Management cohesion

The total mechanical stress σtotal in a brittle film without plasticity deposited on a Si-substrate consists of two components, the thermal stress σ^thermal and the intrinsic stressσ^intrinsic:

rinsic thermal

total σ σint

σ =σthermal + (1)

The thermal stress is due to the difference in coefficient of thermal expansion (CTE) between the film and the substrate. During cool down from deposition temperature to room temperature the thermal stress develops according to the material properties of the film and the substrate. A simple expression for the (maximum) thermal stress is given by:

E T

f s f

Ef

thermal − ∆

= − ⁽ s − ff⁾

1 ^s −

υff

σ (2)

whereα^ff and α^s are the CTE of the film and substrate, respectively. Eff and ν^f are the Young’s modulus and Poisson ratio of the film, and ∆T is the temperature difference between deposition temperature and the temperature of interest.

The total stresses in the film σtotal are calculated using the warpage R of the processed wafers measured at room temperature. Assuming that the film is thin compared to the thickness of the wafer the total film stress can be calculated using the modified Stoney’s equation [6]:

¸¸¸¸¹

¸¸

·¸¸

¨¨¨¨©

§¨¨ −

= −

1 2

2 1 1

1 )

6( t ^¨_©^¨¨R2 R t

E tf

s s

Es total

σ υ (3)

with Es and ν^s the Young’s modulus and Poisson ratio of the substrate, respectively, ts the substrate thickness, and tff the film thickness. R2 is the radius of curvature after processing and R1 the initial radius of curvature of the wafer before film deposition. For thickness ratios tff / ts< 0.1, the error in Stoney’s equation remains below 5%. For thicker films, a more rigorous analysis shows that a correction factor equal to (1 + γδ³)/(1 + δ) is required [7], where δ = tff / tsand γγ= M^ff/ Ms, with the biaxial modulus: M=E/(1 ν).

For thick films (0.1< δ < 0.4) with unknown film properties, the film modulus contribution can be neglected and 1/(1 +δ) can be used as a correction factor [8]. Others presented a correction factor, which includes the effects of a finite film thickness and film modulus as well as the effect of a large deflection [9].

−

Intrinsic stresses are the result of the depositioning process of the layer.

These intrinsic stresses are already present at depositioning temperature and are influenced by the parameters of the depositioning process. The intrinsic stresses remain constant with changing temperatures if the properties of the film are not influenced by the temperature (for example viscous flow at high temperatures) or the environment (influence of humidity). The intrinsic stresses are believed to depend on the thickness of the film. For thin films (<300 nm) an increase of intrinsic stresses is observed where above this level the intrinsic stresses are constant with thickness. This influence of thickness is the result of nucleation phenomena of the film on the substrate. The intrinsic stresses can play a significant role and for some type of films the intrinsic stresses are comparable or even larger than the thermal stresses.

Modern equipment allows control over the intrinsic stress, which gives the process technicians a method of controlling the overall warpage of the wafer at room temperature. It is important that the intrinsic stress is accounted for in FE simulations. Measuring the intrinsic stresses is difficult due to the fact that the measured total stress is usually a combination of thermal and intrinsic stresses. Intrinsic stresses can be both tensile and compressive.

There are several mechanisms for forming intrinsic stresses, such as [10]:

• Density of film-building atoms in absorbed state,

• Absorption of by products,

• Increased surface mobility of reactive species,

• Ion bombardment (PECVD),

• Cross-linking.

For SiO2based layers the intrinsic stress is not a constant value. The as-deposited intrinsic stress is influenced by several factors, which can play a large factor in the total stresses in the SiO2 based layer. For oxynitride, metal or ceramic layers this effect is usually not present. The different factors, which influence this change in intrinsic stresses, are:

• Absorption of water in the layer. CVD deposited PSG films generally exhibit as-deposited tensile intrinsic stresses. This is due to absorbed foreign atoms at deposition temperature, which prohibit the formations of a dense film. The film has a reduced density with elongated bonds and/or microcavities and this leads to tensile stresses in the layer.

However, if this film is subjected to humidity it will absorb the water atoms and swell in the process. This will decrease the tensile stress and eventually lead to compressive intrinsic stresses. PSG films with lower tensile stresses or compressive stresses will show less reactivity with water [11]. This effect of water absorption plays a large role when measuring the film stresses. In order to get the true as-deposited intrinsic stress the measurement should be made directly after depositioning. The effect of water absorption doesn’t play a role when in the process cycle

the film is covered by another film, which prevents the water from reaching the PSG film.

• Densification of the layer due to temperature increase. For SiO2 based films increasing the temperature causes the formation of additional Si-O-Si bonds. This leads to densification of the film and the development of bond strains. These bond strains result in intrinsic tensile stresses in the film. After cooling to room temperature these tensile stresses do not disappear but remain in the film. This effect is present for PSG films but also for TEOS-PECVD films. The result of this phenomenon is the occurrence of hysteresis during thermal cycling of the film. This thermal cycling plays of course a role in practice due to the deposition of additional films [12]. The stress development due the densifications of the layer can be such that the maximum occurring tensile stress is in the order of 200-500MPa.

• Visco-elastic relaxation of the stresses at temperatures above the softening point. SiO2 based films are usually amorphous, glass type structures which exhibit a time-dependent, visco-elastic behaviour. For temperatures above the softening point of the material the viscosity of the material will be low enough for the occurrence of flow phenomena and rearrangement of molecules. The temperature of the softening point will depend on the chemical composition of the layer. For pure SiO2

films this temperature will be higher than for SiO2 films with impurities (such as PSG). At temperature above the softening point the film stresses will relax due to the viscous behaviour of the film. At sufficient high temperatures or for longer holding time at certain temperature the film stress will decrease to zero. During cool down from these high temperatures to room temperature only thermal stresses will develop.

The complete stress behaviour during a temperature cycle to high temperatures shows initially the development of tensile stresses due to the densification. At higher temperatures these stresses will relax and decrease to zero [12].

Through FE simulations the stress and strain levels in IC layers can be predicted, however, it is important to know the properties of the different materials and the mechanisms, which cause stresses in the film to develop.

Currently, a number of techniques are available able to measure the (intrinsic /thermal) stress levels and/or the properties of IC materials. These techniques include:

1. Wafer warpage as a function of temperature, 2. Nano-indentation,

3. IC interface toughness characterization,

4. Other techniques like the bulge test, impulsive stimulated thermal scattering, and X-ray diffraction.