6.1 Temperature as a Limiting Factor

As it has been shown in this dissertation, the increasing transistor densities in today's VLSI devices cause more and more serious heating problems because the locally generated heat cannot be appropriately transfered to the corresponding heat sinks fast enough. The contribution of a single device part can often be neglected compared to the overall power loss. However, present devices have interconnect lines with lengths of several kilometers [19] and hundreds of millions of transistors [2] and the small contributions become considerably large and dominate today's microelectronic devices. Thus, the device structures as a whole tend to heat up globally.

The increased global temperature has aggravated several parasitic effects which are normally not as much anticipated as would be required. However, an unintentional temperature increase can be considered as a stochastic global event which affects the whole chip and requires a global heat load management. Other parasitic effects are amplified by the temperature increase as demonstrated by the example of electromigration, where the activation energy is relatively lowered with respect to the maximum allowed electrical load permissible. Mechanical changes, for instance phase changes, changes in the crystal structure, and interface conditions such as adhesion are thermally enhanced as well and can have a major impact on the long life reliability of semiconductor device structures.

Some of the thermally-induced effects are for instance self-heating, which causes raised resistivity and increasing delay times on interconnect lines. This poses two further serious problems for fast electronic circuits: In a circuit with high speed transistors the maximum frequency is rather high. A increase of temperature due to self-heating causes increased parasitic effects like elevated line resistance, while the transition times increase accordingly and thus slow the circuit. The second example is global heating, which is not only limited to on-chip or on-die heating, but affects also the surrounding discrete devices on the circuit board.

The currently chosen thermodynamic treatment builds first faster, smaller, and denser device arrays and obtains therefore a higher power density distribution on the die. If the already considered heat sink provides enough cooling, everything seems to be working properly. But if not, the problem becomes even more critical if, for instance, the power loss due to the leakage currents is considered. In that case, the device generates heat even if it is not operating. For a modern microprocessor with typically $10^{8}$ transistors and an average leakage current of 10 nA per transistor, the total current would be 1 A. Hence, for a typical supply voltage of 1.33 V, the device consumes 1.33 W in idle mode -- a significant power consumption that is highly undesirably.

With decreasing feature size of the transistors, the power consumption keeps almost constant, while the power-dissipating area shrinks quadratically and the power-loss density explodes at a square ratio. Possible ways to solve this type of heating problem are to use better materials which show less leakage, to reduce the clock frequency, to introduce highly efficient heat conduction paths through the devices, to minimize the current for instance by the reduction of capacitances, and to decrease the supply voltage.