μ-Raman spectroscopy and FE-modeling for TSV-Stress-characterization

Microelectronic Engineering 137 (2015) 105–110

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l-Raman spectroscopy and FE-modeling for TSV-Stress-characterization P. Saettler a,⇑, M. Hecker b, M. Boettcher c, C. Rudolph c, K.J. Wolter a a

Technische Universität Dresden, Electronics Packaging Laboratory, Dresden, Germany Globalfoundries Dresden Module One LLC & Co. KG, Dresden, Germany c Fraunhofer IZM-ASSID, D-01468 Moritzburg, Germany b

a r t i c l e

i n f o

Article history: Received 19 May 2014 Received in revised form 20 January 2015 Accepted 21 January 2015 Available online 29 January 2015 Keywords: TSV Micro Raman spectroscopy Finite element modeling

a b s t r a c t In this paper thermo-mechanical stresses generated by TSV annealing are the center of interest. For this reason TSV die samples underwent annealing at 250 °C for 2 h. In order to characterize the stress state after annealing l-Raman spectroscopy (lRS) line scans were carried out subsequently using a 442 nm laser. Then the respective spectra were fitted with a Lorentz function and the associated peak shifts were calculated. In general these results can be used to identify regions of mechanical tension. Unfortunately, lRS results do not allow any differentiation of the stress tensor components. Therefore a finite element model was developed to determine the stress tensor components after annealing. The FE-model was supplemented by a Matlab script, which converted stress data from simulation into Raman shifts using a general hypothesis. Further on physical aspects like penetration depth and laser spot size were taken into account. So the evaluation moved from single node results to a constrained section similar to the laser excited region in a lRS measurement. Proceeding this way allowed the adaption of FE results to lRS measurement properties. This enabled a bilateral validation of measurement and simulation. In summary our paper contributes valuable results for the TSV stress characterization and demonstrates further progress in lRS measurements in combination with FEM. Ó 2015 Elsevier B.V. All rights reserved.

1. Introduction While first products containing the TSV technology have entered the market, manufactures are still optimizing the processes. For example new bath chemistries are in development, which show a reduced tendency to Cu protrusion after plating. But the annealing procedure subsequent to Cu fill and overburden CMP is still necessary to stabilize Cu’s material behavior. Due to material CTE-mismatches (Cu-SiO2-Si) and the annealing behavior of Cu, mechanical stresses are induced during annealing [1,2]. In order to avoid defects like layer delaminations or even Si cracking it is important to quantify these loads. Fig. 1 shows a cracked TSV array. Obviously, the Si substrate could not stand the stresses induced by the high thermal volume change of Cu during annealing. In the presented case annealing was conducted with remaining Cu on top of the die, which additionally increased the thermo-mechanical load. Nevertheless it clarifies the need of proper stress characterizations to avoid this kind of defects during TSV manufacturing. Several works demonstrated that Raman spectroscopy can be utilized for stress characterization of silicon devices [3–5]. As a ⇑ Corresponding author. Tel.: +49 351 463 33056; fax: +49 351 463 37035. E-mail address: [email protected] (P. Saettler). http://dx.doi.org/10.1016/j.mee.2015.01.024 0167-9317/Ó 2015 Elsevier B.V. All rights reserved.

nondestructive test method the preparation efforts for samples are low and characterization of stresses can be carried out pretty fast. However, the measurement is restricted to mostly semiconductor materials [6]. Due to the lack of Raman signals in Cu, stress measurements can only be carried out at the Si substrate surface surrounding the TSVs. Another problem in utilizing lRS for stress measurements is the restricted conversion of measured peak shifts into thermo-mechanical stresses. Out of measured peak shifts a direct calculation of concrete stress values is only possible for uni- and biaxial stress states [7]. To overcome these restrictions FE simulations can be used to deliver additional information about the stress distribution [5,8–11]. Then, extracted stress values can be converted into their corresponding peak shift, which enables a bilateral validation. For a proper peak shift calculation out of FE results the excitation mechanism of the lRS has to be considered. During measurement the incident laser beam excites the Si lattice over a certain macroscopic area (spot size) and the penetration depth depends on the laser wavelength. In consequence the Raman measurement not only delivers results from one single point on the Si surface. Depending on the measurement parameters the beam excites a certain area and penetrates into silicon. Consequently, all atoms inside the laser excited region contribute to Raman scattering. Aiming at the comparability of measurement and simulation the

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described excitation mechanism has to be considered for the FE results, too. Therefore, weighting algorithms for the simulation results have to be introduced. 2. Experimental Before stress characterization TSV test dies (3 cm  3 cm  700 lm) underwent a 2 h heat treatment at 250 °C. In order to prevent oxidation annealing was carried out under inert atmosphere. The TSVs with 10 lm in diameter and 110 lm in depth were arranged in a hash with a pitch of 55 lm. Die samples were taken after electro chemical deposition (ECD) of Cu and chemical mechanical planarization (CMP) of the Cu overburden, but before thinning. On the die surface a 600 nm SiO2 layer remained after CMP. Fig. 2 shows a cross section of the examined TSVs. 2.1. l-Raman spectroscopy After annealing appropriate lRS measurements were carried out. This was implemented by focusing a laser beam on the die surface and scanning the segment of interest. Thereby the spectrum of the scattered light was recorded. During measurement inelastic Raman light scattering caused lattice phonon excitation and the characteristic Raman peaks were observed. For the measurement the center between 2 TSV’s was determined to be stress-free. Therefore, peak position of x0 was located at 521.5 Rcm1. It was assumed that this was the triply degenerate TO mode of unstrained bulk silicon. Strains in silicon change the phonon frequency and consequently the Raman peak position changes as well (peak shift). Raman peak shift Dx is defined as the deviation of the characteristic peak x from its stress free state x0 and was calculated as follows: [3,4,11]

Dx ¼ x  x 0

ð1Þ

Line scans were carried out like it is demonstrated in Fig. 3. The laser wavelength was 442 nm and the spot size was 1 lm in diameter. Scanning was executed in steps of 100 nm using an excitation time of 2 s. Subsequently, data of the measured spectra were fitted using a Lorentz function. As mentioned before, the interpretation of Raman shifts is complicated, because every element of the strain tensor has an effect on the peak position. Only for uniaxial stress distributions a negative shift denotes tensile stress and positive peak shift denotes compressive stress. For the measurement of an (100) silicon surface in 180° back reflection this case delivers a linear relation between stress and Raman shift [7]:

Dx ¼ 1:9267  103  ru ½Dx ¼ ½cm1 ; ½ru  ¼ ½MPa

intact TSV’s

Fig. 2. TSV cross sections of the examined samples.

ð2Þ

CuOB

cracked out TSV-array

Si

Fig. 1. Cracked TSV array after annealing 1 h at 400 °C.

Fig. 3. Die surface with TSV openings: Cu (orange), SiO2 (gray); measurements were carried out through the SiO2 layer; the arrow (red) denotes the pathway of the executed lRS line scans (sketch not drawn to scale). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Because of this simple linear equation people often tend to a direct conversion of the measured Raman shifts into stresses. To evaluate this approach, results of the uniaxial stress hypothesis were compared to FE results. 3. Simulation For the determination of stress tensor elements a three-dimensional model was implemented in ANSYS. The geometry included the quarter of a TSV shown in Fig. 4. Appropriate boundary conditions enabled to benefit from the symmetric shape. Dimensions of the TSVs were the same as for the measured samples (see Fig. 2). In this model the TSV shape was simplified to cylindrical shape. Consequently, effects of scallops generated by Bosch etching were not considered. Only the curvature at the bottom and the TSV opening were measured and implemented into this modeling approach (see Fig. 5). By means of the introduced simplifications the Cu fill, SiO2 isolation and the Si substrate were modeled. SEM images of TSV cross sections revealed a decreasing SiO2 layer thickness with TSV depth. Therefore, the isolation thickness at the TSV opening equaled 1 lm while only half of the thickness was assigned to the bottom SiO2 layer. The decrease of the layer thickness was

P. Saettler et al. / Microelectronic Engineering 137 (2015) 105–110

Fig. 4. 3D finite element model of the given geometry consisting of only hexahedral solid elements.

107

expected strain and stress results. Therefore a fine mesh was generated at crucial regions of deformation and it coarsens with distance to the Cu-SiO2-Si material interfaces. Table 1 lists the material properties, which were used in this study. For Si and SiO2 elastic material behavior was assumed. To implement elastic–plastic properties a kinetic hardening model was assigned to Cu [12]. All material properties were modeled with a temperature dependency. For the calculation of the TSV annealing many studies change the material properties of copper to reach a fit of measurements and FE-results [5,15–17]. But current investigations allow the conclusion that besides microstructure changes in copper also a stress minimum is present at annealing temperature [1,2,10]. So the stress-free state of the model was set to 250 °C and cooling down to room temperature served as thermal load profile. Due to the changes in microstructure it was assumed that coppers material behavior is stabilized at annealing temperature. For that reason it was abstained from manipulating coppers material constants. For subsequent evaluation steps stress information was extracted from certain depths beneath the SiO2 layer on top. Starting from the SiO2-Si interface in steps of 25 nm into the Si substrate (negative z-direction in our model) all stress tensor elements along the x-axis of the model were used for further calculations. In order to ensure comparability to lRS measurements, the maximum depth for the extracted stress values in the model was determined by the intensity decay of the laser light in silicon. The respective parameters of our measurements, which are needed to determine this depth, are described below. 3.1. Adapting simulation to Raman measurements Basis for the FE results evaluation was the conversion of all extracted stress curves into Raman shifts, so that a comparison to lRS measurements was possible. De Wolf demonstrated the general calculation of Raman shifts on basis of the eigenvalue problem in Eq. (3).

      pex þ q ey þ ez  k 2rexz 2r exy     2r exy pey þ qðez þ ex Þ  k 2r eyz ¼0       2rexz 2r eyz pez þ q ex þ ey  k  ð3Þ and

Dx ¼ x  x 0 ¼

Fig. 5. Cross section of the model geometry for the TSV in detail: TSV opening (a) and bottom (b).

determined to be linear. In this approach, the Ta barrier layer was not considered. For thin films (approximately 20–100 nm) the material behavior is not examined properly yet and because of the narrow dimensions the effect on the estimations was neglected. Furthermore the implementation of scallops and the thin barrier film would have increased the element count, meshing effort and computing time dramatically. In order to find a balanced relation between geometry details and simulation performance the mesh was generated in a way that accurate results were achieved at points of interest. In general the mesh was adapted to the

k 2  x0

In Eq. (3) eij are the strain tensor elements and p, q, r are material constants. This relation is given for a reference coordinate system x, y, z = [1 0 0], [0 1 0], [0 0 1]. For the utilization of this correlation between peak shift and strains further steps were necessary. Strain tensor elements had to be substituted by stress values using Hooke’s law. Additionally, a transformation of the equation into the FE model coordinate system was necessary. [8] and [14] described the procedures in detail. In order to describe the influence of laser intensity on the substrate penetration depth Takahashi assumes exponential behavior in the form of e2aSi ðkÞz [19]. Since the z values were negative in the chosen coordinate system the equation describes exponential decay with increasing penetration depth. It can be recognized that the absorption coefficient aSi is dependent on the wavelength of the applied laser light. Taking this into account the peak shifts derived from FE results were weighted with the following expression:

Dxi ðxÞ ¼

P

z ðD

x ðx; zÞ  e2az Þ

Pi

z ðe

2az Þ

ð4Þ

P. Saettler et al. / Microelectronic Engineering 137 (2015) 105–110

Table 1 Material properties used for FE simulations.

0.25 Si [14]

Deposition Elastic modulus [GPa] Thermal coefficient of elastic modulus [ppm/ K] Poisson ratio [-] plastic-behavior: stress – strain [MPa] - [-]

ECD 121 380

TEOS 71.4 240

168 60

0.3 121– 0.001 186– 0.004 217–0.01 234–0.02 248–0.04 17.3

0.16 -

0.22 -

I ¼ I0  e

2ðxx0 Þ2 b2

R

DxðxÞe

x

Dxðx0 Þ ¼

R x

 e

2ðxx0 Þ b2

2ðxx0 Þ b2

2

2

0 -0.05

0

10

20

30

40

50

position [µm] 0.5

2.8

Fig. 6. Measured peak shift in the Si periphery of Cu-TSVs; measurement parameters: kLaser = 442 nm, spot size = 1 lm, excitation time = 2 s and x0 = 521.5 Rcm1.

 

0.05

-0.1

In this equation x and z stand for the corresponding coordinates in the FE model [18]. As the applied laser light had a wavelength of k = 442 nm, a received the value of 47920 cm1 and the penetration depth in Si was approximately 250 nm [4,20]. According to this weighting step it was necessary to extract stress curves from FEM up to double the penetration depth. At penetration depth the intensity of the incident laser light decreased to 10%. For the weighting with Eq. (4) a depth was chosen where intensity amounted to 1% of the initial value at the surface. This occurred at double the penetration depth. Finally, the laser spot size was included into the evaluation routine. De Wolf demonstrated the data filtering under assumption of Gaussian distribution of the laser light intensity [4,18]:



0.1

-0.15 -50 -40 -30 -20 -10

! ð5Þ

!

In Eq. (5) b is defined as the half-width of the laser spot and was taken equal to 0.5 lm. The calculated Raman shift is filtered with this equation for each position x0 and also takes the oversampling in lRS measurements into account. Due to these two weighting equations measurement effects like penetration depth, laser spot size and oversampling were considered in our modeling approach.

4. Results 4.1. lRS results Summarizing four measurements in Fig. 6 the average calculated peak shift is shown. Results reveal a tension of the Si substrate near the TSV by displaying a strong positive Raman shift up to 0.2 cm1 in average. Up to a distance of 1 lm from the TSV interface a rigorous decrease of the shift can be observed in a way that shift gets negative (0.11 cm1). With increasing distance to the TSV Raman shift recovers to zero. As described in the experimental part it is not possible to analyze the particular stress components or give statements, which stress state is present in the examined sample. The linear relation from Eq. (2) is the only way to calculate specific stress values out of the Raman shift measurements. For this assumption a uniaxial stress state has to be present in the measured samples. Calculated stress values only remain valid for this particular stress state where only tensile and compression is found. Unfortunately, stress

distributions are not that simple in many cases. That is why it is highly likely to be erroneous when using this assumption. In this work it is only done to demonstrate the deviations, which arise due to this approach. Comparisons to FE results will demonstrate the necessity to supplement these lRS measurements with simulation work. Because of the symmetric curve shapes the following graphs only analyze the region from the TSV interface up to half of the pitch. In Fig. 7 the stress curve for the uniaxial stress hypothesis is plotted. According to the calculations Si is under compressive stress at the SiO2-Si interface. This compressive stress abruptly becomes tensile stress, which recovers to zero with increasing distance to the TSV. 4.2. FE results In comparison to the uniaxial stress assumption above Fig. 8 depicts the stress distribution calculated with FE simulation. Stresses from the SiO2 interface and 250 nm beneath are shown in the graph. It is clearly visible that normal stresses in x- and y-direction dominate the regions surrounding the TSV. With increasing distance to the TSV these stresses decrease, but do not recover to zero. The stress component in y-direction starts as compression at the TSV and becomes tensile stress with increasing distance. It can be assumed that stresses with bigger distance to the TSV are mostly caused by the CTE-mismatch between Si and SiO2. Close to the TSV interface Cu’s thermal deformation contributes the main amount of the emerging stresses. In this region additional normal stresses along z-direction rz evolve and shear stresses sxz arise. For the evaluation along the x-axis of our model the other stress components were found to be zero.

300 225

stress [MPa]

CTE [106/K]

0.15

TSV

SiO2 [13]

TSV

Cu [11,12]

peak shift [cm-1]

0.2

Material

150

TSV

108

75 0 -75 -150 -25

-20

-15

-10

-5

0

position [µm] Fig. 7. Derived uniaxial stress curve from the measurement in Fig. 6.

P. Saettler et al. / Microelectronic Engineering 137 (2015) 105–110

σy

σx σx_250

σy_250

σz σz_250

τxz τ xz_250

300

stress [MPa]

225

TSV

150 75 0 -75 -150 -25

-20

-15

-10

-5

0

position [µm] Fig. 8. Stress distribution in the Si periphery of a TSV for specific depths: SiO2-Si interface on top as continuous lines and 250 nm beneath the dashed lines.

weighted 0 µm 0.25µm

-0.2

TSV

peak shift [cm-1]

0 -0.1

-0.3 -0.4

-0.6 -0.7 -20

-15 -10 position [µm]

-5

0

Fig. 9. Predicted peak shift curves for specific depths and after weighting.

measurement simulation

0.1

TSV

peak shift [cm-1]

0.15

0.05 0

The comparison of curves for certain depths in Fig. 8 identifies a change of the stress behavior in z-direction. Due to these changes the weighting for the results out of specific depths has to be performed. This is even clearer after the conversion of the stress values into Raman shifts solving the eigenvalue problem in Eq. (3). The peak shift curves for specific depths differ widely from each other. Fig. 9 displays the calculated Raman shifts for the introduced stress states out of Fig. 8. To make the results comparable to the lRS measurements the weighting procedures using Eqs. (4) and (5) were executed. The peak shift curve after weighting can also be seen in Fig. 9 (green line). Due to the induced stresses from the SiO2 deposition all curves show a parallel shift to zero. For the final comparison of simulation and measurement the parallel shift has to be compensated. This is done by setting the peak shift of the weighted curve at position x = 0 lm to zero. Fig. 10 shows the results of lRS measurements and modeling in one graph. It is visible, that simulation delivers a very good approximation of the measured peak shift curve. The modeling approach slightly underestimates the minimum peak shift at position x = 20.5 lm and the recovery to zero is predicted to be slightly faster. This can be traced back to the simulation boundary conditions, which reproduce reality not exactly enough. Despite of these small deviations the FE-model delivers workable stress data for the evaluation of the TSV annealing. For example a minimum pitch and the maximum annealing temperature can be derived. 5. Conclusions

-0.5

-25

109

-0.05

The presented experimental set up in this work demonstrated, that annealing causes a considerable stress increase in Si substrates surrounding TSVs. It was also demonstrated, that lRS is feasible for characterization of the emerging stresses. In addition FEM demonstrates that the induced stress distribution is very complex and cannot be described by a uniaxial stress thesis. Near the TSV material interfaces simulation results show normal stresses in x, y and zdirection as well as shear stress (sxz). Tensions decrease with increasing distance to the TSV. With increasing distance to the TSV the SiO2 layer on top dominates the stress distribution. The conversion of FE-results into Raman-shifts enables a bilateral verification. In summary this paper succeeds in presenting a modeling approach for stresses caused due to TSV-annealing. It is demonstrated how data-filtering enables a more realistic adjustment of simulation results to measurement data. Consequently, a very good fit of simulation and measurement data is achievable.

-0.1 Acknowledgments

-0.15 -25

-20

-15

-10

-5

0

position [µm] Fig. 10. Comparison of simulation and measurement results of the Raman peak shift at TSV interfaces.

The author would like to acknowledge Fraunhofer IZM ASSID for providing TSV samples and Global Foundries for providing equipment for the lRS measurements. References

The presence of three normal stresses and one shear stress already disagree with the uniaxial stress thesis. FEM results clearly proof a more complicated stress distribution and a direct calculation of specific stress values out of measured Raman shifts is not possible. Besides that, the evaluation of the maximum and minimum stresses for both approaches revealed an underestimation by the uniaxial hypothesis, which can be found by comparing the stress plots of Figs. 7 and 8. In addition FEM results unveil that the range in the middle of two TSVs is not stress free as expected from measurements. Tensile stresses in x- and y-direction indicate a tension, which was generated during the SiO2 deposition.

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