Conclusion

    The project was accomplished ahead of schedule and all the tasks were fulfilled. The comparison between Project 27 (50% Hf) indicates that a higher oxide permittivity will show some of the positive effect on MOS capacitor, but negative side should not be ignored. Further research need to target on the fixed oxide charge density and try to decrease it.

    Apart from the general calculation, a MatLab program was written to calculate the electrical properties of the high-k gate stacks, The output result is shown below:

    The program needs to input the Capacitance, Voltage and Resistance data for calculation. Therefore, it can be used to calculate other gate materials with input data. If you are interested in the source code, please contact us.

Question 9. Compare the Results with Project 27 (50% Hf)

    Finally the results were compared with Project 27 (50% Hf). All the results between two groups are summarized below:

	Project 26 (70% Hf)	Project 27 (50% Hf)
Type of Substrate	P-type	P-type
Oxide Relative Permittivity	10.64	8.67
EOT (nm)	2.81	3.04
Doping Density (m-3)	4.244x1021	2.7x1021
Work Function Difference (eV)	0.065	0.08
Flatband Voltage (V)	0.932	0.53
Midgap Voltage (V)	1.367	1.21
Oxide Charge Density (cm-3)
Flatband Condition	-6.660x1016	-3.23x1016
Mdigap Condition	-7.841x1016	-6.4x1016

    It can be noticed that a higher percentage of Hf will lead to a higher oxide relative permittivity. It could be explained by the fact that the relative permittivity of Hf is higher than SiO2. Also, the equivalent oxide thickness will be decreased. Nevertheless the EOT is still too large for commercial purpose (which should be less than 2 nm). Higher percentage of Hf will also lead to a higher doping density, which will then increase the cost of manufacture.

    Another thing should be considered is that the fixed oxide charge density almost doubled in flatband condition. According to our supervisor, the charge density should be controlled less than 1x10¹⁰ in order to get a better quality of CMOS. Thus further research should be carried out to decrease the amount of fixed oxide charge density.

Question 10. Write program for plotting the ideal high-frequency capacitance voltage plot.

    As mentioned above, there is a small number of negative charges in oxide, which need extra voltage to neutralize to reach the same capacitance according to the equation:

    According to the previous task, the differences between ideal value and real value can be calculated in flat-band and mid-gap conditions.

    As shown above, the two voltage difference are almost same. In fact, there do exist a constant voltage difference between ideal and real values at same capacitance.