1. PDT 264 ELECTRONIC MATERIALS
TOPIC 5:
FUNDAMENTAL SEMICONDUCTORS
(Part 1)

2. Syllabus Introduction to semiconductor Intrinsic semiconductor
Extrinsic semiconductor
Temperature dependence of conductivity
Recombination & minority carrier injection
Diffusion & random motion
Optical absorption
Schottky Junction
Ohmic contact 2

3. Introduction to Semiconductors
Develop basic understanding of the properties of intrinsic and extrinsic semiconductors
Crystal of Si consists perfectly bonded Si atoms in a diamond structure
At temperature > absolute zero (0K), Si atoms in the crystal lattice will vibrate
Few lattice vibration has sufficient energy to rupture the Si-Si bond
When Si-Si bond is broken, a free e- is created
e- can wander around crystal & contribute to electrical conduction in presence of applied field

4. Intrinsic semiconductors
The vacancy left by the missing e- is called a hole.
e- from neighbouring atom can readily tunnel into hole.
Causing hole to be displaced to the original position of the tunnelling e-
So, hole is also free to move around crystal & contribute to the electric conduction in presence of applied field
Intrinsic semiconductors
No impurities added
Number of thermally generated e- = number of holes
Extrinsic semiconductors
Impurities are added to semiconductors that contribute either excess holes/excess e-
Numbers of e- and holes are not equal
E.g.: n-type Si and p-type Si

5. INTRINSIC SEMICONDUCTOR

6. Silicon Crystal & Energy Band Diagram
Electronic configuration of Si atom: [Ne] 3s2 3p2
3s and 3p energy level is too close
Their interaction causes 4 orbitals (ψ3 s), (ψ 3p x), (ψ 3p y) and (ψ 3p z) mixed together to form 4 new hybrid orbitals (ψ hyb )
Hybrid orbital of one Si atom can overlap with a hybrid orbital of neighboring Si atom to form covalent bond.

7. Each Si-Si bond corresponding to a bonding orbital , ψ b
One Si atom bonds with 4 other Si atoms by overlapping the half-occupied hybrid orbitals - fig. (b)
Each Si-Si bond corresponding to a bonding orbital , ψ b
Each bonding orbital has 2 spin-paired e- (full).
Neighbouring Si atoms can form covalent bond with other Si atoms, forming 3D network of Si atoms (diamond structure)

8. A two dimensional pictorial view of the Si crystal showing covalent bonds as two lines where each line is a valence electron.

9. Valence band (VB)
Fig. (c) - energy band of Si crystal at absolute zero temperature (0K).
Valance band (VB)
Contains electronic states correspond to the overlap of bonding orbitals.
All bonding orbitals are full with valence e-, so VB is full with valence e- at 0K

10. Bandgap – energy gap Eg separating CB and VB
Conduction Band (CB)
Contains electronics states that are higher energies (corresponding to the overlap of antibonding orbitals)
CB is empty at 0K.
Bandgap – energy gap Eg separating CB and VB
Electron affinity, X – energy distance from Ec to the vaccum level = width of CB
(solid state physic definition)

11. Electrons and Holes
The only empty electronic states in the silicon crystal are in CB
e- in CB are free to move around crystal & respond to an applied electric field
e- in CB can easily gain energy from the field and move to higher energy levels, because these states are empty
As CB is empty, we need to excite e- into CB from VB.
 The excitation of e- from VB to CB requires a minimum energy of Eg

12. Electron -hole pair generation :
1. When a photon of energy hv > Eg is incident on an e- in VB
e- absorbs incident photon & gain sufficient energy to surmount Eg & reach CB.
A free e- & a hole are created
In some semiconductors (Si & Ge), photon absorption also involves lattice vibrations.

13. Atoms in crystal are constantly vibrating
2. In the absence of radiation, there is an electron hole generation process as the result of thermal generation
Due to thermal energy
Atoms in crystal are constantly vibrating
In certain region, the bond between Si atoms becomes overstretched
The overstretched bind ruptures & releases e- into CB

14. The free e- in CB wander around crystal & contribute to the electrical conduction when an electric field is applied
Remaining region around hole in VB is positively charged
Hole (h +) can also wander around the crystal as if it were free (Fig. a-d)
Because e- in neighbouring bond can jump into the hole to fill the vacant electronic state at this site & create a hole at its original position.
Ehen an electric field is applied, hole will drift in the direction of field & conduct electric.
So there are 2 types of charge carriers – electron & hole

15. When wandering e- in CB meets a hole in the VB, e- occupies the hole (because of empty state of lower energy)
e- falls from CB to VB to fill the hole (Fig. e-f)
This is called recombination
Results in the annihilation of an e- in the CB and hole in VB
The excess energy of the e- falling from CB to VB is emitted as photon (e.g GaAs & InP) or lost as lattice vibration (heat) (e.g Si and Ge)

16. Electron-hole pair generation & Recombination process16
Electron-hole pair generation & Recombination process e- h+ CB h+ h+ h+
(a) E
(d) g VB + h+ h e- e— h+ h+
(b)
(e) e- h+ h+
(c)
(f)

17. Conduction in Semiconductor
When an electric field is applied across a semiconductor, energy bands bend

18. All energy levels and energy bands must tilt up in x direction in presence of applied field.
Under the action of electric field, Ex:
e- moves in opposite direction to electric field
e- in CB moves to left and immediately starts gaining energy from the field
When e- collides with thermal vibration of a Si atom, it loses some energy & thus falls down in energy in the CB.
After collision, e- starts to accelerate again, until next collision and so on.
This process is drift of electron in an applied field.

19. ySimilarly, 

20. yConductivity of a semiconductor:
ySince both electrons & holes contribute to electrical conduction
 envde  epvdh
e = electron charge = C n = electron concentration in CB
p = hole concentration in VB vde = drift velocity of electrons vdh = drift velocity of holes
vde =   
yConductivity of a semiconductor:
  

21.  h2        2m kT N  2    Electron Concentration in CB
 
n = electron concentration in the CB, Nc = effective density of states at the CB edge, Ec = conduction band edge, EF = Fermi energy, k = Boltzmann constant, T = temperature
Effective Density of States at CB Edge
 
3 / 2
2m kT *
N  2 e h2  c
 
Nc = effective density of states at the CB edge, m * = effective mass of the electron e

22. Effective Density of States at VB Edge
Hole Concentration in VB    
 
p = hole concentration in the VB, Nv = effective density of states at the VB edge, EF
= Fermi energy, Ev = valence band edge, k = Boltzmann constant, T = temperature
Effective Density of States at VB Edge
 
3 / 2
2m kT *
N  2 h h2  v
 
Nv = effective density of states at the VB edge, mh* = effective mass of a hole in the VB, k = Boltzmann constant, T = temperature, h 3 O D Q F N ¶ V

23.         Product of n & p (np) Eg = Ec E v
       
Eg = Ec E v
ynp product is a constant that depends on the material properties Nc, Nv, Eg, and the temperature

24. Mass Action Law         
yFor intrinsic semiconductor , n = p, which is denoted as ni (intrinsic concentration )
yni represents free e- and hole concentrations in intrinsic materials
ySo,
  
      

26. yWhen e- and hole meet in the crystal, they recombine
yWhen e- and hole meet in the crystal, they recombine . yRate of recombination (R) is proportional to numbers of e- and holes. 
ySimilarly, rate of generation (G) will depend: 
  
     

27. Tyhus, in semiconductor, we have:

28.                                  
yConsider an intrinsic semiconductor, n = p = ni
ySet p = ni     
   
    
 
yThis leads to Fermi Energy in Intrinsic Semiconductors
 
  
 
 
EFi = Fermi energy in the intrinsic semiconductor, Ev = valence band edge, Eg = Ec - Ev is the bandgap energy, k = Boltzmann constant, T = temperature, Nc = effective density of states at the CB edge, Nv = effective density of states at the VB edge
 
  
 
  28
m * = electron effective mass (CB), m * = hole effective mass (VB)
e h

29. yIf n > p, the semiconductor is called n-type semiconductor
    29

30. Average Electron Energy in CB
E  E  3 kT c CB 2
E CB = average energy of electrons in the CB Ec = conduction band edge
k = Boltzmann constant
T = temperature
yThus, electron in CB has an average energy of 3kT/2 above Ec.

31. Example 1

32. Tutorial Q1
Using the density of states effective masses for electrons and hole, intrinsic concentration and drift mobility of electrons and holes in Table 5.1 below, calculate the intrinsic conductivity and resistivity of Ge at 300 K.

33. 33
Tutorial Q2
Using the density of states effective masses for electrons and hole in Table 5.1 below, determine the position of Fermi energy in intrinsic Ge with respect to the middle of the bandgap (Eg/2) at 27 C.