ion channeling, metrology
Ions align with crystal channels.
923 technical terms and definitions
Ions align with crystal channels.
Analyze ionic species.
Use ion beam to thin samples.
Reuse designs as separate chiplets.
Detect Fe-B complexes affecting lifetime.
CD difference between isolated and dense features.
Leads bent under package.
Industry standard specifications.
Four-terminal measurement to eliminate probe resistance.
Measure work function and surface potential.
Non-contact work function measurement.
Minimum size that causes failures.
Pre-tested dies for multi-die packages.
248nm DUV light source.
Thin sample preparation for TEM.
Contact pads instead of balls.
Measure plasma density and potential.
Direct solid analysis.
Use laser to release temporary bond.
Precise distance measurement using light.
Mark packages with laser.
Laser-based mask writing.
Use laser to fix mask defects.
Non-contact surface inspection.
Use laser for ionization.
Transfer thin layer from one wafer to another.
Length of lead.
Spacing between leads.
Distance across leads.
Thickness of lead.
Width of individual lead.
MSL and reflow for Pb-free.
Use tin-silver-copper alloys.
Measure unwanted current flow.
Double patterning technique.
Combined edge and width roughness characterization.
Match measured spectrum to pre-calculated library.
Attach package lid.
Seal lid to package.
Optical detection of particles.
Random variation along edges of patterned lines.
Quantify edge roughness of patterned lines.
Variation in line width along its length.
Measure width variations along lines.
Verify linear response.
Bias across measurement range.
Accuracy across measurement range.
Liner deposition creates thin conformal layers in contacts and vias providing adhesion diffusion barriers and nucleation surfaces.
Rinse wafer and analyze solution.
# 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