Description of semiconductors Properties of Transition metal oxides

1. Inorganic Materials (2)
Doping and Band Structure
Perovskite / Rocksalt crystals
Transition metal oxides

2. DOPING OF SEMICONDUCTORS

3. Insulator and Semiconductor
The probability to find and electron in the conductor band
can be calculated as:
(For semiconductors, r.t. energy is enough to promote
electrons into the conduction band)

4. Exercise
What would be the energy gap E at room temperature where
the probability to find the electrons to 10% at the conduction
band ?
(R = 8.314 J / (mol·K) / 25oC = 273 + 25 = 298 K)
e E/RT = 1/P – 1 with P = 0.1
E/RT = ln (9) = 2.2
E = 298 K * 8.314 J/(mol K) * 2.2 = 5.45 kJ/mol
(for P= 0.5: E = 0)

5. n-doping
Add some atoms of column 5 into Si, like P (like 1%)
=> there is one more electron per P atom which can move around

6. n(egative)-doping

7. e- from P
The additional electrons from P stay in the band gap of Si
and are easily excited to the conduction band at r.t.
More free mobile electrons than fixed positive “holes”
 the Fermi level is closer to the conduction band now
Major charge carriers are electrons

8. p-doping
Element like B with only 3 electrons
In one bond 1 electron is missing
Instead of an electron moving around,
the positive charge (“hole”) of this
bond moves around, leaving behind
negative charged B anions
https://www.youtube.com/watch?v=XK0pMVwI7Ig

9. p(ositive)-doping

10. The B atoms create electron-acceptor states which are below the Fermi
Energy. Now it is easy for electrons from the valence band to go into this
acceptor state.
 We create mobile positive holes in the valence band
 Major charge carriers are the holes

11. Summary
https://chem.libretexts.org/Textbook_Maps/General_Chemistry_Textbook_Maps/M
ap%3A_Chem1_(Lower)/09._Chemical_Bonding_and_Molecular_Structure/9.11%3A
_Bonding_in_Semiconductors

12. Example:
https://is.muni.cz/el/1431/podzim2017/C7780/um/L4_band_theory.pdf

13. LED
A light-emitting diode or LED is a kind of diode that converts some of the
energy of electron-hole recombination into light.
(radiative recombination process).
When light is emitted from an LED, the photon energy is equal to the bandgap
energy.
Because of this, LED lights
have pure colors and
narrow emission
spectra

14. RELATION MO DIAGRAM - BANDS

15. Extend MO theory
Simple model: a string of 5 H-atoms
2 H-atoms can be
combined
to form 2 orbitals,
with no node and
with 1 node
For 5 H atoms we get 5 combinations
with 0, 1, 2, 3 and 4 nodes
Nodes:
0
1
2
3
4
Draw the missing 4 MO’s for H5
And find if they are :
bonding, non-bonding or
anti-bonding

18. Vector k
We can define a wavenumber for the
electrons that move in a crystal:
k = 2π/λ = 2πp/h
k is proportional to the number of the
nodes n in a molecular orbital
In a linear system with N unit cells
separated by distance a:
(MO with n nodes) λ = 2 Na/n
and k = π n / Na
At the bottom of a bond with λ = infinite: k = 0
and at the top of band with the MO having N nodes: k = π/a and λ = 2a
https://en.wikibooks.org/wiki/Introduction_to_Inorganic_Chemistry/Metals_and_Alloys:_
Structure,_Bonding,_Electronic_and_Magnetic_Properties

21. H2 in unit cell
Unit cell
with 2 el

22. • The valence band runs “uphill”
• The conduction band runs “downhill”
• The bands are narrower due to less overlap between the H2 molecules
compared to the H atoms
• The material now is not metallic anymore compared to H atom chain
• The minimum energy gap between bands occurs at k = /a
Valence band
(full of electrons)
Conduction band
(empty, anti-bonding)
https://cbc-wb01x.chemistry.ohio-state.edu/~woodward/ch754/bandstr.htm

23. Combine 5 times
2s + 2p together

24. DOS – Density 0f States
The density of states is defined as the number of orbitals per unit of energy
within a band.
Because of the parabolic relation between E and k, the density of states for
a 1D metallic crystal is highest near the bottom and top of the energy band
where the slope of the E vs. k curve is closest to zero.

25. Compare Graphite - Diamond

26. Graphite similar to benzene

27. Combination of many benzene MO’s
https://www.seas.upenn.edu/~chem101/sschem/conduction.html

29. Diamond structure
only  bonds
https://www.seas.upenn.edu/~chem101/sschem/conduction.html

30. TiO2 structure
Ti(4+) MOs
(crystal field)
Electrons in the Ti-O bonds
(coming all from O2-)

31. https://cbc-wb01x.chemistry.ohio-
state.edu/~woodward/ch754/lect2003/bandstr1_lect17.pdf

32. Photocatalysis TiO2
Light energy promotes electrons in antibonding orbitals,
leaving a positive charged “hole” in the lower orbitals

33. TM OXIDES

34. Rocksalt Structure
Metal monoxides MO

36. Example: rocksalt structure
Nonpolar:
100 layer
Polar:
111 layer

37. M-O *
M-O *

40. Perovskite Structure ABO3

41. https://cbc-wb01x.chemistry.ohio-
state.edu/~woodward/ch754/lect2003/perovskites_lect24.pdf

42. Example CaMnO3
Fill the electrons for CaMnO3 into this diagram

43. (1) Preparation of metal oxides
Molecular Synthesis Solid state synthesis
• In a solvent
• Low reaction T
(-80 to 250 C)
• Kinetic control
eg. oxidation of alcohol:
CH3CH2-OH  CH3COOH
(thermodynamic:
oxidation leads to CO2 + H2O)
• Normally solvent-free
• High reaction T
( > 300 C)
• Thermodynamic control
Solid state reaction are slow and require high temperatures because ions
have to diffuse from one crystal structure to another

45. Liquid to solid preparation – hydrothermal methods
Similar to reaction – crystallization methods in molecular reactions:
The zeolites framework is made up of SiO2 tetrahedra with the occasional
substitution of Al for Si. To compensate the charge difference (Si(+4), Al(+3))
sodium cations are accommodated on the inner surface of the framework.

46. Modification of solids by ion exchange or intercalatation

47. The existence of complex oxide phases that demonstrate good ionic
conductivity associated with the ability to vary the oxidation state of a
d-metal ion has led to the development of materials for use as the
cathode in rechargeable batteries
Charging a battery happens by removing mobile Li(+)
ions:
LiCoO2  Li(+) + CoO2 + e(-)
(what is the ox.no. of Co in each case ?)
Discharging is the opposite effect.
For practical reasons, Li atoms are intercalated into
graphite:
Example Li-ion batteries

49. (2) Characterization
49
XRD spectroscopy:
X-rays that reflect from the surface
of the sample will have travelled a
shorter distance than those x-rays
that reflect from an internal plane
of the crystal structure.
The x-rays which penetrate and
reflect from internal crystal planes
must travel an added distance
equal to an integer number (n) of
wavelengths (λ)
n = 2 d sin 

50. 50
Each crystal plane gives a signal in the spectrum
= “fingerprint” for a crystal substance
Estimate particle size from peak broadening 
and reflection angle 

51. Electron Microscopy
SEM TEM
= Scanning EM
• Record scattered electrons
• Scans the sample surface
• Produces 3D image indirectly
• Resolution 0.4 nm
= Transmission EM
• Record transmitted electrons
• Electrons goes through the sample
• Gives a 2D image directly
• Resolution 0.05 nm

52. (3) Magnetic Properties

54. Above the Curie-Temperature, a ferromagnet
becomes paramagnetic

55. Paramagnetism

59. Actually the crystal consists of 2 sub-lattices: one with spin-up, the other with spin-
down.
In SPINELS these 2 sub-lattices consist of octahedral and tetrahedral atoms with
different spin => the lattice become ferrimagnetic

60. Estimate magnetic moments in ferrimagnetic Spinels AB2O4
Due to coupling between octahedral and between tetrahedral
atoms, magnetic moments are added and correspond to
  S in the sum
(instead of   S(S+1) )

62. Examples TETRAHEDRAL spins
are opposite to
octahedral !