arc-eager, structured prediction
Arc-eager is a transition system that builds dependencies eagerly allowing left arcs to be added immediately upon recognition.
9,967 technical terms and definitions
Arc-eager is a transition system that builds dependencies eagerly allowing left arcs to be added immediately upon recognition.
Arc-standard is a transition system for dependency parsing using shift reduce and arc operations to construct dependency trees incrementally.
AI2 Reasoning Challenge tests scientific reasoning and knowledge.
Architecture crossover combines parent architectures by exchanging substructures creating offspring networks.
Architecture encoding represents network structures as vectors graphs or sequences enabling architecture optimization.
Design buildings and structures.
Architecture mutations in evolutionary NAS modify network structures through operations like adding layers or changing connections.
AI assists architecture design. Suggest patterns, trade-offs.
Etch rate varies with aspect ratio as mentioned earlier.
Aperture area to sidewall area.
Mismatch decreases with device area.
193nm DUV light source.
Argilla combines annotation and feedback. Human-in-the-loop. Open source.
Invertible functions for discrete data.
Extract arguments from text.
Time series forecasting.
ARIMA models capture autocorrelated process behavior for forecasting and control.
AutoRegressive Integrated Moving Average models time series through differencing and combining autoregression with moving average components.
Operations per byte ratio.
Arrhenius equation models temperature acceleration using activation energy.
Model temperature acceleration of failures.
Apache Arrow is in-memory columnar format. Zero-copy reads. Interoperability standard.
Aerospace quality standard.
Improved version of SAM.
asdf is universal version manager. Python, Node, Ruby, etc.
ASIC = Application-Specific Integrated Circuit. Custom chip designed for one purpose. Maximum efficiency but expensive to develop.
# EUV Lithography ## EUV ## 1. Introduction to EUV ### Market - 100% market share in EUV lithography by top EUV vendor - ~90% market share in advanced DUV lithography - Critical supplier to all leading-edge semiconductor fabs ## 2. Lithography Fundamentals ### The Rayleigh Criterion The fundamental resolution limit in optical lithography is governed by the **Rayleigh Criterion**: $$ R = k_1 \cdot \frac{\lambda}{NA} $$ Where: - $R$ = minimum resolvable feature size (half-pitch) - $k_1$ = process-dependent factor (theoretical minimum: 0.25) - $\lambda$ = wavelength of light - $NA$ = numerical aperture of the optical system ### Depth of Focus (DOF) The depth of focus determines process tolerance: $$ DOF = k_2 \cdot \frac{\lambda}{NA^2} $$ Where: - $DOF$ = depth of focus - $k_2$ = process-dependent constant - $\lambda$ = wavelength - $NA$ = numerical aperture ### Resolution Enhancement Techniques (RET) 1. **Optical Proximity Correction (OPC)** - Sub-resolution assist features (SRAFs) - Serif additions/subtractions - Line-end extensions 2. **Phase-Shift Masks (PSM)** - Alternating PSM - Attenuated PSM - Phase difference: $\Delta\phi = \pi$ (180°) 3. **Multiple Patterning** - LELE (Litho-Etch-Litho-Etch) - SADP (Self-Aligned Double Patterning) - SAQP (Self-Aligned Quadruple Patterning) ## 3. EUV Technology ### Wavelength Comparison | Technology | Wavelength ($\lambda$) | Relative Resolution | |------------|------------------------|---------------------| | i-line | 365 nm | 1.00× | | KrF DUV | 248 nm | 1.47× | | ArF DUV | 193 nm | 1.89× | | ArF Immersion | 193 nm (effective ~134 nm) | 2.72× | | **EUV** | **13.5 nm** | **27.04×** | ### EUV Light Generation Process The **Laser-Produced Plasma (LPP)** source generates EUV light: 1. **Tin Droplet Generation** - Droplet diameter: $\approx 25 \, \mu m$ - Droplet velocity: $v \approx 70 \, m/s$ - Droplet frequency: $f = 50,000 \, Hz$ 2. **Pre-Pulse Laser** - Flattens the tin droplet into a pancake shape - Increases target cross-section 3. **Main Pulse Laser** - CO₂ laser power: $P \approx 20-30 \, kW$ - Creates plasma at temperature: $T \approx 500,000 \, K$ - Plasma emits EUV at $\lambda = 13.5 \, nm$ 4. **Conversion Efficiency** $$ \eta_{CE} = \frac{P_{EUV}}{P_{laser}} \approx 5-6\% $$ ### Optical Since EUV is absorbed by all materials, the system uses **reflective optics**: - **Mirror Material:** Multi-layer Mo/Si (Molybdenum/Silicon) - **Layer Thickness:** $$ d = \frac{\lambda}{2} \approx 6.75 \, nm $$ - **Number of Layer Pairs:** ~40-50 - **Peak Reflectivity:** $R \approx 67-70\%$ - **Total Optical Path Reflectivity:** $$ R_{total} = R^n \approx (0.67)^{11} \approx 1.2\% $$ ### EUV Mask Structure ``` - ┌─────────────────────────────────────┐ │ Absorber (TaN/TaBN) │ ← Pattern layer (~60-80 nm) ├─────────────────────────────────────┤ │ Capping Layer (Ru) │ ← Protective layer (~2.5 nm) ├─────────────────────────────────────┤ │ Multi-Layer Mirror (Mo/Si) │ ← 40-50 bilayer pairs │ ~~~~~~~~~~~~~~~~~~~~~~~~ │ │ ~~~~~~~~~~~~~~~~~~~~~~~~ │ ├─────────────────────────────────────┤ │ Low Thermal Expansion │ ← Substrate │ Material (LTEM) │ └─────────────────────────────────────┘ ``` ## 4. Scanner Systems ### Scanner vs. Stepper | Parameter | Stepper | Scanner | |-----------|---------|---------| | Exposure Method | Full-field | Slit scanning | | Field Size | Limited by lens | Larger effective field | | Throughput | Lower | Higher | | Overlay Control | Good | Excellent | ### Scanning Mechanism The wafer and reticle move in opposite directions during exposure: $$ v_{wafer} = \frac{v_{reticle}}{M} $$ Where: - $v_{wafer}$ = wafer stage velocity - $v_{reticle}$ = reticle stage velocity - $M$ = demagnification factor (typically 4×) ### Stage Positioning Accuracy - **Overlay Requirement:** $$ \sigma_{overlay} < \frac{CD}{4} \approx 1-2 \, nm $$ - **Stage Position Accuracy:** $$ \Delta x, \Delta y < 0.5 \, nm $$ - **Stage Velocity:** $$ v_{stage} \approx 2 \, m/s $$ ## 5. Specifications ### NXE:3600D Current EUV - **Numerical Aperture:** $NA = 0.33$ - **Wavelength:** $\lambda = 13.5 \, nm$ - **Resolution:** $$ R_{min} = k_1 \cdot \frac{13.5}{0.33} = k_1 \cdot 40.9 \, nm $$ With $k_1 = 0.3$: $R_{min} \approx 13 \, nm$ - **Throughput:** $> 160$ wafers per hour (WPH) - **Overlay:** $< 1.4 \, nm$ (machine-to-machine) - **Source Power:** $> 250 \, W$ at intermediate focus - **Cost:** ~€150-200 million ### TWINSCAN EXE:5000 High-NA EUV - **Numerical Aperture:** $NA = 0.55$ - **Wavelength:** $\lambda = 13.5 \, nm$ - **Resolution:** $$ R_{min} = k_1 \cdot \frac{13.5}{0.55} = k_1 \cdot 24.5 \, nm $$ With $k_1 = 0.3$: $R_{min} \approx 8 \, nm$ - **Resolution Improvement:** $$ \frac{R_{0.33}}{R_{0.55}} = \frac{0.55}{0.33} = 1.67\times $$ - **Anamorphic Optics:** 4× reduction in X, 8× reduction in Y - **Cost:** ~€350+ million - **Weight:** ~250 tons ### Throughput Calculation Wafers per hour (WPH) depends on: $$ WPH = \frac{3600}{t_{expose} + t_{move} + t_{align} + t_{overhead}} $$ Where typical values are: - $t_{expose}$ = exposure time per die - $t_{move}$ = stage movement time - $t_{align}$ = alignment time - $t_{overhead}$ = wafer load/unload time ## 6. Geopolitical Context ### Technology Nodes | Company | Node | EUV Layers | |---------|------|------------| | TSMC | N3 | ~20-25 | | TSMC | N2 | ~25-30 | | Samsung | 3GAE | ~20+ | | Intel | Intel 4 | ~5-10 | | Intel | Intel 18A | ~20+ | ### Economic Impact - **EUV System Cost:** $150-350M per tool - **Annual Revenue (ASML 2023):** ~€27.6 billion - **R&D Investment:** ~€4 billion annually - **Backlog:** >€40 billion ## Mathematical ### Equations | Equation | Formula | Application | |----------|---------|-------------| | Rayleigh Resolution | $R = k_1 \frac{\lambda}{NA}$ | Feature size limit | | Depth of Focus | $DOF = k_2 \frac{\lambda}{NA^2}$ | Process window | | Bragg Reflection | $2d\sin\theta = n\lambda$ | Mirror design | | Conversion Efficiency | $\eta = \frac{P_{out}}{P_{in}}$ | Source efficiency | | Throughput | $WPH = \frac{3600}{\sum t_i}$ | Productivity | ### Node Roadmap with Resolution | Node | Half-Pitch | EUV Layers | Year | |------|------------|------------|------| | 7nm | ~36 nm | 5-10 | 2018 | | 5nm | ~27 nm | 10-15 | 2020 | | 3nm | ~21 nm | 20-25 | 2022 | | 2nm | ~15 nm | 25-30 | 2025 | | A14 | ~10 nm | High-NA | 2027+| ## Physical Constants | Constant | Symbol | Value | |----------|--------|-------| | EUV Wavelength | $\lambda_{EUV}$ | $13.5 \, nm$ | | Speed of Light | $c$ | $3 \times 10^8 \, m/s$ | | Planck's Constant | $h$ | $6.626 \times 10^{-34} \, J \cdot s$ | | EUV Photon Energy | $E_{EUV}$ | $91.8 \, eV$ | Photon energy calculation: $$ E = \frac{hc}{\lambda} = \frac{(6.626 \times 10^{-34})(3 \times 10^8)}{13.5 \times 10^{-9}} = 1.47 \times 10^{-17} \, J = 91.8 \, eV $$
# EUV Lithography ## EUV ## 1. Introduction to EUV ### Market - 100% market share in EUV lithography by top EUV vendor - ~90% market share in advanced DUV lithography - Critical supplier to all leading-edge semiconductor fabs ## 2. Lithography Fundamentals ### The Rayleigh Criterion The fundamental resolution limit in optical lithography is governed by the **Rayleigh Criterion**: $$ R = k_1 \cdot \frac{\lambda}{NA} $$ Where: - $R$ = minimum resolvable feature size (half-pitch) - $k_1$ = process-dependent factor (theoretical minimum: 0.25) - $\lambda$ = wavelength of light - $NA$ = numerical aperture of the optical system ### Depth of Focus (DOF) The depth of focus determines process tolerance: $$ DOF = k_2 \cdot \frac{\lambda}{NA^2} $$ Where: - $DOF$ = depth of focus - $k_2$ = process-dependent constant - $\lambda$ = wavelength - $NA$ = numerical aperture ### Resolution Enhancement Techniques (RET) 1. **Optical Proximity Correction (OPC)** - Sub-resolution assist features (SRAFs) - Serif additions/subtractions - Line-end extensions 2. **Phase-Shift Masks (PSM)** - Alternating PSM - Attenuated PSM - Phase difference: $\Delta\phi = \pi$ (180°) 3. **Multiple Patterning** - LELE (Litho-Etch-Litho-Etch) - SADP (Self-Aligned Double Patterning) - SAQP (Self-Aligned Quadruple Patterning) ## 3. EUV Technology ### Wavelength Comparison | Technology | Wavelength ($\lambda$) | Relative Resolution | |------------|------------------------|---------------------| | i-line | 365 nm | 1.00× | | KrF DUV | 248 nm | 1.47× | | ArF DUV | 193 nm | 1.89× | | ArF Immersion | 193 nm (effective ~134 nm) | 2.72× | | **EUV** | **13.5 nm** | **27.04×** | ### EUV Light Generation Process The **Laser-Produced Plasma (LPP)** source generates EUV light: 1. **Tin Droplet Generation** - Droplet diameter: $\approx 25 \, \mu m$ - Droplet velocity: $v \approx 70 \, m/s$ - Droplet frequency: $f = 50,000 \, Hz$ 2. **Pre-Pulse Laser** - Flattens the tin droplet into a pancake shape - Increases target cross-section 3. **Main Pulse Laser** - CO₂ laser power: $P \approx 20-30 \, kW$ - Creates plasma at temperature: $T \approx 500,000 \, K$ - Plasma emits EUV at $\lambda = 13.5 \, nm$ 4. **Conversion Efficiency** $$ \eta_{CE} = \frac{P_{EUV}}{P_{laser}} \approx 5-6\% $$ ### Optical Since EUV is absorbed by all materials, the system uses **reflective optics**: - **Mirror Material:** Multi-layer Mo/Si (Molybdenum/Silicon) - **Layer Thickness:** $$ d = \frac{\lambda}{2} \approx 6.75 \, nm $$ - **Number of Layer Pairs:** ~40-50 - **Peak Reflectivity:** $R \approx 67-70\%$ - **Total Optical Path Reflectivity:** $$ R_{total} = R^n \approx (0.67)^{11} \approx 1.2\% $$ ### EUV Mask Structure ``` - ┌─────────────────────────────────────┐ │ Absorber (TaN/TaBN) │ ← Pattern layer (~60-80 nm) ├─────────────────────────────────────┤ │ Capping Layer (Ru) │ ← Protective layer (~2.5 nm) ├─────────────────────────────────────┤ │ Multi-Layer Mirror (Mo/Si) │ ← 40-50 bilayer pairs │ ~~~~~~~~~~~~~~~~~~~~~~~~ │ │ ~~~~~~~~~~~~~~~~~~~~~~~~ │ ├─────────────────────────────────────┤ │ Low Thermal Expansion │ ← Substrate │ Material (LTEM) │ └─────────────────────────────────────┘ ``` ## 4. Scanner Systems ### Scanner vs. Stepper | Parameter | Stepper | Scanner | |-----------|---------|---------| | Exposure Method | Full-field | Slit scanning | | Field Size | Limited by lens | Larger effective field | | Throughput | Lower | Higher | | Overlay Control | Good | Excellent | ### Scanning Mechanism The wafer and reticle move in opposite directions during exposure: $$ v_{wafer} = \frac{v_{reticle}}{M} $$ Where: - $v_{wafer}$ = wafer stage velocity - $v_{reticle}$ = reticle stage velocity - $M$ = demagnification factor (typically 4×) ### Stage Positioning Accuracy - **Overlay Requirement:** $$ \sigma_{overlay} < \frac{CD}{4} \approx 1-2 \, nm $$ - **Stage Position Accuracy:** $$ \Delta x, \Delta y < 0.5 \, nm $$ - **Stage Velocity:** $$ v_{stage} \approx 2 \, m/s $$ ## 5. Specifications ### NXE:3600D Current EUV - **Numerical Aperture:** $NA = 0.33$ - **Wavelength:** $\lambda = 13.5 \, nm$ - **Resolution:** $$ R_{min} = k_1 \cdot \frac{13.5}{0.33} = k_1 \cdot 40.9 \, nm $$ With $k_1 = 0.3$: $R_{min} \approx 13 \, nm$ - **Throughput:** $> 160$ wafers per hour (WPH) - **Overlay:** $< 1.4 \, nm$ (machine-to-machine) - **Source Power:** $> 250 \, W$ at intermediate focus - **Cost:** ~€150-200 million ### TWINSCAN EXE:5000 High-NA EUV - **Numerical Aperture:** $NA = 0.55$ - **Wavelength:** $\lambda = 13.5 \, nm$ - **Resolution:** $$ R_{min} = k_1 \cdot \frac{13.5}{0.55} = k_1 \cdot 24.5 \, nm $$ With $k_1 = 0.3$: $R_{min} \approx 8 \, nm$ - **Resolution Improvement:** $$ \frac{R_{0.33}}{R_{0.55}} = \frac{0.55}{0.33} = 1.67\times $$ - **Anamorphic Optics:** 4× reduction in X, 8× reduction in Y - **Cost:** ~€350+ million - **Weight:** ~250 tons ### Throughput Calculation Wafers per hour (WPH) depends on: $$ WPH = \frac{3600}{t_{expose} + t_{move} + t_{align} + t_{overhead}} $$ Where typical values are: - $t_{expose}$ = exposure time per die - $t_{move}$ = stage movement time - $t_{align}$ = alignment time - $t_{overhead}$ = wafer load/unload time ## 6. Geopolitical Context ### Technology Nodes | Company | Node | EUV Layers | |---------|------|------------| | TSMC | N3 | ~20-25 | | TSMC | N2 | ~25-30 | | Samsung | 3GAE | ~20+ | | Intel | Intel 4 | ~5-10 | | Intel | Intel 18A | ~20+ | ### Economic Impact - **EUV System Cost:** $150-350M per tool - **Annual Revenue (ASML 2023):** ~€27.6 billion - **R&D Investment:** ~€4 billion annually - **Backlog:** >€40 billion ## Mathematical ### Equations | Equation | Formula | Application | |----------|---------|-------------| | Rayleigh Resolution | $R = k_1 \frac{\lambda}{NA}$ | Feature size limit | | Depth of Focus | $DOF = k_2 \frac{\lambda}{NA^2}$ | Process window | | Bragg Reflection | $2d\sin\theta = n\lambda$ | Mirror design | | Conversion Efficiency | $\eta = \frac{P_{out}}{P_{in}}$ | Source efficiency | | Throughput | $WPH = \frac{3600}{\sum t_i}$ | Productivity | ### Node Roadmap with Resolution | Node | Half-Pitch | EUV Layers | Year | |------|------------|------------|------| | 7nm | ~36 nm | 5-10 | 2018 | | 5nm | ~27 nm | 10-15 | 2020 | | 3nm | ~21 nm | 20-25 | 2022 | | 2nm | ~15 nm | 25-30 | 2025 | | A14 | ~10 nm | High-NA | 2027+| ## Physical Constants | Constant | Symbol | Value | |----------|--------|-------| | EUV Wavelength | $\lambda_{EUV}$ | $13.5 \, nm$ | | Speed of Light | $c$ | $3 \times 10^8 \, m/s$ | | Planck's Constant | $h$ | $6.626 \times 10^{-34} \, J \cdot s$ | | EUV Photon Energy | $E_{EUV}$ | $91.8 \, eV$ | Photon energy calculation: $$ E = \frac{hc}{\lambda} = \frac{(6.626 \times 10^{-34})(3 \times 10^8)}{13.5 \times 10^{-9}} = 1.47 \times 10^{-17} \, J = 91.8 \, eV $$
Average price per chip affects profitability.
Average Selling Price represents typical per-unit revenue across product mix.
Ratio of feature depth to width affects etch difficulty.
High aspect ratio trenches and vias require advanced deposition techniques ensuring complete bottom coverage without void formation.
Sentiment toward specific aspects.
Identify sentiment toward specific aspects.
Percentage surviving packaging.
Generate test assertions.
Identifiable reason for process variation.
Model's response.
Assistant message is model output. Follows user input. May include reasoning, code, structured data.
Different penalties for different errors.
Asymmetric loss functions penalize deviations differently above and below target.
Asynchronous generation handles multiple requests concurrently maximizing throughput.
Async/await enables concurrent I/O without threads. Event loop. Python asyncio, JavaScript promises.
Save state without blocking training.
Clock-free circuit design.
Non-blocking GPU operations.
Allow asynchronous updates.
At-speed testing operates devices at full rated frequency detecting timing failures missed by slower testing.
Test at operational frequency.
High-speed testers for production testing.