tgi,text generation inference
TGI (Hugging Face) is production-ready inference server. Continuous batching, quantization, tensor parallel.
9,967 technical terms and definitions
TGI (Hugging Face) is production-ready inference server. Continuous batching, quantization, tensor parallel.
Temporal Graph Network maintains memory modules for nodes that are updated during temporal random walks for continuous-time dynamic graph learning.
You are welcome! Happy to help with AI, chips, LLMs, and any technical questions. Ask anytime.
Formal verification of mathematical statements.
Theory of constraints focuses improvement on system bottlenecks maximizing throughput.
Focus on bottleneck.
Model others' mental states and beliefs.
Heat treatment required for separation.
Thermal capacitance represents material's heat storage capacity affecting transient thermal response.
Heat conduction performance.
Predict heat transport properties.
Heat transfer between stacked dies.
Thermal coupling between components causes neighboring elements to influence each other's temperatures.
CVD driven by heat without plasma.
Repeated temperature changes.
Reliability under temperature changes.
Thermal cycling testing subjects devices to repeated temperature extremes characterizing reliability under thermal stress and expansion mismatch.
Repeatedly heat and cool.
Thermal cycling alternates hot and cold temperatures stressing interconnects and packages.
# Semiconductor Manufacturing Process Thermal Dynamics ## 1. Introduction and Fundamental Importance Thermal dynamics govern nearly every step in semiconductor fabrication. Temperature control determines chemical reaction rates, diffusion velocities, film properties, stress states, and ultimately device performance. ### 1.1 The Arrhenius Relationship The fundamental equation governing thermally-activated processes: $$ k = A \cdot e^{-\frac{E_a}{k_B T}} $$ Where: - $k$ = reaction rate constant - $A$ = pre-exponential factor (frequency factor) - $E_a$ = activation energy (eV or J/mol) - $k_B$ = Boltzmann constant ($8.617 \times 10^{-5}$ eV/K) - $T$ = absolute temperature (K) **Key Implication:** A temperature variation of just 10°C can change reaction rates by 20-30%. ### 1.2 Diffusion Fundamentals Dopant diffusion follows **Fick's Laws** with temperature-dependent diffusivity: $$ D = D_0 \cdot e^{-\frac{E_a}{k_B T}} $$ **Fick's First Law** (steady-state diffusion): $$ J = -D \frac{\partial C}{\partial x} $$ **Fick's Second Law** (time-dependent diffusion): $$ \frac{\partial C}{\partial t} = D \frac{\partial^2 C}{\partial x^2} $$ Where: - $J$ = diffusion flux (atoms/cm²·s) - $D$ = diffusivity (cm²/s) - $C$ = concentration (atoms/cm³) - $D_0$ = pre-exponential diffusion coefficient ## 2. Key Thermal Processes in Semiconductor Manufacturing ### 2.1 Thermal Oxidation Silicon dioxide growth follows the **Deal-Grove Model**: $$ x_{ox}^2 + A \cdot x_{ox} = B(t + \tau) $$ Where: - $x_{ox}$ = oxide thickness - $A$, $B$ = rate constants (temperature-dependent) - $t$ = oxidation time - $\tau$ = time offset for initial oxide **Oxidation Reactions:** - **Dry oxidation:** $\text{Si} + \text{O}_2 \rightarrow \text{SiO}_2$ (800–1200°C) - **Wet oxidation:** $\text{Si} + 2\text{H}_2\text{O} \rightarrow \text{SiO}_2 + 2\text{H}_2$ **Critical Parameters:** - Temperature uniformity requirement: $\pm 0.5°C$ - Typical temperature range: 800–1200°C - Ramp rate affects interface quality and stress ### 2.2 Chemical Vapor Deposition (CVD) **Deposition Rate Temperature Dependence:** $$ R_{dep} = R_0 \cdot e^{-\frac{E_a}{k_B T}} \cdot P_{reactant}^n $$ | CVD Type | Temperature Range | Pressure | |----------|-------------------|----------| | LPCVD | 400–900°C | 0.1–10 Torr | | PECVD | 200–400°C | 0.1–10 Torr | | APCVD | 300–500°C | 760 Torr | | ALD | 150–400°C | 0.1–10 Torr | **Temperature affects:** - Deposition rate - Film composition and stoichiometry - Step coverage conformality - Intrinsic film stress - Grain structure and crystallinity ### 2.3 Rapid Thermal Processing (RTP) **Heat Balance Equation:** $$ \rho c_p V \frac{dT}{dt} = \alpha_{abs} P_{lamp} A - \varepsilon \sigma A (T^4 - T_{amb}^4) - h A (T - T_{amb}) $$ Where: - $\rho$ = density (kg/m³) - $c_p$ = specific heat capacity (J/kg·K) - $V$ = wafer volume - $\alpha_{abs}$ = optical absorptivity - $P_{lamp}$ = lamp power density (W/m²) - $\varepsilon$ = emissivity - $\sigma$ = Stefan-Boltzmann constant ($5.67 \times 10^{-8}$ W/m²·K⁴) - $h$ = convective heat transfer coefficient **RTP Specifications:** - Ramp rates: 50–400°C/s - Peak temperatures: up to 1100°C - Soak times: 0–60 seconds - Spike anneal: ~1050°C, 0 second soak ### 2.4 Ion Implantation and Annealing **Implant Damage Annealing:** $$ f_{activated} = 1 - e^{-\left(\frac{t}{\tau}\right)^n} $$ Where $\tau$ is the characteristic annealing time (temperature-dependent). **Annealing Methods:** | Method | Temperature | Time | Application | |--------|-------------|------|-------------| | Furnace Anneal | 800–1000°C | 30–60 min | Bulk damage repair | | RTP Spike | 1000–1100°C | ~1 s | USJ activation | | Flash Anneal | 1200–1350°C | 1–20 ms | Minimal diffusion | | Laser Anneal | 1300–1414°C | 0.1–10 μs | Maximum activation | ## 3. Heat Transfer Mechanisms ### 3.1 Conduction **Fourier's Law:** $$ \vec{q} = -k \nabla T $$ **3D Heat Equation:** $$ \rho c_p \frac{\partial T}{\partial t} = k \nabla^2 T + \dot{Q} $$ Or in Cartesian coordinates: $$ \rho c_p \frac{\partial T}{\partial t} = k \left( \frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} + \frac{\partial^2 T}{\partial z^2} \right) + \dot{Q} $$ **Silicon Thermal Properties:** | Property | Value | Temperature Dependence | |----------|-------|------------------------| | Thermal conductivity | ~150 W/m·K @ 300K | $k \propto T^{-1.3}$ | | Thermal diffusivity | ~0.9 cm²/s @ 300K | Decreases with T | | Specific heat | ~700 J/kg·K @ 300K | Increases with T | ### 3.2 Radiation **Stefan-Boltzmann Law:** $$ q_{rad} = \varepsilon \sigma (T_s^4 - T_{surr}^4) $$ **Planck's Distribution:** $$ E_b(\lambda, T) = \frac{2\pi h c^2}{\lambda^5} \cdot \frac{1}{e^{\frac{hc}{\lambda k_B T}} - 1} $$ **Wien's Displacement Law:** $$ \lambda_{max} \cdot T = 2897.8 \text{ } \mu\text{m} \cdot \text{K} $$ Or equivalently: $\lambda_{max} = \frac{2897.8}{T} \text{ } \mu\text{m}$ (where $T$ is in Kelvin) **Silicon Emissivity Considerations:** - Heavily doped Si: $\varepsilon \approx 0.7$ - Lightly doped Si: $\varepsilon \approx 0.3$ (semi-transparent in IR) - With oxide film: interference effects modify $\varepsilon$ - Temperature dependent: $\varepsilon$ changes with $T$ ### 3.3 Convection **Newton's Law of Cooling:** $$ q_{conv} = h(T_s - T_\infty) $$ **Nusselt Number Correlations:** For forced convection over a wafer: $$ Nu = \frac{hL}{k_f} = C \cdot Re^m \cdot Pr^n $$ Where: - $Re = \frac{\rho v L}{\mu}$ (Reynolds number) - $Pr = \frac{c_p \mu}{k_f}$ (Prandtl number) ## 4. Temperature Measurement ### 4.1 Pyrometry Fundamentals **Monochromatic Pyrometry:** $$ T = \frac{c_2}{\lambda \ln\left( \frac{\varepsilon c_1}{\lambda^5 L} + 1 \right)} $$ Where: - $c_1 = 3.742 \times 10^{-16}$ W·m² - $c_2 = 1.439 \times 10^{-2}$ m·K - $L$ = measured spectral radiance - $\varepsilon$ = spectral emissivity **Two-Color (Ratio) Pyrometry:** $$ T = \frac{c_2 \left( \frac{1}{\lambda_1} - \frac{1}{\lambda_2} \right)}{\ln\left( \frac{L_1 \lambda_1^5}{L_2 \lambda_2^5} \cdot \frac{\varepsilon_2}{\varepsilon_1} \right)} $$ **Measurement Challenges:** - Unknown emissivity (varies with films, doping, temperature) - Reflected radiation from chamber walls - Transmission through silicon at certain wavelengths ($\lambda > 1.1$ μm) - Pattern effects causing local emissivity variation ### 4.2 Contact Methods - **Thermocouples:** $V = S_{AB} \cdot \Delta T$ (Seebeck coefficient) - **RTDs:** $R(T) = R_0[1 + \alpha(T - T_0)]$ ## 5. Thermal Stress Analysis ### 5.1 Thermal Stress Equations **Biaxial Thermal Stress in Thin Film:** $$ \sigma_{th} = \frac{E_f}{1 - \nu_f} (\alpha_s - \alpha_f)(T - T_{dep}) $$ Where: - $E_f$ = film Young's modulus - $\nu_f$ = film Poisson's ratio - $\alpha_s$ = substrate CTE - $\alpha_f$ = film CTE - $T_{dep}$ = deposition temperature **Wafer Bow (Stoney's Equation):** $$ \sigma_f = \frac{E_s t_s^2}{6(1-\nu_s) t_f} \cdot \frac{1}{R} $$ Where: - $t_s$ = substrate thickness - $t_f$ = film thickness - $R$ = radius of curvature ### 5.2 Slip Dislocation Criterion Slip occurs when resolved shear stress exceeds critical value: $$ \tau_{resolved} = \sigma \cdot \cos\phi \cdot \cos\lambda > \tau_{CRSS}(T) $$ **Critical Temperature:** Slip typically begins above ~1050°C in silicon. **Temperature Gradient Stress:** $$ \sigma_{gradient} \approx \frac{E \alpha \Delta T}{1 - \nu} $$ ## 6. Nanoscale Thermal Transport ### 6.1 Phonon Transport When feature sizes approach phonon mean free path ($\Lambda_{mfp} \approx 100-300$ nm in Si at 300K): **Ballistic Transport Regime:** $$ q = \frac{1}{4} C v_{ph} \Delta T \quad \text{(when } L < \Lambda_{mfp}\text{)} $$ **Modified Thermal Conductivity:** $$ k_{eff} = k_{bulk} \cdot \frac{1}{1 + \frac{\Lambda_{mfp}}{L}} $$ ### 6.2 Interface Thermal Resistance (Kapitza Resistance) $$ R_{th,interface} = \frac{\Delta T}{q} = R_{Kapitza} $$ **Acoustic Mismatch Model:** $$ R_{Kapitza} \propto \frac{(\rho_1 v_1 - \rho_2 v_2)^2}{(\rho_1 v_1 + \rho_2 v_2)^2} $$ Where $\rho v$ is the acoustic impedance. ## 7. Equipment and Process Parameters ### 7.1 Batch Furnace Specifications - **Temperature uniformity:** $\pm 0.5°C$ across wafer zone - **Ramp rates:** 1–10°C/min - **Maximum temperature:** 1200°C - **Batch size:** 50–150 wafers ### 7.2 RTP System Parameters - **Lamp types:** - Tungsten-halogen: $\lambda_{peak} \approx 1$ μm - Arc lamps: broadband emission - **Ramp rates:** 50–400°C/s - **Temperature uniformity target:** $\pm 2°C$ ### 7.3 Laser Annealing Parameters | Parameter | Excimer Laser | CW Laser | |-----------|---------------|----------| | Wavelength | 308 nm (XeCl) | 532 nm, 808 nm | | Pulse duration | 10–100 ns | Continuous | | Melt depth | 10–100 nm | 1–10 μm | | Peak temperature | >1414°C (melt) | 1200–1414°C | ## 8. Process Integration Considerations ### 8.1 Thermal Budget **Cumulative Thermal Budget:** $$ D_t = \sum_i D_0 \cdot e^{-\frac{E_a}{k_B T_i}} \cdot t_i $$ Where $D_t$ is the total diffusion length squared. **Effective $D \cdot t$:** $$ (Dt)_{eff} = \int_0^{t_{process}} D(T(t')) dt' $$ ### 8.2 Junction Depth Estimation For constant-source diffusion: $$ x_j = 2\sqrt{Dt} \cdot \text{erfc}^{-1}\left(\frac{C_B}{C_s}\right) $$ Where: - $x_j$ = junction depth - $C_B$ = background concentration - $C_s$ = surface concentration ## 9. Key Equations | Process | Key Equation | Critical Parameters | |---------|--------------|---------------------| | Reaction Rate | $k = A e^{-E_a/k_B T}$ | $E_a$, $T$ | | Diffusion | $D = D_0 e^{-E_a/k_B T}$ | $D_0$, $E_a$ | | Oxidation | $x^2 + Ax = B(t+\tau)$ | $A$, $B$ (T-dependent) | | Radiation | $q = \varepsilon \sigma T^4$ | $\varepsilon$, $T$ | | Thermal Stress | $\sigma = \frac{E}{1-\nu}\Delta\alpha\Delta T$ | CTE mismatch | | Heat Conduction | $q = -k\nabla T$ | $k(T)$ |
Resistive heating to evaporate material.
Thermal grease is a compliant TIM with high thermal conductivity typically silicone-based filled with ceramic or metal particles.
Infrared thermal imaging captures temperature distributions across surfaces for non-contact thermal analysis.
Material conducting heat between surfaces.
Heat removal from stacked dies.
Thermal mass flow meters measure gas flow through heat transfer.
SiO2 grown by heating silicon in oxygen.
Thermal oxidizers combust VOCs at high temperature converting them to carbon dioxide and water.
Thermal pads are pre-formed compliant materials providing mechanical compliance and thermal conductivity for interface thermal management.
Thermal resistance networks model heat paths through series and parallel thermal resistances.
Opposition to heat flow.
Thermal runaway occurs when temperature increases cause higher power dissipation leading to uncontrolled temperature rise and potential device failure.
Model heat distribution.
Thermal simulation uses computational fluid dynamics and finite element methods to predict temperature distributions in packages and systems.
Calculate temperature distribution.
Separate via thermal differential.
Large thermal contact area.
Stress from thermal expansion mismatch.
Thermal test chips contain heating elements and temperature sensors for measuring thermal resistance.
Thermal test vehicles are specialized structures with embedded sensors for thermal characterization and model validation.
Thermal time constant characterizes exponential temperature response to step changes in power.
TSV for heat conduction.
Vias for heat transfer.
Couple thermal and electrical models.
Thermal emission over barrier.
Combination of thermal and field emission.
Thermistors are temperature-sensitive resistors with high sensitivity.
Bond using heat and pressure.
Thermocouples generate voltage proportional to temperature for measurement.
Use heated tool for bonding.