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Automated spatial filtering for rapid characterization of LPE bubble garnet films
Mat. Res. BuU., Vol. 15, pp. 1669-1677, 1980. Printed in the USA. 0025-5408/80/111669-09502.00/0 Copyright (c) 1980 Pergamon Press Ltd.
AUTOMATED SPATIAL FILTERING FOR RAPID CHARACTERIZATION OF LPE BUBBLE GARNET FILMS
P. B. 3ohnson, M. Karnezos and R. D. Henry National Semiconductor Corporation 2900 Semiconductor Drive Santa Clara, CA 95051
(Received July 2, 1980; Refereed)
ABSTRACT An automated spatial filtering apparatus used for characterization of magnetic bubble films'with zero field strip widths greater than 1.5~m has been constructed. This apparatus makes measurements of the zero field period and the period in an applied magnetic field. When these two measurements are combined with measured values for the film thickness and the Ne41 temperature, values for relevant material parameters of the bubble films can be calculated using the Kooy and Enz theory. Details of the spatial filter apparatus, the method used for data analysis, and the accuracy of the method are discussed.
Introduction As the production of bubble memory devices increases, the need for rapid characterization of bubble films i s becoming more necessary. Rapid characterization is necessary to evaluate the increasing number of wafers which are being grown in most production facilities. Conventional methods for characterizing films involve visually measuring the film's strip width and collapse fielo in addition to the film's thickness and exchange constant. The first two measurements are time consuming and require a great deal of operator care. To eliminate the need of visually measuring the strip width and collapse field, a spatial filter (I, 2, 3) has been constructed. This device measures the spatial period of the magnetic domains in zero applied magnetic field and in one non-zero appIied fieId. When these two measurements are combined with the measured film thickness and exchange constant, values of the material parameters for the film can be caIculated.
The spatial filter is totally automated and is ideally suited to rapidly characterizing production line films. The errors introduced into the calculated values of the material parameters are comparable to the errors resulting from conventional characterizing techniques and are much smaller than the tolerances in the parameters allowed in our bubble memory devices. The spatial 1ARQ
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filter discussed here can characterize films with zero field periods down to 3~m; however, with minor modifications, films with even smaller zero field period can be characterized.
Theory The behavior of an idealized bubble film in an externai magnetic field applied normai to the fiim's surface is described by the Kooy and Enz equations (4). An ideaiized film is assumed to have a preferential direction of magnetization normal to the film, infinite lateral dimensions, a~d a straight domain pattern with the demagnetization and 81och walls perpendicular to the film's surface. For such a system, the total energy of the film can be written as the sum of the wall energy, the energy of the magnetization in the external field, and the demagnetizing energy of the domain pattern. From the expression for the total energy, the stable period of the domains in an arbitrary applied field can be calculated by minimizing the total energy with respect to the magnetization and also with respect to the domain period. Such a procedure yields two simultaneous equations:
~ f l = ~~' - ~n + ~ \
1
/~_._j n= I
"~ -2n ~ / ~ ) sin [ n ' f f (1 + M)] (1 - e
= 0
n2
and
f2 = _ ~ + ~ 2
E
1
~" n= where P = P, h
(1 - e - 2 n l ~ / ~ (1 + 2 n ~ / ~ ) )
sin 2 [ n ~
n3
(1 +'M)] = 0 2
1
=__~, h
= __M, and H = H MS 4 mf M S
In these equations P is the period of the domain pattern, M is the resulting magnetization in the applied field H, h is the film thickness, ~ is the characteristic length, and M s is the saturation magnetization of the film.
By measuring values for the film thickness h, the zero field period Po, and one set of P and H, the expressions for fl and f2 can be solved self-consistently for M and 4 ~ M s. Using the value for 4 ~ M s along with a measured value for the exchange constant A, other material parameters for the film can be calculated directly.
Description of the Spatial Filter The spatial filter apparatus is used to measure Po and P in an applied field H by utilizing the bubble film as a diffraction grating. When a polarized monochromatic light beam from a He-Ne Laser is normally incident on a bubble film, the beam is diffracted by the mixed domain pattern of the film into a cone of light. If e is the angle of this cone with respect to the normal of the film, then the wavelength of the light ~ (0.6328um) and the period of the domain pattern .P are related by n ~ = P sin 8 where n is the order of the diffraction. By measuring the angle 8, the corresponding period can be caIcuiated.
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To measure B, a spatial filter is used. The spatial filter consists of a clear ring on an opaque chrome covered glass slide. The width of the ring is 0.1cm and its mean radius is r = 1.5cm. The spatial filter is initially placed close and parallel to the bubble film. The center of the ring on the filter is concentric with the zero order undiffracted laser beam. To determine B, the spatial filter is moved away from the bubble film, and the light which passes through the ring is collected by a lens and focused onto a photomultiplier detector. When the cone of diffracted light corresponding to the first order diffraction intersects the clear ring of the filter, an intensity maximum is detected. By measuring the distance from the film to the filter at which maximum intensity is observed, 8 can be calculated by B = tan -I (r/d).
FIG. 1 Block Diagram for the Spatial Filter Apparatus
A block diagram for the spatial filter is shown in Figure I. The entire device is computer controlled. The magnetic field is supplied by a set of Helmholtz coils. Before each measurement, the DC magnetic field is increased to 300 Oe in order to totally saturate the magnetization of the film and collapse any bubbles which may be present. Superimposed on the DC field is an AC field of about 30 Oe. The DC field is then decreased from 300 Oe to any desired value in about 10 seconds and when the desired level is reached the AC field is reduced to zero in a similar amount of time. Such a procedure prepares the film for measurement in a reproducible manner which minimizes the energy of the resulting domain pattern. Once the film is prepared, the spatial filter moves over its range of travel and collects 300 data pairs of position and intensity. From these measured values the computer selects the location of maximum intensity and fits 20 points on either side of the maximum to a quadratic polynomial. The location of the apex of the fitted parabola is used to determine the distance from the film to the filter at maximum intensity. Using this distance the domain period is calculated by the procedure described above.
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SPATIAL FILTER RADIUS = 1.5 cm SPATIAL FILTER TRAVEL RANGE
Po = 5
I 0 I
i 5 I 2
.
2
4
~
~
I i 10 15 DISTANCE FROM FILM (crn) I 3
I I I 4 5 6 PERIO0 (~m)
I 7
I 20 I 8
I 25
I 9
] 10
FIG. 2 Range of travel for the spatial filter. The two horizontal axes show the distance of the filter from the film and the corresponding domain period. The two cones of light correspond to the measurements of diffracted intensity shown in Figure 3. The two vertical lines represent the filter positions when the cones of light intersect the spatial filter's clear ring.
Figure 2 shows the range of travel for the spatial filter and the filter position necessary to intersect the cone of diffracted light as a function of the domain period. An aspherical biconvex lens is placed a distance of 2f from the film focusing the light onto the photomultiplier tube located 2f behind the lens. The aspherical biconvex lens is used to minimize spherical aberration and insure that a light cone of any diameter which intersects the lens is focused onto the detector. In general the lens should have a large diameter and short focal length in order to cq-llect the light diffracted from domain patterns with small periods. The system shown in Figure 2 is capable of measuring periods as small as 3.0~m; however, with a larger diameter lens smaller periods could be measured: Studies by O. Challeton (5) indicate that periods as small as 2~. can be measured. Smaller periods could also be measured without changing the lens by using an Argon laser which has a shorter wavelength ( ~ = 0.51~5~m). There are several differences between the measurements performed by this spatial filter apparatus and the one previously reported by R. O. Henry. (I) The primary difference is that the present spatial filter analyzes only the first order diffraction from the bubble film to determine the zero-field and the finite field domain periods. The earlier apparatus has to measure b o t h the first order diffraction in zero field and then the field atwhich the maximum in the second order diffraction occurred. The current technique has the advantage tha~ the measured first order diffraction is more intense and easier to detect than the second order signal. In addition,.the need for sweeping the field has been eliminated since the present system always sets a field and moves the filter. This procedure eliminates the problem of reproducibly mixing the domains while the magnetic field is being swept.
Vol. 15, No. 11
BUBBLE GARNET FILMS
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Experimental Results 15-~"
-
h
= 2.12~an
-
Wo
: 2.621.ern
A
: 2.59 x 10-7 ergJcm
Q
:. 5.18 = 0.323jan
1.... >n< n-
10
t
4elMs = 360 GAUSS Hcoll = 158 Oe Ku : 2.67 x 104 Im@/cm@ t
Hk
==1583Oe
5
6.63
10.63
15.63
20.63
DISTANCE FROM FiLM TO SPATIAL FILTER (cm)
FIG. ] Measured intensity of diffracted light vs position of the spatial filter. The curve corresponding to Pc = 5.24pm was measured in zero applied field, lhe shoulder to the left of the peak results from the light diffracted by the film on the back surface of the substrate. The curve labeled P = 6.12~m was measured in an applied field of 67 Oe.
Figure ] shows the measurements made on a characteristic film which is used in a quarter mega-bit bubble memory device. Before the film was measured by the spatial filter, the film thickness h = 2.12~. and the exchange constant A = 2.59"10 -7 erg/cm were determined with other techniques. The film thickness was measured using an interf~rometric procedure, and A was calculated from the Ne~l Temperature T N = 207C which was determined by observing the temperature at which magnetic ordering disappeared. As previously noted, once h is known, the spatial filter only needs to measure Pc ( H = O) and one set of P and H so that the Kooy and Enz equations can be solved for 4 1 T M s. The measured zero field period is Pc = 5.24pm and P v H =6"13~m s at H = 67 Oe. lhe solid curve in Figure 4 shows the behavior of P for this film. The solid points on the curve correspond to the measured periods stated above. In general the value of H should be selected so that P is about 20% larger than Pc. For smaller changes in period, the accuracy of the calculated value of 4 ~ M s is reduced. For larger changes in the period, the intensity peak (Figure 3) gets smaller and broader. As a result the accuracy with which P can be measured is decreased. The broadening of the peak is probably due to two causes. First, as the period increases fewer domains intersect the laser beam and the intensity is reduced, and second, slight inhomogeneities in the field can cause a wider spread in the period of the domain pattern. Since all films used in a given bubble memory device have similar P vs H curves, one representative field is adequate for characterizing all such films. If, however, it is necessary to characterize a set of films with noticeably different parameters, a new measuring field should be selected. The dash curve in Figure 4 shows a typical curve for a megabit bubble memory film. As can be seen, for a 20% change in period the characterizing field should now be on the order of 100 Oe.
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.
- 2.,2~M
Vol. 1G, No. 11
I
0 C &l L 5 J
.-J/
~,,,,I,,,,I,,,,Izl,,I 50
100
150
200
H (Oe)
FIG. 4 Domain period vs applied field as predicted by the Kooy and Enz equations. The solid curve is characteristic of a film used in a quarter mega-bit bubble memory. The dash curve is for a mega-bit bubble memory.
Oiscussion Using measured values for h, A, Po, P and H the Kooy and Enz equations can be solved self-consistently using the following procedure:
STEP 1:
7 The value for ~ Copeland (6)
= ~o2 ~
I
is calculated using the equation of Fowlis and
(I - e-2n'I1/~o (1 + 2n~ ))
n3 n; odd
To
1
STEP 2:
f2 (~, ~, M) = 0 is solved for M using an iterative technique.
STEP 3:
Once M is known fl (M, P, H) : 0 can be solved directly for 4~IMs.
STEP 4:
Using the value for 4~Ms, values for the quality factor Q, the collapse field Hcoll , the uniaxial anisotropy Ku, and the anisotropy field Hk can be calculated.
Q
: (4 Ms h)2/32 A
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15, No. 11
BUBBLE GARNET FILMS
1675
HCOII : 4~M s (I + 3"~/4-N~"3~) Ku
= ('~'Ms2)2/A
Hk
= 2 Ku/M s
Unfortunately the equations for ~ , fl and f2 all involve infinite sums which converge very slowly. As a result it is best to include 50 terms in o each function in order to ensure convergence well within the estimated experimental errors.
Several assumptions invoived in the analysis of the data require further discussion. The first of these assumptions is that the Kooy and Enz theory can be applied to the slightly mixed domain pattern of the bubble film. The theory is derived for infinite straight domains and assumes that the film thickness is large and the Bloch wall width is small with respect to the bubble diameter. Visual microscopic examination of bubble garnet films, prepared in the manner prescribed above, reveals large areas of parallel domains, lhese areas are easily generated in both zero applied field and in finite applied field provided the amplitude of the AC mixing field is inltially large enough to easily move the domains. Io ensure that the domain patterns so generated are well represented by the Kooy and Enz theory, the calculated values of Hcoll and Hk were compared with actual values measured on the quarter mega-bit and a mega-bit film. lhe measured and calculated values of Hcoll agree to within 1% while the calculated values of Hk agreed with FMR measurement to better than )~. Finally to insure that the spatial filter results are independent of the field at which the in field measurement is performed, additional period measurements were made on the quarter mega-bit film at various values of the applied field. When these additional in field measurements were combined with the zero field period Po = 5.24~m and used to calculate values for the material parameters for the film, the resulting values were in good agreement with the quoted values obtained for P = 6.13~m and H = 6? Oe. lhe additional pairs of P and H are plotted as open circles on the solid curve in Figure 4.
A second assumption to consider is that the film on the back surface of the garnet does not affect the measurement of the epi-film. Until now we have assumed that the diffraction is only due to the epi-surface film, while in practice there is a second film on the other surface of the wafer. The period of the back film depends on the spacing between neighboring substrates which are grown simultaneously. When films are grown there is either a large separation between substrates (simiIar to growing one substrate at a time), or the substrates are grown in pairs with a smaIi separation between the back surfaces. In the first case, the films on both sides are nearIy identicai and within the resoiution of the spatial filter the resuIting cones of iight due to the two films are the same as for the epi-film alone. In the second case the back fiim is much thinner and its diffracted cone of iight is much iess intense and has a larger vaiue of 9 than the diffracted cone due to the epifiim. In this case the effect of the back film can be negIected. Both of these cases were tested by characterizing a wafer before and after the back film was stripped from the substrate. Similar values for the material parameters were determined with and without the back film.
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TABLE I Mean Values and Standard Deviations of the Measured and Calculated Parameters on the Quarter Mega-bit Film
Measured Parameters
Calculated Parameters
Po = 5 . 2 4 + 0.1% ~Jm
4 ~ M s = 360 + 1.6% Gauss
P
: 6 . 1 3 +_ 0.2% ~Jm
Hcol I = 158 ~ 0.9% Oe
H
: 67 + 0.2%
Oe
Ku
= 2.67 x 104 ÷ 7.1% erg/cm )
h
= 2.12 _.+ I,%
JJm
Hk
:
A
= 2.59 x 10-7 +__ 0.5% erg/cm
1 8 6 ) + 5.5% Oe
All five of the measured parameters h, Po, P, H and A have a certain amount of error. To determine the accuracy of the spatial filtering technique the quarter mega-bit film was run 25 times. The mean values of the measured parameters along with their standard deviations are listed in Table I. The errors in the measured parameters are propagated in the process of calculating 41~Ms, HcoII , Ku and Hk. TabIe I also includes the values of these calcuIated parameters as welI as their standard deviations. The errors in Ku and Hk are the largest, but relative to the material specifications ailowed in our bubble memory devices, the caIcuiated vaiues of Ku and Hk are more than adequate for determining if a film meets those specifications.
To check the reliability of the spatial filter, 500 production line wafers of both quarter mega-bit and mega-bit material were characterized using the spatial filter and also employing the conventional method of visually measuring stripwidth, Wo, and collapse field, Hcoll. The conventional measurements were combined with h and A, and the parameters 41~Ms, Ku, and Hk were calculated. In all cases the values for the calculated material parameters determined by the two methods agreed to within twice the error estimates summarized in Table I. When the value for the collapse field calculated by the spatial filter was compared with the actual measured value, the agreement was always better than 3 0 e .
Conclusions A spatiaI fiiter capable of characterizing bubble films with zero fieid periods greater than 3~m has been presented. The spatial filter is currentIy used to characterize p~oduction line wafers used in a ouarter mega-bit bubble memory. To characterize these fiims the spatial filter determines vaiues of the zero fieId period and the period in fieId of 67 Oe. When these vaiues are combined with the measured fiIm thickness and exchange constant, vaIues for the materiaI parameters of the fi!ms are caiculated using the Kooy and Enz theory. The vaIue of Po on a given film can be measured reproducibly to + 0.1% This accuracy is much greater than the 15% error quoted by Mier et aI, (77 who claim that spatiai filter measurements are not a reiiabIe means of characterizing bubbIe fiims. On the contrary, we have shown that the spatial fiiter is a powerful tooi for characterizing bubble films and that reIiable vaiues for the materiaI parameters of production line fiims are obtained.
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Acknowledgments The a u t h o r s would l i k e to thank R. H. Norton f o r h i s help i n d e s i g n i n g p a r t s o f the i n s t r u m e n t a t i o n used i n the s p a t i a l f i l t e r and f o r h i s c o l l a b o r a t i o n on v a r i o u s aspects o f the p r o j e c t . We would also l i k e to thank W. B. Smith f o r h i s help i n i n c o r p o r a t i n g the s p a t i a l f i l t e r i n t o p r o d u c t i o n l i n e use and f o r performing the r e l i a b i l i t y t e s t s on the p r o d u c t i o n l i n e wafers. References 1.
R. D. Henry, Mat. Res. B u l l . 11, 1295 (1976).
2.
R. O. Henry, IEEE HAG-13, 1547 (1977).
3.
Ming-jau Sun, IEEE I n t e r n a t i o n a l 19U0.
4.
C. Kooy and V. Enz, P h i l i p s
5.
D. C h a l l e t o n , F i r s t I n t e r n a t i o n a l Conference on Bubble Hemory M a t e r i a l s and Process Technology, Santa Barbara, CA, February, 1980.
6.
D. C. Fowlis and 3. A. Copeland, A . I . P .
7.
M. G. Mier e tt a~, J. Appl. Phys. 50, 2185 (1979).
Magnetics Conference, Boston, A p r i l ,
Res. Repts. 15, 7 (1960).
Conf. Proc. No. 5, 240 (1971).
AUTOMATED SPATIAL FILTERING FOR RAPID CHARACTERIZATION OF LPE BUBBLE GARNET FILMS
P. B. 3ohnson, M. Karnezos and R. D. Henry National Semiconductor Corporation 2900 Semiconductor Drive Santa Clara, CA 95051
(Received July 2, 1980; Refereed)
ABSTRACT An automated spatial filtering apparatus used for characterization of magnetic bubble films'with zero field strip widths greater than 1.5~m has been constructed. This apparatus makes measurements of the zero field period and the period in an applied magnetic field. When these two measurements are combined with measured values for the film thickness and the Ne41 temperature, values for relevant material parameters of the bubble films can be calculated using the Kooy and Enz theory. Details of the spatial filter apparatus, the method used for data analysis, and the accuracy of the method are discussed.
Introduction As the production of bubble memory devices increases, the need for rapid characterization of bubble films i s becoming more necessary. Rapid characterization is necessary to evaluate the increasing number of wafers which are being grown in most production facilities. Conventional methods for characterizing films involve visually measuring the film's strip width and collapse fielo in addition to the film's thickness and exchange constant. The first two measurements are time consuming and require a great deal of operator care. To eliminate the need of visually measuring the strip width and collapse field, a spatial filter (I, 2, 3) has been constructed. This device measures the spatial period of the magnetic domains in zero applied magnetic field and in one non-zero appIied fieId. When these two measurements are combined with the measured film thickness and exchange constant, values of the material parameters for the film can be caIculated.
The spatial filter is totally automated and is ideally suited to rapidly characterizing production line films. The errors introduced into the calculated values of the material parameters are comparable to the errors resulting from conventional characterizing techniques and are much smaller than the tolerances in the parameters allowed in our bubble memory devices. The spatial 1ARQ
1670
P.B.
JOHNSON, et al.
Vol. 15, No. I I
filter discussed here can characterize films with zero field periods down to 3~m; however, with minor modifications, films with even smaller zero field period can be characterized.
Theory The behavior of an idealized bubble film in an externai magnetic field applied normai to the fiim's surface is described by the Kooy and Enz equations (4). An ideaiized film is assumed to have a preferential direction of magnetization normal to the film, infinite lateral dimensions, a~d a straight domain pattern with the demagnetization and 81och walls perpendicular to the film's surface. For such a system, the total energy of the film can be written as the sum of the wall energy, the energy of the magnetization in the external field, and the demagnetizing energy of the domain pattern. From the expression for the total energy, the stable period of the domains in an arbitrary applied field can be calculated by minimizing the total energy with respect to the magnetization and also with respect to the domain period. Such a procedure yields two simultaneous equations:
~ f l = ~~' - ~n + ~ \
1
/~_._j n= I
"~ -2n ~ / ~ ) sin [ n ' f f (1 + M)] (1 - e
= 0
n2
and
f2 = _ ~ + ~ 2
E
1
~" n= where P = P, h
(1 - e - 2 n l ~ / ~ (1 + 2 n ~ / ~ ) )
sin 2 [ n ~
n3
(1 +'M)] = 0 2
1
=__~, h
= __M, and H = H MS 4 mf M S
In these equations P is the period of the domain pattern, M is the resulting magnetization in the applied field H, h is the film thickness, ~ is the characteristic length, and M s is the saturation magnetization of the film.
By measuring values for the film thickness h, the zero field period Po, and one set of P and H, the expressions for fl and f2 can be solved self-consistently for M and 4 ~ M s. Using the value for 4 ~ M s along with a measured value for the exchange constant A, other material parameters for the film can be calculated directly.
Description of the Spatial Filter The spatial filter apparatus is used to measure Po and P in an applied field H by utilizing the bubble film as a diffraction grating. When a polarized monochromatic light beam from a He-Ne Laser is normally incident on a bubble film, the beam is diffracted by the mixed domain pattern of the film into a cone of light. If e is the angle of this cone with respect to the normal of the film, then the wavelength of the light ~ (0.6328um) and the period of the domain pattern .P are related by n ~ = P sin 8 where n is the order of the diffraction. By measuring the angle 8, the corresponding period can be caIcuiated.
Vol. 15, No. i i
BUBBLE GARNET FILMS
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To measure B, a spatial filter is used. The spatial filter consists of a clear ring on an opaque chrome covered glass slide. The width of the ring is 0.1cm and its mean radius is r = 1.5cm. The spatial filter is initially placed close and parallel to the bubble film. The center of the ring on the filter is concentric with the zero order undiffracted laser beam. To determine B, the spatial filter is moved away from the bubble film, and the light which passes through the ring is collected by a lens and focused onto a photomultiplier detector. When the cone of diffracted light corresponding to the first order diffraction intersects the clear ring of the filter, an intensity maximum is detected. By measuring the distance from the film to the filter at which maximum intensity is observed, 8 can be calculated by B = tan -I (r/d).
FIG. 1 Block Diagram for the Spatial Filter Apparatus
A block diagram for the spatial filter is shown in Figure I. The entire device is computer controlled. The magnetic field is supplied by a set of Helmholtz coils. Before each measurement, the DC magnetic field is increased to 300 Oe in order to totally saturate the magnetization of the film and collapse any bubbles which may be present. Superimposed on the DC field is an AC field of about 30 Oe. The DC field is then decreased from 300 Oe to any desired value in about 10 seconds and when the desired level is reached the AC field is reduced to zero in a similar amount of time. Such a procedure prepares the film for measurement in a reproducible manner which minimizes the energy of the resulting domain pattern. Once the film is prepared, the spatial filter moves over its range of travel and collects 300 data pairs of position and intensity. From these measured values the computer selects the location of maximum intensity and fits 20 points on either side of the maximum to a quadratic polynomial. The location of the apex of the fitted parabola is used to determine the distance from the film to the filter at maximum intensity. Using this distance the domain period is calculated by the procedure described above.
1672
P . B . JOHNSON, e t al.
Vol. 15, No. 11
SPATIAL FILTER RADIUS = 1.5 cm SPATIAL FILTER TRAVEL RANGE
Po = 5
I 0 I
i 5 I 2
.
2
4
~
~
I i 10 15 DISTANCE FROM FILM (crn) I 3
I I I 4 5 6 PERIO0 (~m)
I 7
I 20 I 8
I 25
I 9
] 10
FIG. 2 Range of travel for the spatial filter. The two horizontal axes show the distance of the filter from the film and the corresponding domain period. The two cones of light correspond to the measurements of diffracted intensity shown in Figure 3. The two vertical lines represent the filter positions when the cones of light intersect the spatial filter's clear ring.
Figure 2 shows the range of travel for the spatial filter and the filter position necessary to intersect the cone of diffracted light as a function of the domain period. An aspherical biconvex lens is placed a distance of 2f from the film focusing the light onto the photomultiplier tube located 2f behind the lens. The aspherical biconvex lens is used to minimize spherical aberration and insure that a light cone of any diameter which intersects the lens is focused onto the detector. In general the lens should have a large diameter and short focal length in order to cq-llect the light diffracted from domain patterns with small periods. The system shown in Figure 2 is capable of measuring periods as small as 3.0~m; however, with a larger diameter lens smaller periods could be measured: Studies by O. Challeton (5) indicate that periods as small as 2~. can be measured. Smaller periods could also be measured without changing the lens by using an Argon laser which has a shorter wavelength ( ~ = 0.51~5~m). There are several differences between the measurements performed by this spatial filter apparatus and the one previously reported by R. O. Henry. (I) The primary difference is that the present spatial filter analyzes only the first order diffraction from the bubble film to determine the zero-field and the finite field domain periods. The earlier apparatus has to measure b o t h the first order diffraction in zero field and then the field atwhich the maximum in the second order diffraction occurred. The current technique has the advantage tha~ the measured first order diffraction is more intense and easier to detect than the second order signal. In addition,.the need for sweeping the field has been eliminated since the present system always sets a field and moves the filter. This procedure eliminates the problem of reproducibly mixing the domains while the magnetic field is being swept.
Vol. 15, No. 11
BUBBLE GARNET FILMS
1673
Experimental Results 15-~"
-
h
= 2.12~an
-
Wo
: 2.621.ern
A
: 2.59 x 10-7 ergJcm
Q
:. 5.18 = 0.323jan
1.... >n< n-
10
t
4elMs = 360 GAUSS Hcoll = 158 Oe Ku : 2.67 x 104 Im@/cm@ t
Hk
==1583Oe
5
6.63
10.63
15.63
20.63
DISTANCE FROM FiLM TO SPATIAL FILTER (cm)
FIG. ] Measured intensity of diffracted light vs position of the spatial filter. The curve corresponding to Pc = 5.24pm was measured in zero applied field, lhe shoulder to the left of the peak results from the light diffracted by the film on the back surface of the substrate. The curve labeled P = 6.12~m was measured in an applied field of 67 Oe.
Figure ] shows the measurements made on a characteristic film which is used in a quarter mega-bit bubble memory device. Before the film was measured by the spatial filter, the film thickness h = 2.12~. and the exchange constant A = 2.59"10 -7 erg/cm were determined with other techniques. The film thickness was measured using an interf~rometric procedure, and A was calculated from the Ne~l Temperature T N = 207C which was determined by observing the temperature at which magnetic ordering disappeared. As previously noted, once h is known, the spatial filter only needs to measure Pc ( H = O) and one set of P and H so that the Kooy and Enz equations can be solved for 4 1 T M s. The measured zero field period is Pc = 5.24pm and P v H =6"13~m s at H = 67 Oe. lhe solid curve in Figure 4 shows the behavior of P for this film. The solid points on the curve correspond to the measured periods stated above. In general the value of H should be selected so that P is about 20% larger than Pc. For smaller changes in period, the accuracy of the calculated value of 4 ~ M s is reduced. For larger changes in the period, the intensity peak (Figure 3) gets smaller and broader. As a result the accuracy with which P can be measured is decreased. The broadening of the peak is probably due to two causes. First, as the period increases fewer domains intersect the laser beam and the intensity is reduced, and second, slight inhomogeneities in the field can cause a wider spread in the period of the domain pattern. Since all films used in a given bubble memory device have similar P vs H curves, one representative field is adequate for characterizing all such films. If, however, it is necessary to characterize a set of films with noticeably different parameters, a new measuring field should be selected. The dash curve in Figure 4 shows a typical curve for a megabit bubble memory film. As can be seen, for a 20% change in period the characterizing field should now be on the order of 100 Oe.
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.
- 2.,2~M
Vol. 1G, No. 11
I
0 C &l L 5 J
.-J/
~,,,,I,,,,I,,,,Izl,,I 50
100
150
200
H (Oe)
FIG. 4 Domain period vs applied field as predicted by the Kooy and Enz equations. The solid curve is characteristic of a film used in a quarter mega-bit bubble memory. The dash curve is for a mega-bit bubble memory.
Oiscussion Using measured values for h, A, Po, P and H the Kooy and Enz equations can be solved self-consistently using the following procedure:
STEP 1:
7 The value for ~ Copeland (6)
= ~o2 ~
I
is calculated using the equation of Fowlis and
(I - e-2n'I1/~o (1 + 2n~ ))
n3 n; odd
To
1
STEP 2:
f2 (~, ~, M) = 0 is solved for M using an iterative technique.
STEP 3:
Once M is known fl (M, P, H) : 0 can be solved directly for 4~IMs.
STEP 4:
Using the value for 4~Ms, values for the quality factor Q, the collapse field Hcoll , the uniaxial anisotropy Ku, and the anisotropy field Hk can be calculated.
Q
: (4 Ms h)2/32 A
Vol.
15, No. 11
BUBBLE GARNET FILMS
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HCOII : 4~M s (I + 3"~/4-N~"3~) Ku
= ('~'Ms2)2/A
Hk
= 2 Ku/M s
Unfortunately the equations for ~ , fl and f2 all involve infinite sums which converge very slowly. As a result it is best to include 50 terms in o each function in order to ensure convergence well within the estimated experimental errors.
Several assumptions invoived in the analysis of the data require further discussion. The first of these assumptions is that the Kooy and Enz theory can be applied to the slightly mixed domain pattern of the bubble film. The theory is derived for infinite straight domains and assumes that the film thickness is large and the Bloch wall width is small with respect to the bubble diameter. Visual microscopic examination of bubble garnet films, prepared in the manner prescribed above, reveals large areas of parallel domains, lhese areas are easily generated in both zero applied field and in finite applied field provided the amplitude of the AC mixing field is inltially large enough to easily move the domains. Io ensure that the domain patterns so generated are well represented by the Kooy and Enz theory, the calculated values of Hcoll and Hk were compared with actual values measured on the quarter mega-bit and a mega-bit film. lhe measured and calculated values of Hcoll agree to within 1% while the calculated values of Hk agreed with FMR measurement to better than )~. Finally to insure that the spatial filter results are independent of the field at which the in field measurement is performed, additional period measurements were made on the quarter mega-bit film at various values of the applied field. When these additional in field measurements were combined with the zero field period Po = 5.24~m and used to calculate values for the material parameters for the film, the resulting values were in good agreement with the quoted values obtained for P = 6.13~m and H = 6? Oe. lhe additional pairs of P and H are plotted as open circles on the solid curve in Figure 4.
A second assumption to consider is that the film on the back surface of the garnet does not affect the measurement of the epi-film. Until now we have assumed that the diffraction is only due to the epi-surface film, while in practice there is a second film on the other surface of the wafer. The period of the back film depends on the spacing between neighboring substrates which are grown simultaneously. When films are grown there is either a large separation between substrates (simiIar to growing one substrate at a time), or the substrates are grown in pairs with a smaIi separation between the back surfaces. In the first case, the films on both sides are nearIy identicai and within the resoiution of the spatial filter the resuIting cones of iight due to the two films are the same as for the epi-film alone. In the second case the back fiim is much thinner and its diffracted cone of iight is much iess intense and has a larger vaiue of 9 than the diffracted cone due to the epifiim. In this case the effect of the back film can be negIected. Both of these cases were tested by characterizing a wafer before and after the back film was stripped from the substrate. Similar values for the material parameters were determined with and without the back film.
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Vol. 15, No. Ii
TABLE I Mean Values and Standard Deviations of the Measured and Calculated Parameters on the Quarter Mega-bit Film
Measured Parameters
Calculated Parameters
Po = 5 . 2 4 + 0.1% ~Jm
4 ~ M s = 360 + 1.6% Gauss
P
: 6 . 1 3 +_ 0.2% ~Jm
Hcol I = 158 ~ 0.9% Oe
H
: 67 + 0.2%
Oe
Ku
= 2.67 x 104 ÷ 7.1% erg/cm )
h
= 2.12 _.+ I,%
JJm
Hk
:
A
= 2.59 x 10-7 +__ 0.5% erg/cm
1 8 6 ) + 5.5% Oe
All five of the measured parameters h, Po, P, H and A have a certain amount of error. To determine the accuracy of the spatial filtering technique the quarter mega-bit film was run 25 times. The mean values of the measured parameters along with their standard deviations are listed in Table I. The errors in the measured parameters are propagated in the process of calculating 41~Ms, HcoII , Ku and Hk. TabIe I also includes the values of these calcuIated parameters as welI as their standard deviations. The errors in Ku and Hk are the largest, but relative to the material specifications ailowed in our bubble memory devices, the caIcuiated vaiues of Ku and Hk are more than adequate for determining if a film meets those specifications.
To check the reliability of the spatial filter, 500 production line wafers of both quarter mega-bit and mega-bit material were characterized using the spatial filter and also employing the conventional method of visually measuring stripwidth, Wo, and collapse field, Hcoll. The conventional measurements were combined with h and A, and the parameters 41~Ms, Ku, and Hk were calculated. In all cases the values for the calculated material parameters determined by the two methods agreed to within twice the error estimates summarized in Table I. When the value for the collapse field calculated by the spatial filter was compared with the actual measured value, the agreement was always better than 3 0 e .
Conclusions A spatiaI fiiter capable of characterizing bubble films with zero fieid periods greater than 3~m has been presented. The spatial filter is currentIy used to characterize p~oduction line wafers used in a ouarter mega-bit bubble memory. To characterize these fiims the spatial filter determines vaiues of the zero fieId period and the period in fieId of 67 Oe. When these vaiues are combined with the measured fiIm thickness and exchange constant, vaIues for the materiaI parameters of the fi!ms are caiculated using the Kooy and Enz theory. The vaIue of Po on a given film can be measured reproducibly to + 0.1% This accuracy is much greater than the 15% error quoted by Mier et aI, (77 who claim that spatiai filter measurements are not a reiiabIe means of characterizing bubbIe fiims. On the contrary, we have shown that the spatial fiiter is a powerful tooi for characterizing bubble films and that reIiable vaiues for the materiaI parameters of production line fiims are obtained.
Vol. 15, No. 11
BUBBLE GARNET FILMS
1677
Acknowledgments The a u t h o r s would l i k e to thank R. H. Norton f o r h i s help i n d e s i g n i n g p a r t s o f the i n s t r u m e n t a t i o n used i n the s p a t i a l f i l t e r and f o r h i s c o l l a b o r a t i o n on v a r i o u s aspects o f the p r o j e c t . We would also l i k e to thank W. B. Smith f o r h i s help i n i n c o r p o r a t i n g the s p a t i a l f i l t e r i n t o p r o d u c t i o n l i n e use and f o r performing the r e l i a b i l i t y t e s t s on the p r o d u c t i o n l i n e wafers. References 1.
R. D. Henry, Mat. Res. B u l l . 11, 1295 (1976).
2.
R. O. Henry, IEEE HAG-13, 1547 (1977).
3.
Ming-jau Sun, IEEE I n t e r n a t i o n a l 19U0.
4.
C. Kooy and V. Enz, P h i l i p s
5.
D. C h a l l e t o n , F i r s t I n t e r n a t i o n a l Conference on Bubble Hemory M a t e r i a l s and Process Technology, Santa Barbara, CA, February, 1980.
6.
D. C. Fowlis and 3. A. Copeland, A . I . P .
7.
M. G. Mier e tt a~, J. Appl. Phys. 50, 2185 (1979).
Magnetics Conference, Boston, A p r i l ,
Res. Repts. 15, 7 (1960).
Conf. Proc. No. 5, 240 (1971).