The influence of the electrical properties of the solid phase on impurity incorparation during crystal growth

Journal of Crystal Grow¢h 13/14 (1972) 818-822 © North-Holland Publishb, I Co.

818

THE INFLUENCE IMPURITY

OF THE ELECTRICAL

INCORPORATION

DURING

PROPERTIES CRYSTAL

OF THE SOLID PHASt

ON

GROWTH

H. C. CASEY, Jr. and M. B. PANISH

Bell Telephone Laboratories, Incorporated, Murray Hill, New Jersey" 07974, U.S.A. Control of impurity ;ncorporation during crystal growth requires consideration of the relationships o, ~¢en the concentration o f the impurity in the ~iquid phase and its concentration in the growing solid phase. ,t the solid-liquid interface, the surface space-charge layer in the solid has been found to dominate the inco p0ra. tion of slowly diffusing impurities. For extrinsic conditions, the amount of slowly diffusing impur ty incorporated ,n the solid varies linearly with the amount in the liquid. Detailed analysis in terms of the st trace. space charge layer is given for GaAs liquid-phase epitaxial layers doped with radioactive "reTM. Nt,~ only is this linear dependence observed for all the group VI donors S, So, and To, but also for the slowly ditiusin acceptor G e For Te in GaAs, the distribution coefficient goes from greater than unity at low temperatur¢~ Io le. : than tinily at high temperatures. Rapidly diffusing impurities are not influenced by the surface spacecharge layer, and for singly ionized substitutional acceptors or donors the amount ofimpurity incorporated into the extrinsic solid is ¢ xpected to vary as the square root of the amount in the liquid. This square.r001 behavior has been obscr-,L .l for the acceptor Zn which diffuses rapidly in GaAs.

I. Introduction

in the preparation and growth o f materials for electronic components and devices, a primary consideration is the removal or the controlled introduction of dilute anaounts of impurities into a host material. Control of impurity incorporation requires consideration of the relationships between the concentration of the impurit3 in the liquid phase and its concentration ,n ttae gro~ing solid phase. This paper describes recent ~tudies in the III V compound semiconductor GaAs ~hich permit the derivation of fundamental concepts for the manner in which the electrical properties of the ~olid phase influence impurity incorporation. Treatment o f impurity incorporation in semiconductors requires consideration of the properties of both the liquid and solid phase. It has been shown by Thurmond ~} and Thurmond and Kowalchik 2) that the binar~ liquid phase of an impurity element with Ge or S, ma} be described by regular solution activity coetficients. Jordan -~) e.~.tended these regular solution calculation.~ to the tee nary liquidus isotherms for G a - A s Zn and Ga P Zn. These thermodynamic treatments adequately descril~e the experimental iiquidus data. The retrograde solidus for the binary Go- impurity and Si-impurity systems was expiator6 by Thurmond and Struthers 't) in terms of regular solution theory. The concepts utilized to :tescribe the ii~cidus and retrograde

solidus are strictly thermodynamic and are not unique to semiconductors. It was shown b y R e i s s and Fuller s) that the ionization of impurities in semiconductors led to departures from the solid solubility expected on the basis of th~ simple thermodynamic concepts described above. They demonstrated that the solubility of Li in Si was als0 dependent on the position of the Fermi level in the semiconductor bulk, where the Fermi level is the dcctron (or hole) chemical potential. Extension ,,f I1~ Reiss and Fuller concepts to the incorporation of .in~]., ionized substitutional impurities in extrinsic GaAs leads to a prediction of a square-root depende¢ ce of the amount of impurity in the solid on the amo nt in the liquid, which agrees with the experimental observed bet.avior of Zn in GaAs °) but disagrees ~ h th~ observed linear dependence for Te in GaAs7). Analysis by Zschauer and Vogel sj shows tl- I the impurity diffusivity in the solid divided by the ~v th of the surface space-charge region must exceed the ; ~x~th rate in order for the liquid phase to be in equil liul~ with the semiconductor bulk. This criterion is apl re,lily met for Ihe rapidly diffusing Zn in GaAs but ~f0r the slowly diffusing Te in GaAs. In this latter '~ ,c. it was shown by Casey et al. 7) that the position ! the Fermi level at the surface dominates the incorp~ ~ti0~ of Te in GaAs. The position of the Fermi level t the surface may be obtained by treating the solid iquid

XVi - 5

THE INFLUENCE OF THE E L E C T R I C A L PROPERTIES

int xface as a metal-semiconductor Schottky barrier. TI : important result described by the above descussion is hat the position of the Fermi level does influence tht incorporation of impurities in semiconductors, as su~ ~ested by Reiss and Fuller ~) However, it is the im .urity diffusivity in the solid that determines whether it i the Fermi level at the surface or in the semicondu, tor bulk that enters the sol-bility equilibrium reL tionships. , n additional consideration occurs at high impurity cot ,:entrations in the solid. The interactions of the free cht :ge carriers at high concentrations affects the positio~ of the Fermi level. For Zn in GaAs, the diffusivity in the solid is sufficiently rapid to ensure equilibrium between the liquid and the semiconductor bulk. However, the effects of the high impurity density influence the solubility equilibria through the decrease in the hole activity coefficient. These two examples, Te in GaAs and Zn in GaAs, demonstrate the manner in which the dectrieal properties of the solid may be included in the equilibrium relationships for the impurity ir~corporation during crystal growth. 2. The surface space-charge layer Analysis by Zschauer and Vogel ~) has shown that /)). (diffusivity D and reciprocal intrinsic Debye length 2) must exceed the growth rate t, for the semiconductor bulk to be in equilibrium with the liquid pha~e. When D). < r, the liquid is in equilibrium with the ,urfacc, while for growth rates between these limits, the impurity incorporation is growth rate dependent. Yh,. reciprocal intrinsic Debye length is given as ;. :

(qZni/ekT)½

Wi ~ n , = 5 × l O

far of an, e~v int lh~ in

(I).

.

17 cm 3

(reE 9), ~ : = I . ! × 1 0 - ~ -

I/cm, k. at 1000 "C is ~ 10 ° cm -z. The actual width e space-charge layer depends on both temperature impurity density in the solid. Therefore, it is not ely clear at the present time whether or not the nsic Debye length is the correct quantity to use for ~pace-charge layer width when the concentration ~e solid is varied under extrinsic conditi~ms. ~e surface space-charge layer at the solid-liquid inl ~face for a heavily doped n-type senaiconductor is. ~own in fig. i. This space-charge layer at the surface of he solid is due to surface states that result fiom di~ uption of the lattice periodicity by the surface and

819

LIQUID SEMICONDUCTOR

~,...._

E¢

firrgJ~

~__

w

't

Eg

Ef

Ev

F~STANCE

Fig. l. Energy-band diagram for a liquid n-type semiconductor interface with a surface space-charge layer width w. The separation between the valance band E~ and the conduction band k,', is the energy gap Eg. The Fermi level is Ef and the barrier height fin, is the position of Ef at the liquid-semiconductor interface.

the unsaturated or dangling bonds of the surface atoms ~o). The surface states result in levels within the energy gap which are characteristic of the surface, and ti~ey tend to compensate the donors (or acceptors) and control the position of the Fermi level at the surface. The significant quantities are the barrier height ~ , which is the separation in energy of the Fermi-level and the conduction band edge at the surface, and the width w of the space-charge layer. Because of the higl~ density of conduction electrons in the liquid, this interface is considered to behave as a metal -semiconducto~ Schottky barrier. It has been observed ~1"~'~) that th~ position of the Fermi level at the surface remains al fixed energy above the valence band as the temperatur~ varies: E~{T ) - q~n,,(T) = constant,

(2

where Eel T) is the lemperalure dependent energy gap 3. Tellurium in GaAs For the incorporation of Te in GaAs at 1(/00 C b: liquid-phase epitaxy, D ~. 10 -I-~ cm2~ec ~ref. 131 2 ~ 10"/cm, and t, ~ 10- ~' cmsec. Therefore. D,~ ~ i approximately 0.1, and the liquid should be in cqmh brium with the surface rather than the .scmiconducto bulk. The reaction lbr Te incorporation during liquid phase epitaxial growth may then be described b~') Tc (t)+ V,,~ ~ Tc

(,,)'-Fc-

(?

In this reaction, Tc in the liquid le (t) is taken to reac

XVI -- 5

820

H . C . C A S E Y , J R . A N D M, B. P A N I S l l

10~o

I

~ ! ! 1111|

A

0 99,$% 80%

1

, !

1

'i fi1','~t'q'

' |l,|

/

I[NRICHEO Te 128 ENRICH(B

Te 128

'

10

~" ,.. f ¢ , r ~

..... '~

'

I

I

'

'i'

''~

"t

f

0 Z

000 ~ C tO ~

'

/

l.,Z

Q

• o

I

m

~. i o - I ~=. r..

z

0 iOtt

I

I I illll|

10-s

I

,o -~

I

I IIIIII

I

,o-'

ATOM F f l t A C T I O N IN / I O U l ( ]

I

I Illli|

, o "s

..1.

I I

I:1

~6 ~

0,6

Fig • ~... "~ A portion o f the 1000 ' C solid-solubility isotherm for Te in GaAs.

with an As vacancy VA~to give an ionized substitutional donor on an As site Te(~) + and a free carrier electron e - . Since the As vacancy concentration is proportional to the activity o f Ga in the liquid 7G~Xc~(/), the equilibrium relationship for eq. (3) may be written as

Kt(T) =

---, 7 T e ( E ) ,'~

...............

io -~'

XT,(! I

(4)

Te(f))~Gaft )XGa(/) '

where 7~ is the activity coefficient of clect~'ons in the solid, n is the electron concentration, and 7T~C~ and CT~,.~ are the activity coefficient and concentration of Tee ,)" on As sites. The quantities 7T¢~r~and 7G~(/) are the activity coefficients for Te and Ga in the liquid• 1~ is convenient to express CT¢~) in units of atoms/cm 3 and the concentrations of the composition in the liquid, XTet/I and XG~(e~, as atom fraction. For discussion o f the incorporation reaction, it is useful to simplify eq. (4). For the experimental data to be considered here, the solid solutions of Te in GaAs are dilute with maximum concentrations of about 5 x 10' 9 era- ~ (0.1 at °,/3; therefore, Henry's law should be obeyed and 7 T , ~ is taken as constant. Also, the Te concentrations in the liquid are quite low, and XG~r~ is essenti~, :;' cGnstant at 0.88 atom fraction. Therefore, 7r¢t¢~ and 7G~er~'t,,~,~ may also t:e taken as constant. Treatment of the elect~.'m activit~ coefficient by Hwang and Brews t*) shows that 7, ;s relatively cGnstant at a value of approximately 0.4 at 1000 °C in the concentration range [email protected] her,:, l~q. (4) reduces to the simple expression

t

I 0.7

,

I 0.8

RECIPROCAL

I

, I,

,,i

0.9

TEMPERATuRF,

I

i

t.O

i I.l

i

1.2

i O $ / T { e K -~)

Fig. 3. The distribution coefficient of Te in G a A s as a flmcti0n o f temperature. ( e ) Refi 7; Ell) Ref. t6; (&) Ref. 17.

K2(T) = Cr,~)n / X Tcv)

(51

for no complex formation occurring at the growth temperature, and with the Te concentration in excess of the intrinsic carrier concentration ni. For the liquid phase in equilibrium with the semiconductor surface, n is a function of temperatm'e only and is given byl:t

n = N, exp ( - ~ B , / k T ) ,

(6)

where N~ is the effective density of states in the conduction band. Eq. (5) may now be written as ('r~,~ = K , ( T ) Xr~r~/N ` exp ( - 66,,/kT),

(7t

and hence CT,t.,) varies linearly with XTa¢~ at a !given temperature. This predicted linear depender:e is demonstrated by a portion of the 1000 °C solid so ~bility isotherm shown in fig 2. The data shown i this figure wer,~ obtained from liquid-phase epitaxial tyers grown in a closed system and were doped with tdi0active T e 129m. The agreement between eq. (7) a t the experimental data verify that when D2 < v, it ; the position of the Fermi level at the surface rather t t n in the semiconductor' bulk that dominates the in' t,.rily incorporation. Because of the linear dependence of Te, a di ;ibtttion coefficient may be assigned at each tempe ture. Kang and Greene' 6) determined the distribution ~eflicient in an open system between 700 and 850 C by measuring the electron concentration and ass, thing

XV! - 5

T H E I N F L U E N C E OF T H E

ELECTRICAL

th~ t CT,(~) = n. Milvidskii and Pelevin ~?) determined tht distribution coefficient at the melting point by ch, rnieal analysis. Fig. 3 is a plot of data from refs. 7, 16 and 17 and illustrates the interesting result that the dis ribution coefficient increases at lower temperature. N~ :e that the distribution coefficient goes f r o m greater th~ a unity at low temperature to less than unity at high te~ perature. I should be noted that a linear dependence between the a m o u n t of impurity in the liquid and in the solid ha.' also been observed for the group VI donors S (tel, 17) and Se (refs. 17 and 18). The linear dependence is not unique to donors and has been observed for the group IV acceptor Ge in GaAsl')). The c o m m o n prol~rty of these impurities in GaAs is that they all diffuse slowly. 4, Zinc in GaAs Zinc in GaAs is an example of the incorporation of a rapidly diffusing impurity. At Zn concentrations in excess of 10 la cm -3 at 1000 °C, D > 10 - ~ cm~/sec (ref. 20). Therefore, with 2 ~ 106 cm -t and v ~ 10-* cm/sec, D2/v > 10, and the liquid phase should be in equilibrium with the semiconductor bulk. The incorporation of Zn in the liquid Z n ( O into a Ga vacancy VG, as a singly ionized substitutional acceptor Zn(~)- ' on a Ga site plus a hole e + is represented by 6) Zll(i)q-Vfi~, ~

Znt.D-

+e

+ .

(8)

Sin
=

.

7z"(~iCz"('i~)~P ........

(9)

7 Zn(i )X zn(/ )~As(~')X^~,(() "

wh e ),~, is the activity coefficient of holes in the solid, p i, the hole concentration, and 7z,(o) and Cz,(~) are the ~ctivity coefficient and concentration ofZn(.,)- ~ on Ga ites. The quantity )'z,(e) and "L~,(<) are the activity cot ieients for Zn and Ga in the liquid. I !. (9) may be simplified by assuming Henry's law apt ies for Zn in the solid so that ?z,(,,) may be taken as, )nstant and included in Ka(T) as K,dT). For (xtrinsic -'onditions and fully ionized Zn in the solid, the co~ ,tition of electrical neutrality may be expressed by C~ ,,) = p. The solid solubility of Zn is then given by Cz,.(~) =

[K~3(T)yznIe)Xzn(t)'gA~(t)XA.~(t)/])I~ ] ½.

(I0) IKV!

821

PROPERTIES

I0 II .'i'

) ~IZn~

) '~1

)

"

))1

)

~ ~)1

'

) )

'E iJ

/

\

.,,¥"d~%

~owc

z

ill

~°o-~

I

I III

I

I ill

I

I lit

1

I Ill

i

III

Io-4 io - 3 Io - z Io-' A'TOllt F R l i C T I O N OF Zn IN THE LIQUID X l n l / i

Fig. 4. The Zn concentration in the solid versus the atom fraction of Zn in the liquid along the G a - A s - Z n t000 C liquidus isotherm. The 1000 ';C liquidus isotherm is shown by the inset.

At a given temperature, the variation of X^,,~/) with Xz,(o may be obtained from the liquidus isotherm of the G a - A s - Z n ternary phase diagram z~) which is shown for 1000 <;C by the inset in fig. 4. Jordan's 3) analysis of the Zn and arsenic pressure measurements by Shih et al. 22) permits evaluation of 7z,(:) and 7A,l:r The complete solid solubility along the 1000 'C liquidus isotherm, as calculated by eq. (10) with 7~ = 1, is given by the dashed line in fig. 4. The double valued solid solubility curve results from the fact that the liquidus isotherm is also double valued in Zn compositior: (see the insert of fig. 4). At high concentrations, the experimental solid solubility exceeds Cz,~,) obtained from eq. (10) with ~:~ = I and indicates that ;'p is less than unity in this region. The hole activity coefficient is a convenient notation that includes all the effects of the charged carrier interactions which perturb the semiconductor band structure at high impurity concentrations. It is related to the Fermi level E r by the usual thermodynamic relation for chendcal potential I~(P) = - E r = Ito4 kT in (~np/N~),

(il)

where l( o is the reference potential and N, is the effective density of states in the valence band. The reference potential may be shown to be the valence band edge E, far ,!;I,t~, ; m n , r i t v e a n e e n t r a t i o n s . When the values of ~,~ from ref. 20 are used in eq. (10), the solid line shown in fig. 4 is obtained and is in agreement with the experimental data. It should also be noted that ~'Z.,(t )TA ~ )X ^.,(r )l ~))

is constant for Xz.(t ) < 0.I atom fraction and the - 5

822

u . c , CASEY~ JR. A N D M. B, P A N I S H

the c o n c e n t r a t i o n d e p e n d e n c e o? the a m o u n t o f Z n in the solid on the a m o u n t in the liquid is given by

C z . , ~ = [K'~(T) Xz.~e~] ~,

(12)

which is a s q u a r e - r o o t d e p e n d e n c e o f the Z n concentration for equilibrium between the liquid a n d the semic o n d u c t o r bulk. 5. C o n c l u s i o n s

Depending on the diffusivity o f a n impurity in the solid, the liquid phase is in equilibrium with either the semiconductor surface or bulk. Equilibrium between the liquid and s e m i c o n d u c t o r surface o c c u r s for a slow impurity diffusivity in the solid a n d results in a linear dependence o f the a m o u n t o f singly ionized impurity in the solid on ti~¢ a m o u n t in the liquid. This linear dependence was d e m o n s t r a t e d by T e in GaAs. Equilibrium between the liquid and s e m i c o n d u c t o r bulk requires rapid i m p u r i t y diffusivity in the solid and results in a s q u a r e - r o o t dependence o f the a m o u n t o f a singly ionized substitutional i m p u r i t y in the solid on the a m o u n t in the liquid. In addition, high impurity concentrations result in interaction between lhe charge carriers and in e n h a n c e d solubility. T h e s e effects were demonstrated by Z n in GaAs. T o treat impurity incorporation in serniconductors d u r i n g crystal growth, i~ is necessary to not only consider the activity coefficien~ in the liquid phase, but to also include the electrical properties o f the solid.

"

References

I) C. D. Thurmond, J. Phys. Chem. $7 (1953) 827. 2) C. D. Thurmond and M. Kowalchik, Bell Syst. Tech I. 39 (1960) 169. 3) A. S. Jordan, Met. Trans. 2 (1971) 1965. 4) C. D. Thurmond and J. D, Struthers, J. Phys. Cht ~. $7 (1953) 831. 5) H. R¢iss and C. S. Fuller, L Metals 8 (1956) 276. 6) M. B. Panish and H. C. Casey, Jr., 3[. Phys, Chem. ~lids 28 (1967) 1673. 7) H, C. Casey, Jr., ~A. B. Panish and K. B. Wolfstirn, J. 'hys Chem. Solids 32 (1971) 571. 8) K.-H. Zschauer and A. Vogel, in: GaAs: 1970 SA,mp Proc. (Inst. of Phys., London, ~971) p. 100. 9) H. C. Casey, Jr., in: Atomic Diffusion in Semiconducto~ , Ed. D. Shaw (Plenum, London, in press). IO) A. Many, Y. Goldstein and N. B. Grover, Semicml,~uctor Surfaces (North-Holland, Amaterdam, 1965) p. 165. i I) S. M. Sze, Ph.vsics of Semiconductor Devices (Wiley, Ne~v York, 1969) p. 363. 12) Y. Nannichi and G. L. Pearson, Solid-State Electron. 12 (1969) 341. 13) J. F. Osborne, K. G. Heinen and H. Riser, unpublished. 14) C. J. Hwang and J. R. Brews, J. Phys. Chem. Solids 32 (1971) 837. 15) Ref. II, p. 429. 16) C. S. Kang and P. E. Greene, in: GaAs: 1968 Syrup. Proc (Inst. of Phys. and Phys. Sot., London, 1969) p. 18. 17) M. G. Milvidskii and O. V. Pelevin, Inorg. Mater. 3 (1967p 1024; translated from [zv. Akad. Nauk SSYR, Neorg. Mater. 3 (1967) 1159. 18) L. J. Vicland and !. Ku,tman, J. Phys. Chem. Solids 24 (1963) 437. 19) F. E. Rosztoczy and K. B. Wolfstirn, J. Appl. Ph>~. 42 11971) 426. 20,~ H. C. Casey, Jr., M. B. Panish and L. L. Chang, Ph.w Rc~ 162 (1967) 660. 21) M. B. Panish, J. EIccwochcm. Soc. 113 (1966~ 861. 22) K. K. Shih. J. W. Allen and G. L. Pearson. J. Phys , hem Solids 29 (1968) 367.

XVI - 5