Self-diffusion in alpha and beta silicon carbide

155

CERAWJRGIA INTERNATIONAL. Vol. 5. n. 4. 1979

Self-Diffusion in Alpha and Beta Silicon Carbide J.D. HONG, M.H. HON and R.F. DAVIS Department

of Materials

Engineering

and Engineering Raleigh,

Research North

The self-diffusion coefficients of “C and %i have been measured for lattice transport in high purity and N-doped q-Sic single crystals and in high purity polycrystalline CVD @-Sic in the temperature range of 2123-2573 K. Grain boundary diffusion of “C has also been determined in the p-Sic material. The results of these studies reveal a vacancy mechanism wherein 14C diffuses considerably faster than “Si in both materials. Furthermore, D,” in the Ndoped single crystals is smaller than for the undoped materials, while the opposite is true for the %i transport in these crystals. Changes in the concentration of the charged C and Si vacancies are reasoned to be the underlying cause of this last phenomena. A discussion of the effect of Si evaporation and its effect upon the value of the diffusion coefficient is also presented.

1 - INTRODUCTION

Silicon Carbide may be considered to exist in two principal modifications: the a form which encompasses a large number of hexagonal or rhombahedral polytypes and the P form which crystallizes in the cubic zincblende structure. By virtue of its intrinsic oxidation, corrosion and creep resistance at high temperatures, as well as its electronic prc$erties, extreme hardness, low neutron absorption cross section, excellent thermal conductivity and thermal shock resistance and because of recent innovations in fabrication techniques. SIC continually remains of considerable interest in several areas of science and technology. In many of the current and projected applications, the primary utilization temperatures are in the range where diffusion processes affect many of the important chemical and physical properties; thus, it is mandatory that one have accurate kinetic data and an understanding of the mechanisms which control the self-diffusion processes of the constituent atoms. Since the initial SIC self-diffusion research of Ghostagore and Coble ‘, higher purity a single crystals and CVD B materials as well as crystals containing carefully controlled additions of impurities have produced. Such materials have been employed in the present research.

2 2.1

- EXPERIMENTAL - Material

evaluation

and

sample

Two sets of high purity * u-Sic single by the Lely process were employed:

preparation

crystals grown (1) colorless,

* Maximum concentrations (ppm) of impurities other than nitrogen and measured by spectrochemical and thermal neutron activation [TNAI analyses are Ni:2. AI:lO. Cu:2. Cr:3. U:3. Si:O.O6, Co:O.2. Sb:O.l, Na:2. K:l.

Services

Carolina,

Division,

North

Carolina

State

University,

U.S.A.

undoped, essentially electronically intrinsic crystals and (2) green, N- doped (= 3 x IO” atoms/m’ = 620 ppm), n-types samples. X-ray diffraction and transmission Laue patterns revealed only the 6H polytype in the former; whereas, both 6H (very dominant) and 15R were present in the latter. Dislocation densities were revealed by molten salt etching only on the Si face and ranged from zero to 6 x lO’/m*; the average distance between cores was 1 iO”m. The theoretically dense (p = 3.213 + 0.005 x IO’ kg/m’) polycrystalline P-Sic was produced by the initial pyrolysis of CHSiCL at 1673K and the subsequent CVD and reaction of C and Si on a graphite substrate. The resulting material was annealed in purified Ar at 10.3 MPa and 2373K to remove residual stresses. Spectrochemical analyses showed only Cu (60 ppm) as a minor impurity. A trace amount of the 15R polytype was detected in this predominantly cubic (3C) material. Molten salt etching revealed a microstructure composed of irregular crystals having a size of = (1.0 x 0.5) x IO-” m* and an equal proportion of lighter transparent bands composed of longer and larger ((5.0 x 1 .O) x IO-” m2 to (25.0 x 2.5) x IO-” m’) crystals. The latter shape is common in the CVD growth of materials; whereas, the former results most frequently from abrupt fluctuations in the feed gas flow or temperature. No evidence of dislocations was revealed by the etching procedure. Selected a crystals or 0 pieces were cut such that the principal diffusion direction would be along the cOOI> in the former and perpendicular to the growth direction in the latter. The resulting samples were diamond lapped with a double plate eccentric system to simultaneously produce a IO” m finish on both the top and bottom sample surfaces, a flatness within two light bands of He and a parallelism of 2 x 1W m between the two surfaces. 2.2 - Tracer

layer

deposition

The Si”C tracer material for both the a and P research was produced from -325 mesh powders of 99.999% pure natural Si and diluted (activity = 309.59 m Ci/g)“C wet-mixed in glycerol in a Si/C atomic ratio of 1.2, brushed evenly on a u source Y crystal, the glycerol vacuum evaporated at 343K and the assembly heated to 1693K 14.4x 10% and 1823K 7.2x 10% in a graphite crucible under = 9.1 x 10' Pa of Ar to form P-Sic. No free Si or C was detected after this reaction. The as-formed tracer powder was subsequently deposited on a second u seed * crystal by a crystal growth technique known as the traveling solvent method (TSM) wherein a Sic/metal, tracer/Sic sandwich configuration is heated in a thermal gradient such that the metal solvent (Y in this research-vacuum evaporated on the tracer .and the top 01source m crystal) is melted

equently dissolves [T employed = 1858K, measthe top of the a source = crystal) the tracer .ecipitates as a polycrystaiiine thin film and ly bonds to the colder SIC substrate. A camp ription of the utilization of TSM in this research lted elsewhere ‘. the deposition of the ?ZGiC tracer, it was reasoned that the 3.1 at % of “Si in the ii of SIC would require an s infinite n source Si tracer to produce statistically meaningful es between the ti background = and profile ? TSM necessitated a much higher (2073K) ure in this case and did not ‘produce a disconrop in the tracer concentration at the interface. ,proble experiments revealed that a scenario (a) the vacuum melting (16g3KI of MSi powder ;iC samples, (b) the coating of the “Si by a der - acetone slurry and (c) the heating of ire arrangement within a time scale such molten “Si initially and completely dissolved equently precipitated the %iC powder during ?r evaporation of the former, prior to reaching sion temperatures, was necessary to produce fl infinite N tracer source. going paragraph is comlpletely correct only u-SIC crystals wherein only a very small )f the sample is dissolved in the molten “Si to the amount of ‘Sic powder. In the polye P-Sic samples: however, the %i dissolved amount of the sample at the grain boundaries Isited both natural SIC and “Sic such that ilm having a much lower concentration of deposited only at sites on the larger 9 grains. lonomena coupled with the very slow %Si rate prevented any true grain boundary diffuindicated by the absence of a high diffusivity ;sian tail in the diffusion profiles.

usion anneals

and tracer

profile

analysis

us tracer/sample arrangements were annealed (or ‘“SIC) - coated graphite inner crucible tapered cap with an external hemispherical held in place by a threaded cap (also with !d head) which was a cover for an outer crucible. The evaporation of Si was further by surrounding (without direct contact) the with 0.5 x IOd Kg of Si (or “Si) contained in iC (or P-“Sic) powder. white tube furnace was slowly (5.4 x 10%) ) about 2073K followed by rapid heating to ted diffusion annealing temperature ?? . Followiid cooling period, the edges of all samples und to eliminate any penetration caused by fiffusion. C studies, the samples were mechanically using equipment of a design described in The collected grindings (92 * 1% efficiency) onsecutively removed layer in the “C diffusion vere coated with colloid, dried in stationary Ilaced into a proportional counter containing window which was continuously flushed with The average accuracy of the determination lenetration distance of each section was

using the latter solution are presented here as it incorporates very few assumptions, was derived for a thin film source and shows that the plot of the concentration of the diffusing species in the boundary portion of the profile vs x6” should be linear. A graphical method employed earlier by Sze and Wei 6 and Lundy and Federer ’ was used to separate the volume diffusion coefficients from those determined for the grain boundary transport, as described in more detail below. Ion microprobe analysis of the “Si as a function of diffusion distance was conducted by scanning a 4x10dm dia. positively charged oxygen ion beam (18.5 keV) perpendicular to the direction of diffusion. A scan width of 50 x lOAm was employed. Initial calibration of the instrument was made by scanning a standard, natural, semiconductor grade Si sample in the same manner at the SIC samples and coupled with continuous adjustment until the ‘“Si/“Si ratio was approximately 3O:l (i.e., the ratio in the natural material). The ion beam current was adjusted such that the absolute ‘“Si count was not below 2000 in a period of 20 seconds. The ion beam scan was initiated from the tracer and moved into the sample at 1 x 10” m steps. The details of the equipment and experimental and analytical techniques employed for the complete set of diffusion studies are presented elsewhere (refs. 8 and 9).

3 - RESULTS AND

DISCUSSION

3.1 - Alpha SIC Profiles of the ‘“C concentration vs the square of the mean distance to the center of each mechanically removed section of the high purity and N-doped crystals were composed of a very steeply sloping region adjacent to the surface and an essentially linear * deep n portion. Detailed discussions of the a near surface n region are given in Irefs. 8 and 91. The linear portion of each curve closely obeyed the thin film solution in every sample. In determining the ‘“Si concentration profile, it was also necessary to define the interface (x = 01 position (i.e., the position at which the absolute value of the concentration gradient is a maximum). Therefore, plots of the concentration gradient calculated from the difference in 5i enrichment per unit length versus the penetration distance for each sample were also produced. Having determined the interface position, plots of the logarithm of the concentration gradient from x = 0 into the crystals vs the square of the penetration distance at each point were found to result in a straight line having a slope of 1/(4Dt) for every sample. This is another indication that the use of an * infinite w source solution is indeed correct. The C self-diffusion coefficients * calculated from the tsdeep m linear sections of the profile and the analogous ‘“Si coerficients determined from the afore-mentioned concentration gradient curves are plotted in Fig. 1 as a function of I/T. The resulting curves can be expressed as follows: for diffusion in the high purity, essentially intrinsic a-Sic single crystals along the direction. -7.41 Dac=(8.62+2.01)x10’

kO.05 eV/atom

exp

(cm’/s) kT

,iin boundary diffusion coefficients in P-Sic culated using the solutions of both Fisher’ oka ‘. However, only the results determined

[I) for diffusion in the N-doped, n-type a-Sic single crystals

ble occurrence of a &+a transformation during the jion anneals was investigated before and during the search; however, no change in the amounts or the e polytypes from that of the as-received samples was I x-ray diffraction.

Although S.I. units are used throughout most of the paper, the units of cm*/s for D are still universally employed. For the sake of comparison with other data and to avoid confusion, this convention is maintained herein. ??

T(K) ICP- 2600

2500

2300 I

2400

2200 I

2100 I

-I

.in PURE in n-TYPE

IO-'0

;::;i:i lo-‘3 -

10-M 38

II

III

I

40

42

along

the

- Self-diffusion N-doped &-Sic



I 46

I.

46

50

coefficients of “C and %i single crystals as a function

in high of I/T;

I/T

FIGURE 1 purity and

III

44

(IO-‘/K)

direction, -8.20*0.008

eV/atom

Dgsi= (3.32k1.43)x107exp,

(cm/s) kT

for high purity, essentially intrinsic along the direction

121

a-Sic

-7.22*0.07

single

crystals

eV/atom

Dgsi = (5.01 f 1.71)x1@ exp

(cm’/s) kT 13)

for diffusion in the N-doped, n-type a-Sic along the direction -8.18+0.10

single

crystals

eV/atom

D’s,=(1.54*0.78)x105exo

(cm’/s) kT

c41

In all equations, the values of the activation energy (Cl) and the pre-exponential constant (Do) were computer fitted to a least squares curve. From these results it is found that “C diffuses considerably faster than “Si in the temperature range investigated. Furthermore, D’c in the N-doped crystals is smaller than for the high purity materials while the opposite is true for the “Si transport in these crystals. These latter effects lie outside the boundaries of experimental error and may be explained from the standpoint of thermodynamics, crystallography and defect interactions. In a covalent or partially covalent compound, the vacancies on each sublattice may form with electron or hole compensation rather than being connected by a Schottky equilibrium. In a semiconductor, the crystal or sublattice contains a concentration of neutral vacancies the amount of which is dependent on the

absolute temperature and the energy of formation of the vacancy. Furthermore there will also be a concentration of charged vacancies having donor (positive) or acceptor (negative) character which depends on the absolute temperature and the position of the Fermi level. The Fermi level is the electronic electrochemical potential; thus, when an impurity species is added to a material, the free energy of the system is increased and the material will make adjustments to lower its free energy by electronic means. One path in which this may be accomplished is in the adjustment of the number of charged and therefore, the total concentration of vacancies. (The concentration of charged vacancies on both sublattices is affected if the material is a compound semiconductor). In addition, the concentration of, for example, a donor impurity (such as N in SIC) also influences the amount of ionization of acceptors and other donor species (whether they be charged vacancies or impurity atoms) which is chemically equivalent to changing their solubility. Reiss and Fuller I0 have confirmed the predictions of the former author (ref. 11) in showing that the solubility of a donor (acceptor) increases with increasing acceptor (donor) content and that the solubility of a donor (acceptor) decreases in the presence of another donor (acceptor). These defect interactions do not, therefore, occur because of the ‘physical proximity of one defect with another but through the law of mass action. In binary semiconductor compounds such as SIC, the donor or acceptor character of the charged vacancies has not been directly ascertained. Lely and Kriiger ‘* have indicated that the charged C vacancies in SIC are donors; however, the most apparent indications of this fact prior to the present research can be derived from the C self-diffusion research of Ghostagore and diffusion studies conducted Coble ‘, and the impurity principally in the Soviet Union. In the former work, it was shown that the diffusion of “C in Al-doped p-type a-Sic was considerably faster than in the N-doped n-type material. This may be accounted for by a decrease in the number of vacancies available for C diffusion caused by the essentially complete ionization of the donor N impurity atoms and their subsequent interaction with donor-type C vacancies, as explained above. Maslakovets, et al. ” have experimentally demonstrated that in N-doped a-Sic, atoms of Be diffuse on C sites with a diffusion coefficient which increases as an inverse function of the excess donor content. By contrast, however, the presence of the acceptor-type species of Al or B results in a dramatic increase in this coefficient. In a similar study, Mokhov and co-workers I’. ” have diffused B (which has been shown (ref. 16) to occupy the three nonequivalent C sites in Sic) into n-type a-Sic crystals containing various concentrations of uncompensated N donors incorporated during growth. These authors found that a gradual increase in the number of excess donors produced a corresponding decrease in the B diffusion coefficient. in terms of the self-diffusion of “C in Sic, the above diffusion research strongly suggests that the C vacancies are donor in character and that a vacancy mechanism is operative in the transport of this species. Thus the doping of positively charged N donors raises the Fermi level of the SIC crystal and its electronic free energy. A return to electronic equilibrium is achieved by the reduction in the number (i.e., the solubility) of donor-type charged C vacancies (at the temperatures of diffusion, essentially all the vacancies are charged) which in turn reduces the total number of vacancies available for the transport of the isotope and thus decreases the diffusion coefficient.

J.D.

lination of the donor or acceptor character vacancy by means analogous to that pre)ve is more difficult because of a dearth tion. Inference must be made from other nvestigations. Id Patrick ” have observed a N donor-Al hair spectra which is in agreement with he C sites and Al on the Si sites. Although investigators have studied the diffusion r-Sic, only Vodokov and Mokhov I’, in their Al and Ga diffusion in this material, note dopants diffuse through Si vacancies. These so indicate that a deceleration of the Al ccurs during the diffusion process because :rease in the total concentration of Si valis is believed to indicate that the charged the Si vacancies are acceptor, and the intro’ the Al acceptor impurity decreases the Si vacancies. Si vacancies. lntaining a-Sic materials of the present study equilibrium is restored by the increase in !r (i.e.; the solubility) of the acceptor-type ;i vacancies. This increases not only the er of vacancies on the Si sublattice but also bility of one being available for ‘“Si diffusion fore the D’,, relative to that found the material. Thus one may see that the presence affects the vacancy concentrations on both ; in the a-Sic compound semiconductor.

HONG.

M.H.

HON

and

R.F. DAVIS

TPC)

2300

2200

2100

2000

1900

IO+

:I$

’

’

‘\i

IO-‘:

I 0-S

$\h_ 3

llY3,

IO“

3.8

I

I 4.0

I

I 4.2

I

I 4.4

I

I 4.6

._ 4-8

I/T X 104(K-‘1

SIC terial. profiles of the “C concentration plotted :tion of X”” consisted of II. a deep linear iich represents the grain boundary diffusion, I long (= 25 - 45 x 10” m) intermediate seaining contribution from both grain boundary ne diffusion and 31 a short (= 2 x 10” ml pface m high gradient, high activity section D be caused for the same reason(s) as noted : case 8,9. o evaluate the volume diffusion coefficients aphical method noted above, the deep linear If the profile were extended to the y (con) axis. If. as is assumed in this research, !nt the total tracer activities in the middle the curves and y2 the analogous activities extended line, respectively, then Ay may be the tracer activities resulting only from ffusion. Subsequent plots of Ay values from le as a function of the square of the penestance resulted in a straight line; thus, the :oefficients calculated from these latter plots to DI, and are presented as a function of I/T The resulting curve can be expressed as

-8.72kO.14

eV/atom

! + 1.83) xl 0’ exp

cm’/ s kT 151

icy of the evaluation of the “C volume diffuslis separation method is not known as the ffusivities in single crystals are not available. Suzuoka’ has estimated from literature va)lume diffusion determined directly on single Ind by the separation technique on polycryjecimens of the same material that the diffu‘ram the latter technique almost always ate the single crystal value by = 10%. The r this difference has been attributed by Sze to the fact that grain boundaries act as sources of vacancies which can, in turn, liffusion by an additional vacancy mechanism.

FIGURE 2 - Self-diffusion boundary diffusion and %i of f/T.

coefficients of “C lattice and grain lattice diffusion in P-Sic as a function

Grain boundary diffusion coefficients (D”tJ calculated using the above solution as well as the values of D*h obtained as described above and an assumed value of the grain boundary width (6 = 5 x 10-‘OmI are also plotted as a function of I/T in Fig. 2. The resulting curve can be expressed as -5.84-+0.09

eV/atom cm*/s

Dfbc=(4.44f2.03)x10’exp kT

C61

It should be noted that there are some problems in the of calculations of. D+bc. in addition to the estimation the grain boundary width, which cannot be overcome using the 0 -Sic samples of this research. For instance, in the Suzuoka equation the grain size and, therefore, the length of the grain boundary is assumed to be much larger or longer than the value of diffusion depth. Furthermore the grains are assumed to be uniformly distributed in size throughout the crystal. These assumptions are not completely true for the P-Sic used in this study. Finally, because of mathematical difficulty, all theoretical treatments of this problem have assumed a discontinuous change in dlffusivity from Db to Di at a distance 6/2 from the center of the boundary. However, the error introduced in assuming a reasonable 6 value should not affect the activation energy unless 6 is influenced by temperature. In the small 2128-2374 K range used in this research, this is considered unlikely. Grain growth was not observed during any of the diffusion anneals. In the %i profiles, the tracer was only detected prior to reaching the sample surface over a distance which, at maximum, was only 3 x 1O”m. At no time was there an extended profile outside the sample, as fdund in the a-Sic material. Because of the slightly uneven sample surface produced by’“Si etching during heating to and at the anealing temperature, the x = 0 position had to be determined with considerable care. The

SELF-DIFFUSION

IN

ALPHA

AND

BETA

SILICON

CARBIDE

159

maximum concentration coincided closely with the edge Of the sample, as determined by microscopic examination (deviation & 1 x lOAm) and was taken to be x = 0. Following this determination, the percentage of ‘“Si in the background was subtracted from the perfrom the reworked ion probe data centage determined and this difference plotted on a logarithmic scale as a function of distance into the sample. In every sample, these graphs resulted in a linear curve indicating that the thin-film solution to Fick’s second law correctly described the profiles and that the tracer was derived from a true thin-film source. Self-diffusion coefficients, D*w, calculated from -the measured profiles adjusted for background contributions are also plotted in Fig. 2. The resulting curve follows closely an Arrhenius relationship and therefore can be expressed as -9.45+-0.05 D*lsi= (8.36*1.99)x10’

eV/atom

exp

cm’/s kT

PI

and the ratio, Vt/(Dt)“’ = 0.015, which is less than the value 0.04 shown to be important by Dawson, et al. Thus, even from this consideration, it can be seen that the diffusion coefficients determined in this work will not be in error by more than 5% if the decomposition is neglected. This value is smaller than the percent deviation of the D, values equal to 7.44% and 5.16% in the N-doped and high purity crystals, respectively. In the ‘“Si diffusion in the same materials, the use of the = infinite p source layer did not allow any decomposition of the tracer surface to influence the diffusion profiles. Considerable effort was also expended to discern the effect of this phenomenon on the values of the diffusion coefficients in the beta material. As such, the decomposition rate of the CVD P-Sic used in this research was determined on samples analogous to and subjected to the same environmental conditions as those used in both the C and the Si diffusion experiments. The rate of movement of a sample boundary is given by -7.40+

The absence of any indication of grain boundary diffusion is directly related to the decomposition of the sample at the grain boundaries, as discussed in the previous section. This coupled with the closeness of fit to the thin-film solution strongly indicates that the diffusion profiles contain no grain boundary contribution.

-6.29

f 0.09 eV/atom kglm’/s kT

181

By comparison with a similar effort by Ghostagore ‘*~” the decomposition rate of the samples used in this research was about an order of magnitude lower. This may be explained by the fact that the more rapid decomposition of the high surface area 1500 mesh a-Sic powder employed in the crucible holding the crystal during diffusion anneals produced a predominantly Si vapor which slowed considerably the decomposition of the crystals. Dawson, et al’” have also studied the effect of evaporation of the sample surface on self-diffusion of Br in KBr and found that as long as the ratio Vtj(DW 5 0.04, the diffusion coefficient, D, will not be in error by more than 5% if sample evaporation is neglected. In this ratio, V is the rate of movement of the sample boundary and t is the diffusion time. Considering, as a worst case in the alpha crystals, the “C diffusion in n-type SIC at the temperature and duration of 2429 K and 2.1 x IO’s, respectively; the calculated diffusion coefficient is 3.45 x 10-l’ m’/sec. The value of R can be determined from Eq. 8 and is equal to 2 x IO-1 kg/m’/sec. The value of V may be determined frnm the equation V = R/p where p = sample = 0.623 x lo-” m/s.

density = 3.213 x lWkg/m’

1111

If the density of P-Sic (= 3.213 x lo3 Kg/m’) is multiplied by the values of V, the values of R can be calculated; an equation of the curve of these latter numbers was determined to be -7.40*

R =2.95x1 0” exp

R=7.74x108

1.20 eV/atom

exp

kg/m’/s

Cl21

kT The decomposition rate of the alpha material is lower than the latter, which confirms similar results of Shaffer” on powders of these two materials. The for the measurable decomposition principal reason differences in the a and 8 samples in the present case is the presence of the large amount of grain boundary interfacial area which facilitates decomposition, pat-ticularly at the higher temperatures, from a number of sites rather than from just the top surface layer, as in the single crystal case. For the more rapid C diffusion in B-Sic, the ratio Vt/(D*W’ was approximately 0.06; thus no correction to D*I, was made. The ratio (Vt/D*~tI”* = 8.0 x IO-’ and correction in this case was also not made. In the case of ‘“Si diffusion into 8, however: the Vt/(D*,,J”* was calculated to be approximately 0.9; thus, the decomposition will play some role in determining the diffusion coefficients. Unfortunately the use of the equations developed by Ghostagore I9 for this phenomenon in accertaining this effect on D’w is not possible in the present case as only a percentage of the ‘“Si was obtained and not the value of the total amount. Furthermore, the diffusion distance of the “Si is short; thus, there are no deep portions which could, with confidence, be considered to be only negligibly affected by the decomposition and therefore amenable to extrapolation to X+0 for comparison with the actual curve and the calculation of D in the affected region. The values of D and V are, however. similar to those used Ghostagore I9 in his example: thus, the s”si diffusion coefficients may be up to 20% lower, as a worst case, than the real values. However, since the rations of Vt/(DtI”* were nearly constant in the temperature range of this study, the calculated activation energy should not be affected.

c91 4 - CONCLUSIONS

Thus, vt = 1.308xlWm (my” = 8.5 x lo” m

Kg/m’/s kT

3.3 - Silicon evaporation It is also important to determine experimentally whether Si evaporation creates errors in the concentration profiles of either of the materials and therefore in the values of the coefficients as a function of temperature and/or Q which are outside the calculated experimental errors in these parameters. In the alpha crystals, the decomposition rate, R, was determined directly from the actual diffusion samples and may be described by the equation.

1.20 eV/atom

V=2.41x103exp

cm

Carbon - 14 self-diffusion in high purity and N-doped u-SIC single crystals and high purity CVD B-Sic is

J.D. HONG, M.H. HON and R.F. DAVl6

bly faster than the ‘“Si transport in the same Furthermore D”, and D”si in the N-doped stals is measurably smaller and larger, resperan in the undoped materials. This difference lues of each of the coefficients in the two is caused by a decrease in the solubility urged, donor-type C vacancies and an increase lubility of the charged, acceptor-type charged ies in the presence of the donor N impurity ‘by in P-Sic is larger by a factor of 105- 106, I on the temperature, while the activation r grain boundary diffusion of C is 66% of that ergy volume diffusion of this component. The Si by decomposition at high temperature, small, is believed to affect the values of :he P-Sic materials but not the calculated energy.

:ES IOSTAGOREand R.L. COBLE. Phys. Rev. 143 (1966) VIS, J.D. HONG and M.H. HON, in H. Palmour III. lvis and T.M. Hare (Eds.]. a The Processing of ie Ceramics m, Materials Science Research, Vol. 11. New York, 1976. p. 653. #NG. W.E. GRIFFIN and R.,F. DAVIS, Rev. of Sci. ._ _.___. ~_ nts 49 11978) 83.

4. 5. 6. 7.

J.C. FISHER, J. APP. Phys. 22 ft951) 74. T. SUZUOKA. J. Phys. Sot Japan 19 (1964) 939. S.M. SZE and L.Y. WEI. Phys. Rev. 124 (1961) 1. T.S. LUNDY and J.I. FEDERER. Trans. Met. Sot. of AIME 224 (1962) 12. 6. J.D. HONG, Ph. D. Thesis. North Carolina State University, May 1976. 9. M.H. HON. Ph. D. Thesis. North Carolina State University, July 1976. IO. H. REISS and C.S. FULLER, Trans. AIME. J. of Metals 6 (1956) 276. 11. H. REISS, J. Chem. Phy. 21 (1953) 1209. 12. J.A. LELY and F.A. KRUGER. in D.M. Schon and H. Welker (Eds.), Semiconductors and Phosphors, Interscience. New York, (1956). p. 525. 13. YU P. MASLAKOVETS. E.M. MOKHOV. YU A. VODAKOV and G.A. LOMAKINA, Sov. Phys. Solid. State 10 (1966) 634. 14. YU A. VODAKOV and E.N. MOKHOV. in R.C. Marshall, J.W. Faust Jr. and C.E. Ryan (Eds.). Silicon Carbide - 1973. University of South Carolina Press, Columbia, 1974, p. 508. 15. E.N. MOKHOV. YU A. VODAKOV, G.A. LOMAKINA. V.G. ODING. G.F. KHOLUYANOV and V.V. SEMENOV. Sov. Phys. - Semicond. 6 (1972) 414. 16. H.H. WOODBURY and G.W. LUDWIG, Phys. Rev. 127 [I9611 1063. 17. W.J. CHOYKE and L. PATRI’CK. Phys. Rev. 82 f1970) 4959. 16. R.N. GHOSHTAGORE, Solid State ‘Electronics 9 (19661 176. 19. R.N. GHOSHTAGORE. Phys. Stat. Sol. 19 f1967) 123. 20. D.K. DAWSON, L.W. BARR and R.A. PITTdPLADDY, Brit. J. APP. Phys. 17 (1966) 657. 21. P.T.B. SHAFFER. Mat. Res. Bull. 4 (1969) S102. Received

March

16. 1979; revised

copy received

October 2. 1979