The nano-resistors were formed from the dielectric breakdown of a MOS capacitor with the ZrHfO high-k film deposited on top of a p-type <100> Si (11-20 Ω∙cm) wafer. The detailed fabrication process of the 300 µm-diameter MOS capacitor and the nano-resistor formation step could be found in refs. 1-5. The sample surface was imaged with the JEOL JSM-7500F SEM after being stressed at the gate voltage (Vg) of -20 V for 20 min. The I-V curve was measured with an Agilent 4155C semiconductor parameter analyzer.
Figure 1 shows the top view of the device after being stressed at Vg = -20 V. Many tiny bumps are evenly distributed across the electrode surface. Each bump correspond to a nano-resistor of which the rough surface is formed from the high local temperature generated from the current flow [1]. The actual nano-resistor is located in the center of the bump and is much smaller than the size of the bump [5]. The total cross-sectional area ratio of bumps to the gate in the Fig. 1 structure is estimated to be approximately 0.04443.
Figure 2 shows the I-V curve of the nano-resistor device. In the large voltage range, the current increases linearly with the increase of the magnitude of Vg (|Vg|). It has a constant resistance (Rs) of 396.6 Ω. It is composed of several resistors connected in series: the bulk Si wafer, the Schottky contact between the Si and the nano-resistor, the nano-resistor, the ohmic contact between the nano-resistor and the gate, and the ITO gate electrode. The bulk Si resistance can be calculated based on ref. 7. At the large |Vg|, the Schottky contact resistance is negligibly small compared with other resistances. If the ohmic contact and gate electrode resistances are also neglected, the total resistance of the nano-resistors can be estimated. We assume that each nano-resistor has the same resistivity. Then, the resistivity of the nano-resistor is estimated to be 2673–7075 Ω∙cm, which is in the order of 103 Ω∙cm.
At the low |Vg| range, we used the Schottky contact equation to fit the device’s I-V curve, as shown in equations 1 and 2 [7]. The voltage drop across the Schottky contact is taken as V-IRs. Figure 3 shows that the Schottky contact equation fits well with the experimental data and the nano-resistor has a barrier height of 0.66 eV on Si.
In summary, the resistivity and barrier height of the nano-resistor can be estimated from the experimental data based on some basic assumption of the material properties.
[1] Y. Kuo et al, APL, 102, 031117 (2013).
[2] Y. Kuo, IEEE TED, 62, 3536-3540 (2015).
[3] Y. Kuo, ECST, 67, 183 (2015).
[4] Y. Kuo, ECST, 69, 23 (2015).
[5] C.-C. Lin et al, APL, 106, 121107 (2015).
[6] A. Avellán et al, IEEE EDL, 29, 366 (2008).
[7] S. M. Sze et al, Physics of Semiconductor Devices, John Wiley & Sons, New Jersey (2007).