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Floating-gate MOSFET
Floating-gate MOSFET
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The floating-gate MOSFET (FGMOS), also known as a floating-gate MOS transistor or floating-gate transistor, is a type of metal–oxide–semiconductor field-effect transistor (MOSFET) where the gate is electrically isolated, creating a floating node in direct current, and a number of secondary gates or inputs are deposited above the floating gate (FG) and are electrically isolated from it. These inputs are only capacitively connected to the FG. Since the FG is surrounded by highly resistive material, the charge contained in it remains unchanged for long periods[1] of time, typically longer than 10 years in modern devices. Usually Fowler-Nordheim tunneling and hot-carrier injection mechanisms are used to modify the amount of charge stored in the FG.

The FGMOS is commonly used as a floating-gate memory cell, the digital storage element in EPROM, EEPROM and flash memory technologies. Other uses of the FGMOS include a neuronal computational element in neural networks,[2][3] analog storage element,[2] digital potentiometers and single-transistor DACs.

History

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The first MOSFET was invented by Mohamed Atalla and Dawon Kahng at Bell Labs in 1959, and presented in 1960.[4] The first report of a FGMOS was later made by Dawon Kahng and Simon Min Sze at Bell Labs, and dates from 1967.[5] The earliest practical application of FGMOS was floating-gate memory cells, which Kahng and Sze proposed could be used to produce reprogrammable ROM (read-only memory).[6] Initial applications of FGMOS was digital semiconductor memory, to store nonvolatile data in EPROM, EEPROM and flash memory.

In 1989, Intel employed the FGMOS as an analog nonvolatile memory element in its electrically trainable artificial neural network (ETANN) chip,[3] demonstrating the potential of using FGMOS devices for applications other than digital memory.

Three research accomplishments laid the groundwork for much of the current FGMOS circuit development:

  • Thomsen and Brooke's demonstration and use of electron tunneling in a standard CMOS double-poly process[7] allowed many researchers to investigate FGMOS circuits concepts without requiring access to specialized fabrication processes.
  • The νMOS, or neuron-MOS, circuit approach by Shibata and Ohmi[8] provided the initial inspiration and framework to use capacitors for linear computations. These researchers concentrated on the FG circuit properties instead of the device properties, and used either UV light to equalize charge, or simulated FG elements by opening and closing MOSFET switches.
  • Carver Mead's adaptive retina[2] gave the first example of using continuously-operating FG programming/erasing techniques, in this case UV light, as the backbone of an adaptive circuit technology.

Structure

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A cross-section of a floating-gate transistor

An FGMOS can be fabricated by electrically isolating the gate of a standard MOS transistor, so that there are no resistive connections to its gate. A number of secondary gates or inputs are then deposited above the floating gate (FG) and are electrically isolated from it. These inputs are only capacitively connected to the FG, since the FG is completely surrounded by highly resistive material. So, in terms of its DC operating point, the FG is a floating node.

For applications where the charge of the FG needs to be modified, a pair of small extra transistors are added to each FGMOS transistor to conduct the injection and tunneling operations. The gates of every transistor are connected together; the tunneling transistor has its source, drain and bulk terminals interconnected to create a capacitive tunneling structure. The injection transistor is connected normally and specific voltages are applied to create hot carriers that are then injected via an electric field into the floating gate.

FGMOS transistor for purely capacitive use can be fabricated on N or P versions. [9] For charge modification applications, the tunneling transistor (and therefore the operating FGMOS) needs to be embedded into a well, hence the technology dictates the type of FGMOS that can be fabricated.

Modeling

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Large signal DC

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The equations modeling the DC operation of the FGMOS can be derived from the equations that describe the operation of the MOS transistor used to build the FGMOS. If it is possible to determine the voltage at the FG of an FGMOS device, it is then possible to express its drain to source current using standard MOS transistor models. Therefore, to derive a set of equations that model the large signal operation of an FGMOS device, it is necessary to find the relationship between its effective input voltages and the voltage at its FG.

Small signal

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An N-input FGMOS device has N−1 more terminals than a MOS transistor, and therefore, N+2 small signal parameters can be defined: N effective input transconductances, an output transconductance and a bulk transconductance. Respectively:

where is the total capacitance seen by the floating gate. These equations show two drawbacks of the FGMOS compared with the MOS transistor:

  • Reduction of the input transconductance
  • Reduction of the output resistance

Simulation

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Under normal conditions, a floating node in a circuit represents an error because its initial condition is unknown unless it is somehow fixed. This generates two problems:

  1. It is not easy to simulate these circuits
  2. An unknown amount of charge might stay trapped at the floating gate during the fabrication process which will result in an unknown initial condition for the FG voltage.

Among the many solutions proposed for the computer simulation, one of the most promising methods is an Initial Transient Analysis (ITA) proposed by Rodriguez-Villegas,[10] where the FGs are set to zero volts or a previously known voltage based on the measurement of the charge trapped in the FG after the fabrication process. A transient analysis is then run with the supply voltages set to their final values, letting the outputs evolve normally. The values of the FGs can then be extracted and used for posterior small-signal simulations, connecting a voltage supply with the initial FG value to the floating gate using a very-high-value inductor.

Applications

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The usage and applications of the FGMOS can be broadly classified in two cases. If the charge in the floating gate is not modified during the circuit usage, the operation is capacitively coupled.

In the capacitively coupled regime of operation, the net charge in the floating gate is not modified. Examples of application for this regime are single transistor adders, DACs, multipliers and logic functions, and variable threshold inverters.

Using the FGMOS as a programmable charge element, it is commonly used for non-volatile storage such as flash, EPROM and EEPROM memory. In this context, floating-gate MOSFETs are useful because of their ability to store an electrical charge for extended periods of time without a connection to a power supply. Other applications of the FGMOS are neuronal computational element in neural networks, analog storage element and e-pots.

See also

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References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Floating-gate MOSFET

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A floating-gate MOSFET (FGMOS), also known as a floating-gate field-effect transistor, is a specialized variant of the metal–oxide–semiconductor field-effect transistor (MOSFET) that features an additional electrically isolated polysilicon gate—termed the floating gate—sandwiched between two layers of oxide and capacitively coupled to a control gate, enabling the long-term storage of electrical charge to alter the device's threshold voltage and facilitate non-volatile memory operations without power supply. This structure was first proposed in 1967 by Dawon Kahng and Simon M. Sze at Bell Labs as a mechanism for non-volatile information storage in semiconductor devices. The operation of an FGMOS relies on the injection, retention, and extraction of electrons onto or from the floating gate, which modifies the effective gate voltage and thus the channel conductivity between the source and drain terminals. Charge programming (writing) typically occurs through mechanisms such as hot-electron injection, where high drain-source voltage accelerates electrons into the floating gate, or Fowler-Nordheim tunneling under high electric fields across a thin layer. Erasure removes stored charge via reverse tunneling or light exposure in early designs, restoring the to its baseline state, while reading involves applying a control gate voltage to sense the resulting drain current, which reflects the stored charge level without altering it. These processes allow the FGMOS to function as a compact cell capable of retaining data for years or decades, making it foundational to non-volatile technologies. Since its invention, the FGMOS has become integral to erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), and flash memory, powering applications from data storage in microcontrollers to high-density solid-state drives and embedded systems in consumer electronics. Beyond digital storage, advancements have extended its use to analog signal processing, adaptive circuits, and neuromorphic computing, where programmable threshold voltages enable tunable synaptic weights or low-power sensor interfaces, often fabricated using standard complementary metal–oxide–semiconductor (CMOS) processes for scalability. Despite challenges like oxide wear from repeated programming cycles and scaling limits in sub-10 nm nodes, ongoing research explores charge-trap alternatives and multi-gate configurations to enhance endurance and density.

Historical Development

Invention and Early Concepts

The floating-gate MOSFET was invented in 1967 by and Simon M. Sze at Bell Laboratories, where it was developed as a element capable of storing charge semi-permanently without external power. This innovation built directly on the (MOSFET), which had been demonstrated earlier in 1959 by and at the same institution, providing the foundational insulated-gate structure for controlling conductivity in silicon devices. Kahng and Sze's work addressed the need for compact, semiconductor-based alternatives to bulky memories prevalent in , proposing the floating-gate device as a means to trap electrons on an isolated conductor to modify device behavior persistently. The core early concept centered on an isolated floating gate—a conductive layer embedded within the and fully insulated by thin oxide layers from the control gate, channel, and substrate—enabling charge trapping to shift the transistor's and represent binary states. Unlike a standard , which relies on a directly connected gate for transient control, the floating-gate variant incorporates this additional insulated electrode to retain trapped charge, allowing non-volatile operation where stored information persists after power removal. Charge injection onto the floating gate was envisioned through mechanisms such as Fowler-Nordheim tunneling under high or hot-carrier () injection, with erasure via thermal or optical emission; initial experiments demonstrated reprogrammable functionality by altering the between high and low states, effectively creating a semiconductor-based (ROM) that could be modified. In their 1967 publication, Kahng and Sze fabricated and tested prototype devices on , observing holding times longer than one hour, which validated the principle of semi-permanent charge storage and laid the groundwork for subsequent enhancements in retention and . This demonstration highlighted the device's potential for dense, integrated arrays, distinguishing it from volatile alternatives by emphasizing electrical isolation for enduring charge confinement.

Key Milestones and Commercialization

The commercialization of floating-gate MOSFET technology began in earnest in the early 1970s, marking a pivotal shift from experimental concepts to practical, market-ready devices. In 1971, introduced the world's first commercial erasable programmable (EPROM), the 1702, a 2K-bit device that utilized floating-gate avalanche-injection MOS (FAMOS) cells for light erasable storage, enabling reusable programming in integrated circuits and revolutionizing development for microprocessors. This innovation, developed by Dov Frohman at , addressed the limitations of one-time programmable ROMs by allowing multiple erase-write cycles, though requiring external UV exposure for erasure. Building on this foundation, the late 1970s saw advancements in electrical erasability, eliminating the need for UV light. In 1980, introduced the 2816, the first commercial electrically erasable programmable (EEPROM), employing a floating-gate structure with Fowler-Nordheim tunneling for byte-level electrical programming and erasing, which facilitated in-system updates and boosted adoption in embedded systems and peripherals. This device, designed by George Perlegos, offered greater flexibility than EPROMs and paved the way for denser non-volatile storage, with Hughes Aircraft also introducing a complementary 8K-bit EEPROM that year. The 1980s witnessed the emergence of flash memory architectures, dramatically increasing density and performance for mass storage applications. In 1987, Fujio Masuoka and his team at invented NAND flash, a serial-access architecture using floating-gate cells arranged in strings for high-density, block-erasable storage, which was first commercialized in 1989 and became dominant for consumer devices like SSDs due to its cost efficiency. Concurrently, developed NOR flash in 1988 under the trademark, featuring parallel access and random byte addressing via floating-gate cells, ideal for code execution in embedded applications such as and . These architectures, both rooted in floating-gate technology, propelled the market, with and leading shipments and enabling the portable electronics boom. Beyond storage, floating-gate MOSFETs found early applications in analog computing. In 1989, Intel researchers introduced the Electrically Trainable Analog Neural Network (ETANN) chip, incorporating 10,240 floating-gate synapses for analog weight storage in hardware neural networks, demonstrating multilevel charge storage for synaptic weights and marking one of the first commercial uses in neuromorphic hardware. In the post-2000 era, aggressive scaling extended floating-gate technology to sub-10 nm nodes in planar NAND flash, achieving densities exceeding 128 Gb per die by the mid-2010s through optimized cell interference management and thinner oxides, though facing reliability challenges like charge leakage. To overcome planar scaling limits, 3D NAND stacking emerged, with commercial introductions in the 2010s; for instance, and Micron's 2015 3D NAND used floating-gate cells in stacked layers for enhanced endurance. Integration with FinFET transistors further advanced embedded flash, enabling low-power, high-reliability non-volatile storage in SoCs at 14 nm and below, as seen in automotive and IoT applications. By the 2020s, while high-density NAND has largely shifted to charge-trap alternatives for better 3D scalability—exemplified by Samsung's 2013 V-NAND, the first mass-produced 3D vertical NAND at 128 Gb using charge-trap flash—floating-gate MOSFETs persist in embedded flash for their mature and suitability in low-density, radiation-hardened environments like microcontrollers and space electronics. Ongoing patents, such as those for enhanced floating-gate uniformity in embedded processors (e.g., TSMC's 2021 innovations), underscore hybrid designs combining floating gates with advanced nodes for continued relevance through 2025, alongside recent 2024-2025 research into multi-bit and tunable floating-gate devices for neuromorphic applications.

Device Structure and Physics

Physical Construction

The floating-gate MOSFET builds upon the standard metal-oxide-semiconductor field-effect transistor () architecture by incorporating an isolated conductive layer, known as the floating gate, for charge storage. In cross-section, the device consists of a p-type substrate with heavily doped n+ source and drain regions separated by a channel region. Over the channel lies a thin tunnel oxide layer, typically 8-10 nm thick and composed of SiO₂, which electrically isolates the substrate from the floating gate made of n+-doped (poly-Si), approximately 100-150 nm thick. Above the floating gate is the interpoly (IPD), a thicker insulating layer (10-20 nm , often an oxide-nitride-oxide or SiO₂ stack) that separates it from the control gate, another layer of n+-doped poly-Si. This stacked configuration ensures the floating gate remains electrically isolated while allowing capacitive interaction with surrounding electrodes. The floating gate is capacitively coupled to the control gate via the IPD (denoted as C_CG), which dominates the overall , and to the source and drain regions through overlap capacitances (C_SD) formed by the gate edges extending over the doped areas. These couplings enable voltage transfer from the control gate to the floating gate without direct electrical connection, a key feature for non-volatile operation. In modern implementations, channel lengths typically range from 10 to 100 nm to support device scaling, while oxide thicknesses are precisely controlled (e.g., tunnel oxide at ~8 nm) to balance tunneling efficiency during programming with long-term reliability by preventing excessive charge leakage over 10-year retention periods. Fabrication of the floating-gate MOSFET is highly compatible with standard complementary metal-oxide-semiconductor () processes, facilitating integration with logic circuitry. The process begins with to grow the tunnel oxide on the silicon substrate, followed by low-pressure (LPCVD) to deposit the first poly-Si layer for the floating , doped via implantation. The IPD is then formed through sequential deposition of SiO₂, Si₃N₄, and another SiO₂ layer (for ONO stacks), after which the second poly-Si layer for the control is deposited and doped. Photolithographic patterning and define the gate stack, with self-aligned source/drain implantation completing the structure. Variations include stacked-gate designs, where the entire multilayer stack is etched as a unit for uniform alignment in NOR-type flash memories, and split-gate designs, which involve additional masking and etching steps to offset the floating and control gates, reducing programming voltages in applications. Traditional materials emphasize SiO₂ for both the tunnel oxide and IPD due to its compatibility with silicon and excellent insulating properties, paired with poly-Si gates for their conductivity and ease of doping. However, as scaling challenges intensify below 20 nm nodes, emerging designs incorporate high-k dielectrics like HfO₂ (dielectric constant ~25) to replace or augment SiO₂ in the IPD and tunnel layers, achieving thinner physical thicknesses while preserving and reducing leakage currents. This material shift, often via (ALD) of HfO₂, enhances scalability without compromising reliability, as demonstrated in nanocrystal-enhanced floating-gate structures.

Charge Storage Mechanism

The floating gate in a floating-gate MOSFET serves as an isolated conductive layer, typically , surrounded by insulating oxide layers that electrically isolate it from the control gate, channel, and substrate. This structure enables the storage of charge carriers, primarily electrons or holes, which are injected onto or removed from the floating gate through quantum mechanical processes. The trapped charge QfgQ_{fg} modulates the VthV_{th} of the underlying MOSFET channel, with the shift approximated by ΔVth≈−Qfg/Ctotal\Delta V_{th} \approx -Q_{fg} / C_{total}, where CtotalC_{total} is the total seen by the floating gate. This voltage shift encodes binary or multilevel data states, forming the basis for operation. Charge retention on the floating gate is maintained by the high energy barrier at the silicon-SiO₂ interface, approximately 3.1 eV for electrons, which suppresses thermal emission and leakage under normal conditions. At , this results in data retention exceeding 10 years, though retention degrades at elevated temperatures due to accelerated charge loss mechanisms. The isolation provided by the surrounding oxide layers, such as the tunnel oxide and inter-poly , minimizes leakage paths, ensuring long-term stability essential for nonvolatile applications. Quantum effects dominate charge injection and potential leakage in the floating gate. For thicker tunnel oxides (typically >4 nm or 40 Å), Fowler-Nordheim tunneling prevails, where electrons tunnel through a triangular potential barrier under high (~10 MV/cm). In thinner oxides (<4 nm), direct tunneling becomes significant, allowing charge carriers to traverse a rectangular barrier without field-induced bending, though this increases power consumption and limits scalability. A key reliability concern is stress-induced leakage current (SILC), arising from oxide traps generated during repeated programming/erasing cycles, which creates localized conduction paths and accelerates charge loss, contributing to retention failure. The efficiency of voltage application to the floating gate is governed by the capacitance coupling factor α=CCG/Ctotal\alpha = C_{CG} / C_{total}, where CCGC_{CG} is the control gate-to-floating gate capacitance. This factor, typically ranging from 0.6 to 0.8 in standard designs, determines how effectively the control gate voltage couples to the floating gate potential, influencing programming efficiency and threshold control. Higher α\alpha values enhance voltage transfer but require optimized oxide thicknesses to balance coupling and isolation.

Operation Principles

Programming and Erasing

Programming of a floating-gate MOSFET involves injecting electrons onto the floating gate to store negative charge, which increases the (V_th) of the device, representing the programmed state. One common method is channel hot-electron injection, where high drain-source voltage (V_ds > 5 V) and gate voltage (V_g > 10 V) accelerate electrons in the channel, allowing a fraction to gain sufficient energy to overcome the gate oxide barrier and inject into the floating gate. This technique, originally developed for cells, achieves a threshold voltage shift of typically 2-5 V in milliseconds. Another programming mechanism is Fowler-Nordheim tunneling, employed in and devices, where a high positive gate voltage (V_g > 15 V) applied for pulses of about 1 ms causes electrons to quantum-mechanically tunnel from the substrate or channel through a thin tunnel oxide (typically 7-10 nm) into the floating gate. This method provides efficient charge injection without requiring high drain currents, enabling denser memory arrays, and also results in a V_th shift of 2-5 V. Erasing removes electrons from the floating gate to restore the original low V_th state. In EPROM devices, erasing is accomplished by exposing the chip to (UV) light, which generates photoelectrons that discharge the floating gate over minutes to hours through the passivation layer. For electrically erasable devices like and flash, erasing uses reverse Fowler-Nordheim tunneling with a high negative gate voltage (V_g < -15 V), tunneling electrons from the floating gate back to the substrate or source/drain regions in pulses lasting milliseconds. This process shifts V_th back to its initial value, completing the erase operation. Repeated programming and erasing degrade the tunnel oxide due to trapped charges and stress-induced leakage, limiting device endurance to approximately 10^5 to 10^6 cycles before significant V_th window closure occurs from oxide wear-out. Variations in erase operations include byte-level erasing in for individual cell access and sector-level erasing in NAND flash, where entire blocks (typically 512 bytes to several kilobytes) are erased simultaneously to optimize performance and density.

Read Operation

In the read operation of a floating-gate MOSFET, a positive control gate voltage VG>0V_G > 0 is applied, typically in the range of 3-5 V, while the drain-source voltage VDSV_{DS} is kept low at approximately 1 V to avoid any charge modification. The floating-gate potential VFGV_{FG} is then determined by from the control gate and the stored charge: VFG=αVG+QFGCtotalV_{FG} = \alpha V_G + \frac{Q_{FG}}{C_{total}} where α\alpha is the control-gate coupling coefficient (typically 0.6-0.8), QFGQ_{FG} is the charge on the floating gate, and CtotalC_{total} is the total seen by the floating gate. This VFGV_{FG} modulates the channel inversion, effectively controlling the transistor's VthV_{th}. The stored negative charge on the floating gate from programming increases VthV_{th} (e.g., shifting it by several volts), reducing the drain-source current IDSI_{DS} in the programmed state, while the erased state (minimal charge) results in a lower VthV_{th} and higher IDSI_{DS}. This leads to a current difference of one or more orders of magnitude between programmed ("0") and erased ("1") states, enabling reliable state discrimination. The read process is non-destructive, as the low voltages prevent charge tunneling or injection, preserving the stored charge; sense amplifiers detect the IDSI_{DS} or associated VthV_{th} shift to output the logical state without altering it. Charge retention on the floating gate ensures stable readout over time. Modern floating-gate-based flash memories achieve read times below 50 ns, supporting high-speed applications, with margining techniques incorporated to maintain reliability by avoiding over-programming and ensuring sufficient separation between state distributions.

Electrical Modeling

Large-Signal DC Model

The large-signal DC model for a floating-gate MOSFET captures the steady-state current-voltage characteristics under applied biases, incorporating the effects of charge stored on the isolated floating gate. This model treats the device as a conventional MOSFET with an effective gate voltage determined by capacitive coupling from the control gate and other terminals to the floating gate, enabling prediction of drain current as a function of terminal voltages and stored charge. The floating gate voltage VfgV_{fg} is obtained from charge conservation on the floating gate, expressed as Vfg=CCGVCG+CDVD+CSVS+CBVB+QfgCtotal,V_{fg} = \frac{C_{CG} V_{CG} + C_{D} V_{D} + C_{S} V_{S} + C_{B} V_{B} + Q_{fg}}{C_{total}}, where Ctotal=CCG+CD+CS+CBC_{total} = C_{CG} + C_{D} + C_{S} + C_{B} is the total capacitance associated with the floating gate, CCGC_{CG}, CDC_{D}, CSC_{S}, and CBC_{B} are the control-gate-to-floating-gate, drain-to-floating-gate, source-to-floating-gate, and body-to-floating-gate capacitances, respectively, VCGV_{CG}, VDV_{D}, VSV_{S}, and VBV_{B} are the corresponding terminal voltages, and QfgQ_{fg} is the net charge on the floating gate. The threshold voltage VthV_{th} observed at the control gate is shifted due to QfgQ_{fg}, given by Vth=Vth0−QfgCCG,V_{th} = V_{th0} - \frac{Q_{fg}}{C_{CG}}, where Vth0V_{th0} is the threshold voltage without stored charge (including body effect dependence on VBSV_{BS}) and CCGC_{CG} is the total control-gate-to-floating-gate capacitance. This formulation links the stored charge directly to the device's turn-on behavior. The drain current IDSI_{DS} follows the standard long-channel MOSFET equations, with VGSV_{GS} referring to the control-gate-to-source voltage and VthV_{th} the shifted threshold. In the linear region (VDS<VGS−VthV_{DS} < V_{GS} - V_{th}), IDS=μCoxWL[(VGS−Vth)VDS−VDS22],I_{DS} = \mu C_{ox} \frac{W}{L} \left[ (V_{GS} - V_{th}) V_{DS} - \frac{V_{DS}^2}{2} \right], and in saturation (VDS≥VGS−VthV_{DS} \geq V_{GS} - V_{th}), IDS,sat=μCox2WL(VGS−Vth)2,I_{DS,sat} = \frac{\mu C_{ox}}{2} \frac{W}{L} (V_{GS} - V_{th})^2, where μ\mu is the carrier mobility, W/LW/L is the channel aspect ratio, and subthreshold operation can be modeled using exponential dependence on VGS−VthV_{GS} - V_{th}. These expressions assume level-1 MOSFET physics but can be extended with more advanced surface-potential-based models for accuracy. CoxC_{ox} here is the oxide capacitance per unit area for the channel. Programming and erasing operations induce shifts in VthV_{th} (ΔVth\Delta V_{th}) proportional to the injected charge ΔQfg\Delta Q_{fg}, as ΔVth=−ΔQfg/CCG\Delta V_{th} = -\Delta Q_{fg} / C_{CG}, enabling non-volatile storage of multiple threshold states for applications. The magnitude of ΔVth\Delta V_{th} typically ranges from 2–5 V for reliable distinction between programmed and erased states, depending on the charge injection mechanism and coupling efficiency.

Small-Signal AC Model

The small-signal AC model of the floating-gate MOSFET is derived by linearizing the nonlinear device equations around a chosen DC operating point, accounting for the between the control gate and the isolated floating gate. This coupling introduces a voltage division effect that scales the AC response relative to a standard . The model highlights how the floating nature of the gate reduces intrinsic device parameters, such as gain, through the coupling coefficient α=CCGCT\alpha = \frac{C_{CG}}{C_T}, where CCGC_{CG} is the control-gate to floating-gate and CTC_T is the total seen by the floating gate (including , overlap, and parasitic capacitances). The effective transconductance, which relates small changes in control-gate voltage to drain current variations, is given by gm,eff=α gmg_{m,\text{eff}} = \alpha \, g_m, where gm=∂IDS∂VGS=μCoxWL(VGS−VTH)g_m = \frac{\partial I_{DS}}{\partial V_{GS}} = \mu C_{ox} \frac{W}{L} (V_{GS} - V_{TH}) is the intrinsic transconductance evaluated at the floating-gate voltage in the saturation region, with μ\mu as carrier mobility, CoxC_{ox} as the oxide capacitance per unit area, W/LW/L as the aspect ratio, VGSV_{GS} as the effective gate-source voltage, and VTHV_{TH} as the threshold voltage. The output conductance gds=∂IDS∂VDSg_{ds} = \frac{\partial I_{DS}}{\partial V_{DS}} remains similar to that of a conventional MOSFET but is augmented by coupling from the gate-drain capacitance, yielding gds,eff=gds+gmCGDCT−CGDg_{ds,\text{eff}} = g_{ds} + g_m \frac{C_{GD}}{C_T - C_{GD}}, where CGDC_{GD} is the floating-gate to drain capacitance; this term arises from feedback through the floating node. Effective capacitances, such as the gate-source capacitance, are modified by the capacitive divider, reflecting the dependence on α\alpha. The floating gate thus reduces the intrinsic voltage gain by the factor α\alpha, typically 0.6–0.8 in practical devices. The small-signal equivalent circuit represents the floating gate as an internal node capacitively coupled to the control gate (CCGC_{CG}), drain (CGDC_{GD}), source (CGSC_{GS}), and bulk (CGBC_{GB}), with the channel current source driven by the floating-gate voltage and including conductances gmvfgg_m v_{fg} and gdsvdsg_{ds} v_{ds}. A large resistance (effectively infinite for AC ) models the charge isolation on the floating gate. Input-referred noise in this model stems from thermal fluctuations in the stored charge and parasitic capacitances, manifesting as voltage noise at the control gate scaled by 1/α1/\alpha, though the fixed charge minimizes low-frequency contributions compared to standard MOSFETs. Frequency dependence in the model arises from the RC time constants associated with the oxide layers and interconnects; the control and tunnel oxides exhibit time constants on the order of picoseconds, enabling valid operation up to GHz frequencies before parasitic effects dominate, limited primarily by the effective bandwidth ω=gm/Ceff\omega = g_m / C_{\text{eff}}, where CeffC_{\text{eff}} incorporates the coupled capacitances.

Simulation Techniques

Challenges in Simulation

Simulating floating-gate MOSFETs presents unique challenges due to the isolated floating gate, which lacks a (DC) path to ground or other reference nodes. In standard circuit simulators like , this floating node can lead to undefined initial conditions and convergence failures during DC analysis, as the solver struggles to establish a valid without a conductive path for charge equilibration. To mitigate this, models often introduce artificial high-resistance paths or dummy nodes, but these approximations can introduce numerical instabilities, particularly in transient simulations where charge dynamics must be preserved. A critical aspect of accurate simulation involves explicit tracking of the floating-gate charge QfgQ_{fg} to ensure , as the device's and operation depend directly on this stored quantity. Standard steady-state models fail to capture transient effects from programming or erasing operations, such as Fowler-Nordheim tunneling or , which alter QfgQ_{fg} over time and require iterative updates in each simulation time step. Without explicit mechanisms, like voltage-controlled current sources tied to QfgQ_{fg}, simulations may exhibit non-physical charge loss or drift, complicating reliability predictions for retention and endurance. Scaling simulations to multi-device arrays, such as those in NAND blocks, introduces further complexities from statistical variations in key parameters like thickness and trapped charge distribution. These variations lead to (VthV_{th}) fluctuations across cells, necessitating probabilistic modeling to account for granularity effects in stored charge, which can widen bit distributions and degrade performance. Handling such arrays demands computationally intensive Monte Carlo-like approaches to capture inter-device and process-induced nonuniformities, often resulting in prohibitive runtime for large-scale designs. Pre-2020 simulation models for floating-gate MOSFETs frequently overlooked three-dimensional (3D) effects, such as edge fringing fields and non-uniform charge distribution in polysilicon gates, leading to inaccuracies in extraction and profiles for scaled devices. Additionally, these models exhibited gaps in accurately representing quantum tunneling through ultra-thin oxides in sub-10 nm nodes, underestimating direct tunneling currents and barrier lowering, which are essential for reliable programming efficiency and leakage assessment in advanced scaling scenarios.

Methods and Tools

Simulation of floating-gate MOSFET circuits often employs the Initial Transient Analysis (ITA) method to accurately capture charge storage dynamics. In ITA, a short voltage is applied to the control gate to induce charge injection or tunneling onto the floating gate, thereby setting the floating-gate charge QfgQ_{fg}, followed by a steady-state DC analysis to evaluate the resulting shift and current characteristics. This approach is particularly useful in BSIM-based models, where the floating-gate voltage VfgV_{fg} is derived from the initial charge state and integrated into standard simulations for circuit-level verification. Behavioral modeling using and languages provides a flexible framework for simulating floating-gate MOSFETs at the system level, encapsulating the floating-gate voltage VfgV_{fg} and charge dynamics through compact equations that account for tunneling currents and . These models enable mixed-signal simulations by representing the non-volatile charge retention and programmable threshold shifts without requiring detailed physical geometries. Spectre and tools natively support Verilog-A/AMS for such behavioral descriptions, allowing seamless integration into larger analog-digital circuits for performance analysis. Advanced simulation techniques leverage Technology Computer-Aided Design (TCAD) tools like Sentaurus for three-dimensional physics-based modeling of floating-gate MOSFETs, incorporating quantum mechanical effects such as Fowler-Nordheim tunneling and trap-assisted charge transport across the tunnel oxide. Sentaurus Device simulates the full device structure, including polysilicon floating gates and control gates, to predict programming/erasing efficiencies and retention times under varying bias conditions. As of 2025, simulation methods have evolved to support neuromorphic applications through integration with specialized frameworks like NeuroSim, which benchmarks hybrid analog-digital circuits using floating-gate MOSFETs as synaptic elements for energy-efficient tasks. These tools model stochastic charge fluctuations and weight updates in floating-gate arrays, facilitating co-simulation with for large-scale neuromorphic systems.

Applications

Non-Volatile Memory Devices

Floating-gate MOSFETs form the foundational technology for several types of non-volatile memory devices, enabling without by trapping charge on an isolated polysilicon gate within the structure. This charge modulates the of the , allowing binary states to be stored and read via standard operations. The concept originated from the 1967 demonstration by and at Bell Laboratories, where a floating gate was shown to enable semipermanent charge storage in a for applications. The earliest practical implementation was the Erasable Programmable Read-Only Memory (), introduced by Dov Frohman-Bentchkowsky at in 1971. EPROM cells use a thick layer around the floating gate, with programming achieved by hot-electron injection to store negative charge, shifting the to represent a logic '0'. Erasure requires (UV) light exposure through a window to photoemit trapped electrons, resetting the cell to a logic '1' state. Designed for single-use programming in applications like , EPROM offered densities up to 1 Mb but became obsolete by the due to the inconvenience of UV erasure and the rise of electrical alternatives. Electrically Erasable Programmable Read-Only Memory () advanced the technology by enabling byte-level electrical erasure, invented by Eli Harari at Hughes Microelectronics between 1976 and 1978. EEPROM cells incorporate a thin tunnel oxide region for Fowler-Nordheim tunneling, allowing electrons to be injected or removed from the floating gate using moderate voltages (around 15-20 V) without UV light. This permitted in-circuit reprogramming, making EEPROM suitable for applications requiring infrequent updates, such as chips, smart cards, and configuration storage. Typical densities reached 1 Mb, with endurance of about 10^5 to 10^6 program/erase (P/E) cycles per cell, though higher costs limited its use to low-density scenarios compared to flash. Flash memory, a high-density evolution, was pioneered by Fujio Masuoka at , with NOR flash demonstrated in 1984 and NAND flash in 1987. Both types use floating-gate cells with tunnel oxides for electrical programming and erasure but operate on block-level erasure to improve efficiency and density. NOR flash architecture connects cells in parallel for fast , suiting storage and execution in embedded systems like microcontrollers. In contrast, NAND flash arranges cells in series for higher density, ideal for in SSDs, USB drives, and mobile devices, where predominates. By 2025, TLC (triple-level cell) and QLC (quad-level cell) NAND flash dies achieve densities up to 2 Tb, enabling SSD capacities exceeding 100 TB through multi-die stacking and 3D architectures. Reliability in floating-gate memories is constrained by degradation from repeated charge injection, limiting P/E to 10^3-10^5 cycles for QLC NAND and up to 10^6 for NOR, primarily due to stress-induced leakage current and charge trapping. Wear-leveling algorithms distribute writes evenly across cells to prevent premature failure in heavily used blocks, while error correction codes (ECC), such as BCH or LDPC, mitigate bit errors from retention loss or read disturbs, achieving effective bit error rates below 10^{-15}. These techniques, combined with overprovisioning, ensure multi-year in commercial devices.

Analog and Mixed-Signal Circuits

Floating-gate MOSFETs enable programmable analog and mixed-signal circuits by leveraging to multiple inputs and the ability to store charge that tunes the , allowing reconfiguration for functions like amplification and without discrete components. This programmability arises from the floating-gate potential, which is a weighted sum of input voltages scaled by coupling capacitances, facilitating continuous analog adjustments in integrated circuits. Such devices have been to low-voltage designs since the , supporting applications in reconfigurable systems where traditional resistor-based tuning is power-intensive or area-consuming. In programmable gain amplifiers and filters, the floating-gate charge modulates the MOSFET's , thereby adjusting and enabling variable gain or without external feedback elements. This approach is particularly advantageous for low-power operation, as demonstrated in a 500 nW floating-gate achieving programmable gains up to 16 through charge sharing on the floating gate. Similarly, rail-to-rail programmable-gain amplifiers operating at 1.5 V have utilized arrays of floating-gate pFETs to tune gain over a 20 dB range, reducing offset and improving in mixed-signal systems. These circuits reference small-signal parameters, such as adjusted gm, to model performance in operational amplifiers. Digital-to-analog converters (DACs) benefit from multi-input floating-gate MOSFETs, where multiple control gates capacitively couple to the floating node for weighted voltage , directly implementing analog output proportional to digital inputs. A 1 V DAC architecture using this principle in a matrix current cell has achieved 8-bit resolution with low , suitable for portable mixed-signal ICs. An 8-bit low-voltage DAC further exploits floating-gate programmability to eliminate resistors, operating at 1 V supply while maintaining below 0.5 LSB, as shown in 0.35 μm implementations. Early neural chips from the 1990s employed such multi-input structures to store synaptic weights as floating-gate charges, enabling adaptive analog computation in VLSI. Adders and multipliers in analog domains use capacitive inputs to the floating gate for charge redistribution, performing arithmetic operations via linear superposition of input signals on the floating node. A four-quadrant based on multi-input floating-gate MOSFETs has realized low-voltage operation below 1 V, with under 1% for inputs up to 0.5 Vpp, using source-coupled configurations for improved matching. Capacitive adders leverage the same weighted for charge-domain arithmetic, as in 1990s VLSI chips where resistorless designs reduced power to sub-μW levels per operation. These techniques highlight advantages like resistor elimination, leading to compact, low-power mixed-signal blocks in field-programmable analog arrays from that era.

Emerging Uses

Floating-gate MOSFETs have gained traction in neuromorphic computing as analog synapses for , enabling efficient in-memory computation by storing synaptic weights as tunable charge levels on the floating gate. These devices mimic biological through mechanisms like and depression, achieved via hot-electron injection or Fowler-Nordheim tunneling to modulate threshold voltages with high precision and low power. For instance, multinanodot floating-gate MOSFET circuits have been proposed to implement integrate-and-fire models, demonstrating spike-timing-dependent plasticity suitable for tasks. Recent research highlights reconfigurable two-dimensional floating-gate field-effect transistors based on van der Waals heterostructures, which support highly integrated in-memory computing with 11-bit resolution and robust exceeding 10 years, outperforming traditional digital synapses in energy efficiency for edge-based neural processing. In quantum and cryogenic applications, floating-gate MOSFETs leverage their stable charge states for precise qubit control and readout in silicon quantum dots, operating reliably at millikelvin temperatures. Post-2022 prototypes integrate floating-gate transistors into quantum dot control circuitry, where trapped charges enable fine-tuned electrostatic potentials for tuning tunnel barriers and spin states without continuous bias, reducing cryogenic power dissipation. Cryogenic characterization of CMOS floating-gate devices has confirmed their reliable operation at 4 K, supporting suitability for scalable qubit arrays. A trilinear quantum dot architecture further utilizes floating gates for charge storage akin to DRAM but with extended retention, facilitating multi-qubit entanglement gates in semiconductor-based quantum processors. Radiation-hardened designs exploit the inherent charge retention of floating-gate MOSFETs for and applications, where total ionizing dose levels exceed 100 krad without significant . These devices maintain floating-gate potentials stable against proton and gamma , with retention times over a decade in geosynchronous orbits, due to the insulating barrier shielding trapped charges from -induced leakage. Comparative studies of floating-gate versus charge-trapping memories reveal advantages for FG structures in radiation environments, enabling reliable non-volatile storage in satellites for and fault-tolerant computing. Optimization techniques, such as thickened tunnel oxides, further enhance immunity while preserving programming speeds below 1 μs. Hybrid floating-gate architectures combined with charge-trap flash are emerging for AI accelerators, bridging the gap between high-retention FG storage and faster charge-trap dynamics to support vector-matrix multiplications in neural networks. These hybrids use FG layers for long-term weight persistence and charge-trap sites for incremental updates, achieving in conductance modulation with endurance cycles exceeding 10^6. In 2025 trends, integration of such devices into edge AI systems enables low-power on wearables and IoT sensors, with optimized split-gate FG memories delivering compute-in-memory performance at 55 nm nodes.

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