Investigation of the Low-Temperature Behavior of FD-SOI MOSFETs in the Saturation Regime Using Y and Z Functions

The saturation regime of two types of fully depleted (FD) SOIMOSFETdeviceswas studied.Ultrathin body (UTB) and gate recessed channel (GRC) devices were fabricated simultaneously on the same silicon wafer through a selective “gate recessed” process. They share the same W/L ratio but have a channel film thickness of 46 nm and 2.2 nm, respectively. Their standard characteristics (IDS-VDS and IDS-VGS) of the devices weremeasured at room temperature before cooling down to 77K. Surprisingly, their respective temperature dependence is found to be opposite. In this paper, we focus our comparative analysis on the devices’ conduction using a Y-function applied to the saturation domain. The influence of the temperature in this domain is presented for the first time. We point out the limits of the Y-function analysis and show that a new function called Z can be used to extract the series resistance in the saturation regime.


Introduction
Planar fully depleted silicon-on-insulator (FD-SOI) technology relies on a silicon wafer having an ultrathin layer of crystalline silicon smartly built over a buried oxide (BOX) layer.Transistors built into this top silicon layer (whose thickness ranges in the decananometer thickness) are called ultrathin body (UTB) devices.Such devices have unique and extremely attractive characteristics for coming technology nodes.Since performance needs are increased together with power consumption control, UTB/FD-SOI is also a key technology for addressing high speed and leakage control.In the past several years, this technology has gained significant momentum in the mobile communications market space [1,2].FD-SOI devices were deeply analyzed across the literature, including the influence of the BOX/Si interface [3].
In a recent publication [4], we analyzed the transfer characteristics of the ultrathin body (UTB) and gate recessed channel (GRC) devices, sharing same / ratio (80 m/8 m) but having a channel film thickness of 46 nm and 2.2 nm, respectively.These characteristics were, respectively, measured in the linear domain for two temperatures: at 300 K and at 77 K.By decreasing the temperature, it was found that the electrical behaviors of these devices were radically opposite: if, for UTB device, the conductivity was increased, the opposite effect was observed for GRC.Moving forward in the research, it was important to check if such kind of phenomenon (decreasing mobility by decreasing temperature) is also occurring in the saturation regime of the devices (higher currents).Using -function and -function analyses, both output and transfer characteristics of UTB and GRC devices were deeply investigated by varying the temperature from 300 K to 77 K.
The results confirmed that, for GRC device, the conduction exhibits a nonregular trend; that is, the extracted mobility is decreased by lowering the temperature.Using function and complementary -function analyses, we could interpret this trend by the existence of very high series resistance values.The -function analysis in the saturation regime was recently published [5] at room temperature; however, no complementary analysis of both  and  functions was used to emphasize the nonstandard and opposite behavior of the mobility between UTB and GRC at low temperature.2-dimensional TCAD process simulations of the UTB and GRC devices are, respectively, given for illustration in Figures 1(a) and 1(b).An HRTEM image of a GRC device zoomed in its channel area is presented in Figure 2.

𝑌-Function Analysis in the Saturation Domain.
Ghibaudo et al. [7] introduced first the -method which has the interest to resolve the respective contributions of the intrinsic channel conduction from the series resistance.
However, this extraction of series resistance usually relies on a set of devices with different channel lengths and is limited to the linear domain of device operation.In a previous study [8], we used this technique to extract the series resistance in the linear domain from the transfer characteristics.As a novelty, we proposed to apply this method to the same devices in the saturation domain.
Starting from the analytic expression of the saturation current [9], With: And  0 is the low field electron mobility. 1 is the "extrinsic" mobility degradation factor including the series resistance according to while  1,0 is the "intrinsic" mobility degradation factor.The saturation voltage can be modeled by [9] From Figure 3, we can point out the  DS,sat value for each  GS for a given device and temperature.  is extracted using the  versus  GS graph as described below.Using (4) and by measuring  DS,sat from Figure 3,  is found to be about 0.75 and 0.2 for UTB and GRC, respectively, for both 300 K and 77 K. Since  is mainly connected to the capacitance ratio between the silicon channel and the front gate [9], it is independent of the temperature.
Assuming the same definition as used in the linear domain, the  function in the saturation domain can be expressed by with the  ,sat being the transconductance in the saturation domain.
For the sake of model's simplicity, we assume that, at sufficiently high  GS ,  1 is no longer dependent on  GS , so Then, by taking the derivative of ( 1) and after reduction of the expression (5), the  function at saturation can be finally described by With: We would consider two limit cases.First, if  SD is negligible, then from (3),  1 should be also negligible relatively to 2/( GS −   ), so  function at saturation can be approximated by Then the  2/3 function is expected to be linear with  GS in this limit case.
Secondly, if  SD is dominating, then, from (3),  1 is also dominating relatively to 2/( GS −   ) and  function at saturation can be approximated by Consequently, the  function is expected to be linear with  GS in this limit case as observed for the classic  function in the linear domain.This feature is useful to extract the   values.But, unlike classic  function, the  sat expression is now dependent of  SD through  1 .
The - GS graphs can be straight forward derived from the  DS - GS characteristics measured at a given  DS,sat (3 V) in the 0-4 V range as shown in Figures 4(a) and 4(b) for UTB at 300 K and 77 K, respectively.In Figures 4(c) and 4(d),  DS - GS and - GS graphs are presented for GRC at 300 K and 77 K, respectively, for / = 80 m/8 m at a given  DS,sat (7 V).In Figures 4(a) to 4(d),  2/3  GS is also plotted for comparison to the first limit case.We can see there that for UTB the  2/3 functions are almost more linear than the  functions, as expected from the first limit case (9), but are significantly bended at lower  GS values at 77 K.For GRC,  V DS (V) GRC, W/L = 80 m/8 m, T = 300 K  the  functions are linear with  GS as expected by the second limit case at high  GS values from (10).
According to (9), we can extract the threshold value   for UTB from the intercept of the  2/3 function with the  GS axis.The extracted values of   , obtained at saturation condition for the different temperatures, are summarized in Table 1.The low field electron mobility  0 can be extracted directly from the slope parameter  of the  2/3 function through the  parameter using (2) and (9).Consequently, where: For UTB, the  ox value is 121 nF/cm 2 since a 38 nm thick nitride layer is capping the pad oxide in the gate region.
The extracted values of  0 obtained at saturation conditions for the different respective temperatures are summarized in Table 1.As mentioned above,  is taken as 0.75 for UTB.

𝑍-Function Analysis in the Saturation Domain for GRC.
If by using (10) the  function can be used to extract the   values for GRC, it cannot be used to extract the GRC low field electron mobility  0 from the slope since  and  1 parameters are coupled.So it is necessary to introduce a new function that decouples theses parameters, by using the so-called  function [10] defined as follows: V GS (V)  However, in our case the  sat function cannot still discriminate between  and  1 .So we will use the  function defined by the product of  and  functions as follows: Now  1 can be extracted from the intercept of the  function with  axis as shown in Figure 5 for GRC's devices having a / of 80 m/8 m.As assumed in (10) a linear fit is taken for sufficient high  GS values.
Note that if at 300 K, the slope of the  versus  GS plot is 1 for 80 m/8 m, it is found to be much lower than 1 (0.58) at 77 K.This seems to indicate a temperature dependence of the limit case presented in (14).However, the slope of the  versus  GS is not critical issue for the parameter extraction method and is ignored.
Finally from the  1 extraction and using the slope of the  function, the  and then  0 parameters for GRC can be extracted using ( 10) and ( 2)-( 8), respectively, and taking  = 0.2.Results are presented in Table 2 for the different temperatures.For GRC the  ox value was (138 nF/cm 2 ) by considering the 26 nm thick gate oxide as seen in Figure 2.
From (3), we can see that the low values of the  parameter for GRC should be compensated by a very high value of  SD in order to get the high  1 (≫1 V −1 ) values as presented in Table 2. Here, the intrinsic parameter  1,0 is assumed  negligible since the gate oxide is relatively thick in such a way that the mobility should be weakly gate dependent.Then, the series resistance  SD could be extracted directly from the following expression:

Interpretation and Discussion
3.1.Behavior of the   -  Saturation at Low Temperature.Firstly, from Figure 3, we can see that both UTB and GRC are depletion-type devices (normally open, i.e., negative   for -type channel) at 300 K and 77 K. From Table 1, the UTB's threshold voltage   is increased by decreasing the temperature which is in accordance with the decreasing of the Fermi potential as observed in similar devices [11].Secondly, the low field electron mobility  0 is increased by decreasing the temperature which is consistent with the classic increasing of mobility at low temperature (<150 K) due to the freezing of phonon scattering [12].However, from Table 2, for the GRC device,  0 parameter is surprisingly decreased by decreasing the temperature.So, when lowering the temperature, the conduction was increased in UTB, while the opposite effect is observed for GRC.As seen in Table 2, this should be correlated to the increase of the series resistance as extracted from the and -function analysis.This trend can be physically explained by the freeze-out of the silicon dopants outside the GRC channel as reported in [13].Moreover, for the UTB device, the extracted  0 values are similar to those expected in similar silicon based devices [14], while, for GRC device, the corresponding  0 values are found to be very low and are inconsistent with such kind of fully depleted SOI MOSFETs [15].Consequently, this corroborates the influence of a series resistance in the GRC's case.

Comparison to Extraction Method in the Linear Regime.
The  DS - GS behavior at low temperature in the linear regime was studied in a previous publication [4].Using the function method based on a first order analysis has been shown to be effective to interpret the radically opposite electrical behavior which was observed at low temperature.In Table 3, for UTB device, the threshold voltage   ,  parameter, and mobility  0 extracted from saturation and linear domain at 300 K and 77 K, respectively, are compared.
The threshold voltage values extracted from the saturation are found more negative and less dispersed than those extracted from the linear domain, especially at 77 K.This seems to be more consistent with the model of the threshold voltage temperature dependence [16].Moreover, the mobility values extracted from the saturation domain are found also to be in better agreement with the expected values for similar devices [17].
In Table 4, threshold voltage   ,  parameter, mobility  0 , and  SD extracted from saturation and linear domain at 300 K and 77 K, respectively, for GRC are compared.
Unlike threshold voltage values extracted from the linear domain, those from the saturation regime are found less negative and are decreasing by lowering the temperature.Again, it seems to be more consistent with the model of the threshold voltage temperature dependence [16].If the extracted mobility values from the saturation domain are about 10 times higher than those extracted from the linear domain, they are still lower than the expected values for such kind of devices [15].However, the series resistance  SD extracted from the saturation domain is still comparable to those extracted from the linear domain.So the series resistance is less sensitive to the extraction domain than the mobility showing the better consistency of this interpretation.

Extraction of the Effective Mobility Using Conventional
- Method.In order to corroborate our previous results about the electron channel mobility and the series resistance extraction method, we could independently extract the mobile channel charge density  inv and finally the effective electron mobility  eff according to the respective definitions [18]:  where  ox is oxide capacitance measured as the step of the - plot at  GDS = 0 V (inversion zone) according to Figure 6, while the threshold voltage   is taken as −0.25 V and is matching the corresponding value in Table 4 at 77 K.The channel conductance   is 21 nS as measured from the slope of the  DS - DS plot at  GS = 0 V in Figure 3(d).
The effective electron mobility (0.074 cm 2 /Vs) is found close to the corresponding value in Table 4 at 77 K (0.11 cm 2 /Vs) which corroborates our extraction method based on -function analysis in the saturation domain.Consequently, this measurement well confirms that the extracted effective mobility is too low in particular at low temperature.So the series resistance seems to be a more valuable parameter to explain the low conductivity of such nanoscale devices.

Conclusion
By studying the electrical characteristics in the saturation regime at room and low temperature (77 K), we confirm the opposite behavior observed in the linear regime between ultrathin body (UTB) and gate recessed channel (GRC) devices having a channel film thickness  SI of 46 nm and 2.2 nm, respectively, and a fixed / ratio.If the apparent conductivity is increased for UTB by lowering the temperature, the opposite effect is observed for GRC.This phenomenon, which is not in accordance with the classical interpretation of the phonon scattering model, is consistently explained by a massive series resistance which is increased at low temperature due to the freeze-out effect of the dopants.By comparison to the linear domain, the use of  and  functions in the saturation regime allows extracting more accurate values of the threshold voltage and mobility parameters for UTB and a consistent series resistance for GRC devices.From a general point of view, such an analysis should be useful to interpret high series resistance effect in new nanoscale devices.

ZFigure 5 :
Figure 5:  function versus  GS for GRC device (/ = 80 m/8 m) at 300 K and 77 K measured in the saturation domain ( DS = 7 V). 1 is extracted from the reciprocal of the  function intercept with vertical axis.
Figure 2: HRTEM image of a gate recessed channel (GRC) device, showing a view of the gate edge region.The silicon GRC film is 2.2 nm thick, while the gate oxide and the buried oxide films are, respectively, 26 nm and 70 nm thick.
2.1.Output Characteristics.The  DS versus  DS output characteristics in saturation mode (ranging from 0 to +3 V for UTB's and from 0 to +8 V for GRC's) were measured for a set of five gate voltage ( GS ) values: 0 V, 1 V, 2 V, 3 V, and 4 V, respectively.In Figures3(a) and 3(

Table 1 :
Summarizing table of the threshold voltage   , the  slope extracted from the  2/3 versus  GS function, the subsequent  parameter, and saturation mobility  0 for UTB device at 300 K and 77 K.  DS = 3 V (saturation domain).

Table 2 :
Summarizing table of the extracted parameters for GRC's having / ratio of 80 m/8 m at  DS = 7 V (saturation) for both 300 K and 77 K. Threshold voltage   is extracted from the  function while the  1 factor is extracted from the  function.The  parameter and the subsequent saturation mobility  0 are extracted from the  function slope.Extracted series resistance  SD is appended accordingly.