Thin Solid Films, 131 (1985) 131-138

PREPARATION AND CHARACTERIZATION 131

A S I M P L E M E T H O D F O R T H E RAPID M E A S U R E M E N T O F T H E T H I C K N E S S OF U L T R A T H I N METAL FILMS

Y. Q. SHENG *, P. MUNZ, R. SCHULTHEIB AND E. BUCHER

Fakultgit ffir Physik, Universitgit Konstanz, 7750 Konstanz ( F.R.G.)

(Received October 22, 1984; revised March 12, 1985; accepted May 29, 1985)

A simple method for the rapid measurement of the thickness of ultrathin metal films in the range from a few gmgstr6ms to about 100/~ was developed. The method is based on measurements of the intensity of electrons backscattered by the film; pr imary electrons with energies of the order of 10 keV were used. A good thickness resolution of at least 0.3/~ was obtained for gold. If the focused electron beam of a scanning electron microscope is used, the method has an inherent lateral resolution of the order of 1 lam. A number of films consisting of metals with atomic numbers Z ~> 13 were successfully analysed. The method is applicable to films of noble metals as well as to reactive materials such as aluminium, scandium and cerium.

1. INTRODUCTION

The increasing interest in the development and application of thin film technology has resulted in new demands for a fast, reliable and simple method of measuring the thickness of ultrathin films. In the thickness region below 100/~ most conventional methods fail. At present the methods used (e.g. ellipsometry) are either very time consuming, owing to the very complicated numerical evaluation required, or the necessary thickness resolution can be obtained only with great effort.

The aim of this work was to develop a simple method which permits rapid measurement of the thickness of metal films below 120/~ deposited onto a substrate. The method is based on measurement of the intensity of backscattered incident electrons. A number of studies based on this principle have been reported 1. However, most studies involve investigations of thicknesses in the range 500-10000 A. In this work the experimental results of investigations of ultrathin films of various materials with atomic numbers between 13 and 79 are discussed. Preliminary investigations of gold films with thicknesses below 900 A have already been reported 2.

* Permanent address: Department of Applied Physics, Shanghai Jiao Tong University, 1954 Hua San Road, Shanghai 200030, China.

0040-6090/85/$3.30 © Elsevier Sequoia/Printed in The Netherlands

132 Y.Q. SHENG et al.

2. THE PRINCIPLE OF THE METHOD

If an electron beam with sufficient energy is incident on a sample both secondary electrons and backscattered electrons are released. In the method investigated here we analyse only the backscattered electrons which, according to the definition, have energies in excess of 50 eV. The backscattering rate of a sample consisting of a thin metal film on a substrate depends on the thickness of the metal film. The larger the difference between the atomic number of the film and the atomic number of the substrate the higher is the sensitivity to the thickness of the metal film. The principle of the method is therefore based on the dependence of the backscattering rate of the sample on the thickness of the metal films. In this work we consider the special case of a film of heavy atoms deposited onto a substrate of light atoms. This choice was made because it is expected that the signal-to-noise ratio, and consequently the thickness resolution, will be better for this configuration. In order to avoid an absolute measurement the ratio of the backscattering current If from the film and the substrate to the backscattering current I s from the substrate alone was measured.

3. E X P E R I M E N T A L S E T - U P

The measuring arrangement is based on a commercial scanning electron microscope (ISI Super I I I A). The electron beam, which is incident perpendicularly on the sample, is scanned over the edge of the investigated film so that the ratio If~Is can be measured. A complete calibration curve can be measured in a single scan if a series of film strips with various thicknesses are located on the substrate. The principle of the experimental arrangement and a schematic diagram of the electrical circuit are shown in Figs. 1 and 2 respectively. In order to obtain a good signal-to- noise ratio it is important to use an efficient detector of backscattered electrons with a sufficiently large solid angle. In the set-up used the sample distance was selected in such a way that a solid angle t2 of about 0.8rt was obtained (see Fig. 1). The analogue

I O--

BSE current

l~il , _ e - b e a m co lumn prirnory energy E o

t ~ BSE detector

Fig. 1. Experimental set-up for the measurement of electron backscattering in a scanning electron microscope. Fig. 2. Schematic diagram of the system for measuring backscattered electrons.

THICKNESS MEASUREMENT OF ULTRATHIN METAL FILMS 133

signal from the backscattered electron detector was processed in a conventional analogue manner as well as digitally using a multichannel analyser. The digital treatment enables the adverse effect of instability in the primary electron beam current to be reduced. During the measurement the primary electron beam must be kept as constant as possible. In order to achieve this the electron gun was operated at saturation. The complete measurement was carried out using an accelerating voltage of 18 keV and a beam current of the order of 10- 9 A. Some measurements at an accelerating voltage of 28 keV were also performed for comparison.

4. SAMPLE PREPARATION

The substrate material was mechanically polished glassy carbon (atomic number Z = 6). The metal thin films were thermally evaporated onto the glassy carbon substrate in an oil-free high vacuum at a pressure of less than 3 x 10 -6 mbar. Samples with 16 thickness steps were prepared at an almost constant evaporation rate. The area mass density was measured during the evaporation process using the oscillating quartz method with specific precautions. Although the area mass density is measured the film thicknesses are also reported in this paper. The thickness is calculated from the area mass density by assuming that the density of the metal films is the same as that of the bulk. However, film thicknesses below 120 ~ are considered as quasi-thicknesses because the density of such thin films is dependent on the thickness itself and the various evaporation parameters. The time during which the sample was exposed to air between its removal from the evaporation apparatus and its mounting in the scanning electron microscope was kept as short as possible.

5. EXPERIMENTS AND RESULTS

The dependence of the backscattering rate on the film thickness was investigated for the following elements: aluminium (Z = 13); scandium (Z = 21); chromium (Z = 24); copper (Z = 29); germanium (Z = 32); silver (Z = 47); cerium (Z = 58); gold (Z = 79). At least two series were measured for each metal. Gold, which was chosen as a model substance, was particularly extensively investigated. The investigations show that the dependence of the relative (or normalized) backscattering rate on the film thickness (calibration curves) can generally be approximated by two straight lines in the case of gold (Fig. 3) or by three straight lines for the remaining materials investigated (the results for copper are shown as an example in Fig. 4). As expected, the curve saturates at large thicknesses. The points where the first change of slope appears are indicated by arrows in Figs. 3 and 4. In the case of gold this point is at about 120 ~ for a primary electron energy of 18 keV (see Fig. 3). At film thicknesses below this value the relative backscattering rate depends linearly on the film thickness, so that a simple and fast method for the determination of film thicknesses below 120/~ can be developed on the basis of measurements of the backscattering rate. The first linear region is therefore of particular interest. A precise representation of the backscattering signal as a function of the gold film thickness below 40 ~ is shown in Fig. 5. The thickness resolution can be defined as t As/s where t is the thickness of the film, s is the signal

134 Y . Q . SHENG e t a l .

N O

v

t~

U

W I10

8.0

6.0

4.0

2.0

AREA MASS DENSITY [mg/m 2]

200 400 600 800 I i ~ I i

0 I I I Z

0 100 200 300 400 500

F I L M T H I C K N E S S [~, ]

Fig. 3. T h e b a c k s c a t t e r e d e l ec t ron (BSE) c u r r e n t v s . the th i ckness o f a go ld film o n a g lassy c a r b o n

s u b s t r a t e fo r t w o acce l e r a t i ng vol tages .

8

T

Z ILl

--~ U

I~1 (/) l IB

AREA MASS DENSITY [mglm2.]

0 500 1000 1500 2000 2500 3000 f I I I I I

2000 / 1oo 200 3~

1 0 0 0

500 / t / - , , ,

0 100 200 3 0 0 FILM THICKNESS [A]

0 I J i I I I I I 0 500 1000 1500 2000 2500 3000 3500

FILM THICKNESS [~]

Fig. 4. The BSE current vs. the thickness of a copper film on a glassy carbon substrate.

350

4 0 0

4000

THICKNESS MEASUREMENT OF ULTRATHIN METAL FILMS 135

AREA MASS DENSITY [mg/mZJ

0 20 40 60 80 I i I

2000

c

8 t . a

"% 1500 T

t - - Z L.t.I K~

1000 U

L.tJ

500

0 t t t J 0 10 20 30 40

FILM THICKNESS EAI

Fig. 5. A precise representation of BSE current as a function of the thickness of a gold film on a glassy carbon substrate. The film thicknesses were 40 ,~ or less.

and As is the noise amplitude in the signal. Figure 5 gives a thickness resolution of 0.3 A or 1.8 x 1014 atoms cm-2. The reproducibility obtained from various regions of the same specimen or on replacement of the given specimen after removal lies within 39/o for thicker films and within 10~ for films less than 20 ,~ thick.

At a primary electron energy of 28 keV the upper limit of the first linear region for gold shifts to a higher thickness of 160 ,~ (see Fig. 3). However, the sensitivity, and consequently the thickness resolution, decreases. Thus the optimum primary electron energy depends on the particular field of application under consideration.

Qualitatively similar behaviour with three linear regions was observed for the other metals investigated. Figure 4 shows a representative example. It should be noted that, in contrast with all the other materials investigated, the slope of the first linear section for aluminium is greater than that of the second. It is possible that the carbon substrate has a stronger influence in this case because o f the relatively small differences between the atomic numbers of aluminium and carbon. The upper limit of the first straight line generally decreases with increasing atomic number as shown in Fig. 6.

Theoretical interpretations of the backscattering rate r/of self-supporting thin films have been proposed 3'4 but a precise calculation is difficult owing to the appearance of multiple scattering processes. For the more complicated case of a thin film on a homogeneous substrate a qualitative analysis can be performed for the first linear region.

The differential backscattering coefficient for an isolated atom is described by

136 v.Q. SHENG et al.

300

200

ul

~ : C r CuC.~ A o Ce Au

,ii i i J i ',, iJ 20 ~ 60 80

ATOMIC NUMBER Z

100

Fig. 6. Thickness Do where the first change in slope occurs as a function of the atomic number of several elements (E 0 = 18 keV).

the Rutherford law. The backscattering rate of a very thin self-supporting film can be derived from this law if it is assumed that only simple scattering processes occur. Our experimental results showed that a superposition law can give an approximate description of the backscattering of the system consisting of a thin film on a substrate:

r /= r/s+ ~/f (1)

where

~lf = k(Eo, Z, , f2)Z2NA d (2)

Eo is the primary electron energy, Z is the atomic number of the element of the film, Z~ is the atomic number of the substrate and NA is the density of the scattering atoms. As a consequence of the Rutherford formula k = k(E o, Q) is proport ional to 1/Eo 2 if t2 is fixed. In our more complicated case in which the film is supported the additional dependence on Z~ is included by writing k = k(Eo, Zs, f2) as in eqn. (2). Equations (1) and (2) show that

rl, Z2NAd

is a constant for different deposit materials on the given substrate if the primary electron energy is kept constant. Graphical representation of our experimental values (Fig. 7) shows that at thicknesses below 120/~

r / - r/s

tlsZ2NA d

is indeed constant within 6 ~ for the various materials investigated. The deviation is somewhat larger at thicknesses less than 30 A, probably because of a larger error in the determination of thickness using the oscillating quartz method. However, if eqn. (2) is valid ~/r must be proport ional to E o- 2 for a given material. Calculation using the values in Fig. 3 shows that k(Eo)Eo 2 is indeed constant within 6~o for fixed Z~ and f2.

THICKNESS MEASUREMENT OF ULTRATHIN METAL FILMS 137

1.2

" o

E 0.8

,_/7~ 0.6

,, 0./-* 1"4

0.2

0

o i i •

• o ° o ¢ I

2

o AI • 5c

• Cu 6e

• Ag o Ce ÷ Au

I ~ I , l i I i I i I

20 40 60 80 100 120

FILM THICKNESS [A]

Fig. 7. Plot of the experimental values of

l - i s ~-~, IsZ2NAd ~I,Z2NAd

below 120 ~ vs. the film thickness for various elements (E o = 18 keV).

4.0

3.0

2.0

1.0

1/.,0

,,?

o

%

According to the model developed for the backscattering method calibra- tion for each material is unnecessary if an error of 6% is acceptable (this accuracy is often satisfactory for the determination of thicknesses below 120/~). If a higher accuracy is required a separate calibration for each film material is necessary.

As these thickness measurements are performed in a scanning electron microscope surface profiles can also be measured, at least for step-like samples consisting of plane parallel film elements. The dependence of the backscattering signal on thickness for wedge-type films where the angle of incidence of the primary electron beam is not oblique requires further investigation.

Within the linear thickness range considered here the films are expected to be discontinuous below some critical thickness which depends on the film and substrate material as well as on the deposition parameters 5. However, no evidence of an effect of the film structure on the relation between the backscattering rate and the film thickness has yet been observed for the film and substrate materials investigated.

6. CONCLUSIONS

The electron backscattering method can be considered as a new general method for the determination of film thicknesses below 120 ~ for all metals that are not too light. The observed linear dependence of the backscattering rate on the film thickness for all the elements investigated provides a simple method of evaluating the thickness. The lateral resolution of the order of 1 pm can be very useful. It depends mainly on the width of the diffusion cloud of electrons in the sample 6. Since the measurement is carried out in a scanning electron microscope, the sample surface can be observed directly and the precise measuring site can be determined

138 Y.Q. SHENG et al.

and indicated on a scanning electron micrograph of the sample. Alternatively a mean value can be measured by scanning. Our investigation shows that the resolution of 0.3/~ for gold could be improved further in the future. The limit of the method is determined not only by the signal-to-noise ratio of the backscattered current but also by the microscopically porous structure of the glassy carbon substrate and a possible small drift in the primary electron current.

ACKNOWLEDGMENTS

One of us (Y.Q.S.) acknowledges the Ministry of Science and Art, Baden- Wiirttemberg, for a postdoctoral fellowship granted during the performance of this work. The authors are grateful to Mr. A. Kling for his technical assistance. This work was supported by the Bundesministerium ffir Forschung und Technologie.

REFERENCES

1 H. Niedrig, J. Appl. Phys., 53 (1982) R15. 2 P. Munz and Z. H. Zheng, Helv. Phys. Acta, 57(1984) 283. 3 H.W. Miiller and B. Schrrder, J. Appl. Phys., 49 (1978) 3595. 4 H. Niedrig, Proc. 9th lnt. Congr. on Electron Microscopy, Toronto, 1978, Vol. 1, Microscopical

Society of Canada, Toronto, 1978, p. 208. 5 L.I . Maissel and R. Glang, Handbook of Thin Film Technology, McGraw-Hill, New York, 1970,

pp. 8-32. 6 L. Reimer and G. Pfefferkorn, in Rasterelektronenmikroskopie, Springer, Berlin, 1973, p. 4.