Introduction to Quantum Modelling

Abstract

Although we all live in a quantum mechanical world we have to look very hard to see quantum effects. This is because quantum phenomena such as the discretisation of energy levels and the wave nature of matter only become apparent at the sub-microscopic level. If we solve Schrodinger’s equation for electrons confined in an infinitely deep one-dimensional potential well then we find that at room temperature the separation between energy levels will only become comparable to the thermal energy for a well with a width of less than 4 nm. In modern semiconductor device processing these dimensions can be readily achieved in the vertical direction where crystal growth can be controlled to atomic dimensions and are now being approached by the lithographic process in the horizontal direction. We would therefore expect to observe, and perhaps exploit, quantum phenomena in present day structures. In practice the familiar semiconductor devices such as MESFETs still appear to operate in a an essentially classical way even when their dimensions are very small (e.g. gate lengths < 30 nm). One of the reasons why quantum effects are not always apparent in semiconductors is that changes in potential tend to occur over a Debye Length which smooths things out over relatively large distances. Although a number of structures have been proposed and fabricated to study the physics of quantum effects most of these only operate at very low temperatures (4 K) where they are of little use as practical devices. However, there is one device, the Double Barrier Resonant Tunnelling Diode (DBRTD), that operates on purely quantum mechanical principles at room temperature and it can also be shown that the inclusion of quantum effects in HEMT models does make a noticeable difference to the device characteristics. It is still early days for quantum devices and quantum modelling but as device dimensions continue to shrink and quantum phenomena are better understood it is expected that these new device concepts will become important.