**Abstract**

This chapter is dedicated to study the semiconductor surface states, which combined with nanolithography techniques could result on remarkable properties of advanced nanodevices suitable for terahertz (THz) signal detection or harvesting. The author presents the use of low-dimensional semiconductor heterostructures for the development of the so-called self-switching diodes (SSDs), studying by simulation tool key parameters in detail such as the shape and size of the two-dimensional electron gas system. The impact of the geometry on the working principle of the nanodevice and the effects on current-voltage behavior will be described in order to acquire design guidelines that may improve the performance of the self-switching diodes when applied to low-power square-law rectifiers as well as elements in rectennas by appropriately setting the size of the components.

**Keywords:** surface states engineering, self-switching diode, L-shape, V-shape, W-shape, rectenna

#### **1. Introduction**

The terahertz frequency range of the electromagnetic spectrum represents a technology gap between the electronic and optical well-stabilized technologies. Thus, the obtention of systems designed to generate, detect, and process THz radiation still is of scientific attention by the full of potential applications. Meanwhile sources available nowadays are typically expensive, fallible, and voluminous. It is possible to extend the electronic and optic concepts, for the THz radiation with millimetric and micrometric wavelength, respectively. However, the use of electronic in the THz range needs small circuits and high-frequency cutoff, while optical requests deal with the dimensions necessaries to work in the THz range [1].

Electronic has been one of the most advanced technologies applied in the modern life, being imperative to extend the electronic concepts such as resistance, diode, and transistor to operate in the THz range with the aim to fill the so-called THz gap by small, efficient, and low-cost technologies. The use of electronic devices in THz implies both high carriers' mobility and short flight time of carriers between electrodes. The nanodevices are one of the most promising alternatives to the development of the THz technology. Recently, the semiconductor nanodevices have been employed for the generation and detection of THz radiation [1–6] showing an enormous potential for their application.

A wide variety of physics phenomena has been used to generate THz radiation by the manipulation of materials systems. THz radiation generation technology can be roughly classified into two categories: photonic and electronic. Phenomena such as the photo-Dember effect [2], Gunn oscillations [3], quantum cascade lasers [4], and difference-frequency mixing in nonlinear crystals [5] have been used to generate THz through the electronic approach. In these techniques, the semiconductor material has a crucial role, and its properties can be further improved by the use of nanostructures. On the other hand, the most applied THz detectors are classified into bolometers and photoconductors. The widely used bolometer is based on temperature variations caused by THz radiation absorption [6].

Important challenges arouse in the development of novel semiconductor nanodevices tuned in THz range to be operated at room temperature (RT). The nanodevice performance at 300 K is reduced principally for the high-impedance nature of this type of technology and the low carrier mobility. In order to improve the RT properties of nanotechnology semiconductor devices, very sophisticate deposition technology has been used where the layer thickness must be controlled as thin as less than one monolayer.

Molecular beam epitaxy (MBE) has been one of the most popular techniques to the fabrication of semiconductor nanostructures used in the development and improvement of nanodevices, achieving faster and efficient electronic and optoelectronic devices like solid-state lasers [7], solar cells [8], and highelectron-mobility transistors (HEMTs) [9]. MBE has allowed the expansion of low-dimensional semiconductor systems, where carriers are restricted to move into two, one, or zero spatial dimensions, becoming an attractive field for researchers due to the possibility to obtain quantum effects that are promisors to fill the so-called THz gap. For example, quantum dots (zero-dimensional restriction) are capable to emit radiation in the THz region as result of their energy states, which depend on its physical dimensions and act as recombination centers for carriers generated in the GaAs layers within the structure when they are exited with a femtosecond optical pump at 800 nm [10]. Additionally, MBE allows for the construction of semiconductor structures with atomically abrupt and flat interfaces that in conjunction with band-structure engineering permit the obtention of high-purity heterostructures embedding a two-dimensional electron gas (2DEG) [11]. In the heterostructures with 2DEG, carriers are confined to a very narrow layer of thickness smaller than De Broglie wavelength which can travel without scattering caused principally by impurities. The large mean free path of electrons in 2DEG is translated into high mobility in the order of 14.4 × 10<sup>6</sup> cm<sup>2</sup> /Vs at low temperature. This high mobility is not possible to be obtained in traditional bulk materials [12].

The use of the modulation-doped semiconductor heterostructures with highmobility electrons confined to two dimensions in field-effect transistors originated the so-called high-electron-mobility transistor (HEMT). In these devices, the lowtemperature mobility was improved over time, leading to innovations in solid-state physics, high frequency, and low-noise electronics [9, 12]. The speed of transistors has been increased over time. HEMTs have demonstrated the highest frequency of operation over 1.5 THz when a combination of techniques such as reducing gate length, material purity, and doping schemes are used in their fabrication [11–13].

High carrier mobility can be proportionated by the appropriate design of modulation-doped heterostructure, where the 2DEG is present. Short flight time of carriers between electrodes is originated by size miniaturization where semiconductor devices enter into the ballistic transport regime, allowing them to be used in high-speed applications. Nevertheless, the current miniaturization technology reaches nanometric dimensions where the extent of surface atoms on

**329**

**Figure 1.**

*Semiconductor Surface State Engineering for THz Nanodevices*

engineer nanoscale devices designed to operate at THz frequencies.

contrasted with the bulk region. This state is illustrated in **Figure 1(b)**.

semiconductor bandgap, which generally serve as traps for free carriers.

*Ideal surface representation of (a) crystal structure and (b) band diagram.*

The ideal surface is not usually exhibited in III–V semiconductors because free surface bonds involve excessively high-energy states. Surface bonds use both mechanisms to reduce energy: surface reconstructions and reaction with atoms in the atmosphere, usually oxygen. After, the three-dimensional symmetry of surface lattice is changed in the last nanometers. This condition is schematized in **Figure 2(a)**. Surface reconstruction and surface reactions produce electronic states. These states have no equivalent in the band structure of the bulk crystal. Consequently, in real surface the existence of surface states NS should be considered, positioned inside the

The presence of NS, sometimes called midgap states, at surface causes important effects on the carrier's distribution and Fermi-level (EF) position relative to the EC

semiconductor materials represents an important percent of the whole device, making the performance of the nanodevices be affected by these outmost atoms. Surface physics plays an important role for the functioning and performance of semiconductor nanodevices, being imperative to understand and predict how surface states, surface charge, and near-surface depletion regions can be manipulated in order to

The characteristics and properties that characterize a semiconductor material such as carrier concentration, band structure, or bandgap result from assuming that translational symmetry of infinite bulk crystal is present in all the material volume. However, when the three-dimensional symmetry in the occurrence of a surface is interrupted, it makes the bulk assumptions inadequate. Therefore, to understand the mode that surface properties can be manipulated to produce nanodevices capable to operate at THz range, it is necessary to understand the different behavior adopted by the surface and the effects over the whole semiconductor characteristics. The sudden termination of the translational symmetry of the crystal lattice at surface originates surface atoms with unpaired electrons. In **Figure 1(a)** the ideal surface atomic arrange is exhibited. In this case, the topmost atomic bonds of surface atoms acquire the same configuration than bulk atoms, in a perfectly periodic two-dimensional surface. The surface bonds assume that lattice cell keeps repeating such if a virtual lattice is deposited above them. Atoms in an ideal surface present similar properties than those atoms from beneath layers in the bulk structure, exhibiting the condition of flat band, where the conduction band (EC) and valence band (EV) have the same energy position

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

**1.1 The semiconductor surface**

semiconductor materials represents an important percent of the whole device, making the performance of the nanodevices be affected by these outmost atoms. Surface physics plays an important role for the functioning and performance of semiconductor nanodevices, being imperative to understand and predict how surface states, surface charge, and near-surface depletion regions can be manipulated in order to engineer nanoscale devices designed to operate at THz frequencies.

#### **1.1 The semiconductor surface**

*Electromagnetic Materials and Devices*

as thin as less than one monolayer.

A wide variety of physics phenomena has been used to generate THz radiation by the manipulation of materials systems. THz radiation generation technology can be roughly classified into two categories: photonic and electronic. Phenomena such as the photo-Dember effect [2], Gunn oscillations [3], quantum cascade lasers [4], and difference-frequency mixing in nonlinear crystals [5] have been used to generate THz through the electronic approach. In these techniques, the semiconductor material has a crucial role, and its properties can be further improved by the use of nanostructures. On the other hand, the most applied THz detectors are classified into bolometers and photoconductors. The widely used bolometer is based on

Important challenges arouse in the development of novel semiconductor nanodevices tuned in THz range to be operated at room temperature (RT). The nanodevice performance at 300 K is reduced principally for the high-impedance nature of this type of technology and the low carrier mobility. In order to improve the RT properties of nanotechnology semiconductor devices, very sophisticate deposition technology has been used where the layer thickness must be controlled

Molecular beam epitaxy (MBE) has been one of the most popular techniques to the fabrication of semiconductor nanostructures used in the development and improvement of nanodevices, achieving faster and efficient electronic and optoelectronic devices like solid-state lasers [7], solar cells [8], and highelectron-mobility transistors (HEMTs) [9]. MBE has allowed the expansion of low-dimensional semiconductor systems, where carriers are restricted to move into two, one, or zero spatial dimensions, becoming an attractive field for researchers due to the possibility to obtain quantum effects that are promisors to fill the so-called THz gap. For example, quantum dots (zero-dimensional restriction) are capable to emit radiation in the THz region as result of their energy states, which depend on its physical dimensions and act as recombination centers for carriers generated in the GaAs layers within the structure when they are exited with a femtosecond optical pump at 800 nm [10]. Additionally, MBE allows for the construction of semiconductor structures with atomically abrupt and flat interfaces that in conjunction with band-structure engineering permit the obtention of high-purity heterostructures embedding a two-dimensional electron gas (2DEG) [11]. In the heterostructures with 2DEG, carriers are confined to a very narrow layer of thickness smaller than De Broglie wavelength which can travel without scattering caused principally by impurities. The large mean free path of electrons in 2DEG is translated into high mobility in the order

/Vs at low temperature. This high mobility is not possible to be

The use of the modulation-doped semiconductor heterostructures with highmobility electrons confined to two dimensions in field-effect transistors originated the so-called high-electron-mobility transistor (HEMT). In these devices, the lowtemperature mobility was improved over time, leading to innovations in solid-state physics, high frequency, and low-noise electronics [9, 12]. The speed of transistors has been increased over time. HEMTs have demonstrated the highest frequency of operation over 1.5 THz when a combination of techniques such as reducing gate length, material purity, and doping schemes are used in their fabrication [11–13]. High carrier mobility can be proportionated by the appropriate design of modulation-doped heterostructure, where the 2DEG is present. Short flight time of carriers between electrodes is originated by size miniaturization where semiconductor devices enter into the ballistic transport regime, allowing them to be used in high-speed applications. Nevertheless, the current miniaturization technology reaches nanometric dimensions where the extent of surface atoms on

temperature variations caused by THz radiation absorption [6].

**328**

of 14.4 × 10<sup>6</sup>

cm<sup>2</sup>

obtained in traditional bulk materials [12].

The characteristics and properties that characterize a semiconductor material such as carrier concentration, band structure, or bandgap result from assuming that translational symmetry of infinite bulk crystal is present in all the material volume. However, when the three-dimensional symmetry in the occurrence of a surface is interrupted, it makes the bulk assumptions inadequate. Therefore, to understand the mode that surface properties can be manipulated to produce nanodevices capable to operate at THz range, it is necessary to understand the different behavior adopted by the surface and the effects over the whole semiconductor characteristics.

The sudden termination of the translational symmetry of the crystal lattice at surface originates surface atoms with unpaired electrons. In **Figure 1(a)** the ideal surface atomic arrange is exhibited. In this case, the topmost atomic bonds of surface atoms acquire the same configuration than bulk atoms, in a perfectly periodic two-dimensional surface. The surface bonds assume that lattice cell keeps repeating such if a virtual lattice is deposited above them. Atoms in an ideal surface present similar properties than those atoms from beneath layers in the bulk structure, exhibiting the condition of flat band, where the conduction band (EC) and valence band (EV) have the same energy position contrasted with the bulk region. This state is illustrated in **Figure 1(b)**.

The ideal surface is not usually exhibited in III–V semiconductors because free surface bonds involve excessively high-energy states. Surface bonds use both mechanisms to reduce energy: surface reconstructions and reaction with atoms in the atmosphere, usually oxygen. After, the three-dimensional symmetry of surface lattice is changed in the last nanometers. This condition is schematized in **Figure 2(a)**. Surface reconstruction and surface reactions produce electronic states. These states have no equivalent in the band structure of the bulk crystal. Consequently, in real surface the existence of surface states NS should be considered, positioned inside the semiconductor bandgap, which generally serve as traps for free carriers.

The presence of NS, sometimes called midgap states, at surface causes important effects on the carrier's distribution and Fermi-level (EF) position relative to the EC

**Figure 1.** *Ideal surface representation of (a) crystal structure and (b) band diagram.*

**Figure 2.**

*Real surface representation of (a) crystal structure with surface atom reconstruction and reaction. (b) Band diagram with surface state effect.*

and EV near the surface. The NS position inside the bandgap offers low energy levels in comparison with EC and EV for carriers, and two types of NS can be recognized according to the charge that is acquired when occupied. Donor-type surface state is obtained when Ns exhibited a positive charge after filled in. On the other hand, acceptor-type surface states are obtained if filled by electrons [14].

In n-type semiconductor, when electrons migrate from their hypothetical bulk positions toward the acceptor-like NS, two phenomena occur. First, the ionized host atoms lead to the formation of a depletion region, DL, with a space charge layer. The charge neutrality principle is accomplished when a charge accumulation in a thin region of the surface, nSS, is created by the filling of the NS. This redistribution of charge is governed by Poisson's equation [15, 16], propitiating the formation of a built-in electric field (ES) and a voltage (VS) close to the surface related by

$$V\_S = E\_S \frac{D\_L}{2}.\tag{1}$$

**331**

**Figure 3.**

*Semiconductor Surface State Engineering for THz Nanodevices*

engineering, allowing current flow only in one direction.

and the use of complex mask alignment steeps [21].

THz detectors are the bolometers, Schottky barrier diodes, pair-braking detectors, hot electron mixers, and field-effect transistors [17]. Special interest in detector lies in the diode concept, since it is one of the more useful components in electronic

The diode concept has a very large variety of applications that stimulate the application of semiconductors in electronics. Nevertheless, the cut-off frequency is still under improvements today. For THz detection, ultrafast metal-insulator-metal (MIM) and metal-insulator-insulator-metal (MIIM) tunnel barriers or p-n semiconductor junctions (reverse Esaki tunnel diodes) have been used [18, 19]. Nonetheless,

One alternative to get a diode device able to operate in the THz regimen is the self-switching diode (SSD) which was first proposed and developed by Song [20]; this device is schematized in **Figure 3(a)**. The properties and performance of the SSD are dependent on both the characteristics of the heterostructure and the grooves etched on it. First, the two-dimensional electron gas (2DEG) created in the heterostructure and illustrated in **Figure 3(b)** is the core of the SSD device, and it is possible to increase the mobility by an adequate layer sequence design. The modulation-doped heterostructures are an excellent example of the importance of the 2DEG properties, since they lead to the development of the high-mobility devices such as the HEMT. The second important element in the SSD structure is the insulating grooves, which can be realized by standard electron beam lithography and wet etching [20]. Due to the groove fabrication process, the symmetry of the crystal structure in the trenches wall is broken, creating NS. The filling process of NS produces the formation of a lateral nSS in the trench walls and therefore a DL inside the nanochannel. The working principle of the SSD is the modulation of the lateral nSS by the bias applied in the ohmic contacts of the device. The current only flows when the anode contact has a positive voltage value with respect to the cathode contact and the grooves force the current to flux only by the nanochannel. In the SSD fabrication process, only one step of lithography is necessary, reducing the cost of production

The SSD device has been demonstrated using heterostructures where the 2DEG is presented such as systems based on InAlAs/InGaAs and AlGaAs/GaAs multilayer structures [21, 22]. The working principle of the device is not dependent on the 2DEG properties, allowing to be fabricated in bulk materials like silicon [23] and transparent semiconductors like ZnO and indium tin oxide (ITO) [24, 25], and graphene-based SSD has been also demonstrated [26]. Those devices have exhibited

*(a) Self-switching diode layout structure, based on a 2DEG-containing heterostructure. (b) Top view of twodimensional SSD L-shape topology. The parameters and the nomenclature to define the L-shape SSD geometry* 

*are channel length L, channel width W, vertical WV, and horizontal WH groove thickness.*

they show low rectification capacity due to their poor diode-like behavior.

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

The existence of NS in the bandgap produces the so-called effects of Fermi-level pinning and the band bending at surface by the formation of a surface barrier with height of Φ = qVS.

With the purpose to avoid surface effects, a lot of methods have been employed, e.g., altering the chemical composition of the surface modifies the energy of the NS [16]. It is crucial to recall that band bending is produced by nSS accumulated at semiconductor-environment interface, being possible to modulate the charge density at surface by illumination that would generate electron-hole pairs, which are recombined at surface. Another form to modulate the carrier's population in NS is by applying an electric field that will exert a selective attraction/repulsion process over the carriers. Accordingly, in surface state engineering, it is imperative to understand and predict how NS, nSS, and DL can be manipulated in order to engineer nanoscale devices capable to operate in the THz region.

### **2. The self-switching diode**

The THz systems for detection are roughly divided into two groups according to the detection of amplitude and phase (coherent heterodyne systems) or only amplitude of the signal (noncoherent forward detection systems). The most applied

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

*Electromagnetic Materials and Devices*

and EV near the surface. The NS position inside the bandgap offers low energy levels in comparison with EC and EV for carriers, and two types of NS can be recognized according to the charge that is acquired when occupied. Donor-type surface state is obtained when Ns exhibited a positive charge after filled in. On the other hand,

*Real surface representation of (a) crystal structure with surface atom reconstruction and reaction. (b) Band* 

In n-type semiconductor, when electrons migrate from their hypothetical bulk positions toward the acceptor-like NS, two phenomena occur. First, the ionized host atoms lead to the formation of a depletion region, DL, with a space charge layer. The charge neutrality principle is accomplished when a charge accumulation in a thin region of the surface, nSS, is created by the filling of the NS. This redistribution of charge is governed by Poisson's equation [15, 16], propitiating the formation of a built-in electric field (ES) and a voltage (VS) close to the surface related by

*DL*

The existence of NS in the bandgap produces the so-called effects of Fermi-level pinning and the band bending at surface by the formation of a surface barrier with

With the purpose to avoid surface effects, a lot of methods have been employed, e.g., altering the chemical composition of the surface modifies the energy of the NS [16]. It is crucial to recall that band bending is produced by nSS accumulated at semiconductor-environment interface, being possible to modulate the charge density at surface by illumination that would generate electron-hole pairs, which are recombined at surface. Another form to modulate the carrier's population in NS is by applying an electric field that will exert a selective attraction/repulsion process over the carriers. Accordingly, in surface state engineering, it is imperative to understand and predict how NS, nSS, and DL can be manipulated in order to engineer

The THz systems for detection are roughly divided into two groups according to the detection of amplitude and phase (coherent heterodyne systems) or only amplitude of the signal (noncoherent forward detection systems). The most applied

<sup>2</sup> . (1)

acceptor-type surface states are obtained if filled by electrons [14].

*VS* = *ES* \_\_\_

nanoscale devices capable to operate in the THz region.

**2. The self-switching diode**

**330**

height of Φ = qVS.

**Figure 2.**

*diagram with surface state effect.*

THz detectors are the bolometers, Schottky barrier diodes, pair-braking detectors, hot electron mixers, and field-effect transistors [17]. Special interest in detector lies in the diode concept, since it is one of the more useful components in electronic engineering, allowing current flow only in one direction.

The diode concept has a very large variety of applications that stimulate the application of semiconductors in electronics. Nevertheless, the cut-off frequency is still under improvements today. For THz detection, ultrafast metal-insulator-metal (MIM) and metal-insulator-insulator-metal (MIIM) tunnel barriers or p-n semiconductor junctions (reverse Esaki tunnel diodes) have been used [18, 19]. Nonetheless, they show low rectification capacity due to their poor diode-like behavior.

One alternative to get a diode device able to operate in the THz regimen is the self-switching diode (SSD) which was first proposed and developed by Song [20]; this device is schematized in **Figure 3(a)**. The properties and performance of the SSD are dependent on both the characteristics of the heterostructure and the grooves etched on it. First, the two-dimensional electron gas (2DEG) created in the heterostructure and illustrated in **Figure 3(b)** is the core of the SSD device, and it is possible to increase the mobility by an adequate layer sequence design. The modulation-doped heterostructures are an excellent example of the importance of the 2DEG properties, since they lead to the development of the high-mobility devices such as the HEMT. The second important element in the SSD structure is the insulating grooves, which can be realized by standard electron beam lithography and wet etching [20].

Due to the groove fabrication process, the symmetry of the crystal structure in the trenches wall is broken, creating NS. The filling process of NS produces the formation of a lateral nSS in the trench walls and therefore a DL inside the nanochannel. The working principle of the SSD is the modulation of the lateral nSS by the bias applied in the ohmic contacts of the device. The current only flows when the anode contact has a positive voltage value with respect to the cathode contact and the grooves force the current to flux only by the nanochannel. In the SSD fabrication process, only one step of lithography is necessary, reducing the cost of production and the use of complex mask alignment steeps [21].

The SSD device has been demonstrated using heterostructures where the 2DEG is presented such as systems based on InAlAs/InGaAs and AlGaAs/GaAs multilayer structures [21, 22]. The working principle of the device is not dependent on the 2DEG properties, allowing to be fabricated in bulk materials like silicon [23] and transparent semiconductors like ZnO and indium tin oxide (ITO) [24, 25], and graphene-based SSD has been also demonstrated [26]. Those devices have exhibited

#### **Figure 3.**

*(a) Self-switching diode layout structure, based on a 2DEG-containing heterostructure. (b) Top view of twodimensional SSD L-shape topology. The parameters and the nomenclature to define the L-shape SSD geometry are channel length L, channel width W, vertical WV, and horizontal WH groove thickness.*

the ability to detect extremely weak signals without applied bias [27, 28]; their high sensitivity [29] and their capability to operate in the terahertz regime [27, 30] make the SSD concept a rewarding tool that has opened a broad range of applications that support the THz gap filling.

#### **2.1 Simulation analysis details**

The SSD schematized in **Figure 3** represents a real device where it is appreciated that basically the SSD is made with two L-shape grooves etched on a heterostructure with a 2DEG. Hence, it is possible to analyze the SSD performance from two points of view: the heterostructure (one-dimensional) and the groove (two-dimensional) geometry in order to avoid three-dimensional numerical analysis required to simulate the electrical behavior of the SSD device.

The heterostructure component of the SSD can be modeled by Schrödinger-Poisson equation, considering the material and layer sequence in order to get the band profile and calculate the electron distribution in the samples [16]. This type of analysis is useful to determinate the properties of a 2DEG in the heterostructure, which gives the carriers high mobility required to operate in THz. **Figure 4(a)** shows the layer sequence of an InGaAs-/InAlAs-based heterostructure, for which the SSD concept has been experimentally proved [20]. The sequence, material, and thickness of each layer are used as input parameters of the 1D model, else the delta doping (δ-doping) concentration.

**Figure 4(b)** exhibits the 1D simulation output; the profile of the conduction band of the heterostructure of **Figure 4(a)** is plotted. As observed in the simulation, at the interface InGaAs/InAlAs, the EC bends toward energies under the Fermi level producing a triangular quantum well with one allowed energy state (E1). When electrons populate the E1 sub-level, electrons can move freely along two dimensions. Thus, the electrons are confined within a 2D sheet embedded in a 3D heterostructure. High concentration and high mobility are exhibited by the electrons trapped in the triangular quantum well, making the heterostructure suitable for THz devices.

With the aim of determining the SSD current-voltage behavior (I-V), we employed a commercial physically based device simulator in two-dimensional mode, similar to that reported for 2DEG-based InGaAs SSD and silicon-oninsulator structures [23, 30, 31]. In this model, only the 2DEG layer geometry resulted after the lithography process is analyzed. This type of numerical analysis requires a 2DEG input, where the top view of the SSD and electrical properties of

#### **Figure 4.**

*(a) Layer sequence of the heterostructure analyzed in this work [20]. (b) 1D analysis of conduction band edge energy diagram of the structure at room temperature. The red line indicates Fermi-level position.*

**333**

**Figure 5.**

(1 × 1017 cm−<sup>3</sup>

*Semiconductor Surface State Engineering for THz Nanodevices*

the 2DEG are considered as simulation inputs. The SSD layout of **Figure 3(b)** is the schematic top view of an L-shape SSD, showing the geometrical frameworks used in the simulation. The electrodes shown in **Figure 3** have been labeled as anode and cathode according to the convention that in the ideal diode, the carriers flow from

The background doping and the electron mobility of the 2DEG samples

under no impurity scattering. The dielectric material filling the grooves was air

standards that exist for THz devices [32]. Finally, the energy balance model at 300 K was used. The model was employed to perform a systematic geometrical analysis and comparing different types of self-switching structures directed to provide an enabling technology for energy harvesting in the terahertz region. Since the self-switching diodes combine size and electronic transport property effects, the performance of different SSD was analyzed and optimized by chang-

The key to understand the DC performance of the SSD lies on the modulation of the nss inside the NS by the built-in electric field, producing a modification in the DL along the nanochannel. In this way, some authors indicate that the SSD can be understood as a two-dimensional field-effect transistor with gate and drain short circuited where flanges act as a double lateral-gate terminal [28, 33]. The principal mechanism that controls the carrier transport of the SSD is explained in terms of the free carriers that can participate in conduction phenomena and travel through the nanochannel [22]. To expose the SSD performance and their rectifying nature, it is necessary to explore the L-shape device shown in **Figure 5(a)** used as simulation input parameter and termed as the reference geometry. The result of the numerical study is the electron-charge distribution along the 2DEG plane illus-

With no applied bias, simulations show a drastic reduction of the background carrier density inside the nanochannel as a consequence of the electron filling of the NS created at groove walls. Carrier density decays from the background rate

of the nanochannel and decreases steadily closer to the groove walls, remaining

*(a) Top view schematic representation of the proposed L-shape self-switching nanochannels. (b) Electron* 

*charge distribution along the 2DEG plane inside the nanostructures under zero bias.*

(εr = 1), inducing a surface charge density of nSS = 0.4 × 1012 cm−<sup>2</sup>

resistivity used in the simulation process was 1 × 10<sup>−</sup><sup>8</sup> Ω cm<sup>2</sup>

and 12,000 cm<sup>2</sup>

 V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup>

(cyan color) along the length

, respectively,

. The contact

, which is similar to

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

utilized in the simulation were 1 × 1017 cm−<sup>3</sup>

**2.2 Self-switching diode working principle**

trated in **Figure 5(b)** when both electrodes are unbiased.

, in orange-red color) to 1014 cm−<sup>3</sup>

ing their shape configuration.

anode to cathode.

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

*Electromagnetic Materials and Devices*

support the THz gap filling.

**2.1 Simulation analysis details**

doping (δ-doping) concentration.

for THz devices.

simulate the electrical behavior of the SSD device.

the ability to detect extremely weak signals without applied bias [27, 28]; their high sensitivity [29] and their capability to operate in the terahertz regime [27, 30] make the SSD concept a rewarding tool that has opened a broad range of applications that

The SSD schematized in **Figure 3** represents a real device where it is appreciated that basically the SSD is made with two L-shape grooves etched on a heterostructure with a 2DEG. Hence, it is possible to analyze the SSD performance from two points of view: the heterostructure (one-dimensional) and the groove (two-dimensional) geometry in order to avoid three-dimensional numerical analysis required to

The heterostructure component of the SSD can be modeled by Schrödinger-Poisson equation, considering the material and layer sequence in order to get the band profile and calculate the electron distribution in the samples [16]. This type of analysis is useful to determinate the properties of a 2DEG in the heterostructure, which gives the carriers high mobility required to operate in THz. **Figure 4(a)** shows the layer sequence of an InGaAs-/InAlAs-based heterostructure, for which the SSD concept has been experimentally proved [20]. The sequence, material, and thickness of each layer are used as input parameters of the 1D model, else the delta

**Figure 4(b)** exhibits the 1D simulation output; the profile of the conduction band of the heterostructure of **Figure 4(a)** is plotted. As observed in the simulation, at the interface InGaAs/InAlAs, the EC bends toward energies under the Fermi level producing a triangular quantum well with one allowed energy state (E1). When electrons populate the E1 sub-level, electrons can move freely along two dimensions. Thus, the electrons are confined within a 2D sheet embedded in a 3D heterostructure. High concentration and high mobility are exhibited by the electrons trapped in the triangular quantum well, making the heterostructure suitable

With the aim of determining the SSD current-voltage behavior (I-V), we employed a commercial physically based device simulator in two-dimensional mode, similar to that reported for 2DEG-based InGaAs SSD and silicon-oninsulator structures [23, 30, 31]. In this model, only the 2DEG layer geometry resulted after the lithography process is analyzed. This type of numerical analysis requires a 2DEG input, where the top view of the SSD and electrical properties of

**332**

**Figure 4.**

*(a) Layer sequence of the heterostructure analyzed in this work [20]. (b) 1D analysis of conduction band edge* 

*energy diagram of the structure at room temperature. The red line indicates Fermi-level position.*

the 2DEG are considered as simulation inputs. The SSD layout of **Figure 3(b)** is the schematic top view of an L-shape SSD, showing the geometrical frameworks used in the simulation. The electrodes shown in **Figure 3** have been labeled as anode and cathode according to the convention that in the ideal diode, the carriers flow from anode to cathode.

The background doping and the electron mobility of the 2DEG samples utilized in the simulation were 1 × 1017 cm−<sup>3</sup> and 12,000 cm<sup>2</sup> V<sup>−</sup><sup>1</sup> s<sup>−</sup><sup>1</sup> , respectively, under no impurity scattering. The dielectric material filling the grooves was air (εr = 1), inducing a surface charge density of nSS = 0.4 × 1012 cm−<sup>2</sup> . The contact resistivity used in the simulation process was 1 × 10<sup>−</sup><sup>8</sup> Ω cm<sup>2</sup> , which is similar to standards that exist for THz devices [32]. Finally, the energy balance model at 300 K was used. The model was employed to perform a systematic geometrical analysis and comparing different types of self-switching structures directed to provide an enabling technology for energy harvesting in the terahertz region. Since the self-switching diodes combine size and electronic transport property effects, the performance of different SSD was analyzed and optimized by changing their shape configuration.

#### **2.2 Self-switching diode working principle**

The key to understand the DC performance of the SSD lies on the modulation of the nss inside the NS by the built-in electric field, producing a modification in the DL along the nanochannel. In this way, some authors indicate that the SSD can be understood as a two-dimensional field-effect transistor with gate and drain short circuited where flanges act as a double lateral-gate terminal [28, 33]. The principal mechanism that controls the carrier transport of the SSD is explained in terms of the free carriers that can participate in conduction phenomena and travel through the nanochannel [22]. To expose the SSD performance and their rectifying nature, it is necessary to explore the L-shape device shown in **Figure 5(a)** used as simulation input parameter and termed as the reference geometry. The result of the numerical study is the electron-charge distribution along the 2DEG plane illustrated in **Figure 5(b)** when both electrodes are unbiased.

With no applied bias, simulations show a drastic reduction of the background carrier density inside the nanochannel as a consequence of the electron filling of the NS created at groove walls. Carrier density decays from the background rate (1 × 1017 cm−<sup>3</sup> , in orange-red color) to 1014 cm−<sup>3</sup> (cyan color) along the length of the nanochannel and decreases steadily closer to the groove walls, remaining

#### **Figure 5.**

*(a) Top view schematic representation of the proposed L-shape self-switching nanochannels. (b) Electron charge distribution along the 2DEG plane inside the nanostructures under zero bias.*

**Figure 6.**

*Electron density distribution (logarithmic scale) for the SSD with the geometry depicted in* **Figure 5(a)** *at (a) V = −0.5 (reverse bias) and (b) V = 0.5 (forward condition).*

homogenous all along the L-shape channel, as it is displayed by **Figure 6(b)**. In other words, the DL created inside the nanochannel limits the free carriers available to participate in conduction phenomena defining high-resistive or not conductive nanochannel.

For reverse bias (V = −0.5 V in the anode, while cathode is set to ground), the charge depletion effects are enhanced along the channel due to the transversal electric field that appears at the groove walls, lowering the carrier density inside channels, according to **Figure 6(a)**. For reverse state, the DL inside the nanochannel is raised by two orders of magnitude in comparison with the zero-bias case, making a pinch-off condition that prevents any current to flow along the nanochannel due to the lack of carriers. However, reverse current can be established when the bias is high enough to overcome the lateral depletion effects.

**Figure 6(b)** displays the carrier distribution at V = +0.5 V for the reference L-shape SSD as forward bias which is settled when a positive voltage is applied to the anode. Under forward polarization the nSS in the NS of the SSD trenches is deflated, reducing the DL inside the nanochannel. On this condition, the carrier density increases several orders of magnitude (∼1015 cm−<sup>3</sup> ), close to the background concentration when the DL is reduced by the transversal electric field. The electron transport along the channel is possible at this condition by the intensifications of the free carrier concentration.

The analysis of the carrier distribution along the 2DEG, where the SSD has been fabricated in addition with the extension/modulation of the DL inside the nanochannel, indicates that it is possible to control the current flux that travels between electrodes by controlling the free carrier inside the nanochannel. This modulation is originated by the sign of the applied voltage in the anode, making the SSD a rectifier element capable to operate in the THz region by the high-mobility nature of the 2DEG of the heterostructure where the nanometric dimensions of the L-shape grooves are lithographed.

In DC injection mode, the performance of a rectifier element can be simply analyzed by the nonlinearity of their current-voltage curve, the threshold voltage (VTH), and the leakage current present in reverse bias. These properties can be examined by the DL width inside the nanochannel. The zero-bias simulations indicate that there is a minimum carrier concentration, which propitiates the formation of the DL necessary to be modulated by the applied bias, being dependent of the groove fabrication process and the nanochannel shape, especially.

Therefore, in the SSD initial design, it is mandatory to achieve a nanochannel with the appropriated carrier concentration at 0 V. As it is going to be analyzed

**335**

*Semiconductor Surface State Engineering for THz Nanodevices*

in the following sections, the nanochannel shape, width, and length ensure that the SSD exhibits diode-like behavior and would provide an estimation of the VTH necessary to turn on the conduction of the SSD. Nevertheless, the NS are difficult to control in a desire range though they can vary considerably depending on the L-shape groove fabrication techniques such as etching methods, leading to crucial

*The effect of the surface charge density (nSS) on (a) the electron concentration along the device and in (b) the* 

According to surface physics, the nSS agglomerated in the interface semiconductor environment is a manifestation of NS. The SSD fabrication determines the available surface states. When the device processing augments the NS density, more electrons will be used to fill these states, magnifying the DL inside the nanochannel. Therefore, the rise (reduction) of the nSS has the effect to decrease (increase) the free carriers' density along the channel. **Figure 7(a)** exhibits the carrier distribution along the SSD device from the nanochannel calculated at 0 V when the nSS

not a modification in the free electron concentration along the channel, declining

the diode typical I-V curve is presented. In the case of nSS = 0, the I-V is completely lineal; in other words, the absence of NS produces that the SSD works like a resis-

exhibited, with a VTH near to zero, a desired value for low-power signal detection. Nevertheless, in this case the reverse bias exhibits an important leakage current.

the diode-like performance, while an excessive nSS steps the VTH up, improving the

According to the simulation results, carrier density exhibited by the nonpolarized structure indicates that a minimum bias, or voltage threshold, is required in order to propitiate electron conduction. In that case, the lower the carrier concentration is, the higher the VTH results. For short DL length, low bias is required to turn the SSD on; nevertheless, an important leakage current is present. By modulating the dimensions of the depletion region inside the nanochannel, the L-shape SSDs are found to be suitable for detection of very weak signals, making the SSD concept an important tool in the development of high-frequency integrated circuits since it has been demonstrated that by choosing appropriate geometrical dimen-

Hence, the carrier density inside the nanochannel and their modulation are used to propitiate the rectifier behavior of the SSD device. The current-voltage curve of

. It is clear to see that for the nSS = 0, there is

) is exhibited in **Figure 7(b)** where

, the nonlinearity of the I-V curve is

and enhancing as nSS increases.

, the reverse current is removed notoriously, improving

effects on the DC and AC performance of the SSD device.

was varied from 0 to 0.5 × 1012 cm−<sup>2</sup>

**Figure 7.**

*current-voltage characteristics.*

considerably for nSS > 0.35 × 1012 cm−<sup>2</sup>

the SSD-based structure (nSS = 0.4 × 1012 cm−<sup>2</sup>

tor device. When the nSS = 0.35 × 1012 cm−<sup>2</sup>

nonlinearity and avoiding leakage current.

sions, the rectification efficiency can be optimized [33, 34].

For nSS > 0.35 × 1012 cm−<sup>2</sup>

*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 7.**

*Electromagnetic Materials and Devices*

nanochannel.

**Figure 6.**

homogenous all along the L-shape channel, as it is displayed by **Figure 6(b)**. In other words, the DL created inside the nanochannel limits the free carriers available to participate in conduction phenomena defining high-resistive or not conductive

*Electron density distribution (logarithmic scale) for the SSD with the geometry depicted in* **Figure 5(a)** *at (a)* 

high enough to overcome the lateral depletion effects.

*V = −0.5 (reverse bias) and (b) V = 0.5 (forward condition).*

density increases several orders of magnitude (∼1015 cm−<sup>3</sup>

the free carrier concentration.

grooves are lithographed.

For reverse bias (V = −0.5 V in the anode, while cathode is set to ground), the charge depletion effects are enhanced along the channel due to the transversal electric field that appears at the groove walls, lowering the carrier density inside channels, according to **Figure 6(a)**. For reverse state, the DL inside the nanochannel is raised by two orders of magnitude in comparison with the zero-bias case, making a pinch-off condition that prevents any current to flow along the nanochannel due to the lack of carriers. However, reverse current can be established when the bias is

**Figure 6(b)** displays the carrier distribution at V = +0.5 V for the reference L-shape SSD as forward bias which is settled when a positive voltage is applied to the anode. Under forward polarization the nSS in the NS of the SSD trenches is deflated, reducing the DL inside the nanochannel. On this condition, the carrier

concentration when the DL is reduced by the transversal electric field. The electron transport along the channel is possible at this condition by the intensifications of

fabricated in addition with the extension/modulation of the DL inside the nanochannel, indicates that it is possible to control the current flux that travels between electrodes by controlling the free carrier inside the nanochannel. This modulation is originated by the sign of the applied voltage in the anode, making the SSD a rectifier element capable to operate in the THz region by the high-mobility nature of the 2DEG of the heterostructure where the nanometric dimensions of the L-shape

In DC injection mode, the performance of a rectifier element can be simply analyzed by the nonlinearity of their current-voltage curve, the threshold voltage (VTH), and the leakage current present in reverse bias. These properties can be examined by the DL width inside the nanochannel. The zero-bias simulations indicate that there is a minimum carrier concentration, which propitiates the formation of the DL necessary to be modulated by the applied bias, being dependent of the

Therefore, in the SSD initial design, it is mandatory to achieve a nanochannel with the appropriated carrier concentration at 0 V. As it is going to be analyzed

groove fabrication process and the nanochannel shape, especially.

The analysis of the carrier distribution along the 2DEG, where the SSD has been

), close to the background

**334**

*The effect of the surface charge density (nSS) on (a) the electron concentration along the device and in (b) the current-voltage characteristics.*

in the following sections, the nanochannel shape, width, and length ensure that the SSD exhibits diode-like behavior and would provide an estimation of the VTH necessary to turn on the conduction of the SSD. Nevertheless, the NS are difficult to control in a desire range though they can vary considerably depending on the L-shape groove fabrication techniques such as etching methods, leading to crucial effects on the DC and AC performance of the SSD device.

According to surface physics, the nSS agglomerated in the interface semiconductor environment is a manifestation of NS. The SSD fabrication determines the available surface states. When the device processing augments the NS density, more electrons will be used to fill these states, magnifying the DL inside the nanochannel. Therefore, the rise (reduction) of the nSS has the effect to decrease (increase) the free carriers' density along the channel. **Figure 7(a)** exhibits the carrier distribution along the SSD device from the nanochannel calculated at 0 V when the nSS was varied from 0 to 0.5 × 1012 cm−<sup>2</sup> . It is clear to see that for the nSS = 0, there is not a modification in the free electron concentration along the channel, declining considerably for nSS > 0.35 × 1012 cm−<sup>2</sup> and enhancing as nSS increases.

Hence, the carrier density inside the nanochannel and their modulation are used to propitiate the rectifier behavior of the SSD device. The current-voltage curve of the SSD-based structure (nSS = 0.4 × 1012 cm−<sup>2</sup> ) is exhibited in **Figure 7(b)** where the diode typical I-V curve is presented. In the case of nSS = 0, the I-V is completely lineal; in other words, the absence of NS produces that the SSD works like a resistor device. When the nSS = 0.35 × 1012 cm−<sup>2</sup> , the nonlinearity of the I-V curve is exhibited, with a VTH near to zero, a desired value for low-power signal detection. Nevertheless, in this case the reverse bias exhibits an important leakage current. For nSS > 0.35 × 1012 cm−<sup>2</sup> , the reverse current is removed notoriously, improving the diode-like performance, while an excessive nSS steps the VTH up, improving the nonlinearity and avoiding leakage current.

According to the simulation results, carrier density exhibited by the nonpolarized structure indicates that a minimum bias, or voltage threshold, is required in order to propitiate electron conduction. In that case, the lower the carrier concentration is, the higher the VTH results. For short DL length, low bias is required to turn the SSD on; nevertheless, an important leakage current is present. By modulating the dimensions of the depletion region inside the nanochannel, the L-shape SSDs are found to be suitable for detection of very weak signals, making the SSD concept an important tool in the development of high-frequency integrated circuits since it has been demonstrated that by choosing appropriate geometrical dimensions, the rectification efficiency can be optimized [33, 34].
