the charged vacancy - impurity diffusion, D- is the negatively charged vacancy - impu-on and D= is the doubly negatively charged vacancy - impurity diffusivity and ni is c carrier concentration - see chapter 1.trinsic silicon

(1.62)

is the extrinsic diffusivity. For specific impurities not all vacancy charge state - ombinations will participate in the diffusivity.

BI+ V0 B- 2h+++

B- BI+ BBcls+

x D

BI0CBI0

x------------- KF

1CB CI0 KR1C

BI0n- KF

2CBI CV0 KR2CB p+ + +=

Di D0 D+ D- D= for n or p > ni+ + + +=


Even though it is now known that substitutional diffusion is not strictly vacancy domi-nated, Fairs model is useful for the reasonable results it obtains without resorting to complex simulation.

The tewill take th

where D0 iArhen

1.6.1. DiAntim

ing. The in

The ex

and D+ and

and

The diAntim

con givingsion is retTable 1.3 pconditionsmperature dependence of the diffusivity values presented in the next several sections e arhenius form

(1.63)

s a pre exponential constant.ius equations form a straight line when ln(D) is plotted versus 1/T.

ffusivity of antimony in siliconony is believed to diffuse by a purely vacancy mechanism with the Sb+V- dominat-trinsic diffusivity of antimony is given by [6]

(1.64)

trinsic diffusivity of antimony is given by [6]

(1.65)

D= = 0, D0 and D- are given by

(1.66)

(1.67)

ffusivity of antimony versus temperature is illustrated in figure 1.13ony has a large tetrahedral radius of 0.136nms versus a radius of 0.118nms for sili- a 1.15 mismatch factor and creating strain in the silicon lattice [3]. Antimony diffu-arded by oxidation due to injected silicon self-interstitials annihilating vacancies. resents the ratio of antimony diffusivity under oxidizing (dry O2)and non-oxidizing

for a variety of times and temperatures [71].

Table 1.3: Oxidation retardation of antimony diffusivity [71]

Temperature (oC) Time (mins.) DOX/D*

1,000 500 0.20

1,000 1,500 0.18

1,100 10 0.25

1,100 60 0.30

1,100 600 0.44

D D0eE a/kT=

Di 0.214e3.65 /kT cm2/s=

Dx D0 D- nni

----+=

D0 0.214e 3.65 /kT cm2/s=

D- 15.0e 4.08 /kT cm2/s=


F a

1.6.2. DiArseni

componentable 1.2. Above appbeing relatdiffusivity

The in

At higArsenic atsection 1.7equations ~1,000oC ity

1x10-11igure 1.13: Diffusivity of antimony in silicon versus temperature and ntimony concentration. Calculated from equations 1.64 through 1.67.

ffusivity of arsenic in siliconc is believed to diffuse primarily through a vacancy mechanism with an interstitialcy t [7]. Estimates of the interstitialcy component of arsenic diffusion are presented in The arsenic interstitial formation energy is estimated to be a relatively high 2.5eV. roximately 1,050oC diffusion is dominated by As+V- vacancy pairs with As+V=

ively rare due to the small pair binding energy. Oxidation has little effect on arsenic due to the high arsenic interstitial formation energy.trinsic diffusivity of arsenic is given by [6]

(1.68)

h concentration (>1020 atoms/cm3) arsenic diffusivity is complicated by clustering. oms are believed to form clusters where 3 arsenic atoms bond with an electron (see - solid solubility). Clusters are virtually immobile at T


(1.69)

and, D+ an

Diffus

Arsenithe silicon

1.6.3. DiIn Fair

nism undesion are pr

Dx D0 D- nni

----+=d D= = 0, D0 and D- are given by

(1.70)

(1.71)

ivity of arsenic versus doping is plotted in figure 1.14.

Figure 1.14: Diffusivity of arsenic in silicon versus temperature and arsenic concentration. Calculated form equations 7.68 through 7.71.

c has exactly the same tetrahedral diameter as silicon and so arsenic does not strain lattice or induce enhanced diffusivity in other dopants for T > ~700oC.

ffusivity of boron in silicon's model of diffusion, boron is assumed to diffuse exclusively by a vacancy mecha-r non-oxidizing conditions. Estimates of the interstitialcy component of boron diffu-esented in table 1.2 and have recently been estimated at >98% [67].

D0 0.066e 3.44 /kT cm2/s=

D- 12.0e 4.05 /kT cm2/s=

800 900 1,000 1,100 1,2001x10-18

1x10-17

1x10-16

1x10-15

1x10-14

1x10-13

1x10-12

1x10-11

1021

1020

1019

Intrinsic

Temperature ( C)o

Diff

usiv

ity (c

m/s

)2


In Fairs model boron diffuses by a B+V- vacancy pair with a migration energy approxi-mately 0.5eV lower than other vacancy-ion pairs. Boron diffusivity is enhanced by p dopants when p > ni and reduced for p < ni, boron diffusion is actually retarded in N type silicon where n > ni.

The in

The ex

and D-

and

The diBoron

of 0.82nmmismatch and reduceimpurities tering ironboron diffenhanced b

The leoxidation e1.16 - 1.1atmospherintrinsic an

Boronoxide duri

1.6.4. DiThe di

mates of thphorus diftrinsic diffusivity of boron is given by

(1.72)

trinsic diffusivity of boron is given by

(1.73)

and D= = 0, D0 and D+ are

(1.74)

(1.75)

ffusivity of boron versus doping is plotted in figure 1.15 is a faster diffuser than either phosphorus or arsenic. Boron has a tetrahedral radius s versus 1.18nms for silicon or a 0.75 mismatch ratio [3]. The relatively large size for boron versus silicon produces lattice strain that can lead to dislocation formation d diffusivity. The strain introduced by boron into the silicon lattice can help to getter by a trapping mechanism. High concentrations of boron are particularly good at get-. Boron has a relatively low energy for interstitial formation of 2.26eV, therefore usivity is enhanced by oxidation. Figure 1.16 presents some data on oxidation oron diffusion.

ft side of figure 1.16 - 1.16a illustrates the increase in boron junction depth due to nhanced diffusion versus time for wet oxidation at 1,100oC. The right side of figure

6b illustrates the diffusivity of boron during dry oxygen oxidation versus an inert e versus temperature. Boron diffusion is enhanced during oxidation for both the d extrinsic cases [15].

forms stable oxides such as B2O5 and HBO2 and readily segregates into the growing ng oxidation processes.

ffusivity of phosphorus in siliconffusivity of phosphorus is again explained as a vacancy dominated diffusion. Esti-e interstitialcy component of phosphorus diffusion are presented in table 1.2. Phos-

fusion exhibits three distinct regions of behavior illustrated in figure 1.17

Di 0.76e3.46 /kT cm2/s=

Dx D0 D+ pni

----+=

D0 0.037e 3.46 /kT cm2/s=

D+ 0.76e 3.46 /kT cm2/s=


Figure 1.1

1x10-105: Diffusivity of boron in silicon versus temperature and boron concentration. Calculated from equations 1.72 through 1.75.

Figure 1.16: Oxidation enhancement of boron diffusivity [13],[14].

800700 900 1,000 1,100 1,2001x10-18

1x10-17

1x10-16

1x10-15

1x10-14

1x10-13

1x10-12

1x10-11

1021

1020

1019

Intrinsic

Temperature ( C)o

Diff

usiv

ity (c

m/s

)2

10-15

10-14

10-13

10-12

10-11

1,000 1,100 1,200Temperature ( C)o

Diff

usiv

ity (c

m /s)2

Non Oxidizing

Dry O Oxidation2

Wet Oxygen - 1,100 C0

1.2

1.4

1.0

0.8

0.6

0.4

0.2

00 1.0 2.0 3.0 4.0

X(

m)

j

Oxidation Time (hrs.)


.

The ph1. The hi

carrier2. A kink3. A tail r

In the noted as (Ptration cub

The in

In the

and D- ~ 0

Total Phosphorus ConcentrationFigure 1.17: Phosphorus diffusion profile and vacancy model [6].

osphorus profile illustrated in figure 1.17 has three distinct regions:gh concentration region where the total phosphorus concentration exceeds the free concentration. in the profileegion of enhanced diffusivity.high concentration region a fraction of P+ ions pair with V= vacancies as P+V= pairs V)-. The concentration of (PV)- pairs is proportional to the surface electron concen-ed (ns

3), which has to be determined experimentally.trinsic diffusivity of phosphorus is given by [6]

(1.76)

high concentration region the extrinsic diffusivity of phosphorus is given by [6]

(1.77)

, D+ = 0, D0 and D= are given by

(1.78)

Log

(Con

cent

ratio

n)

Excess VacancyConcentration

Emitter DipEffect

Kink

(PV) (PV) + e- 0 -->(PV) P + V0 + -

P V Pair Dissociation Region+ =

Electron Concentration, n

Tail RegionD = const. x n3s

ns

ne

0 Xo X

(V)-

(PV) n- s 3D n 2

Di 3.85e3.66 /kT cm2/s=

Dx D0 D= nni

----2

+=

D0 3.85e 3.66 /kT cm2/s=


and

(1.79)

Phospmismatch defect formdue to disFermi leveing energyflux. Otheinto questi

The el

The di

and

The di[6]

and

Figureextrinsic c

The sarus tail cfusions - s

The efing emitteincrease thareas. Thepush.

D= 44.2e 4.37 /kT cm2/s=horus has a tetrahedral radius of 0.110nms versus 0.118nms for silicon resulting in a ratio of 0.93 [3], and at high concentrations - phosphorus lattice strain can lead to ation. Fair and Tsai have proposed that tail formation in the phosphorus profile is

sociation of P+V= pairs when n drops below 1020 /cm3 at the diffusion front (the l is ~0.11eV from the conduction band), the V= vacancy changes state and the bind- decreases enhancing the probability of disassociation and increasing the vacancy r researchers have found evidence of interstitialcy diffusion for phosphorus calling on the physical correctness of the vacancy model [17],[18].ectron concentration in the transition or kink region is given by

(1.80)

sassociation of the (PV)- pairs increase the vacancy concentration tail by

(1.81)

(1.82)

ffusivity in the tail region increase as the V- concentration increases and is given by

(1.83)

(1.84)

1.18 illustrates the diffusivity of phosphorus versus temperature for the intrinsic and ases. Figure 1.19 illustrates the diffusivity of phosphorus in the tail region.me (PV)- dissociation mechanism that creates enhanced diffusivity in the phospho-an increase the diffusivity of dopants in junction pre-existing under phosphorus dif-

ee figure 1.20.fect of heavy phosphorus doping levels on co-diffusing species was first noted dur-r diffusion for bipolar transistors. The heavy phosphorus emitter was observed to e junction depth of the underlying boron doped base region relative to surrounding enhanced diffusion under the phosphorus emitters came to be known as emitter

ne 4.65 1021 e 0.39 /kT n/cm3=

PV( )- PV( )x e-+

PV( )x P+ V-+

Dtail D0 D-

ns3

ne2ni

---------- 1 e0.3/kT+[ ] cm2/s+=

D- 4.44e 4 /kT cm2/s=


Figure 1

Aboveduces lattitrates the iphosphorustrain efferesults.

The in

where (t)related to t

W0 is

1x10-10.18: Phosphorus diffusivity in silicon versus phosphorus concentration and temperature - high concentration region.

Calculated from equations 1.76 through 1.79.

5 x 1020 phosphorus atoms/cm3 the misfit lattice strain from the phosphorus intro-ce strain (band gap narrowing) and reduces (PV)- pair dissociation. Figure 1.20 illus-ncrease in boron doped base junction depth versus phosphorus content for a 1,000C s emitter diffusion. The solid line is the increase in junction depth excluding the ct and the dotted line includes the strain effect, the round circles are experimental

crease in base junction depth directly under the phosphorus diffusion is given by [21]

(1.85)

is the increase in junction depth under the emitter diffusion and W0 is a quantity he profile of the base diffusion prior to emitter diffusion.given by

800700 900 1,000 1,100 1,2001x10-18

1x10-17

1x10-16

1x10-15

1x10-14

1x10-13

1x10-12

1x10-11

1021

1020

1019

Intrinsic

Temperature ( C)o

Diff

usiv

ity (c

m/s

)2

t( ) W0 1 2DinB t

W02

-------------+ 1/2

1 2DiBt

W0--------------+

1/2=


(1.86)

where, Q0dopant priThe diffus

where, Dinphorus - npair.

Figure 1.1te

Phospboron) - se

W0 0.4Q0Cp0--------= is the integrated doping of the base, and Cp0 is the peak concentration of the base or to emitter diffusion.ivity of boron under the emitter region is given by

(1.87)

B is the diffusivity of the boron under the emitter, D0P is the diffusivity of the phos-eutral vacancy pair, and D-P is the diffusivity of the phosphorus - negative vacancy

9: Phosphorus Diffusivity in silicon versus surface electron concentration and mperature - tail region. Calculated from equations 1.78, 1.83 and 1.84.

horus diffusivity (both intrinsic and extrinsic) is enhanced by oxidation (similar to e figure 1.22.

DinB Di

BDP0 DP

-+

DP0

--------------------=

800700 900 1,000 1,100 1,2001x10-18

1x10-17

1x10-16

1x10-15

1x10-14

1x10-13

1x10-12

1x10-11

1x10-10

1x10-9

1021

1020

1019

Intrinsic

Temperature ( C)o

Diff

usiv

ity (c

m/s

)2


Fig

Figureent versus by varyingtion rates.increasing

Heavyphosphorusure 1.20: Enhanced diffusivity under heavy phosphorus doped regions - emitter push.

Figure 1.21: High concentration phosphorus induced strain effect on enhanced diffusion [21].

1.22 plots the ratio of diffusivity during oxidation to diffusivity under an inert ambi-oxidation rate at four different temperatures. The data in figure 1.22 was generated the oxygen partial-pressure and the initial oxide thickness to produce varying oxida- For a given temperature the degree of diffusivity enhancement increases with oxidation rate.

emitter

Region ofenhanced

borondiffusion

Region ofintrinsic

borondiffusion

12

10

8

6

4

2

00 0.4 0.8 1.2 1.6 2.0

Intrinsictheory

Straineffectincluded

C (10

cm)

s

2 0

-3

( m)


Fi

1.6.5. DiIn the

discussed est. Table

I

As

Au

Au (s

B

3.0gure 1.22: Phosphorus diffusivity enhancement versus oxidation rate. Adapted from [22]/

ffusivity of miscellaneous dopants in siliconpreceding four sections the diffusivity of the four most common silicon dopants was in detail. There are a a variety of other impurities whose diffusivity may be of inter-1.4 presents a compilation of diffusivity values.

Table 1.4: Diffusivity of miscellaneous impurities in silicon.

mpurity Temperaturerange (oC) D0 (cm2/s) Ea (eV) Mechanism Reference

Ag 1,100-1,300 2x10-3 1.6 Interstitial 23

Al 0.5

1,350

3.0

4.1

28

6

(intrinsic) 22.9 4.1 Vacancy 6

Au

(interstitial)

ubstitutional)

800-1,200

700-1,300

700-1,300

1.1x10-3

2.4x10-4

2.8x10-3

1.12

0.39

2.04

Interstitial 23

23

23


Bi 396 4.12 6

C 1.9 3.1 28

Co 900-1,200 9.2x10-4 2.8 25

D/D

OX

Oxidation Rate ( m/min)

1.0

1,000 C,990mins

o

(100) Si, dry O2 1,050 C,270mins

o

1,100 C,90mins

o

1,150 C,30mins

o

0.510-7 10-6 10-5 10-4 10-3


Figuregraph is us

As mesilicon lattspecie. Tab

Cu

O (

P

Sb

Si

Table 1.4: Diffusivity of miscellaneous impurities in silicon.

Impurity Temperaturerange (oC) D0 (cm2/s) Ea (eV) Mechanism Reference 1.23 presents the values from table 1.4 in graphical form versus temperature, the eful for comparing relative diffusivities.ntioned in previous sections, the size mismatch between a diffusing specie and the ice can result in lattice strain which may enhance the diffusivity of co-diffusing le 1.5 presents the relative sizes of selected impurities versus silicon.

Cr 1,100-1,250 0.01 1.0 24

Cu

(interstitial)

800-1,100 4.0x10-2

4.7x10-31.0

0.43

Interstitial

Interstitial

23

23

Fe 1,100-1,250 6.2x10-3 0.87 Interstitial 23

Ga 225 4.12 28

Ge 6.26x105 5.28 28

H2 9.4x10-3 0.48 Interstitial 23

He 0.11 1.26 28

In or Tl 16.5

269

3.9

4.19

28

6

K 800-1,000 1.1x10-3 0.76 Interstitial 23

Li 25-1,350 2.3x10-3

to 9.4x10-40.63

to 0.78

Interstitial 23

N 0.05 3.65 6

Na 800-1,100 1.6x10-3 0.76 Interstitial 23

Ni 450-800 0.1 1.9 Interstitial 23

O2interstitial)

700-1,240

330-1,250

7x10-2

0.17

2.44

2.54 Interstitial

26

26


Pt 800-1,100 1.5x102

to 1.7x1022.22

to 2.15

Interstitial 27

S 0.92 2.2 Interstitial 28


(interstitial) 0.015 3.89 Vacancy 6

Sn 32 4.25 28

Zn 0.1 1.4 Interstitial 28


Figu

1.6.6. DiPolysi

other. Witsilicon. In the grains.the grain b

1x10-3D

iffus

ivity

(cm

/s)

2re 1.23: Diffusivities of selected impurities in silicon versus temperature - see table 1.4.

ffusivity of impurities in polysiliconlicon is made up of grains of single crystal silicon randomly oriented relative to each hin the crystalline grains diffusion has characteristics similar to bulk single crystal the grain boundaries diffusion can proceed at 100 times the rate of diffusion within Because the grain boundaries dominate polysilicon diffusion, grain size and hence oundaries determine the diffusivity of impurities in the polysilicon film.

700600 800 900 1,000 1,100 1,200 1,3001x10-25

1x10-23

1x10-21

1x10-19

1x10-17

1x10-15

1x10-13

1x10-11

1x10-9

1x10-7

1x10-5H2

O2C

B

SiGe

NSn

As

P

Bi

GaIn

SbAl

Li

ZnAu

Pt

S

Ag

Ni

CuKCrHeFe Na

Co

Temperature ( C)o


The grysilicon dehistory of of grain bowidely andues for imp

Table 1.5: Size of impurity atoms relative to silicon [3].

Impur

As

B

P

Sbain size for polysilicon can range from 0.1 to 20ms in size and depends on the pol-position conditions and thickness, the underlying film, and the subsequent thermal

the film. Due to the number of variables that effect grain size and the dominant role undaries in polysilicon diffusion, diffusivities reported by various researchers vary it is difficult to make definitive predictions. Table 1.6 presents some reported val-urity diffusion in polysilicon.

Element Tetrahedralradius (nm)Size relative

to silicon

Aluminum 0.126 1.07

Gallium 0.126 1.07

Gold 0.150 1.27

Indium 0.144 1.22

Silicon 0.118 1.00

Table 1.6: Diffusivity for miscellaneous impurities in polysilicon [41].

ity Temperaturerange (oC) D0 (cm2/s) Ea (eV) Mechanism System Reference

700-1,050

800-1,000

800-1,000

750-950

700-850

950-1,100

700-1,000

0.28

8.4x104

1,700

8.6x104

10

0.63

1.66

2.8

3.8

3.8

3.9

3.36

3.22

3.22

-----

Tail region

Peak region

Grain-bound

Grain-bound

Combined

Combined

RTP

RTP

RTP

Furnace

Furnace

Furnace

Furnace

30

31

31

37

38

39

36

1,000-1,200 6.6x10-4 1.87 Grain-bound Furnace 32

800-1,000

1,100-1,200

900-1,100

700-850

700-1,100

700-1,050

1.9x10-2

4.0x10-3

5.3x10-5

44.8

1.0

1.81

1.76

1.71

1.95

3.4

2.75

3.14

Grain-bound

Grain-bound

Grain-bound

Combined

Combined

-----

RTP

Furnace

Furnace

Furnace

Furnace

Furnace

29

33,32

34

35

36

30

1,050-1,150

1,050-1,150

13.6

812

3.9

2.9

Bulk

Grain-bound

Furnace

Furnace

40

40


Figure 1.24 illustrate the diffusivity of selected impurity in polysilicon versus temperature from table 1.4 in graphical form to allow easy comparisons of relative diffusivities.

Figu

1.6.7. DiSilicon

figure 1.8.processingsilicon dio

Diff

usiv

ity (c

m/s

)2re 1.24: Diffusivities of selected impurities in polysilicon - see table 7.4.

ffusivity of impurities in silicon dioxide dioxide is often used to mask against impurity diffusion during pre-deposition - see Silicon dioxide may also become inadvertently doped by ion implantation during . It is therefore important to be able to calculate the diffusion of impurities through xide. Table 1.7 presents the diffusivity of selected impurities in silicon dioxide.

Table 1.7: Diffusivity of selected impurities in silicon dioxide.

Impurity D0 (cm2/s) Ea (eV) Source and ambient Reference

As 67.25

3.7x10-24.7

3.7

Ion implant, N2Ion implant, O2

43

43

Au 8.2x10-10

1.52x10-70.8

2.1

44

44

B 7.23x10-6

1.23x10-4

3.16x10-4

2.38

3.39

3.53

B2O3 vapor, N2+O2B2O3 vapor, Ar

Borosilicate

42

42

42

D2 5.01x10-4 0.455 46

Ga 1.04x105 4.17 Ga2O3 vapor, H2+N2+H2O 42

H+ 1 0.73 46

H2 5.65x10-4 0.446 44

700 800

SbP

P

P

AsAs Sb

As

P

P

As

B

900 1,000 1,100 1,2001x10-17

1x10-15

1x10-13

1x10-11

1x10-9

1x10-7

Temperature ( C)o


Figureson. The dambient dimplanted

1.6.7.1. As IC

has taken approximafeatures haachieved wdevices, thBoron is rgate oxidethreshold interaction

One teFluorine frof boron in

where, FHydro

where, H2

Table 1.7: Diffusivity of selected impurities in silicon dioxide.

Impurity D0 (cm2/s) Ea (eV) Source and ambient Reference 1.25 presents the diffusivity values from table 1.6 in graph form for easier compari-iffusivities presented in table 1.6 for arsenic, boron and phosphorus are nitrogen

iffusion values. Boron and phosphorus are vapor sources and arsenic is an ion source.

Diffusivity of boron in silicon dioxideminimum feature sizes have shrunk the diffusion of boron through silicon dioxide on an increasingly critical aspect. When MOSFET minimum features were above tely 0.5ms, the gate polysilicon was doped N-type with phosphorus. As minimum ve shrunk below approximately 0.5ms, adequate PMOS performance cannot be ithout doping the PMOS gate polysilicon P-type. For


Figure 1

Equatiicon dioxid

Borontherefore b

1.7. SoSteady

1x10-2D

iffus

ivity

(cm

/s)

2

+.25: Diffusivity of selected impurities in silicon dioxide versus temperature - data from table 1.7.

on 1.88 for fluorine effects and equation 1.89 for H2 effects on boron diffusion in sil-e are presented in the left and right side of figure 1.26 respectively.

diffusivity in silicon dioxide is also believed to be increased by SiO content and y decreasing silicon dioxide thickness [66].

lid solubility state solid solubility is defined as:

700600 800 900 1,000 1,100 1,200 1,3001x10-35

1x10-32

1x10-29

1x10-26

1x10-23

1x10-20

1x10-17

1x10-14

1x10-11

1x10-8

1x10-5

Temperature ( C)o

HHe H2

O2

H2O

D2

Na

OH

Au

RAs

SbB

Pt

Ga


The maximum concentration of a substance that can be dissolved in a solid at a given tem-perature.

Figure 1.

The fisilicon wathe solid saccurate d

The dadopant. Dosilicon lattdopant inttributes fredopant ma

1.7.1. So Arsen

is believedtemperatur

The m

10-19

1014

Bor

on

diff

usiv

ity (c

m/s

)2

10-18

10-17

10-16

10-15

10-14

10-1326: Effect of fluorine and hydrogen on boron diffusivity in silicon dioxide [66].

rst attempt to summarize experimental data for the solid solubility of impurities in s performed by Trumbore in 1960 [47]. Recently Borisenko and Yudin reexamined olubility curves for antimony, arsenic, boron and phosphorus utilizing newer more ata [48] - see figure 1.27.ta presented in figure 1.27 represents the solid solubility, not the electrically active pants introduced into silicon may occupy interstitial or substitutional positions in the ice, or form clusters, i.e. arsenic - see the next section. The method of introducing a o silicon and subsequent heat treatments determine the amount of dopant that con-e carriers, i.e., is electrically active. Prior to annealing a significant percentage of a y be electrically inactive.

lid solubility of arsenic in siliconic forms clusters when concentrations in silicon are in excess of 1020 atoms/cm3. It that 3 arsenic atoms and one electron form a cluster that is electrically active at high e and is neutral at room temperature [49].odel for clustering is

(1.90)

10-20

1015 0.001 0.01 0.1 1 10 100BF dose - F (atoms/cm )2 2 2 H (%)2

Bor

on

diff

usiv

ity (c

m/s

)2

1016

10-19800 Co

800 Co

900 Co 900 Co

1,000 Co 1,000 Co

1,100 Co 1,100 Co

10-18

10-17

10-16

10-15

10-14

3As+ e- high temp

As32+ room temp As3+


A genCmax versu

1.7.2. SoThere

be found e

1.7.3. SoAt hig

tion is give

Solu

bilit

y (at

oms/c

m)3

Trumbore [47] AsFigure 1.27: Solid solubility of common dopants in silicon. Summarized from [47],[48].

eralized model of arsenic clustering has been derived [50], and the expression for s temperature is given by

(1.91)

lid solubility of boron in siliconis no physical model for electrically active boron concentrations - the values have to xperimentally.

lid solubility of phosphorus in siliconh concentration the expression for the total electrically active phosphorus concentra-n by [44]

(1.92)

1021

1020

1019400 500 600 700

Temperature ( C)o800 900

Sb

Sb

B

P

PBorisenko and Yudin [48]

B

As

1,000 1,100 1,200 1,300 1,400

Cmax 1.896x1022e 0.453 /kT atoms/cm3=

CT n 2.4x1043 n3 atoms/cm3+=


where, n is the electron concentrations or electrically active phosphorus concentration. Equa-tion 1.92 is valid from 900 to 1,050oC.

For arsenic, boron, and phosphorus in silicon the maximum electrically active dopants match up w

1.7.4. SoFigure

ure 1.27. Tties are no

Ato

ms/

cm3ell with the solid solubility curves of Borisenko and Yudin presented in figure 1.25.

lid solubility of miscellaneous dopants in silicon. 1.28 present additional solid solubility data covering impurities not included in fig-he data in figure 1.28 comes from Trumbore [47], updated curves for these impuri-

t available.

Figure 1.28: Solid solubility of selected impurities in silicon [47].

1020

1019

1018

1017

1016

1015

Sn

AlLi

Ga

600 700 800 900 1,000 1,100 1,200 1,300Temperature ( C)o

Cu

Au

Zn

FeAg

Co

S

O


1.8. Deviations from simple diffusion theoryIn the preceding sections the basics of diffusion theory have been presented, in this section

the complications of selected real world diffusion problems will be examined.

1.8.1. ReIn sect

assumptionperformedfound thattion is dueimpurity forium is reawill be con Segreg

concenThe se

Anothimpurity incan escapthen the improfiles du

The thhas a segreresult in a

Figurewhere oxidthe oxide 1diffusivity

A theo1. The co2. Deep

tion of3. The se4. The im5. The ox

The redistribution of impurities during thermal oxidationion 1.5.2 the solution for two step or drive-in diffusions was presented. One of the s was constant Q during diffusion. It is very unusual for a drive-in diffusion to be

without simultaneous oxidation during at least some part of the cycle. It has been impurities are redistributed in silicon near a growing thermal oxide [55]. Redistribu- to several factors. If any two phases - solid, liquid or gas are brought into contact an und in either of the two phase will redistribute between the two phase until equilib-

ched. In equilibrium the ratio of the concentrations of the impurity in the two phases stant.ation Coefficient - the ratio of the concentration of an impurity in one phase to the tration of the impurity in a second under equilibrium.gregation coefficient m, for the Si - SiO2 system is defined as

(1.93)

er factor effecting impurity redistribution during oxidation is the diffusivity of the silicon dioxide. If the impurity has a high diffusivity in silicon dioxide the impurity e through the oxide layer. If the impurity has a low diffusivity in silicon dioxide purity will be trapped in the silicon. Figure 1.29 illustrates four possible impurity

e to oxidation.ird factor in redistribution is the moving oxide-silicon interface. Even if an impurity gation coefficient of 1, the increase in volume occupied by oxide over silicon will

decrease in the impurity concentration in the oxide layer. 1.29 illustrates four cases of impurity segregation. 1.29a and b illustrate the cases e takes up the impurity with low diffusivity in the oxide 1.29a, and fast diffusivity in .29b. 1.29c and d illustrate the cases where the oxide rejects the impurity with low

in the oxide 1.29c and fast diffusivity in the oxide 1.29d.ry on the redistribution process has been proposed [56]. The assumptions are:ncentration of the impurity at the oxide-gas boundary is constant.inside the silicon the impurity concentration approaches the background concentra- the silicon.gregation coefficient ratio is maintained.purity is preserved at the oxide-silicon interface.idation rate is parabolic and given by:

(1.94)

sulting expression for the concentration on the silicon side of the interface is

m Equalibrium concentration of impurity in siliconEqualibrium concentration of impurity in silicon dixoide----------------------------------------------------------------------------------------------------------------------------------------=

xo Bt=


(1.95)

and

and

where, D iness of siliesting feairrespectiv

Fig

Table 1.7 pBased

concentrat

CSCB------

1 CO CB( )+1 1 m ( ) 2B 4D( )erfc B 4D( ) B 4D m+exp+-------------------------------------------------------------------------------------------------------------------------------------------------------------=(1.96)

(1.97)

s the diffusivity in silicon, DO is the diffusivity in oxide, is the ratio of the thick-con consumed during oxidation to the thickness of oxide produced (0.45). One inter-ture of the theory is that the interface will reach a steady state concentration e of oxidation time.

ure 1.29: Impurity redistribution in silicon due to thermal oxidation [5].

resents some values for segregation coefficient. on equations 1.95 through 1.97 and the values in table 1.7 the ratio of the surface ion of impurity to the background concentration can be calculated.

r 2r2 1( )B 4Dr2[ ]erfc B 4D( )exp

erf B 4DO( )------------------------------------------------------------------------------------------------------

r DO D

1.0

1.0

1.0

1.0

Oxid

eO

xide

Oxid

eO

xide

Silicon

a) diffusion inoxide slow -Boron

c) diffusion inoxide slow -Antimony, Arsenic,Phosphorus

b) diffusion inoxide fast -Boron with H2

d) diffusion inoxide fast -Gallium

Silicon

Silicon

Silicon

1.0

1.0

1.0

1.0

0

0

0

0

x( )

x( )

x( )

x( )

C/CB

C/CB

C/CB

C/CB

Oxide takes up impurity (m < 1)

Oxide rejects impurity (m > 1)


Figurephosphorusegregatiothrough 1.and phosp

Figure 1.

Table 1.8: Segregation coefficient of impurities at the silicon-silicon dioxide interface.s 1.30 through 1.32 illustrate the segregation phenomena for arsenic, boron and s under oxygen and steam oxidation conditions. In each case steam creates a greater n phenomena due to the greater oxidation rate of steam over oxygen. Figure 1.30 32 are calculated from equation 1.95 using Grove's values for segregation for arsenic horus [56] and Kolby and Katz value for boron (100) [57].

30: Surface concentration versus temperature for arsenic following oxidation.

Impurity Segregation coefficient Reference

As ~10

~800

~1,000-,2000

56

58

59

B ~0.3

0.03exp(0.52/kT) for (100)

0.05exp(0.52/kT) for (111)

~0.1-0.3

56

57

58

59

P ~10

~2,000-3,000

56

59

Sb ~10 56

5.0

C/C S

B

4.0

O2

H2O3.0

2.0

1.0

0.0900 1,000

Temperature ( C)o1,100 1,200

CSCB

SiO2

Originalinterface


Figure 1

F

0.5.31: Surface concentration versus temperature for boron following oxidation.

igure 1.32: Surface concentration versus temperature for phosphorus following oxidation.

C/C S

B

0.4O2

CSCBSiO2

Originalinterface

H2O

0.3

0.2

0.1

0.0900 1,000


5.0

C/C S

B

4.0

O2

H2O

3.0

2.0

1.0

0.0900 1,000


CSCB

SiO2

Originalinterface


The distance over which the segregation effect influences the impurity profile is the diffu-sion length given by 2 times the square root of Dt. Figure 1.33 illustrates boron segregation ver-sus oxidation temperature [60].

Figure 1.3

1.8.2. DiThe di

diffusion. layer to bthrough w

Duringblocked bycally, alsotwo dimennormal to illustrates diffusion -

1.8.3. OIf a sil

determine late the oxlayer schem3: Calculated boron concentration versus distance after dry oxygen oxidation to produce a 0.2m thick oxide at various temperatures [60].

ffusion through an oxide maskffusion discussions presented in preceding sections are all based on one-dimensional During pre-deposition - the deposition process is made selective by utilizing an oxide lock pre-deposition in unwanted areas and to diffuse the dopant into the silicon indows in the oxide where the dopant is desired (see figure 1.34). pre-deposition the dopant enters the silicon where the oxide is missing and is the oxide where the oxide is present. The dopant diffusing into the silicon verti-

laterally diffuses under the oxide window. Solving the diffusion equations for the sional problem reveals that dopant diffuses more slowly parallel to the surface than the surface (the parallel diffusion is 75 to 85% of the normal diffusion). Figure 1.35 equal concentrations contours for a pre-deposition (complementary error function) figure 1.35a and a drive-in (gaussian) diffusion - figure 1.35b.

xide thickness to mask against diffusionicon dioxide layer is utilized to create a selective doping process it is necessary to the thickness of oxide required to block the pre-deposition process. In order to calcu-ide thickness required to block deposition, consider pre-deposition through an oxide

atically illustrated in figure 1.36.

1.0

0.892

0Co

1,00

0Co

1,100

Co

1,200 Co

0.6

C/C B

Distance from the Si-SiO interface ( m)2

0.4

0.2

00 0.5 1.0 1.5 2.0


The as1. The co

consta2. The co3. The ra

by the4. The flu

LateralLateral

0

0.5

1.0

1.5

2.0

2.5

3.0

3.52.5

a

y/2

DtFigure 1.34: Pre-deposition through a silicon dioxide window.

Figure 1.35: Lateral diffusion profiles [52].

sumptions used to solve the problem are:ncentration at the surface of the oxide layer Co and the oxide thickness xo are both nt throughout the pre-deposition process.ncentration goes to zero deep inside the silicon.tio of the concentrations on either side of the oxide-silicon interface are determined segregation coefficient m. x of impurities through the interface is continuos.

DD

D DD D

D D

DD

D

DD

D DD

D

D

DD

D

D D

D

DD

DDD

D

WindowDopantgas

Silicon

diffusiondiffusion

Diffuseddopant

Silicon Dioxide Silicon Dioxide

0.50.9

0.30.75

0.10.6

0.03

0.50.3

0.010.1

0.0030.03

0.0010.01

0.00030.003

0.0001

0.001

0.0003

0.0001

C/CsC/Cs0

0.5

1.0

1.5

2.0

2.5

3.0

3.52.52.5 2.52.0 2.02.0 2.01.5 1.51.5 1.51.0 1.01.0 1.00.5 0.50.5 0.50 0

C =consts

) Complementary error function b) Gaussian

Total Dopants = const

y/2

Dt

x/2 Dt x/2 Dt


Fig

The sothat

then the so

The sointo equati

and

The ox= 0 in equpre-deposi

C(x, t)ure 1.36: Impurity distribution from pre-deposition through an oxide [5].

lution to this problem is given by an infinite series [53]. For small values of x such

(1.98)

lution may be approximated by the first term in the series [5]

(1.99)

lution for the junction depth xj is given by the conditions which when substituted on 1.99 result in

(1.100)

(1.101)

ide thickness required to mask against pre-deposition can now be found by setting xjation 1.100 Figure 1.36 presents empirical data on oxide thickness to mask against tion [54].

CO

Oxide SiliconxO xj

CB

x = 0x

x D DOxO

C x t,( )CO

---------------- 2mrm r+-------------erfc

xO2 DOt----------------- x

2 Dt-------------+=

xjt

-----1r---xOt

------ I+=

I 2 Dm r+( )CB2mrCO

-------------------------arg


1.8.4. Diffusion from a uniformly doped oxide layerA doped oxide layer can be deposited on silicon and used as a doping source. Figure 1.38

presents a schematic representation of diffusion from a doped oxide layer.For rel

then

and

For lon

0

0.

0.0

Oxi

de M

askT

hick

ness

(m

)atively short diffusion time such that

(1.102)

(1.103)

(1.104)

Figure 1.37: Oxide thickness to mask against deposition [54].

ger diffusion times or thin oxide [61]

(1.105)

xO 4 DOt>

C x t,( ) CO DO D1 k+( )----------------------------erfcx

2 Dt-------------

k 1m---- DO D=

10

1

.1

01

0110 100

Time (minutes)1,000

Boron - 900 Co

Boron - 1,000 CoBoron - 1,100 Co

Boron - 1,200 CoPhosphorus - 900 CoPhosphorus - 1,000 CoPhosphorus - 1,100 CoPhosphorus - 1,200 Co

C 0 t,( ) COrmm r+-------------- 1 2erfc O( ) 2erfc 2O( )+[ ]


and

(1.106)

where

and

Figu

1.8.5. SoIt is of

depth for p

and for dri

C x t,( ) COrm-------------- erfc ( ) 2erfc +( ) erfc 2 ( )+[ ](1.107)

(1.108)

re 1.38: Schematic of diffusion from a uniformly doped oxide layer [61].

lving for junction depthten useful to define a diffused impurity profile by the junction depth. The junction re-deposition is given by

(1.109)

ve-in by

(1.110)

m r+ O O

O xO2 DOt-----------------=

x2 Dt-------------=

CO

C , DOX O

C, D

C (0, t)OxC (0, t)

C(x, t)Oxide Silicon

xO xj

CB

x = 0x

xj 2 Dt erfc1 CS CB( )=

xj 4Dt Q CS Dt( )ln[ ]1/2=


1.8.6. Successive diffusionsDuring integrated circuit fabrication multiple high temperature processes are used in suc-

cession. Each subsequent thermal process further diffuses any impurities present in the silicon substrate. T

1.8.7. RaIn ord

wafers arethen the freferred toonce againMost commfusion furnfurnace caabove the caes. The 1.7.

For a cof degreesramping mramp furnathe import

Assum

where, TprThe efhe effect of successive diffusions is calculated by summing the Dt as follows

(1.111)

mpinger to prevent crystallographic damage and wafer warpage due to thermal gradients, most commonly inserted into diffusion furnaces at a relatively low temperature and urnace temperature is increased to the process temperature at a controlled rate - as ramping the furnace. At the completion of processing the furnace temperature is ramped down to a lower temperature for the wafers to be removed from the furnace.

only a temperature of 750oC is used for inserting and removing wafers from a dif-ace. 750oC provides manageable thermal stresses, is a temperature from which a

n reach a process temperature and return in a reasonable amount of time, and is transition temperature for devitrification of the quartware commonly used in furn-ramp rate employed in different types of thermal processors are presented in table

onventional furnace the time to ramp from 750oC to a process temperature hundreds higher can result in significant Dt during ramping, the Dt resulting from furnace ay be calculated as follows [2] (note here that the much faster ramp rates of rapid ces and rapid thermal processor systems allow Dt during ramping to be minimized,

ance of low Dt ramping will be discussed in chapter 8)e a furnace is being ramped down at a linear rate C such that

(1.112)

oc is the processing temperature from which the ramp occurs.fective Dt is therefore

(1.113)

Table 1.9: Thermal processor ramp rates

Processor Ramp up rateRamp down

rate

Conventional batch furnace 5-10oC/min. 2-3oC/min.

Rapid ramp batch furnace 80-100oC/min. 60oC/min.

Single wafer rapid thermal processor 25-100oC/sec. 30-50oC/sec.

Dttot D 1t1 D2t2 D3t3 + + +=

T t( ) Tproc Ct=

Dt( )eff D t( ) td0

t0

=


where the ramp down occurs for a time t0. Given that ramping is typically carried out until the diffusivity is negligibly small, the integral can be approximated by taking the upper limit as infinity, since

and substit

where, D(Tthe upper i

1.8.8. DeCurren

impurities dope polysfor genera

Henrycentration,

where H isThe su

(until the sdeposition

The gavoided fotion systemarsenic forBoron and

Boronorder to innitrogen isfraction of

D(1.114)

uting equation 7.114 into the arhenius equation for diffusivity, equation 1.63, gives

(1.115)

proc) is the diffusivity at Tproc. Substituting into equation 1.113 and using infinity as ntegration limit gives

(1.116)

position from a gas phaset state-of-the-art integrated circuit fabrication utilizes ion implantation to introduce into silicon, however trailing edge processes may still utilize gas phase deposition to ilicon. Legacy processes still in use may also utilize gas phase deposition processes

l doping. 's law relates the partial pressure of the impurity in the gas phase p to the surface con- as

(1.117)

Henrys gas law constant.rface concentration therefore depends on the partial pressure of the dopant in the gas urface reaches solid solubility). Same of the candidate doping sources for gas phase are listed in table 1.9.aseous sources listed in table 1.9, arsine, diborane and phosphine are generally r open furnace use due to their high toxicity (these gases are used in closed deposi-s for in-situ doping - see chapter 10). the most commonly used sources are spin-on

buried layers, boron tribromide and phosphorus oxychloride for junction formation. phosphorus solid source discs are also widely used. tribromide and phosphorus oxychloride are both liquids at room temperature. In troduce these sources into a diffusion furnace as a gaseous source an inert gas such as bubbled through the liquids at a controlled flow rate and temperature. The mole dopant entering the gas is given by

(1.118)

1T---

1Tproc Ct------------------------ 1

Tproc------------ 1 Ct

Tproc------------ + + =

t( ) D0Ea

kTproc--------------- 1 Ct

Tproc------------ + + exp D Tproc( )e

CEa/kTproc2( )t

= =

Dt( )eff D Tproc( )kTproc

2

CEa---------------

CS Hp=

MplVC

pC 22 400,------------------------------=


where, M is the molar flow rate in moles/min., pl is the vapor pressure of the liquid at the bub-bler temperature in mm of Hg, pC is the pressure of the carrier gas in mm of Hg (mm of Hg equals PSI multiplied by 51.715), VC is the flow rate of the carrier gas in cm3/min., and 22,400 is the cm3

Figureride and ph

From editions for

The pr

and the pre

In bothproduced. The oxyge

Dopant

As

B

Pper mole at standard temperature and pressure.

s 1.39 presents the vapor pressure curves for boron tribromide, phosphorus oxychlo-osphorus tribromide.quations 1.117 and 1.118 and the data presented in figure 1.39 the appropriate con-

pre-deposition can be calculated. eliminary deposition reaction for phosphorus oxychloride is

(1.119)

liminary deposition reaction for boron tribromide is

(1.120)

reactions a glass layer is formed on the wafer surface and a volatile gas product is Both chlorine and bromine gas can etch silicon if sufficient oxygen is not present. n causes oxide to grow on the wafer surface both incorporating phosphorus or boron

Table 1.10: Pre-deposition sources

Dopant source FormulaUsable

concentrationrange

Temperatureof source

duringdeposition

State atroom

temperature

ArsineArsenic trioxideSpin-onDiscs

AsH3As2O3

High

High

Medium

Low to high

Room temp

200 to 400oC

Room temp

850 to

1,200oC

Gas

Solid

Liquid

Solid

Boron tribromideBoron trichlorideDiboraneSpin-onBoron nitride

BBr3BCl3B2H6

Low to high

Low to high

Low to high

Low to high

Low to high

10 to 30oC

Room temp

Room temp

Room temp

850 to

1,200oC

Liquid

Gas

Gas

Liquid

Solid

Phosphorus pentoxidePhosphorus OxychloridePhosphorus tribromidePhosphineSpin-onDiscs

P2O5POCl3PBr3PH3

Very high

Low to high

Low to high

Low to high

Low to high

Low to high

200 to 300oC

2 to 40oC

170oC

Room temp

Room temp

Low to high

Solid

Liquid

Liquid

Gas

Liquid

Solid

4POCl3 3O2 2P2O5 6Cl2+ +

4BBr3 3O2 2B2O5 6Br2+ +


and liberating phosphorus or boron to diffuse into the wafer. Following pre-deposition the wafer surface is covered with a highly doped glass layer that must be removed by a hydrofluo-ric acid based de-glaze prior to drive-in. During pre-deposition the inside of the furnace tube is also coatedprior to usethe silicon

Fig

The eqsemiconduported to ttion is mewhich for accounting

where

and, hG is

C--- with dopant containing glass. Furnace tubes will typically be saturated with dopant for pre-depositions as saturating the tube helps to insure that the dopant is present at

surface in quantities high enough to insure the silicon is doped to solid solubility.

ure 1.39: Vapor pressure curves for liquid pre-deposition sources [62].

uations for pre-deposition presented in section 1.6.1 assume that the surface of the ctor is at some concentration CS at time zero. In practice the dopant must be trans-he semiconductor surface and diffuse into the semiconductor before the initial condi-t. The time to reach the initial surface doping level is approximately 1.2 minutes short deposition times can be significant [5]. It can be shown that the solution for the initial transport period is [5].

(1.121)

(1.122)

the gas phase mass transfer coefficient.

01

10

100

Temperature ( C)o

Pres

sure

(mm

Hg)

PBr3

POCl3BBr3

atmospheric pressure

1,000

25 50 75 100 125 150

x t,( )CS

------------- erf x2 Dt------------- e ht/ Dt[ ]

2

e ht/ Dt( ) x2/ Dt( )erfc htDt

---------- x2 Dt-------------++=

h hG HkT=


For

(1.123)

equation 1

1.8.9. ReBipola

are formedcussed in cfrom the subution dur

The so

Diffusion in Silicon

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