where Io is a constant around 1 μA (microampere) per micrometer of transistor width at room temperature, Vgs is the voltage applied to the control gate of the transistor, and α is a number greater than 1 (generally around 1.3) that represents how effectively the gate voltage changes the energy barrier. From the equation, it is easy to see that the amount of leakage current through an off transistor (Vgs = 0) depends heavily on the transistor’s threshold voltage. The leakage current increases by about a factor of 10 each time the threshold voltage drops by another 100 mV.
Historically, Vths were around 800 mV, so the residual transistor leakage currents were so small that they did not matter. Starting from high Vth values, it was possible to scale Vth, Vsupply, and L together. While leakage current grew exponentially with shrinking Vth, the contribution of subthreshold leakage to the overall power was negligible as long as Vth values were still relatively large. But ultimately by the 90-nm node, the leakage grew to a point where it started to affect overall chip power.27 At that point, Vth and Vsupply scaling slowed dramatically.
One approach to reduce leakage current is to reduce temperature, inasmuch as this makes the exponential slope steeper. That is possible and has been tried on occasion, but it runs into two problems. The first is that one needs to consider the power and cost of providing a low-temperature environment, which usually dwarf the gains provided by the system; this is especially true for small or middle-size systems that operate in an office or home environment. The second is related to testing, repair, thermal cycling, and reliability of the systems. For those reasons, we will not consider this option further in the present report. However, for sufficiently large computing centers, it may prove advantageous to use liquid cooling or other chilling approaches where the energy costs of operating the semiconductor hardware in a low-temperature environment do not outweigh the performance gains, and hence energy savings, that are possible in such an environment.
Vth stopped scaling because of increasing leakage currents, and Vsupply scaling slowed to preserve transistor speed with a constant (Vsupply – Vth). Once leakage becomes important, an interesting optimization between Vsupply and Vth is possible. Increasing Vth decreases leakage current but also makes the gates slower because the number of carriers that can flow through a transistor is roughly proportional to the decreasing (Vsupply – Vth). One can recover the lost speed by increasing Vsupply, but this also increases the power consumed to switch the gate dynamically. For a given gate delay, the lowest-power solution is one in which the marginal energy cost of increasing Vdd is exactly balanced by the marginal energy savings
27Edward J. Nowak, 2002, Maintaining the benefits of CMOS scaling when scaling bogs down, IBM Journal of Research and Development 46(2/3): 169-180.