14. E-level system of solids. Conductance.

Question 1

Define energy level system and explain related terms

Answer 1

A quantum mechanical system or particle that is bound can only take on certain discrete values of energy. This contrasts with classical particles, which can have any energy. These discrete values are called **energy levels **( → several energy levels form energy level system).

Splitting discrete energy levels into N new levels results in continuous energy bands. Energy bands are seperated by energy gaps ( → clear isolation of E levels).

_Valence band: _

highest range of electron energies in which electrons are normally present at 0 K.

Conduction band:

quantifies the range of energy required to free an e^- from its bond to an atom.

Question 2

Why are energy levels of importance? Classify and relate it to the Boltzmann distribution.

Answer 2

The physical and chemical properties depend on the energetic realations of the highest filled (valence band) and lowest empty energy level.

Thus we can distinguish between three classes of materials:

1. ​Class A1: valence band filled, Δε > 1eV to conduction band
2. Class A2: valence band filled, Δε < 1eV to conduction band
3. Class B: valance band only partially filled

Question 3

Describe the features of class A1 materials and give an example

Answer 3

Class A1 materials are also referred to as insulators. Their valence band is filled, but E_gap > 1eV

e.g. diamond

Properties:

• no conductivity
• no photon absorption in the VIS range → transparent
• ​BUT: UV = absorbed IR = excitation of lattice vibrations

Question 4

Describe the features of class A2 materials and give an example

Answer 4

Class A2 materials are also referred to as intrinsic semiconductors. Their valence band is filled, but E_gap < 1eV

e.g. Ge

Properties:

• photon absorption in the VIS range → **non-transparent → **induces conductivity (photodetectors)
• reasonable n_cond.

Question 5

Describe the features of class B materials and give an example

Answer 5

Class B materials are also referred to as metals. Their valence band is not filled.

e.g. 1-valence, 2-valence metals

Properties:

• high conductivity
• optical non-transparent

Question 6

Define conductivity

Answer 6

quantifies how strongly a given material opposes the flow of electric current

types of conductivity:

• n-type: e^- conduction
• p-type: e^--hole + charge conduction

σ = const * e^-E_gap/2kT

BUT: specific conductivity decreases with T-increase