The question is quite simple.Why intrinsic semiconductor has less conductivity than extrinsic semiconductor? I want to know the exact doping concentration per atoms in extrinsic semiconductor relative to room temperature excited intrinsic ions.
[Physics] Intrinsic semiconductor having less conductivity than extrinsic conductor
conductorselectrical-resistanceelectronic-band-theoryelectronssemiconductor-physics
Related Solutions
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.
Sze's book 'Physics of Semiconductor Devices' has a derivation in section 1.4 (of the second edition). One finds the effective density of states in the conduction band, the effective density of states near the top of the valence band, use those to get the carrier concentrations $n$ and $p$, solve for the Fermi level by equating the two, and then use $np = n^{2}_{i}$ to relate $n_{i}$ back to the density of states (conduction and valence) and the Fermi level. The $T^{3/2}$ you are probably wondering about comes from the effective density of states in the valence band.
Best Answer
Intrinsic semiconductors have a dissociated population (a bunch of holes and electrons that separate due to temperature, and can contribute to conduction until they recombine). Because a high population of holes and electrons would cause a very FAST rate of recombination (faster than thermal generation occurs) , and a very low population of holes or electrons would cause very SLOW recombination (slower than thermal generation of pairs), it should be no surprise that at equilibrium, the fractional population of holes $ n_p$ and electrons $n_e$, is related by an equation $$constant = n_p \times n_e = n_i^2$$ where the $n_i^2$ symbolizes the at-thermal-equilibrium numbers of holes and also of electrons.
For intrinsic silicon, $$n_p = n_e = n_i$$
Doping generates a large number of (for instance) electrons, pushing $n_e$ up, and by the equilibrium equation, forces $n_p$ down. But, conduction of electricity depends on the SUM of the holes and electrons. If one has undoped material conduction is $$K \times (n_e + n_p) = K \times 2 n_i$$ but for $n_e = 100 \times n_i$ doped material, that conduction goes up to $$ K \times (n_e + n_p) = K \times 100.01 \times n_i$$
That's the basics (but holes are less mobile than electrons and the real conductivity is a messier formula).
All doped silicon has more charge carriers than if it were intrinsic (undoped). The doping level is controllable over many orders of magnitude, which allows a wide range of properties of near pure material.