## 3 Experimental Results  
The room temperature (RT) deposition of GeTe thin layers keeps the fabricated resistors in the amorphous state. The change in amorphous state resistance with GeTe layer thickness for horizontal and vertical resistors is shown in Figure 3. Since the focus of this work is to emphasize DC/RF circuit and switching applications, it makes good sense to use device parameters like resistance and S-parameters instead of material properties like resistivity. In our experimental limits, the horizontal resistors were found more resistive than the vertical ones. Such behavior can be attributed to large inter-electrode distance and small cross-sectional area of horizontal resistors. Here, an increment in GeTe layer thickness increases the effective cross-sectional area, which further leads to a reduction in horizontal resistor's resistivity. For example, 5 \(\times\) 5 \(\upmu\)m\({}^{2}\) device resistance decreases from ~1 G\(\Omega\) to 10 M\(\Omega\) (corresponding resistivity change is from ~2.0 \(\times\) 10\({}^{7}\) to 5.0 \(\times\) 10\({}^{5}\)\(\Omega\)-cm) as GeTe layer thickness increases from 100 to 400 nm. On the other hand, the resistance of vertical devices increases nearly by an order of magnitude upon increasing GeTe layer thickness. For example, resistance changes from 1.0 \(\times\) 10\({}^{4}\)\(\Omega\) to 8.0 \(\times\) 10\({}^{4}\)\(\Omega\) (resistivity changes from 1.2 \(\times\) 10\({}^{3}\) to 1.4 \(\times\) 10\({}^{4}\)\(\Omega\)-cm) as 10 \(\times\) 10\(\upmu\)m\({}^{2}\) device thickness increases from 100 to 400 nm. Such behavior can also be explained by Equation (1), in which GeTe thickness determines the inter-electrode distance. Therefore, the resistivity of vertical resistors increases with GeTe layer thickness. Overall, device geometry is one of the main factors for fine tuning the device resistance. For example, a 10 \(\times\) 0.4 \(\times\) 10 \(\upmu\)m\({}^{3}\) horizontal resistor (where A = 4 \(\upmu\)m\({}^{2}\) and L = 10 \(\upmu\)m) would have at least 2 orders of magnitude larger resistance than a 10 \(\times\) 10 \(\times\) 0.4 \(\upmu\)m\({}^{3}\) vertical resistor, where A = 100 \(\upmu\)m\({}^{2}\) and L= 0.4 \(\upmu\)m, despite having the same device volume (Figure 3). Figure 3: Amorphous phase resistance versus GeTe layer thickness plot for vertical and horizontal resistors. After characterizing amorphous GeTe resistors, two different heating methods, (1) thermal conduction, and (2) Joule heating, were applied to initiate amorphous to crystalline state phase transition. In the thermal conduction mechanism, resistors were mounted on a thermal chuck and resistance was measured with increasing temperature. The resulting plot of a horizontal resistor (5 \(\times\) 5 \(\times\) 0.15 \(\upmu\)m\({}^{3}\)) is shown in Figure 4. A steady reduction in resistance value (from few 'hundred M\(\Omega\)' to 'few M\(\Omega\)') with increasing temperature (from RT to 220 \({}^{\circ}\)C) was recorded. Such behavior was attributed to the thermally activated charge carriers those increase with temperature. An abrupt drop in resistance was observed at 220 \({}^{\circ}\)C \(<\) T \(<\) 230 \({}^{\circ}\)C. This large resistance change (few M\(\Omega\) to few \(\Omega\)) in 10 \({}^{\circ}\)C temperature window confirms amorphous to crystalline phase transition. A similar phase transition was observed for vertical devices but with a small initial resistance (not shown here). Similar results can be obtained by Joule heating where an electrical current passing through GeTe resistor increases the temperature of the device and induces the phase transition. The experimental demonstration of Joule heating-induced phase transition is shown in Figure 5, in which three vertical resistors of same via holes (3 \(\times\) 3 \(\upmu\)m\({}^{2}\)) but different GeTe thickness (0.09 to 0.40 \(\upmu\)m) are tested.