# 3. Silicon: General Properties and Technologies

## 3.1 General Properties

### 3.1.1 Conductivity, Lifetime and Lattice Defects

General Remarks

 Silicon is by far the most common semiconductor used for all kinds of products; it accounts for more than 90% (my estimate) of semiconductor products (measured in kg or \$; whatever). It is also by far the most perfect semiconductor in terms of crystalline perfection, the cheapest in its field of applications if you consider value for money, and perhaps the best understood. There are, however, plenty of questions concerning the properties of Si that are not well understood and thus there is plenty of research opportunity and enough room for new uses of the good old Si. Most of the basic properties of Si were already covered in the illustrations to the preceding chapter. Here only a short summary will be given.
The intrinsic conductivity is governed by the band gap which determines the carrier density. The resistivity, in turn, is given by carrier density times mobility. It should thus be possible to give precise values.
However, upon closer inspection it turns out that not only carrier mobilities are temperature dependent, but the band gap, and the effective masses, too. That makes precise calculations difficult. We have, e.g.
Eg(300 K)=1,1242 eV
Eg(0 K)=1,1700 eV.
Measurements, while always possible, must allow for non-perfection - there is no such thing as an perfect intrinsic semiconductor. With lots of precautions, it is possible to grow crystals with a resistivity (at room temperature) of about 1 000 Wcm - still far lower than the intrinsic value.
This should motivate a little exercise:
 Exercise 3.1.1 What is perfection?
All in all, the precise temperature dependence of truly intrinsic Si is not so interesting anyway - because we never encounter it.
What is interesting are some basic numerical values:
Bandgap (indirect) Eg(300 K)=1,1242 eV
Effective density of states (conduction band) 3,22 · 1019 cm–3
Effective density of states (valence band) 1,83 · 1019 cm–3
Intrinsic carrier density ni (300K) 1,3 · 1010 cm–3
Intrinsic mobility of electrons (300K) ca. 1400 cm2/Vs
Intrinsic mobility of holes (300K) ca. 500 cm2/Vs
Lifetime (max). 1 ms ( für » 100 Wcm)
Density 2.33 g/cm–3 » 5 · 1022 atoms/cm–3
Surface density
 11.8 9.6 6.8 ö ÷ ø × 1014 atoms cm2 æ ç è on {111} on {110} on {100}

Conductivity and Initial Doping

As stated above, it is not easy to produce Si with a conductivity close to the intrinsic limit.
Si wafers commercially available therefore have resistivities r £ 100 Wcm (at room temperature); if you want something better than that you have to negotiate with the supplier.
An example for what is on the market can be found in the link.
At the other end, large conductivities, obtained by heavy doping, are limited by the maximum solubility of the dopants. The term "solubility" refers to the (temperature dependent) equilibrium concentration of impurity atoms that can be incorporated into a crystal as single atoms.
For concentrations higher than the solubility limit, the surplus impurity atoms would tend to precipitate - and precipitates of As, B, or P, while possibly introducing defect levels in the band gap, are not active as dopants.
The highest achievable meaningful doping levels are thus given by the highest solubility of a doping element (always at a high temperature) - provided it can be kept in solid solution. This means that precipitation must be suppressed because at room temperature the solubility is usually low.
The picture below shows solubility data for the common Si dopants. In all cases the solubility is rather large (with a maximum between 1200 oC and 1400 oC), and may surpass the 1% level.
If the maximum concentration could be kept in solid solution while the crystal is grown, the resistivity could be lower than what has been listed above. However, this is neither feasible nor sensible. Making devices always involves some heating, and if dopants are present in a high supersaturation, precipitation may start during processing, leading to all kinds of unwanted effects besides the unavoidable change in conductivity.
There is, however, no particular need for high doping levels and a high precision of doping. Making devices always means that local doping is optimized -e.g. while making a source/drain area - and this requires medium to low doping levels of the substrate which are easily achieved.
High doping is only important if the wafers are used as substrate for epitaxial layers, and then the exact doping level is not crucially important.
The real importance of the solubility curves thus is in specifying how much doping can be achieved on top of the initial doping by e.g. diffusion or ion-implantation. This will of course depend on the temperature!
Ion implantation done at room temperature thus always needs an annealing step to "activate" the dopants, i.e. to dissolve them in the Si up to the solubility limit at the chosen temperature. At the same time, this high temperature process also (hopefully) "anneals" the lattice defects produced by ion implantation.
There are limits to defect annealing, too: High doping levels change the average lattice constant - especially the small B ion reduces this parameter. Heavily B-doped layers thus want to contract, and since this is not possible on top of a solid substrate, mechanical stress is introduced which may lead to the formation of so-called "misfit dislocations" - the link shows an example.

Silicon is an indirect semiconductor, we expect relatively large lifetimes and diffusion lengths.
This is indeed the case, lifetimes as large as 1 ms can be observed in extreme cases (This is an exceedingly long time for an electron!)
The corresponding diffusion length approach mm; again a very large distance for an atomic particle.