Raman active modes of NiSi crystal

ARTICLE IN PRESS Physica B 404 (2009) 2324–2326

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Physica B journal homepage: www.elsevier.com/locate/physb

Raman active modes of NiSi crystal Li Wan , Bo Tang, Xinhong Cheng, Yiming Ren, Xuefei Zhang, Dapeng Xu, Haijun Luo, Yunmi Huang Department of Physics, Wenzhou University, People’s Republic of China

a r t i c l e in f o

a b s t r a c t

Article history: Received 4 January 2009 Accepted 22 April 2009

Raman scattering intensities of the NiSi Raman-active modes have been calculated with three Raman measurement configurations, which can be used for the symmetry assignment of the NiSi Raman peaks. Raman-active vibrations of the NiSi crystal have also been theoretically studied. Results show that the lattices with Ag and B2g modes vibrate only in the plane normal to the NiSi[0 1 0] direction while the lattices with B1g and B3g modes vibrate only along the NiSi[0 1 0] axis. Based on such study, the relationship between the anisotropic strain distribution in the NiSi thin film and the Raman peak shifts has been briefly discussed. & 2009 Elsevier B.V. All rights reserved.

PACS: 78.30.Hv 63.22.-m Keywords: NiSi Raman Vibration

Silicides have been widely used in complementary metaloxide-semiconductor (CMOS) technology as interconnect and contacts application [1]. In order to improve the performance of the CMOS devices, the silicide materials used in the CMOS devices should have low resistances to decrease the RC delay time of circuits. Presently, silicide materials such as TiSi2 and CoSi2 have been widely used in the CMOS device fabrication. However, those materials have certain limitations for their application. The sheet resistance of TiSi2 shows remarkable line width dependence. And the main shortcoming of CoSi2 is the high silicon consumption. Furthermore, the interfaces of CoSi2/Si junctions are non-uniform, which can induce high diode leakage. Recently, it was found that NiSi material has line-width-independent resistance and low silicon consumption [1–3]. Thus, intense efforts have been focused on NiSi material to replace the TiSi2 and CoSi2 in the CMOS device fabrication. Various substrates have been used for the growth of the NiSi thin films [4–6]. The crystal quality of the NiSi thin films becomes improved with the development of growth techniques. Raman spectroscopy as a powerful and none-destructive tool can be used to understand the growth duration of thin films [7–10]. Each peak in a Raman spectrum corresponds to a unique lattice vibration mode. The Raman spectrum then can serve as material fingerprint for the study of the phase identification. Furthermore, line shapes of Raman peaks are strongly influenced by microstructures in the materials [11]. For example, strains in the materials can change the lattice parameters and shift the Raman peaks by several wave

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E-mail address: [email protected] (L. Wan). 0921-4526/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2009.04.031

numbers. Grain size and defects can break the q-vector selection and then change the line shapes of the Raman peaks. Some defects even can induce new Raman scattering peaks. Thus, based on the Raman spectroscopy study, microstructure information of the materials can be figured out. The Raman spectroscopy has been extensively used to study TiSi2 and CoSi2 thin films [3,12]. However, for NiSi thin films, even symmetries of Raman peaks have not been assigned yet and application of the Raman spectroscopy has seldom been performed to investigate microstructures of the films. For the latter, Raman active modes of the NiSi crystal are responsible for the relationship between the Raman peaks and the microstructures. Thus, it is important to study the Raman active modes of the NiSi crystal for a better application of the Raman spectroscopy on the NiSi films. In this context, we theoretically calculate the Raman scattering intensities of the NiSi Raman active modes and propose a method for the symmetry assignment of Raman peaks. Furthermore, we calculate the lattice vibrations of the NiSi Raman active modes and discuss the application of the Raman spectroscopy on the strain investigation of NiSi films. According to the group theory, the NiSi film with an orthorhombic crystal structure (space group Pnma,D16 2h ) has 12 Raman active phonon modes at the Brillouin zone center: GRaman ¼ 4Ag+4B1g+4B2g+2B3g [13]. To calculate the Raman scattering intensities of each Raman mode, we only consider the back scattering configuration with the wave vector of the incident laser beam parallel to the scattered light. The back scattering configuration is commonly used for the Micro-Raman spectroscopy study. We note that VH represents the scattering intensity with the crossed scattering configuration and HH is for the parallel scattering configuration. The coordinates are fixed in the NiSi

ARTICLE IN PRESS L. Wan et al. / Physica B 404 (2009) 2324–2326

crystal with x==NiSi½1 0 0; y==NiSi½0 1 0, z==NiSi½0 0 1 There exists a symmetry center in the NiSi crystal with the space group of Pnma. Thus, the NiSi crystal is non-polar. The Raman scattering intensity then can be obtained from the following formula: 2   X    e2a P ab e1b  . (1) I   a;b

Configuration one: Incident laser beam

Here, a and b represent the coordinates of x,y,z. e1b is the b component of the polarization vector of the incident light while e2a is the a component of the polarization vector of the scattering light. P represents the polarizability tensor, shown as the following [13]: 2 3 2 3 a 0 0 0 0 d 6 7 6 7 PðAg Þ ¼ 4 0 b 0 5; PðB1g Þ ¼ 4 d 0 0 5;

Ag B1g B2g B3g

Configuration one

Configuration two

Configuration three

[b cos(y)2+c sin(y)2]2

[a cos(y)2+c sin(y)2]2

[a cos(y)2+b sin(y)2]2

½12 ðc  aÞ sinð2yÞ2 0

½12 ðb  aÞ sinð2yÞ2

HH

½12 ðc  bÞ sinð2yÞ2 0

VH HH VH HH VH

0 0 0 [f sin(2y)]2 [f cos(2y)]2

[d sin(y)2]2 [e sin(2y)]2 [e cos(2y)]2 0 0

HH VH

½2d sinð2yÞ2 [d cos(y2)2] 0 0 0 0

z

N iS i [0 0 1]

E

θ

y

y

N iS i [0 1 0 ]

x

N iS i [1 0 0 ]

θ

E

z N iS i [0 0 1]

Configuration three:

Incident laser beam

Table 1 Raman scattering intensities for the three measurement configurations indicated in Fig. 1.

N iS i [1 0 0 ]

Configuration two:

0 0 0 2 3 0 0 0 6 7 pðB3g Þ ¼ 4 0 0 f 5: 0 f 0

For the calculation of the Raman scattering intensities of each Raman active mode, three Raman measurement configurations are studied. In configuration one, the NiSi[1 0 0] is parallel to the incident laser beam (ILB). In configuration two and three, the ILB is parallel to the NiSi[0 1 0] and NiSi[0 0 1], respectively. By using the formula (1), the scattering intensities of the three configurations can be calculated and have been listed in Table 1. The parameter y in the table represents the angle between the polarization vector of the incident light and the in-plane coordinates, which have been indicated in Fig. 1. It indicates in Table 1 that the Raman scattering intensity of Raman Ag mode is y dependent. By carefully choosing the measurement condition of y ¼ 0, one can get completely polarized Ag phonon. For the B1g Raman mode, the scattering intensity can not be detected at all in configuration one and is y dependent in configuration three. In configuration two, the scattering intensity of the B1g Raman mode has no polarization component. The B2g Raman mode can appear only in the configuration two while the B3g mode only in the configuration one. Thus, based on the results presented in the Table 1, the symmetries of the Raman peaks can be assigned by alternating the scattering configurations. It has been reported that in NiSi powders only nine Raman peaks can be detected [5]. The rest three undetected peaks were thought due to their too weak scattering intensities. In the case of the NiSi thin film with a uniform crystal orientation, less Raman peaks can be detected due to the selection rules shown in Table 1. To assign the symmetries of Raman peaks of NiSi thin film, we suggest that the cleaving of NiSi thin film should be applied to get the three measurement configurations. Raman spectroscopy can be used to investigate the microstructures in the NiSi films, such as strain distribution, size effects, and laser heating effects [7–10]. Line shapes of the Raman peaks

x

N iS i [0 1 0 ]

Incident laser beam

0 0 c 2 3 0 0 e 6 7 pðB2g Þ ¼ 4 0 0 0 5; e 0 0

2325

z

N iS i [0 0 1]

y

N iS i [0 1 0 ]

E

θ

x N iS i [1 0 0 ]

Fig. 1. Three back scattering configurations for Raman measurement. The coordinates are fixed in the NiSi crystal with x//NiSi[1 0 0], y//NiSi[0 1 0] and z// NiSi[0 0 1]. Configuration one: the incident laser beam is parallel to the x axis, and y is the angle between the polarization vector of the light and the y axis. In configuration two and three, the incident laser beam is parallel to the y and z axis, respectively, and y is the angle between the polarization vector of the light and the x axis.

can be fitted to reveal the microstructure information. For the strain distribution study, it is comparably simple by measuring the peak shifts. The strain components in the thin film change the lattice parameters and the lattice interaction forces, which results in the changing of the lattice vibration frequencies. The Raman peaks have been understood as the results of inelastic scattering between the incident light and lattice vibrations. Thus, the changing of the lattice vibration frequencies makes the Raman peaks shift. Furthermore, anisotropic strain components in the thin film make each Raman peak shift to different sense due to the anisotropic nature of the lattice vibrations of the Raman modes. The value of the peak shift can reach several wave numbers. In order to reveal the relationship between the Raman peak shifts and the strain components in the film, it is necessary to understand the lattice eigen-vibrations. To calculate the lattice eigen-vibrations, group theory is used. The projection operator of the atom movement is shown as the following: X qj X ðfRjtgÞ P fRjtg . (2) P fRjtg

Here, P{R|t} represents the symmetry operation with rotation operation R and translation operation t. For the space group of

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L. Wan et al. / Physica B 404 (2009) 2324–2326

Table 2 symmetric positions of one atom with the coordinates of (x,y,z). The symmetric positions of the atom can be obtained after the application of the summetry operator. E A

(x,y,z) 1  þ x; 1  y; 12  z 2 1 2  x; 2 þ y; z 1  1 2  x; y; 2 þ z

B AB

I IA

(x,y,z) 1   x; 1 þ y; 1 þ z 2 1 2  2 x; 2  y; z 1  1 2 þ x; y; 2  z

IB IAB

Table 3 Character table of point group D2h. D2h ðD16 2h Þ

E(E)

C2z(AB)

C2y(B)

C2x(A)

I(I)

sz(IAB)

sy(IB)

sx(IA)

Ag B1g B2g B3g

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 D16 2h , the basic symmetry operations are A ¼ fC 2x j2; 2; 2g, B ¼ fC 2y j12; 0; 0g and I ¼ fIj1; 0; 0g. The rest symmetry operations of the space group D16 2h are E, AB, IA, IB, and IAB. For an atom assumed with coordinates of (x,y,z), the symmetric positions of the atom can be obtained after the application of the symmetry operators on the atom. The symmetric positions of the atom have been listed in Table 2 to show the function of the symmetry operators. X qj ðfRjtgÞn in the projection operator is the trace of the jth irreducible representation with the phonon wave vector of q. For the Raman scattering measurement, the wave vector q is very close to the Brillouin zone center and can be considered to be equal to q ¼ 0. Thus, the traces of the symmetry operations of the space group D16 2h can be obtained from the character table of the point group D2h(Table 3). The symbol j is used to represent the Raman modes of Ag, B1g, B2g and B3g. The projection operator of each Raman mode then can be obtained as the following:

Table 4 Positions of the referred Ni and Si atoms in one NiSi unit cell with fractional coordinates.

Ni1 Ni2 Ni3 Ni4

x

y

z

0.0061 0.4939 0.0061 0.5061

0.25 0.75 0.75 0.25

0.1962 0.6962 0.1962 0.3038

Si1 Si2 Si3 Si4

x

y

z

0.1884 0.3116 0.1884 0.6884

0.25 0.75 0.75 0.25

0.569 0.069 0.431 0.069

Table 5 Vibrations of the Ni atoms for each Raman mode.

Ni1 Ni2 Ni3 Ni4

Ag

B1g

B2g

B3g

(+x,0,+z) (x,0,+z) (x,0,z) (+x,0,z)

(0,+y,0) (0,y,0) (0,y,0) (0,+y,0)

(+x,0,+z) (+x,0,z) (x,0,z) (x,0,+z)

(0,+y,0) (0,+y,0) (0,y,0) (0,y,0)

the strain component in the plane normal to y axis can make the peak shift of Ag and B2g peaks but takes little effects on the peak shift of B1g and B3g peaks. Thus, the relationship between the Raman peak shift and the anisotropic strain distribution in the NiSi thin films can be understood by using the knowledge of the lattice vibrations of the Raman modes. In this paper, we have no attempts to give the formula of the relationship. As a conclusion, we have calculated the Raman scattering intensities of NiSi crystal with three scattering configurations. A method is proposed for the symmetry assignment of NiSi Raman peaks by applying the selection rules of the Raman scattering intensities of the NiSi thin films. NiSi lattice eigen-vibrations of each Raman mode have also been calculated by using the group theory. The lattice eigen-vibrations can be used to understand the relationship between the peaks shifts and the anisotropic strain distribution in the NiSi films.

PðAg Þ ¼ E þ A þ B þ AB þ I þ IA þ IB þ IAB, Acknowledgement

PðB1g Þ ¼ E  A  B þ AB þ I  IA  IB þ IAB,

We thank the National Natural Science Foundation of China for financial support (No. 60807002).

PðB2g Þ ¼ E  A þ B  AB þ I  IA þ IB  IAB, PðB3g Þ ¼ E þ A  B  AB þ I þ IA  IB  IAB.

(3)

There are four Ni atoms and four Si atoms in one NiSi crystal cell. The atoms are referred to Ni1, Ni2, Ni3, Ni4, Si1, Si2, Si3, and Si4. Since the exact positions of the Ni and Si atoms in one unit cell have not been obtained, we use the atomic positions in MnP cell for the atomic reference due to the same space group of the MnP and NiSi cells. Positions of the eight atoms in one unit cell have been indicated in Table 4 with fractional coordinates. By applying the projection operator of each Raman active mode (Eq. 3) on the atomic movement, the lattice eigen-vibrations of the atoms can then be figured out. Since the Ni atoms have the similar behaviors to the Si atoms, we only list the lattice vibrations of the four Ni atoms for simplicity, which are shown in Table 5. It shows that the lattices of Ag and B2g modes vibrate only in the plane normal to y coordinate while the lattices of B1g and B3g modes vibrate only along the y axis. Therefore, the strain component along y axis takes direct effects on the Raman peak shift of B1g and B3g peaks, but has little effect on the peak shift of Ag and B2g peaks. Inversely,

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