Schottky-barrier Field-effect Transistors Research Articles

High-performance Schottky-barrier field-effect transistors based on two-dimensional GaN with Ag or Au contacts

The performance of two-dimensional (2D) monolayer GaN Schottky barrier field effect transistors (SBFETs) with four different metals (Ag, Au, Al, and Pt) as electrodes were studied by using ab initio simulations. The N-type Schottky contact is formed on Ag-GaN, Au-GaN, and Pt-GaN, characterized by electron Schottky barrier heights (SBH) of 0.6, 0.5, and 0.38 eV, respectively. Whereas, Al-GaN contact formed P-type Schottky contact with hole SBH of 1.42 eV. The 5.1 nm GaN SBFETs with four metal electrodes all could overcome the short-channel effect. Additionally, GaN SBFETs with Ag and Au electrodes have excellent performance, whose ON-currents are 1151.1 μA/μm and 1258.9 μA/μm, respectively. They could satisfy the demands of International Technology Roadmap for Semiconductors for high-performance transistor. Furthermore, research indicates that the device's current increases with increasing temperature. Notably, under the constant bias and gate voltage, the current is unaffected by temperature variations between the left and right electrodes.

Bias-tunable temperature coefficient of resistance in Ge transistors

Ge-based bolometers are widely used for near-infrared detection for a broad range of applications such as thermography or chemical analysis. Notably, for the thermometers used in bolometers, integration, scaling, and sensitivity as well as functionality are of utmost importance. In this regard, Ge exhibits a favorable temperature sensitivity due to the relatively low bandgap and a high intrinsic charge carrier concentration. In this work, we demonstrate a nanoscale thermometer for bolometric applications on the base of Ge-on-insulator nanosheets with monolithic Al source/drain contacts envisioned for future wafer-scale integration. Importantly, electrostatic gating of the nanosheets allows the operation as a Schottky barrier field-effect transistor, providing tunability of the energy landscape and the involved charge carrier injection in interaction with the metal-semiconductor junctions. In this approach, the top-gate electrode and drain contact are connected, thus resembling a two-terminal device with bias-tunable temperature coefficient of resistance (TCR) values between 0%/K and −3.8%/K in the temperature range of T = 125–150 K. Moreover, in this configuration, even at room temperature, a maximum TCR value of −1.6%/K is achieved. The bias-tunable TCR exhibited in these devices may enable advanced concepts for room temperature bolometric applications and allow co-integration with nanoelectronics.

Recent Advancements in α‐Ga2O3 Thin Film Growth for Power Semiconductor Devices via Mist CVD Method: A Comprehensive Review

AbstractThis review discusses the impact of alpha‐gallium oxide (α‐Ga2O3) on potential high‐power device applications. To date, there are high requirements for efficient high‐power delivery and low‐power loss device material in power industries. III‐VI oxide semiconductor family, α‐Ga2O3, is recognized as a promising, future power semiconductor material owing to its ultrawide bandgap of 5.3 eV, high breakdown field of 10 MV cm−1, and a large Baliga's figure of merit. A highly expected α‐Ga2O3 power semiconductor electronic device (Schottky barrier diode and field effect transistor) can perform better than conventional semiconductor materials Si, SiC, and GaN. However, there is a lack of research into using mist CVD to cultivate high‐quality α‐Ga2O3 for high‐power devices like FETs and SBDs. Currently, the mist CVD‐grown α‐Ga2O3 thin film power device is still in its early stages, and one of the main reasons for this is defects of the thin film, which impede material electron mobility. The purpose of writing this article is to provide an overview of the development of α‐Ga2O3 heteroepitaxial thin film by the mist CVD process for use in high‐power devices such as Schottky barrier diodes (SBD) and field effect transistors (MOSFET). 1. α‐Ga2O3 α‐Ga2O3. Furthermore, multiple viewpoints highlight the challenges and future trends toward device performance sustainability in a scientific society.

Physics-based compact current model for schottky barrier transistors at deep cryogenic temperatures including band tail effects and quantum oscillations

This paper presents a compact model for the DC current of Schottky barrier field-effect transistors at deep cryogenic temperatures, close to absolute zero kelvin. The proposed model is physics based and calculates the injection current over a device’s Schottky barriers, by considering physical effects at these temperatures (e.g. quantum oscillations, band tail effect, phonon-assisted tunneling, etc.). For model verification, it is compared to measurements performed on nanowire Schottky barrier transistors at a temperature of 5.5K.

Compact modeling of Schottky barrier field-effect transistors at deep cryogenic temperatures

In this paper, a physics-based DC compact model for Schottky barrier field-effect transistors at deep cryogenic temperatures is presented. The model uses simplified tunneling equations at temperatures of ϑ≈0K in order to calculate the field emission injection current at the device’s Schottky barriers. Additionally, an empirical expression for including resonant tunneling effects is introduced. The compact model is also compared to and verified by measurements performed on ultra-thin body and buried oxide SOI Schottky barrier field-effect transistors and is able to capture the signature of resonant tunneling effects in the transfer characteristics.

Controlling Hot Charge Carrier Transfer in Monolithic AlSiAl Heterostructures for Plasmonic On-Chip Energy Harvesting.

The generation of hot carriers by Landau damping or chemical interface damping of plasmons is of particular interest to the fundamental aspects of extreme light-matter interactions. Hot charge carriers can be transferred to an attached acceptor for photochemical or photovoltaic energy conversion. However, these lose their excess energy and relax to thermal equilibrium within picoseconds and it is difficult to extract useful work thereof with thermodynamic efficiencies that are of interest for practical devices. Without a detailed understanding of the underlying plasmon decay processes and transfer mechanisms, proper material matching and design considerations for novel plasmonic devices are extremely challenging. Here, a multifunctional AlSiAl heterostructure device with tunable Schottky barriers is presented to control plasmon-induced hot carrier injection at an abrupt metal-semiconductor interface. Light absorption, surface plasmon generation, and separation of hot carriers arising from the non-radiative decay of surface plasmons are realized in a monolithic Schottky barrier field effect transistor. Aside from barrier modulation, a virtual p-n junction can be emulated in the semiconductor channel with the distinct merit that carrier concentration and polarity are tunable by electrostatic gating. The investigations are carried out with a view to possible use for CMOS-compatible plasmonic photovoltaics, with versatile implementations for autonomous nanosystems.

Physics-Based Modeling and Validation of 2-D Schottky Barrier Field-Effect Transistors

In this work, we describe the charge transport in 2-D Schottky barrier field-effect transistors (SB-FETs) based on the carrier injection at the Schottky contacts. We first develop a numerical model for thermionic and field-emission processes of carrier injection that occur at a Schottky contact. The numerical model is then simplified to yield an analytic equation for current versus voltage ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit{I}$</tex-math> </inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit{V}$</tex-math> </inline-formula> ) in the SB-FET. The lateral electric field at the junction, controlling the carrier injection, is obtained by accurately modeling the electrostatics and the tunneling barrier width. Unlike previous SB-FET models that are valid for near-equilibrium conditions, this model is applicable for a broad bias range, as it incorporates the pertinent physics of thermionic, thermionic field-emission (TFE), and field-emission processes from a 3-D metal into a 2-D semiconductor. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit{I}$</tex-math> </inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit{V}$</tex-math> </inline-formula> model is validated against the measurement data of two-, three-, and four-layer ambipolar MoTe <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_\text{2}$</tex-math> </inline-formula> SB-FETs fabricated in our laboratory, as well as the published data of unipolar 2-D SB-FETs using MoS <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_\text{2}$</tex-math> </inline-formula> . Finally, the model’s physics is tested rigorously by comparing model-generated data against TCAD simulation data.

Dual material tri-gate Schottky barrier FET as label free biosensor

In this work, the Dual Material Tri Gate Schottky Barrier Field Effect Transistor (DM-TG-SB-FET) is designed and explored for the biosensing applications. The device uses two different materials of gates and the cavities are created near drain-channel and source-channel junction under gates. The biomolecules with dielectric constant K = 5 to K = 12 have been filled in the cavities and the change has been sensed in the device parameters that are electrical in nature. The sensing parameters have been calculated and compared with the already existing Dielectric Modulated FET based biosensor and a significant improvement has been seen in the DM-TG-SB-FET biosensor. The ION sensitivity, gm sensitivity, SS sensitivity, fT sensitivity has been calculated as 28.41, 13.44, 209 (mV/decade), 30.58 × 1011 Hz, respectively, for the biomolecule having dielectric constant, K = 12 in the proposed DM-TG-SB-FET. Also, the change in potential and energy band diagrams has been seen for different dielectric constants that has led to the change in the electrical parameters of the device.

Effect of different dielectrics on performance of sub-5.1 nm blue phosphorus Schottky barrier field-effect transistor from quantum transport simulation

Two-dimensional materials have attracted great attention because of their ultra-thin atomic layer thickness and high carrier mobility. In this work, we investigated the electronic transport of in-plane (IP) heterojunction based on Cu/Blue Phosphorus (BlueP), and the results suggest the metallization at the IP Cu/BlueP contact interface and a small Schottky barrier. Then, we investigated the performance of 5.1 nm IP BlueP Schottky barrier field-effect transistors (SBFET) with different dielectrics (SiO2, Al2O3, Y2O3, and La2O3) using quantum transport simulations. The results show that IP BlueP SBFETs with four dielectrics satisfy the off-state requirement of the International Technology Roadmap for Semiconductors (ITRS) for the high-performance (HP) device. However, the on-state current of only IP BlueP SBFET with La2O3 satisfies the requirements of ITRS. This will provide a reference for designing BlueP SBFETs.

Increasing of the ON-state current of 5.1 nm MoTe2 in-plane Schottky barrier field-effect transistors by O-passivation and W-doping

Increasing of the ON-state current of 5.1 nm MoTe2 in-plane Schottky barrier field-effect transistors by O-passivation and W-doping

Two-Dimensional Gallium Selenide (GaSe) Material for Nanoelectronics Application

As silicon-based transistors have approached their physical limits, it is urgent to explore alternative materials with a suitable bandgap and high mobility for next generation electronic logic devices. Two‐dimensional (2D) materials have attracted significant attention in the last few years due to their potential exotic transport physics and technological applications in various fields, such as a significant device downscaling for high intensity integration. Recently, a variety of 2D materials have been explored, including graphene [1] and transition metal dichalcogenides (TMDs), e.g., MoS2 [2,3], WS2 [4], and PtSe2 [5-7]. Although most research has focused on TMDs, recently 2D layered metal monochalcogenides, e.g., GaSe, have attracted increasing interest as a result of their unique electronic properties, making this class of materials different from TMDs.GaSe crystal structure comprises vertically stacked Ga-Se-Se-Ga layers with relatively weak van der Waals interactions. There are two main GaSe polytypes which differ in the stacking sequence of the basis layer units. Side- and top-view schematics of β‐GaSe and ε‐GaSe are shown in Fig. 1a. In this study, the electronic structure of both GaSe layered material polytypes is investigated using density functional theory (DFT) as implemented in QuantumATK [8]. Brillouin-zone integrations were performed according to the Monkhorst-Pack scheme [9] with a density of approximately 10 k-points per angstrom. Geometry optimizations were performed with the convergence criterion of 0.02 eV/Å [10]. Van der Waals (vdW) interactions improve the structural and electronic properties description obtained by DFT calculations and is included in our calculations through D3 version of Grimme’s dispersion corrections [11].To provide an improved determination of the bandgap energies, the GW (G: Green's function and W: screened Coulomb interaction) method in conjunction with a many body perturbation theory (MBPT) correction could be used. However, GW technique is computationally very expensive and could be implemented for systems with very limited number of atoms [12,13]. Hence, for this study, methods such as Heyd-Scuseria-Ernzerhof (HSE) hybrid functional [14,15] and GGA-1/2 [16] methods were included in our model to achieve more accurate bandgap compared to the experimental values. The β‐GaSe exhibits a DFT-obtained direct bandgap of ~1 eV while the corrected value is 2 eV. ε‐GaSe, however, shows slight indirect bandgap of 0.8 eV (DFT) and 1.7 eV (corrected), with just 25 meV difference between the indirect gap and indirect gap.A double-gate Schottky barrier field-effect transistor (FET) consisting of Ti source and drain contacts and ultrathin GaSe channel is also investigated. Schematic of the FET is shown in Fig. 1b. The device performance analysis such as current-voltage characteristics, subthreshold slope, and on/off ratio are carried out by means of non-equilibrium Green’s function together with DFT Hamiltonian [17]. The output characteristic of the proposed device exhibits an ON/OFF current ratio of more than 7 orders of magnitude.The presence of point defects in ultrathin 2D films is largely inevitable [18], even under optimized synthesis conditions, which can be either engineered and considered as a useful feature, or undesirable. In either case, understanding the impacts of point defects on the electronic structure of 2D materials are required to allow application-based optimization. In this talk, to provide insight into the defect-induced modifications to the GaSe electronic properties, in particular the properties of the states associated with the defects, we will compare the band-structure of the pristine GaSe with the band-structure of the GaSe with Ge and Se vacancies, for both GaSe polytypes.We have also fabricated back-gated devices by mechanically exfoliating ultrathin GaSe flakes from bulk crystal onto oxide-on-Si substrate. Fig. 1c shows an SEM image of the device. Our experimental results demonstrate the basic transport characteristics of thin-film transistor, which may offer more opportunities for potential applications such as photodetectors, gas sensors, and optoelectronic devices, in addition to nanoelectronics FETs, due to GaSe large bandgap.

Ultra-Low Power Schottky Barrier TFT-Based Neurotransmitter Detection and Regenerative Studies

There is limited work on understanding Schottky barrier (SB) field-effect transistor (FET) behavior, and subsequent evolution of sensitivity metrics under wet detection conditions for neurotransmitter sensing applications. In this work, we report low-power deep subthreshold (DST) characteristics of SB InGaZnO₄ (IGZO) thin film transistors (TFTs) and implement this regime for sensitive and selective <i>ex vivo</i> detection of Dopamine against Adenosine Triphosphate (ATP). Device regeneration was performed under liquid solution environment over 34 days and sensor response was observed to drift less than two orders of magnitude. Nevertheless, the quantified trends due to buffer solution baseline versus target conjugation were virtually preserved across the TFTs. Widely improved detection metrics were extracted from the detection tests, namely the limit of detection (LoD) in the 100fM-100pM range, a binding affinity (<inline-formula> <tex-math notation="LaTeX">$k_{D}$ </tex-math></inline-formula>) between <inline-formula> <tex-math notation="LaTeX">$2.03\times 10^{-11}$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$3.02\times 10^{-9}\text{M}$ </tex-math></inline-formula> limits, and high sensitivity around 31-42mV/decade of target concentration. Although a steady drift with clear, repeatable differences between the device state at the start and end of the 34-day period were obtained, these devices were functional even after the regeneration test period. Such results can be used to estimate the regenerative lifetime of TFT biosensors under aptamer-immobilized solution environment detection conditions.

High-performance monolayer or bilayer SiC short channel transistors with metallic 1T-phase MoS2 contact

In this paper, high-performance monolayer or bilayer SiC short channel transistors with metallic 1T-Phase MoS2 contact have been proposed and investigated by using ab initio simulations. The results show that monolayer or bilayer SiC Schottky-barrier field-effect transistors (SBFET) could conquer the short channel effect, even if the channel length is reduced to 4.1 nm. The p-type ON-currents of monolayer SiC-SBFET, bilayer AB-stacked SiC-SBFET, and bilayer AA-stacked SiC-SBFET are 1132 μA/μm, 980 μA/μm, and 1457 μA/μm, respectively. The all could satisfy the requirement of the high-performance transistor outlined by International Technology Roadmap for Semiconductors (ITRS, 2013 version) for production year 2028. However, the n-type ON-currents of above SiC-SBFETs are 35 μA/μm, 21 μA/μm, and 229 μA/μm, which are much lower than that of p-type ON-currents. Comparing spectral current and spatial local density of states are used to explore the great differences between the p-type and n-type ON-currents.

P-type doping induced performance improvement of two-dimensional SiC transistors with 1T-phase MoS2 electrode

Using nonequilibrium Green's functions in combination with the density-functional theory, we explored the performance of two-dimensional (2D) SiC Schottky-Barrier field effect transistor (SBFET) with different concentration of p-type doping in source/drain region. The corresponding hole Schottky barrier height would be gradually reduced with the increasing of the p-type doping concentration. The ON-state current of SBFETs with different p-type doping concentration (1×1020 cm−2, 5×1020 cm−2, 1×1021 cm−2, 5×1021 cm−2) are 1184 μA/μm, 1263 μA/μm, 1659 μA/μm, 1200 μA/μm, respectively, which could satisfy the ITRS (International technology road-map for semiconductors, 2013 version) high-performance (HP) standards for the 2028 horizon. In addition, the intrinsic gate capacitance, the dynamic power indicator and the intrinsic transistor delay time of p-type doping SBFETs with different doping concentration all satisfy the performance requirement of HP transistor outlined by ITRS.

Four-Terminal Ferroelectric Schottky Barrier Field Effect Transistors as Artificial Synapses for Neuromorphic Applications

In this paper, artificial synapses based on four terminal ferroelectric Schottky barrier field effect transistors (FE-SBFETs) are experimentally demonstrated. The ferroelectric polarization switching dynamics gradually modulate the Schottky barriers, thus programming the device conductance by applying negative or postive pulses to imitate the excitation and inhibition behaviors of the biological synapse. The excitatory post-synaptic current can be modulated by the back-gate bias, enabling the reconfiguration of the weight profile with high speed of 20 ns and low energy (< 1 fJ/spike) consumption. Besides, the tunable long term potentiation and depression show high endurance and very small cycle-to-cycle variations. Based on the good linearity, high symmetricity and large dynamic range of the synaptic weight updates, a high recognition accuracy (92.6%) is achieved for handwritten digits by multilayer perceptron artificial neural networks. These findings demonstrate FE-SBFET has high potential as an ideal synaptic component for the future intelligent neuromorphic network.

A Ge-based dual channel rectified single ended Schottky barrier field effect transistor for 2.45 GHz microwave wireless energy transmission

Rectifier component is a core part of a microwave wireless energy transmission system, and the development of new rectifier components is an important research direction in this field. Schottky diodes and field-effect transistors are currently the mainstream rectifier devices, but they have a limited rectification range and cannot achieve a wide-range rectification of both weak energy and medium energy density at the same time. In view of this, in this work proposed and designed is a Ge based p-type single-ended Schottky barrier field effect transistor (Schottky contact at the source and standard p&lt;sup&gt;+&lt;/sup&gt; doping at the drain) for 2.45 GHz microwave wireless energy transmission. Based on this, the Schottky structure of the device is fully utilised and a new diode connection is used in order to realize a dual channel wide range rectification of the trench and source lined Schottky structure opened at different bias voltages. Simulations are carried out by using the Silvaco TCAD software. For a half-wave rectifier circuit with a load of 0.3 pF and 70 kΩ, a wide range from –20 to 24 dBm rectification is achieved, which is 8 dBm wider than the range of Ge field-effect transistors under the same conditions, and the overall rectification efficiency is higher in the range, with a peak rectification efficiency of 57.27% at 16 dBm. The rectification efficiency at –10 dBm weak energy density reaches 6.17%, which is more than 7 times that of Ge FETs under the same conditions.

Physics-Based DC Compact Modeling of Schottky Barrier and Reconfigurable Field-Effect Transistors

A closed-form and physics-based compact model is presented for calculating the DC characteristics of Schottky barrier field-effect transistors and dual gated reconfigurable field-effect transistors. The given model calculates the charge-carrier injection over the Schottky barriers. This current is separated into a field emission current, given by charge carriers tunneling through the Schottky barriers and a thermionic emission current, given by charge carriers overcoming the Schottky barriers. The model verification is done by comparing the model results to measurements and TCAD simulations.

Suppression of short channel effects in 5.1 nm WTe2 in-plane Schottky barrier field-effect transistors by Mo-doping

Single layer Schottky barrier field-effect transistors (SBFETs) composed of the in-plane (IP) hetero-junctions of 1T-WTe2(metallic phase WTe2) and 2H–WTe2(semiconducting phase WTe2) have been proposed in this paper. However, the transfer characteristic show that the 5.1 nm IP 1T-2H-1T WTe2 SBFET cannot suppress the short channel effect causing the leakage current beyond the OFF current (IOFF) requirement (0.1 μA/μm) of the International Technology Roadmap for Semiconductors (ITRS, 2013 version) for production in 2028. To solve this problem, we replace the W atoms of 2H–WTe2 near the source electrode with Mo atoms to conquer the short channel effect. We found that the leakage currents of the 5.1 nm IP 1T-2H-1T WTe2 SBFETs decrease gradually with the increase of the number of substitution Mo atoms. When the number of substitutions increases to six periods, the leakage drain current of the 5.1 nm IP 1T-2H-1T WTe2 SBFETs is lower than 0.1 μA/μm. Fortunately, the corresponding ON current (ION) is 961 μA/μm which also conforms to the ON current requirement (900 μA/μm) of ITRS (2013 version) for production in 2028. Therefore, the monolayer WTe2 with the Mo atom substitution also can be used as the channel material in future 5 nm transistor.

Electronic and optical properties and device applications for antimonene/WS2 van der Waals heterostructure

The antimonene and WS2 monolayers have widely studied recently. Here, we construct the Sb/WS2 van der Waals heterostructures to explore their combined effects on electronic and optical properties based on density functional method. The calculated results show that the most stable heterostructure is a type-Ⅱ semiconductor with a medium band gap of 1.183 eV. The external electric field can alter its band gap significantly, for example, the small negative electric field can make the band gap narrowed sharply and linearly. Based on this behavior, a high-performance heterostructure Schottky-barrier field effect transistor is designed. And under vertical strain, the heterostructure is robust to sustain a type-Ⅱ band alignment, but the band gap can be reduced rapidly by pressure. Accordingly, a strain-gated high switch-ratio mechanical switch device by working reversibly between the “compressive” and “unstrained” states is suggested. Also shown is that this heterostructure prefers the visible light adsorption, and the photoelectric power conversion efficiency (PCE) is as high as 20.98%. Particularly, under small positive electric field, the light adsorption and PCE for this heterostructure is enhanced significantly up to 22.845%. Thus a photovoltaic cell with a high PCE is proposed.

The in-plane graphene and boropheneβ12 contacted sub-10 nm monolayer black phosphorous Schottky barrier field-effect transistors

Using ab initio quantum transport calculations, we investigate the performance of the in-plane (IP) graphene and boropheneβ12 contacted sub-10 nm (gate length = 5.1, 6.1, 7.3, 8.8 nm) single-gated (SG) and double-gated (DG) monolayer (ML) black phosphorous (BP) Schottky barrier field-effect transistors (SBFETs). The transfer characteristics, total gate capacitance, intrinsic delay time and dynamic power indicator are studied. The calculated on-state currents of the IP graphene contacted sub-10 nm SG ML BP SBFETs are 1064.8, 1272.3, 1676.5, 1363.8 μA/μm, which are far beyond the requirements of International Technology Roadmap for Semiconductor (ITRS) high performance (HP) application targets. Compared with graphene electrode, the on-state currents of IP boropheneβ12 contacted sub-10 nm SG ML BP SBFETs can only satisfy about 10%–70% requirement of HP standards because of the strong metal induced gap states (MIGS) in the channel. Moreover, we further investigated the effect of DG model on the device performance. The results indicated that the gate electrostatic control is significantly improved by using DG model. The on-state currents of IP graphene and boropheneβ12 contacted sub-10 nm DG ML BP SBFETs are increased by a factor of 1.37–1.56 and 1.16–3.59 compared with SG model. As a result, the large on-state currents of IP configurations based on graphene/ML BP/graphene can greatly stimulate the potential of BP transistors.