# Investigation of the Low-Temperature Behavior of

Authors: A. Karsenty; A. Chelly
Journal: Active and Passive Electronic Components
 (2014)

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## Abstract

The saturation regime of two types of fully depleted (FD) SOI MOSFET devices was 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 sameW/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 were measured at room temperature before cooling down to 77 K. 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.


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## Body

## 1. 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 W/L ratio (80 μm/8 μm) 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 Y-function and Z-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. UsingY-function and complementary Z-function analyses, we could interpret this trend by the existence of very high series resistance values. The Y-function analysis in the saturation regime was recently published [5] at room temperature; however, no complementary analysis of both Y and Z 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.(a) 2-dimensional TCAD process simulation of the UTB device (scales are microns). (b) 2-dimensional TCAD process simulation of the GRC device (scales are microns).
(a)
(b)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. Electrical Characterizations and Analysis

### 2.1. Output Characteristics

TheIDS versus VDS 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 (VGS) values: 0 V, 1 V, 2 V, 3 V, and 4 V, respectively. In Figures 3(a) and 3(b), these characteristics are presented for the UTB device (46 nm channel thick) at 300 K (room temperature) and 77 K (liquid nitrogen), respectively. In Figures 3(c) and 3(d), the same characteristics are presented for the GRC device (2.2 nm channel thick) having the same W/L ratio of 80 μm/8 μm for theses temperatures, respectively. By comparing Figures 3(a) to 3(c), the GRC’s drain saturation current measured at 300 K (for VDS = 7 V) is three orders of magnitude lower than those measured for UTBs at the same temperature (for VDS = 3 V). But at 77 K, by comparing Figures 3(b) to 3(d), the saturation current ratio has almost reached five orders of magnitude. Such a huge current attenuation is not necessarily connected to a dumping of the electron mobility but can be related to the apparition of a huge series resistance during the channel thinning (“gate recessed” process) [6].I
DS
-
V
DS output characteristics measured for UTB (tSI = 46 nm) and GRC (tSI = 2.2 nm), for five VGS values (0 V, 1 V, 2 V, 3 V, and 4 V) and at two temperatures: (a) UTB at T = 300 K, (b) UTB at T = 77 K, (c) GRC at T = 300 K, and (d) GRC at T = 77 K.
(a)
(b)
(c)
(d)


### 2.2.Y-Function Analysis in the Saturation Domain

Ghibaudo et al. [7] introduced first the Y-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],
(1)IDS,sat⁡≡βVGS-VT-αVDS,sat⁡1+θ1VGS-VTVDS,sat⁡(2)With:β=WLCoxμ0.Andμ0 is the low field electron mobility. θ1 is the “extrinsic” mobility degradation factor including the series resistance according to
(3)θ1=θ1,0+RSDβ,whileθ1,0 is the “intrinsic” mobility degradation factor.The saturation voltage can be modeled by [9]
(4)VDS,sat⁡=12αVGS-VT.From Figure3, we can point out the VDS,sat⁡ value for each VGS for a given device and temperature. VT is extracted using the Y versus VGS graph as described below. Using (4) and by measuring VDS,sat⁡ from Figure 3, α is found to be about 0.75 and 0.2 for UTB and GRC, respectively, for both 300 K and 77 K. Since α 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, theY function in the saturation domain can be expressed by
(5)Ysat⁡≡IDS,sat⁡gm,sat⁡with thegm,sat⁡ being the transconductance in the saturation domain.For the sake of model’s simplicity, we assume that, at sufficiently highVGS, θ1 is no longer dependent on VGS, so
(6)∂θ1∂VGS≪θ1VGS-VT.Then, by taking the derivative of (1) and after reduction of the expression (5), the Y function at saturation can be finally described by
(7)Ysat⁡=AVGS-VT3/2θ1VGS-VT+2=AVGS-VTθ1+2/(VGS-VT)(8)With:A≡β4α.We would consider two limit cases.First, ifRSD is negligible, then from (3), θ1 should be also negligible relatively to 2/(VGS-VT), so Y function at saturation can be approximated by
(9)Ysat⁡≈A2VGS-VT3/2.Then theY2/3 function is expected to be linear with VGS in this limit case.Secondly, ifRSD is dominating, then, from (3), θ1 is also dominating relatively to 2/(VGS-VT) and Y function at saturation can be approximated by
(10)Ysat⁡≈Aθ1VGS-VT.Consequently, theY function is expected to be linear with VGS in this limit case as observed for the classic Y function in the linear domain. This feature is useful to extract the VT values. But, unlike classic Y function, the Ysat⁡ expression is now dependent of RSD through θ1.TheY-VGS graphs can be straight forward derived from the IDS-VGS characteristics measured at a given VDS,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),   IDS-VGS and Y-VGS graphs are presented for GRC at 300 K and 77 K, respectively, for W/L = 80 μm/8 μm at a given VDS,sat⁡ (7 V). In Figures 4(a) to 4(d), Y2/3  VGS is also plotted for comparison to the first limit case. We can see there that for UTB the Y2/3 functions are almost more linear than the Y functions, as expected from the first limit case (9), but are significantly bended at lower VGS values at 77 K. For GRC, the Y functions are linear with VGS as expected by the second limit case at high VGS values from (10).I
DS
-
V
GS characteristics measured in the saturation domain and corresponding Y-functions (Y1 and Y2/3) for UTB (tSI = 46 nm) and GRC (tSI = 2.2 nm) taken at VDS = 3 V and VDS = 7 V, respectively: (a) UTB, W/L = 80 μm/8 μm, T = 300 K. (b) UTB, W/L = 80 μm/8 μm, T = 77 K. (c) GRC, W/L = 80 μm/8 μm, T = 300 K. (d) GRC, W/L = 80 μm/8 μm, T = 77 K.
(a)
(b)
(c)
(d)According to (9), we can extract the threshold value VT for UTB from the intercept of the Y2/3 function with the VGS axis. The extracted values of VT, obtained at saturation condition for the different temperatures, are summarized in Table 1. The low field electron mobility μ0 can be extracted directly from the slope parameter b of the Y2/3 function through the β parameter using (2) and (9). Consequently,
(11)μ0=βLWCox,(12)where:β≡4αA=α2b3.
For UTB, the Cox value is 121 nF/cm2 since a 38 nm thick nitride layer is capping the pad oxide in the gate region. The extracted values of μ0 obtained at saturation conditions for the different respective temperatures are summarized in Table 1. As mentioned above, α is taken as 0.75 for UTB.Table 1
Summarizing table of the threshold voltageVT, the b slope extracted from the Y2/3 versus VGS function, the subsequent β parameter, and saturation mobility μ0 for UTB device at 300 K and 77 K. VDS = 3 V (saturation domain).
Temperature [K]
300
77
Shift or ratio 300 K/77 K
V
T [V]
−0.89
−0.40
−0.51
b = slope Y2/3 versus VGS [metric units]
0.0563
0.0774
0.73
β [mS/V] from (12)
1.064
2.775
0.38
μ
0 [cm2/Vs] from (11)
880
2300
0.38


### 2.3.Z-Function Analysis in the Saturation Domain for GRC

If by using (10) the Y function can be used to extract the VT values for GRC, it cannot be used to extract the GRC low field electron mobility μ0 from the slope since A and θ1 parameters are coupled. So it is necessary to introduce a new function that decouples theses parameters, by using the so-called X function [10] defined as follows:
(13)Xsat⁡,GRC≡1gm,sat⁡=θ1A1θ1VGS-VT+1.However, in our case theXsat⁡ function cannot still discriminate between A and θ1. So we will use the Z function defined by the product of X and Y functions as follows:
(14)Zsat⁡,GRC≡Xsat⁡,GRC·Ysat⁡,GRC=IDS,sat⁡gm,sat⁡=1θ1+VGS-VT.Nowθ1 can be extracted from the intercept of the Z function with Z axis as shown in Figure 5 for GRC’s devices having a W/L of 80 μm/8 μm. As assumed in (10) a linear fit is taken for sufficient high VGS values.Figure 5
Z function versus VGS for GRC device (W/L = 80 μm/8 μm) at 300 K and 77 K measured in the saturation domain (VDS = 7 V). θ1 is extracted from the reciprocal of the Z function intercept with vertical axis.Note that if at 300 K, the slope of theZ versus VGS plot is 1 for 80 μm/8 μm, 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 Z versus VGS is not critical issue for the parameter extraction method and is ignored.Finally from theθ1 extraction and using the slope of the Y function, the A and then μ0 parameters for GRC can be extracted using (10) and (2)–(8), respectively, and taking α=0.2. Results are presented in Table 2 for the different temperatures. For GRC the Cox value was (138 nF/cm2) by considering the 26 nm thick gate oxide as seen in Figure 2.Table 2
Summarizing table of the extracted parameters for GRC’s havingW/L ratio of 80 μm/8 μm at VDS = 7 V (saturation) for both 300 K and 77 K. Threshold voltage VT is extracted from the Y function while the θ1 factor is extracted from the Z function. The β parameter and the subsequent saturation mobility μ0 are extracted from the Y function slope. Extracted series resistance RSD is appended accordingly.
Temperature [K]
300
77
Shift or ratio 300 K/77 K
V
T [V] from (10)
−0.55
−0.24
+0.31
|
θ
1
| [V−1] from (14)
7.87
2.65
3
β [μS/V] from (12)
3.84
0.15
26
μ
0 [cm2/Vs] for GRC from (11)
2.78
0.11
26
μ
0 [cm2/Vs] for UTB (given as reference)
880
2300
0.38
R
SD [MΩ] from (15)
2.05
17.4
0.12From (3), we can see that the low values of the β parameter for GRC should be compensated by a very high value of RSD in order to get the high θ1 (≫1 V−1) values as presented in Table 2. Here, the intrinsic parameter θ1,0 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 RSD could be extracted directly from the following expression:
(15)RSD=θ1β.


## 2.1. Output Characteristics

TheIDS versus VDS 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 (VGS) values: 0 V, 1 V, 2 V, 3 V, and 4 V, respectively. In Figures 3(a) and 3(b), these characteristics are presented for the UTB device (46 nm channel thick) at 300 K (room temperature) and 77 K (liquid nitrogen), respectively. In Figures 3(c) and 3(d), the same characteristics are presented for the GRC device (2.2 nm channel thick) having the same W/L ratio of 80 μm/8 μm for theses temperatures, respectively. By comparing Figures 3(a) to 3(c), the GRC’s drain saturation current measured at 300 K (for VDS = 7 V) is three orders of magnitude lower than those measured for UTBs at the same temperature (for VDS = 3 V). But at 77 K, by comparing Figures 3(b) to 3(d), the saturation current ratio has almost reached five orders of magnitude. Such a huge current attenuation is not necessarily connected to a dumping of the electron mobility but can be related to the apparition of a huge series resistance during the channel thinning (“gate recessed” process) [6].I
DS
-
V
DS output characteristics measured for UTB (tSI = 46 nm) and GRC (tSI = 2.2 nm), for five VGS values (0 V, 1 V, 2 V, 3 V, and 4 V) and at two temperatures: (a) UTB at T = 300 K, (b) UTB at T = 77 K, (c) GRC at T = 300 K, and (d) GRC at T = 77 K.
(a)
(b)
(c)
(d)


## 2.2.Y-Function Analysis in the Saturation Domain

Ghibaudo et al. [7] introduced first the Y-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],
(1)IDS,sat⁡≡βVGS-VT-αVDS,sat⁡1+θ1VGS-VTVDS,sat⁡(2)With:β=WLCoxμ0.Andμ0 is the low field electron mobility. θ1 is the “extrinsic” mobility degradation factor including the series resistance according to
(3)θ1=θ1,0+RSDβ,whileθ1,0 is the “intrinsic” mobility degradation factor.The saturation voltage can be modeled by [9]
(4)VDS,sat⁡=12αVGS-VT.From Figure3, we can point out the VDS,sat⁡ value for each VGS for a given device and temperature. VT is extracted using the Y versus VGS graph as described below. Using (4) and by measuring VDS,sat⁡ from Figure 3, α is found to be about 0.75 and 0.2 for UTB and GRC, respectively, for both 300 K and 77 K. Since α 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, theY function in the saturation domain can be expressed by
(5)Ysat⁡≡IDS,sat⁡gm,sat⁡with thegm,sat⁡ being the transconductance in the saturation domain.For the sake of model’s simplicity, we assume that, at sufficiently highVGS, θ1 is no longer dependent on VGS, so
(6)∂θ1∂VGS≪θ1VGS-VT.Then, by taking the derivative of (1) and after reduction of the expression (5), the Y function at saturation can be finally described by
(7)Ysat⁡=AVGS-VT3/2θ1VGS-VT+2=AVGS-VTθ1+2/(VGS-VT)(8)With:A≡β4α.We would consider two limit cases.First, ifRSD is negligible, then from (3), θ1 should be also negligible relatively to 2/(VGS-VT), so Y function at saturation can be approximated by
(9)Ysat⁡≈A2VGS-VT3/2.Then theY2/3 function is expected to be linear with VGS in this limit case.Secondly, ifRSD is dominating, then, from (3), θ1 is also dominating relatively to 2/(VGS-VT) and Y function at saturation can be approximated by
(10)Ysat⁡≈Aθ1VGS-VT.Consequently, theY function is expected to be linear with VGS in this limit case as observed for the classic Y function in the linear domain. This feature is useful to extract the VT values. But, unlike classic Y function, the Ysat⁡ expression is now dependent of RSD through θ1.TheY-VGS graphs can be straight forward derived from the IDS-VGS characteristics measured at a given VDS,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),   IDS-VGS and Y-VGS graphs are presented for GRC at 300 K and 77 K, respectively, for W/L = 80 μm/8 μm at a given VDS,sat⁡ (7 V). In Figures 4(a) to 4(d), Y2/3  VGS is also plotted for comparison to the first limit case. We can see there that for UTB the Y2/3 functions are almost more linear than the Y functions, as expected from the first limit case (9), but are significantly bended at lower VGS values at 77 K. For GRC, the Y functions are linear with VGS as expected by the second limit case at high VGS values from (10).I
DS
-
V
GS characteristics measured in the saturation domain and corresponding Y-functions (Y1 and Y2/3) for UTB (tSI = 46 nm) and GRC (tSI = 2.2 nm) taken at VDS = 3 V and VDS = 7 V, respectively: (a) UTB, W/L = 80 μm/8 μm, T = 300 K. (b) UTB, W/L = 80 μm/8 μm, T = 77 K. (c) GRC, W/L = 80 μm/8 μm, T = 300 K. (d) GRC, W/L = 80 μm/8 μm, T = 77 K.
(a)
(b)
(c)
(d)According to (9), we can extract the threshold value VT for UTB from the intercept of the Y2/3 function with the VGS axis. The extracted values of VT, obtained at saturation condition for the different temperatures, are summarized in Table 1. The low field electron mobility μ0 can be extracted directly from the slope parameter b of the Y2/3 function through the β parameter using (2) and (9). Consequently,
(11)μ0=βLWCox,(12)where:β≡4αA=α2b3.
For UTB, the Cox value is 121 nF/cm2 since a 38 nm thick nitride layer is capping the pad oxide in the gate region. The extracted values of μ0 obtained at saturation conditions for the different respective temperatures are summarized in Table 1. As mentioned above, α is taken as 0.75 for UTB.Table 1
Summarizing table of the threshold voltageVT, the b slope extracted from the Y2/3 versus VGS function, the subsequent β parameter, and saturation mobility μ0 for UTB device at 300 K and 77 K. VDS = 3 V (saturation domain).
Temperature [K]
300
77
Shift or ratio 300 K/77 K
V
T [V]
−0.89
−0.40
−0.51
b = slope Y2/3 versus VGS [metric units]
0.0563
0.0774
0.73
β [mS/V] from (12)
1.064
2.775
0.38
μ
0 [cm2/Vs] from (11)
880
2300
0.38


## 2.3.Z-Function Analysis in the Saturation Domain for GRC

If by using (10) the Y function can be used to extract the VT values for GRC, it cannot be used to extract the GRC low field electron mobility μ0 from the slope since A and θ1 parameters are coupled. So it is necessary to introduce a new function that decouples theses parameters, by using the so-called X function [10] defined as follows:
(13)Xsat⁡,GRC≡1gm,sat⁡=θ1A1θ1VGS-VT+1.However, in our case theXsat⁡ function cannot still discriminate between A and θ1. So we will use the Z function defined by the product of X and Y functions as follows:
(14)Zsat⁡,GRC≡Xsat⁡,GRC·Ysat⁡,GRC=IDS,sat⁡gm,sat⁡=1θ1+VGS-VT.Nowθ1 can be extracted from the intercept of the Z function with Z axis as shown in Figure 5 for GRC’s devices having a W/L of 80 μm/8 μm. As assumed in (10) a linear fit is taken for sufficient high VGS values.Figure 5
Z function versus VGS for GRC device (W/L = 80 μm/8 μm) at 300 K and 77 K measured in the saturation domain (VDS = 7 V). θ1 is extracted from the reciprocal of the Z function intercept with vertical axis.Note that if at 300 K, the slope of theZ versus VGS plot is 1 for 80 μm/8 μm, 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 Z versus VGS is not critical issue for the parameter extraction method and is ignored.Finally from theθ1 extraction and using the slope of the Y function, the A and then μ0 parameters for GRC can be extracted using (10) and (2)–(8), respectively, and taking α=0.2. Results are presented in Table 2 for the different temperatures. For GRC the Cox value was (138 nF/cm2) by considering the 26 nm thick gate oxide as seen in Figure 2.Table 2
Summarizing table of the extracted parameters for GRC’s havingW/L ratio of 80 μm/8 μm at VDS = 7 V (saturation) for both 300 K and 77 K. Threshold voltage VT is extracted from the Y function while the θ1 factor is extracted from the Z function. The β parameter and the subsequent saturation mobility μ0 are extracted from the Y function slope. Extracted series resistance RSD is appended accordingly.
Temperature [K]
300
77
Shift or ratio 300 K/77 K
V
T [V] from (10)
−0.55
−0.24
+0.31
|
θ
1
| [V−1] from (14)
7.87
2.65
3
β [μS/V] from (12)
3.84
0.15
26
μ
0 [cm2/Vs] for GRC from (11)
2.78
0.11
26
μ
0 [cm2/Vs] for UTB (given as reference)
880
2300
0.38
R
SD [MΩ] from (15)
2.05
17.4
0.12From (3), we can see that the low values of the β parameter for GRC should be compensated by a very high value of RSD in order to get the high θ1 (≫1 V−1) values as presented in Table 2. Here, the intrinsic parameter θ1,0 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 RSD could be extracted directly from the following expression:
(15)RSD=θ1β.


## 3. Interpretation and Discussion

### 3.1. Behavior of theIDS-VDS Saturation at Low Temperature

Firstly, from Figure3, we can see that both UTB and GRC are depletion-type devices (normally open, i.e., negative VT for p-type channel) at 300 K and 77 K. From Table 1, the UTB’s threshold voltage VT 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 μ0 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, μ0 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 Y- and Z-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 μ0 values are similar to those expected in similar silicon based devices [14], while, for GRC device, the corresponding μ0 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.


### 3.2. Comparison to Extraction Method in the Linear Regime

TheIDS-VGS behavior at low temperature in the linear regime was studied in a previous publication [4]. Using the Y-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 VT, β parameter, and mobility μ0 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].Table 3
Comparative table of the threshold voltageVT, β parameter, and mobility µ0 extracted from saturation and linear method [4] at 300 K and 77 K, respectively, for UTB device (W/L = 80 μm/8 μm).
Extraction domain
Saturation
Linear
Temperature [K]
300 K
77
Shift or ratio 300 K/77 K
300
77
Shift or ratio 300 K/77 K
V
T [V]
−0.89
−0.40
−0.51
−0.65
+0.26
−0.91
β [mS/V]
1.064
2.775
0.38
1.47
2.41
0.61
μ
0 [cm2/Vs]
880
2300
0.38
1210
2000
0.61In Table4, threshold voltage VT, β parameter, mobility μ0, and RSD extracted from saturation and linear domain at 300 K and 77 K, respectively, for GRC are compared.Table 4
Comparative table of threshold voltageVT, β, and mobility μ0 extracted from saturation and linear domain [4] at 300 K and 77 K, respectively, for GRC device (W/L = 80 μm/8 μm).
Extraction domain
Saturation
Linear
Temperature [K]
300
77
Shift or ratio  300 K/77 K
300
77
Shift or ratio 300 K/77 K
V
T [V]
−0.55
−0.24
−0.31
−2.35
−2.60
+0.25
β [μS/V]
3.84
0.15
26
0.31
0.007
44
μ
0 [cm2/Vs]
2.78
0.11
26
0.222
0.005
44
R
SD [MΩ]
2.05
17.4
0.12
1.73
8.93
0.19Unlike 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 RSD 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.


### 3.3. Extraction of the Effective Mobility Using ConventionalC-V 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 densityQinv and finally the effective electron mobility μeff according to the respective definitions [18]:
(16)Qinv≡1WL∫-∞VGDSCpdVGDS~1WLCoxVGDS-VT~29nC/cm2(17)μeff≡gdL/WQinv=0.074cm2/Vs,
where Cox is oxide capacitance measured as the step of the C-V plot at VGDS = 0 V (inversion zone) according to Figure 6, while the threshold voltage VT is taken as −0.25 V and is matching the corresponding value in Table 4 at 77 K. The channel conductance gd is 21 nS as measured from the slope of the IDS-VDS plot at VGS = 0 V in Figure 3(d).Figure 6
Parallel modeCP-VGDS characteristics for GRC with 2.2 nm channel film thickness. The device has the same gate W×L = 80 × 8 μm2 = 6.4 × 10−6 cm2. The capacitance CP was measured at 100 kHz. Drain and source are shorted.The effective electron mobility (0.074 cm2/Vs) is found close to the corresponding value in Table 4 at 77 K (0.11 cm2/Vs) which corroborates our extraction method based on Z-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.


## 3.1. Behavior of theIDS-VDS Saturation at Low Temperature

Firstly, from Figure3, we can see that both UTB and GRC are depletion-type devices (normally open, i.e., negative VT for p-type channel) at 300 K and 77 K. From Table 1, the UTB’s threshold voltage VT 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 μ0 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, μ0 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 Y- and Z-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 μ0 values are similar to those expected in similar silicon based devices [14], while, for GRC device, the corresponding μ0 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.


## 3.2. Comparison to Extraction Method in the Linear Regime

TheIDS-VGS behavior at low temperature in the linear regime was studied in a previous publication [4]. Using the Y-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 VT, β parameter, and mobility μ0 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].Table 3
Comparative table of the threshold voltageVT, β parameter, and mobility µ0 extracted from saturation and linear method [4] at 300 K and 77 K, respectively, for UTB device (W/L = 80 μm/8 μm).
Extraction domain
Saturation
Linear
Temperature [K]
300 K
77
Shift or ratio 300 K/77 K
300
77
Shift or ratio 300 K/77 K
V
T [V]
−0.89
−0.40
−0.51
−0.65
+0.26
−0.91
β [mS/V]
1.064
2.775
0.38
1.47
2.41
0.61
μ
0 [cm2/Vs]
880
2300
0.38
1210
2000
0.61In Table4, threshold voltage VT, β parameter, mobility μ0, and RSD extracted from saturation and linear domain at 300 K and 77 K, respectively, for GRC are compared.Table 4
Comparative table of threshold voltageVT, β, and mobility μ0 extracted from saturation and linear domain [4] at 300 K and 77 K, respectively, for GRC device (W/L = 80 μm/8 μm).
Extraction domain
Saturation
Linear
Temperature [K]
300
77
Shift or ratio  300 K/77 K
300
77
Shift or ratio 300 K/77 K
V
T [V]
−0.55
−0.24
−0.31
−2.35
−2.60
+0.25
β [μS/V]
3.84
0.15
26
0.31
0.007
44
μ
0 [cm2/Vs]
2.78
0.11
26
0.222
0.005
44
R
SD [MΩ]
2.05
17.4
0.12
1.73
8.93
0.19Unlike 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 RSD 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.


## 3.3. Extraction of the Effective Mobility Using ConventionalC-V 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 densityQinv and finally the effective electron mobility μeff according to the respective definitions [18]:
(16)Qinv≡1WL∫-∞VGDSCpdVGDS~1WLCoxVGDS-VT~29nC/cm2(17)μeff≡gdL/WQinv=0.074cm2/Vs,
where Cox is oxide capacitance measured as the step of the C-V plot at VGDS = 0 V (inversion zone) according to Figure 6, while the threshold voltage VT is taken as −0.25 V and is matching the corresponding value in Table 4 at 77 K. The channel conductance gd is 21 nS as measured from the slope of the IDS-VDS plot at VGS = 0 V in Figure 3(d).Figure 6
Parallel modeCP-VGDS characteristics for GRC with 2.2 nm channel film thickness. The device has the same gate W×L = 80 × 8 μm2 = 6.4 × 10−6 cm2. The capacitance CP was measured at 100 kHz. Drain and source are shorted.The effective electron mobility (0.074 cm2/Vs) is found close to the corresponding value in Table 4 at 77 K (0.11 cm2/Vs) which corroborates our extraction method based on Z-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.


## 4. 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 thicknesstSI of 46 nm and 2.2 nm, respectively, and a fixed W/L 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 Y and Z 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.



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*Source: 782417-2014-12-15.xml*