Basic Physical Insights and Electrical Characteristics of DTMOS with Different Gate Stack System
2.3 Results and Discussions
2.3.1 A Novel Threshold Voltage (V TH ) and Body Effect Coefficient (m) Extraction Method (m-model) of DTMOS
2.3 Results and Discussions
2.3.1A Novel Threshold Voltage (VTH) and Body Effect Coefficient (m) Extraction Method (m-model) of DTMOS
2.3.1.1 M-Modeling
Before starting to build our m-model, the VTH of DTMOS here should be defined its meaning, due to its dynamical change of VTH, as the gate voltage point which DTMOS works from subthreshold region to triode region. Figure 2.1 shows the VTH-VBS characteristics of transistor with fixed body bias mode. The decrease in the VTH as the forward body bias increases may be considered a continued reduction of the depletion charge. The VTH of device is extracted by the linearly extrapolated threshold voltage of the maximum transconductance method, where VD=0.1V [2.8].
The straight lines demonstrate that the body bias varies dynamically with the gate bias.
As same as mentioned before, because the DTMOS transistors are operated by connecting the gate with the substrate, the body bias may be given as:
G
BS V
V (01) (2.4) The is defined as a constant ratio of the dynamical biases between the gate and substrate. It should be noted that, the crossover points in Fig. 2.1 show the VTH of
DTMOS. For the junction turn-on limitation of VBS < 0.7V in DTMOS, the validation range of
is also defined in equation (2.4). Devices are operated under normal and DT-modes in which
= 0 and
> 0, respectively.The physical insight of VTH is usually defined as the gate voltage when the surface potential (s) reaches 2fp, where the potential fp is the difference between EFi and EF. At the threshold condition, the total capacitance of MOSFET acts like the oxide capacitance (Cox) and bulk depletion capacitance (Cdm) in series condition. Thus, the variation of surface potential may be expressed as a function of gate voltage [2.7]:
S change of surface potential due to incremental change of gate voltage. While equation (2.6) is valid for both uniform and nonuniform bulk doping profiles, based on the physical concepts, by considering the surface potential (s) can be controlled by gate and source terminals under DT mode, simultaneously. The control capability of the channel potential in our m-model can be expressed as:
condition is =1, the threshold voltage relationship between normal and DT-modes can be given as:This is directly referred to as the body effect coefficient (m), as a result, called it m-model. In advanced CMOS technology, the body effect coefficient (m) is a very important factor in short-channel-effect (SCE) control. It relates to the substrate doping profiles design, subthreshold slope and on/off current. Compared to the conventional body effect coefficient extraction method with its complicated variable substrate biases and fitting process, equation (2.8) provides a very fast and direct method to extract the body effect coefficient once the VTH of normal and DT-modes is known. Further, equation (2.8) also provides a clear rule for designing the VTH of DTMOS in deep-submicron device with a nonuniform doping profile. Unlike that of conventional devices, the body effect coefficient of DTMOS may be higher, with low gate work function material, for a high performance with low power consumption application.
2.3.1.2 MODELING VALIDATION
Figure 2.2 shows the ID-VG and Gm characteristics of NMOS under normal and DT-modes, respectively. It is obvious that the driving current of the DTMOS can be greatly enhanced by its lower threshold voltage and higher mobility resulting from the body effect. Unlike the conventional method as shown in Fig. 2.1, the VTH of DTMOS is directly extracted by the linearly extrapolated threshold voltage of the maximum transconductance method. Figure 2.3 and Fig. 2.4 show comparisons of the VTH
extraction results of the conventional method and the Gm,max extraction method for long channel and short channel devices, respectively. For both long channel (1m) and short channel devices (0.16m), the maximum errors are below 2.5% for different alpha ratios of devices under DT mode. Furthermore, from Fig. 2.5 to Fig. 2.8 show the extraction methods of the conventional method and the Gm,max linearly extrapolated method for both Poly/SiO2 and TaC/HfSiON devices with elevated temperature range from 298 K to 398 K, respectively. The gradual reduction in threshold voltage results from the increase in ni with increasing measuring temperature. The maximum errors are lower than 1%, as shown in Fig. 2.9 and Fig.
2.10, in both Poly/SiO2 and TaC/HfSiON gate stacks, confirming the good agreement between our method and the experimental data, respectively. Furthermore, the predicted values of the VTH,DT of the m-model and the experimental date extracted from the complicated variable substrate bias with fitting process are both shown in Fig.
2.11 and Fig. 2.12, respectively. For both long channel (1m) and short channel devices (0.16m), the maximum errors are less than 2% for different alpha ratios of devices under DT mode. It shows that our method can be still useful in short channel device. In addition, Fig. 2.13 and Fig. 2.14 shows the extraction results of the threshold voltage over the temperature range of 298 to 398K for the three methods under DT mode. The maximum errors are lower than 2% in both Poly/SiO2 and TaC/HfSiON gate stacks, confirming the good agreement between our model and the experimental data, respectively. Furthermore, Fig. 2.15 details our m-model with using equivalent circuit for both normal and DT-modes, respectively. It demonstrates the surface potential can be controlled simultaneously under DT mode. The predicted values of the body effect coefficient of the m-model and the experimental date extracted from the complicated variable substrate bias with fitting process are both shown in Fig. 2.16. It includes the two different kinds of gate stack and bulk doping concentration with elevated temperatures range from 298 to 398K. The gradual increase in body effect coefficient results from the increase in ni with increasing measuring temperature. Estimations of the disagreement between the m-model and the conventional method, roughly 2.5%, are obtained. These results show that our proposed m-model gives results that are sufficiently accurate to predict the VTH and m of DTMOS.
2.3.2Comparison with Performance and Short Channel Effect (SCE) for Different