Applied Surface Science 117/l 18 (1997) 216-220

surface science EISEVIER

Spectral shape analysis of infrared absorption of thermally grown silicon dioxide films

Naoki Yasuda * , Shin-ichi Takagi, Akira Toriumi ULSI Research Laboratories, Toshiba Corporation, I, Komukai Toshiba-cho, Saiwai-ku, Kawasaki 210, Japan

Abstract

The shape of the infrared absorption spectra of thermally grown silicon dioxide films on Si (100) is analyzed in order to characterize the oxide quality as a function of distance from the Si/SiO, interface. The analysis includes (1) an exact extraction of the thickness-deconvoluted dielectric function of the SiO, films from the infrared absorption spectra measured on a series of etched-back SiO, films, thereby eliminating the multiple reflection effect at the surface and the interface and (2) evaluation of the Si-0-Si bond angle distribution from the dielectric function, assuming the central-force model. It is found that, as the distance from the Si/SiO, interface decreases, a significant broadening of the Si-0-Si bond angle distribution occurs only for the small bond angle region (less than 130”). This means that an average indicator of oxide quality such as the peak wave number of the infrared absorption spectrum is insufficient to describe the structural change inside the thermally grown SiO, films. A possible model for the asymmetric broadening of the Si-0-Si bond angle distribution is that the thermally grown SiO, films are essentially composed of two components, i.e., one is locally existing regions with strained SiO, structure and the other is a region with the bulk oxide quality. It is considered that the lattice mismatch at the Si/SiO, interface is relaxed by changing the volume ratio of the two components.

Keywords: Silicon dioxide; SiO,; Thermally grown oxide; Gate oxide; MOSFBT, Infrared absorption spectroscopy; Multiple reflection;

Dielectric function; Spatial distribution; Bond angle; Central force model

1. Introduction

As the size of MOS (metal-oxide-semiconductor) devices becomes smaller, the thickness of the gate oxide is also decreasing. At present, ultra-thin gate oxides such as 5 nm are used in commercial devices. The structural transition of thermally grown SiO, films near the Si/SiO, interface should not be ne- glected as the thickness of the gate oxide film is reduced. Therefore, it is important to investigate structural inhomogeneity of thermally grown SiO,

* Corresponding author. E-mail: yasuda@ull.rdc.toshiba.co.jp.

films in the direction perpendicular to the Si/SiO, interface.

Infrared spectroscopy in combination with wet etching of the SiO, film [l-6] has been used as a sensitive method to investigate the change of SiO, structure in the thickness direction. Most previous work has concentrated on the shift of peak position of the infrared absorption spectra and there has been no quantitative analysis of spectral shape. Although the peak position is a useful quantity to describe the average oxide structure, a component far away from the average SiO, structure should also be important from the viewpoint of electrical reliability of the gate oxide films. It is considered that highly strained

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N. Yasuda et al. /Applied Surface Science 117 / 118 (1997) 216-220 217

Si-0 bonds are responsible for dielectric breakdown of the gate oxide [7-91. Therefore, in this paper the authors focused on the spectrum shape in order to understand the structural distribution of the thermally grown SiO, network. In general, the spectrum shape implies the lifetime of excitation mode. However, in thermally grown SiO, films, the linewidth of the

absorption band due to the Si-0-Si stretching vibra- tion is about an order of magnitude larger than that of the quartz (single crystalline SiO,) [lO,ll]. This means that the absorption spectrum of the thermally grown SiO, film is composed of various excitation modes with different resonant frequencies. Thus, an analysis of spectrum shape will yield information on the structural distribution of the thermally grown SiO, films.

This paper is organized as follows. In Section 2, the analysis method of the spectral shape is de- scribed. The analysis includes: (1) an exact extrac- tion of the thickness-deconvoluted dielectric function of the SiO, films from the infrared absorption spec- tra measured on a series of etched-back SiO, films, thereby eliminating the multiple reflection effect at the surface and the interface and (2) evaluation of the Si-0-Si bond angle distribution from the dielec- tric function, assuming the central-force model [ 12,131. After a description of experimental proce- dure in Section 3, it is found in Section 4 that a significant broadening of the Si-0-Si bond angle distribution occurs only for the small bond angle region (less than 130”). and a new model for discussed in Section 4.

2. Analysis method

The implication of the result the SiO, structure are also

The analysis is carried out for the infrared spectra of the SiO, films measured in the transmission configuration with the infrared beam incident per- pendicular to the sample, which is the simplest mea- surement configuration with the least experimental ambiguity. First, the refractive index of the thermally grown SiO, films is evaluated from the measured infrared spectra of SiO, films. Subsequently, the Si-0-Si bond angle distribution is derived from the refractive index in order to infer the physical mean- ing of the infrared spectra.

2. I. Refractive index

There are two important points to be considered when evaluating the refractive index from the in- frared spectra. One is that the infrared spectra is distorted by the multiple reflection of infrared beam at the air/SiO, surface and the Si/SiO, interface [4]. The other is that a raw infrared spectrum gives the information summed over the entire film thick- ness [5]. Considering these two points, the following calculation procedures (1 and 2) are adopted.

(1) The refractive index of the SiO, film is calculated in a self-consistent manner so that the measured infrared absorption spectra of the SiO, film (subtraction spectra of the sample ‘with respect to the Si substrate) and the Kramers-Kronig relation for the refractive index are satisfied simultaneously.

As shown in Fig. 1, the absorption spectrum of the SiO, film is calculated with an initial refractive index of SiO, [14] first. Then, the imaginary part of the refractive index is corrected by an amount pro- portional to the difference between the measured and calculated absorbances. The real part of the refrac-

tive index is calculated with the Kramers-Kronig integration [15] from the corrected imaginary part.

This procedure is repeated until the measured and calculated absorbances become equal. Note that the absorption spectrum of the SiO, film ( Acalc) is

I Initial (n, k) I

Calculation of Absorbance : kcalc Ak 0~ h(Ameas - A,& I tax

Kramers - Kronig Integration

(n+An) + (k+Ak)

Fig. 1. Algorithm for self-consistent calculation of refractive index

of the SiO, film, (n, k). A: wavelength, A,,,,: measured ab- sorbance, Acalc: calculated absorbance and t,,: thickness of SiO,

layer.

218 N. Yasuda et al./Applied Surface Science 117/118 (1997) 216-220

calculated as a subtraction absorbance with respect to the Si substrate. The refractive index of the Si substrate used in the calculation is derived in the appendix.

(2) The infrared spectra of the SiO, films etched back to different oxide thicknesses are deconvoluted in the thickness direction in order to obtain the refractive index as a function of distance from the Si/SiO, interface. For this purpose, the authors use the deconvolution method proposed by Ishikawa et al. [5]. The SiO, film is divided into multiple layers with the thickness of each layer being equal to the incremental depth of wet etching. The refractive indices of the multiple layers are determined consec- utively from the infrared spectra of the etched-back SiO, films. (The self-consistent calculation shown in Fig. 1 is applied to the surface layers of the etched- back SiO, films consecutively.)

The refractive index (n, k) of the SiO, film thus obtained as a function of distance from the Si/SiO, interface is then transformed into the imaginary part of the dielectric function, Im(E) = 2nk, in order to analyze the bond angle distribution as described in Section 2.2.

2.2. Bond angle distribution

The structural distribution of the SiO, network is evaluated generally by decomposing the imaginary part of the dielectric function, Im(.s), into Lorentzian functions with different resonant frequencies. Since

the band half-width of the thermally grown SiO, films is an order of magnitude larger than the Lorentzian band half-width [ 10,111, the Lorentzian function can be approximated as the delta function. Under this approximation, Im(&) is regarded as rep- resenting the structural distribution of the SiO, net- work.

Within the framework of the central-force model [ 12,131, the structural distribution is considered to be the Si-0-Si bond angle distribution. The imaginary part of the dielectric function is then transformed into the Si-0-Si bond angle distribution, using the relation f( 13 )d 19 a Im( E )d u, where f( 8) is the distri- bution function of the Si-0-Si bond angle 8, and v is the wave number. According to the central force model [ 12,131, the characteristic wave number of the

stretching vibration of the Si-0-Si bonds is related to the Si-0-Si bond angle as

v = v0 sin( e/2) (1)

where v0 = 1134 cm -’ [ll. Using Eq. (l), the distri- bution of the Si-0-Si bond angle is expressed as

f(e) aIm(E)/m. (2)

Note that Im(&) has a shoulder band observed for v > vO. The shoulder band is subtracted from Im( E) before Eq. (2) is applied to obtain f(e) because the shoulder band is considered to be due to vibration modes different from the main absorption band [ 11,16,17]. The subtraction procedure was carried out by approximating the shoulder band as being symmetric with respect to ~a.

3. Experimental

The starting silicon substrates were n-type 800 R cm (100) FZ wafers, with both surfaces polished. The wafers were cleaned in hot HCl-H,O, and dipped in a diluted HF acid. Thermal oxidation was carried out in a conventional furnace at atmospheric pressure. The wafers were loaded into the furnace in a diluted 0, ambient and then exposed to pure 0, ambient at 800°C. After the thermal oxidation, the wafers were loaded out of the furnace in pure N, ambient. The thermal oxides were grown to the thickness of 87 nm. They were then etched back in a chemical solution (HF : NH,F = 0.3% : 1.5%) to var- ious remaining thicknesses down to 3.3 nm. The thicknesses of the SiO, films were measured by ellipsometry using He-Ne laser as a source. Infrared absorption spectra of the samples were measured by FT-IR (Fourier transform infrared spectroscopy) us- ing an MCT (mercury cadmium telluride) detector cooled to 77 K. Reference spectra were measured by preparing the samples with SiO, layer completely etched off (H-terminated silicon substrate). All the infrared measurements were carried out in the trans- mission configuration, with the infrared beam inci- dent perpendicular to the sample. The spectral reso- lution was 4 cm-’ and 1024 scans were performed for each measurement.

N. Yasuda et al./Applied Surface Science 117/118 (1997) 216-220 219

4. Results and discussion

The change of spectral shape in the thickness direction can be characterized by two wave numbers corresponding to the half-maximum points of the absorption peak. Fig. 2 shows the wave numbers of upper and lower half-maximum points of the raw infrared spectra as functions of oxide thickness. The two wave numbers decrease in parallel as the oxide thickness is reduced. On the other hand, Fig. 3 shows the upper and lower half-maximum points of the imaginary part of the dielectric function, Im(s), as functions of the distance from the Si/SiO, inter- face. A noticeable feature of Fig. 3, compared to Fig. 2, is that the wave number of the upper half-maxi- mum point is nearly constant over a wide range of distance from the Si/SiO, interface, whereas the wave number of the lower half-maximum point sig- nificantly changes with the distance from the Si/SiO, interface. The large change of the lower half-maxi- mum point in Fig. 3 as compared to Fig. 2 is owing to the thickness deconvolution procedure in the anal- ysis. On the other hand, the lack of any substantial change of the upper half-maximum point in Fig. 3 indicates that the shift of the upper half-maximum point of the raw infrared spectrum (Fig. 2) is only apparent and is entirely due to the multiple reflection effect. Thus, we find from Fig. 3 that the spectral shift due to the quality change of SiO, films is not parallel in all wave numbers. Instead, asymmetric broadening of the spectra is observed as the distance from the Si/SiO, interface decreases.

‘E

2 0

!z

20 40 60 80 100 2

Oxide Thickness (nm) 9

Fig. 2. Wave numbers corresponding to upper and lower half-

maximum points of the raw infrared absorption spectra (Si-0-Si

stretching vibration) as a function of oxide thickness.

'E ZL 5 1110

; 1105

81100 1 z 1095

k 1090

z' 1085

1025 2

1020 $

9 0 20 40 60 80 100

2

$

Distance from Si/SiO2 interface (nm) 2

Fig. 3. Wave numbers corresponding to upper and lower half-

maximum points of Im(&) as a function of distance from the

Si/SiO, interface.

Next, let us discuss the physical meaning of the asymmetric spectral broadening. As shown in Fig. 4, the Si-0-Si bond angle distributions were analyzed for three typical distances from the Si/SiO, inter- face. Fig. 4 indicates that only the distribution in the small bond angle region (less than 130”) significantly changes in the thickness direction, while the change of distribution in large bond angle regions is negligi- ble. Based on the asymmetric change of oxide qual- ity, the authors suppose that thermally grown SiO, films are essentially composed of two components, i.e., regions with strained SiO, structure and a region with the bulk oxide quality. As shown in Fig. 5, the strained SiO, regions are considered to exist locally in a scattered manner in the bulk oxide. Thus, the overall SiO, structure does not change much from the bulk oxide, but the number density of the strained

$03 110 120 120 140 150 1M)

Bond Angle (deg)

Fig. 4. Si-0-Si bond angle distribution for three different dis-

tances from the Si/SiO, interface. Reverse solid triangle: O-3.3

nm. Open circle: 3.3-5.3 nm. Solid circle: 36.7-53.4 nm.

220 N. Yasuda et al./Applied &face Science 117/ 118 (1997) 216-220

Si substrate

Fig. 5. Structural model of thermally grown SiO, films. The solid

circles represent regions with strained SiO, components, while the

surrounding region corresponds to the component with bulk oxide

quality.

regions increases near the Si/SiO, interface. It is considered that the lattice mismatch at the Si/SiO, interface is relaxed according to the change of vol-

ume ratio of the two components.

5. Conclusions

The shape of the infrared absorption spectra of thermally grown silicon dioxide films on Si (100) was analyzed. It was found that the Si-0-Si bond angle distribution changes asymmetrically in the thickness direction and only the distribution in the small bond angle region (less than 130”) was found to change significantly. This means that an average indicator of oxide quality such as the peak wave number of the infrared absorption spectra is insuffi- cient to describe the structural change of the ther- mally grown SiO, films. A possible model for the structural change is that the thermally grown SiO, films are essentially composed of two components, i.e., locally existing regions with strained SiO, struc-

ture and a region of bulk oxide quality.

Acknowledgements [71

The authors would like to thank H. Satake for his valuable comments and suggestions. Thanks are also due to M. Hotta for his help with the FT-IR measure- ments.

Dl

[91

Appendix A

The refractive index of the Si substrate ( lzsi + i ksi) is derived as follows. The absorbance of the Si substrate is expressed as Asub = - log,,lt,,,12 where

t, t,,exp( - 2aks,d,Jh) ,_\ t s”b = 1 - r,“,exp( -4~ksidsi/h) (3)

This equation approximates the transmission rate of the Si substrate when the interference fringe in the spectra are eliminated. In the equation, h is the wavelength of the infrared beam, and d,,(= 0.63 mm) is the thickness of the Si substrate. The trans- mission and reflection ates at the Si surface are approximately expressed as t,, = 2/(1 + n,,), t,, =

2nsi/(nsi + 1) and rsa = (nsi - l)/(n,, + 1) be- cause nsi B- ksi [ 181. For the wave number range of interest (between 1000 and 1200 cm-’ >, the ab-

sorbance of the measured infrared spectrum of the Si substrate was approximated as constant (Asub = 0.22). The imaginary part of the refractive index of

the Si substrate was derived from the equation as ksi = 3.1 X 10m4, assuming nsi = 3.42. (Note that ksi incorporates all the absorption factors of the Si substrate, including the Si phonon absorption.)

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