Indeed this is a handy counter example to people who, not understanding the second law, claim that evolution is impossible on the basis that entropy decreases (nevermind that by this misunderstanding life itself would be impossible as well). The growing crystal is not a closed system: it exchanges energy and matter with the surrounding environment, and this can lead to a local entropy decrease if it is compensated by an entropy increase of the environment. The thermodynamic potential that is truly minimized, taking these exchanges into account, is the free energy. (Note that there are slightly different definitions of the free energy which apply to slightly different types of process, but they are all morally the same.)
Perhaps this wiki link of Epitaxial growth would be helpful.
While adding the impurity in the fabrication of semiconductor devices we break up the whole crystalline structure and after adding the impurity the atoms rearrange them to form a regular crystal while getting cooled.
It should be noted that making a homogeneous doped crystal is a difficult task.
You said in your question:
"In chemistry we are taught about defects i.e some of the atoms might be missing from the crystal. So, I assumed some of silicon atoms to be missing, thus impurity atoms can be thought to go and fit into those vacancies."
Well that might be the case but when we do the doping we just replace the $Si$ atoms with the impurity atoms. In fact your book also mentions this clearly:"...its atoms replace the silicon atoms here and there..."
There are a vast number of methods used for doping semiconductors. One I remember is by diffusion. In this process we place the dopant in contact with the surface of substrate and then heat the substrate. The dopants starts moving from high concentration region towards the low concentration region. I am not going into the details because the concept is very broad to wright like i skipped to explain that the diffusivity depends exponentially upon the temperature and many things more.
There are many good books on the different types of doping processes and doping concepts. I am giving you further reference which might be helpful.
- References:
1. This has always been the most recommended- "Solid State Electronic Devices"
2. Fundamentals of Semiconductor Fabrication by May, Gary S., Sze
You also said :
" how could this single impurity atom make such a difference in conductivity (in a crystal of $10^6$ silicon atoms)?"
Let's talk about 1cm cube of the crystal and see how its conductivity changes if we place $1$ impurity atom along with $10^{6}$ $Si$ atoms.
At room temperature a small fraction of $Si$ atoms is ionized. If there are say $10^{12}$ $Si$ atoms out of these only $1$ will get ionised. Also a single $Si$ atom will not ionize completely, that is all the four bonds will not break up( only 1 electron-hole pair is generated if one bond is broken). On the other hand if we add $10^{12}$ impurity atoms say phosphorus then all these $10^{12}$ phosphorus atoms will provide $10^{12}$ electrons for conduction at room temprature, that is at room temparature each $P$ atom provide 1 electron for conduction.
A solid crystal of pure $Si$ has $5 \times 10^{22}$ atoms per $c.m^3$. If all the $Si$ atoms get ionized we will get $4$ e's and $4$ h's corresponding to each $Si$ atom. In 1 c.m cube there will be $4\times 5\times 10^{22}$ electrons and $4\times 5\times 10^{22}$ holes.
Actually at a temperature $T$ the concentration of intrinsic e's is given by
$$n_i=N_ce^{E_c-E_i}/kT$$ and similarily of holes is given by $$p_i=N_ve^{E_i-E_v}/kT$$ Also $$n_ip_i={N_cN_v}e^{-E_g/kT}$$ where $N_c$ and $N_v$ are constants and $E_g$ is the band gap.
For intrinsic materials $n_i=p_i$.
The intrinsic concentration for $Si$ at room temperature is approximately $n_i=1.5\times 10^{10}\ cm^{-3}$.
So out of $20 \times 10^{22}$ electrons only $1.5\times 10^{10}$ electrons are available for conduction in one centimeter cube of the crystal.
Loosly speaking $1\ cm^{3}$ of pure $Si$ crystal contains $10^{10}$ electrons carriers.
Now let's find out how the concentration of available e's changes if we add "impurities to the pure semiconductor in a very small ratio $(1:10^{6})$".
$10^{6}$ $Si$ contains $1$ electron available for conduction(because of one $P$ existing atom between them).
$10^{6}\times 10^{16}$ $Si$ atoms contains $1 \times 10^{16}$ electrons for conduction.
$10^{22}$ $Si$ atoms contains $10^{16}$ electrons for conduction.
Loosly speaking $1\ cm^{3}$ of doped $Si$ crystal contains $10^{16}$ electron carriers.
Compare this with the pure $Si$ crystal. The carrier concentration has become $10^{6}$ times greater. This is really a drastic change in the carrier concentration which causes a drastic increase in conductivity of 1cm cube of crystal. The conductivity is proptional to the carrier concentration so the doped material has $10^{6}$ times more conductivity as compared to the pure material.
Best Answer
Don't listen anyone. It is possible, but I have to admit - hard. Otherwise, how were first mono-crystals grown?
Initially, you may buy 'pure' silicon (pure for chemical reactions, not electronics). First of all you need to make a rod. To do that you'll need form out of material which can withstand 1600C (hard part, can't name ones at the moment), and heat Si in it using induction heating.
Induction heating might be the hardest part - but there are lots of guides around. Induction heater able to melt metal is 100% doable at home.
Once you have Si rod - you need to purify it using 'zone melting' using your induction heater. Will take ages, so you might want to make motorized thing which will move rod or heater for several days/weeks.
After that your rod is polycrystalline - which is already ok for solar cells.
For Czochralski process you may reuse again your induction heater, but the hardest part is getting clean 'form' for molten Si, as silicon is ultrapure and very easy to contaminate.
Alternatively, you may get mono-crystalline or large-grain polycrystalline Si right out of your zone heating station if you would do slow pass at the end and add seed crystal. But this might be tricky a little.
If your rod in thin enough (1-3cm) you may cut it using diamond disks, sold in usual shops. Thicker rods will require larger disks (which are not easy /cheap to buy) or 'diamond wire'.
Whole process is quite complex, but will give you lots of experience working with tough things. Dealing with silicon is much harder than Steel ;-)
PS. If you would do everything except getting seed crystals, I can send you some.