# Comparison of Temperature Dependent Carrier Transport in FinFET and Gate-All-Around Nanowire FET
## 4 Discussion  
To understand the temperature dependence of \(SS\), the parameter of the on-off switching capability, the following equation is used [23]:  
\[SS\approx\ \frac{k_{B}T}{q}ln10\left[1+\frac{(C_{D}+C_{it})}{C_{ox}}\right] \tag{2}\]  
Here, \(C_{D}\) is the depletion capacitance, \(k_{B}\) the Boltzmann's constant, and \(T\) the temperature, respectively. The channel region of GAA NW-FET and FinFET is sufficiently shallow (\(D_{mw}\) = 8 nm for GAA NW-FET and \(W_{fin}\) = 5 nm for FinFET) so that the channel is fully depleted. Thus, the depletion charge (\(Q_{D}\)) of these devices are not a function of \(V_{G}\), and \(C_{D}\) (= \(dQ_{D}/dV_{G}\)) is negligible [23]. GAA NW-FET shows smaller \(SS\) at any temperature condition (\(SS\)s of GAA NW-FET and FinFET are about 65 and 69 mV/dec at 25 \({}^{o}\)C, respectively). The large \(SS\) is induced by poor gate control, punch through, and \(C_{it}\). Similar to \(dV_{TH}/dT\), the \(dSS/dT\) for both devices is approximately equal to \(-\)0.24 mV/dec/\({}^{o}\)C, as shown in Figure 4b. Thus, the identical slope of Figure 4b shows \(ln10\) [\(1+C_{it}/C_{ox}\)] is same for both devices. By considering identical \(dSS/dT\) and similar \(dV_{TH}/dT\) between GAA NW-FET  
Figure 4: **(a)**\(V_{TH}\) as a function of temperature for GAA NW-FET and FinFET from Figure 3. Similar temperature sensitivities of \(V_{TH}\) are observed for both GAA NW-FET and FinFET. **(b)** Subthreshold swing (\(SS\)) as a function of temperature also shows same slopes for both GAA NW-FET and FinFET. and FinFET, \(C_{it}\) is also regarded as identical (\(C_{it}=6.28\times 10^{-7}\) F/cm\({}^{2}\) when the capacitance equivalent thickness was 1.1 nm for both devices). In Figure 5, the temperature dependent \(\mu_{eff}\) is investigated for \(L_{G}=70\) nm. The \(\mu_{eff}\) was experimentally extracted from [24]:  
\[\mu_{eff}=\left.\frac{L_{eff}}{W_{eff}}\frac{g_{D}}{qN(V_{GS})}\right|_{V_{DS} \to 50\text{ mV}} \tag{3}\]  
where \(g_{D}\) [A/V] is the drain conductance, \(V_{GS}\) the gate-source voltage, \(V_{DS}\) the drain-source voltage, and \(W_{eff}\) and \(L_{eff}\) the effective width and length of the channel, respectively. \(qN(V_{GS})\) was calculated in the strong inversion region assuming by \(qN(V_{GS})=C_{ox}\) (\(V_{GS}-V_{TH}\)). From [PERSON]'s rule, the \(\mu_{eff}\) is composed of several mobility limited scattering mechanisms such as Coulomb, phonon, and surface roughness (SR) [25]. When a device is suffering from serious SR scattering, a large mobility degradation can be observed at high \(V_{OV}\) compared to the mobility behavior limited by phonon scattering, etc. [26]. The mobility limited by SR scattering is analyzed quantitatively by the following relationship [11; 27]:  
\[\mu_{SR}\propto\frac{E_{eff}^{-\alpha}}{\Delta^{2}\lambda^{2}} \tag{4}\]  
where \(E_{eff}\) is the effective field across the channel, which can be substituted to \(N_{inv}\) proportional to \(E_{eff}\), \(\Delta\) the rms value of the SR, and \(\lambda\) its correlation length. The \(\mu_{SR}\) is inversely proportional to the mobility degradation coefficient \(\alpha\). The extracted \(\alpha\) of GAA NW-FET is 0.6, which is smaller than that of FinFET (0.96). This means that less SR scattering is shown for GAA NW-FET compared to FinFET (Figure 5a). In addition, the \(\mu_{SR}\) has weak temperature dependence compared to the mobility limited by phonon scattering [28]. GAA NW-FET (Figure 5b) shows a stronger temperature dependent \(\mu_{\text{eff}}\) than FinFET (Figure 5c). These are investigated with two operating conditions: at weak \(N_{inv}=5\times 10^{12}\) and strong \(N_{inv}=1.5\times 10^{13}\) cm\({}^{2}\)/V-s. At weak \(N_{inv}\), similar \(d\mu_{eff}\)/\(dT\) is observed between both devices (\(-0.165\) for GAA NW-FET and \(-0.156\) cm\({}^{2}\)/V-s\({}^{\prime}\)C for FinFET) because the phonon scattering is dominant than the SR scattering at low \(E_{eff}\).