3. Simulated results of UL-HTFET

thickness at the tunnel junction, high-k gate oxide is used so that the gate-tunneling current can be reduced. Actually, due to these reasons, the recent trend is to use high-k materials as a better replacement of the conventional SiO2 (silicon dioxide). On the other hand, it causes a significant ambipolar current. The gate-drain underlap structure in association with heterojunction can be adopted to diminish ambipolar current [2]. A silicon-germanium (SiGe) layer is used at the tunnel junction so that bandgap and tunnel width can be modulated. Electrical parameters have been

Technology Computer Aided Design (TCAD) simulation is a complex iterative mathematical process, and hence various analytical models have been proposed in order to develop a better understanding of the physics-based principles of TFETs and obtain results not constrained by computational time [11]. A number of analytical models based on Poisson equation have been proposed in the study for different geometries [12–14]. In this chapter, a mole fraction-

This chapter is organized as follows: first, the heterojunction gate-drain underlap tunnel is discussed, and in the second section, the electrical parameters of the heterojunction gate-drain underlap tunnel FET (UL-HTFET) is investigated with the help of TCAD simulation. The third section discusses the physics-based compact model and the validation of the model with simulated results. In the last section, the effect of temperature on the electrical parameters is investigated.

A 2-D structure of the proposed UL-HTFET is shown in Figure 1. Here, a p + source and n + drain with an intrinsic channel and a δp + Si1-xGex layer at the source-channel tunnel

investigated for various Ge-mole fractions.

38 Design, Simulation and Construction of Field Effect Transistors

Figure 1. A 2-D geometry of the device (UL-HTFET).

dependent model has been proposed and validated.

2. Heterojunction gate-drain underlap tunnel FET

junction are present. The δp + layer can be replaced by a δn + layer too.

Figure 2 shows the Ids-Vgs characteristics of the Si/Ge heterojunction UL-HTFET at different lengths of Lp. When the HTFET is turned on, it shows very high on-current due to the effective bandgap narrowing at the interface of source-channel junction. The Ids-Vgs curves are mainly dependent on n + doped pocket length (Lp) as shown in Figure 2; as Lp gets longer, the effective area for tunneling width is extended for HTFET. However, the low off-state current in UL-HTFET (9.205 <sup>10</sup><sup>20</sup> A/μm) when Lp is less than 2 nm, and this indicates that the ambipolar-tunneling effect at drain channel is suppressed. When Lp is 2 nm, as observed, the tunneling width becomes extremely thin to concede tunneling current at Vgs = 0.5 V. This tunneling current interrupts UL-HTFET device performance at off-state. The low Ioff can be achieved at Lp = 1 and 2 nm, and Ion is greatly higher at Lp = 4 nm in TFET. Therefore, an optimum Lp can be located at 1 nm where high ion is achieved and the leakage is suppressed as shown in Ids-Vgs characteristics.

Figure 2. Transfer characteristics for varying Lp lengths at Vds = 0.7 V.

Figure 3. Id-Vgs characteristics of UL-HTFET with varying Ge-mole fractions.

In Figure 3, the Id-Vgs characteristics of the UL-HTFET is shown. The mole fraction of SiGe layer is varied. With germanium mole fraction of 0.4, the best Ion/Ioff ratio has been achieved (1012). For Ge-mole fractions below 0.5, the device exhibits a better ratio. As the mole fraction increases beyond 0.5, the properties of the n + layer align more with those of germanium than of silicon. With an increase in mole fraction greater than 0.4, the on-current increases but the increase in off-current is more. This is due to an effective band bending at the source-channel tunnel junction by which the tunnel width can be modulated. For a reduced tunnel width in ON state (Vgs = 1 V), more ON current is achieved. However, at OFF state, the current is due to thermionic emission as the tunnel current is insignificant.

The energy band diagram is plotted at different mole fractions at ON state (Vds = 0.7 V, Vgs = 1.2 V) shown in Figure 4. It is observed that at 0.8-mole fraction of germanium, the ON current is more. With an increase in Ge-mole fraction, the tunnel width reduces and hence enhanced ON current is achieved. In the inset of Figure 4, the variation of valence band with mole fraction is shown. The conduction band variation is insignificant with mole fraction.

In Figure 5, the electric field is shown at different mole fractions. The peak electric field is observed around 20-nm length along the lateral direction. This is the source-channel tunnel junction. A high electric field at this location is due to the presence of a large tunnel barrier. With the increased mole fraction (at x = 1), a highest peak is observed, and hence tunneling probability will increase and be responsible for the increased current in ON state.

The ON/OFF current ratio and the subthreshold swing are shown in Figure 6. The best ION/IOFF ratio is achieved for Ge-mole fraction of 0.3. In TFETs, an abrupt Id-Vgs plot is obtained where the subthreshold swing varies with gate voltage. Therefore, two types of SS [15] are defined in TFETs: one is the average SS and the other is known as point SS. The average SS is defined mathematically as

$$\text{SSav} = (V\_T - V\_{\text{OFF}}) / [\log \left( I\_T \right) - \log \left( I\_{\text{OFF}} \right) ] \tag{1}$$

where VT is the threshold voltage and VOFF is the value of gate voltage at which the drain current just begins to take off. IT and IOFF are the drain currents at the respective voltages. Point SS, on the other hand, is the minimum SS at any point on the Id-Vgs plot. The plot of average SS for different Ge-mole fractions is shown in Figure 6. A remarkable average SS (37 mV/dec) is

Band Gap Modulated Tunnel FET

41

http://dx.doi.org/10.5772/intechopen.76098

achieved at 0.2 Ge-mole fraction.

Figure 4. Energy band diagram at ON state.

Figure 5. Electric field along the channel length in UL-HTFET.

Figure 4. Energy band diagram at ON state.

In Figure 3, the Id-Vgs characteristics of the UL-HTFET is shown. The mole fraction of SiGe layer is varied. With germanium mole fraction of 0.4, the best Ion/Ioff ratio has been achieved (1012). For Ge-mole fractions below 0.5, the device exhibits a better ratio. As the mole fraction increases beyond 0.5, the properties of the n + layer align more with those of germanium than of silicon. With an increase in mole fraction greater than 0.4, the on-current increases but the increase in off-current is more. This is due to an effective band bending at the source-channel tunnel junction by which the tunnel width can be modulated. For a reduced tunnel width in ON state (Vgs = 1 V), more ON current is achieved. However, at OFF state, the current is due to

The energy band diagram is plotted at different mole fractions at ON state (Vds = 0.7 V, Vgs = 1.2 V) shown in Figure 4. It is observed that at 0.8-mole fraction of germanium, the ON current is more. With an increase in Ge-mole fraction, the tunnel width reduces and hence enhanced ON current is achieved. In the inset of Figure 4, the variation of valence band with mole fraction is shown. The conduction band variation is insignificant with mole fraction.

In Figure 5, the electric field is shown at different mole fractions. The peak electric field is observed around 20-nm length along the lateral direction. This is the source-channel tunnel junction. A high electric field at this location is due to the presence of a large tunnel barrier. With the increased mole fraction (at x = 1), a highest peak is observed, and hence tunneling

The ON/OFF current ratio and the subthreshold swing are shown in Figure 6. The best ION/IOFF ratio is achieved for Ge-mole fraction of 0.3. In TFETs, an abrupt Id-Vgs plot is obtained where the subthreshold swing varies with gate voltage. Therefore, two types of SS [15] are defined in TFETs: one is the average SS and the other is known as point SS. The

SSav ¼ ð Þ VT � VOFF =½ � log ð Þ� IT log ð Þ IOFF (1)

probability will increase and be responsible for the increased current in ON state.

thermionic emission as the tunnel current is insignificant.

Figure 3. Id-Vgs characteristics of UL-HTFET with varying Ge-mole fractions.

40 Design, Simulation and Construction of Field Effect Transistors

average SS is defined mathematically as

Figure 5. Electric field along the channel length in UL-HTFET.

where VT is the threshold voltage and VOFF is the value of gate voltage at which the drain current just begins to take off. IT and IOFF are the drain currents at the respective voltages. Point SS, on the other hand, is the minimum SS at any point on the Id-Vgs plot. The plot of average SS for different Ge-mole fractions is shown in Figure 6. A remarkable average SS (37 mV/dec) is achieved at 0.2 Ge-mole fraction.

where C0ið Þx , C1ið Þx , and C2ið Þx are coefficients that are functions of mole fraction.

<sup>∂</sup><sup>y</sup> <sup>¼</sup> <sup>ε</sup><sup>i</sup>

∂Ψið Þ x; 0

and at the lowermost part of the device (y ¼ ts)

(� 1.10 eV) and Ge (� 0.66 eV):

expressed as

and <sup>ξ</sup><sup>i</sup> <sup>¼</sup> qNi εik<sup>2</sup> i � vi:

Eq. (7) has a solution of the form:

with

In each of the four regions, three vertical boundary conditions must be satisfied to confirm the continuity of potential and electric field at the gate insulator–semiconductor interface (y ¼ 0)

Ψið Þ¼ x; 0 Ψsið Þx

εoxtox

where Ψsið Þx is the surface potential, ℇox is the permittivity of gate dielectric, tox is the gate dielectric thickness, and vi ¼ VGS � Vfbi. The gate voltages with respect to source and the flatband voltage are represented by VGS, and Vfbi, respectively. The bandgap EGi is a function of Ge-mole fraction in Si1-xGex expressed as a linear interpolation of the bandgaps of Si

∂Ψið Þ x; ts

Using the boundary conditions of Eq. (4), we obtain the coefficients of Eq. (3) as follows:

2εoxtoxts

ki ¼

C1i <sup>¼</sup> <sup>ε</sup><sup>i</sup> εoxtox

<sup>C</sup>2<sup>i</sup> <sup>¼</sup> <sup>ε</sup><sup>i</sup>

Ψsi == � <sup>k</sup><sup>2</sup>

Ψsið Þ¼ x Aie

C0i ¼ Ψsið Þx

Using the coefficients of Eq. (6) in the polynomial in Eq. (3), the 2-D Poisson's equation can be

<sup>i</sup> <sup>Ψ</sup>si <sup>¼</sup> <sup>k</sup><sup>2</sup>

ffiffiffiffiffiffiffiffiffiffiffiffi εox εitoxts

<sup>þ</sup>kix <sup>þ</sup> Bie

r

f g Ψsið Þ� x vi

f g Ψsið Þ� x vi

<sup>∂</sup><sup>y</sup> <sup>¼</sup> <sup>0</sup> (4)

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EGi ¼ 1:10 � 0:34x (5)

f g vi � Ψsið Þx (6)

<sup>i</sup> ξ<sup>i</sup> (7)

�kix � <sup>ξ</sup><sup>i</sup> (8)

Figure 6. ON and OFF current ratios (ION/ IOFF) and subthreshold swing (SS) versus Ge-mole fraction.
