Si heterostructures with electron energy loss spectroscopy

Ultramicroscopy 41 (1992) 41-54 North-Holland

uUronaero

Profiling of the dielectric function across A 1 / S i O 2 / S i heterostructures with electron energy loss spectroscopy M a r e k A. T u r o w s k i and T h o m a s F. Kelly Materials Science Program and Department of Materials Science and Engineering, Unit,ersity of Wisconsin, Madison, WI 53706, USA Received 19 August 1991

A I / S i O 2 / S i heterostructures which are typical of actual electronic devices have been studied with high-spatial-resolution scanning transmission electron microscopy. Electron energy loss spectra were recorded over the low-loss region (0 to 100 eV) at 2.5 to 5 nm intervals across interfaces viewed in cross-section. The energy loss function was then obtained from experimental spectra after Fourier-log deconvolution of multiple scattering. Finally, the complex dielectric function and molar polarizability were determined at each point through a K r a m e r s - K r o n i g transformation and analytical formulae. Profiles across heterostructures show that minima exist in the molar polarizability at the interfaces, which suggests that the interfaces have a lower intrinsic dielectric strength.

1. Introduction

Spectroscopic methods, in general, are very important for probing physical and chemical phenomena. These methods utilize a variety of excitations by photons and neutral and charged particles like atoms, neutrons, electrons, positrons, protons, ions, etc. Some provide bulk information about elemental composition, crystallographic structure, electronic structure, and lattice dynamics, while others are surface sensitive (for a review see refs. [1,2]). Among these techniques, scanning transmission electron microscopy (STEM) plays a very important role by offering high-resolution imaging in conjunction with analytical capabilities such as electron diffraction, X-ray analysis, and electron energy loss spectroscopy. A review of its impact on the microelectronic age has been given by Brown [3]. The best combination of all of the above-mentioned features is offered in STEMs equipped with a field-emission gun. These instruments can provide a 1 nm probe with 1 nA current which far exceeds current densities available in conventional TEMs with either thermionic tungsten or

LaB 6 sources [3,4]. Moreover, for a very thin sample (several nanometers thick) with the beam stopped one can gain information about X-ray elemental analysis, electron diffraction and inelastic scattering processes from sub-ten-nm 3 volumes which no other instrument can match. This latter avenue is being pursued here for the characterization of dielectric materials. Our interest in AI/Si02/Si heterostructures was inspired by new developments in VLSI circuits technology and the gradual reaching of the physical limits of the dielectric layers used in variety CMOS transistors and memory chips [5]. The smaller and smaller distances between capacitor plates increased the demands on manufacturing processes in order to improve the quality of such layers and reach the intrinsic value for their dielectric strength. The behavior of such composite structures under strong electric fields is governed by their dielectric function. Our motivation for this work was, thus, to characterize these materials with respect to their response to an electric field and to look for any contributions to the inelastic scattering probability due to the constituent layers. Electron energy loss spec-

0304-3991/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved

42

M.A. Turowski, T.F. Kelly / Profiling of the dielectric Jhnction across heterostructures

troscopy (EELS) in STEM was our tool for probing the structure. From the experimentally obtained energy loss function, and based on the dielectric formulation of the inelastic scattering of electrons, we have calculated the dielectric permittivity of the A I / S i O 2 / S i system using the Kramers-Kronig transformation [6-9].

2. Experiment Silicon wafers with a thermally grown silicon dioxide layer and a subsequently evaporated aluminum overlayer were prepared at the IBM East Fishkill Facility [10]. Cross-section-view TEM samples were prepared using standard techniques for this kind of material [11,12]. Electron microscopy and electron energy loss spectroscopy studies were carried out on a field emission VG HB501 STEM. Fig. 1 shows a STEM bright-field image of a cross-section-view sample

of films prepared by IBM. This sample was made by gluing together two pieces of a wafer with the respective A1 overlayers facing each other. The nominal thickness of the SiO z layer was 40 rim. The central blank part is a hole left after the epoxy was preferentially removed by ion-milling. The silicon wafer was single-crystalline with [ll0]-type direction in, and perpendicular to, the image plane (the top surface of Si wafer was (100) plane). The dark bands and grains in the A1 layer are due to the diffraction contrast in a polycrystalline material. The uniform, vertical stripe (darker in appearance) is the amorphous SiO 2 layer. These characteristics were verified by microdiffraction and energy-dispersive X-ray analysis. The E E L data were taken point by point, on the left part of this particular sample, across two interfaces: S i / S i O 2 and SiO:/AI, starting from the aluminum and finishing in the silicon region. The step in beam position between spectra was 5

Fig. 1. Bright-field STEM micrograph of two MOS heterostructures.

M.A. Turowski, T.F. Kelly / Profiling of the dielectric function across heterostructures

020988K IBM X-SEC SCAN PTI.5 EELS

4000

3000

2000

1000

0 -1LiO0 - t . i O 0

8.900 38.900 28.900 38.900 48.900 58.900 68.900 78.900 88.900

ENERGY

(eV)

Fig. 2. An example of "as-acquired" EEL spectrum for AI.

020988K IBM X-SEC SCAN PT4 EELS 400

300

-

200

o~

-7.400 2.600 12.600 22.600 32.600 42.600 52.600 62.600 72.600 82.600 92.600

ENERGY

(eV)

Fig. 3. An example of "as-acquired" EEL spectrum Ior 51(-.I 2,

43

M.A. Turowski, T.F. Kelly / Profiling of the dielectric function across heterostructures

44

nm away from the interface and half of that near each interface. Individual E E L spectra were acquired in the analogue mode, with a single sweep into 1024 channels, and with a dwell time of 17 ms per channel. The energy loss range was usually 100 eV which covered the whole low-loss region. The energy resolution of the spectrometer was of the order of 0.6 eV (FWHM). Spectra were recorded from high energy to low energy so that the scintillator afterglow from the zero-loss peak (ZLP) would not interfere with the data. An electronic background was recorded at the lowenergy side of the Z L P and was subtracted for the entire spectrum. Software for plural scattering deconvolution and K r a m e r s - K r o n i g transformation (KKT) was adopted from a program listed in Egerton's book [15]. This program was used to extract a dielectric function versus energy from an experimental single-scattering distribution (SSD) of any material at a given electron beam position. Optical constants such as molar polarizability, optical con-

ductivity, absorption coefficient and normal incidence reflectivity are readily calculated from the dielectric function [6,13,14].

3. Results and data analysis Representative spectra of each material, A1, Si and SiO2, are shown in figs. 2, 3, and 4. The data are reduced as follows. The position of the zeroloss maximum is defined as the zero in energy. The integrated intensity in the Z L P is determined as that signal up to the first minimum in the spectrum beyond the ZLP. The Z L P is then stripped from a spectrum, and the entire intensity is stored in a single c h a n n e l The spectra are then extrapolated to zero at both energy ends. A cosine-bell function [15] is used at the low-energy end of the spectrum. At the high-energy end, an exponential decrease is used. Examples of such processed spectra are given in figs. 5a, 6a and 7a), for A1, Si, and SiO 2, respectively. A fast Fourier

020988 XSEC IBM SCAN PT8 EELS 5000

4000

3000 03 Z CD 2000

I000

0

-10.800 -0.800

9.200 19.200 29.200 39.200 49.200 59.200 69.200 79.200 89.200

ENERGY

(eV)

Fig. 4. An example of "as-acquired" EEL spectrum for Si.

M.A. Turowski, T.F. Kelly / Profiling of the dielectric function across heterostructures

transform (FFT) is used to remove the plural scattering by the Fourier-log method described in ref. [15]. The end result of this procedure is a single-scattering distribution (SSD) for every raw spectrum recorded. Representative SSD spectra for all three solids are given in figs. 5b, 6b and 7b.

1600

i400

1200

iO00 .f-(

l

'l

45

An aperture correction [15] is applied to the SSD to obtain the experimental electron energy loss function (EELF). The E E L F is equal to the imaginary part of - 1 / c ( E ) . The final step is the application of the KKT to the E E L F data by means of the FFT. The result of these calcula-

lll'l

l

lll'laJ_

800

2 600

400

200

0 t0

20

30

40

50

60

70

80

90

Loss Energy (eV) 1600

'

I

l l i ' l l l ' l ' l ' l

b

t400

I

SSD

m

1200

~"

1000

of--I

m

u] ¢'-

800

C I--I

6O0

m

m

400

200

!,Ill,I, o

lo

20

30

40

50

60

70

80

90

Loss Energy (eV) Fig. 5. EEL spectra for AI. (a) Processed spectrum before multiple scattering has been removed. (b) Single scattering distribution after multiple scattering has been removed.

46

M.A. Turowski, T.F. Kelly / Profiling of the dielectric function across heterostructures

4. D i s c u s s i o n

tions is the real part of 1/E(E). The real and imaginary parts of dielectric function (e 1 and E2) and other optical constants are obtained from analytical formulas given in refs. [6,13,14] which relate the real and imaginary parts of 1/c(E).

400

'1'

The most prominent feature in each spectrum is the zero-loss peak (ZLP) which consists mostly of unscattered and quasi-elastically scattered

'lll'l'l'l

l

a

t

300

(o c nl

200

C

100

10

20

30

40

50

60

70

BO

90

Loss Energy (eV) 400

'l'l'lll'l'l

l'l

b

SSD 300

4..J oe-'l

03 r-

2OO

c

iO0

o

10

20

30

40

50

60

70

-, [~-,1 80

90

Loss Energy (eV) Fig. 6. EEL spectra for SiO 2. (a) Processed spectrum before multiple scattering has been removed. (b) Single scattering distribution after multiple scattering has been removed.

M.A. Turowski, T.F. Kelly /Profiling of the dielectric function across heterostructures

electrons [14,15]. For a metal like aluminum at a thickness of about 100 to 150 nm, the ZLP intensity is typically 3 to 4 times higher than the next most intense feature, i.e., the bulk plasmon. The intensity ratio between the ZLP and the bulk plasmon depends on sample thickness. For a nor-

47

mally doped semiconductor (1018 cm-3), in our case silicon, this ratio is about 5-6, and reaches 10 for a large-band-gap insulator like SiO 2. Multiple plasmon scattering peaks are present in the spectra at higher energies. These peaks of multiple losses have to be deconvoluted from any

1000

'1

I~ I ' 1 ' 1 '

l'l'l,I a

8OO

°r-I

600

2 40O

2OO

0 0.0

10.0

20.0

30.0

40.0

g0.0

60.0

70.0

80.0

90.,

Loss Energy (eV)

'°°°f '

lll~l'l~

I'1~1

--

I b

SSD

-

800

-f-4

03 ¢...

600

--

(]3

cI.--t

4OO

200

o I I 0.0

t0.0

,l,I 20.0

30.0

40.0

50.0

60.0

70.0

f 80.0

90.

Loss Energy (eV) Fig. 7. EEL spectra for Si. (a) Processed spectrum before multiple scattering has been removed. (b) Single scattering distribution after multiple scattering has been removed.

48

M.A. Turowski, ZF. Kelly / Profiling of the dielectric function across heterostructures

M O L A R POLARIZABILITY a 2 1 0

-1 N m n*

-2 0 0.

--3 0.,j

-4

-7 5

0.1

10

15

20

25

30

ENERGY LOSS

35

'3N4

10.45

40

(eV)

4~

50

b

o

O2

2,,45 0,25

E

I (eV)

10.25

Fig. 8. (a) An experimental molar polarizability spectrum for SiO 2 derived from the complex dielectric function. (b) Calculated polarizabilities for some insulators from ref. [8].

spectrum before undertaking further steps in the data evaluation procedure [15]. The energy positions of the bulk plasmon peaks observed in our spectra are listed in table 1. If we compare our experimental values for energy positions of plasmon peaks with Egerton's values, we find that ours are high by 0.2 eV for A1 and 0.6 eV for Si but they are the same for SiO 2.

Table 1 Energy position and FWHM of plasmon peaks Material

AI Si SiO 2

This work

Egerton [15]

Ep (eV)

A E o (eV)

Ep (eV)

AEo (eV)

15.2 17.3 23.0

1.8 5.6 16.5-17.0

15.0 16.7 23.0

0.5 3.2

49

M.A. Turowski, T.F. Kelly / Profiling of the dielectric function across heterostructures

These differences vary from material to material, so they cannot be a systematic error. We scaled our spectra using two-point calibration, where two peaks of known energy are used to determine the scale. Thus these plasmon peak values lie within the experimental error inherent to this technique and experimental set-up. One example of an optical constant which can be used to characterize dielectric materials is the molar electronic polarizability, a e. Usually it is derived from the well known L o r e n t z - L o r e n z relation [7] and has been used by Ravindra and Narayan to classify some insulators with respect to their resistance to dielectric breakdown and potential applications in electronic devices [8]. Ravindra and Narayan argue that the greater the electronic polarizability, the higher the intrinsic dielectric strength. Using that reasoning and optical data from the H a n d b o o k of Optical Constants of Solids [16], they selected silicon nitride as a better material than silicon dioxide despite its lower energy gap. Fig. 8 is a comparison of our

molecular polarizability spectrum for SiO 2 and their fig. 7 [8]. The negative value of polarizability above 13 eV is due to the decrease of the value of the refractive index below 1, which continues until the end of the energy range of 50 eV. Since our data are extrapolated from about 4 eV to zero energy, we cannot be sure of the values of the polarizability derived from them in this energy range. We note that the polarizability results in fig. 8a go to negative values at energies below 5 eV, and they should tend smoothly to a positive value. We attribute this discrepancy to imprecision in the extrapolation process. Note also that the position in energy of the maximum in the molar polarizability corresponds approximately to the band gap energy. Above the band gap energy, the polarizability decreases rapidly. In fig. 9, the variation of the maximum of the molar polarizability and its energy magnitude, Era, with position in the A 1 / S i O 2 / S i are plotted. Clearly, the dielectric properties of the oxide layer are not uniform across its thickness. The

03 -r--I

c

15.0

Em

E_ (13 E._ 4-J -*'--I

10.0 £_ ro

sio2

E_ 0 > (1)

\1

/

si

1 1

/

5.0

/

\

~.i/

\ \

/

__--

E_ (1.) ¢-LLI 0.0

0.0

I0.0

20.0

30.0

40.0

Beam Position

50.0

60.0

70.0

80.0

(nm)

Fig. 9. Variation of the molar polarizability (dashed line) and the energy position of the maximum in the molar polarizability function (solid line) across an AI/SiO 2/Si heterostructure.

50

M.A. Turowski, T.F. Kelly / Profiling of the dielectric function across heterostructures

electronic polarizability at the two interfaces is markedly lower than its surroundings. Moreover, the value of the polarizability at the A I / S i O 2 interface is slightly lower than the value at the SiO2/Si interface. The lower polarizability values in the vicinity of the A1/SiO 2 interface indicate a smaller intrinsic dielectric breakdown field in that area. Batson has suggested [17] that this effect at the A1/SiO 2 interface my be due to aluminum oxide interdiffusion with silicon dioxide. Batson [17] found evidence of A10 x using E D X analysis in the A I / S i O 2 system. We found no features in our E E L spectra which could be attributed to aluminium oxide. The solid curve in fig. 9, which represents the position in energy of the maximum of the molar polarizability curve, is more symmetric with respect to the center of the oxide. This p a r a m e t e r indicates that both interfaces are extended into the solid. If we relate this p a r a m e t e r to the band gap energy for the SiO2, then these results suggest that the SiO 2 is weaker at the interfaces.

The entire heterostructure can be studied by presenting a complete set of data taken across the Si/SiO2/A1 heterostructure in the form of 3D plots. In this case, the X and Y axes are the position of the electron b e a m (in nm) and the electron energy loss (in eV), respectively. As a Z-axis we plot the following physical quantities; the EELF, e 1 and e2, and a e. The grid is created of equally spaced X, Y points with Z values which are interpolated using an inverse square of the distance method. Some of the grid data were smoothed using a cubic spline before making a 3D plot. Fig. 10 shows a profile of the EELF, - I r a ( i / e ) , across the A 1 / S i O 2 / S i System. The starting point for these profiles was 10 nm from the A1/SiO 2 interface, and the finishing point was 10 nm from the SiO2/Si interface. The values of the E E L F for lower energy losses, 0.1 to 5 eV, for A1 and Si, and 0.1 to about 8 eV for SiO2, are not found to be reliable due to the nature of the Z L P stripping and cosine-bell termination. This difficulty has an impact on the dielectric function calculations in these energy ranges.

A -%.. -°

'--"®® Fig. 10. EELF surface profile across the AL/SiO 2 / S i heterostructure.

M.A. Turowski, T.F. Kelly / Profiling of the dielectric function across heterostructures

51

REAL PART OF EPSILON

!

% °e "~lP

_~-

i02

-"

"°

"~

c~'~

Fig. 11. The real part of e(E) surface profile across the AI/SiO z / S i heterostructure.

As expected, the dominant feature in these plots is the aluminum-plasmon-peak ridge which gradually changes into the weak oxide-peak ridge of the SiO 2. The ridge then shifts again towards lower energy and increases in intensity for silicon. The interpolated 3D plots are well suited for bringing together all data on one graph and displaying any variation or nonuniformities in the material properties. Details of the data, like plasmon peak positions, their FWHM, or other small spectral details, are best obtained from the original spectra. e~ and e z are presented in figs. 11 and 12. These surfaces are dominated by strong variations at low energies which partially obscure the higher-energy part. This difficulty is again attributable to the limitations imposed by the finite

energy resolution of EELS in STEM. The strong fluctuations in the low-energy part of the dielectric function and optical constants are due to inexact stripping of the ZLP. In order to improve this situation, one has to either switch to dedicated EELS instruments with very high energy resolution or develop a better way of zero-loss peak removal with the correct extrapolation of intensities to zero before applying a KKT. In this regard, the recent work of Wang [18] may be helpful in modelling the ZLP for stripping purposes. In figs. 11 and 12, we have minimized the problems of ZLP stripping by truncating the data at 2 eV. The contributions of interface states and surface plasmons to the optical functions have been considered. There are small features present in

M.A. Turowski, T.F. Kelly / Profiling of the dielectric function across heterostructures

52

IMAGINARY PART OF EPSILON

Fig. 12. The imaginary part of E(E) surface profile across the A I / S i O 2 / S i heterostructure.

6 ~

-o

4

m

~

~.~. 24

4~ o ,

? Fig. 13. Two views of the molar polarizibility surface profile across the A I / S i O 2 / S i heterostructure.

M.A. Turowski, T.F. Kelly / Profiling of the dielectric function across heterostructures

these data (see, e.g., fig. 7 at 7 to 10 eV). In a separate paper [19], we have developed a model for the origin of these features and have shown that they have a minor effect on the bulk properties presented here. Finally, fig. 13 shows the molar electronic polarizability surface for the same spectra. Note that the data have been truncated at 5 eV in this case. This figure should be compared with fig. 9. In the aluminum layer (position 0 to 10 nm), there is a clear evolution of the polarizability as the A I / S i O 2 interface is approached. There are large changes in the polarizability function within 20 nm of the interface on the SiO 2 side and within about 10 nm of the interface on the Al side. It is clear that the electronic properties of the heterostructure are not divided into distinct layers by material interfaces, but rather, the properties of one layer are extended into adjacent layers in a continuous way. The technological implications of these findings are centered on the fact that the dielectric properties of the individual layers are not abrupt. Even for a 40 nm thick layer of SiO 2, it appears that the dielectric strength is diminished over most of the layer. Indeed, the effects of the aluminum and silicon layers, though small, are found in our model [19] even at the opposite interfaces. Despite these findings, it is found experimentally that dielectric layers of SiO 2 as thin as 5 to 7 nm still resist catastrophic dielectric breakdown for fields which are technologically useful in microelectronic devices [5].

5. Conclusions

Here we have provided evidence that it is possible to obtain information about the dielectric function from interfacial regions, and not only from the bulk. Changes in the electronic structure near the A I / S i O 2 and SiO2/Si interfaces occur on a sub-5-nm scale. The plasmon peaks from each phase bordering an interface remain distinct near the interface. The near-interface region contains both peaks with changing relative amplitudes and energy po-

53

sitions shifting slightly toward each other (see Howie [20]). Low-energy (0 to 5 or even 10 eV ) data from a field emission STEM do not provide reliable information on the dielectric function because of difficulties in stripping the zero-loss peak (ZLP). Deconvolution of the ZLP from each spectrum may be best accomplished by stripping the experimental spectrometer transfer function (measured with the same alignment parameters). This approach should be more satisfactory than the cosine-bell extrapolation or step function stripping. Nonetheless, our efforts to do this were unsuccessful because the ZLP width and shape varies from point to point within the sample, and from material to material, mostly due to quasi-elastic electron-phonon interactions. Evaluation of optical constants like the refractive index, absorption coefficient, molar polarizability, conductivity, etc., is a straightforward process when both parts of the dielectric function are available. A composite picture of the molar polarizability behavior was extracted from a serial experimental E E L profile across a Si/SiO2/A1 heterostructure. This profile indicates a weakening (as far as dielectric strength is concerned) of the A I / S i O 2 interface at larger distances than one might expect from the typical extent of structural imperfections (about 1-2 nm) at a boundary between two media. The Al/SiO2 interface exhibited slightly different optical behavior from the S i / S i O 2 interface which may be attributed to development of aluminum oxide inside the SiO 2. This type of examination of dielectric materials appears to offer promise for developing a greater understanding of the dielectric breakdown phenomena. Further work should address such issues as studying these effects in a variety of dielectric materials and metallizations as a function of dielectric thickness. Multiple dielectric layers should also be studied. EELS in a field emission STEM offers very high lateral spatial resolution analyses but suffers from a lack of high-energy resolution. Dedicated EELS instruments offer very-high-energy resolution from large areas. A study which combines the advantages of each could lead to improved

54

M.A. Turowski, T.F. Kelly / Profiling of the dielectric function across heterostructures

p r e c i s i o n in t h e d e t e r m i n a t i o n o f t h e p r o p e r t i e s a n d t h e i r v a r i a t i o n s in s p a c e .

optical

Acknowledgements T h i s w o r k was s u p p o r t e d by a g r a n t f r o m t h e International Business Machines Corporation und e r t h e s u p e r v i s i o n o f D r . D e x t e r A. J e a n n o t t e . W e w o u l d like to t h a n k M a r k K a p f h a m m e r for h e l p w i t h s a m p l e p r e p a r a t i o n a n d Jofio L. V a r g a s for h e l p w i t h t h e p r e l i m i n a r y e x p e r i m e n t a l w o r k .

References [1] H.J. Higatsberger, Adv. Electron. Electron Phys. 56 (1981) 291. [2] G.B. Larrabee, SEM/77, Ed. O. Johari (IITRI, Chicago, 1977) Vol. 1, p. 639. [3] L.M. Brown, J. Phys. F 11 (1981) 1. [4] J.F. Hainfeld, SEM/77, Ed. O. Johari (IITRI, Chicago, 1977) Vol. 1, p. 591. [5] Proc. SRC Topical Research Conference on High Reliability Gate Dielectrics, Albuquerque, New Mexico, 1990.

[6] L.D. Landau and E.M. Lifshitz, Electrodynamics of Continuous Media, 2rid ed. (Pergamon, New York, 1984). [7] H. Frohlih, Theory of Dielectrics (Oxford University Press, 1958). [8] N.M. Ravindra and J. Narayan, J. Appl. Phys. 61 (1987) 2017. [9] E. Tosatti, Phys. Lett. A 27 (1968) 446. [10] These structures were kindly fabricated by G. Schwartz of IBM East Fishkill. [11] J.C. Bravman and R. Sinclair, J. Electron Microsc. Tech. 1 (1984) 53. [12] See also MRS Proceedings, Ed. R. Anderson, Vol. 199 (1990). [13] J. Daniels, C.V. Festenberg, H. Raether and K. Zeppenfeld, Springer Tracts Mod. Phys. 54 (1970) 78. [14] H. Raether, Springer Tracts Mod. Phys. 38 (1967) 85. [15] R.E. Egerton, Electron Energy-Loss Spectroscopy in the Electron Microscope (Plenum, New York, 1986). [16] Handbook of Optical Constants of Solids, Ed. E. Palik (Academic Press, New York, 1985). [17] P.E. Batson, private communication, 1990. [18] Z.L. Wang, in: Proc. 49th Annu. EMSA Meeting (San Francisco Press, San Francisco, 1991). [19] M.A. Turowski, T.F. Kelly and P.E. Batson, in preparation. [20] A. Howie and R.H. Milne, UItramicroscopy 18 (1985) 427.