Oxide thickness-dependent effects of source doping profile on the performance of single- and double-gate tunnel field-effect transistors

Superlattices and Microstructures 102 (2017) 284e299

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Oxide thickness-dependent effects of source doping profile on the performance of single- and double-gate tunnel field-effect transistors Nguyen Dang Chien a, *, Chun-Hsing Shih b a b

Faculty of Physics, University of Dalat, Lam Dong 671460, Viet Nam Department of Electrical Engineering, National Chi Nan University, Nantou 54561, Taiwan

a r t i c l e i n f o

a b s t r a c t

Article history: Received 22 September 2016 Received in revised form 25 December 2016 Accepted 26 December 2016 Available online 26 December 2016

Operated by the band-to-band tunneling at the source-channel junction, the source engineering has been considered as an efficient approach to enhance the performance of tunnel field-effect transistors (TFETs). In this paper, we report a new feature that the effects of source doping profile on the performance of single- and double-gate germanium TFETs depend on equivalent oxide thickness (EOT). Based on the numerical simulations, it is shown that the effect of source concentration on the on-current is stronger with decreasing the EOT, particularly in the double-gate configuration due to the higher gate control capability. Importantly, when the EOT is decreased below a certain value, abrupt source-channel junctions are not only unnecessary, but gradual source doping profiles even improve the performance of TFETs because of the increase in vertical tunneling generation. With the continuous trend of scaling EOT, the oxide thickness-dependent effects of source doping profile should be properly considered in designing TFET devices. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Source doping effects EOT scaling Band-to-band tunneling Tunnel field-effect transistor Low-bandgap TFET

1. Introduction In the era of portable electronic devices, high energy efficiency is one of the most important requirements for a transistor to be used as a fundamental component in integrated circuits. A highly energy-efficient transistor is necessary not only to ensure the low-power consumption but also to resolve the power density problem of highly-scaled integrated circuits [1,2]. The essential advantage that makes tunnel field-effect transistors (TFETs) suitable for low-power applications is the breakthrough in the subthreshold swing limit of 60 mV/decade which is the physical limit of traditional metal-oxidesemiconductor field-effect transistors (MOSFETs) [3,4]. The steep on-off switching of TFETs allows of scaling down the supply voltage and associated dynamic power consumption. In order to establish the conduction state, however, valence electrons in TFETs have to tunnel through an energy barrier formed by the forbidden gap of semiconductors to become free carriers on the conduction band [3,5]. Since the probability of band-to-band tunneling (BTBT) is relatively low, TFET devices suffer from low on-current which is the most difficulty in applying them to practical uses [5,6]. Many relevant techniques based on minimizing the tunnel barrier have been proposed to ameliorate the on-current, such as device parameter optimizations [7,8], low-bandgap materials [9,10] and advanced TFET structures [11,12]. The excellent combinations of those techniques have also been considered to boost the on-current most effectively [13,14].

* Corresponding author. E-mail address: [email protected] (N.D. Chien). http://dx.doi.org/10.1016/j.spmi.2016.12.048 0749-6036/© 2016 Elsevier Ltd. All rights reserved.

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For a given TFET structure, in general principle, the on-current is usually only improved by shortening the tunneling path of electrons at on-state to increase the tunneling probability [7]. Since the on-state tunneling is generated at the sourcechannel junction, there are two basic factors that mainly determine the tunnel barrier width in TFETs, including the source doping profile and equivalent oxide thickness (EOT). The source profile composed of doping concentration and gradient directly decides the tunnel width [8,15], whereas the EOT indirectly affects the tunnel width through the gatecontrolled field [7]. Both theoretical and experimental researches have shown that the on-current is increased with increasing the source concentration because of the narrowed tunnel width [9,15]. A similar conclusion has also been made for the effect of source junction abruptness, i.e., the steeper the lateral doping gradient of source, the higher the on-current is [16,17]. For the effect of EOT, experimental results have confirmed the theoretical and numerical predictions that decreasing EOT helps to significantly increase the on-current because a higher gate control capability results in a smaller tunnel width [18]. Those conclusions have been demonstrated to be appropriate for both homo- and hetero-junction, high- and lowbandgap, single- and double-gate TFETs [8,9,15e18]. It is important to note that the conclusions on the effects of source doping profile do not depend on the EOT because the roles of source doping profile and EOT have been examined independently. In other words, the EOT was kept constant when studying the effects of source doping profile. However, while the tunnel width in TFETs is directly governed by the source doping profile, the EOT also concurrently determines the tunnel width. Therefore, the effects of source doping profile probably depend on the EOT. In this paper, the dependence of the source profile effects on the EOT is numerically examined in single- and double-gate TFETs by using two-dimensional device simulations [19]. The physics of the oxide thickness-dependent effects is properly clarified to provide a comprehensive understanding on the mutual roles of the source profile and EOT in designing TFET devices. Both single- and double-gate structures are investigated because the control capability of the gate to the channel depends considerably on the gate structure which exhibits a role similar to the EOT in term of determining the gate control capability. Furthermore, the investigations of single- and double-gate TFETs are presented in parallel for convenient comparisons. The paper consists of five sections, including the Introduction (section 1) and the Conclusion (section 5). Section 2 first describes the device structures, physical models used in the simulations and then preliminarily inspects the role of EOT in the different TFET structures. The effects of source doping concentration on the performance of TFETs with a wide range of EOT are appropriately investigated in section 3, whereas section 4 is devoted to proper discussions on the oxide thicknessdependent effects of source doping gradient. 2. Device structures and physical models Fig. 1 shows the schematic views of homojunction Ge TFETs with single- and double-gate structures. Since using lowbandgap semiconductors has been realized as the most effective technique to enhance the on-current of TFETs, lowbandgap Ge was adopted for the practical significance of the investigations. To exactly filter out the mutual effects of source doping profile and EOT, a typical homojunction structure was chosen to exclude the influences of material and structure parameters. The single- and double-gate structures were investigated in parallel because their different gate control capabilities may lead to the significantly different roles of the source profile and EOT. A long n-channel with a 150 nm length and 1017 cm
3 concentration was utilized to avoid short-channel effects which may cause difficulties in studying the impacts of the source profile and EOT on the TFET performance. The drain of TFETs was lightly doped with a donor concentration of 5  1018 cm
3 for minimizing the ambipolar off-leakage [15]. The EOT of high-k gate-dielectric HfO2 and the source profile including doping concentration and gradient were appropriately altered for studying purposes. The dielectric constant was varied to change the EOT while the physical oxide thickness was intentionally fixed at 3 nm to retain the identical fringing

(a) Single-Gate TFET Source

p

Gate

i

(b) Double-Gate TFET Drain

n

Source

p

Gate

i

Fig. 1. Schematic structures of (a) single-gate (SG) and (b) double-gate (DG) TFETs using low-bandgap germanium.

Drain

n

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field effect [20]. The doping gradient determining the source junction abruptness of Gaussian doping profile was specified by the diffusion characteristic length (X.CHAR) defined as the length for the dopant concentration to degrade by the factor 1/e [19]. To concentrate on the EOT and source profile effects, a specific length of 50 nm was designed for the source and drain of both single- and double-gate TFETs to maintain similar source/drain series resistances in the two device structures. The gate workfunction was set at 4.2 eV in all simulations. For double-gate TFETs, a 10 nm body thickness was used to maximize the tunneling current density [21]. Two-dimensional device simulations [19] were carried out with calibrated models and parameters to analyze the electrical characteristics of TFETs and provide associated physical explanations. For relaxed germanium, the direct BTBT contribution is much greater than the indirect BTBT component [22]. However, the indirect tunneling is triggered earlier since the indirect bandgap is smaller than the direct one by 0.14 eV [23]. This premature onset of indirect tunneling can affect the subthreshold region and the drive current of TFETs. In this study, therefore, both the direct and indirect tunneling generations in the framework of the nonlocal BTBT approach based on the Kane model are considered to determine the total tunneling current in TFETs as [5]:

GBTBT ¼ A

xg 1=2

Eg

3=2

exp


B

Eg

! ;

x

(1)

Drain Current (A/µ m)

where Eg is the semiconductor bandgap, x is the nonlocal electric field at tunneling junction, g ¼ 2 for direct tunneling and g ¼ 2:5 for indirect tunneling. Manually modified parameters A and B depend on electron and hole effective masses of semiconductors. The values of A, B have been calculated to get 6.6  1015 eV1/2/cm s V2, 11.5  106 V/cm eV3/2 for indirect tunneling and 1.6  1020 eV1/2/cm s V2, 9.6  106 V/cm eV3/2 for direct tunneling, respectively. Because the BTBT generation is much more sensitive to B than to A, one usually uses B to be calibrated with experimental data [24,25]. With considering the effect of heavy-doping bandgap narrowing, the calculated parameter B for the direct tunneling is very close to the experimental value of 9.0  106 V/cm eV3/2 [24]. A small deviation of about 5% is mainly attributed to the uncertainty of the effective masses used. Since tunneling probability is sensitive to effective bandgap, the quantum mechanical effect due to electron/hole confinement in the narrow structure of double-gate TFETs [26] was suitably incorporated. For more realistic simulations, the Fermi-Dirac distribution and Shockley-Read-Hall recombination were also enabled. Because this study focuses mainly on the on-state tunneling determined by the source profile and EOT, the simulations did not include the trap-assisted tunneling which only affects the subthreshold region [27]. Moreover, the trap density is process sensitive and the trap-assisted tunneling shows a less impact on the performance of low-bandgap TFETs [28]. Before going to detailed investigations on the EOT-dependent effects of source doping profile on the TFET performance, we first preliminarily inspect the roles of the EOT in determining the performance of single- and double-gate TFETs. Up to now, it is accepted that scaling down the EOT is always helpful in increasing the on-current regardless of the source doping profile and device structure because of the enhanced gate control. To verify the appropriateness of this long-established conclusion, Fig. 2 shows the current-voltage characteristics of single- and double-gate TFETs with different EOTs. Instead of using a heavily-doped source as usual, a medium source concentration (Na) of 1019 cm
3 is exampled. The direct tunneling component is also plotted to examine the different contributions of direct and indirect tunneling to the total current. Firstly, it is seen that the background off-current produced by the drift motion of minority carriers is lower in the double-gate than in

10

-5

10

-7

10

-9

Solid Circle: SG Total (Direct + Indirect) Open Circle: DG Solid Line: Direct

EOT = 0.3 nm

Ge TFETs -11

10

3 nm Na = 1019 cm-3 X.CHAR = 2 nm Vds = 0.7 V

-13

10

-15

10

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Gate-to-Source Voltage (V) Fig. 2. Current-voltage characteristics of single- and double-gate Ge TFETs with different equivalent oxide thicknesses (EOT).

SG-TFETs -5

10

Increase Na (1018 cm-3) (2, 5, 10, 20, 50, 100)

Drain Current (A/µm)

Drain Current (A/µm)

10-5

10-3

(a)

-7

10

10-9

10-11

10-13 -0.2

EOT = 1 nm X.CHAR = 2 nm Vds = 0.7 V

0.0

0.2

0.4

0.6

0.8

Gate-to-Source Voltage (V)

1.0

1.2

(b)

DG-TFETs

Increase Na (10 18 cm-3) (2, 5, 10, 20, 50, 100)

10-7 10-9 10-11 EOT = 1 nm X.CHAR = 2 nm Vds = 0.7 V

10-13 10-15 -0.2

0.0

0.2

0.4

0.6

0.8

Gate-to-Source Voltage (V)

Fig. 3. Current-voltage curves of (a) single-gate and (b) double-gate TFETs with various source doping concentrations (Na).

1.0

1.2

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10-3

287

288

(a)

SG-TFETs

10-5 10-6 10-7 10

10-9

Decrease EOT (nm) (5, 3, 2, 1, 0.5, 0.3)

1

X.CHAR = 2 nm Vds = 0.7 V Vgs - Vonset = 1 V

10

100 18

-3

Source Concentration (10 cm )

On-Current (A/µm)

On-Current (A/µm)

10

-8

(b)

10-4

-4

DG-TFETs

10-5 10-6 10-7

Decrease EOT (nm) (5, 3, 2, 1, 0.5, 0.3)

10-8 10-9 10-10

X.CHAR = 2 nm Vds = 0.7 V Vgs - Vonset = 1 V

10-11 10-12

1

10

100 18

-3

Source Concentration (10 cm )

Fig. 4. On-current versus source concentration of (a) single- and (b) double-gate TFETs with various equivalent oxide thicknesses.

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10-3

10-3

10-3 (a)

SG-TFETs

On-Current (A/µm)

On-Current (A/µm)

X.CHAR = 2 nm Vds = 0.7 V Vgs - Vonset = 1 V

10-5 10-6 -7

10

Increase Na (1018 cm-3) (2, 5, 10, 20, 50, 100)

-8

10

10-9

0

1

2

10-5 10-6 10-7 10-8

Optimal EOT decreased

-9

10

10-10

X.CHAR = 2 nm Vds = 0.7 V Vgs - Vonset = 1 V

-11

10

3

4

Equivalent Oxide Thickness (nm)

5

(b)

DG-TFETs

10-4

10-4

10-12

0

1

2

Increase Na (1018 cm-3) (2, 5, 10, 20, 50, 100)

3

4

Equivalent Oxide Thickness (nm)

Fig. 5. On-current versus equivalent oxide thickness of (a) single- and (b) double-gate TFETs with various source concentrations.

5

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10-3

289

290

1.0

1.0

(a)

DG TFETs

Source

Electron Energy (eV)

0.5

On-State (Vgs - Vonset = 1 V)

0.0

-0.5 : EOT = 5 nm : EOT = 0.3 nm

-1.0

-1.5 -30

Channel

Na = 5×1018 cm-3 X.CHAR = 2 nm Vds = 0.7 V

-20

-10

0.5

10

20

30

On-State

Source

(Vgs - Vonset = 1 V)

0.0

-0.5

-1.0

-1.5 0

(b)

: EOT = 5 nm : EOT = 0.3 nm

Na = 5×1018 cm-3 X.CHAR = 2 nm Vds = 0.7 V

-30

-20

Distance to Source (nm)

Channel

-10

0

10

20

Distance to Source (nm)

1.0

(c)

Electron Energy (eV)

DG TFETs 0.5

Source

0.0

On-State (Vgs - Vonset = 1 V)

-0.5

-1.0

: EOT = 5 nm : EOT = 0.3 nm 19

-1.5 -30

Channel

-3

Na = 5×10 cm X.CHAR = 2 nm Vds = 0.7 V

-20

-10

0

10

20

Distance to Source (nm) Fig. 6. Energy-band diagrams at on-state of (a) single-gate and (b)e(c) double-gate TFETs with different source concentrations and equivalent oxide thicknesses. The two-arrow lines represent the tunnel barrier widths.

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Electron Energy (eV)

SG TFETs

10-2 (a)

(b)

SG-TFETs

-4

10

Drain Current (A/µm)

Drain Current (A/µm)

10

10-6

Increase X.CHAR (0, 4, 8, 12, 16 nm)

-8

10

EOT = 2 nm

10-10 10-12 10-14 -0.2

SG-TFETs

-4

Na = 10 20 cm-3 Vds = 0.7 V

0.0

0.2

0.4

0.6

0.8

Gate-to-Source Voltage (V)

1.0

1.2

10-6 Increase X.CHAR (0, 4, 8, 12 , 16 nm)

-8

10

EOT = 0.5 nm

10-10 10-12 10-14 -0.2

Na = 1020 cm-3 Vds = 0.7 V

0.0

0.2

0.4

0.6

0.8

1.0

Gate-to-Source Voltage (V)

Fig. 7. Current-voltage curves of single-gate TFETs using (a) 2 nm and (b) 0.5 nm equivalent oxide thicknesses with various diffusion characteristic lengths (X.CHAR).

1.2

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10-2

291

292

A

0.0 -0.5 On-State

-1.0

(Vgs - Vonset = 1 V)

-1.5 -20

EOT = 2 nm Na = 1020 cm-3 Vds = 0.7 V

-10

0

10

20

30

40

Distance to Source (nm)

50

60

32 29 22 18 15 0

0.5 (i)

0.0

0 BTBT Rate

: X.CHAR = 0 nm : X.CHAR = 16 nm

(b)

Gate [Log (cm-3s-1)]

Source

0.5

Electron Energy (eV)

Electron Energy (eV)

SG TFETs

(a)

SG TFETs

10 20 30 40

On-State

0 10

(ii)

-0.5

20 30

Á

-1.0

-10

-1.5 -18

(Vgs - Vonset = 1 V)

0

40 20

10

30

40

50

(i)

: X.CHAR = 0 nm

(ii)

: X.CHAR = 16 nm

-12

-6

EOT = 0.5 nm Na = 1020 cm-3 Vds = 0.7 V

0

6

12

18

Distance to Gate-Oxide (nm)

Fig. 8. (a) Lateral and (b) vertical energy-band diagrams at on-state of single-gate TFETs with different characteristic lengths. The inset in (b) shows the BTBT generation rates of the TFETs at on-state. The vertical band diagrams in (b) are extracted along the cut-line AA0 .

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1.0

1.0

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the single-gate TFETs because the effective bandgap of Ge is larger due to the stronger quantum confinement effect in the double-gate than in the single-gate structure. The indirect tunneling only affects the low-current region of subthreshold regime. Decreasing the EOT makes the difference in the onset between the direct and indirect tunneling increased because the indirect tunneling is triggered earlier in the thinner EOT TFETs due to the stronger gate control. For the investigated structures of point-tunneling TFETs, this onset difference is close to the difference of bandgap voltages (0.14 V) when the EOT approaches to zero [29]. For the single-gate TFETs, the on-current increases largely with decreasing the EOT. Specifically, the on-current increases two orders of magnitude by scaling down the EOT 10 times from 3 to 0.3 nm. For the double-gate TFETs, on the contrary, the on-current is degraded with decreasing the EOT. This on-current lowering due to the decrease of EOT in the double-gate TFETs is an unusual effect which has not been observed yet. The only difference in the investigation that can observe this new feature is the use of the relatively low source concentration. For this reason, the role of EOT has to be adequately considered when designing the source doping profile. In other words, the effects of source doping profile and EOT are no longer independent, but depend on each other. The dependence on one another of these two effects is understandable if we note that the on-state tunneling in TFETs always occurs at the source-channel junction and right beneath the gate-oxide layer. In this region, both the source doping profile and EOT jointly determine the tunnel width. Therefore, the joint effects of EOT and source doping profile on the tunneling current should exist in TFET devices. Furthermore, those effects are probably different in single- and double-gate structures. In subsequent sections, therefore, the effects of source doping concentration and gradient on the performance of single- and double-gate TFETs are investigated in detail to show their dependences on the EOT.

3. Effects of source doping concentration Since the on-state tunneling occurs at the source-channel junction, the source doping concentration plays an important role in determining the on-current of TFETs. At low doping concentrations, the on-current increases exponentially with increasing the source concentration. At high doping levels, the on-current starts to saturate [15]. The increase in the oncurrent when the source concentration increases is due to two main reasons: (1) the source depletion reduction [30] and (2) the band gap narrowing [15]. The saturation of on-current is observed when the source Fermi level lies below the shortest tunneling path [31]. The band gap narrowing influencing tunnel barrier height and the source Fermi energy determining tunneling electron number are defined solely by the doping concentration. However, the source depletion width is considerably determined by the channel potential profile which is controlled by the gate field through the gate-oxide layer. The smaller the source depletion width, the higher the source-side electric field and the narrower the tunnel width are. In this section, therefore, we show that the effects of source concentration on the device performance of TFETs depend appreciably on the EOT. Fig. 3 depicts the gate transfer characteristics for uniform Ge TFETs with single- and double-gate structures as a function of source doping concentration. To study the effects of the doping concentration, the diffusion characteristic length and EOT are fixed at reasonable values of 2 nm and 1 nm, respectively. It should be noted that since the switching mechanism of investigated TFETs is based on modulating the tunnel barrier width, their on-off characteristics are basically not influenced by the band tailing effect even with as high concentration as 1020 cm
3 [32]. Generally, the on-current increases significantly with increasing the source concentration in both the single- and double-gate configurations. Similar to previous predictions, the increase in the on-current is fast at low doping concentrations, but weaken at high doping levels. Notably, with the same range of source concentrations, the on-current of the double-gate TFETs increases much more quickly than that of the single-

(a)

10-3

DG-TFETs

10-5

Drain Current (A/µm)

Drain Current (A/µm)

10-3

10-7 Increase X.CHAR (0, 4, 8, 12, 16 nm)

10-9 10-11

EOT = 2 nm

10-13 10-15 -0.2

Na = 1020 cm-3 Vds = 0.7 V

0.0

0.2

0.4

0.6

0.8

Gate-to-Source Voltage (V)

1.0

1.2

(b)

DG-TFETs

10-5 Increase X.CHAR (0, 4, 8, 12 , 16 nm)

10-7 10-9

EOT = 0.5 nm

10-11 10-13 10-15 -0.2

Na = 1020 cm-3 Vds = 0.7 V

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Gate-to-Source Voltage (V)

Fig. 9. Current-voltage curves of double-gate TFETs using (a) 2 nm and (b) 0.5 nm equivalent oxide thicknesses with various characteristic lengths.

294

0.3 nm

10

0.5 nm

10-4

1 nm

10-5

2 nm

10-6

3 nm

10

0

2

4

6

8

10

X.CHAR (nm)

12

14

0.3 nm

10-4

0.5 nm

10-5

1 nm 2 nm

10-6

3 nm

10

EOT = 5 nm

(a)

DG-TFETs

-7

10-7 -8

Na = 1020 cm-3 Vds = 0.7 V Vgs - Vonset = 1 V

-3

On-Current (A/µm)

10-3

On-Current (A/µm)

SG-TFETs

Na = 1020 cm-3 Vds = 0.7 V Vgs - Vonset = 1 V

10-8

16

EOT = 5 nm

(b)

0

2

4

6

8

10

X.CHAR (nm)

Fig. 10. On-current versus characteristic length of (a) single- and (b) double-gate TFETs with various equivalent oxide thicknesses.

12

14

16

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10-2

10-2

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gate counterparts, namely six compared with three orders of magnitude respectively. The stronger dependence of the oncurrent on the source concentration is obviously ascribed to the higher gate control capability in the double-gate TFETs. Particularly, the wide range of the on-currents in the double-gate TFETs is mostly due to the extremely low on-currents at the low concentrations. The on-current of the single-gate TFETs starts increasing from ~10
7 A/mm while that of the double-gate devices is ~10
10 A/mm at the source concentration of 2  1018 cm
3. At this low concentration, the on-current of the doublegate TFET is dramatically lower than that of the single-gate TFET even though the gate control capability is higher in the double-gate than in the single-gate structure. It is inferred that the effect of source concentration on the TFET performance depends considerably on the gate control capability. Since the EOT determines the gate control capability, the source concentration effects should also depend on the EOT. To investigate the oxide thickness-dependent effects of source concentration, Fig. 4 shows the on-currents versus source concentration of single- and double-gate TFETs with various EOTs. For fair comparisons, the on-current is determined at the gate voltage of 1 V higher than the onset voltage (Vonset) which is defined as the gate voltage when the band-to-band tunneling begins. Firstly, the degradation of on-current due to the quantum confinement in the double-gate structure can be realized by comparing the on-currents of single- and double-gate TFETs for the case of 1020 cm
3 concentration and 0.3 nm EOT. The fact that the on-current of the double-gate TFET (0.16 mA/mm) is slightly lower than that of the single-gate TFET (0.19 mA/mm) can only be attributed to quantum confinement effects. This is because both the highest doping concentration and the thinnest EOT show positive effects on the on-currents in the two device structures so that without quantum confinement effects, the on-current of the double-gate TFET would be considerably higher than that of the single-gate counterpart. It is noted that the quantum confinement degrades the on-current by two effects including (1) the increase of effective bandgap and (2) the lowering of tunneling window. For TFETs based on lateral tunneling, the latter effect is negligible because the decrease of the height of lateral tunneling window caused by the former effect is extremely small compared with the window height. Therefore, the on-current degradation due to the quantum confinement effects is almost similar for every EOT and doping concentration. The weakening of the increase in the on-current is clearly observed at high doping levels in both the single- and double-gate TFETs for every EOTs. For the single-gate TFETs, the rates of increasing the on-current are rather similar, except for the sub-1 nm EOTs which the increase in the on-current is slightly more pronounced. It is inferred that the rate of increasing the on-current is higher with enhanced gate control capability. Even so, the effect of source concentration on the on-current of single-gate TFETs does not depend largely on the EOT. With a given EOT, the oncurrent of the double-gate TFETs is much more dependent on the source concentration than that of the single-gate devices. Decreasing the EOT makes the on-current increased more strongly. Both using the double-gate structure and scaling the EOT result in boosting the rate of increasing the on-current because they all enhance the gate control capability. Therefore, the effect of source concentration in double-gate TFETs depends strongly on the EOT. With the continuous trend of scaling EOT, the design of source concentration becomes a more important factor to enhance the on-current of double-gate TFETs effectively. To find out a guideline for designing the source concentration to optimize the TFET performance when considering the scaling of gate-oxide thickness, Fig. 5 plots the on-currents as a function of EOT for the different source concentrations of the single- and double-gate TFETs. Overall, scaling EOT is more efficient in improving the on-current of the single-gate TFETs compared with the double-gate TFETs. For the single-gate TFETs, the decrease in the EOT is always useful in increasing the oncurrent irrespective of the source concentration. For the double-gate TFETs, however, there are the optimal values of EOT that make the on-currents maximized. For a given source concentration, decreasing the EOT beyond the optimal value results in degrading the on-current. Noticeably, the optimal point of EOT shifts to the left when the source concentration increases as shown by the dash-dot arrow in Fig. 5(b). The optimal value of EOT approaches to zero when the source concentration reaches to 5  1019 cm
3. In addition, scaling EOT will be more beneficial in enhancing the on-current if a higher source concentration is applied. To get the high benefit of scaling EOT, even down to very small thicknesses, the source of double-gate TFETs should be heavily doped, namely greater than 5  1019 cm
3. The physical explanations for the oxide thickness-dependent effects of source doping concentration can be provided by the energy-band diagrams at on-state sketched in Fig. 6 for single- and double-gate TFETs with different EOTs. For the singlegate TFETs as shown in Fig. 6(a), the gate with the thinner EOT of 0.3 nm controls the channel potential more efficiently to pull the channel energy bands lower and flatter. By the coupling between the channel potential profile and the source depletion, the tunneling path is shorter and thus the on-current is higher in the thinner gate-oxide TFET. Because this mechanism holds for all source concentrations, the effect of source concentration is rather independent of the EOT. For the double-gate TFETs, the energy-band diagrams are plotted separately for two values of source concentrations, 5  1018 cm
3 in Fig. 6(b) and 5  1019 cm
3 in Fig. 6(c). For the low source concentration of 5  1018 cm
3, although the channel energy bands are still lower and flatter in the case of 0.3 nm EOT, the extremely higher gate control capability due to the thinner EOT associated with the double-gate structure results in a much larger depletion width of the source. Consequently, the source-side electric field is smaller, the tunneling path is longer and the on-current is lower in the EOT ¼ 0.3 nm than in the EOT ¼ 5 nm TFET. For the source concentration of 5  1019 cm
3, although the gate control capabilities of the TFETs are unchanged, the high doping concentration of the source inhibits the extension of the depletion width even with the EOT of 0.3 nm. Once the source depletion width is relatively limited, the role of low and flat channel energy bands is dominant in determining the tunneling path at the source-channel junction through the field continuity at the junction edge [33]. As a result, the tunneling path is shorter and hence the on-current is higher with the EOT of 0.3 nm than with that of 5 nm. Because the role of gate control

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capability is different in double-gate TFETs with different source concentrations, the effect of source concentration on the oncurrent depends on the EOT which determines the gate control capability. 4. Effects of source doping gradient Together with the doping concentration of source, its doping gradient is also an important factor in determining the TFET on-current. The doping gradient affects the tunnel width through determining the source depletion width. A narrower depletion width of source further increases the band bending at source-channel junction, which results in a smaller tunnel width and thus higher on-current regardless of EOT [8,17]. In previous works, however, the lateral tunneling dominates the total current because the vertical tunneling is non-observable due to either (1) large EOT [34], (2) high energy bandgap associated with ultra-thin body [16], or (3) limited doping gradient and gate voltage [35]. In this section, we show that the effect of source doping gradient on the on-current of TFETs depends significantly on the EOT. To obtain a high on-current at very thin EOTs as suggested in the previous section, a heavily-doped source of 1020 cm
3 is employed for both single- and double-gate TFETs. We first explore the EOT dependence of the doping gradient effect in single-gate TFETs by depicting their input characteristics in Fig. 7 as a function of the characteristic length for different EOTs. For the large EOT of 2 nm, the on-current is increased with decreasing the characteristic length, which is similar to previous reports on the effect of source doping gradient. An opposite trend observed in Fig. 7(b) for the small EOT of 0.5 nm is that the on-current is decreased with decreasing the characteristic length. Remarkably, there is a turning point of gate voltage around 0.6 V at which the drain currents of all TFETs are equal. At gate voltages lower than the turning point voltage, the drain current of larger X.CHAR TFETs is lower than that of smaller X.CHAR TFETs. At gate voltages higher than the turning point voltage, however, the drain current is higher in the larger X.CHAR than in the smaller X.CHAR TFETs. This is a remarkable effect of the doping gradient that has not been observed before. This new effect cannot be explained as usual by the variation of the lateral tunnel width at the sourcechannel junction, but has to be related to the role of the gate-oxide thickness. To adequately elucidate the physical mechanisms of the doping gradient effect in the single-gate TFETs, Fig. 8(a) shows the lateral energy-band diagrams of the EOT ¼ 2 nm TFETs, whereas Fig. 8(b) shows the distributions of the BTBT generations and the vertical energy-band diagrams of the EOT ¼ 0.5 nm TFETs with different characteristic lengths. In Fig. 8(a), the lateral tunnel width at on-state is thinner in the X.CHAR ¼ 0 nm than in the X.CHAR ¼ 16 nm TFET. Therefore, the on-current of the abrupt junction TFET is higher than that of the gradual junction TFET. For the EOT of 0.5 nm, the lateral tunnel width of the X.CHAR ¼ 0 nm TFET is still smaller than that of the X.CHAR ¼ 16 nm TFET because their doping profiles are unchanged. As shown in Fig. 8(b), however, the tunneling area in the X.CHAR ¼ 16 nm TFET is much larger than that in the X.CHAR ¼ 0 nm TFET due to the extension of tunneling generation into the channel region. The extended tunneling area is due to the tunneling in the vertical direction, but not the lateral tunneling. The mechanism of appearing the vertical tunneling can be interpreted by the vertical energy-band diagrams extracted along the cut-line AA0 which is 10 nm far from the source edge. In the X.CHAR ¼ 16 nm TFET, the gate overlaps on a long distance of heavily-doped p-type region because the p-type dopant is deeply diffused into the channel. Associated with the high gate control capability due to the small EOT, the large vertical band bending results in the thin vertical tunnel width and thus the high tunneling current. In such cases, the vertical tunneling (or line-tunneling) dominates the on-current of TFETs [36]. When the characteristic length is shortened, the on-current is decreased because the vertical tunneling area is shrunk correlatively. For double-gate TFETs, the EOT dependence of the doping gradient effect can be demonstrated by considering their current-voltage curves as a function of the characteristic length with two different EOTs as shown in Fig. 9. With EOT ¼ 2 nm, decreasing the characteristic length always helps to increase the on-current because of narrowing the lateral tunnel width. With EOT ¼ 0.5 nm, the on-current is slightly increased with increasing the characteristic length. This on-current boosting is also originated from the increase in the vertical tunneling contribution, but considerably mitigated compared with the singlegate TFETs because of the late turning point voltage of around 1 V. In order to have an overall view of the oxide thicknessdependent effects of source doping gradient on the TFET performance, Fig. 10 shows the on-current versus the characteristic length of single- and double-gate TFETs with various EOTs ranging from 5 to 0.3 nm. By comparing the on-currents in Fig. 10(a) and (b) for the case of 0.3 nm EOT, it is inferred that the on-currents of double-gate TFETs are degraded by quantum mechanical effects. However, when the contribution of vertical tunneling to the total current is dominant, the effect of lowering the vertical tunneling window plays an important role in degrading the on-current because the lowering of the vertical tunneling window due to the quantum confinement is considerable compared with the window height. The larger the characteristic length, the stronger the degradation of on-current is due to the greater contribution of vertical tunneling. For example, the on-currents of single- and double-gate TFETs, respectively, are 0.15 and 0.13 mA/mm for X.CHAR ¼ 0 nm, but they are 1.40 and 0.72 mA/mm for X.CHAR ¼ 16 nm. For both single- and double-gate TFETs, in general, the effects of source doping gradient on the TFET on-current are significantly dependent on the EOT. The two opposite trends of the doping gradient effects are clearly observed. For large EOTs, the on-current is degraded with increasing the characteristic length. For very small EOTs, increasing the characteristic length even enhances the on-current. For each TFET structure, there exists an intermediate EOT at which the on-current is almost independent of the characteristic length. In this circumstance, the decrease in the lateral tunneling when increasing the characteristic length is equally compensated by the increase in the vertical tunneling. In other words, that EOT makes the turning point voltage located at the center of and close to the defined on-state voltages. Such EOTs are approximately 0.9e1.0 nm and 0.5e0.6 nm for the single- and double-gate TFET structures,

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respectively. When the EOT is scaled below those values, using a gradual source doping profile not only does not degrade, but on the contrary enhance the on-current of TFETs. This new feature of the source doping gradient effects is a significant advantage because fabricating a sharp source-channel junction usually requires sophisticated techniques [17,34,37,38]. To understand the difference in the EOT limit which separates two opposite trends of the source doping gradient effects in the single- and double-gate TFETs, Fig. 11 shows the energy-band diagrams in the vertical direction at on-state of single- and double-gate TFETs with the electrical oxide thickness of 1 nm and the characteristic length of 8 nm. For the single-gate TFET, a vertical tunneling window is opened at the region 10 nm far from the source junction edge. At the same location and gate voltage, the vertical tunneling is not allowed yet in the double-gate device because (1) the superposition of the two opposite vertical electric fields in the central region of the body reduces the band bending in the vertical direction, and (2) the increase in the effective bandgap lowers the vertical tunneling window. Both the reductions in the vertical band bending and tunneling window result in the late onset of vertical tunneling and the associated decrease of vertical tunneling contribution. To open the vertical tunneling window in the double-gate TFET, the EOT has to be decreased further to enhance the gate control capability for increasing the vertical electric field and associated band bending. Therefore, the EOT limit is smaller in the double-gate TFETs than in the single-gate devices to produce enough the vertical tunneling generation for compensating the decrease in the lateral tunneling component when increasing the characteristic length. Equivalently, if the EOTs used in single- and double-gate TFETs are equal, it will require a higher gate voltage to reach the turning point in double-gate than in single-gate TFETs. In short, although the more exact values of EOT limits and turning point voltages in single- and double-gate TFETs should be further examined by experiments, the existences of the EOT limits and turning point voltages have been clearly observed by the simulation results and soundly explained by the associated physical mechanisms. 5. Conclusion Using the two-dimensional numerical simulations, the dependence of the source profile effects on the EOT has been investigated for the first time in both single- and double-gate TFETs based on low-bandgap germanium. Associated physical explanations have been properly provided to clearly understand the new properties of the effects of source doping concentration and gradient on the TFET performance. 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