Electrothermal Monte Carlo Modelling of Submicron HFETs
Over the last ten years the electronics industry has seen a continuous stream of engineering advances that have permitted a logarithmic growth in the capability of integrated circuits (ICs). This trend was first publicised by Gordon E. Moore (co-founder of Intel) in 1965, who suggested that the number of transistors on an IC doubled every two year (his observation is now known as Moore's Law).
The passage of an electric current through a conventional conductor or semiconductor generates I2R Joules of heat per second. While the currents in each element of a modern microprocessor are very small, the density at which they can now be packed together results in a lot of heat having to be dissipated from a small area of the IC surface. The thermal output of ICs have, in fact, closely paralleled Moore's Law, in a trend that suggests serious thermal problem in the near future (see feature).
As the thermal output per unit surface area of the IC rapidly approaches that at the surface of the core of a nuclear power plant, engineers face serious problems in several areas. The heat generated results in changes to the semiconductor's electrical properties, but it also generates voltages, ('thermopower' or Seebeck effect) which can drive spurious currents in the circuit.
The animation plots the power density of several families of microprocessor used in desktop computers. Before 2010 we expect the power density to exceed that of a swimming pool type nuclear reactor. Shortly after, on the current trend, the power density on a conventional microprocessor chip would excede that of a rocket engine exhaust...
With the high cost of tooling to manufacture modern ICs, it is vital to be able to predict the behaviour of a circuit before it goes into production. This means increasingly that the thermal response of a circuit at the sub-micron level must be understood if the device is to work as intended.
While the I2R relationship calculates the average power output of a device based on the current flowing, it does not predict the microscopic thermal responses caused by the movements of small numbers of electrons. To understand behaviour at this level we need to be able to work with individual electrons, and model how these interact with the semiconductor lattice directly.
The most important interaction of electrons with the underlying semiconductor lattice is through phonons. A phonon is a quantised lattice vibration, but it can be treated as a particle that the electron can collide with. Each collision causes the electron to be deflected, and an amount of energy is transferred between the phonon and the electron depending upon the dynamics of the collision (i.e. the collisions are 'inelastic'). Electrons can heat a local bit of the lattice by transferring energy to a phonon in that region, or it can cool it by absorbing energy from the phonon, and transporting it elsewhere in the device.
In the Monte Carlo method, the paths followed by electrons inside the device, and the collisions that they undergo, are modelled using random numbers. Scientists at Leeds are using this approach to determine exactly when and where electrons emit (or absorb) phonons. In any part of the device, counting all the electron-phonon collisions within a given amount of time gives a measure of the rate of heat generation (i.e. the power dissipation) in that part of the device. Power dissipation can then be mapped throughout the volume of the entire device, as shown in the graph above.
References
"Simulation of Electron transoport in InGaAs/AlGaAs HEMTs using an Electrothermal Monte Carlo Method" Toufik Sadi, Robert Kelsall and Neil Pilgrim IEEE Transactions on Electron Devices, .
More about electrothermal device simulation, including self-consistent electrothermal Monte Carlo modelling and nanoscale thermal transport, can be found on Robert Kelsall's website: website link.
HFET stands for Heterostructure Field Effect Transistor, these devices are also known as High Electron Mobility Transistors (HEMT), or modulation-doped FET (MODFET) (Wikipedia link).
Acknowledgements
"Launch of Apollo 8 lunar orbit mission", December 21, 1968, photo courtesy JSC Digital Image Collection.
"Idaho National Laboratory's Advanced Test Reactor", photo courtesy Idaho National Laboratory/US Federal Government
