lazy class, code ai
Class not doing enough.
169 technical terms and definitions
Class not doing enough.
Networks stay close to initialization.
Improve drug candidate properties.
Lead time management optimizes procurement and delivery schedules minimizing delays and carrying costs.
Fixed small negative slope.
Position embeddings as parameters.
Train which layers to use per input.
Train noise schedule.
Learned routing trains networks to assign tokens to experts.
Learned step size quantization optimizes quantization scale factors during training.
Learning curve prediction forecasts final performance from initial training enabling efficient architecture selection.
Plan for adjusting learning rate during training (cosine linear step decay).
ML approaches to ranking.
Framework for privileged information.
LED lighting in fabs reduces energy consumption for illumination while providing compatible wavelengths for photolithography processes.
Legal-BERT is trained on legal text. Contract analysis, case law.
Analyze contracts and legal texts.
Answer questions about law.
Find relevant cases and statutes.
Generalize to sequences longer than seen during training.
Channel length depends on nearby diffusions.
Length penalty adjusts probabilities favoring shorter or longer sequences.
Edit sequences via insertions and deletions.
Discover reusable code abstractions.
Licensing models grant rights to use semiconductor IP through royalties or upfront fees.
Networks using Lie group theory.
Life cycle assessment evaluates environmental impacts across entire product lifecycle from materials to disposal.
Continuous learning over time.
Bond pad delamination.
Explain individual predictions using local linear approximations.
Network embedding method.
Linear attention reduces complexity by avoiding softmax normalization.
Approximate attention with linear complexity.
Linear bottlenecks remove nonlinearity from final layer preserving information in low-dimensional spaces.
Linearly increasing variance.
Test if syntax is linearly encoded.
Count code lines.
Linformer projects keys and values to lower dimension reducing attention complexity.
Linear attention using low-rank projections.
Linear Non-Gaussian Acyclic Models discover causal structure exploiting non-Gaussianity and independence of noise.
Link prediction estimates likelihood of edges between node pairs for graph completion and recommendation.
Memory-efficient optimizer using sign of gradients.
Bound sensitivity to input changes.
Architectures with bounded Lipschitz constant.
Use liquid crystals to find hot spots.
# Liquid Crystal Hot Spot Failure Analysis: Advanced Techniques ## 1. Introduction Liquid crystal thermography (LCT) is a **non-destructive failure analysis (FA)** technique used in semiconductor and electronics testing. It exploits the temperature-sensitive optical properties of **cholesteric (chiral nematic) liquid crystals**. ## 2. Fundamental Principles ### 2.1 Thermochromic Behavior Cholesteric liquid crystals selectively reflect light at wavelengths dependent on their helical pitch $p$, which changes with temperature $T$. The **Bragg reflection condition** for peak wavelength: $$ \lambda_{\text{max}} = n_{\text{avg}} \cdot p $$ Where: - $\lambda_{\text{max}}$ = peak reflected wavelength (nm) - $n_{\text{avg}}$ = average refractive index of the liquid crystal - $p$ = helical pitch (nm) The pitch-temperature relationship: $$ p(T) = p_0 \left[ 1 + \alpha (T - T_0) \right]^{-1} $$ Where: - $p_0$ = pitch at reference temperature $T_0$ - $\alpha$ = thermal expansion coefficient of the pitch ($\text{K}^{-1}$) ### 2.2 Joule Heating at Defect Sites Power dissipation at a defect location: $$ P = I^2 R = \frac{V^2}{R} $$ Temperature rise due to localized heating: $$ \Delta T = \frac{P}{G_{\text{th}}} = \frac{P \cdot R_{\text{th}}}{1} $$ Where: - $P$ = power dissipation (W) - $G_{\text{th}}$ = thermal conductance (W/K) - $R_{\text{th}}$ = thermal resistance (K/W) ### 2.3 Thermal Diffusion The **heat diffusion equation** governing temperature distribution: $$ \frac{\partial T}{\partial t} = \alpha_{\text{th}} \nabla^2 T + \frac{Q}{\rho c_p} $$ Where: - $\alpha_{\text{th}} = \frac{k}{\rho c_p}$ = thermal diffusivity ($\text{m}^2/\text{s}$) - k = thermal conductivity (W/m-K) - $\rho$ = density (kg/m³) - c_p = specific heat capacity (J/kg-K) - $Q$ = volumetric heat source (W/m³) **Thermal diffusion length** (for pulsed excitation at frequency $f$): $$ \mu = \sqrt{\frac{\alpha_{\text{th}}}{\pi f}} $$ ## 3. Spatial Resolution and Sensitivity ### 3.1 Resolution Limits The effective spatial resolution $\delta$ is limited by: $$ \delta = \sqrt{\delta_{\text{opt}}^2 + \delta_{\text{th}}^2} $$ Where: - $\delta_{\text{opt}}$ = optical resolution limit (diffraction-limited: $\delta_{\text{opt}} \approx \frac{\lambda}{2 \cdot \text{NA}}$) - $\delta_{\text{th}}$ = thermal spreading in the substrate ### 3.2 Minimum Detectable Power $$ P_{\text{min}} = \frac{\Delta T_{\text{min}} \cdot k \cdot A}{d} $$ Where: - $\Delta T_{\text{min}}$ = minimum detectable temperature change (~0.1°C) - $k$ = thermal conductivity of substrate - $A$ = defect area - $d$ = depth of defect below surface ## 4. Advanced Failure Modes Detectable ### 4.1 Electrical Defects - **Gate oxide shorts and leakage paths** - Current through defective oxide: $I_{\text{leak}} = \frac{V_{\text{ox}}}{R_{\text{defect}}}$ - Power: $P = I_{\text{leak}} \cdot V_{\text{ox}}$ - **Metal bridging and shorts** - Bridge resistance: $R_{\text{bridge}} = \frac{\rho L}{A}$ - Localized dissipation creates thermal signature - **Junction leakage and latch-up** - Parasitic thyristor current: $I_{\text{latch}} = \frac{V_{DD}}{R_{\text{well}} + R_{\text{sub}}}$ - **Electromigration damage** - Current density threshold (Black's equation): $$ \text{MTTF} = A \cdot J^{-n} \cdot \exp\left(\frac{E_a}{k_B T}\right) $$ ### 4.2 Thermal/Mechanical Defects - **Die-attach voids** - Effective thermal resistance with void fraction $\phi$: $$ R_{\text{th,eff}} = \frac{R_{\text{th,0}}}{1 - \phi} $$ - **Delamination** - Creates thermal barrier, increasing local $\Delta T$ ## 5. Advanced Methodologies ### 5.1 Backside Analysis For flip-chip or devices with opaque frontside metallization: - **Die thinning requirement**: Thickness $t \approx 50-100 \, \mu\text{m}$ - **Silicon transparency**: $\lambda > 1.1 \, \mu\text{m}$ (bandgap energy $E_g = 1.12 \, \text{eV}$) $$ E_g = \frac{hc}{\lambda_{\text{cutoff}}} \Rightarrow \lambda_{\text{cutoff}} = \frac{1.24 \, \mu\text{m} \cdot \text{eV}}{E_g} $$ ### 5.2 Lock-in Thermography Modulated power excitation with lock-in detection: $$ P(t) = P_0 \left[1 + \cos(2\pi f_{\text{mod}} t)\right] $$ **Temperature response (amplitude and phase)**: $$ T(x, t) = T_0 + \Delta T(x) \cos\left(2\pi f_{\text{mod}} t - \phi(x)\right) $$ Phase lag due to thermal diffusion: $$ \phi(x) = \frac{x}{\mu} = x \sqrt{\frac{\pi f_{\text{mod}}}{\alpha_{\text{th}}}} $$ **Signal-to-noise improvement**: $$ \text{SNR}_{\text{lock-in}} = \text{SNR}_{\text{DC}} \cdot \sqrt{N_{\text{cycles}}} $$ ### 5.3 Pulsed Excitation For transient thermal analysis: $$ \Delta T(t) = \frac{P}{G_{\text{th}}} \left(1 - e^{-t/\tau_{\text{th}}}\right) $$ Where thermal time constant: $$ \tau_{\text{th}} = R_{\text{th}} \cdot C_{\text{th}} = \frac{\rho c_p V}{k A / d} $$ ## 6. Comparison with Other Thermal Techniques | Technique | Resolution | Sensitivity | Speed | Equation Basis | |-----------|-----------|-------------|-------|----------------| | Liquid Crystal | $5-20 \, \mu\text{m}$ | $\sim 0.1°\text{C}$ | Moderate | Bragg: $\lambda = np$ | | IR Thermography | $3-5 \, \mu\text{m}$ | $\sim 10 \, \text{mK}$ | Fast | Stefan-Boltzmann: $P = \varepsilon \sigma T^4$ | | Thermoreflectance | $< 1 \, \mu\text{m}$ | $\sim 10 \, \text{mK}$ | Fast | $\frac{\Delta R}{R} = \kappa \Delta T$ | | Scanning Thermal | $< 100 \, \text{nm}$ | $\sim 1 \, \text{mK}$ | Slow | Fourier: $q = -k\nabla T$ | ## 7. Practical Workflow ### 7.1 Sample Preparation 1. **Decapsulation** - Chemical (fuming $\text{HNO}_3$, $\text{H}_2\text{SO}_4$) - Plasma etching - Mechanical (for ceramic packages) 2. **Surface cleaning** - Solvent rinse (acetone, IPA) - Plasma cleaning for organic residue 3. **Liquid crystal application** - Airbrush: layer thickness $\sim 10-50 \, \mu\text{m}$ - Spin coating: $\omega \sim 1000-3000 \, \text{rpm}$ ### 7.2 Bias Conditions - **DC bias**: $V_{\text{test}} = V_{\text{DD}} \times (1.0 - 1.2)$ - **Current limiting**: $I_{\text{max}}$ to prevent thermal runaway - **Power budget**: $$ P_{\text{total}} = P_{\text{quiescent}} + P_{\text{defect}} $$ ### 7.3 Temperature Control Stage temperature setpoint: $$ T_{\text{stage}} = T_{\text{LC,center}} - \Delta T_{\text{expected}} $$ Where $T_{\text{LC,center}}$ is the center of the liquid crystal's active color-play range. ## 8. Detection Limits ### 8.1 Minimum Detectable Power For a defect at depth d in silicon (k_Si = 148 W/m-K): $$ P_{\text{min}} \approx 4\pi k d \cdot \Delta T_{\text{min}} $$ **Example calculation**: - $d = 10 \, \mu\text{m} = 10 \times 10^{-6} \, \text{m}$ - $\Delta T_{\text{min}} = 0.1 \, \text{K}$ - k = 148 W/m-K $$ P_{\text{min}} = 4\pi \times 148 \times 10 \times 10^{-6} \times 0.1 \approx 1.86 \, \text{mW} $$ ### 8.2 Defect Size vs. Power Relationship Assuming hemispherical heat spreading: $$ \Delta T = \frac{P}{2\pi k r} $$ Solving for minimum detectable defect radius at given power: $$ r_{\text{min}} = \frac{P}{2\pi k \Delta T_{\text{min}}} $$ ## 9. Integration with Physical Failure Analysis ### 9.1 FIB Cross-Sectioning Workflow 1. **Coordinate transfer** - Optical microscope coordinates $\rightarrow$ FIB stage coordinates - Alignment markers for registration 2. **Protective deposition** - Pt or W layer: $\sim 1-2 \, \mu\text{m}$ thick 3. **Cross-section milling** - Rough cut: $30 \, \text{kV}$, high current ($\sim \text{nA}$) - Fine polish: $30 \, \text{kV}$, low current ($\sim \text{pA}$) ### 9.2 Failure Signature Correlation | Thermal Signature | Likely Physical Defect | |-------------------|------------------------| | Point source | Gate oxide pinhole, metal spike | | Linear | Metal bridge, crack | | Diffuse area | Junction leakage, ESD damage | | Periodic pattern | Systematic process defect | ## 10. Error Analysis ### 10.1 Temperature Measurement Uncertainty $$ \sigma_T = \sqrt{\sigma_{\text{LC}}^2 + \sigma_{\text{stage}}^2 + \sigma_{\text{optical}}^2} $$ ### 10.2 Position Uncertainty Due to thermal spreading: $$ \sigma_x \approx \mu = \sqrt{\frac{\alpha_{\text{th}} \cdot t_{\text{exposure}}}{\pi}} $$ ## 11. Equations | Parameter | Equation | |-----------|----------| | Bragg wavelength | $\lambda_{\text{max}} = n_{\text{avg}} \cdot p$ | | Power dissipation | $P = I^2 R = V^2/R$ | | Thermal diffusion length | $\mu = \sqrt{\alpha_{\text{th}} / \pi f}$ | | Temperature rise | $\Delta T = P \cdot R_{\text{th}}$ | | Lock-in phase | $\phi = x/\mu$ | | Minimum power | $P_{\text{min}} = 4\pi k d \cdot \Delta T_{\text{min}}$ | ## 12. Standards - **JEDEC JESD22-A** — Failure analysis procedures - **MIL-STD-883** — Test methods for microelectronics - **SEMI E10** — Equipment reliability metrics
Liquid neural networks adapt dynamics based on inputs enabling continual learning.
Dynamically adapting networks with time-varying parameters inspired by biological neurons.
Continuously adapting networks inspired by biological neurons.
Continuous-time RNNs with adaptive dynamics.