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

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

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.

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

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-

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

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

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.

Enthalpy of Vaporization

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

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

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.

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

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.

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.

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

Intrinsic Semiconductors Group 4A Band gap (eV) C 6.0 Si 1.1 Ge 0.7 Sn (>13 ˚C) 0.1 Sn (white) (<13 ˚C) 0 Lead 0 conduction band e- e- e- Energy gap + + + Valence band

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).

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

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

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