**4.2. THz detection: TCAD versus experimental**

The TCAD simulation model of the transistor was validated through comparison with DC and AC measurements. The agreement between TCAD and experimental results across the whole ranges of gate-to-source and drain-to-source biases studied is excellent as shown in

**Figure 4.** (a) Experimental and simulated transfer characteristics for device 3 for two values of the drain voltage plotted

in a log scale and (b) output characteristics for three different values of VGS.

60 Design, Simulation and Construction of Field Effect Transistors

Agreement between measurement and simulation magnitudes involving first derivatives of the drain current was also analyzed. In the first place, the efficiency of the transconductance was analyzed. This magnitude defined as the ratio of transconductance (gm) to drain-tosource DC current (IDS), is a key parameter used to compare the performance of different technologies of transistors. The efficiency of the transconductance is used here, on the one hand, because it clearly shows the operation region of the device and, on the other hand, because the efficiency of the transconductance is linearly dependent on a current derivative and discrepancies between simulation and experimental results are readily revealed. **Figure 5(a)** gives the experimental and calculated efficiency of the transconductance versus the gate voltage (VGS) of the device D3. The maximum value of the efficiency of the transconductance measured

**Figure 5.** (a) Efficiency of the transconductance versus the gate voltage obtained from measurements and numerical TCAD simulations and (b) drain conductance versus drain voltage for three different values of gate bias obtained from

measurements and numerical TCAD simulations.

**Figure 4**.

A TCAD study of the THz photovoltaic response of the transistor was implemented, as in measurements, grounding the source, biasing the gate, and floating the drain contact while a THz small sinusoidal signal (0.15 or 0.3 THz) was superimposed to the gate voltage as described in [17–19]. As the DC drain voltage setup in the photovoltaic mode must be supported by a net charge in the drain region, in TCAD simulations, a charge boundary condition was implemented at the floating drain contact with a distributed boundary condition over all nodes of the mesh of the drain electrode. The boundary condition is as follows:

$$
\oint \vec{D} \cdot d\vec{S} = Q \tag{8}
$$

where *D* → is the electric displacement field, Q is the total net charge, and the integral is evaluated over the entire surface of the drain electrode. Eq. (8) forces the potential on the drain (i.e., the photoresponse of the detector) to be adjusted to produce the correct total charge on the electrode. HDM equations (Eqs. (1)–(6)) were solved in the time domain to obtain the transistor photoresponse. The amplitude of the sinusoidal signal superimposed in the gate contact was fixed to an arbitrary value of 5 mV. Since this value is arbitrary, the magnitude of the THz response obtained in simulations will be presented henceforward as arbitrary magnitude in figures.

In TCAD simulations, it was found that the drain voltage (ΔU) induced by the THz sinusoidal signal exhibits both the same shape (sinusoidal) and the frequency than the AC signal superimposed to the gate bias; this ensures that no frequency conversion takes place in the simulated devices. In addition, it was found that its amplitude is considerably smaller than one of the gate's signal in agreement with the fact that in the THz range the transistor is unable to amplify signals and it is merely working as a THz detector. The mean value of the induced drain voltage by the radiation was negative as predicted by theoretical models [17–19]. The photoresponse obtained in TCAD simulations was extracted by subtracting the value of drain-to-source voltage when the THz signal was applied (Δ*UTHz-on*) from the drainto-source voltage when no signal was applied (Δ*UTHz-off*):

$$
\Delta \mathbf{U} = \Delta \mathbf{U}\_{\text{THz-off}} - \Delta \mathbf{U}\_{\text{THz-on}} \tag{9}
$$

**Figure 6.** Measured (a) and TCAD simulation (b) photoresponse versus gate voltage under excitation of 0.3 (blue dots) and 0.15 THz (red squares) of D2.

**Figure 6** gives the room-temperature photovoltaic response of device D2 with L<sup>G</sup> = 250 nm obtained experimentally and from TCAD simulations at 0.3 (blue squares) and 0.15 THz (red dots).

The main effect of imposing a DC source-to-drain current bias is that THz detection is significantly enhanced, and the photoresponse grows when the bias current is increased. The bias current introduces an additional asymmetry between the source and the drain, creating a depletion of the electron density on the drain side of the channel, and consequently, the maximum value of the photoresponse is increased [24, 41, 42]. Moreover, a noticeable additional effect (the insets in **Figure 7**) is that the maximum in the photoresponse is shifted toward more negative values of the gate voltage. **Figures 6** and **7** show that the MODFET photoresponse exhibits the same dependence with respect to the gate bias voltage both in measurements and in simulations. An excellent agreement between TCAD and experimental results is found in the photovoltaic mode (IDS = 0) and even when a bias current (IDS) is applied to the transistor. Therefore, the measured photoresponse of the strained-Si MODFET must be mainly attributed to the plasmonic response of the channel carriers rather than to the antenna role played by bonding wires or

**Figure 7.** Photoresponse versus gate voltage measured experimentally (red color) and obtained from TCAD simulations (blue color) for different values of IDS at 0.3 (a) and 0.15 THz (b) for D1. The insets show a zoom of the region of maximum

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

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63

photoresponse.

metal pads as simulations reproduce correctly the experimental photoresponse.

mance, asymmetry should be introduced as close as possible to the source pad.

In addition, to the abovementioned channel asymmetry created by the current bias, a built-in asymmetry can be introduced geometrically by imposing an asymmetric design of the contact pads of the transistor. **Figure 8** shows the obtained photoresponse from TCAD simulations as a function of the asymmetry factor. The latter is defined as the ratio LGS/LGD, where LGS is the distance between the right edge of the source and the left edge of the gate and LGD is the distance between the right edge of the gate and the left edge of the drain (**Figure 1(a)**). LGS/LGD = 1 means that the transistor is symmetric. The gate length was kept constant at 500 nm for all the transistors. A higher photoresponse signal was obtained for an asymmetry factor of 0.2 where the gate finger is very close to the source contact. However, in the opposite case, when the finger is close to the drain pad, no enhancement of the photoresponse was obtained. In the non-resonant regime, the oscillation of the plasma occurs close to the source pad where the electrons are injected into the channel and hence the gate finger close to the source pad could control efficiently the damped oscillation of the plasma waves. We conclude that for a better perfor-

The higher value in the photoresponse was found when the gate electrode was voltage-biased at a voltage close to the threshold voltage of the transistor [40]. This behavior has been observed earlier in FETs [16, 20] and it was attributed to a non-resonant (broadband) response of the detector. It is related to over-damping of the plasma waves in the channel where the AC current generated by the incoming radiation at the source cannot reach the drain side of the channel. A theoretical study of the photoresponse in this regime is presented in [21, 22]. The quality factor [19] is given by: Q = ωτ, where τ is the relaxation time given by m\* μ/e (m\* : the electron effective mass, μ: the electron mobility, and e: the absolute value of the electron charge). In the present case, the devices show a higher channel mobility (∼1600 cm2 /V·s) as compared to the conventional Si-MOSFET (∼200 cm2 /V.s); the value of the quality factor was estimated to be 0.14 at *f* = 0.15 THz and ∼0.29 at *f* = 0.3 THz; any of these values fulfills the resonance condition. The experimental photoresponse (**Figure 6(a)**) is more intense under excitation at 0.3 THz than at 0.15 THz. The photoresponse obtained in TCAD simulations exhibits the opposite behavior: the photoresponse at 0.15 THz is more intense than at 0.3 THz. This must be partly attributed to the fact that in measurements, the source's output power at 0.3 THz is twice than at 0.15 THz. Moreover, the coupling of the THz radiation to the devices could vary at 0.15 and 0.3 THz. These possibilities will be explored and further discussed subsequently. As in TCAD simulations, the amplitude of the sinusoidal gate signal was fixed to 5 mV for both frequencies, and no coupling and/or effects related to the differences in the incoming THz power at both frequencies can be found.

Besides the photovoltaic mode, the efficiency of the detector can be improved, creating additional asymmetries between the drain and the source [30, 41, 42]. One method to generate these asymmetries is to apply a DC current between the drain and the source (IDS > 0). **Figure 7** shows the photoresponse obtained experimentally and from TCAD simulations when a drain-to-source current bias, IDS = 50 μA, is imposed to the transistor D1 at 0.15 and at 0.3 THz.

Room-Temperature Terahertz Detection and Imaging by Using Strained-Silicon MODFETs http://dx.doi.org/10.5772/intechopen.76290 63

**Figure 7.** Photoresponse versus gate voltage measured experimentally (red color) and obtained from TCAD simulations (blue color) for different values of IDS at 0.3 (a) and 0.15 THz (b) for D1. The insets show a zoom of the region of maximum photoresponse.

**Figure 6** gives the room-temperature photovoltaic response of device D2 with L<sup>G</sup> = 250 nm obtained experimentally and from TCAD simulations at 0.3 (blue squares) and 0.15 THz (red

**Figure 6.** Measured (a) and TCAD simulation (b) photoresponse versus gate voltage under excitation of 0.3 (blue dots)

The higher value in the photoresponse was found when the gate electrode was voltage-biased at a voltage close to the threshold voltage of the transistor [40]. This behavior has been observed earlier in FETs [16, 20] and it was attributed to a non-resonant (broadband) response of the detector. It is related to over-damping of the plasma waves in the channel where the AC current generated by the incoming radiation at the source cannot reach the drain side of the channel. A theoretical study of the photoresponse in this regime is presented in [21, 22]. The quality factor [19] is

μ: the electron mobility, and e: the absolute value of the electron charge). In the present case,

and ∼0.29 at *f* = 0.3 THz; any of these values fulfills the resonance condition. The experimental photoresponse (**Figure 6(a)**) is more intense under excitation at 0.3 THz than at 0.15 THz. The photoresponse obtained in TCAD simulations exhibits the opposite behavior: the photoresponse at 0.15 THz is more intense than at 0.3 THz. This must be partly attributed to the fact that in measurements, the source's output power at 0.3 THz is twice than at 0.15 THz. Moreover, the coupling of the THz radiation to the devices could vary at 0.15 and 0.3 THz. These possibilities will be explored and further discussed subsequently. As in TCAD simulations, the amplitude of the sinusoidal gate signal was fixed to 5 mV for both frequencies, and no coupling and/or effects

related to the differences in the incoming THz power at both frequencies can be found.

Besides the photovoltaic mode, the efficiency of the detector can be improved, creating additional asymmetries between the drain and the source [30, 41, 42]. One method to generate these asymmetries is to apply a DC current between the drain and the source (IDS > 0). **Figure 7** shows the photoresponse obtained experimentally and from TCAD simulations when a drain-to-source current bias, IDS = 50 μA, is imposed to the transistor D1 at 0.15 and at 0.3 THz.

μ/e (m\*

/V.s); the value of the quality factor was estimated to be 0.14 at *f* = 0.15 THz

: the electron effective mass,

/V·s) as compared to the conventional

given by: Q = ωτ, where τ is the relaxation time given by m\*

the devices show a higher channel mobility (∼1600 cm2

dots).

Si-MOSFET (∼200 cm2

and 0.15 THz (red squares) of D2.

62 Design, Simulation and Construction of Field Effect Transistors

The main effect of imposing a DC source-to-drain current bias is that THz detection is significantly enhanced, and the photoresponse grows when the bias current is increased. The bias current introduces an additional asymmetry between the source and the drain, creating a depletion of the electron density on the drain side of the channel, and consequently, the maximum value of the photoresponse is increased [24, 41, 42]. Moreover, a noticeable additional effect (the insets in **Figure 7**) is that the maximum in the photoresponse is shifted toward more negative values of the gate voltage. **Figures 6** and **7** show that the MODFET photoresponse exhibits the same dependence with respect to the gate bias voltage both in measurements and in simulations. An excellent agreement between TCAD and experimental results is found in the photovoltaic mode (IDS = 0) and even when a bias current (IDS) is applied to the transistor. Therefore, the measured photoresponse of the strained-Si MODFET must be mainly attributed to the plasmonic response of the channel carriers rather than to the antenna role played by bonding wires or metal pads as simulations reproduce correctly the experimental photoresponse.

In addition, to the abovementioned channel asymmetry created by the current bias, a built-in asymmetry can be introduced geometrically by imposing an asymmetric design of the contact pads of the transistor. **Figure 8** shows the obtained photoresponse from TCAD simulations as a function of the asymmetry factor. The latter is defined as the ratio LGS/LGD, where LGS is the distance between the right edge of the source and the left edge of the gate and LGD is the distance between the right edge of the gate and the left edge of the drain (**Figure 1(a)**). LGS/LGD = 1 means that the transistor is symmetric. The gate length was kept constant at 500 nm for all the transistors.

A higher photoresponse signal was obtained for an asymmetry factor of 0.2 where the gate finger is very close to the source contact. However, in the opposite case, when the finger is close to the drain pad, no enhancement of the photoresponse was obtained. In the non-resonant regime, the oscillation of the plasma occurs close to the source pad where the electrons are injected into the channel and hence the gate finger close to the source pad could control efficiently the damped oscillation of the plasma waves. We conclude that for a better performance, asymmetry should be introduced as close as possible to the source pad.

each angular position of the devices. **Figure 9** shows the photoresponse signal as a function of

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

For all the devices at 0.3 THz, a maximum of the photoresponse signal was found when the incoming radiation was parallel to the gate finger pads (see the inset of **Figure 9(a)** at 0°), showing a maximum photoresponse for all the devices at the same angular position. At 0.15 THz the maximum photoresponse was obtained at different angular positions for each device. It is clearly shown that at a lower frequency (0.15 THz), bounding wires play an important role to couple the terahertz radiation to the channel of the device. Moreover, at a higher frequency (0.3 THz), the coupling is performed by the contact pads and/or the gate fingers. These

Responsivity (*RV*) and noise equivalent power (NEP) are the two key parameters (figures of merit) that determine the performance of THz detectors. Responsivity is calculated according

> \_\_\_\_t P<sup>t</sup> Sa \_\_*π* √ \_\_

where ΔU is the photoresponse signal measured with the lock-in amplifier, *St*

calibrated pyroelectric detector at the MODFET position (see **Figure 3**); the *Pt*

single transistor, including the contact pads, is less than 0.05 mm2

*Pt* = 0.5 mW at 0.15 THz and *Pt* = 1 mW at 0.3 THz. The spot area is given by *πr<sup>2</sup>*

is the active area of the transistor, and *Pt*

surrounding the detector. The radiation beam power and spot area were measured using a

the radius of the beam spot (≈1.5 mm at 0.3 THz and 3.3 mm at 0.15 THz). The area of each

replaced by *Sλ* to avoid overestimation of the *Rv* as well as NEP. The factor π/√2 originates from the Fourier transform of the square wave-modulated THz signal detected as RMS value

The NEP is given by *Nth*/*RV*, where *Nth* is the thermal noise of the transistor in V/Hz0.5 and *RV* is the responsivity in V/W. Since *RV* and the NEP were studied at zero drain current bias, the

the drain-to-source resistance that can be extracted from the transfer characteristics measured

**Figure 10** presents the responsivity and NEP curves for D1 with L<sup>G</sup> = 100 nm at 0.15 and 0.3 THz. **Table 2** summarizes the obtained NEP and Rv for the Si-MODFETs at 0.15 and at 0.3 THz. Device 1, with the shorter gate, exhibits the best performance at 0.3 THz with RV = 46.4 V/W and NEP ~0.12nW/Hz0.5 and Device 2 exhibits the best performance at 0.15 THz with RV = 74.5 V/W and NEP ~0.06 nW/Hz0.5. This must be attributed to the large photoresponse signal provided by the Si/SiGe MODFET and to a better coupling of the incoming terahertz radiation. The values obtained for the NEP and the responsivity are comparable to

at a low drain bias (20 mV) corresponding to the linear regime (i.e., **Figure 5(a)**).

<sup>2</sup> (10)

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65

*/4*. Accordingly, to calculate *Rv* in Eq. (6), *Sa* was

0.5 is the only relevant source of noise of the transistor. Here, *Rds* is

is the radia-

values were

where *r* is

is the total incident power

(**Figure 2**), that is, it is much

the polarization of the incoming THz radiation for 0.3 (a) and 0.15 THz (b).

results are in agreement with previously published ones [46].

**4.4. Responsivity, NEP, and imaging**

RV <sup>=</sup> ΔUS

smaller than the diffraction limit area *Sλ = λ<sup>2</sup>*

to the expression:

tion beam spot area, *Sa*

with a lock-in.

thermal noise *Nth* = (*4kTRds*)

**Figure 8.** Photoresponse obtained from TCAD simulations versus VGS for different horizontal positions of the gate contact.

#### **4.3. Polarization sensitivity of photoresponse**

It can be observed in **Figures 6(a)** and **7** that the obtained photoresponse is more intense under excitation at 0.3 than at 0.15 THz. This must be partly attributed to the higher power at 0.3 THz (~6 mW) than at 0.15 THz (~3 mW) and to the coupling of the THz radiation to the device that varies with frequency. Moreover, the bonding wires and the metallic pads could play an antenna role to couple the incoming terahertz radiation (linearly polarized) to the 2D electron channel [43–45]. To understand how radiation is coupled, devices were rotated in the plane perpendicular to the terahertz beam, and the photoresponse signal was measured for

**Figure 9.** Photoresponse versus rotation angle for all devices under excitation of 0.3 (a) and 0.15 THz (b). The inset figure shows the devices at the zero-angle position.

each angular position of the devices. **Figure 9** shows the photoresponse signal as a function of the polarization of the incoming THz radiation for 0.3 (a) and 0.15 THz (b).

For all the devices at 0.3 THz, a maximum of the photoresponse signal was found when the incoming radiation was parallel to the gate finger pads (see the inset of **Figure 9(a)** at 0°), showing a maximum photoresponse for all the devices at the same angular position. At 0.15 THz the maximum photoresponse was obtained at different angular positions for each device. It is clearly shown that at a lower frequency (0.15 THz), bounding wires play an important role to couple the terahertz radiation to the channel of the device. Moreover, at a higher frequency (0.3 THz), the coupling is performed by the contact pads and/or the gate fingers. These results are in agreement with previously published ones [46].
