**3. Self-switching diode design guidelines**

In order to get a rectifier with cut-off in the THz region by the SSD device, it is important to follow design considerations that may improve the current rectification with low VTH and optimize the SSD up for the best efficiency. These considerations are related to the geometry-depletion region relationship between the SSD dimensions, shape, and the DL extension. In this section, we evaluate the rectification performance of the L-shape SSD device in DC injection mode by a systematic analysis where the width, W; the length, L; and the vertical and horizontal trench width (WV and WH) of the channels are varied in order to get their effect on the I-V behavior of the device. The layout shown in **Figure 5(a)** defines the reference geometries where we have a varied chosen parameter, while the others were fixed.

The simulations were carried out in order to obtain the I-V curves of each geometrical variation with the aim to evaluate the ability of channels to detect the electrical energy of low-voltage THz signals. On this way, the SSDs can be considered as square-law rectifiers that generate electrical power from the incoming THz radiation. In order to understand the size effect on the detection, we use three criteria that define the performance of the SSD. Fist, differential resistance, RV, of the SSD can be found using the I-V response, key issue for determining the impedance matching between the channels and the signal acquisition system, and it is defined by

$$R\_V = \left(\frac{dI}{dV}\Big|\_{V=0}\right)^{-1} \tag{2}$$

The nonlinearity (NV), which expresses the diode-like I-V curve behavior, can be determined by evaluating

$$N\_V = \frac{d^2I}{dV^2}\bigg|\_{V=0}.\tag{3}$$

**337**

reaches 37 V<sup>−</sup><sup>1</sup>

**Figure 8.**

length, rendered in **Figure 9(a)**.

*Semiconductor Surface State Engineering for THz Nanodevices*

decrease in DL inside the nanochannel. Small DL length facilitates ballistic transport; in the meantime that carrier's mean free path is larger than the DL and reduces RV. For this case, when L is reduced from 1.5 to 0.5 μm induces a change on RV from 1.3 MΩ to 423 kΩ. Nevertheless, the reduction of DL through the reduction of L favors the presence of an important leakage current for reverse bias, affecting the

*Current-voltage behavior of the L-shape SSD-based geometry when (a) the channel width (W) parameters are* 

Therefore, for 2DEG-based SSD intended to work at THz frequencies, it is necessary to reduce the carrier's time of flight between electrodes, which can be achieved by improving the electron mobility of the 2DEG, the carrier's mean free path getting better or shortening the L extension, considering that at THz frequencies the electron transport is in the ballistic regime [30]. To design a cost-effective SSD THz device, the election of the appropriated length L for the working frequency in

The impact of the geometrical dimensions on the I-V characteristic of the SSD was performed by the numeric analysis for all geometric parameters indicated in **Figure 5(a)**, and it is resumed by the nominal sensitivity of the SSD in **Figure 9(a)**. For example, the reduction of the W thickness increases the magnitude RV while weakens the rectifier performance of the SSD by the apparition of an important leakage current, indicating that the NV is reduced with this modification. The γ<sup>0</sup>

other hand, the largest nanochannel length (L = 1.5 μm) originates that γ0 = 25 V<sup>−</sup><sup>1</sup>

The reduction of DL width and length is not the only mechanism to modify the DC performance of the SSD. Controlling the magnitude of the electric field that modulates electrons in the Ns would have the effect of improving the I-V behavior. In this task, both the vertical and horizontal width trenches (WV and WH, respectively) are the main geometrical elements that can be used to achieve modulation of surface states. It was found that WV in the range of 5–50 nm did not affect the I-V performance of the SSD and consequentially the γ0 is constant for these modifications and being reduced with WV > 50 nm. On the other hand, small changes in WH affected strongly the DC performance of the SSD; meanwhile variation of WH from 5 to 30 nm resulted in a variation of VTH from 0 to 0.2 V [33, 34], and γ0 is optimized for WH = 30 nm. The effect of WV and WH trenches is seen in **Figure 9(a)**. The SSD ability to rectify signals in the THz region relies in the γ0 value, which can be improved for nanochannel geometry that exhibits long and wide DL, amplifying RV and NV. Nevertheless, narrow W and large L sizes imply to enlarge the VTH.

and conversely the sensitivity is reduced by the reduction of the nanochannel

for the narrower W of 60 nm, being reduced for wider W. On the

,

I-V nonlinearity and inducing a reduction in the sensitivity of the devices.

*varied from 60 to 80 nm and (b) the channel length (L) is modified from 0.2 to 1.5 μm.*

function of the 2DEG mobility is mandatory, keeping γ0 as high as possible.

*DOI: http://dx.doi.org/10.5772/intechopen.86469*

NV is a main issue for the performance of the rectifier because of higher nonlinearity result in a larger DC output. The impact of RV and NV is resumed in the sensitivity, γ0, of the device, which is calculated by γ0 = NVRV. RV, NV, and γ0 are usually studied at zero bias, heeding the fact that detection must be performed with no feed bias [35].

#### **3.1 Geometry dimension impact on I-V characteristics**

In **Figure 8(a)** the effect of modification in the channel width (W) through I-V curves is presented. It is observed that when W is widened, VTH is reduced as a consequence of the spatial restriction of the electrons that could occupy the surface states inside the grooves in order to maintain charge neutrality. Large DL indicates high diode resistance and requires high voltage in order to deplete or drain the surface states, producing that RV goes from 143 MΩ to 233 kΩ when W is broadened from 60 to 80 nm, respectively.

According to Ohm's law, the current is improved as the thickness W is widened by the reduction of RV. Therefore, by the design of the channel width, it is possible to control the SSD's worth VTH and RV. Nevertheless, large W generates reverse current at low negative bias, and, as a result, the diode-like character disappears lowering γ0. Therefore, in order to avoid a reverse current flow and design for a lowthreshold voltage VTH device, it is necessary to consider the relationship between the surface charge and W [22, 30].

**Figure 8(b)** shows I-V characteristics of SSDs with several channel lengths, L, where it is appreciated that VTH shifts to lower voltages when L is reduced due to the *Semiconductor Surface State Engineering for THz Nanodevices DOI: http://dx.doi.org/10.5772/intechopen.86469*

**Figure 8.**

*Electromagnetic Materials and Devices*

**3. Self-switching diode design guidelines**

*RV* <sup>=</sup> (

*NV* <sup>=</sup> *<sup>d</sup>*<sup>2</sup> \_\_\_\_*<sup>I</sup>*

**3.1 Geometry dimension impact on I-V characteristics**

determined by evaluating

from 60 to 80 nm, respectively.

the surface charge and W [22, 30].

In order to get a rectifier with cut-off in the THz region by the SSD device, it is important to follow design considerations that may improve the current rectification with low VTH and optimize the SSD up for the best efficiency. These considerations are related to the geometry-depletion region relationship between the SSD dimensions, shape, and the DL extension. In this section, we evaluate the rectification performance of the L-shape SSD device in DC injection mode by a systematic analysis where the width, W; the length, L; and the vertical and horizontal trench width (WV and WH) of the channels are varied in order to get their effect on the I-V behavior of the device. The layout shown in **Figure 5(a)** defines the reference geometries where we have a varied chosen parameter, while the others were fixed. The simulations were carried out in order to obtain the I-V curves of each geometrical variation with the aim to evaluate the ability of channels to detect the electrical energy of low-voltage THz signals. On this way, the SSDs can be considered as square-law rectifiers that generate electrical power from the incoming THz radiation. In order to understand the size effect on the detection, we use three criteria that define the performance of the SSD. Fist, differential resistance, RV, of the SSD can be found using the I-V response, key issue for determining the impedance matching

between the channels and the signal acquisition system, and it is defined by

\_\_\_ *dI dV*| *<sup>V</sup>*=0)

The nonlinearity (NV), which expresses the diode-like I-V curve behavior, can be

*dV*2| *V*=0

NV is a main issue for the performance of the rectifier because of higher nonlinearity result in a larger DC output. The impact of RV and NV is resumed in the sensitivity, γ0, of the device, which is calculated by γ0 = NVRV. RV, NV, and γ0 are usually studied at zero bias, heeding the fact that detection must be performed with no feed bias [35].

In **Figure 8(a)** the effect of modification in the channel width (W) through I-V curves is presented. It is observed that when W is widened, VTH is reduced as a consequence of the spatial restriction of the electrons that could occupy the surface states inside the grooves in order to maintain charge neutrality. Large DL indicates high diode resistance and requires high voltage in order to deplete or drain the surface states, producing that RV goes from 143 MΩ to 233 kΩ when W is broadened

According to Ohm's law, the current is improved as the thickness W is widened by the reduction of RV. Therefore, by the design of the channel width, it is possible to control the SSD's worth VTH and RV. Nevertheless, large W generates reverse current at low negative bias, and, as a result, the diode-like character disappears lowering γ0. Therefore, in order to avoid a reverse current flow and design for a lowthreshold voltage VTH device, it is necessary to consider the relationship between

**Figure 8(b)** shows I-V characteristics of SSDs with several channel lengths, L, where it is appreciated that VTH shifts to lower voltages when L is reduced due to the

−1

(2)

. (3)

**336**

*Current-voltage behavior of the L-shape SSD-based geometry when (a) the channel width (W) parameters are varied from 60 to 80 nm and (b) the channel length (L) is modified from 0.2 to 1.5 μm.*

decrease in DL inside the nanochannel. Small DL length facilitates ballistic transport; in the meantime that carrier's mean free path is larger than the DL and reduces RV. For this case, when L is reduced from 1.5 to 0.5 μm induces a change on RV from 1.3 MΩ to 423 kΩ. Nevertheless, the reduction of DL through the reduction of L favors the presence of an important leakage current for reverse bias, affecting the I-V nonlinearity and inducing a reduction in the sensitivity of the devices.

Therefore, for 2DEG-based SSD intended to work at THz frequencies, it is necessary to reduce the carrier's time of flight between electrodes, which can be achieved by improving the electron mobility of the 2DEG, the carrier's mean free path getting better or shortening the L extension, considering that at THz frequencies the electron transport is in the ballistic regime [30]. To design a cost-effective SSD THz device, the election of the appropriated length L for the working frequency in function of the 2DEG mobility is mandatory, keeping γ0 as high as possible.

The impact of the geometrical dimensions on the I-V characteristic of the SSD was performed by the numeric analysis for all geometric parameters indicated in **Figure 5(a)**, and it is resumed by the nominal sensitivity of the SSD in **Figure 9(a)**. For example, the reduction of the W thickness increases the magnitude RV while weakens the rectifier performance of the SSD by the apparition of an important leakage current, indicating that the NV is reduced with this modification. The γ<sup>0</sup> reaches 37 V<sup>−</sup><sup>1</sup> for the narrower W of 60 nm, being reduced for wider W. On the other hand, the largest nanochannel length (L = 1.5 μm) originates that γ0 = 25 V<sup>−</sup><sup>1</sup> , and conversely the sensitivity is reduced by the reduction of the nanochannel length, rendered in **Figure 9(a)**.

The reduction of DL width and length is not the only mechanism to modify the DC performance of the SSD. Controlling the magnitude of the electric field that modulates electrons in the Ns would have the effect of improving the I-V behavior. In this task, both the vertical and horizontal width trenches (WV and WH, respectively) are the main geometrical elements that can be used to achieve modulation of surface states. It was found that WV in the range of 5–50 nm did not affect the I-V performance of the SSD and consequentially the γ0 is constant for these modifications and being reduced with WV > 50 nm. On the other hand, small changes in WH affected strongly the DC performance of the SSD; meanwhile variation of WH from 5 to 30 nm resulted in a variation of VTH from 0 to 0.2 V [33, 34], and γ0 is optimized for WH = 30 nm. The effect of WV and WH trenches is seen in **Figure 9(a)**.

The SSD ability to rectify signals in the THz region relies in the γ0 value, which can be improved for nanochannel geometry that exhibits long and wide DL, amplifying RV and NV. Nevertheless, narrow W and large L sizes imply to enlarge the VTH.

#### **Figure 9.**

*(a) Sensitivity of the L-shape SSD devices as a function of the size of the geometrical parameters. (b) Effect of modification of W in the VTH and γ0.*

The low-power THz radiation detection needs a rectifier with a threshold voltage close to zero, and according to the simulations, the channel width is the element that strongly defined the γ0 and VTH performance of an L-shape SSD. Numerical simulations were carried out modifying the W to explore the dependence of γ0 and VTH with the aim to determine the dimensions of W that propitiate γ0 > 20 V<sup>−</sup><sup>1</sup> y *VTH* < 50 mV (see **Figure 9(b)**). These desirable conditions are stablished in order to overcome the current performance of the best MIM-tunnel barriers, which exhibit sensitivities between 2.5 and 4 V<sup>−</sup><sup>1</sup> [36, 37].

According to the graph in **Figure 9(b)**, it is possible to obtain γ0 > 20 V<sup>−</sup><sup>1</sup> for W ≤ 70 nm, improving the rectifier performance of the SSD. On the other hand, when W < 70 nm, the VTH is higher. The best configuration is labeled by the dotted red line at W = 70 nm. For W < 70 nm, the sensitivity of the SSD is improved, expanding the voltage necessary to turn on the device. Conversely, for W values at the right hand of the dotted red line, the threshold voltage necessary to produce a conductive nanochannel is cut down in the same way with that of γ0. In other words, the geometrical design of the SSD must consider the application where the SSD is going to be used. The design should consider the power of the signal to be detected in order to choose the tolerance margin between γ0 and VTH that improves the performance of the SSD.

Rendering to numerical results, the SSD devices combine geometrical effects with the 2DEG properties to act like a rectifier, the nanochannel and trench width in conjunction with the appropriate choice of channel length being key parameters. The optimization of W, WH, and L induces that the nominal sensitivity of the devices raised to measurement around 40 V<sup>−</sup><sup>1</sup> . Self-switching diodes are good candidates for zero-bias detection and harvesting applications as square-law rectifier elements in the rectenna concept. Nevertheless, the high-impedance nature of the SSD will introduce drawbacks that limit the power transfer between the rectifier and the antenna as it will be shown in the next section.

#### **3.2 Rectennas based on self-switching diodes for THz detection**

When the L-shape SSD has been optimized to obtain the best rectifier performance, it is possible to use the device in the detection or harvesting of THz electromagnetic signals. In order to evaluate the efficiency of the SSD as rectifier element in the rectenna concept, we analyze the SSDs coupling to gold-made Archimedean spiral antenna lying on the surface of a semi-infinite SiO2 substrate and designed to operate between 0.25 and 2 THz with a right-hand circular polarization [38]. **Figure 10(a)** illustrates this antenna design. The simulated performance of the designed micrometric

**339**

*Semiconductor Surface State Engineering for THz Nanodevices*

antenna was obtained when it is excited with monochromatic plane waves with

**Figure 10(a)** the antenna impedance, Zin, is plotted as a first result. In this numeric analysis, we assume that the cut-off frequencies reported for high mobility struc-

*Performance of L-shape SSD-based rectenna to harvest the optical energy of a terahertz source obtained by the simulation process. (a) Input impedance. Inset shows the Archimedean spiral antenna. (b) Rectified voltage* 

The DC voltage generated from the received terahertz radiation by the SSD rectenna is illustrated in **Figure 10(b)**, where a full width at half-maximum parameter of more than 1.8 THz is exhibited with a maximum voltage obtained of 1.25 mV at 1.5 THz. The conversion efficiency of the rectennas is also shown in **Figure 10(b)** as a function of frequency where the total efficiency is found to be ∼0.032%. This numerical analysis indicates that in this configuration, the use of L-shape SSDs as rectifiers instead of MIM nanometer diodes enhances the efficiency of the recten-

based on MIM barriers due to their I-V characteristic curves, which are more asym-

From **Figure 10** it is clear that the major voltage and efficiency of the rectenna are obtained when the Zin is raised to about 125 Ω. Higher antenna impedance means a better electrical coupling between the antennas and the diode and more efficient transfer of energy between antenna and rectifier [38]. The coefficient of

> *RV* − *Zin RV* + *Zin*

which exhibits a value around 99.96% for the rectenna system analyzed in this work. In other words, the high magnitude of Γ indicates that only 0.04% of the optical energy is transmitted from the spiral antenna to the L-shape SSD and the

The SSD device performance as rectifier element is modified under unmatched conditions, making necessary to study the RV behavior on Γ. We use a reference source with a Zin = 50 Ω in order to define the effective sensitivity (γ50Ω) to consid-

where Γ is calculated using the Zin = 50 Ω. The γ50Ω criteria describe the performance of the SSD when their electrodes are short circuited to the antenna arms.

2

erer the effects of the unmatched source through the relationship [28]:

accredited to the mismatch impedance between the rectifier and the antenna.

[39] incoming from a precisely tuned terahertz laser. In

[38]. Rectennas based on SSDs are more efficient than those

%) obtained by this SSD rectenna is

, (4)

), (5)

*DOI: http://dx.doi.org/10.5772/intechopen.86469*

an irradiance of 1 W∕cm2

**Figure 10.**

nas by a factor of 106

tures SSD are around 5 THz [22].

*and optical-to-electrical conversion efficiency.*

metrical. The relatively low efficiencies (∼10<sup>−</sup><sup>2</sup>

reflection between both elements is defined by

Γ = \_\_\_\_\_\_

rest of the optical power is returned to the spirals [38].

γ50Ω = γ0(1 − |Γ|

*Semiconductor Surface State Engineering for THz Nanodevices DOI: http://dx.doi.org/10.5772/intechopen.86469*

**Figure 10.**

*Electromagnetic Materials and Devices*

**Figure 9.**

*modification of W in the VTH and γ0.*

exhibit sensitivities between 2.5 and 4 V<sup>−</sup><sup>1</sup>

the devices raised to measurement around 40 V<sup>−</sup><sup>1</sup>

and the antenna as it will be shown in the next section.

**3.2 Rectennas based on self-switching diodes for THz detection**

the performance of the SSD.

The low-power THz radiation detection needs a rectifier with a threshold voltage close to zero, and according to the simulations, the channel width is the element that strongly defined the γ0 and VTH performance of an L-shape SSD. Numerical simulations were carried out modifying the W to explore the dependence of γ0 and VTH with the aim to determine the dimensions of W that propitiate γ0 > 20 V<sup>−</sup><sup>1</sup>

*(a) Sensitivity of the L-shape SSD devices as a function of the size of the geometrical parameters. (b) Effect of* 

*VTH* < 50 mV (see **Figure 9(b)**). These desirable conditions are stablished in order to overcome the current performance of the best MIM-tunnel barriers, which

According to the graph in **Figure 9(b)**, it is possible to obtain γ0 > 20 V<sup>−</sup><sup>1</sup>

W ≤ 70 nm, improving the rectifier performance of the SSD. On the other hand, when W < 70 nm, the VTH is higher. The best configuration is labeled by the dotted red line at W = 70 nm. For W < 70 nm, the sensitivity of the SSD is improved, expanding the voltage necessary to turn on the device. Conversely, for W values at the right hand of the dotted red line, the threshold voltage necessary to produce a conductive nanochannel is cut down in the same way with that of γ0. In other words, the geometrical design of the SSD must consider the application where the SSD is going to be used. The design should consider the power of the signal to be detected in order to choose the tolerance margin between γ0 and VTH that improves

Rendering to numerical results, the SSD devices combine geometrical effects with the 2DEG properties to act like a rectifier, the nanochannel and trench width in conjunction with the appropriate choice of channel length being key parameters. The optimization of W, WH, and L induces that the nominal sensitivity of

candidates for zero-bias detection and harvesting applications as square-law rectifier elements in the rectenna concept. Nevertheless, the high-impedance nature of the SSD will introduce drawbacks that limit the power transfer between the rectifier

When the L-shape SSD has been optimized to obtain the best rectifier performance, it is possible to use the device in the detection or harvesting of THz electromagnetic signals. In order to evaluate the efficiency of the SSD as rectifier element in the rectenna concept, we analyze the SSDs coupling to gold-made Archimedean spiral antenna lying on the surface of a semi-infinite SiO2 substrate and designed to operate between 0.25 and 2 THz with a right-hand circular polarization [38]. **Figure 10(a)** illustrates this antenna design. The simulated performance of the designed micrometric

[36, 37].

y

for

. Self-switching diodes are good

**338**

*Performance of L-shape SSD-based rectenna to harvest the optical energy of a terahertz source obtained by the simulation process. (a) Input impedance. Inset shows the Archimedean spiral antenna. (b) Rectified voltage and optical-to-electrical conversion efficiency.*

antenna was obtained when it is excited with monochromatic plane waves with an irradiance of 1 W∕cm2 [39] incoming from a precisely tuned terahertz laser. In **Figure 10(a)** the antenna impedance, Zin, is plotted as a first result. In this numeric analysis, we assume that the cut-off frequencies reported for high mobility structures SSD are around 5 THz [22].

The DC voltage generated from the received terahertz radiation by the SSD rectenna is illustrated in **Figure 10(b)**, where a full width at half-maximum parameter of more than 1.8 THz is exhibited with a maximum voltage obtained of 1.25 mV at 1.5 THz. The conversion efficiency of the rectennas is also shown in **Figure 10(b)** as a function of frequency where the total efficiency is found to be ∼0.032%. This numerical analysis indicates that in this configuration, the use of L-shape SSDs as rectifiers instead of MIM nanometer diodes enhances the efficiency of the rectennas by a factor of 106 [38]. Rectennas based on SSDs are more efficient than those based on MIM barriers due to their I-V characteristic curves, which are more asymmetrical. The relatively low efficiencies (∼10<sup>−</sup><sup>2</sup> %) obtained by this SSD rectenna is accredited to the mismatch impedance between the rectifier and the antenna.

From **Figure 10** it is clear that the major voltage and efficiency of the rectenna are obtained when the Zin is raised to about 125 Ω. Higher antenna impedance means a better electrical coupling between the antennas and the diode and more efficient transfer of energy between antenna and rectifier [38]. The coefficient of reflection between both elements is defined by

$$
\Gamma = \frac{R\_V - Z\_{\text{tot}}}{R\_V \star Z\_{\text{tot}}},
\tag{4}
$$

which exhibits a value around 99.96% for the rectenna system analyzed in this work. In other words, the high magnitude of Γ indicates that only 0.04% of the optical energy is transmitted from the spiral antenna to the L-shape SSD and the rest of the optical power is returned to the spirals [38].

The SSD device performance as rectifier element is modified under unmatched conditions, making necessary to study the RV behavior on Γ. We use a reference source with a Zin = 50 Ω in order to define the effective sensitivity (γ50Ω) to considerer the effects of the unmatched source through the relationship [28]:

$$
\chi\_{50\,\text{\textdegree}} = \chi\_0 \left\{ \mathbf{1} - \|\Gamma\|^2 \right\},\tag{5}
$$

where Γ is calculated using the Zin = 50 Ω. The γ50Ω criteria describe the performance of the SSD when their electrodes are short circuited to the antenna arms.

**Figure 11.** *Effect of the modification of the SSD reference geometry parameters on the effective sensitivity γ50<sup>Ω</sup>.*

The trade-off between γ<sup>50</sup>Ω and RV is depending on the geometrical parameters; this relationship is illustrated in **Figure 11**.

The numerical results illustrated in **Figure 11** have shown that the reference geometry is the best configuration possible even with the high Γ when they are plugged to a Zin = 50 Ω drive source. This confirms that even when the narrower channels are more sensitive than other structures, they are not the best option to generate and transmit DC electrical power thanks to the high value RV which heightens the Γ, reducing the power transfer between the antenna and the rectifier. This study indicates that those parameters of the channels that would propitiate to reach higher sensitivities γ0 are the same with that which produces high γ<sup>50</sup>Ω: the nanochannel width (W), length (L), and the thickness of WV.

The SSD as square-law detector or rectifier element in energy harvester systems represents an interest alternative, improving the performance of the rectennas based on MIM tunnel barriers, which exhibit very low efficiencies and reduce the technological process required for the rectennas' manufacture, involving only one step of high-resolution lithography. However, to produce terahertz rectennas useful for energy-harvesting applications, an efficient strategy to better match the impedance of the spiral antennas and the self-switching nanodiodes should be incorporated.

### **4. Self-switching diode shape variations**

According to the rectenna performance, a key issue that reduces the use of the self-switching diodes in detection or harvesting applications concerns their high resistance by the nanometric nature of this device. The impedance matching is very difficult, and the losses of the electrical power by reflection will be predominant. The SSD geometry plays the fundamental role defining the DC performance of the device, the design process being a trade-off between geometrical dimensions that exhibits low reverse current in a nonlinear I-V curve with a VTH close to 0 V and, at same time, low channel resistance in conjunction with a high sensitivity quantity. In this section we explore three different SSD shapes to improve their performance as low-power THz rectifier.

The first method to intensify the performance of the SSD is to raise the rectification efficiency by augmenting the numbers of paths through which the carriers travel. In this task, **Figure 12(a)** shows the schematic array of four L-shape SSDs, connected in parallel with geometrical dimensions based on the single SSD of **Figure 5(a)**. The numerical analyses of arrangement for 1, 2, 4, 8, and 16 single

**341**

*Semiconductor Surface State Engineering for THz Nanodevices*

SSDs placed in parallel are exhibited in **Figure 12(b)**. The I-V behavior of the SSD arrays exhibits a small gain of leakage current, while they show threshold voltage of ∼0 V. The current is incremented from 1.72 (single SSD) to 28 μA (16 SSD array), representing 16 times larger current in parallel than for a single SSD when the SSD

*(a) Top view layout of four L-shape SSDs in parallel array. (b) I-V characteristics of parallel coupled SSD* 

*arrangements. The inset shows the R0 and γ0 as functions of the number of SSD elements.*

The augment of SSD elements present in the arrays is translated into a better performance in the current behavior, generating a reduction in the overall resistance, RO, of the array-based SSD. The changes in device resistance could be considered as RO = RV/N, where RV refers to the resistance of the single L-shape element as it is shown in the inset of **Figure 12**. Accordingly, the effect of increasing the number of nanochannels produces Ro changes from 87 to 41 kΩ for a single SSD and 16 SSD arrays, respectively. This reduction in the nanochannel resistance is translated into a reduction in the γ0 of ~25% as it is plotted in the inset of **Figure 11**. Contrarily, the γ<sup>50</sup><sup>Ω</sup>

array-based SSD [33]. It is clear that the major quantity of SSD in parallel results in the reduction of the device resistance, which improves the impedance matching between rectifier elements and antennas by using the appropriate number of SSD [40]. **Figure 13(a)** exhibits the top view and carrier's distribution for the termed V-shape SSD. In this case, the shapes of the grooves have been modified to reduce the extension of DL inside the nanochannel by expanding the channel area with the aim to reduce the RV of the SSD device. According to the SSD working principle, the formation of the DL along the nanochannel defines the I-V performance of the device. The structure of **Figure 13(a)** and the 2DEG properties described in Section 2.1 were used as input parameters in numerical simulations to analyze the carrier

When no bias is applied, simulations in **Figure 13(b)** show a drastic reduction of the background carrier density with a width-dependent spatial charge distribution in this shape where electron concentration diminishes close to the channel vortex,

localized region. Reverse polarization is established for V = −0.5 V in **Figure 13(c)**. The pinch-off condition does not occur at −0.5 V occasioned by the small DL along the channel length, contrasting to the case of the L-shape geometry. Therefore, the carrier distribution can be easily modified to allow the current to flow even at a low reverse bias because of the nanochannel receiving similar carrier concentration for

for a single base SSD to 63 × 10<sup>−</sup><sup>3</sup>

V<sup>−</sup><sup>1</sup>

with effective width of 50 nm in a

for a 16

*DOI: http://dx.doi.org/10.5772/intechopen.86469*

system is biased at 0.5 V.

**Figure 12.**

exhibits a modification from 4 × 10<sup>−</sup><sup>3</sup>

concentration along the V-shape SSD.

reaching populations as low as 6.3 × 1012 cm−<sup>3</sup>

**Figure 12.**

*Electromagnetic Materials and Devices*

relationship is illustrated in **Figure 11**.

*Effect of the modification of the SSD reference geometry parameters on the effective sensitivity γ50<sup>Ω</sup>.*

nanochannel width (W), length (L), and the thickness of WV.

**4. Self-switching diode shape variations**

The trade-off between γ<sup>50</sup>Ω and RV is depending on the geometrical parameters; this

The numerical results illustrated in **Figure 11** have shown that the reference geometry is the best configuration possible even with the high Γ when they are plugged to a Zin = 50 Ω drive source. This confirms that even when the narrower channels are more sensitive than other structures, they are not the best option to generate and transmit DC electrical power thanks to the high value RV which heightens the Γ, reducing the power transfer between the antenna and the rectifier. This study indicates that those parameters of the channels that would propitiate to reach higher sensitivities γ0 are the same with that which produces high γ<sup>50</sup>Ω: the

The SSD as square-law detector or rectifier element in energy harvester systems

According to the rectenna performance, a key issue that reduces the use of the self-switching diodes in detection or harvesting applications concerns their high resistance by the nanometric nature of this device. The impedance matching is very difficult, and the losses of the electrical power by reflection will be predominant. The SSD geometry plays the fundamental role defining the DC performance of the device, the design process being a trade-off between geometrical dimensions that exhibits low reverse current in a nonlinear I-V curve with a VTH close to 0 V and, at same time, low channel resistance in conjunction with a high sensitivity quantity. In this section we explore three different SSD shapes to improve their performance as

The first method to intensify the performance of the SSD is to raise the rectifica-

tion efficiency by augmenting the numbers of paths through which the carriers travel. In this task, **Figure 12(a)** shows the schematic array of four L-shape SSDs, connected in parallel with geometrical dimensions based on the single SSD of **Figure 5(a)**. The numerical analyses of arrangement for 1, 2, 4, 8, and 16 single

represents an interest alternative, improving the performance of the rectennas based on MIM tunnel barriers, which exhibit very low efficiencies and reduce the technological process required for the rectennas' manufacture, involving only one step of high-resolution lithography. However, to produce terahertz rectennas useful for energy-harvesting applications, an efficient strategy to better match the impedance of the spiral antennas and the self-switching nanodiodes should be

**Figure 11.**

incorporated.

low-power THz rectifier.

**340**

*(a) Top view layout of four L-shape SSDs in parallel array. (b) I-V characteristics of parallel coupled SSD arrangements. The inset shows the R0 and γ0 as functions of the number of SSD elements.*

SSDs placed in parallel are exhibited in **Figure 12(b)**. The I-V behavior of the SSD arrays exhibits a small gain of leakage current, while they show threshold voltage of ∼0 V. The current is incremented from 1.72 (single SSD) to 28 μA (16 SSD array), representing 16 times larger current in parallel than for a single SSD when the SSD system is biased at 0.5 V.

The augment of SSD elements present in the arrays is translated into a better performance in the current behavior, generating a reduction in the overall resistance, RO, of the array-based SSD. The changes in device resistance could be considered as RO = RV/N, where RV refers to the resistance of the single L-shape element as it is shown in the inset of **Figure 12**. Accordingly, the effect of increasing the number of nanochannels produces Ro changes from 87 to 41 kΩ for a single SSD and 16 SSD arrays, respectively. This reduction in the nanochannel resistance is translated into a reduction in the γ0 of ~25% as it is plotted in the inset of **Figure 11**. Contrarily, the γ<sup>50</sup><sup>Ω</sup> exhibits a modification from 4 × 10<sup>−</sup><sup>3</sup> for a single base SSD to 63 × 10<sup>−</sup><sup>3</sup> V<sup>−</sup><sup>1</sup> for a 16 array-based SSD [33]. It is clear that the major quantity of SSD in parallel results in the reduction of the device resistance, which improves the impedance matching between rectifier elements and antennas by using the appropriate number of SSD [40].

**Figure 13(a)** exhibits the top view and carrier's distribution for the termed V-shape SSD. In this case, the shapes of the grooves have been modified to reduce the extension of DL inside the nanochannel by expanding the channel area with the aim to reduce the RV of the SSD device. According to the SSD working principle, the formation of the DL along the nanochannel defines the I-V performance of the device. The structure of **Figure 13(a)** and the 2DEG properties described in Section 2.1 were used as input parameters in numerical simulations to analyze the carrier concentration along the V-shape SSD.

When no bias is applied, simulations in **Figure 13(b)** show a drastic reduction of the background carrier density with a width-dependent spatial charge distribution in this shape where electron concentration diminishes close to the channel vortex, reaching populations as low as 6.3 × 1012 cm−<sup>3</sup> with effective width of 50 nm in a localized region. Reverse polarization is established for V = −0.5 V in **Figure 13(c)**. The pinch-off condition does not occur at −0.5 V occasioned by the small DL along the channel length, contrasting to the case of the L-shape geometry. Therefore, the carrier distribution can be easily modified to allow the current to flow even at a low reverse bias because of the nanochannel receiving similar carrier concentration for

**Figure 13.**

*(a) Schematic representation of the V-shape self-switching diode. Electron charge distribution along the 2DEG plane under (b) zero, (c) reverse (V = −0.5 V), and (d) forward (V = +0.5 V) voltage bias.*

reverse and forward condition (at 0.5 V bias), where the redistribution of charge reduces the size of the DL and enlarges the free carrier concentration. Forward condition is illustrated in **Figure 13(d)**.

**Figure 14(a)** shows the I-V characteristics for the V-shape SSDs with the reference geometry depicted in **Figure 13(a)** in red solid-line plot where the weak diodelike I-V behavior is appreciated. For this V-shape design, a VTH of ∼100 mV and the presence of important current-leakage at reverse breakdown voltage of ∼140 mV are presented. Both phenomena are consequence of the short DL width (along the channel) that is easily filled up when a reverse bias above this voltage is applied. Hence, the DL extension for the L-shape is larger than the one exhibited by the V-shape SSD, according to **Figures 5(b)** and **13(b)**, respectively. This produces that the V-shape SSD needs a smaller voltage to reach VTH and makes the electrons to flow. Nevertheless, under reverse polarity a leakage current can appear for voltages as low as −0.25 V, reducing the nonlinearity of the device.

The I-V characteristics of V-shape SSDs are sensitive to modifications in their dimensions, as in the case of the L-shape. The performance of the I-V when the channel width, W, is varied is presented in **Figure 14(a)**, while the inset displays the DC behavior when the V leaning angle (α0) is modified. For this shape, the small DL between the trenches implies that the diode-like characteristics can be observed only at small W < 45 nm and for thicker size the I-V has a resistor-like behavior. To avoid a reverse current flow and design for a low-VTH V-shape device, to study the relationship between the DL and α0 is required. The leaning angle controls the number of free carriers that could occupy the NS. Therefore, α0 > 7° is translated in a decay of the DL width, producing low RV and VTH in conjunction with poor diode-like behavior. Opposite effect is found to narrow V leaning angles [34] as seen in the inset of **Figure 14(a)**.

**Figure 14(b)** resumed the impact of the geometry parameters that conform the V-shape SSD by the analysis of the γ<sup>50</sup>Ω framework where the maximum sensitivity for this analysis is less of 2 × 10<sup>−</sup><sup>3</sup> V<sup>−</sup><sup>1</sup> caused by the fact that the low RV and NV reduce drastically γ0. According to **Figure 14(b)** in this shape, all modifications have an important role defining the DC characteristics, producing that the design of this device to be more sensitive to the 2DEG and heterostructure properties. The

**343**

these situations.

**Figure 15.**

**Figure 14.**

*curves for several leaning angles, α0.*

by the electric field applied to electrodes.

*Semiconductor Surface State Engineering for THz Nanodevices*

V-shape SSD exhibits poor diode-like characteristics for the 2DEG characteristics used. The fact of the small DL formed in the channel vortex can be raised if the nSS is strongly elevated or the carrier's concentration is low. Consequently, the L-shape SSD is useless on this condition, being the V-shape the appropriated choice for

*(a) Two-dimensional scheme of the W-shape SSD where the main geometrical framework is illustrated. Simulation of the W-shape SSD carrier's density for (b) zero bias, (c) reverse bias, and (d) forward bias.*

*(a) I-V characteristics of L-shape SSD when the channel width, W, is modified. (b) The inset shows the I-V* 

Rendering to previous results, it is necessary to develop a shape of the SSD device that mixed the good rectifier behavior of the L-shape with the low-DL extension of the V-shape that reduces RV with the aim to improve the performance of the SSD concept as rectifier. The authors explored the novel SSD shape shown in **Figure 15(a)** labeled as W-shape SSD [40]. In this device, the DL along the nanochannel has been modified from the completely depleted channel in the L-shape SSD and the less depleted V-shape into a punctual region where the depletion is maximum and easily modified

For the no-bias situation illustrated in **Figure 15(b)**, the population of electrons inside the nanochannel is enlarged with the vertical distance from the trenches.

*DOI: http://dx.doi.org/10.5772/intechopen.86469*

*Semiconductor Surface State Engineering for THz Nanodevices DOI: http://dx.doi.org/10.5772/intechopen.86469*

#### **Figure 14.**

*Electromagnetic Materials and Devices*

condition is illustrated in **Figure 13(d)**.

**Figure 13.**

for this analysis is less of 2 × 10<sup>−</sup><sup>3</sup>

as low as −0.25 V, reducing the nonlinearity of the device.

reverse and forward condition (at 0.5 V bias), where the redistribution of charge reduces the size of the DL and enlarges the free carrier concentration. Forward

*plane under (b) zero, (c) reverse (V = −0.5 V), and (d) forward (V = +0.5 V) voltage bias.*

*(a) Schematic representation of the V-shape self-switching diode. Electron charge distribution along the 2DEG* 

The I-V characteristics of V-shape SSDs are sensitive to modifications in their dimensions, as in the case of the L-shape. The performance of the I-V when the channel width, W, is varied is presented in **Figure 14(a)**, while the inset displays the DC behavior when the V leaning angle (α0) is modified. For this shape, the small DL between the trenches implies that the diode-like characteristics can be observed only at small W < 45 nm and for thicker size the I-V has a resistor-like behavior. To avoid a reverse current flow and design for a low-VTH V-shape device, to study the relationship between the DL and α0 is required. The leaning angle controls the number of free carriers that could occupy the NS. Therefore, α0 > 7° is translated in a decay of the DL width, producing low RV and VTH in conjunction with poor diode-like behavior. Opposite effect is found to narrow V leaning angles [34] as seen in the inset of **Figure 14(a)**.

**Figure 14(b)** resumed the impact of the geometry parameters that conform the V-shape SSD by the analysis of the γ<sup>50</sup>Ω framework where the maximum sensitivity

reduce drastically γ0. According to **Figure 14(b)** in this shape, all modifications have an important role defining the DC characteristics, producing that the design of this device to be more sensitive to the 2DEG and heterostructure properties. The

caused by the fact that the low RV and NV

V<sup>−</sup><sup>1</sup>

**Figure 14(a)** shows the I-V characteristics for the V-shape SSDs with the reference geometry depicted in **Figure 13(a)** in red solid-line plot where the weak diodelike I-V behavior is appreciated. For this V-shape design, a VTH of ∼100 mV and the presence of important current-leakage at reverse breakdown voltage of ∼140 mV are presented. Both phenomena are consequence of the short DL width (along the channel) that is easily filled up when a reverse bias above this voltage is applied. Hence, the DL extension for the L-shape is larger than the one exhibited by the V-shape SSD, according to **Figures 5(b)** and **13(b)**, respectively. This produces that the V-shape SSD needs a smaller voltage to reach VTH and makes the electrons to flow. Nevertheless, under reverse polarity a leakage current can appear for voltages

**342**

*(a) I-V characteristics of L-shape SSD when the channel width, W, is modified. (b) The inset shows the I-V curves for several leaning angles, α0.*

#### **Figure 15.**

*(a) Two-dimensional scheme of the W-shape SSD where the main geometrical framework is illustrated. Simulation of the W-shape SSD carrier's density for (b) zero bias, (c) reverse bias, and (d) forward bias.*

V-shape SSD exhibits poor diode-like characteristics for the 2DEG characteristics used. The fact of the small DL formed in the channel vortex can be raised if the nSS is strongly elevated or the carrier's concentration is low. Consequently, the L-shape SSD is useless on this condition, being the V-shape the appropriated choice for these situations.

Rendering to previous results, it is necessary to develop a shape of the SSD device that mixed the good rectifier behavior of the L-shape with the low-DL extension of the V-shape that reduces RV with the aim to improve the performance of the SSD concept as rectifier. The authors explored the novel SSD shape shown in **Figure 15(a)** labeled as W-shape SSD [40]. In this device, the DL along the nanochannel has been modified from the completely depleted channel in the L-shape SSD and the less depleted V-shape into a punctual region where the depletion is maximum and easily modified by the electric field applied to electrodes.

For the no-bias situation illustrated in **Figure 15(b)**, the population of electrons inside the nanochannel is enlarged with the vertical distance from the trenches.

#### **Figure 16.**

*I-V performance of the W-shape SSD where it is appreciated that the threshold voltage can be modulated by the separation of the grooves.*

On the other hand, the electron concentration increases and decreases periodically along the channel, producing an island-like population of electrons with rhombus shape. In this numerical analysis, it is appreciated that the spatial distribution of electrons close to the center of the rhombus is maximum (red color) and it is reduced away to the center of each rhombic electron cluster (cyan color). In this condition the absence of free carriers between the high populated centers of the rhombus can avoid the current flow.

For reverse condition in **Figure 15(c)**, the reduction of the carrier density in the center of the rhombus is obtained, and in the same way, the size of the electron agglomeration is reduced at the left-hand side in contrast with the 0 V case, avoiding free electrons to participate in conduction. When positive voltage is applied to the anode electrode to reduce the DL, a conducting path close to the chevron corners connects the dots, and a wirelike electron distribution is formed as it is indicated in **Figure 15(d)**, and the current flux can be obtained.

The W-shape SSD current-voltage behavior is dependent on their geometrical dimensions, as in the case of the L- and V-shape devices. Accordingly, the DC performance is optimized by the modification of the shape guidelines, i.e., in the I-V shown in **Figure 16**, the channel width is varied from 20 to 28 nm, being the principal component that determines the DC performance of the SSD as in the case of the L- and V-shape. For the reference geometry with W = 20 nm, the diode-like behavior is present with a negligible negative current, but the VTH is around 4.5 V, undesirable for THz rectification. The slow modification of 1 nm in the channel width modifies strongly the I-V curve in the W-shape SSD.

For instance, the VTH can be tailored by changing the separation of the grooves or the effective channel width from 4.5 to 2.5 V as the channel width is raised from 20 to 24 nm. The inset of **Figure 16** exhibits that when the W-shape SSD is calculated with W > 26 nm, the I-V characteristic behavior turns capable to operate with small power signals owing to the VTH which is near to 0 V. It is important to note the absence of leakage current for reverse bias when the channel width is widened and different behaviors displayed by L- and V-shape designs. The optimization of this device and their performance as rectifier element will be shown in future works.

**345**

*Semiconductor Surface State Engineering for THz Nanodevices*

This chapter analyzes the emerging self-switching diode to deal with detection

and harvesting of THz radiation from the numerical analysis of their rectifier behavior. The authors have shown the effect of geometry shape and size on the current-voltage performance, finding that the most important values that define the SSD's properties are the channel width and length in conjunction with the trench width for the L-, V-, and W-shape SSDs which are technologically promising by their simplicity in the manufacturing process. We found that the threshold voltage can be tuned to ~0 V, appropriated range for the low power THz signals. The L-shape SSD was analyzed as rectifier element in the rectenna concept where simulations indicate their ability to reach overall efficiencies of ∼0.032%, improving the performance of the rectennas based on MIM tunnel barriers for THz applications. The reflection coefficient analysis reveals that one of the problems exhibited by the SSD devices lies in the high-resistance nature of the nanochannel. The reduction of the SSD resistance can be obtained using different shapes which controls the depletion region formed inside the nanochannel. Finally, we conclude that the adequate geometry size and shape of the SSD-based devices must be considered in conjunction with the current development of high-mobility heterostructure and nanolithography process in order to get the ideal rectifier to

The authors acknowledge the financial support from CEMIE-SOL 22, FRC-UASLP, and CONACYT-Mexico through grants INFR-2015-01-255489, CB 2015- 257358, PNCPN2014-01-248071, and the Catedras CONACyT (Project No. 44).

All authors declare that they have no conflict of interest.

*DOI: http://dx.doi.org/10.5772/intechopen.86469*

**5. Conclusions**

work in the THz range.

**Acknowledgements**

**Conflict of interest**
