**2. Theoretical background of Raman spectroscopy in silicon**

The aim of this section is to provide the basic equations and their interpretation necessary to understand the experimental results shown throughout the present chapter. A rigorous mathematical derivation is extensively documented in many textbooks and papers published during the long history of the Raman effect [4,5,8-14].

In a Raman experiment described from a classical point of view, monochromatic light of frequency *ωi* originating from a laser is incident on a crystal in a direction *ki* with *E* = *E0*exp[i(*ki*·*r* – *ωit*)]. The electric field of light will induce an electric moment *P* = *ε0χE*, with the interaction between light and crystal at position *r* being mediated by lattice vibrations or phonons characterized by a wavevector *qj* and a frequency *ωj* with *Qj* = *Aj*exp[±i(*qj·r* – *ωjt*)]. It is the electrical susceptibility χ, which is changed by phonons. This means that the induced electric moment will emit besides the elastic scattered Rayleigh light of *ωi*, Raman light of *ω<sup>i</sup>* + *ωj* and *ωi* - *ωj* resulting from anti-Stokes and Stokes Raman scattering, respectively [5]:

$$\mathbf{P} = \varepsilon\_0 \underline{\chi}\_0 \cdot E\_0 \exp[i(\mathbf{k}\_i \cdot \mathbf{r} - \alpha\_i t)] + \varepsilon\_0 E\_0 \left(\frac{\partial \underline{\chi}}{\partial Q\_j}\right)\_0 A\_j \times \exp[-i(\alpha\_i \pm \alpha\_j)t] \exp[i(\mathbf{k}\_i \pm \mathbf{q}\_j) \cdot \mathbf{r}]. \tag{1}$$

From a quantum mechanical point of view, a photon described by *ki*, *ωi* produces an electron-hole pair. The electron is excited from the ground state to a higher energy state and interacts with a phonon characterized by *qj*, *ωj*. As a result of this interaction, the electron gains or losses energy and trough the recombination of the electron-hole pair a photon *ks*, *ω<sup>s</sup>* is emitted, where *ωs* = *ωi* + *ωj* and *ωs* = *ωi* - *ωj* for anti-Stokes and Stokes Raman scattering, respectively. In most cases, only the silicon Stokes Raman peak known also as the first-order silicon Raman peak occurring in the absence of internal and external perturbations at *ω0* ~ 520 cm-1 is measured and examined. This peak is referred as the silicon Raman peak throughout the next sections. It corresponds to lower energy scattered photons *λ1* than the incident ones *λ0*. The conversion formula from nm to cm-1 is written as:

$$
\Delta\text{ao(cm}^{-1}) = \left(\frac{1}{\lambda\_0(nm)} - \frac{1}{\lambda\_1(nm)}\right) \times 10^7. \tag{2}
$$

#### **2.1. Orientation evaluation**

222 Advanced Aspects of Spectroscopy

investigations on the micrometer scale [4,5].

to internal and external perturbations. A short but relevant theoretical introduction in the case of silicon will be given in Section 2. Back to early 70th, it was Anastassakis et. al. first reporting on the shift of the first-order silicon Raman peak under uniaxial *external* stress [8]. This work triggered the application of Raman spectroscopy in measuring *internal* stresses present in semiconductor materials and structures. Particularly important for the present contribution are the studies on *local* internal stresses in microelectronics devices such as silicon integrated circuits using confocal micro-Raman spectroscopy where the exciting laser light is focused onto the sample's surface through a microscope objective thus enabling

The first experimental part of this chapter (Sections 3.2 and 4.1) is mainly focused on the application of confocal *micro-Raman spectroscopy* to map the spatial distribution of internal stresses, their magnitude and sign in different solar silicon materials following the existing work in silicon microelectronics. Because internal stresses may decrease mechanical strength increasing the breakage rate and induce recombination active defects when combined with external stresses, their understanding and control will improve both process yields and solar cell efficiencies. In addition to mechanical information, other useful material properties can be obtained from the *same* first-order silicon Raman peak. We will show how internal stresses, defects, doping, and microstructure can be directly correlated with each other on the same map, enabling the basic understanding of their interactions. The micro-Raman measurements are supported and complemented at identical positions by other techniques such as EBSD, EBIC, and defect etching. Such a combination allows the correlation of

internal stresses, recombination activity and microstructure on the micrometer scale.

In the second experimental part of this contribution (Sections 3.3 and 4.2), confocal *macro-Raman spectroscopy* is introduced and its application to solar silicon is demonstrated for the first time. Macro-Raman spectroscopy represents the state-of-the-art in fast, large area Raman mapping being initially developed to analyze the chemical homogeneity in pharmaceutical tablets. We will present a statistical analysis using Macro-Raman mapping of solar silicon, which is usually characterized by large spatial properties variations. The combination of the two mapping techniques offers insights into the interplay between solar silicon properties at different length scales. Finally, the potential use of macro-Raman spectroscopy for optimization and in-line quality check in a PV factory will be discussed.

Such detailed Raman studies are not limited to solar silicon materials but they can be performed on all Raman active materials. In this context, it is clear that today Raman spectroscopy is a versatile and mature characterization method, which can be applied both at micro- and macro-scale to learn about the interaction between materials properties and

The aim of this section is to provide the basic equations and their interpretation necessary to understand the experimental results shown throughout the present chapter. A rigorous mathematical derivation is extensively documented in many textbooks and papers

their optimization in relation to individual processing steps.

published during the long history of the Raman effect [4,5,8-14].

**2. Theoretical background of Raman spectroscopy in silicon** 

The Raman scattering efficiency or intensity depends on the polarization direction of the incident (*ei*) and backscattered (*es*) light and on the three silicon Raman tensors *R´ <sup>j</sup>* which are proportional to *(∂χ/∂Qj)0* (see Equation 1), *I0* is a constant including all fixed experimental parameters [5,10,14]:

$$I\left(\mathbf{e}\_{i\prime},\mathbf{e}\_{s}\right) \approx I\_0 \cdot \sum\_{j=1}^{3} \left|\mathbf{e}\_i \cdot \mathbf{R}\_j^{\cdot} \cdot \mathbf{e}\_s\right|^2. \tag{3}$$

Here the polarization directions are defined in the stage coordinate system, while the Raman tensors refer to the crystal coordinate system. The crystal - stage transformation is performed by means of a rotation matrix *T(α,β,γ)* applied to the Raman tensors *R´ <sup>j</sup>*, where *α, β,* and *γ* are the three Euler angles [10]:

$$I\left(\mathbf{e}\_{i},\mathbf{e}\_{s}\right) \approx I\_{0} \cdot \sum\_{j=1}^{3} \left| \mathbf{e}\_{i} \cdot \left( \mathbf{T}^{-1}(\alpha,\emptyset,\gamma) \cdot \dot{\mathbf{R}}\_{j}^{\cdot} \cdot \mathbf{T}(\alpha,\emptyset,\gamma) \right) \cdot \mathbf{e}\_{s} \right|^{2}.\tag{4}$$

By continuously rotating the polarization direction of the incident laser light *θ* with a *λ/2* plate for two analyzer positions *x* and *y*, it is possible to obtain two experimental curves showing the intensity variations of the silicon Raman peak. The data fitting based on Equation (4) results in the numerical evaluation of the three Euler angles which are needed to describe the crystallographic orientation of a particular grain with respect to the stage (reference) coordinate system. Having the grain orientation, the intensity variations of the three optical phonons with polarization settings *IXj(θ)* and *IYj(θ)* can be simulated separately. These six intensity variations can be transformed into six intensity ratio functions [10]:

$$W\_1^{X,Y}(\theta) = \frac{I\_1^{X,Y}(\theta)}{I\_2^{X,Y}(\theta) + I\_3^{X,Y}(\theta)},\\W\_2^{X,Y}(\theta) = \frac{I\_2^{X,Y}(\theta)}{I\_1^{X,Y}(\theta) + I\_3^{X,Y}(\theta)},\\W\_3^{X,Y}(\theta) = \frac{I\_3^{X,Y}(\theta)}{I\_1^{X,Y}(\theta) + I\_2^{X,Y}(\theta)}\tag{5}$$

It has been shown that for almost any arbitrary oriented grain, distinct polarization settings (*θ*, *x* or *y*) for which the intensity of one phonon prevails over the intensity sum of the other two phonons can be found [10]. Performing three Raman measurements on the same grain, one for every single-phonon polarization settings, several stress tensor components can be determined as experimentally shown in Section 4.1.1.

#### **2.2. Stress evaluation**

In the absence of stress (internal or external), the three Raman optical phonons of silicon are degenerate leading to a single Raman peak at *ω0* ~ 520 cm-1. Large mechanical stresses in the GPa range lift the degeneracy causing frequency shifts of the three optical phonons *Δωj* = *ω<sup>j</sup>* – *ω0* , which appear as separate peaks in the Raman spectrum depending on the direction of the applied stress and measurement conditions [8,12,13]. When the stress level is below 1 GPa, these frequency shifts are too small to be resolved being masked by the natural width of the silicon Raman peak. In such cases, particular polarization settings for the incident and backscattered Raman light can be found that allow the excitation and probing of the three optical phonons almost separately and consequently their frequency shifts can be determined. These settings vary with the orientation of the investigated grain as discussed in the previous section. Next step consists in using the secular equation that relates the frequency shifts to the strain tensor components [5,9,10]:

$$\begin{vmatrix} p \cdot \dot{\boldsymbol{\varepsilon}}\_{xx} + q \cdot (\boldsymbol{\varepsilon}\_{yy} + \dot{\boldsymbol{\varepsilon}}\_{zz}) - \lambda & 2r \cdot \dot{\boldsymbol{\varepsilon}}\_{xy} & 2r \cdot \dot{\boldsymbol{\varepsilon}}\_{xz} \\ 2r \cdot \dot{\boldsymbol{\varepsilon}}\_{xy} & p \cdot \dot{\boldsymbol{\varepsilon}}\_{yy} + q \cdot (\boldsymbol{\varepsilon}\_{xx} + \dot{\boldsymbol{\varepsilon}}\_{zz}) - \lambda & 2r \cdot \dot{\boldsymbol{\varepsilon}}\_{yz} \\ 2r \cdot \dot{\boldsymbol{\varepsilon}}\_{xz} & 2r \cdot \dot{\boldsymbol{\varepsilon}}\_{yz} & p \cdot \dot{\boldsymbol{\varepsilon}}\_{zz} + q \cdot (\dot{\boldsymbol{\varepsilon}}\_{xx} + \dot{\boldsymbol{\varepsilon}}\_{yy}) - \lambda \end{vmatrix} = 0. \tag{6}$$

Here *p*, *q*, and *r* are material constants so-called phonon deformation potentials being the only three independent components for cubic symmetry crystals such as silicon, *ε´ ij* are the strain tensor components in the crystal coordinate system, while the eigenvalues *λj* (j = 1,2,3) are given by

$$
\lambda\_{\dot{j}} = \alpha\_{\dot{j}}^2 - \alpha\_0^2 = (\alpha\_{\dot{j}} - \alpha\_0) \cdot (\alpha\_{\dot{j}} + \alpha\_0) \approx \Delta \alpha\_{\dot{j}} \cdot 2\alpha\_0. \tag{7}
$$

The stress tensor components are finally obtained from the inverse Hooke's law *ε´ ij* = *Sij*·*σ´ ij* where *Sij* represents the elastic compliance tensor whose components are material constants. It is evident from Equation (6,7) that the three frequency shifts *Δωj* are not enough to determine the six independent stress tensor components *σ´ ij*. The probing depth in silicon ranges from a few hundreds of nm to a few µm for visible excitations, and from a few nm to a few tenths of nm for UV excitations. Thus, due to wavelength dependent absorption, only the stress state close to the sample's surface is measured. This implies a predominant planar stress state described by three stress components *σ´ xx*, *σ´ yy*, and *τ´ xy* that can be numerically evaluated using the three frequency shifts *Δωj*. The residual stress components in the *z* direction given by *σ´ zz*, *τ´ xz*, and *τ´ yz* are included in *Δ´ <sup>z</sup>* which also serves as a correction parameter [10]:

224 Advanced Aspects of Spectroscopy

**2.2. Stress evaluation** 

By continuously rotating the polarization direction of the incident laser light *θ* with a *λ/2* plate for two analyzer positions *x* and *y*, it is possible to obtain two experimental curves showing the intensity variations of the silicon Raman peak. The data fitting based on Equation (4) results in the numerical evaluation of the three Euler angles which are needed to describe the crystallographic orientation of a particular grain with respect to the stage (reference) coordinate system. Having the grain orientation, the intensity variations of the three optical phonons with polarization settings *IXj(θ)* and *IYj(θ)* can be simulated separately. These six intensity variations can be transformed into six intensity ratio functions [10]:

, , ,

 

(5)

(6)

*ij* are the

*XY XY XY XY XY XY*

2 3 1 3 1 2 ( ) ( ) ( ) ( ) , () , () () () () () () () *X Y X Y X Y*

*II II II*

It has been shown that for almost any arbitrary oriented grain, distinct polarization settings (*θ*, *x* or *y*) for which the intensity of one phonon prevails over the intensity sum of the other two phonons can be found [10]. Performing three Raman measurements on the same grain, one for every single-phonon polarization settings, several stress tensor components can be

In the absence of stress (internal or external), the three Raman optical phonons of silicon are degenerate leading to a single Raman peak at *ω0* ~ 520 cm-1. Large mechanical stresses in the GPa range lift the degeneracy causing frequency shifts of the three optical phonons *Δωj* = *ω<sup>j</sup>* – *ω0* , which appear as separate peaks in the Raman spectrum depending on the direction of the applied stress and measurement conditions [8,12,13]. When the stress level is below 1 GPa, these frequency shifts are too small to be resolved being masked by the natural width of the silicon Raman peak. In such cases, particular polarization settings for the incident and backscattered Raman light can be found that allow the excitation and probing of the three optical phonons almost separately and consequently their frequency shifts can be determined. These settings vary with the orientation of the investigated grain as discussed in the previous section. Next step consists in using the secular equation that relates the

' '' ' '

*p q r r*

2 2

() 2 2

*r pq r r r pq*

only three independent components for cubic symmetry crystals such as silicon, *ε´*

*xx yy zz xy xz*

' '' '

' ' ''

*xz yz zz xx yy*

2 2 ( )

Here *p*, *q*, and *r* are material constants so-called phonon deformation potentials being the

strain tensor components in the crystal coordinate system, while the eigenvalues *λj* (j = 1,2,3)

*xy yy xx zz yz*

2 ( ) 2 0.

 

0 00 0 ( )( ) 2 . *jj j j j* (7)

,,, 1 2 3 1 23 , , , , , ,

*I I <sup>I</sup> WWW*

*X Y X Y X Y*

determined as experimentally shown in Section 4.1.1.

frequency shifts to the strain tensor components [5,9,10]:

'

'

are given by

$$\boldsymbol{\sigma}^{\prime} = \begin{pmatrix} \boldsymbol{\sigma}^{\prime}\_{xx} & \boldsymbol{\pi}^{\prime}\_{xy} & \boldsymbol{0} \\ \boldsymbol{\pi}^{\prime}\_{xy} & \boldsymbol{\sigma}^{\prime}\_{yy} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{0} & \boldsymbol{\Delta}^{\prime}\_{z} \end{pmatrix} . \tag{8}$$

The following equation can be used to transform the stress tensor components into average or von Misses stress:

$$\boldsymbol{\sigma}\_{av}^{\dot{\prime}} = \sqrt{\boldsymbol{\sigma}\_x^{\dot{\prime}2} + \boldsymbol{\sigma}\_y^{\dot{\prime}2} + \boldsymbol{\sigma}\_z^{\dot{\prime}2} - \boldsymbol{\sigma}\_x^{\dot{\prime}}\boldsymbol{\sigma}\_y^{\dot{\prime}} - \boldsymbol{\sigma}\_x^{\dot{\prime}}\boldsymbol{\sigma}\_z^{\dot{\prime}} - \boldsymbol{\sigma}\_y^{\dot{\prime}}\boldsymbol{\sigma}\_z^{\dot{\prime}} + \mathbf{3}(\boldsymbol{\sigma}\_{xy}^{\dot{\prime}2} + \boldsymbol{\sigma}\_{xz}^{\dot{\prime}2} + \boldsymbol{\sigma}\_{yz}^{\dot{\prime}2})} \tag{9}$$

Another more straightforward way to relate measured Raman shifts to stress values is the use of a simple stress model illustrating the stress state in the sample. The classical example in the case of silicon is the presence of uniaxial stress *σ* along the [100] direction and the measurement of the backscattered Raman signal from the (001) surface [5]. In this configuration, only one stress tensor component is non zero:

$$
\Delta\text{ao}\_3\text{(cm}^{-1}) = -2 \cdot 10^{-9} \text{ } \text{\textdegree } \text{(Pa)} \text{ } \text{ or } \text{ } \text{\textdegree } \text{(MPa)} = -500 \times \text{\textdegree } \text{\textdegree } \text{(cm}^{-1}). \tag{10}
$$

If biaxial stress in the *x-y* plane with stress components *σxx* and *σyy* (or *σxx* = *σyy* for isotropic stress) describes the stress distribution in the sample:

$$
\Delta\alpha o\_3(cm^{-1}) = -4 \cdot 10^{-9} \left(\frac{\sigma\_{xx} + \sigma\_{yy}}{2}\right) (Pa) \quad or \quad \sigma\_{xx} = \sigma\_{yy} \text{ (MPa)} = -2S0 \times \Delta\alpha o(cm^{-1}).\tag{11}
$$

These two formulas (10,11) written in the stage coordinate system are commonly used in the community for a fast and reliable estimation of the *average stress* independently of the crystallographic orientation of grains in multicrystalline silicon. Thus, 1 cm-1 shift of the silicon Raman peak with respect to the stress free value of ~ 520 cm-1 corresponds to a uniaxial stress of 500 MPa or to a biaxial in-plane isotropic stress of 250 MPa. It can be seen that tensile stress shifts the silicon Raman peak to lower frequency, while compressive stress to higher frequency as sketched in Figure 1(a). Experimental examples of the stress state evaluation using both methods described above will be given in Section 4.1.

**Figure 1.** (a) Typical Raman spectrum of a silicon wafer used as reference. In the absence of stress, the three Raman optical phonons of silicon (1 x LO, 2 x TO) are degenerate resulting in a single Raman peak at *ω0* ~ 520 cm-1. The plasma lines originating from an external reference lamp are used to correct the silicon peak position with respect to the thermal drift of the spectrometer grating. Tensile or compressive stresses (internal or external) below 1 GPa may shift the silicon Raman peak to lower or higher frequencies, respectively. (b) Comparison between Raman spectra of stress-free silicon reference and tensile stressed thin film solar silicon on glass. The peak asymmetry caused by high boron doping is clearly visible.

#### **2.3. Doping evaluation**

In the case of highly doped silicon, a resonant interaction occurs between the discrete optical phonon states (phonon Raman scattering) and the continuum of electronic states in the valence or conduction bands (electronic Raman scattering) because of electron-phonon coupling. This leads to Fano-type silicon Raman peak asymmetries, which can be observed as tails either on the right side (for p-type doping) or on the left side (for n-type doping) of the otherwise symmetric silicon Raman peak as shown in Figure 1(b) [11,14-17]. The function used to fit the intensity of the silicon Raman peak *I(ω)* is given by [11]

$$I(\text{co}, q, \Gamma, \text{co}\_{\text{max}}) = I\_0 \frac{\left[q + \text{2(co-co}\_{\text{max}}\right) / \left\lceil \Gamma \right\rceil^2}{1 + \left\lceil \text{2(co-co}\_{\text{max}}\right\rceil / \left\lceil \Gamma \right\rceil^2} \,. \tag{12}$$

Here *I0* is a scaling factor, *q* is so-called symmetry parameter, *Γ* is the linewidth of the peak, and *ωmax* is the peak position in the presence of Fano interaction. The symmetry parameter *q* describes the shape of the silicon Raman peak affected by Fano resonances. Large *q* > 150 values correspond to standard doping (< 1016 cm-3) resulting in a nearly symmetric peak, while small *q* < 50 values correlate with high doping (> 1018 cm-3) and pronounced peak asymmetry. For highly doped silicon, *1/q* is approximately proportional to the free carrier concentration [11]. Thus, an accurate quantitative evaluation of doping on the micrometer scale is possible, provided a good calibration curve exist.

#### **2.4. Qualitative defect density evaluation**

226 Advanced Aspects of Spectroscopy

**2.3. Doping evaluation** 

**Figure 1.** (a) Typical Raman spectrum of a silicon wafer used as reference. In the absence of stress, the three Raman optical phonons of silicon (1 x LO, 2 x TO) are degenerate resulting in a single Raman peak at *ω0* ~ 520 cm-1. The plasma lines originating from an external reference lamp are used to correct the silicon peak position with respect to the thermal drift of the spectrometer grating. Tensile or compressive stresses (internal or external) below 1 GPa may shift the silicon Raman peak to lower or higher frequencies, respectively. (b) Comparison between Raman spectra of stress-free silicon reference and tensile stressed thin film solar silicon on glass. The peak asymmetry caused by high boron doping is clearly visible.

In the case of highly doped silicon, a resonant interaction occurs between the discrete optical phonon states (phonon Raman scattering) and the continuum of electronic states in the valence or conduction bands (electronic Raman scattering) because of electron-phonon coupling. This leads to Fano-type silicon Raman peak asymmetries, which can be observed as tails either on the right side (for p-type doping) or on the left side (for n-type doping) of the otherwise symmetric silicon Raman peak as shown in Figure 1(b) [11,14-17]. The

2

(12)

max

max

max 0 2

[ 2( ) / ] (,, , ) . 1 [2( ) / ] *<sup>q</sup> Iq I*

Here *I0* is a scaling factor, *q* is so-called symmetry parameter, *Γ* is the linewidth of the peak, and *ωmax* is the peak position in the presence of Fano interaction. The symmetry parameter *q* describes the shape of the silicon Raman peak affected by Fano resonances. Large *q* > 150 values correspond to standard doping (< 1016 cm-3) resulting in a nearly symmetric peak, while small *q* < 50 values correlate with high doping (> 1018 cm-3) and pronounced peak asymmetry. For highly doped silicon, *1/q* is approximately proportional to the free carrier concentration [11]. Thus, an accurate quantitative evaluation of doping on the micrometer

function used to fit the intensity of the silicon Raman peak *I(ω)* is given by [11]

scale is possible, provided a good calibration curve exist.

As shown in the previous three sections, Raman spectroscopy can provide detailed information about semiconductor materials, in this contribution solar silicon, including crystal orientation, internal stresses and doping, which can be extracted from the intensity, position and asymmetry of the silicon Raman peak. In addition, the linewidth of the peak relates to the presence of extended crystal defects. In a perfect crystal, the phonon lifetimes are theoretically infinite in the harmonic approximation that neglects third- and higherorder derivatives of the crystalline potential resulting in narrow delta function-like linewidths of the optical phonon Raman spectra [18]. Defects act as anharmonic perturbations leading to finite phonon lifetimes that manifest themselves as a broadening of the peak described by its full-width at half maximum denoted FWHM or *Γ*. Therefore, the anharmonic lifetimes of phonons are defined as *1/Γ* being evaluated using first principles calculations including both kinematic effects; i.e., the decay of phonons into vibrations of lower frequency and dynamic effects; i.e., the magnitude of the tensor of the third derivates of the crystal potential with respect to atomic displacements that describes the instability of one-phonon states. The calculated *Γ* values of the Raman-active optical phonons were found to agree well with those determined experimentally in the case of single crystalline semiconductors (defect free) such as diamond, Si, Ge, GaAs, GaP and InP [19,20].

Anharmonic effects and consequently broadening can also be induced by internal or external stresses approaching the stress-induced splitting limit of the peak as discussed in Section 2.2 or by large stress gradients within the probed volume [5]. Moreover, doping and/or impurities can either produce new Raman peaks through their own vibrational modes or alter/broaden the Raman spectrum of the host material through the change in mass and bond length (atomic effects) as well as through the resonant Fano interaction of free carriers (donors or acceptors) with the lattice (electronic effects). Because all these information originates from the silicon Raman peak, one can separate between the effects of stresses, doping and/or impurities and that of defects on the FWHM values. The Raman linewidths were also found to broaden in the case of relatively small grains (in the nm range) due to the phonon confinement effect, that is, the frequency distribution of the scattered light comes from a broader interval in *k*-space around the *Γ*-point in the Brillouinzone since the *Δk = 0* selection rule is partially lifted by the phonon scattering at grain boundaries [21]. Such a broadening does not occur in large grained solar silicon as presented here.

## **3. Experimental details**

#### **3.1. Sample preparation for Raman measurements**

Raman spectroscopy investigates materials nondestructively, the appropriate excitation laser power to avoid damage being material dependent, without elaborated sample preparation. In the case of silicon thin film solar cells on glass, no sample preparation is needed because the as-grown material has low roughness. This is different for wafer- and

ribbon-based solar cells for which a simple sample preparation procedure is necessary. Their surfaces have to be evened out by mechanical polishing prior to the Raman measurements to avoid artifacts induced by uncontrolled reflections at rough surface facets. The standard polishing procedure applied to small pieces consists in changing gradually from larger to smaller diamond particle sizes with the final polishing step removing most of the previously damage surface layer, thus leaving the samples in a negligible polishing-induced stress state. The cutting into small pieces leads to stress relaxation due to the creation of free surfaces as discussed in Section 4.1.2. After polishing, the samples are Secco-etched [22] for 5 seconds to make the grain boundaries and dislocations visible. This short defect etching step does not affect the Raman scattering or the other measurement techniques used herein.

#### **3.2. Micro-Raman spectroscopy**

The incident light needed for Raman excitation is provided by a laser with a main emission with narrow line width. An interferential filter is used to block the other emissions of the laser. After being reflected by an edge or a notch filter, the light is focused onto the sample's surface through a microscope objective, thus giving rise to the term micro-Raman spectroscopy. Depending on the objective (magnification, numerical aperture) as well as on the excitation wavelength, the diameter of the incident laser beam is different. For the 100x objective (numerical aperture 0.9) and 633 nm excitation employed in the micro-Raman measurements presented here, the probing diameter is ~ 1 µm. The laser power density can be quite high, thus a low laser power of ~ 2 mW at the silicon sample's surface should be used. In these conditions, no shift or increase in the FWHM of the silicon Raman peak due to the local heating of the sample by the laser beam were observed.

As already mentioned in Section 2.2, the probing depth is controlled by the material absorption, which is wavelength dependent. In crystalline silicon, an excitation wavelength of 633 nm results in a penetration depth of ~ 3 µm, while 457 nm gives ~ 300 nm. Since we use 633 nm, the entire thickness of the silicon thin films on glass is probed, while only the surface of the ~ 200 – 250 µm thick silicon wafers and ribbons is measured. The backscattered Raman light passes back through an edge or a notch filter which cuts most of the Rayleigh light, it is dispersed using a grating and then detected by a silicon CCD detector. All Raman measurements herein were performed at room temperature in the backscattering configuration using a LabRam HR800 spectrometer from Horiba Jobin Yvon. A schematic picture of our micro-Raman spectrometer is displayed in Figure 2.

In order to draw correct conclusions about materials with varying spatial properties, not only several but many Raman spectra are acquired while moving the microscope stage with the sample in *x-* and *y-*directions in steps equal or smaller than the diameter of the laser probing beam as shown in Figure 2. This results in a complete micro-Raman mapping of the investigated areas, which are usually in the range of a few tens of µm2. The exposure time is typically up to 1 s per spectrum. These spectra are fitted with a Gauss-Lorentzian function and maps of the shift, FWHM and intensity of the silicon Raman peak corresponding to the spatial distributions of internal stress, defect density and grain orientation are obtained. A Fano-like fitting function as in Equation 12 is used for doping evaluation [11]. To ensure correct interpretation of the Raman data as well as to be able to visualize small mechanical stresses, the effect of the thermal drift of the spectrometer grating on the silicon peak position is corrected [5,14]. This is done by using one of the plasma lines visible in Figure 1(a) emitted by an external lamp located either close to the spectrometer's confocal hole or above the microscope [23,24].

**Figure 2.** Schematic picture of the used micro-Raman spectrometer. The *λ/2* plate and the analyzer adjust the polarization direction of the incident and backscattered light with respect to the stage (fixed) coordinate system. The polarized micro-Raman procedure enables the evaluation of the crystallographic orientation of arbitrary grains and of stress components as described in Sections 2.1 and 2.2. A graphical representation of micro-Raman mapping obtained by moving the microscope stage with the sample (multicrystalline silicon wafer) in *x-* and *y-*directions under a 633 nm exciting laser along with the Raman probing volume are also shown.

#### **3.3. Macro-Raman spectroscopy**

228 Advanced Aspects of Spectroscopy

**3.2. Micro-Raman spectroscopy** 

heating of the sample by the laser beam were observed.

ribbon-based solar cells for which a simple sample preparation procedure is necessary. Their surfaces have to be evened out by mechanical polishing prior to the Raman measurements to avoid artifacts induced by uncontrolled reflections at rough surface facets. The standard polishing procedure applied to small pieces consists in changing gradually from larger to smaller diamond particle sizes with the final polishing step removing most of the previously damage surface layer, thus leaving the samples in a negligible polishing-induced stress state. The cutting into small pieces leads to stress relaxation due to the creation of free surfaces as discussed in Section 4.1.2. After polishing, the samples are Secco-etched [22] for 5 seconds to make the grain boundaries and dislocations visible. This short defect etching step does not affect the Raman scattering or the other measurement techniques used herein.

The incident light needed for Raman excitation is provided by a laser with a main emission with narrow line width. An interferential filter is used to block the other emissions of the laser. After being reflected by an edge or a notch filter, the light is focused onto the sample's surface through a microscope objective, thus giving rise to the term micro-Raman spectroscopy. Depending on the objective (magnification, numerical aperture) as well as on the excitation wavelength, the diameter of the incident laser beam is different. For the 100x objective (numerical aperture 0.9) and 633 nm excitation employed in the micro-Raman measurements presented here, the probing diameter is ~ 1 µm. The laser power density can be quite high, thus a low laser power of ~ 2 mW at the silicon sample's surface should be used. In these conditions, no shift or increase in the FWHM of the silicon Raman peak due to the local

As already mentioned in Section 2.2, the probing depth is controlled by the material absorption, which is wavelength dependent. In crystalline silicon, an excitation wavelength of 633 nm results in a penetration depth of ~ 3 µm, while 457 nm gives ~ 300 nm. Since we use 633 nm, the entire thickness of the silicon thin films on glass is probed, while only the surface of the ~ 200 – 250 µm thick silicon wafers and ribbons is measured. The backscattered Raman light passes back through an edge or a notch filter which cuts most of the Rayleigh light, it is dispersed using a grating and then detected by a silicon CCD detector. All Raman measurements herein were performed at room temperature in the backscattering configuration using a LabRam HR800 spectrometer from Horiba Jobin Yvon. A schematic picture of our micro-Raman spectrometer is displayed in Figure 2.

In order to draw correct conclusions about materials with varying spatial properties, not only several but many Raman spectra are acquired while moving the microscope stage with the sample in *x-* and *y-*directions in steps equal or smaller than the diameter of the laser probing beam as shown in Figure 2. This results in a complete micro-Raman mapping of the investigated areas, which are usually in the range of a few tens of µm2. The exposure time is typically up to 1 s per spectrum. These spectra are fitted with a Gauss-Lorentzian function and maps of the shift, FWHM and intensity of the silicon Raman peak corresponding to the spatial distributions of internal stress, defect density and grain orientation are obtained. A Fano-like Macro-Raman spectroscopy enables fast, large area Raman mapping in the cm2 range needed for statistical studies of materials properties and the correlations between them and with processing. In the context of PV, this technique can be used not only for fundamental studies in laboratory scientific research but also for optimization and in-line quality check in a PV factory. Macro-Raman mapping is possible through two add-ons that can be integrated in any existing micro-Raman spectrometer. The two new DuoScanTM (hardware) and SWIFTTM (software) Raman scanning modules developed by HORIBA Jobin Yvon provide significant reduction by orders of magnitude of the measurement times by means of large area probing beam (macro-beam) and high speed detector-stage coordination, respectively. Even faster Raman imaging is possible by combing these two technologies [7].

DuoScanTM Raman imaging technology extends the imaging capabilities of micro-Raman instruments from (sub-) micron to macro-scale mapping. The integration of the DuoScan

unit to an existing micro-Raman spectrometer is shown in Figure 3(left). This mode is based on a combination of two orthogonally rotating piezo-mirrors that scan the laser beam across the sample following a user-defined pattern as displayed in Figure 3(middle). The size of the resulting macro-beam is adjustable being limited only by the opening of the used microscope objective. The maximum macro-beam sizes achievable with our 50x (NA 0.80) or 10x (NA 0.30) NIKON microscope objectives are 100 x 100 µm2 or 1 x 1 mm2. DuoScan allows to integrate the Raman signal over the macro-beam area giving an average spectrum, which contains the same spectral information as that obtained by averaging all micro-Raman spectra for the same area. The gain in acquisition time is evident, macro-Raman being orders of magnitude faster than conventional micro-Raman. For example, if an area of 30 x 30 µm2 is entirely probed by macro-Raman in one second, micro-Raman with a spotsize of 1 x 1 µm2 needs 900 seconds to cover the same area. The price one has to pay is the loss of lateral resolution.

Furthermore, DuoScan can be used in a step-by-step mode where the mapping takes place without moving the stage with the sample. A minimum step size of 50 nm is reached by deflecting the laser beam, which complements successfully the stepping capability of the stage specified to be ~ 500 nm. This mode applies for Raman imaging of nanoscale objects and features. The DuoScan mapping capabilities are summarized in Figure 3(right).

SWIFTTM Raman imaging technology enables ultra fast mapping without losing lateral resolution and thus image quality. In this mode, the time intervals needed for the stage to accelerate/decelerate as well as for the shutter in front of the detector to open/close for each measurement point are eliminated. Basically, these are dead times, which are not used for the acquisition of the Raman signal. The breakthrough consists in continuously moving the stage with the sample while keeping the shutter open and measuring continuously Raman spectra by means of high speed detector-stage coordination coupled with the high optical throughput of the Raman system. The SWIFT option can also be used for time resolved Raman imaging provided the investigated processes occur on the measurement time scale.

**Figure 3.** (left) DuoScan unit attached to a micro-Raman spectrometer. (middle) Schematic drawing illustrating the DuoScan working principle. The probing micro-beam is scanned by two orthogonally rotating piezo-mirrors resulting in a macro-beam, thus giving rise to the term macro-Raman spectroscopy. (right) Comparison between standard and DuoScan mapping modes described in the text. The left and middle pictures are taken from HORIBA's official webpage.
