**2.1. Strained-silicon MODFET**

A MODFET is based on a single or a double heterojunction of two semiconductors with different bandgaps. In an n-channel MODFET, electrons diffuse from a highly doped layer toward a lowly doped layer of a high-mobility material where they are confined by means of the conduction-band discontinuity between the two materials. These electrons form a two-dimensional electron gas (2DEG) conductive channel at the heterointerface. Single-device strained Si/Si0.6Ge0.4 MODFETs with 100-nm T-gates with up to 74-GHz current gain cutoff frequency

The terahertz (THz) region (~0.1–10 THz; ~0.03–3 mm; ~3–300 cm−1) lies in the gap between the microwaves and infrared regions of the electromagnetic (EM) spectrum. THz radiations have extraordinary properties; it is a non-ionizing radiation and it is capable of penetrating through many non-conductive materials [2]. THz radiations have shown a great potential in a huge range of THz applications including astronomy [3, 4], spectroscopy (rotational, vibrational, and translational modes in the THz range are specific to a particular substance allowing to obtain a THz fingerprint) [5–7], thickness measurement of multilayer objects [8], communications with a bandwidth significantly higher than those based on microwaves [9], nondestructive inspection based on both imaging of concealed objects and spectroscopy [10], metrology [11], quality control [12], and so on. THz rays (T-rays) permit imaging with a diffractionlimited resolution similar to that of the human eye [13], and, since common optically opaque packaging materials are transparent to T-rays, the inspection of concealed objects is possible. During the last decade, new promising 2D materials have recently attracted interest to develop room-temperature solid-state THz sensors [14]. However, so far, only devices based on III–V materials [15] and silicon [16] have proved experimentally their potential to build low-cost, compact, scalable, and reliable systems; accordingly, the extension of the frequency range of

Solid-state devices are rising as one of the most promising ways to obtain THz detection and emission at room temperature. Dyakonov and Shur proposed in [17–19] the use of field-effect transistors (FETs) as detectors, multipliers, and mixers in the THz range using the oscillations of the plasma waves in the channel. Nonlinear properties of the two-dimensional plasma permit the detection of the THz radiation. Plasma wave-based detectors can directly convert the incoming EM radiation into measurable voltage or current. They demonstrated that a FET under excitation by THz radiation generates a DC drain-to-source voltage when the drain is open and, therefore, operating in the photovoltaic-mode detection. The value of this voltage can be modulated by the gate-to-source bias voltage, as the gate bias controls the plasma density and therefore the carrier concentration in the FET channel. The increasing availability of continuous-wave compact sources based on solid-state oscillators in the millimeter-wave

This chapter presents a study of room-temperature terahertz detection using strained-silicon modulation field-effect transistors with three different gate lengths. Detection of THz radiation [21, 22] and imaging using Si/SiGe transistors have been previously demonstrated [23, 24]. A main distinct interest of the high-mobility n-type FETs based on the Si/SiGe system is that, unlike the ones based on III–V plasmon detectors, it will be easy to integrate MODFET THz detectors with mainstream Si technology circuits, since both are fabricated on conventional

and 107-GHz maximum oscillation frequency were demonstrated [1].

54 Design, Simulation and Construction of Field Effect Transistors

these devices generates a great interest in THz detection.

range raises the interest on the development of direct detectors [20].

The devices under study are based on the Si/SiGe system, and the layout of the transistors is shown in **Figure 1(a)**. The epistructure of the MODFETs used in this work is as follows: a thick relaxed linearly graded SiGe virtual substrate is grown over a p-doped conventional Si wafer. The final top Ge molar concentration in the virtual substrate was 0.3. The structure has an undoped 12-nm tensile strained Si channel, sandwiched between two n-doped Si0.70Ge0.30 relaxed supply layers (reddish layers) to generate a high density of electrons in the strained-Si quantum well [26, 27]. The highlighted bluish layer marks out the strained-Si quantum well. Pt/Au was evaporated to fabricate the Schottky gate that was not symmetrically placed between the source and the drain. A more detailed description of the transistor fabrication can be found in [26].

The material system Si/SiGe allows the creation of a thin layer of strained silicon under tetragonal (biaxial tensile) strain due to the different values of the Si and the SiGe lattice constants. Tetragonal strain has the effect of lifting the sixfold degeneracy of the conduction band in

**Figure 1.** (a) Epistructure of the Si/SiGe MODFETs showing the vertical layout of the transistors. (b) Conduction and valence band profiles and the Fermi level under the gate in equilibrium [26].

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.

detectors and on the coupling of the incoming THz radiation. Strained-Si MODFETs were mounted and wire-bonded on the same dual in-line package (DIP14) shown in **Figure 2(a)**. An optical microscope image of the three different devices under study is given in **Figure** 

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

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

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

*<sup>ε</sup>*(*p* − *n* + *ND*

<sup>+</sup> − *NA* −

) (1)

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

57

→ *n* (*J* → *p* )

*<sup>n</sup>*) − *Un* (2)

*<sup>p</sup>*) − *Up* (3)

(*un n*)] (4)

(*up p*)] (5)


) represents the net electron (hole) recombination rate. *J*

(Eq. (1)) and the continuity equations for electrons (Eq. (2)) and holes (Eq. (3)) [31]:

<sup>∂</sup>*<sup>t</sup>* <sup>=</sup> \_\_<sup>1</sup> *q*(∇ → ⋅ →*J*

<sup>∂</sup>*<sup>t</sup>* <sup>=</sup> <sup>−</sup>\_\_<sup>1</sup>

*<sup>n</sup>* = *q μn*(*un*)[*nE*

*<sup>p</sup>* = *q μp*(*up*)[*nE*

*q*(∇ → ⋅ →*J*

where φ is the electric potential, q is the absolute value of the electron charge, n/p is the elec-

is the current density of electrons (holes) in the drift-diffusion model given by the following

<sup>→</sup> + ∇ →

<sup>→</sup> + ∇ →

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

*q* \_\_

**2(b)**. A SEM image of D3 with L<sup>G</sup> = 500 nm is shown in **Figure 2(c)**.

condition the performance of the FET as a THz detector.

<sup>+</sup> (N<sup>A</sup>

(*Up*

∇<sup>2</sup> φ = −

\_\_\_ <sup>∂</sup>*<sup>n</sup>*

<sup>∂</sup>*p*\_\_\_

tron/hole concentration, ND

equations:

where E →

material permittivity, and *Un*

<sup>→</sup>*<sup>J</sup>*

<sup>→</sup>*J*

**2.2. TCAD modeling**

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


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

**Figure 2.** Strained-Si MODFETs under study mounted and bounded on a DIP14 (a) and their optical microscope image (b). (c) SEM image of device 3 (500-nm T-gate transistor).

detectors and on the coupling of the incoming THz radiation. Strained-Si MODFETs were mounted and wire-bonded on the same dual in-line package (DIP14) shown in **Figure 2(a)**. An optical microscope image of the three different devices under study is given in **Figure 2(b)**. A SEM image of D3 with L<sup>G</sup> = 500 nm is shown in **Figure 2(c)**.
