5.1.2 Factor Extraction

The factors are extracted based on the fundamental theorem of factor analysis [22], which says, that every observed value can be written as a linear combination of hypothetical factors. The base of factors is chosen in a way that the base vector is an element which is most responsible for occurring variances. The components are sorted according to their contribution to the variance. Thus, PCA is primarily a method to simplify data sets and only at a second stage a means to extract physically interpretable quantities.

For the reduced example two factors are considered. The criterion for the chosen number of factors in the extraction is an Eigenvalue $\geq$ 1, as can be seen in the so-called Scree plot in Fig. 5.3, which is a plot of Eigenvalue vs. factor number [53].

Figure 5.3: Scree plot of the example.

Extracting the factors via SPSS it is found that the first extracted factor accounts for 62% of the occurring variance, while the second factor accounts for an additional 25 %. This leads to an overall 87% explanation of the variance. The resulting factor matrix is found in Table 5.1.

Table 5.1: Final statistics: factor matrix.

Variable	Factor 1	Factor 2
${\it C}_{\mathrm{gs}}$	0.91	-0.284	Gate source capacitance
${\it R}_{\mathrm{D}}$	-0.882	0.429	Drain resistance
${\it R}_{\mathrm{S}}$	-0.868	0.441	Source resistance
${\it C}_{\mathrm{gd}}$	0.822	0.432	Gate drain capacitance
${\it C}_{\mathrm{ds}}$	0.731	0.50	Drain-source capacitance
${\it BV}_{\mathrm{GD}}$	-0.369	-0.8	Gate drain breakdown voltage

A similar quantity as Factor 1 has been extracted in [153] for InAlAs/InGaAs HEMTs. The physical explanation was attributed to variations of doping during MBE growth, however, also mechanisms due to the semiconductor process are likely, as explained in the next section.