3.1 Effect on Lattice and Carrier temperature
The onset of self-heating occurs when the nearly free conduction band electrons in the channel region are accelerated by the electric field because of rise in the drain voltage (VDS). The electrons (carriers) gain energy from the field and consequently, carrier temperature (TC) increases. The carriers lose energy by inelastically scattering with the lattice phonons, where the carriers with energies below 50 meV scatter mainly with acoustic phonons, whereas, those with higher energy scatter strongly with the optical modes [27]. Such scattering events result in transfer of energies (heat) to the crystal lattice, and hence carrier temperature (TC) is found much higher than the lattice temperature (TL) (i.e., TC > > TL). In Fig. 3, the variations of the maximum lattice temperature (TLmax) and carrier temperature (TCmax) against VDS for VGS = 1 are shown. It be observed that TCmax and TLmax increase gradually up to 0.1V of VDS owing to low-field transport (LFT) mechanism. On the other hand, for VDS from 0.1V to 1V, TLmax and TCmax could be seen rising from 303K to 398K and 360K to 2664K because of high-field transport (HFT) mechanism. It may be noted that enhancement in carrier temperature results in phonon emission, where a significant portion of the generated phonons correspond to optical modes (low group velocity) or acoustic modes. Figure 4 deals with the changes in TLmax and TCmax against change in spacer lengths (LSP) at VDS = VGS = 1V. The expansion in spacer length (LSP) at fixed channel length extended the space between side contacts with the channel. It produced two effects (a) the induced electric field gets reduced along the channel length at the same value of VDS and diminished the carrier energy, as a result of which TCmax got reduced. (b) The heat dissipation path extended for the channel from cooling sinks (metallic contacts of D/S) and caused the increase in TLmax. As per Fig. 4, against the variation of LSP from 10nm to 30nm, the TLmax rises from 333K to 398K(~ 16% increase), and conversely TCmax falls from 3131K to 2664K(~ 15% decrease). Figure 5 displays the contour plots of (a) lattice temperature and (b) electron temperature in silicon nanowire along device length (nm) at VGS = VDS = 1V. Hot carriers (high energy carriers) moving from the source undergo heavy scattering near the drain side and give their energy in the form of phonons to the lattice. Consequently, there is increase in lattice temperature (TL) near the drain region locally. Note that, the area of maximum lattice temperature (TLmax) is known as a ‘Hotspot’, where the density of optical phonons is the maximum. The variations in TL and TC against the device length for the fixed values of VDS and VGS at 1V are demonstrated in Fig. 6. It is already mentioned earlier that near the channel-drain interface, the energy of carriers gets sufficiently high owing to high electric field which make them hot. In Fig. 6, it can be easily observed that the electron temperature (TC) near the channel-drain interface (\(\approx 55\text{n}\text{m}\)) reaches the peak value which is near 2500K. Note that, in the course of journey from source to drain, the carriers gain energy, and at the same time they also got scattered with lattice ions which results in generation of phonons. Therefore, an increase in lattice and carrier temperature may be observed in the plot. When the hot carriers enter the drain region, due to reduced mean free path length, there is a surge in electron-lattice scattering events resulting in a steep increment in lattice temperature as obvious from the Fig. 6. At the same time, it can be seen that the carriers lose their energy through scattering and their temperature starts decreasing from the channel-drain interface. Near the metallic contact, the lattice temperature again starts decreasing due to heat dissipation through the metallic contact.
3.2 Output and Transfer characteristics under SHE
Figure 7 shows the behaviour of output characteristics of the DPGAA MOSFET versus VDS with SHE and without SHE for different VGS. Self-heating causes the carrier mobility to degrade in the channel near the drain side due to populated hot carriers scattering, which result in the downfall of drain saturation current with the increase of VDS at a particular value of VGS. As per Fig. 7, the drain saturation current decreases due to SHE by approximately 8% in DPGAA MOSFET at VGS=1V. The next figure (Fig. 8) depicts the transfer characteristics of DPGAA versus VGS with SHE and without SHE.at VDS=0.75V. It depicts that the on-state current of DPGAA degrades with SHE on increasing value of VGS. The degradation of electron mobility and electron velocity along device length (nm) at VGS=VDS=1V is shown in Fig. 9. The electron mobility degrades by approximately 50% from source-channel to drain-channel interface. However, the electron velocity increases suddenly with a significant peak value (1.37×108 cm/s) in the channel region and tends to decrease near the drain and channel interface in the drain region.
3.3 SHE variations due to thermal contact resistances (Rth)
Thermal contact resistance (Rth) plays a vital role in the heat transfer mechanism of the device. The low value of Rth provides a fast thermal conducting path for heat flow from the device through source and drain contacts. Figure 10 & Fig. 11 depict the increase in Lattice and carrier temperature for higher values of thermal contact resistances (Rth), respectively. According to Fig. 10, when Rth varies from 1×10− 5cm2KW− 1 to 1×10− 4cm2KW− 1, lattice temperature (TL) increases from 332K to 472K (~ 42%increase). On the other hand, in Fig. 11, the electron temperature (TC) can be seen increasing with an increase in Rth near the source and drain contacts, but the ‘hotspot’ carrier temperature TCmax seems independent against the variation in Rth. The variation of maximum lattice temperature (TLmax) with thermal conductivity of spacers for various values of Rth is plotted in Fig. 12. It has been observed that if the thermal conductivity of spacers increases from 0.14W/K-cm to 0.185W/K-cm, the TLmax gets reduced by around ~ 5.1% for Rth = 5×10− 5cm2KW− 1. Obviously, the thermal conductivity of spacers may play important role in fighting with self-heating effects. Figure 13 shows the variation of the drain current versus Rth for various types of gate insulators. The drain current decreases from 39.8µA to 25.3µA (~ 36.4% decrease) for Al2O3, 38.9µA to 24.6µA (~ 36.8% decrease) for Si3N4 and 35.5µA to 22.3µA (~ 37.2% decrease) for SiO2, respectively, which claims the scope of high K-dielectric (Al2O3) material to get the high drain current.
3.4 Gate Leakage current under HCI degradation
This section is dedicated to discuss the gate leakage current (IG) under hot carrier injection with SHE for the DPGAA MOSFET. The hot carrier injection model (LUCKY) [28] is used in the ET simulation of the device. It is used to extract the significant values of the carriers injected into the gate oxide near the ‘hotspot’ region. Because of the presence of a strong vertical electric field in the channel region, the significant tunnelling current occurs through the gate oxide near the 'hotspot' region. These injected carriers break the ionic bonds of the gate oxide and create a tunnel, as a result of which gate leakage current (IG) enhances and the drain saturation current (ON-current) degrades in the device [29]. In Fig. 14, the variation of the gate leakage current versus spacer length (LSP) is plotted. Against the variation of spacer length from 10nm to 30nm, the gate leakage current (IG) decreases from 13.5nA to 4.8nA (~ 64.5% decrease). It is explained earlier that the considerable spacer length reduces the carrier temperature (TC) and hence causes a reduction in leakage current.
3.5 Effect of Ambient temperature (TA) variations
The ambient temperature (TA) is one of the crucial factors of SHE degradation [14]. Here, ET simulation has been used to investigate the SHE in DPGAA MOSFETs to analyse the impact of TA. Figure 15 demonstrates the variation of the maximum lattice temperature (hotspot temperature) (TLmax) versus ambient temperature (TA) for the various values of Rth. The TLmax increases from 398K to 494K (~ 24.1% increase) with the rise in TA from 300K to 400K for Rth = 5×10− 5cm2KW− 1. The variation of the drain current (ID) against ambient temperature (TA) for the various values of Rth is plotted in Fig. 16. Increasing TA from 300K to 400K, the ID decreases from 37.8µA to 35µA (~ 7.5% decrease) because the lateral electric field degrades the carrier mobility at Rth = 5×10− 5cm2KW− 1. Figure 17 demonstrates the cutline plot of the variation in lattice temperature (TL) versus device length (nm) for increasing TA values (300K to 400K in a step of 20K). The drain lattice temperature (TL) is higher than the channel and source regions because the high electric field enhances the scattering in the drain region. However, the TL increases with an increase in TA.