Micron 40 (2009) 365–369

Determination of complex dielectric functions at HfO2/Si interfaceby using STEM-VEELS

Jucheol Park *, Mino Yang

Analytical Engineering Center, Samsung Advanced Institute of Technology, Nongseo-Dong Mt. 14-1, Giheung-Gu, Yongin-si, Gyeonggi-do 446-712, Republic of Korea

A R T I C L E I N F O

Article history:

Received 16 June 2008

Received in revised form 11 September 2008

Accepted 3 October 2008

Keywords:

Complex dielectric functions

Dielectric constant

HfO2

STEM

VEELS

A B S T R A C T

The complex dielectric functions and refractive index of atomic layer deposited HfO2 were determined by

the line scan method of the valence electron energy loss spectrum (VEELS) in a scanning transmission

electron microscope (STEM). The complex dielectric functions and dielectric constant of monoclinic HfO2

were calculated by the density functional theory (DFT) method. The resulting two dielectric functions

were relatively well matched. On the other hand, the refractive index of HfO2 was measured as 2.18 by

VEELS analysis and 2.1 by DFT calculation. The electronic structure of HfO2 was revealed by the

comparison of the inter-band transition strength, obtained by STEM-VEELS, with the density of states

(DOS) calculated by DFT calculation.

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1. Introduction

As scaling of feature sizes in complementary metal–oxide–semiconductor (CMOS) continuously decreases, a need to replaceSiO2 as gate dielectric with high-k materials has been increasedbecause of its high leakage current. HfO2 is one of the mostextensively studied alternate materials (Baik et al., 2004). In general,the dielectric constants and the electronic structure of high-k

materials themselves have been measured with optical methods,such as vacuum ultraviolet spectroscopy (VUV) and ellipsometer(van Benthem et al., 2001a,b). However, these optical methods arenot applicable to a site-specific nm-area analysis of the dielectriccharacteristics in the internal structure of memory devices. One ofthe prominent alternatives to the limited optical method is thevalence electron energy loss spectroscopy (VEELS) method usingwith a scanning transmission electron microscopy (STEM) (Ryenet al., 1999). EELS technique has the advantage of covering thecomplete energy range, including valence inter-band transitions(from VEELS) and core level excitations (from energy-loss near edgestructure (ELNES)). When performed with STEM, it has a spatialresolution in the nanometer range, which allows the selection ofsmall feature within a specimen. Recently, the investigations on thecomplex dielectric functions by STEM-VEELS have been reported forthe high-k materials such as SrTiO3 (Hu and Jones, 2005; van

* Corresponding author.

E-mail address: jucheol.park@samsung.com (J. Park).

0968-4328/$ – see front matter � 2008 Elsevier Ltd. All rights reserved.

doi:10.1016/j.micron.2008.10.006

Benthem et al., 2001a,b), Al2O3 (Mullejans and French, 1996; Frenchet al., 1998) and AlN (Dorneich et al., 1998). However, the dielectricproperties of HfO2 studied by STEM-EELS have been rarely reported.

In this study, we measured the complex dielectric functions andrefractive index at the interface region between HfO2 and Si withnm-order spatial resolution by using valence electron energy lossspectroscopy in scanning transmission electron microscopy.Assignments of the inter-band transitions in the electronicstructure of HfO2 have been determined by comparison of VEELSspectra and the ab-initio calculated densities of states, based on thedensity functional theory (DFT).

2. Experiments

HfO2 dielectrics were prepared with atomic layer deposition(ALD) method and annealed in N2 ambient at 700 8C. TEM samplepreparation was done by conventional ion milling method. Ion-milling specimens were prepared by mechanical grinding anddimpling down to 20 mm, followed by argon ion milling on a GatanPIPS machine, operating at an accelerating voltage of 3.5 kV and 68incidence angle. In order to decrease contamination effects, thespecimens were plasma-cleaned prior to insertion into themicroscope.

EELS spectra were obtained with Enfina parallel electron energyloss spectrometer (PEELS) attached to a FEI Tecnai UT (300 keV),which offers an energy resolution of 0.8 eV. The electron probe sizewas below 1 nm. The spectra were acquired using a dispersion of0.05 eV/channel in order to record spectra up to 60 eV. The

Fig. 1. STEM dark field image of the interface of HfO2/Si and a spectrum image of 20

spectra (right side).

Fig. 2. A series of 20 low-loss spectra corresponding to a spectrum image of Fig. 1.

Fig. 3. Valence electron energy-loss spectrum of HfO2, the extracted zero-loss peak,

and the corresponding single-scattering distribution (SSD) spectrum after Fourier-

log deconvolution.

Fig. 4. Twenty spectra of single-scattering distribution (SSD) obtained by the

subtraction of zero-loss peaks.

J. Park, M. Yang / Micron 40 (2009) 365–369366

convergence semi-angle was chosen to be equal to the collectionsemi-angle, which was given to be 6.3 mrad by the PEELS apertureof 3 mm. A series of 20 spectra were acquired while scanning theprobe perpendicularly across the interface with scan lengthsbetween 40 and 100 nm (Figs. 1 and 2). The subtraction of zero-losspeak from the EELS spectra, Fourier-log deconvolution andKramers–Kronig analysis were carried out with electronic struc-ture tools (EST), including the SS_COR, CONCOR and KKEELSprograms.

3. Results

3.1. Determination by VEELS analysis method

For all VEELS spectra the center of the zero-loss peak was fittedfor the zero energy calibration. Subsequently, the spectra were

corrected for multiple scattering events by Fourier-log deconvolu-tion. During this procedure the wings of the zero-loss peak werefitted separately with an asymmetric Pearson VII line shape andsubtracted (see Fig. 3). The resulting single-scattering distribution(SSD), S(E), is related to energy-loss function (ELF), Im(�1/e) by

SðEÞ ¼ I0t

pa0m0v2Im

�1

eðEÞ

� �ln 1þ b

uE

� �2 !

(1)

where I0 is the zero-loss beam intensity, t is the specimen thickness,v is the incident electron velocity, b is the collection semi-angle, a0 isthe Bohr radius, and m0 is the electron rest mass and uE is thecharacteristic scattering angle for energy loss. Fig. 4 shows the 20SSD spectra resulted from the subtraction of zero-loss peaks.

Fig. 6. Measured dielectric constants at HfO2/Si interface.

J. Park, M. Yang / Micron 40 (2009) 365–369 367

In order to obtain ELF from the SSD spectrum, scale factor,including the collection and geometrical factors, was determinedby using Kramers–Kronig f-sum rule (Egerton, 1996) given by

1� 1

n2¼ 2

p

ZIm�1

eðEÞ

� �dE

E¼ 2

p

Z½Scale Factor� SSD�dE

E(2)

After we determined scale factor by using the refractive index ofsilicon, known as 3.42, the determined scale factor was applied toscale energy-loss function of HfO2 and Si. The real part of thedielectric function, Re[1/e(E)], was obtained from an experimen-tally determined loss function, Im[�1/e(E)], by use of the Kramers–Kronig transformation

Re1

eðEÞ

� �¼ 1� 2

pP

Z 10

Im�1

eðEÞ

� �E0 dE0

E02 � E2

(3)

where P denotes the Cauchy principal part of the integral. Finally,the complex dielectric function, e1 and e2, was obtained from therelation to Re[1/e(E)] and Im[�1/e(E)] by

Re1

eðEÞ

� �¼ 1� 2

pP

Z 10

Im�1

eðEÞ

� �E0 dE0

E02 � E2

(4)

Fig. 5 shows the dielectric functions, Re(e) and Im(e), calculatedthrough the normalization using the scaling factor and Kramers–Kronig transformation. Also, we determined the dielectric constantat each graph of epsilon real part (e1) by measuring the y-axisintercepts of the graphs. The averaged dielectric constants of the

Fig. 5. Complex dielectric functions for HfO2 obtained by the Kramers–Kronig

analysis of the 3rd SSD. Notice that a refractive index is measured from the y-axis

intercept of the graph of epsilon real part (e1).

HfO2 and Si layers were measured as 4.75 and 11.93, respectively.The values of the dielectric constants at the zero energy are about asquare of refractive index (nHfO2 = 2.18 and nSi = 3.45) because theVEELS method gets only the electronic contributions to thedielectric function, and neglect the vibrational and dipolarcontributions. The measured dielectric constants at the 20 pointsare plotted in Fig. 6. It is found that in the interface region of Fig. 1,the values of dielectric constants were higher than in the bulk sideof the Si substrate and in the HfO2 layer. We speculated that thechange of the dielectric constants at the interface is due to thethickness reduction by Ar+ ion milling during the samplepreparation (Stoger-Pollach et al., 2004).

3.2. Determination by the DFT calculation

The calculations of dielectric functions and total density of states(DOS) of HfO2 were performed using the generalized gradientapproximation (GGA) and the full potential linearized augmentedplane-wave method (FLAPW) plus local orbital (LO) embodied in thelatest WIEN2K code. The crystal structure and space group of HfO2were supposed to be monoclinic phase and P21/c. Integrations inreciprocal space were performed by using the tetrahedrons methodwith a k mesh of 16 k points in the two-dimensional irreducibleBrillouin zone. In the FLAPW method the relevant convergenceparameter is RmtKmax defined by the product of the smallest atomicsphere radius (Rmt) times the largest reciprocal lattice vector of theplane-wave basis (Kmax). For controlling the size of the basis set forthe wave functions, the parameter RmtKmax was set to 8.0, containinga well-converged basis set of about 1300 LAPW’s and 150 LO’s.Convergence test indicates that only small changes result from goingto a dense k mesh or to a larger value of RmtKmax. The self-consistentcalculations are considered to be converged only when theintegrated charge difference is less than 0.0001.

Fig. 7 shows complex dielectric functions of HfO2 resulted fromthe DFT calculation. From the dielectric constants of Fig. 7,refractive index of HfO2 and Si at the zero energy was obtained as2.1 and 3.5, respectively. The results show that the calculateddielectric constants are similar to the measured ones. Thesimilarity of the experimental and calculated values is reasonablebecause DFT calculation, like the VEELS method, reflect only theelectronic contributions to the dielectric function.

3.3. Electronic structure of HfO2

Since the real part of Jcv corresponds to transitions fromoccupied valence band states to unoccupied conduction bandstates, assignments of the orbital origins of these transitions can be

Fig. 7. Comparison of DFT calculated and experimental complex dielectric functions

for HfO2.

J. Park, M. Yang / Micron 40 (2009) 365–369368

obtained by a comparison with DOS calculations near the Fermilevel. Fig. 8 shows the real part of the inter-band transitionstrength Re[Jcv] of HfO2 which is obtained by VEELS. The inter-bandtransitions are dominated by excitations around 6.3–11.5 eV (A),by a peak at 19.6 eV (B), and by excitation around 24.8 and 35.9 eV(C and D). Fig. 9 shows our results of the PDOS calculations for pureHfO2 projected onto the sites of Hf and O. The occupied bands fromwhich inter-band transitions originate are the Hf 5p levels at�28.7 eV, Hf 4f levels at �9.9 eV, and the O 2s and O 2p levels at

Fig. 8. Inter-band transition strength for HfO2 determined by STEM-VEELS analysis.

Fig. 9. Calculated total projected density of states (PDOS) for HfO2 and the site

projected PDOS for hafnium and oxygen, respectively.

�16.2 eV and�4.2 to�0.8 eV. The unoccupied energy bands in theconduction band are the Hf 5d levels at +5.5 to 10.5 eV.

In Fig. 8, the Re(Jcv) peaks labeled A at 6.3–11.5 eV originatefrom transitions of O 2p electrons into Hf 5d conduction bands,while transitions C at 24.8 eV corresponds to O 2s to Hf 5dexcitations. Peak B at 19.6 eV and peak D at 35.9 eV are due to Hf4f! Hf 5d and Hf 5p! Hf 5d transitions, respectively.

4. Conclusions

We measured the dielectric constants of HfO2 by STEM-EELSline scan method and DFT calculation method. The refractive indexof HfO2 and Si at the zero energy was measured as 2.18 and 3.45 bythe STEM-EELS method and 2.1 and 1.18 by DFT calculation,respectively. It is found that the measured values and thecalculated values are similar.

J. Park, M. Yang / Micron 40 (2009) 365–369 369

After we confirm that the measured complex dielectric functions(CDF)are well matchedwiththe calculatedfunctions, wedeterminedthe electronic structure of HfO2 by comparing the measured inter-band transition strength with the calculated density of states.

It is demonstrated that the STEM-VEELS line scan methodcombined with Kramers–Kronig analysis is a very useful techniqueto measure the dielectric functions and constant of the unknownmaterials at nm-scale local area for the high-k materials.

Acknowledgements

The authors would like to acknowledge Dr. Lin DeNoyer for hersupport in data analysis with the electronic structure tools. We arealso grateful to Dr. Roger H. French and Dr. Masami Terauchi formany helpful discussions.

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