**2.2. TCAD modeling**

silicon into a twofold and fourfold degenerate sets lowering the energy of the two valleys with their long axis perpendicular to the Si/SiGe interface. Consequently, the strained-Si gap is reduced as well as the electron conductivity mass as compared to bulk as a lower value, leading to an enhancement of the electron mobility by a factor of 2 [28, 29]. Since intervalley carrier scattering may only occur between degenerate minima, electrons in a layer of (tensile)-strained silicon would undergo a lower number of intervalley scattering events per unit time than in bulk silicon. The combination of the effect pointed earlier makes tensile strained silicon devices excellent candidates to build the high-mobility FET channel that is necessary to detect THz radiation. The energy band diagram at zero voltage is presented in **Figure 1(b)** [26]. The value of the conduction band offset of the heterojunction Si/Si0.70Ge0.30 is about 180 meV, ensuring an excellent electron confinement in the strained-Si quantum well layer that is necessary for room-temperature high-mobility operation of the detector. **Table 1** summarizes the geometrical parameters and the value of the threshold voltage of the strained-Si MODFETs under study.

56 Design, Simulation and Construction of Field Effect Transistors

The channel's length (LDS) and width (WG) were kept constant for all devices (LDS = 2 μm, W<sup>G</sup> = 30 μm). However, the gate lengths of the transistors were varied. Transistors with 100-, 250-, and 500-nm gate lengths were characterized. The gates were asymmetrically placed between the source (S) and the drain (D) contacts in all transistors; the distance between the right edge of the source and the left edge of the gate (LGS) was equal to 1 μm for all the transistors (**Table 1**). An asymmetrical position of the gate is of interest to enhance THz detection by the transistor [30]. Measuring devices with different values of the gate length allows the study of the influence of the gate length on the performance of the transistors as THz

Device 1 (D1) 2 1 100 30 −0.75 Device 2 (D2) 2 1 250 30 −0.67 Device 3 (D3) 2 1 500 30 −0.62

**Figure 2.** Strained-Si MODFETs under study mounted and bounded on a DIP14 (a) and their optical microscope image

**Table 1.** Geometrical and electrical parameters of the strained-Si MODFETs under study.

(b). (c) SEM image of device 3 (500-nm T-gate transistor).

**LDS (μm) LGS (μm) LG (nm) WG (μm) Vth (V)**

Dyakonov and Shur obtained an analytical solution of the unidimensional Euler equation that demonstrated the ability of the plasma waves in FET channels [17–19] to generate and detect THz radiation. A single equation cannot account for important parameters (such as doping profiles, high electric fields that locally modify the carrier mobility, device geometry, etc.) that condition the performance of the FET as a THz detector.

A better description of the charge transport in a transistor may be achieved through the numerical solution of the drift-diffusion model (DDM) that consists of the Poisson equation (Eq. (1)) and the continuity equations for electrons (Eq. (2)) and holes (Eq. (3)) [31]:

$$\nabla^2 \Psi = -\frac{q}{\varepsilon} (p - n + \mathcal{N}\_D^+ - \mathcal{N}\_A^-) \tag{1}$$

$$\frac{\partial n}{\partial t} = \frac{1}{q} \left( \vec{\nabla} \cdot \vec{f\_n} \right) - \mathsf{L}I\_n \tag{2}$$

$$\frac{\partial p}{\partial t} = -\frac{1}{q} \left( \vec{\nabla} \cdot \vec{f\_p} \right) - \mathcal{U}\_p \tag{3}$$

where φ is the electric potential, q is the absolute value of the electron charge, n/p is the electron/hole concentration, ND <sup>+</sup> (N<sup>A</sup> - ) is the ionized donor (acceptor) concentration, ε is the local material permittivity, and *Un* (*Up* ) represents the net electron (hole) recombination rate. *J* → *n* (*J* → *p* ) is the current density of electrons (holes) in the drift-diffusion model given by the following equations:

$$
\vec{f}\_{\boldsymbol{n}} = q \,\mu\_{\boldsymbol{n}}(\boldsymbol{\mu}\_{\boldsymbol{n}}) \left[ \boldsymbol{n} \vec{\boldsymbol{E}} + \vec{\nabla} \langle \boldsymbol{\mu}\_{\boldsymbol{n}} \boldsymbol{n} \rangle \right] \tag{4}
$$

$$
\vec{J}\_p = q \,\mu\_\rho(\mu\_p) \left[ n \vec{E} + \vec{\nabla}(\mu\_p p) \right] \tag{5}
$$

where E → is the electric field, μn (μp) is the electron (hole) mobility, and un (up) is the electron (hole) thermal voltage. In deep-submicron FETs, the drain and gate biases give rise to large electric fields that rapidly change over small length scales giving leading to nonlocal phenomena that dominate the transistor performance [26, 27]. As carriers are intensely heated by the electric field in the channel of deep-submicrometer FETs, energy balance equations accounting for electron and hole heating and energy relaxation in the device must be self-consistently added to the transport model. The DDM only considers moment relaxation [32], and therefore it is unable to describe a hot carrier transport. As channel mobility is closely dependent on the carrier temperature, an extended model needs to be used to study the electric properties of deep-submicron FET transistors used in plasma wave THz detection. This extended model is known as the hydrodynamic model (HDM).

The HDM [32, 33] includes a carrier energy balance by coupling to the set of DDM equations and the electron and hole energy flow densities that are given as follows:

$$\vec{\nabla} \cdot \overrightarrow{S}\_n = \frac{1}{q} \overrightarrow{f}\_n \cdot \vec{E} - \frac{3}{2} \left( n \frac{u\_n - u\_0}{\tau\_u} + \frac{\partial (u\_n \eta)}{\partial t} \right) \tag{6}$$

$$\vec{\nabla} \cdot \overrightarrow{S}\_p = \frac{1}{q} \vec{f}\_p \cdot \vec{E} - \frac{3}{2} \left( p \frac{u\_p - u\_o}{\tau\_p} + \frac{\partial \{u\_p p\}}{\partial t} \right) \tag{7}$$

multiplication to reach 0.15 THz with a power of 3 mW and 0.3 THz with a power of 6 mW was used to excite the transistors. The output power was measured close to the source using a highly sensitive calibrated pyroelectric detector. The incoming THz radiation was modulated by a mechanical chopper between 0.233 and 5 kHz, collimated and focused by an indium tin oxide (ITO) mirror and off-axis parabolic and plane mirrors. A red LED (or laser) was used

**Figure 3.** Photograph of the experimental setup and schematic description of the THz (blue) and red laser (red line)

Room-Temperature Terahertz Detection and Imaging by Using Strained-Silicon MODFETs

http://dx.doi.org/10.5772/intechopen.76290

59

The photo-induced drain-to-source voltage, ΔU, was measured using a lock-in technique.

Transfer characteristics of Device 3 are shown in **Figure 4(a)** for two values, 20 and 200 mV, of the drain-to-source voltage (VDS). The three transistors are depletion-mode devices, so a negative bias voltage must be applied to the gate (i.e., a negative gate-to-source voltage) to cut off the c hannel [25, 39]. Transfer characteristics in a log scale show that a total switch-off of the device was not possible, and a constant level of drain current (IDS) persists for a gate bias of −1 V (8 μA for Vds = 20 mV and 80 μA for Vds = 200 mV). As the drain voltage is moderately raised from 20 to 200 mV, the above-described behavior is enhanced, and the sub-threshold current at VGS = -1 V increases when VDS increases. As pointed out earlier, this behavior reveals a moderate control of the channel by the gate electrode due to the double supply layer; in return, this double deck ensures a suitable concentration of the electron plasma in the channel that is of paramount importance to achieve a good performance of the transistor in THz detection.

Finally, a X-Y stage was used to generate pixel-by-pixel THz images.

for the alignment of the THz beams.

**4. Results and discussion**

**4.1. DC characterization**

beams.

where <sup>→</sup> *Sn* (→ *Sp* ) is the electron (hole) energy relaxation time, un (up) is the electron (hole) thermal voltage, and the electric field that is self-consistently obtained from the Poisson equation.

Strained-Si MODFET is essentially a majority carrier device; then the hole energy balance equation (Eq. (7)) was disregarded in the model. In this work, a two-dimensional HDM (Eqs. (1)–(6)) was used. It was implemented with Synopsys TCAD [34]. Carrier relaxation times were obtained from uniform-field Monte Carlo simulations [35, 36]. In TCAD simulations, impurity de-ionization, Fermi-Dirac statistics, and mobility degradation due to both longitudinal and transverse electric field were considered. All TCAD simulations were carried out at room temperature.

The geometry and dimensions used in the simulations are the ones shown in **Figure 1(a)**. The doping level of the supply layers was 1019 cm−3 for the upper supply layer and 1.8 × 1018 cm−3 for the lower one. The thicknesses of the virtual substrate and the p-Si wafer were chosen to be 600 and 500 nm, respectively, to economize computer memory. A uniform residual n-type-doping density of 1015 cm−3 was assumed in the non-intentionally doped regions of the transistor. Under both source and drain contacts, highly doped regions were considered to ensure ensure low values of contact resistance for the ohmic contacts of the device. The values of the conduction and valence bands offsets between the strained-Si and the relaxed Si1-xGex as a function of the Ge molar fraction (x = 0.30) were extracted from [37]. Low electric field mobility in the channel was modeled using Roldan's model for biaxially strained Si on relaxed SiGe [38], and the maximum value electron mobility in the channel was 1600 cm2 /(Vs).
