The determination of thin layer thicknesses with an electron microprobe

SURFACE SCIENCE 34 (1973) 693-704 © North-Holland Publishing Co.

THE DETERMINATION

OF THIN LAYER THICKNESSES

WITH AN ELECTRON MICROPROBE R. BUTZ and H. WAGNER

lnstitut fiir Technische Physik der Kernforschungsanlage Jiilich, Postfach 365, D 517 Jiilich, Germany

Received 22 June 1972; revised manuscript received 4 September 1972 Electron microprobe analysis has been performed on W, Nb~ Mo, and A1 layers of 2 to 300/~ thickness deposited on refractory metals. For this thickness range a linear relation is found between layer thickness and characteristic X-ray intensity. The importance of a correct background measurement and its influence on the accuracy of the determination of the layer thickness is demonstrated. Additional effects arising from the backscatter coefficient of the substrate material and the fluorescence excitation within the layer are investigated. It is found that the highest sensitivity in the thickness measurement occurs at primary electron energies of 2.5 to 3 times the excitation energy of the used characteristic X-ray line of the layer material. This experimental finding is discussed in terms of the dependence of the X-ray background intensity and the ionization probability on the energy of the primary electrons. 1. I n t r o d u c t i o n

The usual methods for determining layer thicknesses by electron microprobe analysis are based on the fact that electrons passing t h r o u g h a material lose energy continously. T h o m s o n - W h i d d i n g t o n ' s law 1) or a similar law given by Castaing 2) describe these energy losses. According to these laws, the thickness o f the layer to be determined, is calculated f r o m the energy loss which the electrons suffer while passing through the layer. This energy loss can be determined experimentally f r o m the characteristic X-ray intensity o f either the layer material or the substrate material as function o f the primary electron energy. If a characteristic X-ray radiation o f the layer material is used, its intensity will increase with increasing primary energy, until the mean residual energy o f the electrons having passed t h r o u g h the entire layer, will be equal to the excitation energy o f the X-ray line in question. I f a characteristic X-ray line o f the substrate material is used its signal will become detectable when the mean residual energy o f the primary electrons having passed through the layer surpasses the excitation energy o f this line. The energy loss to be determined is then equal to the difference between the excitation energy o f either the substrate or the layer material and the c o r 693

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R. BUTZ AND H. WAGNER

responding primary electron energies at which the breakpoint in the X-ray signal occurs. These two methods can be applied to layers of as much as 1000 A or more in thickness. Their precision is largely dependent upon the validity of the aforementioned laws. The sensitivity of the electron microprobe allows one to determine and even to measure much thinner layers 3), down to monolayer coatings 4, 5). In those cases, a characteristic X-radiation of the layer material having a very low energy must be chosen 5). With X-ray lines of low excitation energy, low primary electron energies can be used, so that the penetration depth of the electrons will be kept small. In this manner, the signal to background ratio will be more favorable for investigating the very surface region of a sample. We have shown in a special example 5) that in the range from a monoatomic coating up to a thickness of several hundred AngstrSm, the intensity of the characteristic X-radiation is proportional to the thickness of the layer. In the presence of such thin layers, no considerable energy loss is suffered by the electrons passing through them. Just this fact causes the above mentioned favorable proportionality concerning the measuring technique. For this reason, a few calibration measurements will suffice to establish a calibration curve which enables the determination of unknown layer thicknesses. In contrast to the initially indicated measuring methods, it is no more necessary with this procedure, to use laws of so limited validity as those of T h o m s o n Whiddington, or similar formulas. In this paper we shall demonstrate by some characteristic examples, which factors influence the detection sensitivity and thereby determine the lower limit of layer thicknesses to be measured. The accuracy of the measurements is estimated and it is shown which microprobe parameters provide the most favorable conditions of investigation. Furthermore, we shall describe how a relative determination of the ionisation probability of the inner shells by electron impact can be carried out as a function of the electron energy.

2. Layer preparation and microprobe measurements In table 1, the combinations of layer and substrate materials tested, are TABLE I

Layer W W Nb Nb Nb AI Mo

Substrate Mo Ta Ta Mo W W W

DETERMINATION OF THIN LAYER THICKNESSES

695

summarized. The calibration layers were produced by evaporation of the different materials in vacuo of approx. 5 × 10-8 Torr. Prior to the deposition the substrates were ground and polished by standard metallographic techniques. The thicknesses of the layers were determined with a water-cooled quartz balance (Balzers QSG 101), rearranged for UHV conditions. The frequency change of the oscillator quartz, Af, is a linear function of the mass thickness (Ad) of the deposited layers A f = kQ Ad.

(1)

In this formula, ~ is the density of the deposited material which was always represented by the value of the bulk material. The constant of the device k was 0.474 x 108 (sec g)-I cm 2. With a tungsten layer of l0 A one obtains a frequency change Af=91.5 Hz. With evaporation velocities of from 50 to 100 A/h, the instability of the device causes an error of 1-2~o. An electron microprobe of type ARL-SM was used for which the X-ray take-off angle amounts to 52.5 °. In all investigations, the sample current was set to 10 hA. The X-ray counting rate was integrated for 100 sec and a sample area of approx. 50 x 60 gm was scanned by the electron beam. For low X-ray intensities the counting rate was also determined by measuring the time required for a preset number of counts. 3. Results

3.1. BACKGROUND MEASUREMENTS Layer thicknesses in the monolayer range correspond with the coating materials chosen by us to a mass thickness of approx. I-6 x 10 - 7 g / c m 2. With an electron beam diameter of approx 0.5 gm an absolute detection sensitivity of approx. 0.7-5 x 10-15 g is necessary. In this detection range the background measurements are of special importance. The usual methods used for the background determination, as for instance its determination at a wavelength neighbouring the characteristic X-ray line, are insufficient in most cases because of the background signal being a function of the wavelength. For the layer thickness range investigated by us, only the contribution of the X-ray radiation of the substrate material at the wavelength of the characteristic layer radiation is of primary importance for the background signal. For this reason, the X-ray intensity from an uncoated substrate can be chosen to measure the background intensity. This measurement is taken at the same spectrometer setting as the measurement with coating. The actual background signal of the substrate depends in two ways upon the thickness of the deposited layer: (1) The substrate background signal is absorbed a little in the layer.

696

R. BUTZ AND H. WAGNER

(2) The energy of the primary electrons hitting the substrate is somewhat decreased by this layer. The following arguments show, however, that both effects are of relatively little importance for the method dealt with here: (1) The absorption of the background radiation while passing through the layer, can be neglected for all layer thicknesses considered here. (2) The energy loss of the primary electrons in the layer can also be neglected for very thin layers. For thicker layers, the energy loss can not be neglected, and the intensity of the X-ray radiation of the substrate material is thus reduced. The signal to background ratio is however much more favorable in those cases, so that the contribution of the substrate background radiation can be neglected. In a special example it is demonstrated that even in the presence of a neighbouring characteristic X-ray radiation of the substrate material, no considerable influence can be recorded. On account of the aforesaid proportionality existing between the characteristic X-ray intensity of the layer material and the layer thickness, the signal for a known thickness can be subtracted as being the "background". In such a case, the calibration curve will no more pass through the origin of the coordinate system. Owing to the fact that uncovered substrate surfaces were not present in all cases investigated by us, the signal for the smallest layer thickness was generally used as "background". Figs. 1 and 2 show for the various substrate-layer combinations the X-ray counting rates as function of layer thickness on a double logarithmic scale. The signal for the smallest thickness was always subtracted as being the background from the signal for the other layer thicknesses. The abscissa values of the data points were corrected accordingly. In the log-log scale, one obtains straight lines with slope 1 for all substrate layer combinations, i.e. a linear relationship exists between counting rate and layer thickness. Fig. 3 shows for the example of a 50/~ thick W layer on Ta the counting rates of the W-M~I radiation as function of the electron beam voltage. The dot-dashed curve represents the counting rate without background correction. The dashed line represents the signal of an uncovered Ta-sample at the wavelength of the W-M~I line. The solid curve results from the difference between the corresponding counting rates of the 50 ~ thick W layer and a layer of 2/~ thickness, respectively. When adding the values of the solid line and those of the dashed one, one obtains exactly the course of the dotteddashed curve. This example (W on Ta) has been chosen because it represents a relatively unfavorable layer-substrate combination, since the background signal partially surpasses the layer signal considerably. This is due to the fact that the W-M~I line (1.7754 kV) is very close to the Ta-M~I line (1.7655 kV),

D E T E R M I N A T I O N OF T H I N L A Y E R T H I C K N E S S E S

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Fig. 1. X-ray intensities as function o f layer thickness: (A) M o on W, Mo-L=I, 10 kV; (B) N b o n Ta, Nb-L=z, 10 kV; (C) N b on Mo, Nb-L=a, 10 kV; (D) N b on W, Nb-L~I, 6 kV.

and that these two lines are separated incompletely by the spectrometer. Nevertheless, this example underlines the usefulness of the background determination. Other usual methods would produce wrong results. In the presence of other combinations of materials tested by us, the signal to background ratio has always been more favorable than with W on Ta. 3.2. RELATIVEMEASURINGACCURACYOF LAYERTHICKNESSES The example W on Ta, and the examples of the other material combinations show that there exists an optimal value of the electron beam voltage, concerning the signal to background ratio. As mentioned in ref. 5 and discussed below, the solid curve shown in fig. 3, represents the dependence of the ionization probability of the corresponding energy level, and thus the intensity of the characteristic X-ray emitted, on the electron energy. This curve reaches a maximum value at about four times the ionization energy. On the other hand, the background signal (dashed curve) rises monotonically with the electron energy. If the counting rate for a layer thickness d is called

698

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Fig. 2.

X-Ray intensities as function of layer thickness: (E) W on Ta, W-M~i, 7 kV; (F) W on Mo, W-M=i, 7 kV; (G) A1 on W, A1-K=i, 3 kV.

T(d) that for the background B, the layer signal S(d) is proportional to T(d)-B. When taking into consideration only the statistical scatter of the counting rates, as being the sources of error in the determination of the layer thickness, one obtains the following formula for the relative measurement accuracy: Ad d

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2B/S(d)] ~S (d)

(2)

In fig. 4, the measured counting rates B and T are plotted for a 113 A thick Nb layer on Ta, as function of the electron beam voltage. In the same figure, also the ratio Ad/dcalculated according to eq. (2), is represented. For Ad/d a minimum is reached at about three times the ionization voltage, while S reaches its maximum value at about five times the ionization voltage. In view of the measurement accuracy, it is therefore advisable, not to perform the measurement at the electron beam voltage that corresponds to the maximum of the excitation probability, but due to the influence of the background

699

DETERMINATION OF THIN LAYER THICKNESSES

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Fig. 3. X-ray intensities as function of accelerating potential: ([~) W-Max intensity for 50 AE W on Ta without background correction; (O) X-ray intensity for Ta standard taken at spectrometer setting for W-Max line; (V) W-Max intensity for 48 AE W on Ta with background correction.

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Fig. 4. X-ray intensity as function of accelerating potential: (T) Nb-Lal intensity for 113 AE Nb on Ta without background correction; (B) background intensity taken at Nb-L~I line; (S) Nb-L=I intensity for 113 AE Nb on Ta with background correction. Ad/d = relative error in thickness determination according to eq. (2).

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R. BUTZ AND I-I. WAGNER

radiation at a somewhat lesser voltage. Since the layer signal S is proportional to the layer thickness, the relative error increases with decreasing thickness, the background intensity remaining unchanged [see eq. (2)]. For the given example of a 113 A thick Nb layer on Ta and an integration time of 100 sec the minimal relative error was 3.5~. For a ten times thinner layer the corresponding error calculated with eq. (2), would be 22~. For thinner layers a higher accuracy can of course be obtained, by using longer counting times, and higher probe currents. The substrate material is not only responsible for the background radiation. It exerts moreover an influence on the electron backscattering owing to the atomic number effect. Figs. 1 and 2 show that the counting rates for a special layer material deposited on two different substrates differ from each other, the electron beam voltage and the sample current b~ing the same in both cases. A substrate material of higher atomic number causes a higher counting rate. The estimation of the influences exerted by the backscattering coefficient according to Archard 6) in both cases explains roughly the measured differences in the counting rates. 3.3.

I N F L U E N C E O F T H E D I S T R I B U T I O N O F T H E L A Y E R M A T E R I A L I N T O T H E SUBSTRATE

The electron penetration depths are rather large in the examples described, as compared with the layer thicknesses. Hence, the problem arises whether it is possible to recognize if the layer material covers the surface of the substrate as a film, or whether it has been distributed into the very substrate. This question can be answered in relying upon the fact that for very thin layers the electrons pass through the layer with an almost constant velocity, i.e. that they suffer no significant energy loss. That means that the relationship between layer signal and electron energy corresponds to that of the ionization probability as a function of the electron energy. If the layer material has been distributed within the substrate, a quite different curve of the signal will occur, as the number of the distributed atoms that contribute to the signal increases with increasing electron beam energy, and thus with a greater depth of penetration. Furthermore in this case, the absorption of the characteristic X-ray radiation must be taken into consideration, as well as the fact that the ionization probability being a function of the electron energy, depends also upon the depth of penetration. In fig. 5, the intensity of the W-M~I radiation of a W layer of 36 A is shown as a function of the primary electron energy. This film covers a Mo substrate. We have plotted comparatively, the curve for the X-ray intensity obtained with a W concentration of 0.24~o in Mo. This concentration corresponds to the quantity of W in a compact layer of 36 A, distributed homogeneously to a depth of 1.5 Ixm, into the

D E T E R M I N A T I O N OF T H I N L A Y E R T H I C K N E S S E S

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Fig. 5. X-ray intensities as function of accelerating potential: (A) W-M~I intensity for 36 AE W on Mo; (O) W-M=1 intensity for 0.24~ W in Mo.

Mo substrate. The question whether there is a distribution of the investigated material into the substrate, or whether the substrate is covered by a film of the same material, can be answered by recording an eventual qualitative difference between the course of the measured X-ray signal and that of the ionization probability.

Appendix It has already been mentioned that the solid curve in fig. 3 mainly represents the course of the ionization probability of the W-M m level as a function o f the electron energy. This is true under the following conditions: (1) the primary electrons suffer no considerable energy loss in the layer, (2) the backscattered electrons from the substrate material possess the energy of the primary electrons, and (3) the influence of the fluorescence excitation in the layer can be neglected. With the thicknesses of layers used by us, the first condition can be considered as being fulfilled, down to the ionization energy

702

R. BUTZ AND H. WAGNER

of the energy level considered. The fulfillment of the second condition causes much more difficulties. In order to eliminate the influence of the backscattered electrons, it would be advisable to use substrate materials of low atomic number, since these have small backscatter coefficients. With elements of high atomic number, the maximum of the energy distribution of the backscattered electrons is close to the energy of the primary electrons, but the total portion of backscattered electrons is much bigger. According to measurements of BishopT), up to 15~ of the electrons that might contribute to the ionization in the layer, have energies below 80~ of the primary energy for the substrate materials used by us. The influence of the fluorescence excitation could be neglected as a rule in our experiments. In the case of Nb on Mo, however, the Mo-L~I line (2.394 kV) is very close to the Nb-LIII band etch (2.371 kV). The rather intensive Mo-L~I radiation at higher electron beam voltages is preferentially absorbed in the Nb layer, thus causing a more considerable fluorescence excitation. Fig. 6 shows how the Nb-L~I radiation

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703

DETERMINATION OF THIN LAYER THICKNESSES

intensity of a 30/~ thick Nb layer depends upon the primary electron energy with both substrate materials Ta and Mo. The much lesser decrease of the Nb-L=I radiation for higher electron energies for the Mo substrate is caused by the increasing influence of the fluorescence excitation due to the Mo-L=I radiation.

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Fig. 7. X-ray intensities as function of overvoltage ( ~ ) 78 AE A1 on W, A1-K~I; ( 0 ) 28 AE W on Mo, W-M~I; (©) 60 AE N b on W, Nb-L=I; (D) 74 AE Mo on W, Mo-L=I. For comparison are shown theoretical curves of (B) Bethel°), (G) Gryzinski8), and (D) Drawing).

Fig. 7 shows the X-ray intensity for different layer materials as function of the overvoltage. The latter is defined as the ratio of the primary electron energy E and the ionization energy E o. The X-ray intensity has always been normalized at its maximum. Theoretical curves of the ionization probability according to GryzinskiS), Drawin 9) and Beth 1°) have been plotted comparatively to the points obtained by our investigations. For the absolute determination of the ionization probability by the procedure dealt with here, some other microprobe parameters must be known additionally, as for instance the solid angle of the recorded X-ray radiation, and the detector sensitivity. Finally, the fluorescence probability of the atom energy level considered, must be known.

Acknowledgement We should like to thank Prof. Dr. E.A. Niekisch for his encouraging

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g. BUTZANDn. WAONER

interest a n d profitable discussions. We t h a n k Mr. C. Elsaesser who has carried out the m i c r o p r o b e measurements.

References 1) C. J. Calbick, Interaction of Electron Beams with Thin Films, in: Physics of Thin Films (Academic Press, New York, 1964) p. 64. 2) R. Castaing, Advan. Electron. Electron Phys. 13 (1960) 317. 3) K. L. Chopra, M. R. Randlett and S. L. Bender, Rev. Sci. Instr. 39 (1968) 1755. 4) J. Herberger, W. Gloede, W. Kr/imer, H. Leistner and E. Roll, Exp. Techn. Phys. 20 (1972) 3. 5) R. Butz and H. Wagner, Phys. Status Solidi (a) 3 (1970) 325. 6) G. D. Archard, J. Appl. Phys. 32 (1961) 1505. 7) H. E. Bishop, in: Optique des Rayons X et Microanalyse, 4e Congr. Intern. Orsay, Sept. 1965 (Paris, Hermann, 1966). 8) M. Gryzinski, Phys. Rev. 138 (1965) A 336. 9) H. W. Drawin, Z. Physik 165 (1961) 513. 10) H. Bethe, Ann. Physik 5 (1930) 325.