Effects of alternating current voltage amplitude and oxide capacitance on mid-gap interface state defect density extractions in In0.53Ga 0.47As capacitors

This work looks at the effect on mid-gap interface state defect density estimates for In0.53Ga0.47As semiconductor capacitors when different AC voltage amplitudes are selected for a fixed voltage bias step size (100 mV) during room temperature only electrical characterization. Results are presented for Au/Ni/Al2O3/In0.53Ga0.47As/InP metal–oxide–semiconductor capacitors with (1) n-type and p-type semiconductors, (2) different Al2O3 thicknesses, (3) different In0.53Ga0.47As surface passivation concentrations of ammonium sulphide, and (4) different transfer times to the atomic layer deposition chamber after passivation treatment on the semiconductor surface—thereby demonstrating a cross-section of device characteristics. The authors set out to determine the importance of the AC voltage amplitude selection on the interface state defect density extractions and whether this selection has a combined effect with the oxide capacitance. These capacitors are prototypical of the type of gate oxide material stacks that could form equivalent metal–oxide–semiconductor field-effect transistors beyond the 32 nm technology node. The authors do not attempt to achieve the best scaled equivalent oxide thickness in this work, as our focus is on accurately extracting device properties that will allow the investigation and reduction of interface state defect densities at the high-k/III–V semiconductor interface. The operating voltage for future devices will be reduced, potentially leading to an associated reduction in the AC voltage amplitude, which will force a decrease in the signal-to-noise ratio of electrical responses and could therefore result in less accurate impedance measurements. A concern thus arises regarding the accuracy of the electrical property extractions using such impedance measurements for future devices, particularly in relation to the mid-gap interface state defect density estimated from the conductance method and from the combined high–low frequency capacitance–voltage method. The authors apply a fixed voltage step of 100 mV for all voltage sweep measurements at each AC frequency. Each of these measurements is repeated 15 times for the equidistant AC voltage amplitudes between 10 mV and 150 mV. This provides the desired AC voltage amplitude to step size ratios from 1:10 to 3:2. Our results indicate that, although the selection of the oxide capacitance is important both to the success and accuracy of the extraction method, the mid-gap interface state defect density extractions are not overly sensitive to the AC voltage amplitude employed regardless of what oxide capacitance is used in the extractions, particularly in the range from 50% below the voltage sweep step size to 50% above it. Therefore, the use of larger AC voltage amplitudes in this range to achieve a better signal-to-noise ratio during impedance measurements for future low operating voltage devices will not distort the extracted interface state defect density.

On classical and other methods of discriminant analysis and estimation of log-odds

For two multinormal populations with equal covariance matrices the likelihood ratio discriminant function, an alternative allocation rule to the sample linear discriminant function when n1 ≠ n2 ,is studied analytically. With the assumption of a known covariance matrix its distribution is derived and the expectation of its actual and apparent error rates evaluated and compared with those of the sample linear discriminant function. This comparison indicates that the likelihood ratio allocation rule is robust to unequal sample sizes. The quadratic discriminant function is studied, its distribution reviewed and evaluation of its probabilities of misclassification discussed. For known covariance matrices the distribution of the sample quadratic discriminant function is derived. When the known covariance matrices are proportional exact expressions for the expectation of its actual and apparent error rates are obtained and evaluated. The effectiveness of the sample linear discriminant function for this case is also considered. Estimation of true log-odds for two multinormal populations with equal or unequal covariance matrices is studied. The estimative, Bayesian predictive and a kernel method are compared by evaluating their biases and mean square errors. Some algebraic expressions for these quantities are derived. With equal covariance matrices the predictive method is preferable. Where it derives this superiority is investigated by considering its performance for various levels of fixed true log-odds. It is also shown that the predictive method is sensitive to n1 ≠ n2. For unequal but proportional covariance matrices the unbiased estimative method is preferred. Product Normal kernel density estimates are used to give a kernel estimator of true log-odds. The effect of correlation in the variables with product kernels is considered. With equal covariance matrices the kernel and parametric estimators are compared by simulation. For moderately correlated variables and large dimension sizes the product kernel method is a good estimator of true log-odds.