Modeling heating effects in nanoscale devices: the present and the future

In this review paper we give an overview on the present state of the art in modeling heat transport in nanoscale devices and what issues we need to address for better and more successful modeling of future devices. We begin with a brief overview of the heat transport in materials and explain why the simple Fourier law fails in nanoscale devices. Then we elaborate on attempts to model heat transport in nanostructures from both perspectives: nanomaterials (the work of Narumanchi and co-workers) and nanodevices (the work of Majumdar, Pop, Goodson and recently Vasileska, Raleva and Goodnick). We use our own simulation results which we have used to examine heat transport in nanoscaling devices to point out some important issues such as the fact that thermal degradation does not increase as we decrease feature size due to the more pronounced non-stationary transport and ballistic transport effects in nanoscale devices. We also point out that instead of using SOI, if one uses Silicon on Diamond technology there is much less heat degradation and better spread of the heat in the Diamond material. We also point out that tools for thermal modeling of nanoscale devices need to be improved from the present state of the art as 3D tools are needed, for example, to simulate heat transport and electrical transport in a FinFET device. Better models than the energy balance equations for the acoustic and optical phonons what we presently use in our simulators are also welcomed. The ultimate goal is to design the tool that can be efficient enough but at the same time can simulate most accurately both electrons and phonons within the particle pictures by solving their corresponding Boltzmann transport equations self-consistently. Investigations in integration of Peltier coolers with CMOS technology are also welcomed and much needed to reduce the problem of heat dissipation in nanoscale devices and interconnects.

[1]  P.K. Chu,et al.  Novel silicon-on-insulator structures for reduced self-heating effects , 2005, IEEE Circuits and Systems Magazine.

[2]  D. Cahill,et al.  Thermal conductance of epitaxial interfaces , 2003 .

[3]  H. Nalwa Nanostructured materials and nanotechnology , 2002 .

[4]  Gang Chen,et al.  Nonlocal and Nonequilibrium Heat Conduction in the Vicinity of Nanoparticles , 1996 .

[5]  S. P. Gaur,et al.  Two-dimensional carrier flow in a transistor structure under non-isothermal conditions , 1974 .

[6]  Leathen Shi,et al.  Enhanced thermoelectric cooling at cold junction interfaces , 2002 .

[7]  E. Pop,et al.  Non-Equilibrium Phonon Distributions in Sub-100nm Silicon Transistors , 2006 .

[8]  G Chen,et al.  Ballistic-diffusive heat-conduction equations. , 2001, Physical review letters.

[9]  A. Majumdar,et al.  Concurrent thermal and electrical modeling of sub‐micrometer silicon devices , 1996 .

[10]  D.H. Navon,et al.  Two-dimensional carrier flow in a transistor structure under nonisothermal conditions , 1976, IEEE Transactions on Electron Devices.

[11]  S.S. Wong,et al.  Heating mechanisms of LDMOS and LIGBT in ultrathin SOI , 1997, IEEE Electron Device Letters.

[12]  Ali Shakouri,et al.  NONEQUILIBRIUM ELECTRONS AND PHONONS IN THIN FILM THERMIONIC COOLERS , 2004 .

[13]  Kazuyoshi Fushinobu,et al.  Effect of gate voltage on hot‐electron and hot phonon interaction and transport in a submicrometer transistor , 1995 .

[14]  Gerhard K. M. Wachutka,et al.  Rigorous thermodynamic treatment of heat generation and conduction in semiconductor device modeling , 1990, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[15]  T. Sadi,et al.  Electrothermal Monte Carlo Simulation of Submicrometer Si/SiGe MODFETs , 2007, IEEE Transactions on Electron Devices.

[16]  F. Reif,et al.  Fundamentals of Statistical and Thermal Physics , 1965 .

[17]  Ali Shakouri,et al.  Cooling Power Density of SiGe/Si Superlattice Micro Refrigerators , 2003 .

[18]  C. Cercignani The Boltzmann equation and its applications , 1988 .

[19]  A. Majumdar,et al.  Microscale energy transport , 1998 .

[20]  A. Majumdar Microscale Heat Conduction in Dielectric Thin Films , 1993 .

[21]  Ali Shakouri,et al.  Heat Transfer in Nanostructures for Solid-State Energy Conversion , 2002 .

[22]  S. Wong,et al.  Temperature-Dependent Thermal Conductivity of Single-Crystal Silicon Layers in SOI Substrates , 1996, Microelectromechanical Systems (MEMS).

[23]  Kenneth E. Goodson,et al.  Phonon scattering in silicon films with thickness of order 100 nm , 1999 .

[24]  Shigeo Maruyama,et al.  Evaluation of the Phonon Mean Free Path in Thin Films by Using Classical Molecular Dynamics , 2003 .

[25]  Mehdi Asheghi,et al.  Thermal Conductivity Measurements of Ultra-Thin Single Crystal Silicon Layers , 2006 .

[26]  Eric Pop,et al.  Heat Generation and Transport in Nanometer-Scale Transistors , 2006, Proceedings of the IEEE.

[27]  J. Craggs Applied Mathematical Sciences , 1973 .

[28]  Kenneth E. Goodson,et al.  Measurement of ballistic phonon conduction near hotspots in silicon , 2001 .

[29]  Tso-Ping Ma,et al.  Scattering of silicon inversion layer electrons by metal/oxide interface roughness , 1987 .

[30]  Peter J. Price,et al.  Hot phonon effects in silicon field‐effect transistors , 1989 .

[31]  Ashok Raman,et al.  Simulation of nonequilibrium thermal effects in power LDMOS transistors , 2003 .

[32]  L. Geppert Solid state [Semiconductors. 1999 technology analysis and forecast] , 1999, IEEE Spectrum.

[33]  Cristina H. Amon,et al.  Submicron heat transport model in silicon accounting for phonon dispersion and polarization , 2004 .

[34]  R. W. Keyes,et al.  Fundamental limits of silicon technology , 2001, Proc. IEEE.

[35]  Shekhar Y. Borkar,et al.  Design challenges of technology scaling , 1999, IEEE Micro.

[36]  M. Dresselhaus,et al.  Alternative energy technologies , 2001, Nature.

[37]  Mehdi Asheghi,et al.  Phonon–boundary scattering in ultrathin single-crystal silicon layers , 2004 .

[38]  Ali Shakouri,et al.  Electronic and thermoelectric transport in semiconductor and metallic superlattices , 2004 .