Atlas: Investigation of microscale heat transfer effects in nanoscale electronic devices by Spectral methods by Ahmet Umid Coskun

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International Conference on Mathematical Modeling and Scientific Computing
April 2-6, 2001
Middle East Technical University and Selcuk University
Ankara and Konya, Turkey

Organizers
F. Bornemann (Munich University of Tecnology, Germany), H. Bulgak (Selcuk University, Konya, Turkey), V. Ganzha (Munich University of Technology, Germany), B. Karasozen (METU, Ankara, Turkey), A. Sinan (Selcuk University, Konya, Turkey), C. Zenger (Munich University of Technology, Germany)

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Investigation of microscale heat transfer effects in nanoscale electronic devices by Spectral methods
by
Ahmet Ümid Çoskun
Departmant of Mechanical, Industrial and Manufacturing Engineering, Northeastern University, USA

Silicon-based solid-state technology has traditionally followed Moore's Law that the number of transistors that can be fabricated on a unit area of an integrated circuit and, therefore, the speed of such a circuit will double every 1.5 to 2 years. Today, solid-state microelectronics has advanced to a degree at which key features measure about only 180 nm. It is believed that further downscaling can only proceed to a limit of about 20-30, nm channel length in CMOS technology. This trend toward miniaturization has created profound challenges in the thermal management of electronic devices. Thermal effects (e.g. lattice self-heating) and non-local transport effects (e.g. hot carrier) become increasingly important. For nanoscale devices (characteristic lengths of less than 0.1 micron) operating at very high frequencies (gate switching on the order of nanoseconds to picoseconds), transient thermal effects also come into play.

Microscale heat transport in semiconductors occurs primarily through phonon-phonon interactions (phonon collisions). Recently, Tzou represented the effect of these interactions with a phase shift between the heat flux and the temperature gradient vectors. In nanoscale devices, length scales are on the order of the thermal wave enetration depth and the characteristic time at high frequencies is comparable to the phase lag time. The thermal field in nanoscale devices ould therefore be significantly different from that predicted by the conventional Fourier's law, which assumes instantaneously existing heat flux and temperature gradient vectors. The governing equation of microscale heat transfer becomes a time-dependent, third-order partial differential equation. We studied the microscale heat transport problem in a simplified model to investigate the limits of conventional Fourier's law. The model problem consists of a two-dimensional array of similar semiconductor devices (32 Si MOSFETs) on a silicon substrate. The net electronic effect is approximated as internal heat generation below the transistor gate.

Spectral methods are used to solve the governing partial differential equation by taking advantage of the symmetry and periodicity of the problem. Truncated Fourier series are used as both the expansion and test function. The Galerkin method is used to minimize the residual. Fast Fourier Transforms (FFT) are employed for computational economy. The solution method employed results a fast implicit solution of the governing equation for the particular problem considered such that the total computation time is less than 7 s on a 700 MHz Pentium-III PC. The results indicate that the silicon devices with characteristic lengths of less than 0.1 micron and operating at frequencies in the GHz range are vulnerable to the effect of phase lag between the temperature gradient and the heat flux vectors. Results, further, show that the phase lag effects are particularly significant when voltage rises sharply in such devices. Spectral methods can be employed as efficient numerical tools especially when such devices are in cyclic operation.

Date received: February 18, 2001