1. Impurities & Defects, Continued More on Shallow Donors & Acceptors

2. More on Shallow Donors & Acceptors
As we’ve discussed, usually, semiconductors can relatively easily be doped with shallow donors and/or acceptors.
Doping  Incorporation of (substitutional) impurities into a semiconductor in order for it to have certain desired electrical (or other) properties. That is, doping is the process of purposely introducing impurities into the material in a controlled manner. This is done because
Impurities can drastically alter the material conductivity so that it can be useful in a device.

3. Extrinsic Semiconductors.
Impurities can drastically alter the material
conductivity so that it can be useful in a device.
Materials which have been doped in this way are called
Extrinsic Semiconductors.
We’ve already discussed the fact that impurity atoms can be either
Substitutional Impurities:
Foreign atoms occupying host atom sites. OR
Interstitial Impurities:
Foreign atoms “squeezed” between lattice sites.
Here, we focus on substitutional impurities only!

4. What happens to the 5th valence electron?
Donors
Use silicon (Si) as an illustration:
Consider substitution of one Si (Group IV) atom with a Group V atom (e.g. As or P)
Si atoms have 4 valence electrons which participate in the sp3 covalent bonding.
Group V atoms have 5 valence electrons.
When a Group V atom replaces a Si atom, it uses 4 of its valence electrons to form sp3 covalent bonds with it’s 4 Si nearest-neighbors.
What happens to the 5th valence electron?

5. Semiconductors doped by donors are called n-type materials.
Single Donor in the
Direct Lattice picture
The 5th valence electron will not be very tightly bound to it’s Group V
atom “parent”. So, it can be fairly
easily ionized at temperatures T > 0K
In the lattice picture, that ionized electron is “almost free”, so it can relatively easily take part in conduction. In the band structure, this electron is in the conduction band.
Group V impurities are called Donors, since they “donate” electrons to the material. Because of these extra (negatively charged) electrons:
Semiconductors doped by donors are called n-type materials.

6. “Effective Hydrogen Atom”.
Donor Energy Levels
Single donor in the
band picture
From the energy band viewpoint, such impurities “create” energy levels in the band gap, close to conduction band edge.
As we’ve already discussed, the extra electron from a donor can be treated as an
“Effective Hydrogen Atom”.

7. “Effective Hydrogen Atom”
Donor Energy Levels
Single donor in the
band picture
A donor as an
“Effective Hydrogen Atom”
It is a positive charge with a single electron within its Coulomb potential. Such impurities are called HYDROGENIC Donors.
Their energy levels are called “shallow” levels because they are very close to the conduction band edge. So, the energy required to ionize the “atom” is small.
Further, a sizable fraction of donor atoms will be ionized at room temperature.

8. Donor Levels: Summary A single donor in the lattice & band
pictures. These are
complementary
pictures & both
are valid.

9. in the Lattice &Band Pictures Again.
Single Donor
in the Lattice &Band Pictures Again.

10. Cartoon of a Si crystal doped with a pentavalent
(Group V atom) impurity.
The almost free electrons in n type silicon support
the flow of current.

11. Hydrogenic Donors “Effective Hydrogen Atom”.
As a first approximation to calculating donor energy levels, treat the problem as an
“Effective Hydrogen Atom”.
Take the energy zero of energy at the bottom of the conduction band.
Substitute the conduction band effective mass for the electron mass.
Screen the Coulomb potential by the dielectric constant κ of the solid
(dielectric constant of free space, κ = 1)
It is important to note that, in this model,
all donor impurities have the same energy levels!

12. Hydrogenic Donors

13. Examples Ge: me* = 0.04m0; κ = 16  ED = -2.1 meV (1 meV = 10-3 eV)
GaAs: me*= 0.067m0; κ = 13  ED = -5.4 meV
Si: me* = 0.26m0; κ =  ED = -25 meV
ZnSe: me* = 0.21m0; κ =  ED = -35 meV

14. Acceptors
Again use silicon (Si) as an example
Substitute one Group III atom (e.g. Al or In) for a Si (Group IV) atom
Si atoms have 4 valence electrons that participate in the covalent bonding
When a Group III atom replaces a Si atom, it cannot complete a tetravalent bond scheme.

15. Acceptors At T = 0 K this hole “stays” with atom – localized hole
When a Group III atom replaces a Si atom, it cannot complete a tetravalent bond scheme.
An “electronic vacancy” – hole – is formed when an electron from the valence band is grabbed by the atom so that the core is negatively charged, the hole created is then attracted to the negative core
At T = 0 K this hole “stays” with atom – localized hole
At T > 0 K, electron from the neighboring Si atom can jump into this hole – the hole can then migrate & contribute to the conductivity.

16. Acceptors: Accept electrons, but “donate” free holes
At T > 0 K, an electron from a neighboring Si atom can jump into this hole – the hole starts to migrate, contributing to the current
We can say that this impurity atom accepted an electron, so we call them
Acceptors:
Accept electrons, but
“donate” free holes

17. By “incorporating” the electron into the impurity atom we can represent this (T = 0 K) as a negative charge in the core with a positive charge (hole) outside the core attracted by its Coulomb potential.
At T > 0 K this hole can be ionized. Such materials are called p-type semiconductors since they contribute positive charge carriers

18. Acceptor Energy Levels
From the Band Structure Viewpoint:
Such impurities “create” energy levels within the band gap, close to the valence band. They are similar to “negative” hydrogen atoms Such impurities are called hydrogenic acceptors. They create “shallow” levels - levels that are very close to the valence band, so the energy required to ionize the atom (accept the electron that fills the hole and creates another hole further from the substituted atom) is small

19. Single Acceptor in the lattice & band pictures.
The 2 pictures are
complementary.
Both are valid.

20. The holes in p type silicon contribute to the current.
This crystal has been doped with a trivalent impurity.
The holes in p type silicon contribute to the current.
Note that the hole current direction is opposite to the electron current so the electrical current is in the same direction

22. Examples
Since holes are generally “heavier” than electrons, the acceptor levels are deeper than the donor levels.
The valence band has a complex structure & this formula is too simplistic to give accurate values for acceptor energy levels

23. Acceptor energy levels
Examples
Acceptor energy levels
Ge: 10 meV
Si: 45 – 160 meV
GaAs: 25 – 30 meV
ZnSe: 80 – 114 meV
GaN: 200 – 400 meV
Acceptor and donor impurity levels are often called ionization energies or activation energies

24. Doped Semiconductors
p-type
n-type