1. BASIC ELECTRONICS Module 1 Introduction to Semiconductors
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

2. Syllabus for module 1 Semiconductor Theory Energy bands
Classification of materials based on energy bands
Intrinsic semiconductor
Covalent bonding
Conduction in semiconductors
Doping, Extrinsic semiconductor
Conduction in extrinsic semiconductor
Drift and Diffusion current
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

3. Classification of materials
Insulators, Semiconductors and Metals
Insulator
poor conductor of electricity
Metal
good conductor of electricity
Semiconductor
conductivity lies between above two
Energy band diagram
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

4. Classification of materials
Diamond crystal (insulator)
EG ≈ 6 eV (1 eV = 1.6 × 10 –19 J)
Valence band is full, Conduction band is empty
Even with applied electric field, energy will not be sufficient to put the electrons in the conduction band, crossing the forbidden gap
Hence diamond is insulator
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

5. Classification of materials
Semiconductor
Silicon : EG ≈ 1.21 eV at 0 K (1.1 eV at 300 K)
Germanium : EG ≈ 0.79 eV at 0 K (0.67 eV at 300 K)
At 0 K, valence band is full, conduction band is empty
Si and Ge are insulators at 0 K
Conductivity increases (or resistivity decreases) with increase in temperature
Semiconductors possess negative temp coeff of resistance
At room temp and above, Si and Ge are semiconductors i.e., some electrons are present in conduction band
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

6. Classification of materials
At room temperature, some valence electrons acquire thermal energy sufficient to cross the forbidden gap
These electrons are now free to move under the influence of small electric field
Now the material begins to conduct. Hence the name semiconductor
When an electron leaves the valence band and enters conduction band, a vacancy called “hole” is created in valence band
Parent atom now has less number of negatively charged electrons than positively charged protons – ionization
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

7. Classification of materials
Metal
The valence band and conduction band overlap
Even at 0 K, conduction band has electrons
So metals are good conductors of electricity
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

8. Intrinsic Semiconductors
Semiconductors such as Si and Ge have 4 electrons (tetravalent) in the outermost shell
In crystal structure of these materials, atoms are arranged in tetrahedron structure with one atom at each vertex
Each atom contributes 4 valence electrons to the crystal; Each atom shares one electron each from its 4 neighbours, thus forming covalent bond
Because of covalent bonding, electrons are tightly bound to crystal – not available for conduction
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

9. Intrinsic Semiconductors
Bond structure of Si and Ge at 0 K Si Si Si
Covalent bond Si Si Si
Valence electrons Si Si Si
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

10. Intrinsic Semiconductors
Bond structure of Si and Ge at 300 K Si Si Si
Covalent bond Si Si Si
Hole
Valence electrons
Free electron Si Si Si
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

11. Intrinsic Semiconductors
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

12. Intrinsic Semiconductors
Free electrons are “free” to wander throughout the crystal
Hole is the absence of an electron in the covalent bond
In intrinsic semiconductor, each free electron gives rise to one hole.
Concentration of holes and free electrons are same. Denoted as ni (called intrinsic charge concentration)
Free electrons and holes are now available for conduction
A hole may get filled up by another electron liberated from another covalent bond – effective movement of hole
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

13. Intrinsic Semiconductors
Hole effectively moves in opposite direction as that of free electron
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

14. Conduction in semiconductors
Both free electrons and holes contribute to current flow
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

15. Conduction in semiconductors
Let concentration of free electrons = n
Let concentration of holes = p
In intrinsic semiconductor, n = p = ni
Current density = conductivity × electric field intensity
J = σ E (Ohm’s law)
Conductivity is given by: σ = n q μn + p q μp
= ni q (μn + μp)
μn is mobility of free electrons
μp is mobility of holes (μn > μp)
q is electronic charge = 1.6 × 10 –19 C
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

16. Conduction in semiconductors
Some properties at 300 K Ge Si
Electron mobility μn (m2/V-s)
0.38
0.13
Hole mobility μp (m2/V-s)
0.18
0.05
Intrinsic Concentration ni (m–3)
2.5 × 1019
1.5 × 1016
Intrinsic resistivity (Ω-m)
0.45
2300
Concentration of atoms in crystal (cm–3)
4.4 × 1022
5.0 × 1022
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

17. Conduction in semiconductors
Determine the conductivity and resistivity of pure germanium at 300 K. If the length of the Ge is 4 cm and cross section area is 1 cm2, then what is its resistance? If a potential difference of 5 V is applied between the two ends of semiconductor, what is the amount of current that flows?
Resistivity ρ = 1/σ
Resistance R = ρ L / A
Repeat the above calculations with silicon. L I V
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

18. Conduction in semiconductors
Velocity of charge particle = mobility × electric field
v = μE
Free electron velocity is vn = μnE
Hole velocity is vp = μpE
What is the electron velocity and hole velocity in a bar of silicon at room temperature (300 K), when an electric field of 1800 V/m is applied across it? (Ans: 234, 90 m/s)
A bar of intrinsic Ge, 6 cm long, has a potential difference of 12 V applied across its ends. If the electron velocity in the bar is 76 m/s, what is the electron mobility? (Ans: 0.38 m2/V-s)
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

19. Conduction in semiconductors
A bar of pure silicon at 300 K is applied with electric field of 500 V/m. Determine:
Component of current density in bar due to free electrons
Component of current density in bar due to holes
Total current density in the bar (Ans: 156, 60, 216 mA/m2)
A bar of silicon has cross sectional area of 3×10–4 m2. How long the bar should be in order that current in it be 1.2 mA, when 9 V is applied across its ends. (Ans: mm)
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

20. Conduction in semiconductors
As noted from previous examples, conductivity is very low
What is the reason for low conductivity?
For silicon, ni = 1.5 × 1016 m–3
atom concentration in crystal is 5.0 × 1022 cm–3
= 5.0 × 1028 m–3
i.e., approximately 3 free electrons for every 1012 Si atoms !!
For germanium, situation is only slightly better –
approximately 2 free electrons for every 109 Ge atoms !!
Concentration of free electrons, and thereby conductivity can be increased by a process called “Doping”
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

21. Doping
Addition of small percentage of foreign atoms into the crystal lattice of silicon or germanium in order to change its electrical properties is called Doping
Atoms used for doping are called “dopants”
Two types of dopants – Donors and Acceptors
Donor – Pentavalent (5 electrons in outermost shell)
Examples: Phosphorus (P), Arsenic (As),
Antimony (Sb), and Bismuth (Bi)
Donates one electron to the crystal lattice
One free electron per donor atom
Concentration of free electrons increases
Concentration of holes decreases
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

22. Doping N-type semiconductor Si Si Si Free electron Si P Si Si Si Si
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

23. N-type Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

24. Doping
Semiconductor doped with donor impurity is called N-type semiconductor, because free electrons are in majority than holes (thermally generated)
Donor energy level is just below the conduction band
Conduction band
0.05 eV (0.01 for Ge)
Donor energy level
1.1 eV
Valence band
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

25. Doping Acceptor – Trivalent (3 electrons in outermost shell)
Examples: Boron (B), Aluminum (Al),
Gallium (Ga) and Indium (In)
Accepts one electron from the crystal structure
One hole per acceptor atom
Concentration of holes increases
Concentration of free electrons decreases
Resulting semiconductor is called P-type semiconductor, because holes are in majority than free electrons (thermally generated)
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

26. Doping P-type semiconductor Si Si Si Si B Si Hole Si Si Si
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

27. Doping-p type Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

28. Doping Acceptor energy level is just above the valence band
Most valence electrons can easily jump (hop) into the hole even at lower temperatures
Conduction band
Acceptor energy level
1.1 eV
0.05 eV (0.01 for Ge)
Valence band
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

29. Charge densities
In intrinsic (pure) semiconductor, concentration of free electrons is equal to concentration of holes (n = p = ni)
In extrinsic N-type semiconductor, n >> p
In extrinsic P-type semiconductor, p >> n
Under thermal equilibrium, product of negative and positive charge concentrations is a constant, equal to square of intrinsic concentration – called law of Mass Action
n p = ni2
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

30. Charge densities
Suppose that a semiconductor is doped with both donor and acceptor impurities
Let donor atom concentration = ND
Let acceptor atom concentration = NA
After donating one free electron to the crystal structure, donor atom now has deficit of one negative charge (i.e., net positive)
Similarly, after accepting one electron from crystal structure, acceptor atom now has one extra electron (i.e., net negative)
Total negative charge concentration = n + NA
Total positive charge concentration = p + ND
Under equilibrium condition, n + NA = p + ND
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

31. Charge densities In N-type semiconductor, NA = 0. Hence n = p + ND
But n >> p. Hence n ≈ ND
Now, p = ni2/n = ni2 / ND
Similarly in P-type semiconductor, ND = 0. Hence
p = n + NA
But p >> n. Hence p ≈ NA
Now, n = ni2/p = ni2 / NA
Note: If ND = NA then, semiconductor behaves like intrinsic
If ND > NA then semiconductor is N-type
If NA > ND then semiconductor is P-type
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

32. Conduction in Extrinsic Semiconductors
A bar of silicon with intrinsic concentration of 1.5 × 1016 m–3 is doped until the hole density becomes 8.5 × 1021 m–3. The mobilities of free electrons and holes are 0.13 and 0.05 m2/Vs respectively. Determine free electron concentration and electrical conductivity. (Ans: 2.65 × 1010 m–3, 68 S/m)
How many free electrons are present in a bar of extrinsic germanium measuring 5mm×50mm×2mm, if the extrinsic hole density is 7.85×1014 m–3, given that intrinsic concentration is 2.5×1019 m-3 ? (Ans: 3.98×1017 electrons)
Determine the concentrations of free electrons and holes in p-type Ge at 300 K, if conductivity is 100 S/cm. (Ans: ?)
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

33. Conduction in Extrinsic Semiconductors
What is the current density in an extrinsic silicon whose hole density is 4.5×1018 m–3 when an electric field of 8 kV/m is applied. Given that for silicon, ni = 1.5×1016 m–3, μn and μp are 0.13 and 0.05 m2/Vs respectively. (Ans: 288 A/m2 ?)
For a pure silicon sample, indium is added at the rate of 1 atom per 2×108 silicon atoms. Find the nature of the material and charge carrier concentration given that ni= 1.5×1016 m–3 , concentration of Si atoms in the crystal is 5.0×1028 m–3.
(a) Find the conductivity of pure germanium at 300K.
(b) If donor impurity is added at the rate of 1 per 107 Ge atoms, then find the conductivity.
(c) If acceptor impurity is added at the rate of 1 per 107 Ge atoms, then find the conductivity. (Ans: 2.24, , S/m)
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

34. Drift and Diffusion currents
Drift current
Motion of charge carriers due to applied electric field
Free electrons move towards positive potential
Holes move towards negative potential
Conduction so far discussed is due to drift mechanism
Drift current densities given by:
Electron drift current density
Hole drift current density
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

35. Drift and Diffusion currents
Results due to flow of charge carriers from the region of higher concentration to the region of lower concentration
Suppose that hole-concentration varies with distance x, then concentration gradient is dp/dx
If dp/dx is negative, then it results in a current in positive x direction
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

36. Drift and Diffusion currents
Hole diffusion current density is:
Electron diffusion current density is:
Dp and Dn are diffusion constants
Diffusion constants are related to mobilities
VT is volt-equivalent of temperature
T is temperature in kelvin
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

37. Drift and Diffusion currents
So, total current density is the sum of drift current density and diffusion current density
Overall total current density due to both holes and free electrons is:
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

38. End of module 1
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA