Electronics use wafer sizes from 100 to 450 mm diameter. The size of wafers for photovoltaics is 100–200 mm square and the thickness is 100–500 μm. The boule is then sliced with a wafer saw (a type of wire saw), machined to improve flatness, chemically etched to remove crystal damage from machining steps and finally polished to form wafers. Donor impurity atoms, such as boron or phosphorus in the case of silicon, can be added to the molten intrinsic material in precise amounts in order to dope the crystal, thus changing it into an extrinsic semiconductor of n-type or p-type. In this process, a cylindrical ingot of high purity monocrystalline semiconductor, such as silicon or germanium, called a boule, is formed by pulling a seed crystal from a melt. One process for forming crystalline wafers is known as the Czochralski method, invented by Polish chemist Jan Czochralski. Nearly defect-free single crystalline material, with a purity of 99.9999999% ( 9N) or higher.

The mean time between successive collisions in (d) is an average over the entire history of each electron, while the mean time between the last and next collision in (c) is an average over all electrons at a specific moment in time.See also: Boule (crystal) The Czochralski method

This is not inconsistent with the result in (d) because the two quantities represent different averages. (e) Part (c) implies that at any moment the time $T$ between the last and next collision averaged over all electrons is $2 au$. This integral is the same as the one in part (c), so the mean time between successive collisions is also $ au$. (c) Show as a conscquence of (a) that at any moment the mean time back to the last collision dt$ (b) Slrow that the probability that the time interval between two successive collisions of an electron falls in the range between t and t+d t is (d t / τ) e^-t, n. Show that it will have no collision during the next t seconds with the same probability. (a) Show that an electron picked at random at a given moment had no collision during the preceding t seconds with probability e^-lit. SOLVED:Poisson Distribution In the Drude model the probability of an clectron suffering a collision in any infinitesimal interval dt is just d t / τ.

Electron 25.3.2 free