Self Annealing Process Essay

MTRL 578

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Debanga Kashyap

88851150

Introduction:

The objective of this analysis is to study the self-annealing process of copper deposited in interconnects using a resistivity model. The data set provided gives the measurements of voltage and current with time of a four-point probe experiment. A four-point probe based instrument is used to measure the average resistance of a thin film or sheet. The instrumental set up consists of passing a current through the two outer probes and measuring the voltage through the inner probe, thus allowing the measurement of the substrate resistivity. The data provided shows a constant current from the 4-point probe measurement. Whereas the voltage decreases with time, this indicates

The grain size of as-deposited copper is around 50-100 nm, which is comparable to the mean free path of copper (39 nm). As self-annealing progresses with time, we see a decrease in the resistivity as copper undergoes transformation from nano-crystalline to micro-crystalline structure, which gives us the nominal resistivity.

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Fig 2: Fractional Recrystallization vs Time after deposition in Log scale(base 10)

During self-annealing, copper undergoes transformation from nano- to micro-crystalline structure. The plot above shows the fractional recrystallization vs Time after deposition.

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Fig 3: Linear JMAK model based on Fractional recrystallization from data set

A JMAK model for the problem is being derived based from Fig. 3. From the linear fit of the plot, we obtain the values of b and n. A simplification of Eqn. 3 gives us the relation

Ln(Ln(1/(1-X)))=nLn(t)+Ln(b)

Hence, the values of n and b can be obtained from the slope and y-intercept of the linear equation fitted to the data. n = 1.9411 b = exp(-14.468) = 5.20748E-07

So, the JMAK equation for this case is

This indicates a 2- Dimensional growth undergoing the mechanism of Site Saturation, which is in accordance with the thin film thickness in our case (1µm).

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Fig 4: Comparison of Fractional recrystallization from experimental data with JMAK model results

Fig 4 shows plots of fractional recrystallization vs time obtained from experimental data vs JMAK model. An acceptable fit can be seen for the two models which verifies the JMAK model used in this analysis. From calculations, errors in measurement were found to be quite high during the initial transformation period, however in the domain of fractional recrystallization from 0.05 to 0.95, error in the model was well within acceptable limits (<