KAHIBARO
Table of Contents
Purpose of Doping
Pure semiconductors are useful, but their electrical behavior becomes far more practical when we intentionally add very small amounts of impurity atoms. This process is called doping. The added atoms change the number of mobile charge carriers inside the material.
In an intrinsic semiconductor such as pure silicon, electrical conduction comes from electrons that reach the conduction band and from holes left behind in the valence band. In a doped semiconductor, the impurity atoms make it much easier to create one kind of carrier. This lets us control conductivity in a precise way.
Doping does not mean replacing a large fraction of the crystal. Usually, only a tiny number of atoms are added compared with the total number of semiconductor atoms. Even so, the electrical effect is enormous.
Doping is the intentional addition of impurity atoms to a semiconductor in order to control the concentration of charge carriers.
How Impurity Atoms Change Conduction
Silicon has four valence electrons and forms four covalent bonds with neighboring atoms in the crystal. If we place a different kind of atom into some lattice sites, the bonding is disturbed in a useful way.
If the impurity has five valence electrons, four electrons form bonds and one extra electron is only weakly bound. That extra electron can easily become a free conduction electron.
If the impurity has three valence electrons, one bond is short of an electron. This creates a vacancy in bonding, which behaves like a hole.
So doping works by introducing atoms that either donate electrons or create holes.
Donor and Acceptor Atoms
There are two main kinds of dopants.
| Dopant type | Typical valence electrons | Effect in semiconductor | Main carrier produced |
|---|---|---|---|
| Donor | 5 | Donates an extra electron | Electron |
| Acceptor | 3 | Accepts an electron, leaving a hole | Hole |
Common donor atoms for silicon include phosphorus, arsenic, and antimony. Common acceptor atoms include boron, aluminum, and gallium.
The impurity atoms create energy levels very close to the conduction band or valence band, so only a small amount of thermal energy is needed to free carriers.
n-Type Doping
When donor atoms are added, the semiconductor becomes n-type. The letter n refers to negative charge carriers, meaning electrons.
A donor atom such as phosphorus has five valence electrons. In silicon, four of them participate in covalent bonding. The fifth is weakly attached and can easily move into the conduction band. This increases the number of free electrons.
In an n-type semiconductor, electrons are the majority carriers and holes are the minority carriers.
In an n-type semiconductor, electrons are majority carriers and holes are minority carriers.
p-Type Doping
When acceptor atoms are added, the semiconductor becomes p-type. The letter p refers to positive charge carriers, meaning holes.
An acceptor atom such as boron has only three valence electrons. When it replaces a silicon atom, one bond is incomplete. An electron from a nearby bond can move to fill this missing bond, leaving behind a hole somewhere else in the crystal. That hole can move through the material.
In a p-type semiconductor, holes are the majority carriers and electrons are the minority carriers.
In a p-type semiconductor, holes are majority carriers and electrons are minority carriers.
Majority and Minority Carriers
Doping does not remove the other type of carrier completely. Thermal effects still create some electron-hole pairs. But one type becomes much more numerous than the other.
This distinction is very important in semiconductor devices. A material may conduct mainly by electrons or mainly by holes, depending on the dopant used.
| Semiconductor type | Majority carriers | Minority carriers |
|---|---|---|
| Intrinsic | Electrons and holes in equal numbers | None favored |
| n-type | Electrons | Holes |
| p-type | Holes | Electrons |
Charge Neutrality
Even though doped semiconductors contain charged carriers, the whole crystal remains electrically neutral overall. In n-type material, when a donor gives up an electron, the donor atom becomes a fixed positive ion in the lattice. In p-type material, when an acceptor captures an electron, it becomes a fixed negative ion.
The mobile carriers move through the crystal, but the ionized dopant atoms stay fixed at lattice positions.
Energy Band Picture
Doping is often understood using the band model. Donor atoms introduce donor levels just below the conduction band. Acceptor atoms introduce acceptor levels just above the valence band.
Because these impurity levels are close to the bands, carriers can be created with little energy.
In n-type material, electrons are easily excited from the donor level into the conduction band. In p-type material, electrons can move from the valence band into the acceptor level, leaving holes in the valence band.
Effect on Conductivity
Electrical conductivity depends on the number of mobile charge carriers. Doping greatly increases this number, so the conductivity rises strongly compared with an intrinsic semiconductor.
In a simple qualitative form, conductivity increases when carrier concentration increases. For electrons and holes together, the conductivity is
$$
\sigma = q \left( n\mu_n + p\mu_p \right)
$$
where $q$ is the elementary charge, $n$ is the electron concentration, $p$ is the hole concentration, and $\mu_n$, $\mu_p$ are the mobilities of electrons and holes.
In n-type material, the term $n\mu_n$ usually dominates. In p-type material, the term $p\mu_p$ usually dominates.
A key effect of doping is to increase conductivity by increasing the concentration of mobile charge carriers.
Lightly and Heavily Doped Semiconductors
The amount of doping matters. A lightly doped semiconductor has fewer impurity atoms and a moderate increase in carrier concentration. A heavily doped semiconductor has many more impurity atoms and much higher conductivity.
However, more doping is not always better. Very heavy doping can reduce carrier mobility because the extra impurity ions scatter moving carriers more strongly.
So doping involves a balance between increasing carrier number and preserving mobility.
Compensation Doping
Sometimes both donor and acceptor impurities are present in the same semiconductor. Then they partially cancel each other.
If the donor concentration is greater than the acceptor concentration, the material is overall n-type. If the acceptor concentration is greater, the material is overall p-type.
This is called compensation doping.
A simple net doping idea is
$$
N_{\text{net}} = N_D - N_A
$$
for donor concentration $N_D$ and acceptor concentration $N_A$, if $N_D > N_A$.
Or
$$
N_{\text{net}} = N_A - N_D
$$
if $N_A > N_D$.
Doping and the Fermi Level
Doping changes the position of the Fermi level. In intrinsic material, the Fermi level lies near the middle of the band gap. In n-type material, it shifts closer to the conduction band. In p-type material, it shifts closer to the valence band.
This shift reflects which carriers are more abundant.
Practical Importance
Doping is one of the central tools of semiconductor technology. By choosing the type and amount of dopant, engineers can produce materials with desired electrical properties.
This controlled modification is what makes semiconductor devices possible. Regions with different doping can be combined to create useful electrical behavior, which is the basis for later topics such as p-type materials, n-type materials, and p-n junctions.
Summary
Doping is the deliberate addition of impurity atoms to a semiconductor crystal. Donor impurities create n-type material by supplying extra electrons. Acceptor impurities create p-type material by creating holes. Doping changes carrier concentration, conductivity, and the Fermi level, while the crystal remains electrically neutral overall.
Important facts to remember:
$n$-type, donor impurities, majority carriers are electrons.
$p$-type, acceptor impurities, majority carriers are holes.
Doping controls semiconductor conductivity by controlling carrier concentration.