94
Anal. Chem. 1986, 58,94-101
Evaluation of Ion Microscopic Spatial Resolution and Image Quality Mark T. Bernius, Yong-Chien Ling, and George H. Morrison* Baker Laboratory of Chemistry, Cornell University, Ithaca, New York 14853-1301
Practial technlques for lnterpretlng the spatlal resolutlon and Image quallty In Ion mlcroscopy are proposed. A flrst-order examination of those instrumental parameters that Influence the image-generatlng process in the stlgmatlc ion microscope Is presented. Mlcrotest patterns that have been fabrlcated by using electron beam llthographictechnlques along wlth the lnstrumehal modulation transfer function are employed for the evaluatlon of Imaging performance. Wlth the asslstance of dlgltal processing, the fundamental prlnclples of Image analysis outlined In thls paper are offered as a base llne for the quantification of chemical information In Ion mlcrographs.
During the past decade ion microscopy (based on secondary ion mass spectrometry) has become increasingly important as an analytical tool for qualitative elemental localization in solid-state and biological matrices (1). Its role in the analytical laboratory will expand with the advent of ultrahigh-resolution scanning ion microscopes (2) to complement electron microscopy with surface and near-surface chemical information not easily accessible to the latter. With increasing dependence on imaging techniques to supply quantitative microchemical information, the need for objective standard criteria to characterize the image becomes apparent. Conventional ion microscopy is good only for those sample structures that can easily be identified in the formed image, which are typically evaluated by purely subjective measures. Therefore a basic problem in the use of ion microscopic analysis is the ability to resolve fine detail and to separate the image signal of true elemental distributions in the sample from any artifacts due inherently to the instrumental technique. The instrumental operation coupled with the specific physical characteristics of the sample can cause visual distortions in the sample’s image. When features of interest are on the order of the resolution limit of the instrument, the nature of these artifacts becomes extremely important. The ultimate limiting capabilities of an instrument will vary from analysis to analysis depending on the nature of the sample and the operating conditions. In order to apply methods of quantification to ion images for features nearing the resolution limit of the ion microscope, it is first necessary to examine quantitatively the image-generating process in terms of the resolution and contrast of the images formed. The objective of this study is to provide the basic principles to evaluate the imaging quality of the ion microscope. Research was undertaken not only to produce a method of quantitatively measuring the instrumental resolution under various operating conditions but also to establish procedures for the description of the instrumental ability to generate quality images. This study was performed by using a direct imaging stigmatic ion microscope but was kept general when possible to be applicable to other types of imaging instruments. Fabricated elemental imaging test patterns on the micrometer scale are proposed with subsequent image quality assessments accomplished by digital image processing. From a system
point of view, the instrumental modulation transfer function is used to describe the imaging system performance in the frequency domain. This transfer function incorporates those important variables typically not considered and is offered to fulfill the need of objective image quality assessment for microanalytical studies.
EXPERIMENTAL SECTION Sample Preparation. Samples were fabricated and tested as standard patterns for use on the ion microscope for quantitative image evaluation. They are (a) polished silicon wafers with polymer resist bar patterns and (b) polished silicon wafers with aluminum bar patterns, both made at the National Research and Resource Facility for SubmicronStructures (NRRFSS)at Cornell, and (c) silicon crystal edges, which were made by cleaving polished silicon wafers along the crystal planes. The latter sample was prepared by imbeddingthe silicon shards in a Sn-Bi eutectic. By surrounding the silicon pieces, the eutectic prevents any distortion from the vertical sides of the silicon when imaging an edge, as the primary beam strikes the sample at an angle to the sample’s normal. The polymer resist used for fabricating test patterns on the silicon wafers is poly(methy1methacrylate) electron-beamresist (PMMA),which is spun on the silicon prior to pattern exposure on a Cambridge EBMF-2 electron beam lithography system. Patterns were directly written on the PMMA, and the irradiated resist was removed by a developer to leave the polymer that was not exposed to the electrons. The thickness of the resist is about 0.4 pm. The PMMA bars are imaged by tuning the ion microscope to the silicon substrate material. The overall pattern is a series for four bar patterns contained in a 1 X 1mm area; the four patterns have exposed silicon rectangles of 1.30, 0.75, 0.55, and 0.25 pm widths, having periods of 3.00 pm (for the 1.30-pm bar set) and 2.00 pm (for the others). Under primary ion bombardment in the ion microscope, the PMMA resist slowly sputters away. Therefore this sample is removed after an image is recorded and examined with a scanning electron microscope (SEM) to verify the bar dimensions, which are then used in numerical calculations. The Al/Si bar pattern was fabricated the same way, but with the addition of depositing 900 A of A1 on the silicon wafer before washing the resist away. This resulted in a pattern that could alternately yield an aluminum or silicon bar image. This pattern consisted of four bar widths patterned in the same way but coupled with a square-wavesignal, which resulted in bars and spaces of the same dimensions: 2.00, 1.00, 0.75, and 0.50 pm. Another type of sample structure was fabricated with the aid of the ion microscope for the examination of depth of field and topology effects. Shards of polished silicon that showed signs of damage from the cleaving process were reactive ion-beam etched primary beam at high current (RIBE) by using a focused 02+ density with 12-keV primary ion energy. It was found that the damage site assists in the development of a rough surface under these conditions; a structure that was then used in this study. Instrumental Methods. The images in this study were obtained with a Cameca IMS-3f ion microscope (3) operated with primary beam under the instrumental parameters given an 02+ in Table I. A schematic showing the instrumental sections pertinent to this study is presented in Figure la. Images were taken with the instrument optimally tuned and checked by various operators. In all cases, the positive secondary ions were detected. Comparisons of available image recording techniques were performed with emphasis on resolution and contrast, using an
0003-2700/86/0358-0094$01.50/00 1985 American Chemical Society
ANALYTICAL CHEMISTRY. VOL. 58. NO. 1, JANUARY 1988
95
Table 1. Ion Microscope Instrumental Parameters parameter
description
instrument primary ions primary ion energy primary ion current primary ion beam size transfer optics field aperture contrast aperture
Camecn IMS-3f SIMS ion microscope 02+
5.5-13 keV 1-5 f i -150 pm 150-, 4Wpm imaged field 1800 pm 20, Bo, 150,400,un
Table 11. Microdensitometer Specifications specifiontion
description
instrument data format scan made scan steps scanning aperture positional accuracy density accuracy
Joyee-hbl Microdensitometer-6 10 bits XandY 2.5-pm increment interval 0.8 X 0.8 mm' +10 pm over 250 mm travel
'Effective -dine
*0.002
b
IMMERSION LENS OEOYETR"
EXTRACTED SECONDAR"
D
awrture: 10 X 10 urn.
optical National Bureau of Standards Standard Reference Material (NBS SRM) lOlOa ( 4 ) and the microbar resolution test patterns. The NBS standard presents a series of bar patterns with the size and frequency of adjacent patterns scaled by a constant factor. The resolving power of an imaging system is related to the frequency of the smallest imaged pattern that can be clearly identilied. An on-line image digital acquisition system (MIDAS) developed in this laboratory ( 5 ) was compared to photographic methods using various types of 35-mm film. The latter method utilized a Cannon A E I SLR 35mm camera with an f / 1.2 55-mmlens to take pictures from the fluorescent acreen on the ion micmsmpe. The developed negatives were then digitized on a J o y c e - h b l Model 6 scanning microdensitometer interfaced to a PDP-I1/34A minicomputer. The instrumental parametera for the microdensitometerare given in Table II. After the developed negatives are digitized, the data are transferred tn a PDP.1 I/M.wluch is interfaced to a Grinnell image processor Model CMR-27 for further processing. Software. Instrumental control was maintained through an interfaced Hewlett-Packard9@45B microcomputer. Digital images were obtained from the microdensitometerunder IMWN (IMaGe SCaN) program control through a PDP-l1/34A minicomputer. Further image procegsing was manipulated with RAP (Resolution Analysis Package). Both programs were mitten for this study. LMWN was anitten in FORTRAN N. Kernel 1/0subroutines were coded in MACRO-I1 to speed up real4me data acquisition. Overall digitization time can k improved further by implementing a medium-size disk 1.0 buffer. Information recovery has the highest priority if any hardware malfunction occurs. This is handled by the program iuelf with minimum user intervention. The user can control the size of the image by assigning the number of readings in both X and Y directions and the distance between each reading. R*P WBJ written in FORTRAN N, except the devicedependent display I 0 subroutines which were mded in MACRO-11 to gain speed. KAP is a collection of a total of 68 subroutines that can he classified, according to their function, into display I/O, disk 110, mathematical manipulation, Fourier transform manipulation. convolution, correlation. SavitzkyColay smoothing and differ. entiation (ti). integration. statistic analysis, stimulation of various noise levels and line shapes. and curve fitting through SIMPIXX optimization (7). Multiple window display is pussible with the adaptation of a Grinnell256 X 240 frame buffer as the display medium. The user ran view the same portion of various images simultaneously before further processing. The fitted line shape can also be overlapped on the original data to view the result. RAP is interactive,80 intermediate results can be viewed as generated, if desired. All the necessary working parameters are entered diapncetically. in numerical form and in one line. Additional lines, in alphanumerical form, are required only if disk I, 0 operation
WEHNELT
ELECTRODE
Flgura 1. (a) A slmpllfied schematic of iha Cameca IM-f ion mC croscope used in lhis study. Shown are me prlmary Ion source (IS) and acceleration wlumn (PC) hihpimary ions lranSwKSe before impinging on a sample surface in +hesample chamber (SC). The transfer optics (TO) extracts and focuses the secondary ion benm. immersion and field apertures (CA), lhe electrostatic and megnetk analyzers (ES and MA). the projection lens system (PL), and microchannelplatel Auorescent screen image detector (ID). (b) Immersion O b m lensused in the siigmaik lar The sample. which fwms part of the lens, is shown emnting a secmdary ion beam inwted by the incombg primary ion beam. The secondary beam fllis a spatial
*-.
mic dsbibuUon as ii is accelerated toward ll?s Wehnelt e!+ckuda dtw to a potential diflerenca.
is involved. Default values, the most commonly used ones, are aaeigned to these working parameters beforehand. The user has the option to enter only those parameters to be modified. Thus the convenienceof interactivity and the rapid response of manmachine interface are attained simultaneously. RAP is data based in the sense that all the variables passed between the subroutines are data array only. All I/O and display-related parameters are initialized in the main program and are passed through common areas to speed communication between subroutines and to ease future program maintenance work. All operations are designed to treat the data array as operands. The user can concentrate more on data analysis instead of data communication. RAP is function-orientedin the sense that all subroutines were originated from practical need during the ourse of this study. The single main menu and two overlayer p w a m structure simplify the job of adding new functions. I
RESULTS AND DISCUSSION Analytical Figures of Merit. The resolution of the microscope is the measure of the ability to maintain the separate identity of features in the images formed by adjoining objects. The beat resolution possible with an instrument under ideal conditions will be described here as the limiting resolving power (LRP,in cyclea/pm) or the smallest resolvable distance (SRD,in pm) of that instrument. Consider the projection of two independent point sources as shown in Figure 2, with equal intensities and located symmetrically on the X axis drawn. The combined intensity distribution is given as the s u m of the individual intensities, hence I = I,(x- A)
+ 1Jx + A)
(1)
Q6
ANALYTICAL CHEMISTRY, VOL. 58, NO. 1, JANUARY 1980
b
-A
0
+A
X
Flgure 2. Intensity distribution from the two sources located symmetrically on the X axis at fA, This model is used to arrive at a working deflnition of resolution (see text for details).
where I is the intensity and A is the distance between the maxima and the origin (the subscripts 1and 2 refer to the two peaks shown). If the separation factor, A, is large, there exists two maxima, and if it is small there exists only one. At some critical value of A, the two peaks will just merge into one. As A is reduced the second derivative at the point between the two maximas will go from a negative value to a positive one, with the second derivative being identically zero when the two peaks merge. If a t this critical point ZA is set equal to y (a parameter that will be used here to describe the SRD), then an expression that allows the evaluation of y would be 11”(y/2)
+ I,”(y/2)
=0
where the double prime denotes the second derivative. As I is an even function, eq 2 is equivalent to I,”(y/2) = 0
(3)
and hence it is sufficient to consider only a single spread function curve. Since the second derivative is zero a t the inflection points, the separation of the two inflection points on a single intensity distribution can be regarded as a criterion of resolvability (8). For this study, computer simulations of various types of spread functions have been performed with varying increments of y, including the Airy function (characteristic of diffraction limited systems), and it was found that they all follow the rule that at separations greater than y, two peaks are discernible. The above argument may be applied to an imaging system’s spread function, a fundamental characteristic of the formed image, which also describes the imaging efficiency of the image generating system. The intensity distribution in an image is the convolution of the spread function of the imaging system with the function representing the object. The image of a point source for example will have a finite area roughly circular in shape, and the characteristic of this resulting spread in the image, known as the point spread function (PSF), describes the image-forming characteristics for the system at that point. The PSF, however, is insufficient for the description of the system LRP, as the PSF is actually a projection in three dimensions, and alone is not sensitive to distortion of the image field. The line spread function (LSF), the summation of an array of PSFs giving rise to an image density distribution, is easier to measure and can be represented in two dimensions. The LSF can be generated by examining the edge profile of an imaged bar pattern or other sharp boundary. The spread of the edge profile describes the edge spread function (ESF),an intensity distribution that is the easiest to experimentally generate, as it represents the image of any sharp separation between a field of uniform brightness from a dark field. The imaged edge profile is the convolution of the imaging system’s LSF and the step function. The intensity at any point in the image (say, xo) is the sum of the ordinates of the overlapping
Frequency ( a r b i t r a r y
units)
Flgure 3. Plots of mcdulatlon transfer functions describing two systems that have the same llmlting resolving power (arrow) but different Imaging characteristics. System a demonstrates better modulation contrast capabilities at lower frequencies and hence will produce sharper images than system b.
LSFs a t the selected point. The value of the LSF at x o is the slope of the edge trace a t that point (91,viz.
(4) which demonstrates that the LSF allows an evaluation of the imaging characteristics of the system. The spread function, taken out of context, is an imperfect measure of image quality; contrast and signal overlap must also be taken into account. An imaged feature will be visible only when the projected intensity of that feature exceeds its surroundings. For the ion microscope, measurements of the LRP are insufficient to evaluate image quality especially for samples with variations in chemical gradients (as in biological tissue). In light optical studies using the high-contrast NBS bar pattern, for example, the loss in resolution in smaller patterns is coupled to a reduction in contrast with the increased spatial frequency in the image until the remaining contrast is so low that fine detail is lost. The concept of contrast is incorporated with system spread functions in an overall description of image quality by describing the ratio of the difference of the maximum and minimum intensities in a projected feature to their sum as the modulation contrast, written as
M=
(5) + Imin The change in modulation contrast as a function of the spatial frequency in an information pattern is defined as the modulation transfer function (MTF) of the system (10). The MTF can be found from the ESF, as it is the Fourier transform of the system’s LSF. The LRP of the system (in cycles/pm) is typically given as the frequency a t which the modulation contrast is at the normalized value of 0.04, the so-called visual threshold (11). In Figure 3, examples of different MTFs are shown with same LRP but having different imaging performances. The system with greater modulation contrast values a t lower frequencies will yield images with higher contrast. It is also more convenient to use the MTF since the MTF values of the various components that make up the imaging system are simply multiplied together to give the system’s MTF, whereas the components’ LSF must be convoluted to give the system’s response. So, block separations of component contributions are more straightforward with this approach. Numerical Calculations. The microbar test patterns are used to study the contrast and resolution obtained by examining the ESF from the bar’s edge. These bar patterns also allow the examination of signal sensitivity vs. the resolution capability, as some of the bars are structurally recognizable when below the LRP of the instrument. Shown in Figure 4a is the sample procedure to obtain the relevant image information from a microdensitometer scan Imax
ANALYTICAL CHEMISTRY, VOL. 58, NO. 1, JANUARY 1986 40
-
97
8 %
A
30-
2.0 0
D
A
-/i-
kl.Oprn4
0.4 0
b
0
A
0.5
1.0
1.5
2.0
2.5
Z
0
y [SRD] (,urn)
B
Flgure 5. The effect of bar width on the SRD directly, without considering the LSF method. Shown is a simulation study (A) and experimental data (B) for a vacuum of 1 X lo-' torr and 250 instrumental magnlflcation. The origlnal bar widths are represented by (0)1.30-pm (0) 0.75-pm (A)0.55-pm, and (0)0.25-pm bar widths. (The ordlnate represents the resulting bar width observed due to instrumental convolution effects.) Experimentally the resolution was varied with the choice of contrast aperture. This demonstrates that the SRD cannot be determined from the bar profile directly as the slope of resulting bar width vs. resolution is not zero, and use of the LSF is therefore essential.
r
ic-1Orm-+l Flgure 4. (a)Procedural example to extract the limiting resolving power
(or the smallest resolvable distance)from the PMMA/Si bar pattern. The 0.55-pm bars of 2.0-pm period were imaged, and a profile was obtained (A). Each bar profile is fitted with the difference of two edge spread profiles (B),from which a best fit curve is obtained (C). This results in the line spread function, which describes the resolving power. The parameters used here are vacuum, 1 X lo-' torr: instrumental magnification, 220; and BO-pm contrast aperture. (b) Procedural example to extract the LRP (or the SRD) from the SI edge sample. The Si edge sample was imaged and a profile was obtained (A). This was fitted to a curve (6)describing the edge spread function, from which the line spread function was obtained (C). The experimental parameters used here are vacuum, 1 X lo-' torr: instrumental magnification, 200; and 20-pm contrast aperture. of two of the 0.55-pm imaged PMMA/Si bar patterns (A). From this the four ESFs were obtained by deconvolution (B). The best fit curve is shown in (C)and is compared with the LSF obtained (D) under the instrumental conditions used to obtain the image. The ESF is also obtained from the Si edge sample, as is shown in Figure 4b. From the microdensitometer scan (A) a best fit describing the ESF is obtained (B), which is used to generate the LSF (C)for the instrumental condition under examination. All LSFs used in this study are approximated by Gaussians (12,13). The y from the LSF (the distance between the inflection points) is then equal to twice the standard deviation of the Gaussian function. The relationship between the individual microbar widths and resolution has been examined with both experimentaldata and computer simulation to assist in data interpretation. The results are shown in Figure 5. A t no time was the imaged
bar profile equal to the LSF, even when the smallest pattern was half of the resolution value. Finally, microdensitometer scans of the Al/Si bar images were used to obtain the MTF for the stigmatic ion microscope. Figure 6 shows typical data from the 150- and 400-pm fields of view settings with instrumental magnifications of 215 and 73, respectively. This was used to generate the MTF for those instrumental settings, shown in Figure 6c. Instrumental Considerations. Image Recording. The photographic method of image acquisition was used as it was found to be superior to that of the TY camera (MIDAS). The Technical Pan 2415 film demonstrated the best quality with regard to resolution and film grain size. Therefore this study continued using the Tech Pan 2415 film analyzed by the microdensitometer system as it provided the method of least degradation in image fidelity. Ion Microscope Illumination. The ion microscope has developed primarily along two lines: the scanning ion microprobe, where a highly focused primary beam of ions is slowly rastered over a sample where resulting secondary ions are detected as a function of the primary beam position, and the direct imaging ion microscope, where the primary beam of ions simultaneously sputters secondary ions from a large area with a defocused primary beam and permits the direct (stigmatic) imaging of secondary ions using a matrix array detector (14).With an ion microscope based on isotopically selected sputtered ions (i.e., secondary ion mass spectrometry (SIMS)), the fundamental limit to lateral resolution is on the order of 100 8,due to the primary collision cascade diameter, which is also the diameter of the secondary ion escape circle (15). Typically, a primary beam of reactive ions in the kilovolt energy range strikes the sample to be analyzed. Atoms at or
98
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ANALYTICAL CHEMISTRY, VOL. 58. NO. 1, JANUARY 1986
near the surface are sputtered off, some of which are charged. In the stigmatic ion microscope, the choice of primary ion beam energy dictates the angle of incidence of the primary beam on the sample surface due to the presence of the secondary acceleratingfield at the sample surface. The resolution capabilities of the stigmatic ion microscope have been examined with various primary ion energies, with the results indicating that this variable has no affect on image quality, holding all other parameters fixed. However the intensity of primary current, which directly influences the intensity of secondary ions generated, does affect the image characteristics. The relationship of secondary ion current and y has been examined, and good images are obtained with a broad range of secondary ion current (depending on the area of emission, which affects localized space charge density). Too little secondary ion current results in a low signal-to-noise ratio, and current values too high observably tend to unnaturally broaden features in the image. The latter is not corrected by adjusting the gain of the microchannelplate image detector. Results obtained from this study, dependent on the geometry and element imaged, are too limited to quote numerical values. The important faetor here is the secondary ion current density emanating from a sample's feature, which is dependent on specific sample element, surrounding matrix, and primary ion heam used. A probable explanation of this feature broadening is localized space charge effects in the low-energy region of the immersion lens (close to the sample) with excessive secondary ion current densities. The aberrations of the lens elements in the stigmatic ion microscope limit the ion-optical SRDs to approximately 2 orders of magnitude higher than the theoretical limit. When the ions have their lowest velocity, they are most susceptible to deflections due to imperfections in the lens field; and 88 the secondary ions are emitted from the sample with a few electronvolts of energy, the greatest source of ion-optical dispersion in the stigmatic ion microscope is the immersion objective lens (Figure lh). When used with an aperture placed a t the image crossover, the immersion objective lens gives rise to two types of ion-optical dispersions: spherical and chromatic (16, 17). The limit of resolution in the presence of spherical aberrations is given by
R. = Cjao3
C
Transfer Funclmn IGourrian Approximolionl
Modulolion
and with chromatic aberration by
1.00
l 5 O p m I.o.Y. 400 p m f.0.".
E
.
0.50
0
5
0.25
a
0.2
0.6
1.0
1.4
LRP ( c y c l e / p d 2.00 1.00 0.75 0 . 5 0
(6)
R, = CJao(
$)
(7)
where C is a dimensionless proportionality constant characteristic of the objective lens, f being its focal length; OLD is the immersion aperture size; and Vis the accelerating potential (18). The maximum deviation from Vof the ions contributing to the angle allowed by a,,is AV. Another property of the apertured immersion lens that was examined is its depth of field, which refers to the range of distances about the plane focused upon that can be tolerated to produce an image with details of acceptable sharpnes. This is expressed by
IISROI (pml
Flgwe 8. Typical data from (a) the 150-@mand (b) 400-pm inshumental Reus 01 view with insbumental magniflcatbns of 215 and 73, respectiveby. Shown in each are the 2.W. 1.00-. 0.75, and 0.50-pm bars of aluminum with equal spacings. Superimposed is a microdensnmw.tw profile scan. vhidr vlsibty demonstrates the dependence of resolution on contrast. From this the mcdulation transfer function (c)was obtahed by using me Gausshn tit m e w in the text. These MTF c w e s the hnage quality ablliiy of the instrument at meSe
operating settings. which is an objective way of interpreting the information contained in (a) and (b).
where Tois the depth of field and As is the maximum permissable displacement of the imaged plane by the objective from the object plane (18). The farther the emitting points are from the object plane focused upon, the greater the defocusing effect. It is seen from eq 6-8 that the magnitude of the immersion lens aberrations are determined by the aperture, a0 This dependence is seen in the light-optical analogy of Figure 7. Here, aberrations give rise to the imperfection of an object
ANALYTICAL CHEMISTRY. VOL. 58. NO. 1. JANUARY I986
99
a
A A
b
S C
PrOieCled Circle Of
COnfuIion
Chromatic Abermtion
A Projcsled Circle 01 C O " f Y l i 0 "
I
I
C
1 Flgura 8. Example of imaglng surface relbf with the stigmatic km microscope. (a) Ion micrograph of a pure silicon surface showlng surface relief in focus demonsbating the depth of field abiilty of the immersion objectbe with a 20-pm conbast apertue. The bar r e p r s sen* a 2&pm scab. (b) SEM of the surface relief in highlighted area of (a). Here, the sample is tilted at 60' to the nwmal. and Hw, bar represents a I-pm scale. From this and other comparisons, l was determined mat sufaca topolosy as s m l as 0.2 pm can be seen with the "shadow contrast" visible in (a). See section on ion microscoDa
illumination in text for details
-7. ~+plkaianaloJfdamrmraag the iuwptkaie f f e c t h l a rmaiq angular apahre has on laa abdrmtbrm and imaged depth of fbld. A smaller projected circle of conhmbn implies a sharper spread hnctbn and improved imaging Characteristics.
feature transfer, resulting in the spread of projected intensity in the image. What is Been in the image about a feature point is a "circle of confusion" due to the spread function generated by the lens. This aperture is known as the contrast aperture and limits the spread of ion trajectories at the image crmover (19).
It has been found that image contrast from the ion microscope is attributed not only to the nature of the chemical gradients in the sample but also to irregularitiesin the sample surface. It is therefore difficult to interpret the elemental nature of the sample from the image when the surface relief is pronounced. Figure 8 demonstrates how topology of the emission surface in an immersion lens geometry gives rise to distortions in the image. Here, an ion micrograph of silicon that has undergone RIBE by action of the primary ion beam shows features distinguished against the background purely by contrast that is due entirely to the surface relief. The ion image w a ~obtained with a primary ion current density of 0.015 A/m2 using an 02+ beam and the smallest aperture setting (20rm). The differences in surface structure do not create a defocused image, so the depth of field obtained with this aperture dimension is great enough to allow s clear image. The
perception of depth is enhanced by the shadow effect, which is made by taking advantage of the angle of incidence of the primary ion beam. Positioning the contrast aperture slightly off-center will make this effect more pronounced. By the use of SEM,it is estimated that surface structure as small as 0.2 pm can be Been in this way in the ion microscope. This effect could lead to erroneous results in image quantification studies where the brightness a t each point in an image is related to the concentration of the element of interest. In real samples effects such as differential sputtering, which yields surface relief, can give rise to this effect (20, 21). Image Distortion. If the sample surface is not uniformly electrically conducting, or made so with a coating of a conducting material, localized charging may bring about significant distortion that would influence the ion image. Parts of the sample may also have a high secondary emission coefficient, or some areas may l d y drain charge from the primary beam better than others. In either case different zones of the image may be distorted from the true geometry and elemental structure of the sample. This can be checked if slits located after the electrcatatic energy analyzers are adjusted for a small energy window and then moved laterally back and forth, which permits somewhat energy-resolved imaging. The vacuum,imaged field of view, and tuning characteristics that influence the spectrometer transmission also influence the image. By use of the smallest contrast aperture, an ex-
100
ANALYTICAL CHEMISTRY, VOL. 58, NO. 1, JANUARY 1986
Table 111. Resolution vs. Vacuum
I .o
rISRB1, wm‘
vacuum, torr
0.57 f 0.04 0.72 & 0.11 1.01 f 0.11 1.03 f 0.31
1 x 10-7
2 x 10-7 1 x 10-6 1 x 10-6
‘Determined values are as follows: correlation coefficient = lo4, and Y intercept = -4.25 f 2.92 X lo4. Instrumental conditions are as follows: 2O-wm contrast aperture, 250X magnification.
Simulation
0.8 0.6 0.4
0.502, slope = 8.13 f 3.40 X
Table IV. Resolution vs. Contrast Aperture
r[SRDl, pma 0.54 0.70 1.07 2.53
f 0.02 f 0.05 & 0.48
f 1.06
aperture, pm 20 60 150 400
‘Determined values are as follows: correlation coefficient = 0.853, slope = 137.7 f 23.3, and Y intercept = -13.0 & 32.9. Instrumental conditions are as follows: 250X magnification, 1X
0.2
,
0
Data
1.0
2.0
3.0
4.0
B
““i 0.4
torr vacuum. amination of image quality as dependent on the vacuum in the sample chamber was performed, with results given in Table 111. The increasing uncertainty in the SRD with increasing pressure is due to the difficulty in ascertaining the spread function under these conditions. The image degrades as the vacuum becomes worse, with the features becoming invisible at torr. Collisions with residual gas molecules tend to increase the chromatic (Le., energy) spread of the secondary ion beam. With improvement in the operating vacuum, the SRD should reach a limiting value as determined by the optics of the system. Immersion Lens Aperture. If smaller apertures were employed at the image crossover, aberration contributions would be reduced. However, the stigmatic ion microscope is at the point where smaller mechanical apertures cannot easily be made and used. They must be positioned at the exact ion optical center of the crossover, and the observed image quality is more sensitive to the exact position when using smaller contrast apertures. Reducing this aperture further increases the level of difficulty involved with fine instrument tuning for a good image. Experiments were conducted to determine the dependence of image resolution and modulation contrast on the size of this aperture. The ion microscope resolution microbar patterns were imaged by using the four available sizes of apertures (20,60,150, and 400 pm) from which the change in modulation contrast and its influence on resolution were monitored. Results are given in Table IV and illustrated in Figure 9. The SRD degrades with increasing size of contrast aperture used. As the contrast likewise decreases, the precision of y also becomes worse with increasing aperture dimension: an effect that was seen in the vacuum study of SRD. If an extrapolation is attempted based on a linear fit to smaller aperture sizes, one finds that not too much improvement can be expected. Instrumental modifications involving smaller apertures therefore become difficult to justify. Image Detection. The ion beam is finally focused onto a matrix array image intensifier using a two-lens zoom projection system. In general, the image intensifier is a microchannelplate and fluorescent screen combination that converts the incoming ion rays to electron rays, multiplied by the gain of the microchannelplate, and then to light as the electrons strike the phosphor of the fluorescent screen. The spatial orientation is preserved due to the separate channel multiplier circuit of the microchannelplate.
I
0
I
I
I
2.0
1.0
y
I
I
3.0
I
1
0
[SRD] ( p m )
Figure 9. The relationship between the modulation contrast,the llmlting
resolving power, and the smallest resolvable distance. Shown Is both a simulation study (A) and experimental data (B) correspondlng to a vacuum of 1 X lo-’ torr and an instrumental magnlflcation of 250. The symbols used represent ( 0 ) 1.30-pm, (0)0.75-pm (A)0.55-pm,and (0) 0.25-pm PMMAISI bar widths. This image transduction process is significant since it can change the inherent quality of the image significantly. For this study a microchannelplate was used that has 10 pm wide channel multipliers with a maximum gain of about lo4. Each incoming ion produces a copious supply of electrons that are accelerated toward the fluorescent screen due to a voltage difference between the microchannelplate and the screen. (Worth mentioning is the fact that during the course of this study, the microchannelplate’s response has been found not to be independent of the ion species detected, all other parameters being held constant.) With voltages of about 6 kV and the distance between the microchannelplate and the fluorescent screen being 1mm, the secondary electrons bloom out due to the radial velocity component of their energy spread to a final spot size approximately 100 pm in diameter (22,23). Therefore some features that were potentially resolvable before image transduction are no longer differentiable afterward. The microchannelplate voltage, which governs the detector’s gain, was examined with relation to the image quality. The results demonstrate a minimum gain value above which the image’s resolution is not affected, but below which image degradation occurs. This minimum is concluded that for voltages up to this “workable microchannelplate gain”, which is sample dependent, the image resolution is proportional to the gain. Similar to the argument regarding the intensity of the primary ion current, images of weak intensities should be avoided if possible. With increasing use, the center of the microchannelplate becomes less sensitive than the periphery, as the center receives the most ions considering visually assisted instrument tuning and other uses. Relative contrasts become lower toward the center, and as a result the resolution is expected to vary depending on where it is measured on the microchannelplate. By magnification of the incoming beam to the microchannelplate, otherwise unresolvable features resolve as the ratio of blooming to incoming ion ray size becomes smaller. The
ANALYTICAL CHEMISTRY, VOL. 58, NO. 1, JANUARY 1986
Table V. R e s o l u t i o n vs. M a g n i f i c a t i o n (150-pmField o f View) r [ S R D ] , pma
magnification
0.53 f 0.05 0.87 f 0.05 0.96 f 0.07
250 220 162
r [ S R D ] , pmn
1.04 f 1.39 f 1.83
*
0.04 0.05 0.04
magnification
140 103 83
a Determined values are as follows: correlation coefficient = 0.924,slope = -6.43 X and Y intercept = 2.13. Instrumental conditions are as follows: 20-pm contrast aperture, 1 X torr
vacuum.
projector lens pair does provide some control in image magnification, depending on the field of view chosen. However, as the magnification increases, the intensity of the observed image decreases as the original intensities of the secondary ions are fixed for a given set of parameters (I, = I J W , where I, is the measured intensity from the signal intensity, I,, which is affected by the degree of magnification, M). With the immersion lens and transfer optics optimized at their greatest undistorted magnifications,the effect on image quality due to changes in the projector lens settings was examined. Results of the study are summarized in Table V. The LRP improves with increasing magnification. With the settings available on the instrument, the relationship between instrumental magnification and resolution is reasonably linear. This supports the contention that the microchannelplate/fluorescent screen image transduction reduces the information content in the image, thus establishing the fact that this area of the image-generating process is the limiting factor with all other conditions optimized in the conventional stigmatic ion microscope today.
CONCLUSION It has been found that the best images on the stigmatic ion microscope are obtained with flat conducting samples taken at pressures a t or below lo-’ torr with the smallest contrast aperture and the maximum instrumental magnification. The best SRD obtained in this study with the samples described is 0.53 f 0.3 gm. High-resolutionimaging is easier with smaller test patterns to focus on rather than the standard grid supplied by the manufacturer, which has 10 pm wide pressed copper wires. With this grid, any focusing below this dimension is not easily seen. With test strucures on the order of 1 gm and below, accurate and reproducible image tuning is faster and more precise. An interactive, data-based, function-oriented software package (RAP) was designed specifically for this study, which has also proven to be indispensable in resolution studies ongoing in this laboratory. With the assistance of RAP, a firstorder description of the image-generating system of the
101
stigmatic ion microscope has been made possible. The important factors obtained in this description have been presented as a complementary aid to users of this ion microscopic system. However the methodology incorporated in this study should be characteristic of any imaging system that seeks to reproduce an object’s spatial features. Aside from differences in instrumental detail, which will affect the instrumental convolution effects, the methods proposed in this study are easily extended, for example, to the new breed of scanning ion microscopes of 200 A resolution (24). And any improvements in image quality either instrumentally or digitally can be evaluated more objectively and accurately with the adoption of the MTF as the criterion.
ACKNOWLEDGMENT The authors wish to thank Gregory Sonek of Cornell’s National Research and Resource Facility for Submicron Structures for his assistance in fabricating the microbar test patterns used in this study and M. Guignes of Cameca, France, for sharing his expertise with the IMS-3f.
LITERATURE CITED Turner, N. H.; Duniap. 8. I.; Colton, R. J. Anal. Chem. 1984, 56, 373R-416R. Bayly, A. R.; Waugh, A. R.; Anderson, K. Nucl. Instrum. Methods 1983, 278, 375-382. Lepareur, Revue Technique Thomson-CSF 1980, 72, 225-265. International Standard IS0 Test Chart No. 2, National Bureau of Standards: Washington, DC. Furman, B. K.; Morrison, G. H. Anal. Chem. 1980, 52, 2305-2310. Savitzky, A.; Golay, M. J. E. Anal. Chem. 1964, 36. 1627-1639. Deming, S. N.; Morgan, S. L. Anal. Chem. 1973, 45, 278A-263A. Luneburg, R. D. “Mathematical Theory of Optics”; Unlverslty of California: Berkeley, CA, 1964; p 347. James, T. H.; Higgins, G. C. “Fundamentals of Photographic Theory”; Morgan & Morgan: New York, 1960 pp 298-304. Smith, W. “Modern ODtical Enalneerinp”: McGraw-HIII: New York. 1966; pp 308-312. Brock, G. C. “Image Evaluatlon”; Focal Press, Ltd.: London, 1970; pp
-
131-132
Vandegiste, B.; Kowaiski, B. Anal. Chem. 1983, 55, 557-564. Hasegawa, S. A&. Electron. Phys. 1969, 288, 553-565. Liebl, H. Scannlng 1980, 3 , 79-89. Liebl, H. J . Phys. E. 1975, 8 , 797-808. Liebl, H. Optlk (Stuttgart) 1979, 53, 69-72. Rempfer, G. J . Appl. Phys. 1985, 57, 2385-2401. Drummond, I. W. Vacuum 1984, 34, 51-61. Hanszen, K. J. Adv. Opt. Electron. Microsc. 1971, 4 , 1-85. Patkln, A. J.; Chandra, S.; Morrison, G. H. Anal. Chem. 1982, 54, 2507-2510. UntOn, R. W.; Farmer, M. E.; Ingram, P.; Walker, S. R.; Shelburne, J. D. Scannlng Electron Mlcrosc. 1982, I I I , 1191-1204. Wiza, J. L. Nucl. Instrum. Methods 1979, 162, 587-601. LePrade, B., Galiieo Optics Corp., prlvate communication, 1985. Levi-Setti, R.; Crow, G.; Wang, Y. L. Scannlng Electron Microsc. 1985, I I , 535-551.
RECEIVED for review June 14,1985. Accepted August 27,1985. The National Science Foundation and the Office of Naval Research are gratefully acknowledged for their financial support.
