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title: 'Lecture 19: Heat Sink and its types'
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  ## DI02011011: Electronics Circuit and Application (ECA)
  Transistor Biasing circuits And Thermal stability
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# DI02011011: Electronics Circuit and Application (ECA)
## Lecture 19: Heat Sink and its types
### Transistor Biasing circuits And Thermal stability

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Welcome to Lecture 19. Today we focus on heat sink engineering. Once power transistors dissipate heat, that heat must be efficiently transferred from the semiconductor case into the ambient atmosphere. We will cover heat transfer physics, thermal interface materials, heat sink types, and step-by-step sizing procedures.
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# Lecture Blueprint: Thermal Management & Heat Sink Types

- Fundamentals of Heat Transfer Modes: Conduction, Convection, and Thermal Radiation.
- Thermal Interface Materials (TIM): Greases, Phase-Change Materials, Elastomeric Pads, and Gap Fillers.
- Analysis of Thermal Contact Resistance $\theta_{CS}$ & Mounting Torque Effects.
- Classification & Architecture of Heat Sinks: Stamped, Extruded, Pin-Fin, and Skived-Fin.
- Advanced Cooling Topologies: Two-Phase Vapor Chambers, Heat Pipes, and Liquid Cold Plates.
- Natural Convection vs. Forced Air Convection Volumetric Performance.
- Heat Sink Sizing Equation Methodology ($\theta_{SA}$ Calculation) & Worked Examples.

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This lecture covers heat transfer mechanisms, TIM materials, heat sink geometries, advanced 2-phase cooling, and step-by-step heat sink calculation.
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# Fundamentals of Heat Transfer Mechanisms in Electronics

- Conduction (Solid Material Transfer): Heat flow through solid silicon, copper flange, and aluminum heat sink body, governed by Fourier's Law.
- Convection (Fluid/Air Interface Transfer): Heat dissipation from heat sink fins to surrounding air, governed by Newton's Law of Cooling.
- Radiation (Electromagnetic Waves): Direct infrared radiative heat loss from heat sink surface to surrounding enclosures, governed by Stefan-Boltzmann Law.
- Dominant Mode in Heat Sinks: Convection across fin surface area accounts for $80\%-90\%$ of total heat dissipation in forced air systems.

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Heat moves through three sequential mechanisms: conduction through the semiconductor packaging, convection from fins to air, and infrared radiation to the enclosure.
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# Governing Equations of Thermal Dissipation Modes

- Fourier's Law of Conduction: $Q_{cond} = -k A \frac{dT}{dx} = \frac{k A}{L} (T_1 - T_2) \implies \theta_{cond} = \frac{L}{k A} \, \left(^\circ\text{C/W}\right)$, where $k$ is thermal conductivity ($\text{W/m}\cdot\text{K}$).
- Newton's Law of Convection: $Q_{conv} = h A_{surface} (T_s - T_\infty) \implies \theta_{conv} = \frac{1}{h A_{surface}}$, where $h$ is heat transfer coefficient ($\text{W/m}^2\cdot\text{K}$).
- Stefan-Boltzmann Law of Radiation: $Q_{rad} = \epsilon \sigma A_{surface} (T_s^4 - T_{surr}^4)$, where $\epsilon$ is surface emissivity ($0.85-0.95$ for black anodized aluminum) and $\sigma = 5.67 \times 10^{-8} \,\text{W/m}^2\text{K}^4$.
- Combined Sink Resistance Equation: $\theta_{SA} = \frac{1}{h A_{fin} + h_{rad} A_{rad}}$.

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Here are the mathematical equations governing all three heat transfer modes. Notice that thermal conductivity $k$, fin area $A$, and convective coefficient $h$ control performance.
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# Thermal Interface Materials (TIM) and Thermal Contact Resistance $\theta_{CS}$

- Microscopic Surface Imperfections: Microscopic air gaps ($k_{air} \approx 0.026\,\text{W/m}\cdot\text{K}$) between transistor case and heat sink create high thermal contact resistance.
- Role of Thermal Interface Material: TIM displaces air voids with higher conductivity compounds ($k_{TIM} \approx 1.5 - 8.0\,\text{W/m}\cdot\text{K}$).
- Primary Classes of TIM Materials:
-   • Thermal Greases / Pastes: Lowest thermal impedance ($0.05 - 0.15^\circ\text{C}\cdot\text{in}^2\text{/W}$); requires manual application.
-   • Phase-Change Materials (PCM): Melts at $45-60^\circ\text{C}$ to fill microscopic voids; clean automated application.
-   • Elastomeric Silicone Pads: Provides electrical isolation with moderate thermal resistance ($0.5 - 1.5^\circ\text{C/W}$).
-   • Graphite / Gap Fillers: Compressible thick pads for bridging large mechanical tolerances.

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Without TIM, microscopic surface roughness traps air, which is a terrible thermal conductor. TIM fills these air pockets, reducing case-to-sink resistance $\theta_{CS}$.
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# Mounting Hardware, Torque Controls, and $\theta_{CS}$ Optimization

- Impact of Mounting Pressure: Increasing clamping pressure compresses TIM, reducing bond-line thickness (BLT) and lowering $\theta_{CS}$.
- Optimal Torque Specification: Screw-mounted packages (TO-220, TO-247) require $0.5 - 0.8\,\text{N}\cdot\text{m}$ mounting torque.
- Over-Torquing Hazard: Excessive torque warps the copper header tab, bowing the contact surface away from the heat sink and INCREASING $\theta_{CS}$.
- Spring Clip Mounting: Provides constant uniform clamping pressure across thermal cycles, compensating for thermal expansion stress.

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Mounting torque is crucial. Under-torquing leaves thick TIM layers; over-torquing warps the package tab. Spring clips maintain optimal uniform pressure.
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# Extruded & Stamped Heat Sinks: Structure & Performance

- Stamped Heat Sinks: Fabricated by stamping thin aluminum or copper sheets ($0.5 - 1.5\,\text{mA}$ thick). Low cost; suited for low-power board-level components ($P_D < 5\,\text{W}$, $\theta_{SA} \approx 10 - 25^\circ\text{C/W}$).
- Extruded Aluminum Heat Sinks (6063-T5): Fabricated by forcing hot aluminum billets through shaped dies. High thermal conductivity ($k \approx 200\,\text{W/m}\cdot\text{K}$).
- Fin Design Profiles: Straight vertical fins optimize natural convection chimney effects. Aspect ratios (fin height to gap width) typically reach $8:1$ to $10:1$.
- Application Window: Standard choice for medium-to-high power amplifiers ($P_D = 10\,\text{W} - 100\,\text{W}$, $\theta_{SA} \approx 0.5 - 5.0^\circ\text{C/W}$).

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Stamped heat sinks are cheap solutions for low-power parts. Extruded aluminum heat sinks are the industry workhorse for medium to high power electronics.
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# High-Density Surface Architectures: Pin-Fin & Skived-Fin

- Pin-Fin Heat Sinks: Array of round, square, or elliptical pins. Omnidirectional air flow capability; disrupts boundary layers to increase convective heat transfer coefficient $h$.
- Skived-Fin Heat Sinks: Produced by shaving thin, continuous fins directly from a solid copper or aluminum block using a precision blade.
- High Aspect Ratio Advantage: Enables extremely dense fin spacing with aspect ratios up to $25:1$ and zero thermal interface resistance between fins and base plate.
- Material Advantage of Copper: Skived copper heat sinks ($k \approx 390\,\text{W/m}\cdot\text{K}$) provide double the thermal conductivity of aluminum, ideal for space-constrained high-flux power density.

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Pin-fin heat sinks work well in multidirectional airflow. Skived-fin heat sinks cut dense fins directly out of solid copper, offering maximum surface area in compact spaces.
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# Two-Phase Passive Cooling: Heat Pipes & Vapor Chambers

- Phase Change Thermodynamics: Utilizes latent heat of vaporization of working fluid (water/alcohol under vacuum) to transport heat with near-zero temperature drop.
- Operation Cycle: Liquid vaporizes at hot evaporator interface $\to$ Vapor travels at high speed to cold condenser section $\to$ Vapor condenses releasing latent heat $\to$ Liquid returns to evaporator via capillary wick action.
- Effective Thermal Conductivity: Ultra-high equivalent conductivity ($k_{eq} \approx 5,000 - 50,000\,\text{W/m}\cdot\text{K}$), $10\times-100\times$ higher than solid copper.
- Vapor Chamber Application: Planar 2D heat spreader placed directly under high-power density chips to eliminate localized thermal hot spots.

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Heat pipes and vapor chambers use phase-change boiling and condensation inside a sealed vacuum tube to move heat at velocities near the speed of sound with virtually zero thermal resistance.
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# Forced Air Convection vs. Natural Convection Performance Dynamics

- Natural Convection: Driven solely by buoyant forces of heated air ($v_{air} \approx 0.1 - 0.5\,\text{m/s}$). Convective coefficient $h \approx 5 - 15\,\text{W/m}^2\cdot\text{K}$. Requires wide fin spacing ($5 - 10\,\text{mm}$) to prevent boundary layer overlap.
- Forced Air Convection: Driven by fans/blowers ($v_{air} \approx 2.0 - 5.0\,\text{m/s}$). Convective coefficient $h \approx 30 - 150\,\text{W/m}^2\cdot\text{K}$ ($5\times - 10\times$ increase!).
- Thermal Resistance Reduction: Forced airflow reduces $\theta_{SA}$ of an extruded heat sink by $60\% - 75\%$ compared to natural convection.
- Pressure Drop Trade-off: Denser fin spacing increases airflow impedance, requiring higher static pressure fans.

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Adding a cooling fan increases convective coefficient $h$ up to 10-fold, dramatically dropping heat sink thermal resistance $\theta_{SA}$.
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# Liquid Cooling Cold Plates & Direct Substrate Management

- Liquid Cold Plate Architecture: Internal microchannels machined into copper/aluminum blocks connected to a closed-loop liquid pump, radiator, and reservoir.
- Coolant Properties: Water/glycol mixtures possess $4\times$ higher specific heat capacity ($c_p \approx 4184\,\text{J/kg}\cdot\text{K}$) and $25\times$ higher thermal conductivity than air.
- Performance Metric: Achieves extremely low thermal resistances ($\theta_{SA} < 0.05^\circ\text{C/W}$).
- Application Scope: Essential for high-power electronics ($> 500\,\text{W}$ to several $\text{kW}$) such as EV inverters, motor drives, server racks, and high-power RF transmitters.

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Liquid cold plates are required when power levels exceed hundreds of watts or when high power density makes air cooling physically impossible.
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# Numerical Example: Step-by-Step Heat Sink Sizing Calculation ($\theta_{SA}$)

- Given Requirements: Transistor TO-247 package dissipating $P_D = 45\,\text{W}$. Maximum junction temperature $T_{J,\max} = 150^\circ\text{C}$. Maximum ambient temperature $T_A = 50^\circ\text{C}$. Transistor datasheet specifies $\theta_{JC} = 0.8^\circ\text{C/W}$. Mounted with thermal grease and mica washer $\theta_{CS} = 0.4^\circ\text{C/W}$.
- Step 1: Calculate Maximum Allowable Total Thermal Resistance $\theta_{JA,\max}$:
-   $\theta_{JA,\max} = \frac{T_{J,\max} - T_A}{P_D} = \frac{150^\circ\text{C} - 50^\circ\text{C}}{45\,\text{W}} = \frac{100^\circ\text{C}}{45\,\text{W}} = 2.22^\circ\text{C/W}$.
- Step 2: Solve for Maximum Allowable Heat Sink Thermal Resistance $\theta_{SA}$:
-   $\theta_{SA,\max} = \theta_{JA,\max} - \theta_{JC} - \theta_{CS} = 2.22 - 0.8 - 0.4 = 1.02^\circ\text{C/W}$.
- Step 3: Heat Sink Selection: Select a commercial catalog heat sink rating $\theta_{SA} \le 1.0^\circ\text{C/W}$ under natural convection or $\le 0.4^\circ\text{C/W}$ under forced air.

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Let's perform this step-by-step heat sink calculation. Subtracting $\theta_{JC}$ and $\theta_{CS}$ from total allowable $\theta_{JA}$ gives our heat sink specification: $\theta_{SA} \le 1.02^\circ\text{C/W}$.
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# Numerical Example: Evaluating TIM Impact on Junction Temperature

- Comparison Scenario: Same $45\,\text{W}$ transistor setup with $\theta_{SA} = 1.0^\circ\text{C/W}$, $\theta_{JC} = 0.8^\circ\text{C/W}$, $T_A = 50^\circ\text{C}$.
- Option A — High-Grade Thermal Grease: $\theta_{CS} = 0.2^\circ\text{C/W}$.
-   • Total $\theta_{JA} = 0.8 + 0.2 + 1.0 = 2.0^\circ\text{C/W}$.
-   • Junction Temp $T_J = 50^\circ\text{C} + (45\,\text{W} \times 2.0^\circ\text{C/W}) = 50 + 90 = 140^\circ\text{C}$ (SAFE!).
- Option B — Dry Joint without TIM: Microscopic air gaps yield $\theta_{CS} = 1.8^\circ\text{C/W}$.
-   • Total $\theta_{JA} = 0.8 + 1.8 + 1.0 = 3.6^\circ\text{C/W}$.
-   • Junction Temp $T_J = 50^\circ\text{C} + (45\,\text{W} \times 3.6^\circ\text{C/W}) = 50 + 162 = 212^\circ\text{C}$ (DESTRUCTIVE FAILURE!).
- Conclusion: Omitting thermal interface grease increases $T_J$ by $72^\circ\text{C}$, causing catastrophic thermal destruction.

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Look at the dramatic difference TIM makes! Operating dry pushes junction temperature to 212°C, causing instant device failure.
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# Summary & Heat Sink Selection Matrix

- Sizing Formula: $\theta_{SA} = \frac{T_{J,\max} - T_A}{P_D} - \theta_{JC} - \theta_{CS}$.
- Low Power ($< 5\,\text{W}$): Stamped sheet metal heat sinks or direct PCB copper pour plane.
- Medium Power ($5\,\text{W} - 100\,\text{W}$): Extruded aluminum heat sinks with natural or forced convection.
- High Power Density ($100\,\text{W} - 300\,\text{W}$): Skived copper pin-fin heat sinks with heat pipe vapor chambers.
- Ultra Power ($> 300\,\text{W}$): Closed-loop liquid cooling cold plates.
- Golden Rule: Always specify high-grade TIM ($k_{TIM} > 2.0\,\text{W/m}\cdot\text{K}$) and apply proper mounting torque to minimize $\theta_{CS}$.

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To summarize: compute $\theta_{SA}$, pick the right cooling technology for your power density, and never neglect thermal interface material. Next lecture: Amplifier Gain, Bandwidth, and Gain-Bandwidth Product.
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