As seen in Problem 3.109, silicon carbide nanowires of diameter D=15 nm can be grown onto a sol

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As seen in Problem 3.109, silicon carbide nanowires of...

As seen in Problem $3.109$, silicon carbide nanowires of diameter $D=15 \mathrm{~nm}$ can be grown onto a solid silicon carbide surface by carefully depositing droplets of catalyst liquid onto a flat silicon carbide substrate. Silicon carbide nanowires grow upward from the deposited drops, and if the drops are deposited in a pattern, an array of nanowire fins can be grown, forming a silicon carbide nano-heat sink. Consider finned and unfinned electronics packages in which an extremely small, $10 \mu \mathrm{m} \times 10 \mu \mathrm{m}$ electronics device is sandwiched between two $d=100$-nm-thick silicon carbide sheets. In both cases, the coolant is a dielectric liquid at $20^{\circ} \mathrm{C}$. A heat transfer coefficient of $h=1 \times 10^{5} \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}$ exists on the top and bottom of the unfinned package and on all surfaces of the exposed silicon carbide fins, which are each $L=300 \mathrm{~nm}$ long. Each nano-heat sink includes a $200 \times 200$ array of nanofins. Determine the maximum allowable heat rate that can be generated by the electronic device so that its temperature is maintained at $T_{t}<85^{\circ} \mathrm{C}$ for the unfinned and finned packages.

Key Concepts

Conduction Heat Transfer

Conduction heat transfer is the process by which thermal energy is transmitted through a material due to a temperature gradient. In the context of electronic packaging, conduction occurs through thin solid layers and substrates, and understanding it is essential for predicting how heat will spread from high-power components to surrounding materials.

Convective Heat Transfer

Convective heat transfer involves the movement of heat due to fluid motion around a surface. It defines how efficiently a coolant or ambient fluid can remove heat from a device. The rate of convective heat transfer is influenced by the fluid's properties and the flow conditions, making it a critical factor in thermal management solutions.

Heat Transfer Coefficient

The heat transfer coefficient quantifies the effectiveness of convective heat transfer at the interface between a solid surface and a fluid. It is a key parameter in thermal analysis, reflecting the rate at which heat is exchanged per unit area per unit temperature difference. A higher coefficient indicates more efficient cooling, which is fundamental in designing systems to control device temperatures.

Micro/Nano-Structured Heat Sinks

Micro and nano-structured heat sinks, such as finned designs with nanowires or nanofins, increase the surface area available for heat transfer. These structures enhance convective cooling by providing more interface area between the electronic components and the coolant. The design and arrangement of such small-scale features are crucial in improving heat dissipation in compact electronics.

Thermal Management of Electronics

Thermal management of electronics involves strategies to control and dissipate heat generated by electronic components to maintain safe operating temperatures. It integrates concepts from conduction and convection heat transfer, as well as innovative material and structural design approaches like micro/nano heat sinks, to ensure device reliability and performance under thermal stress.

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