Semiconductors’ miniaturization through time: from Moore’s law to Eroom’s Law?

Transistors’ miniaturization has been restless since the very beginning of their invention in 1947. Among their early applications, a fundamental one was as substitutes for vacuum tubes (or valves). In 1965 Gordon Moore enunciated what was to become “Moore’s law”, that is the fact that the number of components that could be crammed into an integrated circuit would double every year. The “law” has slowed down, but it has been running ever since. The end of the validity of Moore’s law has been announced quite a few times, and this explains why IBM invested heavily in superconductors, proclaiming in 1980 the coming ‘Josephson computer revolution’ (a revolution which, maybe, will materialize fifty years later than expected). So far, neither newer (superconductors) nor old (vacuum tubes) technologies could threaten the dominance of semiconductors – miniaturization of these latter being the essential part of the game. The continuous process of miniaturization of semiconductors, though, has come at a cost, and that cost is research and developments (R&D), which is continuously increasing. This is why one can speak of a reversed Moore’s law, namely “Eroom’s law”. The latter “law” points at the growing expenditure on R&D to miniaturize transistors as well as to the growing capital outlays necessary to build production facilities capable of producing the latest 5- and 3-nanometre semiconductors. In this work we refer to a simple model which – given certain assumptions – clarifies up to which point it is worthwhile to spend on R&D in which technology, Eroom’s law being an intrinsic feature when we want to improve a technology at a constant rate.