What Is an Intrinsic Semiconductor
A semiconductor is a material whose forbidden energy gap between the top of the valence band and the bottom of the conduction band is finite but small, $E_g < 3\ \text{eV}$. An intrinsic semiconductor is simply a chemically pure such material, containing no deliberately added impurity. The two most important examples for NEET are pure silicon and pure germanium, both tetravalent elements from group IV of the periodic table.
In a pure crystal the electrons are all tightly held in the crystalline structure, so at low temperature there are essentially no free carriers and the material behaves like an insulator. Its ability to conduct, when it conducts at all, arises entirely from thermal effects on its own atoms — never from impurities. This distinguishes it from the doped, or extrinsic, semiconductors studied next, whose conductivity is engineered by adding dopant atoms.
The intrinsic case is the baseline. Understanding how a perfectly pure lattice manages to conduct at all — and why so feebly — is what makes the dramatic effect of doping intelligible later. NCERT §14.3 develops this picture through the lattice geometry, the broken bond, and the resulting pair of mobile charges.
| Property | Carbon (C) | Silicon (Si) | Germanium (Ge) |
|---|---|---|---|
| Crystal structure | Diamond-like | Diamond-like | Diamond-like |
| Valence electrons | 4 | 4 | 4 |
| Lattice spacing $a$ | 3.56 Å | 5.43 Å | 5.66 Å |
| Bonding electrons lie in | 2nd orbit | 3rd orbit | 4th orbit |
| Behaviour at room T | Insulator | Semiconductor | Semiconductor |
All three elements share the same diamond-like geometry, but their bonding electrons sit in different orbits. The energy required to free an electron (the gap $E_g$) is highest for carbon and least for germanium, which is precisely why C is an insulator while Si and Ge conduct slightly at room temperature (NCERT Example 14.1).
Covalent Bonding in Si and Ge
Each Si or Ge atom is surrounded by four nearest neighbours in the diamond-like structure. Having four valence electrons, every atom shares one of its electrons with each neighbour and, in turn, takes a share of one electron from each of them. The shared electron pairs are the covalent bonds (valence bonds). The two electrons in a bond can be pictured as shuttling back and forth between the two atoms, holding them together strongly.
At low temperature this bonding is complete: every electron is locked into a bond and none is free to move. The idealised two-dimensional picture below shows this perfect, all-bonds-intact state. In this condition the crystal can carry no current, and so an intrinsic semiconductor at low temperature is an insulator.
Thermal Generation of Electron–Hole Pairs
As the temperature is raised above absolute zero, thermal energy becomes available to the bonding electrons. A small fraction of bonds receive enough energy to break, and the electron concerned leaves its bond to roam the crystal as a free conduction electron carrying charge $-q$. Crucially, the place it left behind is not neutral. The neighbourhood from which the electron departed now has a net effective charge of $+q$.
This vacancy with effective positive charge is called a hole. It behaves as an apparent free particle of charge $+q$. So a single act of bond-breaking produces two mobile charge carriers at once: one free electron and one hole. This paired creation is the central fact of the intrinsic semiconductor, and it is what the NIOS text emphasises when it states that "electrons and holes are always generated in pairs."
A hole is not a stray proton or a real positive particle
The hole is only the absence of an electron in a covalent bond, treated as a particle with effective charge $+q$. It is a bookkeeping device for the motion of bound electrons, not a new fundamental particle. Examiners exploit this by asking what "carries" the positive charge — the answer is the vacancy, not a proton.
A free electron and a hole are born together; the hole is the empty bond left behind, behaving as $+q$.
Why $n_e = n_h = n_i$
Because each freed electron leaves behind exactly one hole, the number of free electrons must always equal the number of holes in a pure semiconductor. There is no other source of either carrier: no impurity adds a spare electron, and no impurity steals one to make an extra hole. Thus
$$n_e = n_h = n_i$$
where $n_i$ is called the intrinsic carrier concentration (NCERT Eq. 14.1). The symbol $n_i$ stands for the common value of the electron and hole concentrations and depends only on the material and its temperature. For germanium at room temperature (300 K), NIOS quotes an intrinsic carrier concentration of about $2.5\times10^{19}\ \text{m}^{-3}$ electron–hole pairs — a very large absolute number, yet minuscule compared with the density of atoms in the crystal, which is why the conductivity is so small.
In a sample of pure germanium at 300 K, the electron concentration is measured as $2.5\times10^{19}\ \text{m}^{-3}$. What is the hole concentration, and what is the intrinsic carrier concentration?
The sample is intrinsic (pure), so generation occurs strictly in pairs and $n_e = n_h = n_i$. Hence the hole concentration is also $n_h = 2.5\times10^{19}\ \text{m}^{-3}$, and the intrinsic carrier concentration is $n_i = 2.5\times10^{19}\ \text{m}^{-3}$. No separate calculation is needed — the equality is forced by the pairwise creation of carriers.
Hole Motion and the Total Current
Semiconductors possess a property metals lack: not only electrons but also holes move and carry current. The motion of a hole is a convenient way of describing the actual motion of bound electrons whenever there is an empty bond somewhere in the crystal. Suppose a hole sits at site 1. An electron from a neighbouring covalent bond at site 2 may jump into the vacant site 1. After this jump the bond at site 1 is complete again, but site 2 now has the vacancy — the hole has apparently moved from site 1 to site 2.
Note that the originally freed conduction electron plays no part in this process; it travels independently. Under an applied electric field the free electrons drift toward the positive terminal, giving an electron current $I_e$, while the holes drift toward the negative terminal, giving a hole current $I_h$. The two carrier types move in opposite directions, but because they carry opposite charges, both currents add in the same sense. The total current is
$$I = I_e + I_h$$
Holes move opposite to free electrons — but it is electrons that physically move
Under an electric field the free electrons travel toward the positive terminal and the holes "travel" toward the negative terminal, so the two carriers go in opposite directions. The physical motion behind hole current is still a chain of bound electrons hopping into vacancies — the hole itself is not an object that moves. Conventional current is taken in the direction the holes move.
$I = I_e + I_h$: opposite-direction carriers, opposite charges, currents add.
The whole point of doping is to make $n_e \ne n_h$ on purpose. See how a few ppm of impurity transforms conduction in Extrinsic Semiconductor.
Generation, Recombination, Equilibrium
Bond-breaking (generation) is not the only process at work. The reverse process, recombination, also occurs continuously: a free electron, in its wandering, can collide with a hole and drop back into the vacant bond. When this happens the electron–hole pair simply disappears, removing one electron and one hole from the pool of carriers at the same time.
At a fixed temperature the crystal reaches thermal equilibrium, in which the rate of generation of electron–hole pairs equals the rate of recombination. This balance fixes the carrier population: $n_i$ stays steady at any given temperature, even though individual pairs are constantly being created and destroyed. Raising the temperature shifts the balance toward more pairs and therefore a higher $n_i$.
| Process | What happens | Effect on carriers |
|---|---|---|
| Generation | Thermal energy breaks a covalent bond | Creates one electron + one hole |
| Recombination | A free electron falls into a hole on collision | Removes one electron + one hole |
| Equilibrium | Generation rate = recombination rate | $n_e = n_h = n_i$ stays constant at fixed T |
Band Picture and Temperature Dependence
The same physics reads cleanly in the energy-band language. At $T = 0\ \text{K}$ the valence band is completely full and the conduction band is completely empty, separated by the small gap $E_g$. With no electrons in the conduction band, the intrinsic semiconductor behaves as an insulator. At $T > 0\ \text{K}$, thermal energy excites some electrons across the gap into the conduction band, leaving an equal number of holes in the valence band — exactly the paired creation seen in the bond picture.
The number of carriers thus rises steeply with temperature: hotter crystal, more broken bonds, more electron–hole pairs. Because conductivity grows with the number of available carriers, the conductivity of an intrinsic semiconductor increases with temperature and its resistivity decreases. NIOS captures this by saying that semiconductors have a negative temperature coefficient of resistance — the opposite of metals, whose resistance rises with temperature.
Semiconductor resistance falls when heated — unlike a metal
In a metal the carrier number is fixed, so heating only increases scattering and the resistance rises. In an intrinsic semiconductor heating creates more carriers, so conductivity rises and resistivity falls. Statements like "conductivity of a pure semiconductor decreases on heating" are deliberately wrong distractors.
More heat → more electron–hole pairs → higher conductivity → negative temperature coefficient of resistance.
Intrinsic Semiconductor in One Glance
- Pure Si or Ge with the diamond-like structure; each atom shares its four valence electrons in covalent bonds with four neighbours.
- At low temperature all bonds are intact and the crystal behaves as an insulator.
- Thermal energy breaks a bond, freeing an electron $(-q)$ and leaving a hole $(+q)$ — carriers are always created in pairs.
- Carrier balance: $n_e = n_h = n_i$, the intrinsic carrier concentration; for Ge at 300 K, $n_i \approx 2.5\times10^{19}\ \text{m}^{-3}$.
- Total current $I = I_e + I_h$; electrons and holes drift in opposite directions, currents add.
- Generation is balanced by recombination at equilibrium, keeping $n_i$ steady at fixed T.
- Conductivity rises with temperature; intrinsic semiconductors have a negative temperature coefficient of resistance.