MOSFET Simulation Mastery: Parameter Extraction, Mobility Analysis & Scaling Insights (2025-2026 Guide)

Introduction: Why MOSFET Simulation Matters in 2025-2026

As semiconductor technology pushes toward 2nm nodes and beyond, understanding MOSFET behavior through simulation is more critical than ever. Whether you are tackling an ELEC3207 assignment or exploring advanced device physics, mastering parameter extraction and scaling analysis gives you an edge in the chip industry—think Apple's M4 Ultra or AMD's next-gen AI accelerators. This tutorial breaks down the core tasks: electrical and physical parameter extraction, Ion vs. low-field mobility plots, and device scaling investigation. No exact simulation data is provided; instead, you will learn the methods and reasoning to apply in your own projects.

Part I: Electrical Parameter Extraction – Methods and Results

Extracting Threshold Voltage (Vth) and Transconductance (gm)

To extract electrical parameters from simulated I-V curves, start with the linear extrapolation method for Vth. Plot Id vs. Vgs at low Vd (e.g., 0.1 V) and find the maximum slope (gm). Extrapolate the tangent at max gm to Id=0; the Vgs intercept is Vth. For example, if your simulation yields a peak gm of 50 µS, the intercept might be around 0.4 V. Document your method clearly: use a pre tag for code snippets like:

% MATLAB snippet for Vth extraction
Vgs = data(:,1); Id = data(:,2);
gm = diff(Id)./diff(Vgs);
[max_gm, idx] = max(gm);
Vth = interp1(Id(idx:idx+1), Vgs(idx:idx+1), 0, 'linear');

Compare results with the constant current method (Vth at Id = 0.1 µA × W/L). A discrepancy of 10-20 mV is typical. In your report, include a table summarizing extracted Vth, gm, and output conductance (gds).

Physical Device Parameter Extraction

Extract oxide capacitance (Cox) from the accumulation region of a C-V simulation. Use Cox = εox / tox. For a tox of 2 nm, Cox ≈ 1.73 µF/cm². Then compute effective mobility (µeff) using µeff = (L/W) × (Id / (Vd × (Vgs – Vth – 0.5Vd))). At low Vd, this approximates field-effect mobility. Plot µeff vs. Vgs to observe degradation at high vertical fields. This is crucial for understanding modern high-k dielectrics like HfO2.

On Current (Ion) at Vd = 3V

For a typical 45nm node MOSFET, Ion at Vd=3V might be around 600 µA/µm (actual values depend on your simulation). Use the maximum Id at Vgs = Vdd = 1.2V (or your supply). Note: Vd=3V is high for scaled devices; ensure your model accounts for velocity saturation. In your report, discuss the method: sweep Vgs from 0 to Vdd, record Id at Vd=3V, and extract Ion. Compare with the theoretical value from the long-channel formula: Ion = (W/L) × µeff × Cox × (Vgs – Vth)² / 2, but adjust for short-channel effects.

Theoretical MOSFET Parameters

Calculate theoretical parameters using the gradual channel approximation. For a device with W=1 µm, L=45 nm, tox=2 nm, Vth=0.3 V, µeff=300 cm²/Vs, and Vgs=1.2 V, the saturation current is Id_sat = (W/L) × µeff × Cox × (Vgs – Vth)² / (2 × (1 + λVds)). Include λ (channel-length modulation) from your output conductance. Compare with extracted Ion: if the theoretical value is 800 µA and extracted is 600 µA, the difference may be due to velocity saturation or series resistance. This comparison is a key part of your assignment.

Part II: Ion vs. Low-Field Electron Mobility – Plots and Discussion

Plot for Vd = 0.1 V

Low-field mobility (µ0) is extracted from the linear region. For Vd=0.1 V, Id ≈ (W/L) × µ0 × Cox × (Vgs – Vth) × Vd. Plot Ion (Id at a fixed Vgs, say 1.2 V) vs. µ0 varied by changing doping or temperature in simulation. You should see a linear relationship: as µ0 increases, Ion increases proportionally. Use a scatter plot with a linear fit. In your assignment, include the plot and the slope (which should equal (W/L) × Cox × (Vgs – Vth) × Vd).

Plot for Vd = 3 V

At high Vd, velocity saturation dominates. Plot Ion vs. µ0; the curve saturates because carriers reach saturation velocity (vsat). The transition occurs when µ0 × Vd/L exceeds vsat. For L=45 nm and Vd=3 V, the critical mobility is around 450 cm²/Vs. Below that, Ion is linear; above, it plateaus. This explains why modern devices use strained silicon to boost µ0 but not beyond the saturation limit. In your discussion, relate this to real-world chips: Intel's strained silicon in 14nm improved mobility by 10-20%, but further gains required new materials like SiGe channels.

Discussion of Results

Explain the physics: at low Vd, the channel is uniform, and mobility directly controls current. At high Vd, the electric field near the drain is high, causing carriers to scatter and reach a constant velocity. This is analogous to a highway: at low traffic (low Vd), speed (current) is proportional to car speed (mobility); at heavy traffic (high Vd), speed is limited by the road's capacity (saturation velocity). In gaming terms, think of a GPU rendering frames: low resolution (low Vd) allows high FPS (current) with a fast GPU (high mobility), but at 4K (high Vd), the frame rate caps due to memory bandwidth (saturation).

Part III: Device Scaling Investigation – Methods, Results, and Discussion

Scaling Methodology

Simulate MOSFETs with channel lengths from 180 nm down to 7 nm (use a predictive technology model like PTM). For each node, extract Vth, Ion, Ioff, and subthreshold swing (SS). Keep W fixed (e.g., 1 µm) and scale tox accordingly (e.g., tox = 1.5 nm for 45 nm, 0.8 nm for 7 nm). Record data in a table. Plot Ion and Ioff vs. L on a log scale. You should observe that Ion increases for shorter channels (due to velocity saturation), but Ioff increases dramatically due to DIBL and punchthrough. SS degrades from ~60 mV/dec to >100 mV/dec for L < 20 nm.

Results and Discussion

For a 7 nm node, Ion might be 1.2 mA/µm but Ioff could be 10 nA/µm (actual values vary). Compare with the 45 nm node (Ion ~600 µA/µm, Ioff ~1 nA). The power consumption (P = Vdd × (Ion + Ioff)) becomes dominated by leakage at short lengths. This is why FinFETs and GAAFETs are used: they provide better electrostatic control. In your discussion, mention how scaling affects circuit performance: in AI accelerators like NVIDIA's H100, billions of transistors must balance speed and leakage. Use a trend analogy: scaling is like upgrading a smartphone—smaller transistors mean more cores (higher performance) but also more battery drain (leakage). New architectures (e.g., chiplets) are like external battery packs.

Conclusion

This tutorial covered the essential steps for a MOSFET simulation assignment: parameter extraction, mobility analysis, and scaling investigation. By applying these methods, you can produce a thorough report that meets the ELEC3207 requirements. Remember to present your results in tables and plots, and discuss discrepancies between theory and simulation. As semiconductor technology evolves—with trends like 3D stacking and backside power delivery—the fundamentals you learn here remain the foundation of innovation. Good luck with your assignment!