1. Chemical Bond in Metals and Semiconductors
It must explain:
Brightness
Thermal and electrical conductivity.
Malleability
These properties are connected with the electronic mobility
Valentim Nunes, Engineering Unit, Chemical Section, February, 2018

2. Electrical Conductivity
Metals — conductivity decreases with temperature.
Semiconductors — increases with temperature
Isolators — conductivity is extremely low.

3. Bands Theory
The basic idea behind the description of the electronic structure of solids is that the valence electrons are spread trough the entire solid structure.
~1023 atoms !
Theory of bands for conductivity ― delocalized electrons move freely trough bands formed by the sobreposition of molecular orbitals.

4. Comparisation of the energetic band gap betwen the valence and conduction bands in a metal, semiconductor and isolator

5. One chemical bond per each Be atom
Beryllium and MO
2000 MOs
1500 MOs
empty
Pi*
empty
1500 MOs pi
MOs mixes
2000 MOs
Semi filled s *
500 MOs
filled
500 MOs s
1000 atoms of Be -->
1000 MOs from s orbitals
One chemical bond per each Be atom
and
3000 MOs from p orbitals
1000 pairs of e-

6. These results in 3/2 bonds per Al atom
Aluminum and MO
2000 MO
Using 1000 atoms of Al we obtain 4000 MO
We have 3000 e- or 1500 pairs
These fills 3/4 of the energy levels.
1.5 pairs per Al atom
These results in 3/2 bonds per Al atom

7. Silicon and MO Considering 1000 atoms of Si 4000 e- or 2000 pairs
2 pairs per Si atom
Band completely filled
2 bonds per Si atom

8. Enthalpy of vaporization
∆H of vaporization (or atomization) its a good measure of the strength of bonds in solids.
M(s) ---> M(g)
Higher values of ∆H for transition metals indicates the participation of d orbitals.

9. Enthalpy of Vaporization

10. Fermi Level the HOMO at T = 0 is the Fermi level.
At T > 0, electrons near the Fermi level can be promoted for empty levels.
These e- are mobile and moves under the application of na electrical field.
These promotion origins e- in higher levels and “holes” in the lower levels.
Band gap
Fermi
level
In metals the bonding and anti bonding levels mixes
The band gap disappears

11. Electrical Conductivity
Conduction Band
Filled Levels + e-
Empty levels
energy
Valence band

12. Electrical Conductivity
Metallic Conductivity Decreases with the increasing in T.
The ability of e- to move along the solid depends on the uniformity of atomic spatial distribution.
The increasing in vibration causes rupture of the crystalline web.
Then, higher T implies lower conductivity.

13. Isolators
Few e- from the valence band have enough energy to move for the conduction band.
6 eV in diamante
Valence band is complete

14. Semiconductors Elements of Group 4A C (diamante) is an isolator.
Si, Ge, and grey Sn are semiconductors
Diamante structure is particularly favorable for the isolator or semiconductor behavior.
White Sn and Pb are metals.

15. Band Theory & Semiconductors
Semiconductors have a band structure similar to isolators but the energy gap is lower.
Gap = 0.5 a 3.0 eV
At least a few electrons have enough thermal energy to be promoted to an empty band.

16. Band Theory & Semiconductors
Conduction band
Electrons can be thermally promoted.
At high temperature more electrons are promoted. e- e- e-
Small gap + + +
Valence band

17. Intrinsic Semiconductors
Group 4A Band gap (eV) C Si Ge
Sn (>13 ˚C)
Sn (white) (<13 ˚C) 0
Lead 0
conduction band e- e- e-
Energy gap + + +
Valence band

18. Extrinsic Semiconductors
Conductivity is controlled by traces (~5x10-6) of dopants like Ga (or Al) or As
The dopant atom takes the place of the Si atom.
The dopant atom has less one e- than Si (= Ga or B) or one more electron than Si (= As or P).

19. Semiconductors of type n Semiconductors of type pSi
[Ne]3s23p2
Semiconductors of type n
Semiconductors of type p
donor impurities
Acceptor impurities P B
[Ne]3s23p3
[Ne]3s23p1

20. Semiconductor Type-p Accepting level is higher than the Fermi level.
Electrons are easily promoted to the acceptor level.
Conduction band e- e- e-
1.1 eV
Acceptor level + + +
Valence band

21. Semiconductor Type-n As — has 5 e- then we have one extra e-.
Electrons are promoted to the donor level from the conduction band.
The electrons are the charge carriers.
Conduction band e- e- e-
Donor level
1.1 eV
Valence band