Electrons In 2DEG Research Articles

Electronic Properties of Group-III Nitride Semiconductors and Device Structures Probed by THz Optical Hall Effect.

Group-III nitrides have transformed solid-state lighting and are strategically positioned to revolutionize high-power and high-frequency electronics. To drive this development forward, a deep understanding of fundamental material properties, such as charge carrier behavior, is essential and can also unveil new and unforeseen applications. This underscores the necessity for novel characterization tools to study group-III nitride materials and devices. The optical Hall effect (OHE) emerges as a contactless method for exploring the transport and electronic properties of semiconductor materials, simultaneously offering insights into their dielectric function. This non-destructive technique employs spectroscopic ellipsometry at long wavelengths in the presence of a magnetic field and provides quantitative information on the charge carrier density, sign, mobility, and effective mass of individual layers in multilayer structures and bulk materials. In this paper, we explore the use of terahertz (THz) OHE to study the charge carrier properties in group-III nitride heterostructures and bulk material. Examples include graded AlGaN channel high-electron-mobility transistor (HEMT) structures for high-linearity devices, highlighting the different grading profiles and their impact on the two-dimensional electron gas (2DEG) properties. Next, we demonstrate the sensitivity of the THz OHE to distinguish the 2DEG anisotropic mobility parameters in N-polar GaN/AlGaN HEMTs and show that this anisotropy is induced by the step-like surface morphology. Finally, we present the temperature-dependent results on the charge carrier properties of 2DEG and bulk electrons in GaN with a focus on the effective mass parameter and review the effective mass parameters reported in the literature. These studies showcase the capabilities of the THz OHE for advancing the understanding and development of group-III materials and devices.

Ab initio calculations of nonlinear susceptibility and multiphonon mixing processes in a 2DEG-piezoelectric heterostructure

Solid-state elastic-wave phonons are a promising platform for a wide range of quantum information applications including facilitating quantum transduction from microwave to optical electromagnetic fields, long-lived quantum memories, in addition to potentially acting as qubits themselves. An outstanding challenge and enabling capability in harnessing phonons for quantum information processing is achieving sufficiently strong nonlinear interactions between them. To this end, we propose a general architecture for generating strong quantum phononic nonlinearity using piezoelectric-semiconductor heterostructures consisting of a piezoelectric acoustic material hosting phononic modes that is in direct proximity to a two-dimensional electron gas (2DEG). Each phonon in the piezoelectric material carries an electric field, which extends into the 2DEG. The fields induce polarization of 2DEG electrons, which in turn interact with other piezoelectric phononic electric fields. The net result is coupling between the electric fields associated with the various phonon modes. We derive, from first principles, the nonlinear phononic susceptibility of a piezo-2DEG system and provide a prescription to calculate all orders of the susceptibility in a perturbative expansion. We show that many nonlinear processes are strongly favored at high electron mobility, motivating the use of the 2DEG to mediate the nonlinearities. We derive the first, second, and third-order susceptibilities and calculate them for the case of a lithium niobate surface acoustic wave interacting with a GaAs-AlGaAs heterostructure 2DEG. We show that, for this system, the strong third-order phononic nonlinearities generated could enable single-phonon Kerr shift in an acoustic cavity that exceeds realistic cavity linewidths, potentially leading to a new class of acoustic qubit. We further show that the strong second-order nonlinearity could be used to produce a high-gain, traveling-wave parametric amplifier to amplify—and ultimately detect—the outputs of the acoustic cavity qubits. Assuming favorable losses in such a system, the combination of these capabilities, combined with the ability to efficiently transduce phonons from microwave electromagnetic fields in transmission lines, thus hold promise for creating all-acoustic quantum information processors. Published by the American Physical Society 2024

Different spectral features near the energy bandgaps of normal and inverse heterostructures of In<sub>0.52</sub>Al<sub>0.48</sub>As/InP

Photoconductivity (PC) spectroscopy and photoluminescence (PL) spectroscopy were used to characterize two heterostructure configurations of InAlAs/InP grown by molecular beam epitaxy (MBE) on the InP (100) substrate. The sample A is the type called normal heterostructure, which has an In<sub>0.52</sub>Al<sub>0.48</sub>As layer grown on InP, while sample B is called the inverse type formed by an InP cap layer on In<sub>0.52</sub>Al<sub>0.48</sub>As. The front excitation was employed in both PC experiment and PL experiment and the measurements were conducted at 77 K. The PC spectrum of sample A shows an abnormal step-like drop when the photon energy is larger than the energy band gap of In<sub>0.52</sub>Al<sub>0.48</sub>As. The phenomenon implies that the conductance of sample is a multilayer effect including the contribution of interfacial two-dimensional electron gas (2DEG). Moreover, a conductance peak is observed at 916 nm below the bandgap of InP. Accordingly, an intense luminescent peak at the wavelength manifests in the PL spectrum. The origin of the 916 nm peak is attributed to the recombination of 2DEG electrons with the valence band holes excited near the interface. However, the spectral feature of the above energy does not exist in both PC and PL spectra of sample B. This difference may be explained by the different interface electronic structures of the inverse interface. For the latter case, considering that a graded variation in In-As-P composition is related to the inverse interface of InP/InAlAs, the band bending effect should be weak. In such a case, the bound energy of 2DEG in the interface potential well is raised closer to the conductance band of the bulk. Consequently, the recombination energy of 2DEG at the inverse interface with the holes in the valence band is close to the band-to-band transition of InP bulk and the luminescence is difficult to be distinguished from that of bulk InP. The work also demonstrates that the comparative study with both PC technique and PL technique is helpful to provide a full insight into the interface electronic property.

Recent Progress in Non-Contact Electrical Characterization for SiC and Related Compounds

An increasing interest in the non-contact corona charge-based electrical characterization technique, CnCV, for wide bandgap semiconductors, is justified by the reduction of cost and the reduction of testing feedback time [1]. In addition, the technique expands measurement capabilities. Regarding SiC, recent progress includes expanded dopant concentration range and dopant measurement on fresh epitaxial wafers. The latter is made possible with an ultraviolet wafer pretreatment technique [2]. The novel applications to AlGaN/GaN HEMT on insulating substrates demonstrate the benefits of a noninvasive top side edge contact, TSEC [3], that eliminates the problem of the floating surface potential. This development enables a unique three variable, charge-voltage-capacitance (Q-V-C), characterization of AlGaN/GaN on sapphire and SI-SiC. The quasistatic CnCV measurement, not affected by series resistance, is shown to be suitable for wafer mapping of HEMT parameters. The CnCV version with TSEC can be combined with an eddy current technique enabling non-contact 2DEG mobility measurements vs. electron sheet density.

AlGaN-based metal–semiconductor–metal photodiodes fabricated with nonplanar structure geometry for ultraviolet light detection

Based upon GaN-on-Si wafers with a Al0.24Ga0.76N/AlN/GaN heterostructure, metal–semiconductor–metal photodetectors (MSM PDs) with nonplanar structure geometry are proposed for ultraviolet (UV) light detection. Although the presence of a highly conductive two-dimensional electron gas (2DEG) channel in the Al0.24Ga0.76N/AlN/GaN heterostructure is beneficial for realizing a high-electron-mobility transistor with a drain current of 600 mA/mm and a transconductance of 96 mS/mm, a high dark current is also observed in Schottky-barrier based MSM PDs. Using the nonplanar structure design for the MSM PDs (i.e., one Schottky contact formed on the top surface of the AlGaN mesa while the other is on the GaN buffer) achieves a significant decrease in PD’s dark current (<6 × 10−10 A). In addition, an anomalous increase in dark current of the proposed MSM PDs was found at forward bias, which could be attributed to the reduced potential barrier of the electrons in 2DEG and/or the lowering of the Schottky barrier height by hole trapping at the metal/semiconductor interface. Due to the improved signal to noise ratio and increased dissociation of the photogenerated carriers at the reverse junction (i.e., the reversely biased Schottky contact), the proposed MSM PDs operating at reverse bias exhibit enhanced UV photoresponsivity at λ < 360 nm. In addition to being used for UV light detection, these MSM PDs with a 3-dB bandwidth of 29.6 Hz are also useful for potential optical communications applications.

Study of electrical transport properties of GaN-based side-gate heterostructure transistors

In this study, GaN-based side-gate heterostructure transistors (SGHTs) with two electrical operating modes were fabricated. In the first operating mode, the SGHT was utilized as a common-source voltage amplifier with low power consumption and a broad input signal range. Analysis of the main scattering mechanisms affecting the electrical transport of two-dimensional electron gas (2DEG) in the channel revealed that polar optical phonon scattering and polarization Coulomb field (PCF) scattering play dominant roles under different side-gate voltages. In addition, channel current modulation of 2DEG electron mobility is primarily attributed to PCF scattering. Due to PCF scattering, the channel width also modulates the threshold voltage in this mode of operation. Moreover, in the second operating mode, the SGHT functioned as a traditional GaN high electron mobility transistor, allowing for electrically modulated threshold voltage and transconductance.

Improved Electrical Performance of InAlN/GaN High Electron Mobility Transistors with Post Bis(trifluoromethane) Sulfonamide Treatment

An enhancement of the electrical performance of the InAlN/GaN high electron mobility transistors (HEMTs) is demonstrated by the incorporation of post bis(trifluoromethane) sulfonamide (TFSI) treatment. The surface treatment of TFSI solution results in the increase of 2DEG electron mobility from 1180 to 1500 cm2/Vs and thus a reduction of on-state resistance and an increase in transconductance. The results indicate that the positive charge of H+ will decrease the polarization charges of the InAlN barrier under the access region due to the converse piezoelectric effect, leading to the reduced polarization Coulomb field (PCF) scattering in InAlN/GaN HEMT. This offers a possible way to improve the electron mobility and device performance of InAlN/GaN HEMTs for further application.

HEMT Controlled Ultraviolet Light Emitters Enabled by P-GaN Selective Epitaxial Growth

This letter demonstrates a novel HEMT controlled ultraviolet light emitter by directly modifying the drain of AlGaN/GaN HEMTs. The selective epitaxial growth (SEG) p-GaN on HEMTs contacts with two dimensional electron gas (2DEG) to form a lateral p-GaN/2DEG junction, which utilizes the recombination of holes in p-GaN and high-density electrons in 2DEG to realize luminescence. Our results show that the ultraviolet light with a maximum intensity of 374.9 nm is emitted by the new devices, which is also able to realize color conversion by driving quantum dots (QDs). The new method shows an idea of converting electrical devices into light-emitting devices, which is different from the traditional integration. This work represents the first light emitting HEMT without integrated LEDs.

Enhancement of 2DEG effective mass in AlN/Al0.78Ga0.22N high electron mobility transistor structure determined by THz optical Hall effect

We report on the free charge carrier properties of a two-dimensional electron gas (2DEG) in an AlN/AlxGa1–xN high electron mobility transistor structure with a high aluminum content (x = 0.78). The 2DEG sheet density Ns=(7.3±0.7)×1012 cm−2, sheet mobility μs=(270±40) cm2/(Vs), sheet resistance Rs=(3200±500) Ω/◻, and effective mass meff=(0.63±0.04)m0 at low temperatures (T=5 K) are determined by terahertz (THz) optical Hall effect measurements. The experimental 2DEG mobility in the channel is found within the expected range, and the sheet carrier density is in good agreement with self-consistent Poisson–Schrödinger calculations. However, a significant increase in the effective mass of 2DEG electrons at low temperatures is found in comparison with the respective value in bulk Al0.78Ga22N (meff=0.334 m0). Possible mechanisms for the enhanced 2DEG effective mass parameter are discussed and quantified using self-consistent Poisson–Schrödinger calculations.

Structure parameters design of InP based high electron mobility transistor epitaxial materials to improve radiation-resistance ability

In order to improve the radiation-resistance ability of the InP based high electron mobility transistor (InP HEMT) by optimizing the epitaxial structure design, a series of InP HEMT epitaxial structure materials with different structure parameters is grown by gas source molecular beam epitaxy. These samples are irradiated at room temperature by a 1.5-MeV electron beam at the same irradiation fluence of 2 × 10&lt;sup&gt;15&lt;/sup&gt; cm&lt;sup&gt;–2&lt;/sup&gt;. The electrical properties of the two-dimensional electron gas (2DEG) for InP HEMT epitaxial materials before and after irradiation are measured by Hall measurements to obtain the changes of the normalized 2DEG density and electron mobility along with the epitaxial structure parameters. The relation between 2DEG radiation damage and epitaxial structure parameters (such as Si-δ-doping density, spacer thickness, channel thickness and channel In content) of InP HEMT epitaxial structure materials is analyzed. The results show that the 2DEG of the InP HEMT epitaxial structure material with higher Si-δ-doping density, thinner spacer thickness, thicker channel thickness and lower channel In content has lower radiation damage, which possesses the stronger radiation-resistance ability.

Electrical properties of 90-nm InAlN/GaN HEMT on silicon substrate

GaN high-electron-mobility transistors (HEMTs) on silicon substrate have attracted much attention owing to the low-cost and the large area availability of the Si substrate. In this paper, the 90-nm-gate-length InAlN/GaN HEMT on silicon was fabricated and the device electrical properties were studied. The device presents a low drain-induced barrier lowing (DIBL) of 43 mV/V, a parasitic source resistance ( R S ) of 0.91 Ω⸱mm, and a peak of the intrinsic transconductance ( g m0 ) of 553 mS/mm. To the best of our knowledge, this is the lowest DIBL value among the reported GaN HMET on Si with gate length ( L g ) below 100 nm. The low-filed two-dimensional electron gas (2DEG) electron mobility ( μ n ) was extracted and the dominated polarization Coulomb field scattering contributed to the increased μ n with the increased of two-dimensional electron gas electron density ( n 2D ). A current gain cutoff frequency ( f T ) of 175 GHz was achieved on InAlN/GaN HEMTs with a gate length of 90-nm.

Influence of AlGaN back-barrier on irradiation tolerance of AlGaN/AlN/GaN HEMTs

The introduction of AlGaN back-barrier increases the confinement of the two-dimensional electrons and further improves the high-frequency performance of AlGaN/AlN/GaN HEMTs. We investigate the effect of AlGaN back-barrier on irradiation tolerance of GaN-based HEMTs in terms of 2DEG density and electron scattering. The Schroödinger-Poisson equations are solved using a self-consistency method to calculate the conduction energy band and 2DEG density, which takes into account the Ga vacancies caused by proton irradiation. The electron scattering depending on phonons, ionized impurities, dislocations, and the interface AlN/GaN interface roughness is also studied, and 2DEG mobility is calculated for GaN-based HEMTs with and without back-barrier. The calculation results show that, after the same proton irradiation, the 2DEG density and mobility in GaN-based HEMT with back-barrier decrease more dramatically than that without back-barrier. The results may give some suggestions to those designing the radiation-resistant GaN-based HEMTs.

Analysis and modeling of OFF-state hysteretic losses in GaN power HEMTs

We present a detailed analysis of large-signal Sawyer–Tower measurements on a power GaN HEMT device in OFF-state. The measurements show hysteresis which results in an energy loss dissipated as heat in the range of sub-μJ’s. We model this important phenomenon in this paper using a previously calibrated model of the same device. We propose two models, one with linear Effective Series Resistance (ESR) and another using non-linear ESR (NLESR). It is found that to model the non-linear profile of hysteretic curve from Sawyer–Tower measurements, non-linear ESR and output capacitance are needed. The similarities and differences between these two models have been explained in detail. While linear ESR is shown to be a simple model for modeling the hysteretic losses, non-linear ESR and output capacitance model the dynamics of charge imbalance that occurs during the charging and discharging processes more accurately. A detailed analysis based on recent literature suggests that 2DEG electron trapping by acceptor type traps in the underlying buffer layers are the primary cause of this charge imbalance.

InAlN/GaN HEMT on Si With fmax = 270 GHz

Device surface properties are critical for its performance such as channel electron density, leakage current, subthreshold swing (SS), and noise in gallium nitride high-electron-mobility transistors (HEMTs). In this article, the improved surface property of InAlN/GaN HEMTs with forming gas (FG, 5% H2, and 95% N2) annealing is demonstrated. X-ray photoelectron spectra (XPS) show that the number of Ga–O bonds decreases while that of the Ga–N bonds increases, an indication of the surface native oxide removal after FG annealing. Compared with N2 annealing, an increase of two-dimensional electron gas (2DEG) electron density with FG annealing is determined by both energy band simulation and capacitance–voltage measurement. Transmission line measurement (TLM) shows that N2 annealing offers a lower ohmic contact resistance ( ${R}_{\text {C}}$ ) while FG annealing features a lower sheet resistance ( ${R}_{\text {sheet}}$ ). Herein, a FG/N2 two-step ohmic contact annealing is developed to achieve a SS of 110 mV/dec, a transconductance ( ${g}_{\text {m}}$ ) peak of 415 mS/mm, a record low drain-induced barrier lowing (DIBL) of 65 mV/V, and a record high power gain cutoff frequency ( ${f}_{\text {max}}$ ) of 270 GHz on a 50-nm InAlN/GaN HEMT on Si.

On the Challenges of Reliable Threshold Voltage Measurement in Ohmic and Schottky Gate p-GaN HEMTs

For large scale testability of p-GaN HEMTs it is essential to investigate threshold voltage ( $\text{V}_{\mathrm{ th}}$ ) instability from the perspective of the measurement induced instability. In this paper the impact of accumulated gate bias stress during standard transfer characteristic measurements ( $\text{I}_{\mathrm{ D}}$ - $\text{V}_{\mathrm{ G}}$ ) in a p-GaN AlGaN/GaN-on-Si normally off HEMT is quantitatively analysed and modeled. This illustrates the associated threshold voltage ( $\text{V}_{\mathrm{ th}}$ ) instabilities and leads to a better understanding of the $\text{V}_{\mathrm{ th}}$ measurement challenges of a p-GaN HEMT. Upon an application of a constant gate bias close to nominal $\text{V}_{\mathrm{ th}}$ the drain current $\text{I}_{\mathrm{ D}}$ shows an initial marginal rise, followed by a short stable period ( $\text{I}_{\mathrm{ Dstable}}$ - $\text{T}_{\mathrm{ zone}}$ ) and a steep decay period. The effective bias history built on the gate stack varies when pulse on-time (Ton) or step time (Tstep), corresponding to pulsed or DC step $\text{I}_{\mathrm{ D}}$ - $\text{V}_{\mathrm{ G}}$ measurements, are varied. We find that this can lead to a $\text{V}_{\mathrm{ th}}$ variation of up to 20%. It is also observed that the choice of Ton and Tstep determines whether $\text{I}_{\mathrm{ D}}$ is measured in $\text{I}_{\mathrm{ Dstable}}$ - $\text{T}_{\mathrm{ zone}}$ or the rise or decay periods. Measurement induced $\text{V}_{\mathrm{ th}}$ instability is attributed to trapping of 2DEG electrons at the AlGaN barrier and we demonstrate that an ohmic gate contact, in comparison to the Schottky gate contact, may compensate for the trapped 2DEG electrons by hole injection across the AlGaN barrier. Experimental results of $\text{V}_{\mathrm{ th}}$ stability under the same stress conditions for a Schottky and ohmic gate contact are supported by a detailed TCAD analysis.

Degradation Behavior and Trap Analysis Based on Low-Frequency Noise of AlGaN/GaN HEMTs Subjected to Radio Frequency Overdrive Stress

In this article, the degradation behavior of the electrical characteristics of AlGaN/GaN HEMTs subjected to radio frequency (RF) overdrive stress has been studied. Trap analysis based on low-frequency noise (LFN) and electroluminescence (EL) characterizations was carried out for AlGaN/GaN HEMTs before and after RF stress. The experimental results show that drain-to-source current of AlGaN/GaN HEMTs after RF stress is obviously lower than that of the fresh devices. The maximum change of drain-to-source current was up to 79 mA in the saturation zone. The threshold voltage drifted forward and gate-lag characteristic became worse for the AlGaN/GaN HEMTs after RF stress. The EL characterizations also showed the nonuniformity of channel illumination intensity, which indicates the distribution of electron of the channel nonuniform. Trap analysis was performed by using the LFN method, and the LFN results showed that the trap density increased by about one order of magnitude in the AlGaN/GaN HEMTs after RF stress, which would lead to more depletion of the channel two-dimensional electron gas (2DEG) electrons. The mechanism of increasing trap density could be attributed to defects induced by RF stress at AlGaN surface and AlGaN barrier layer. The experimental results may offer a useful reference in the design and application of RF of AlGaN/GaN HEMTs.

Effects of N2O surface treatment on the electrical properties of the InAlN/GaN high electron mobility transistors

Various surface treatment methods have been previously applied on the GaN high electron mobility transistor (HEMT). In this study, the effects of N2O surface treatment on the electrical properties of InAlN/GaN HEMT were studied. With this surface treatment, the ideality factor of the gate Schottky barrier diode decreases from 7.70 to 1.30, and the barrier height of SBD increases from 0.508 eV to 1.053 eV (~two folds), an indication of the improved Schottky contact characteristic. Negative-shifted threshold voltage, decreased gate capacitance and two-dimensional electron gas (2DEG) electron density were observed. Both the intrinsic transconductance and 2DEG electron mobility are improved. The 2DEG electron mobilities limited by various scattering mechanisms are extracted using two-dimensional (2D) scattering theory. It is found that N2O surface treatment results in the increase of the 2DEG electron mobility due to the weakened polar optical phonon, interface roughness, and polarization Coulomb field scatterings. This study offers a feasible way to further enhance InAlN/GaN HEMT performances by using N2O surface treatment.

The effect of negative substrate bias on the electrical characteristics of InAlN/GaN MIS-HEMTs

The effect of the negative substrate bias (Vsub) on the device performance of the InAlN/GaN metal–insulator–semiconductor high-electron-mobility transistors (MIS-HEMTs) is studied. When the Vsub decreased from 0 V to −40 V, the two-dimensional electron gas (2DEG) electron density (n2D) under the gate region decreased, while the 2DEG electron mobility (µ2DEG) under the gate region was significantly improved. Due to the InGaN back barrier layer and the thin GaN channel layer (15 nm), the 2DEG electrons in the channel are injected into the InGaN back barrier layer with negative Vsub, leading to the decreased n2D. The decrease of the n2D caused the decrease of the collision probability between the polar optical phonon (POP) and the 2DEG electrons, and the enlarged distance between the 2DEG electrons and the AlN/GaN interface, resulting in the weaker POP and interface roughness scatterings and higher µ2DEG. This provides a possible way to increase 2DEG electron mobility and further improve the device performance of InAlN/GaN MIS-HEMTs.

Positive temperature dependence of time-dependent breakdown of GaN-on-Si E-mode HEMTs under positive gate stress

We report an extensive analysis of the time-dependent breakdown of E-mode GaN-on-Si power HEMTs subjected to positive gate stress and demonstrate that TTF (time-to-failure) has a positive temperature dependence. The analyzed devices have a p-type gate; large (60 A) power transistors were subjected to positive stress at different voltages and temperatures ranging from 25 °C to 250 °C. The original results collected in this paper demonstrate that (i) constant voltage stress induces a gradual decrease in gate leakage current, which is ascribed to hole-trapping in Mg-acceptors located at the p-GaN/AlGaN interface; (ii) this trapping process becomes less pronounced at high temperatures, due to a faster detrapping from the shallow Mg-related traps; (iii) the devices stressed at the same voltage and different temperatures show a similar initial gate leakage, due to the fact that in the analyzed regime, gate conduction is dominated by Fowler-Nordheim tunneling, a field-related, rather than thermally activated, process; (iv) the time-to-failure has a positive temperature dependence. The latter result is explained by considering that time-dependent breakdown occurs due to the accumulation of positive charges at the p-GaN/AlGaN interface, which results in an increased injection of 2DEG electrons into the p-GaN layer, where they are accelerated by the electric field. High temperatures favor the detrapping of holes, thus reducing this process and leading to a better stability.

A Rigorous Investigation of Electrostatic and Transport Phenomena of GaN Double-Channel HEMT

This paper presents a comprehensive investigation of electrostatics and transport characterization of GaN double-channel (DC) MOS-HEMT. Upon derivation of a polynomial analytical expression establishing a relationship between the Fermi level and the 2-D electron gas density (2DEG), a relationship between the sheet carrier density and applied gate voltage has been obtained. To confirm the validity of the model in both subthreshold and strong inversion regions, the charge density profile and capacitance–voltage profile have been attained from self-consistent simulation incorporating the quantum mechanical effect. The impact of GaN channel thickness on the conduction band profile as well as charge density profile has also been investigated. A 2-D analytical model for current–voltage characteristics of GaN-DC-MOS-HEMT has been developed for the first time. Assuming velocity saturation of electrons in 2DEG, the effects of spontaneous and piezoelectric polarization at the heterointerface, field dependent mobility, and the parasitic source and drain resistance have been taken into account in evolution of this model. The ON-resistance extracted from the analytical model was found to be 7.1 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Omega \cdot $ </tex-math></inline-formula> mm, which is in close proximity with experimental results. A steep subthreshold swing of 79 mV/dec was determined from the current–voltage characteristics with an ON– OFF drain current ratio of the order of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">9</sup> , which holds the promising application for enhancement mode operation with minimal leakage current. For corroboration, the derived results were compared with experimental data acquired from the literature, thereby enhancing the reliability of this model.