US3788890A - Method of preparing dislocation-free crystals - Google Patents

Abstract

DISCLOSED IS A METHOD FOR GROWING CRYSTALS UPON NONINDENTICAL SUBSTRATE OR SEED CRYSTAL IN WHICH THE GROWN CRYSTALS HAVE A HIGH DEGREE OF CRYSTAL PERFECTION. MORE PARTICULARLY, THE INVENTION IN A METHOD OF SELECTING SUITABLE SEED OR SUBSTRATE CRYSTALS WHICH PERMIT THE GROWTH OF DISLOCATION-FREE CRYSTALS, A METHOD OF SELECTING THEOPTIMUM PLANE ON WHICH TO GROW THE CRYSTALS AS WELL AS APPROXIMATING A LARGE NUMBER OF SUITABLE PLANES, AND THEN GROWING THE CRYSTAL TO A MINIMUM THICKNESS AT WHICH ALL DISLOCATIONS ARE REMOVED FROM THE GROWING CRYSTAL. THIS INVENTION IS PARTICULARLY APPLICABLE TO THE GROWTH OF DISLOCATION-FREE THIN FILM CRYSTALS SINCE THE MINIMUM THICKNESS CAN BE READILY CALCULATED AND IS OFTEN QUITE SMALL.

D R A W I N G

Description

Jan. 29, 1974 s MADER ETF AL METHOD OF PREPARING DISLOCATION CRYSTALS.

2 Sheets-Sheet l Filed March 5, 1972 SLIP PLANE FIGJa FIG.2

FIG.I b

FlG.1c

FlG.1d

FIGJO Jan. 29, 1974 s. R. MADER ETAL 3,788,890

METHOD OF PREPARING DISLOCATION CRYSTALS Filed March 5, 1972 3 Sheets-Sheet 2 Emma. 4EKEE%%E% United States Patent U.S. Cl. 117-201 11 Claims ABSTRACT OF THE DISCLOSURE Disclosed is a method for growing crystals upon nonidentical substrate or seed crystals in which the grown crystals have a high degree of crystal perfection. More particularly, the invention includes a method of selecting suitable seed or substrate crystals which permit the growth of dislocation-free crystals, a method of selecting the optimum plane on which to grow the crystal as well as approximating a large number of suitable planes, and then growing the crystal to a minimum thickness at which all dislocations are removed from the growing crystal. This invention is particularly applicable to the growth of dislocation-free thin film crystals since the minimum thickness can be readily calculated and is often quite small.

BACKGROUND OF THE INVENTION Field of the invention This invention relates to a crystal growth process, and is particularly directed to the growth of dislocation-free crystals useful in semiconductor applications.

Description of the prior art Dislocation-free crystals are most desirable in the manufacture of semiconductors. Dislocation lines on semiconductors may act as electron acceptor Cites in addition to being areas for the accumulation of gross impurities. If the impurities accumulated are electrically active, which is often the case, the electrical behavior in the vicinity of the dislocation lines may be substantially different from the electrical behavior in other areas of the semiconductor. In doped semiconductor crystals where impurity atoms are diffused into the semiconductor crystal, the depth and concentration of the impurity atoms in the vicinity of the dislocations may substantially differ from the rest of the crystal, causing erratic electrical behavior of the device. In certain cases where electrically conductive impurities have accumulated, shorting of the device may occur.

An early method for growing large, dislocation-free single crystals was developed by Dash and is described in U.S. Pat. 3,135,586. Propagation of dislocations to the edges of the growing crystal were accomplished by tapering the charge ingot, and by using the crystal pulling technique with the seed crystal oriented in the (111) or (100) plane, growing the crystal with a fine neck so that no dislocations in the seed were propagated down by the neck. Rather, the dislocations were terminated either on the surface of the seed or on the surface of the neck. Thus, Dash relied upon the extremely small diameter of the seed crystals and the crystal to be grown to remove dislocations. Since it is often inconvenient or even impossible to fabricate such a neck in many crystals, this method has inherent disadvantages. It is also limited to the crystal pulling technique in which the materials must be heated to their melt temperature and relatively thick crystals of small diameter are produced. The process is inapplicable for the making of dislocation-free single crystal thin films.

Patented Jan. 29, 1974 The ability to deposit dislocation-free crystal thin films upon a wide'variety of substrates can greatly simplify integrated circuit manufacture as well as enhance the reliability of the device.

U.S. Pat. 3,476,592, assigned to the same assignee as the present invention, recognized that improved epitaxially grown semiconductor layers for certain substrates could be obtained by misorienting the substrate crystal a certain number of degrees away from its major crystallographic plane.

In the U.S. Pat. 3,520,810, assigned to the same assignee as the present invention, it was discovered that perfect crystals of GaAs could be produced by growing the crystal along the 031 direction using the Horizontal Bridgman technique. This and other teachings specify the crystal planes and growth directions which have been found suitable for the growth of specific crystals upon specific substrates. Accordingly, if one wishes to grow crystals with improved surface morphologies upon substrates which have not been described in the prior art, it is necessary to imperically determine suitable geometries and crystallographic planes.

It is the object of this invention to provide a method of growing dislocation-free crystals upon a large variety of substrates.

It is another object of this invention to provide a method of selecting suitable substrates without experimentation.

It is yet another object of this invention to provide a method of selecting suitable growth planes without experimentation.

It is another object of this invention to provide a method of growing dislocation-free single crystal thin films.

SUMMARY OF THE INVENTION The above objects are accomplished by selecting suitable seed or substrate crystals so that dislocations propagated in the growing crystal will be forced to the edges, selecting suitable crystallographic planes of the substrate upon which to grow the crystal so that all of the dislocations propagated into the growing crystal will be forced to the edges, and determining the minimum thickness required so that the process is particularly applicable to the growth of perfect crystal thin films.

BRIEF DESCRIPTION "OF THE DRAWINGS FIGS. la1d show cross-sectional views following the growth of a dislocation-free crystal upon a dislocation containing substrate.

FIG. 2 depicts the relationship of the slip plane to the crystal growth interface so as to show the Burgers vector and the angles A and FIG. 3 demonstrates constructing a stereographic projection.

FIG. 4 is the standard (001) stereo-graphic projection for an fcc. crystal.

FIG. 5 shows the family of planes in an fcc. crystal in which cos A and cos 5 are equal to zero.

FIGS. 6-9 show the suitable interfaces upon which to grow dislocation free crystals for various crystalline structures.

FIG. 10 shows a dislocation-free crystal upon a substantially identical substrate made in accordance with the process of this invention.

DETAILED DESCRIPTION (A) Selection of suitable crystals FIG. 1 shows the growth of a dislocation-free crystal B upon a seed or substrate crystal A which contains dislocation lines.

FIG. 1a shows the growth of crystal B in which dislocations contained in A extend into the growing crystal B. Since the lattice parameters of A and B differ, an elastic strain is produced which, upon further growth, exerts a force on the dislocation lines of B forcing them to bow out as shown in FIG. 1b. As the thickness of B is increased, the force on the dislocation lines in B also increases until a critical thickness is obtained in which the dislocation lines in B glide to the edge of the specimen as shown in FIG. and finally escape as shown in FIG. 1d. This process leaves dislocation lines at the interface between A and B but removes the dislocations from B.

An understanding of the forces which remove the dislocations from crystal B is required to properly select a suitable seed or substrate crystal on which to grow the dislocation-free crystal desired. It is first necessary to choose a substrate or seed crystal which is non-identical with the crystal to be grown so that there is a difference in lattice parameters between said crystals. Thus, the chemical composition of crystals A and B must not be identical. However, it is possible for A to be an impure crystal and B to be a pure one of the same material. Also, B may be a doped version of the material which constitutes A.

The difference in lattice parameters between A and B creates an elastic strain or misfit. In selecting suitable materials for A and B, the magnitude of the misfit between the unstrained lattice parameters of A and B must be large enough to remove all dislocations from B but less than that which would spontaneously create new dislocations. We have found the minimum misfit needed to remove dislocations, which is dependent upon the materials employed.

The elastic strain or misfit needed to create new dislocations has been estimated by F. C. Frank, Symposium on Plastic Deformation on Crystal and Solids, Carnegie Institute of Technology: Pittsburgh, 1950, p. 89, and J. P. Hirth, Relation Between Structure and Strength in Metals and Alloys, H. M. Stationery Office: London, 1948, p. 218. It is estimated that greater than 1.5% misfit at room temperature will cause the spontaneous growth of dislocations while approximately half that or .75% at a 1000 C. is required. Since the crystal growth techniques contemplated by this invention require elevated temperatures, the maximum elastic strain or misfit should generally not exceed .75%. The minimum misfit needed to remove all dislocations may be given by the equation:

where p is the dislocation density, b is the Burgers vector of misfit dislocation, L is the diameter across the AB interface and is the angle between the Burgers vector of the dislocations and that direction in the AB interface which is perpendicular to the line of intersection of the slip plane and the interface as shown in FIG. 2.

By approximating the misfit from the lattice parameters of A and B, the maximum number of dislocations allowable in the seed or substrate crystal can be calculated by using the equation:

L bL cos A can thus be obtained from the lattice parameters of the crystal. Table I gives the lattice parameters of some common crystalline materials.

TABLE I Material: Lattice parameter (s) A. Aluminum 4.0496 Gold 4.0788 Germanium 5.6570 Silicon 5.4305 Silver 4.0857 Gallium arsenide 5.6530 Chromium 2.8846 Iron 2.8664

The lattice parameters of other crystals can be readily obtained from standard texts, such as The International Tables for X-Ray Crystallography, vol. 3, Kynoch, England, 1962, and Handbook of Lattice Spacings o Metals and Alloys, Pergamon Press: New York, 1958.

The effect of dopants on the equilibrium lattice parameter for which there is no known value can be estimated using Vegards law and the tetrahedral bond radius of the dopant atom as given by L. Pauling, The Nature of the Chemical Bond, Ithaca, N.Y., Cornell University, p. 179. The relationship between the dopant concentration and the misfit between doped and undoped material, such as silicon is given by the equation:

where N and N are the number of dopant and Si atoms/cc. while r and m are their bond radii.

The results of calculations made for B, P, As, Al, Ga, In, and Sb dopants at a concentration of 10 atoms/ cc. in silicon are summarized in Table II.

TABLE II Dopant (10 atoms/cc): Misfit Boron 2 X 10- Phosphorus 1x 10- Arsenic 1x10- Aluminum 1X 10 Gallium 1X 10- Indium 2X 10- Antimony 2X10- Accordingly, it can be seen from the equation that a decrease in the number of dopant atoms will result in a proportionate decrease in the percentage misfit between the doped and undoped silicon.

Table III gives the slip plane and slip direction of common crystalline structures.

TABLE III Slip Crystal Slip plane direction Fcc metals (e.g. A], Ni, Cu, Au, Pd, Ag, Pt,

stainless steel) Si, Ge, Diamond GaAs,

GaP, InSb 111 Boc metals (e.g., Fe, Nb, Cr, W, Ta) 110, 112, 123 111 Alkali halides structure 110 110 PbS, PbSe, PbTe structure 001 110 By knowing the direction of Burgers vector, one can readily determine the angle A shown in FIG. 2. Thus, the minimum misfit or the maximum dislocation density of the substrate can be calculated for any crystal whose lattice parameters and slip system are known.

(B) Selecting the orientation of the interface For dislocations to be removed there should be a large total force acting on all dislocations present. This total force is given by:

6 cos 4: cos

where r=shear stres resolved along the Burgers vector of the dislocation;

e=elastic misfit strain in the film;

=angle between the normal to the slip plane and the plane of the interface as seen in FIG. 2;

G=shear modulus of the film;

v=Poissons ratio; and

)\=angle between the slip direction and that direction in the interface which is perpendicular to the line of intersection of the slip plane and the interface as shown in FIG. 2.

Therefore,

This expression is zero if e= or if cos 7\=0. Thus, the method of this invention requires a misfit between crystals, and that cos A is not equal to zero for all the dislocations that are present.

However, in addition, it must be noted that dislocations moving to the edge may meet obstacles which they can overcome only if the force per unit length of each dislocation is large. The condition that the force per unit length be large is that be large for all the dislocations present in the crystal. Thus, for elfective removal of dislocations not only must e not be equal to 0 and cos A not be equal to 0 as before, but in addition, cos should not be equal to 0. The magnitude of e is determined by the misfit and thickness. Cos A and cos depend upon the orientation of the interface, on the slip direction (i.e., the direction of the Burgers vector), and on the orientation of the slip plane. The orientation in which cost. and cos are both large for all possible dislocations can be determined by using standard projection of the crystal and knowledge of its slip system.

To construct a stereographic projection, referring to FIG. 3, place a small crystall 11 at the center of a large sphere 12 and draw straight lines 13 so that they pass through the center of the sphere and normal to the planes of atoms in the crystal. Where straight lines intersect the surface of the sphere, dots 1.4 are made and labeled with the Miller indices of the planes involved. When all the major planes have been drawn a sphere with many dots is obtained. Each set of planes has two dots, where each end of the straight line meets the sphere. Thus, only one hemisphere is needed to define all the planes in the crystal.

If the sphere is transparent and the dots are opaque and a point source of light 15 is placed on the surface of the sphere, then the dots can be projected onto a planar surface 16. If the planar surface is placed so that its plane is perpendicular to the diameter of the sphere that touches the light source then the array of dots on the paper is a stereographic projection 17.

If a low index crystallographic direction is made to coincide with the light on the surface of the sphere the projection will be a particularly symmetrical one. Projections of this type are called standard projections. One of these is the (001) standard projection shown for a cubic crystal in FIG. 4.

Generally fcc. crystals silp on the slip systems 1l0 and {111} as shown in Table III. In the Miller indices system, the symbol 110 means all directions of the type [110]; the symbol {111} means all planes of the type (111). By using the standard projection of such a crystal as shown in FIG. 4 and then marking all the {111} planes and 110 directions, the projection of FIG. 5 is obtained.

lines gives the loci of positions where cos x is 0.

lines gives the loci of positions where cos p is 0.

Desirable growth directions, or orientations for the interface between the two crystals, should be away from all the lines shown in FIG. 5.

Actually, cubic crystals are so symmetrical that most of this projection can be dispensed with. FIG. 4 contains 24 triangles each of which have indices of the type and (111) at their comers. All of these triangles are essentially the same. Thus, any interface AB of FIG. 1 can be represented by a point on one of these triangles. The most desirable AB interface in fee. materials like Si, GaAs, Au, Al, Cu is shown by the hatched area in FIG. 6, tlieptiiaangle of which is obtained from the hatched portion 0 5.

By drawing areas away from the lines of FIG. 5, where 7 cos A and cos 'are equal to zero, an infinite number of suitable planes on which to grow perfect crystals can be predicted. Any interface defined by points inside the hatched areas in FIG. 6 are satisfactory for face centered cubic (fcc.) metals and semi-conductors. However, the plane farthest away from the lines of FIG. 5 is most desirable. This would be the 012 plane for fee. crystals as shown in FIG. '6.

In the same manner, similar triangles can be constructed for other crystals where slip planes and slip directions are known such as those shown in Table III.

FIG. 7 shows suitable interfaces for growing alkali halide (NaCl) type crystals while FIG. 8 shows areas for body centered cubic (bcc.) crystals and FIG. 9 for PbS type crystals.

(C) Thickness of perfect crystals to ge grown The thickness at which the dislocations in crystal B migrate to the edge of the specimen can be derived by equating the forces tending to push the dislocations to the edges to the forces which oppose this motion. This is derived in the literature by W. A. Jesser and J. W. Matthews, Phil. Mag. 15, 1097 (1967).

The thickness of B in FIG. 1 at which the dislocations Wlll escape is given approximately by:

where b is the magnitude of the Burgers vector of the dislocation, v is Poissons ratio, 1 is the misfit between the equilibrium lattice parameters of A and B, and )t is the angle between the slip direction and that direction in the film plane which is perpendicular to the line of intersection of the slip plane and specimen surface as shown in FIG. 2. Suitable interfaces are those in which h is always finite, so, cos A must eirceed zero for all dislocations.

As discussed earlier, the lattice parameters of the substrate or seed crystal must be different than the crystal to be grown. Thus, the two materials cannot be identical.

However, for some applications, the same material for the substrate and the perfect crystal is required.

This can be achieved by the method illustrated in FIG. 10. Onto the substrate crystal A is grown 'a narrow band of material B with unstrained lattice parameter different same material as the substrate, may then be grown dislocation-free.

In this case, the critical thickness of B must be greater than 2h to ensure that dislocations will be' removed from B during the growth of B, and will not be drawn back into B when A is grown.

(D Crystal growth After selection of a suitablesubstrate or seed crystal, a suitable plane on which to grow the dislocation-free crystal is determined using the stereographicprojections discussed above. By placing the substrate or seed crystal on a goniometer and taking X-ray laue photographs of the crystals, or by any other known method, the suitable plane and orientation is marked and the crystal is 'cut along these lines.

The dislocation-free crystal can be grown on the substrate, by a variety of techniques, to a thickness greater than the critical thickness discussed above. Well known single crystal growth methods from a melt or solution, including the Czochralski crystal pulling technique, floating-zone technique, the gradient-freeze technique, the Horizontal-Bridgman method and the horizontal zone melt technique may be employed.

In addition, vapor-growth methods including vacuum evaporation, sputtering, and chemical vapor deposition can be used. Also, other methods such as molecular beam techniques and electro-deposition may be employed. The vapor-growth methods are particularly applicable to the manufacture of thin films, and are fully discussed in references on that subject such as Handbook of Thin Film Technology, Maissel, L. I. and Glang, R. (McGraw Hill, New York), 1970, and Thin Film Technology, Berry, Hall & Harns (D. van Nostrand, 00., Princeton), 1968.

While the invention has now been described with particularity, the following examples are given as illustrations.

EXAMPLE I Germanium is grown on gallium arsenide. Since the lattice parameters are known, the misfit between the unstrained lattice parameters are calculated;

Thus, since the dislocations of the specimenare less than the maximum which can be removed, a dislocation. free crystal is assured if it is grown to a critical height. It should be noted that if the number of dislocations in .the specimen is greater than the maximum to be removed, then the size of the specimen substrate (L). must be decreased so that p is equal to or less than the dislocation density of the specimen.

Thus, 4f. bp cos x In calculating the'critical thickness, wherein Poissons ratio is approximately equal to .3:

Thus, a thin film of 1500 A. may be grown in which all the dislocations of the substrate are removed.

Single-crystal films of germanium is grown on gallium arsenide by the process described in US. Pat. 3,345,209 and assigned to the same assignee as the present invention. The method includes thepassage of GeI- over the substrate material which is maintained at 350 C.

EXAMPLE II A silicon ingot 1 cm. in diameter, is cut to expose a suitable plane at the interface. Since silicon is an fcc. crystal, a suitable plane is the (210) plane, as shown in FIG. 6. The maximum density of dislocation which can be removed is calculated from the equation:

The misfit is calculated using Vegards law, the results of which for a boron concentration of 10 atoms/cc. is shown in Table II. The maximum dislocation density removable is 4x10 The dislocation density of the silicon ingot interface is then measured using X-ray techniques. For silicon ingot specimens the dislocation density is generally 'lessthan about 1X10. Thus, all of the dislocations can be removed from silicon doped with 10 atoms/ cc. of boron on a 1 cm. diameter substrate.

i The boron' doped silicon is then grown on the silicon substrate by introducing a boron containing gas with a gaseous stream of 'Si which is formed by the reduction of SiCl The gaseous mixture is then allowed 'to flow across the silicon substrate until a critical thickness of 500 A. is obtained at which height all dislocations are removed. The use of this method of chemical vapor deposition is discussed in Thin Films Technology, supra, p. 269 and in US. Pats. 3,184,348 and 3,361,600, assigned to the same assignee as the present invention.

EXAMPLE III A pure, silicon dislocation-free crystal may be grown on a silicon substrate using an intermediate layer as shown in FIG. 10. Thus, the boron-doped silicon is grown to twice the critical thickness of 1000 A., as in Example II. Pure. silicon may then be vapor grown on the boron doped silicon by discontinuing the flow of boron-supplying gas to yield a dislocation-free silicon crystal on a silicon substrate with a boron doped silicon intermediate layer.

EXAMPLE IV Dislocation-free chromium films can be grown on iron substrates. Since these materials have bcc. crystalline structures the iron substrate is cut and oriented on some plane within the shaded area" of FIG. 8 such as the (001) or (111') plane. The misfit is first determined from the difference in lattice parameters, so

Cr i rrm 12- From Table II,

Since the Burgers vector for bcc. crystals is approximately la -w ars A the maximum number of dislocations which can be removed in 6.1 10 for a 1 cm. diameter substrate.

After ascertaining by X-ray techniques that less than 6.1 l dislocations/cc. are present at the iron crystal interface, chromium is vapor deposited onto the iron crystal to a thickness of 50 A. or more.

While the invention has been shown and described with reference to preferred embodiments-thereof, it will be appreciated by those of skill in the art that variations in form may be made therein without departing from the spirit and scope of the invention.

What is claimed is:

1. A method of preparing dislocation free crystals from a dislocation containing substrate crystal comprising the steps of: I

selecting a suitable substrate crystal such that the percentage misfit between the lattice parameters of said seed crystal and the crystal to be grown is at least equal to bL cos A wherein p is the dislocation density, b is the magnitude of Burgers vector of'the misfit dislocation, L is the diameter at the interface of the substrate crystal and the crystal to be grown and A is the angle between the Burgers vector and that direction in said interface which is perpendicular to the line of intersection of the slip plane and the interface, but less than .7%.

cutting said substrate crystal at the plane selected from a group of planes determined from the slip system of the crystal as calculated graphically from stereographic projections;

growing a crystal upon said plane of the seed crystal to a thickness at least equal to l7( 111) fll-i-v) cos A wherein b is said magnitude of the Burgers vector, v is Poissons ratio, 1 is said percentage misfit and A is said angle measured from the Burgers vector the cosine of A not equaling zero.

2. The method of claim 1 wherein said substrate crystals are selected from the group of fcc. crystals, consisting of Al, Ni, Cu, Au, P'd, Ag, Pt, Si, Ge, GaAs, GaP, and InSb.

3. The method of claim 1 wherein said substrate crystals are selected from the group of bcc. crystals, consisting of Fe, Nb, Cr, W, Ta and Mo.

4. The method of claim 1 wherein said substrate crystals are selected from the group consisting of PbS, PbSe and PbTe.

5. The method of claim 2 wherein the plane is in the vicinity of the (012) plane.

6. The method of claim 3 wherein the plane is in the vicinity of the (001) plane.

7. The method claim 4 wherein the plane is in the vicinity of the (1 23) plane.

8. A method of growing a dislocation free germanium crystal on a gallium arsenide monocrystalline substrate comprising the steps of:

cutting said gallium arsenide monocrystalline substrate in the vicinity of the (012) plane to form an interface on which to grow the germanium crystal;

measuring the dislocation density p of said substrate at said interface;

adjusting the size of said interface, L, to less than wherein f is the percentage misfit between the unstrained lattice parameters of the crystals, b is the Burgers vector and the A is the angle between the Burgers vector and that direction in the interface which is perpendicular to the line of intersection of the slip plane and the interface;

growing a germanium crystal onto the GaAs interface to a thickness at least equal to wherein b is said magnitude of the Burgers vector, v is Poissons ratio, 1 is said percentage misfit and A is said angle measured from the Burgers vector the cosine of A not equaling zero 9. A method of growing dislocation free doped silicon crystals on a monocrystalline silicon substrate comprising the steps of:

cutting said monocrystalline silicon substrate in the vicinity of the (012) plane to form an interface on which to grow the doped silicon crystal; passing over said silicon substrate silicon vapors containing dopant atoms comprising the group consisting of B, P, As, Al, Ga, In, Sb and whose concentration is such that the percentage misfit between the crystals is greater than pbL cos 4 wherein p is the dislocation density of the interface of the monocrystalline silicon substrate, b is the magnitude of the Burgers vector of the misfit disclocations, L is the diameter at the interface and A is the angle between the Burgers vector and that direction in the interface which is perpendicular to the line of intersection of the slip plane and the interface;

growing a doped silicon crystal on said interface from said vapors to a thickness of at least equal to wherein b is the magnitude of the Burgers vector, 1 is Poissons ratio, f is the percentage misfit and A is said angle measured from the Burgers vector the cosine of A not equaling zero.

10. The method of growing dislocation free silicon crystals on a silicon substrate comprising the steps of:

cutting said monocrystalline silicon substrate in the vicinity of the (012) plane to form an interface on which to grow the doped silicon crystal;

passing over said silicon substrate silicon vapors containing dopant atoms selected from the group consisting of B, P, As, A], Ga, In, Sb and whose concentration is such that the percentage misfit between the crystals is greater than pbL cos A 4 wherein p is the dislocation density of the interface of the monocrystalline silicon substrate, b is the magnitude of the Burgers vector of the misfit dislocations, L is the diameter at the interface and A is the angle between the Burgers vector and that direction in the interface which is perpendicular to the line of intersection of the slip plane and the interface;

No. 75445 Rampmeyer, C. M. 1-7-74 Day Mach. 58

growing a doped silicon crystal on said interface from said vapors to a thickness of at least equal to wherein b is the magnitude of the Burgers vector, v is Poissons ratio, f is the percentage misfit and A is said angle measured from the Burgers vector the cosine of A not equaling zero;

growing a silicon crystal on said dope silicon crystal 'by passing over said doped silicon crystal silicon vapors containing no dopant atoms whereby a dislocation free crystal is grown on a substantially identical substrate.

11. A method of growing dislocation free chromium filrns on a monocrystalline iron substrate comprising the steps of:

cutting said iron substrate in the vicinity of the (001) plane to form an interface on which to grow the chromium crystal;

12 adjusting the size of the interface L to less than 1 b cos A wherein f is the misfit between the unstrained lattice parameters of the crystals, b is the Burgers vector and A is the angle between the Burgers vector and that direction in the interface which is perpendicular to the line of intersection of the slip plane and the interface; vacuum depositing a chromium film onto the interface to a thickness greater than References Cited UNITED STATES PATENTS 3,476,592 11/1969 Berkenblit 117 201 3,309,553 5/1967 Kroemer 313-108 3,047,423 7/1962 Eggenberger 117107 ALFRED L. LEAVI'IT, Primary Examiner M. F. EsPosrro, Assistant Examiner US. Cl. X.R. 1l7-l06 R, 106 A, 1 67, 227, 230; l48-175 Po-ww UNITED ST$1TES PATENT OFFICE CERTIFICATE OF CORRECTION Patent: No. 3,788,890 named January 29, 197 1 Inventor) S. R. Mader and J. W. Matthew:

It is eertified that error appears in the above-identified patent and that said Letters Patent are hereby corrected as shown below:

FColumn 9, lirie 1o, Claim 1, the equation ""b'L' cos x" should read 'b'L' cos' A 5 Column 11, line 9 delete the line reading "No. 75 4 15 Rampmeyer', C. M. 1-7-7 'Day Mach. 58"

Signed and sealed this 5th day of November 1974.

(SEAL) Attest:

McCOY M. GIBSON JR. C. MARSHALL DANN Attesting Officer Commissioner of Patents

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