1. BASICS OF SEMICONDUCTOR
LECTURE 6
BASICS OF SEMICONDUCTOR
PHYSICS
Semiconductor Manufacturing Technology
It has been fifty years since the invention of the transistor. The technology behind this topic cannot be addressed adequately in a single presentation, but has been separated into four modules:
Module 1: Basic Principles
Module 2: Transistor Design and Manufacturing Overview
Module 3: Semiconductor Manufacturing Processes
Module 4: Semiconductor Economics
In this third module, we will review the key semiconductor processes, materials and equipment used to fabricate devices, and discuss process conditions and chemistry.
Praxair Semiconductor Manufacturing Technology, Module 3: Semiconductor Manufacturing Processes 1

2. Semiconductor Manufacturing Technology
It has been fifty years since the invention of the transistor. The technology behind this topic cannot be addressed adequately in a single presentation, but has been separated into four modules:
Module 1: Basic Principles
Module 2: Transistor Design and Manufacturing Overview
Module 3: Semiconductor Manufacturing Processes
Module 4: Semiconductor Economics
In this third module, we will review the key semiconductor processes, materials and equipment used to fabricate devices, and discuss process conditions and chemistry.
Praxair Semiconductor Manufacturing Technology, Module 3: Semiconductor Manufacturing Processes 1

3. Semiconductor Manufacturing Technology
It has been fifty years since the invention of the transistor. The technology behind this topic cannot be addressed adequately in a single presentation, but has been separated into four modules:
Module 1: Basic Principles
Module 2: Transistor Design and Manufacturing Overview
Module 3: Semiconductor Manufacturing Processes
Module 4: Semiconductor Economics
In this third module, we will review the key semiconductor processes, materials and equipment used to fabricate devices, and discuss process conditions and chemistry.
Praxair Semiconductor Manufacturing Technology, Module 3: Semiconductor Manufacturing Processes 1

4. DENSITY OF STATES Current is due to the flow of charge carriers
To know the number of electrons and holes in semiconductor
is important in order to calculate the current flow
Number of electrons and holes as a function of available energy levels
Based on Pauli’s exclusion principle, 1 electron per energy level
Electrons and holes concentration are calculated based on the
calculation of density of allowable energy levels or density of states
DENSITY OF STATES IS CALCULATED BY SOLVING FREE ELECTRON
IN 3-DIMENSIONAL INFINITE POTENTIAL WELL USING SCHRODINGER
WAVE EQUATION.
Semiconductor Manufacturing Technology
It has been fifty years since the invention of the transistor. The technology behind this topic cannot be addressed adequately in a single presentation, but has been separated into four modules:
Module 1: Basic Principles
Module 2: Transistor Design and Manufacturing Overview
Module 3: Semiconductor Manufacturing Processes
Module 4: Semiconductor Economics
In this third module, we will review the key semiconductor processes, materials and equipment used to fabricate devices, and discuss process conditions and chemistry.
Praxair Semiconductor Manufacturing Technology, Module 3: Semiconductor Manufacturing Processes 1

5. DENSITY OF STATES PER UNIT VOLUME OF THE CRYSTAL
________
√ E
……… (1)
g (E) = h3
Semiconductor Manufacturing Technology
It has been fifty years since the invention of the transistor. The technology behind this topic cannot be addressed adequately in a single presentation, but has been separated into four modules:
Module 1: Basic Principles
Module 2: Transistor Design and Manufacturing Overview
Module 3: Semiconductor Manufacturing Processes
Module 4: Semiconductor Economics
In this third module, we will review the key semiconductor processes, materials and equipment used to fabricate devices, and discuss process conditions and chemistry.
As the energy of this free electron becomes small, the number of
available states decreases.
Praxair Semiconductor Manufacturing Technology, Module 3: Semiconductor Manufacturing Processes 1

6. Example
Consider the density of states for a free electron given by Equation 1.
Calculate the number of states per unit volume with energies between
0 and 1 eV.
1 eV
1 eV
4 π (2m)3/2 ∫ ∫
________
N =
g (E) dE =
√ E dE h3
4 π (2m)3/2
________
. 2/3 . E3/2
N = h3
Semiconductor Manufacturing Technology
It has been fifty years since the invention of the transistor. The technology behind this topic cannot be addressed adequately in a single presentation, but has been separated into four modules:
Module 1: Basic Principles
Module 2: Transistor Design and Manufacturing Overview
Module 3: Semiconductor Manufacturing Processes
Module 4: Semiconductor Economics
In this third module, we will review the key semiconductor processes, materials and equipment used to fabricate devices, and discuss process conditions and chemistry.
4 π [ 2 (9.11 x 10-31)]3/2
__________________
N =
. 2/3 . (1.6 X 10-19) 3/2
(6.625 x10-34)3
= 4.5 x 1027 states / m3
= 4.5 x 1021 states / cm3
Praxair Semiconductor Manufacturing Technology, Module 3: Semiconductor Manufacturing Processes 1

7. STATISTICAL MECHANICS
THREE DISTRIBUTION LAWS DETERMINING THE DISTRIBUTION
OF PARTICLES AMONG AVAILABLE ENERGY STATES
MAXWELL-BOLTZMANN PROBABILITY FUNCTION
PARTICLES ARE CONSIDERED AS TO BE DISTINGUISHABLE
GAS MOLECULES IN A CONTAINER AT LOW PRESSURE
BOSE-EINSTEIN FUNCTION
PARTICLES ARE INDISTISTINGUISHABLE
BLACK BODY RADIATION
FERMI-DIRAC FUNCTION
PARTICLES ARE INDISTINGUISHABLE
ELECTRONS IN CRYSTAL
Semiconductor Manufacturing Technology
It has been fifty years since the invention of the transistor. The technology behind this topic cannot be addressed adequately in a single presentation, but has been separated into four modules:
Module 1: Basic Principles
Module 2: Transistor Design and Manufacturing Overview
Module 3: Semiconductor Manufacturing Processes
Module 4: Semiconductor Economics
In this third module, we will review the key semiconductor processes, materials and equipment used to fabricate devices, and discuss process conditions and chemistry.
Praxair Semiconductor Manufacturing Technology, Module 3: Semiconductor Manufacturing Processes 1

8. FERMI-DIRAC PROBABILITY FUNCTION
GIVES THE PROBABILITY THAT A QUANTUM STATE AT ENERGY
E WILL BE OCCUPIED BY AN ELECTRON 1
_________________
F (E) =
….. (2)
1 + exp (E – EF) / kT
k – Boltzman constant = 1.38 x J/K, T in K
Where EF is Fermi Energy, and defined as the energy where the
probability of a state being occupied is 0.5 or 50%.
Semiconductor Manufacturing Technology
It has been fifty years since the invention of the transistor. The technology behind this topic cannot be addressed adequately in a single presentation, but has been separated into four modules:
Module 1: Basic Principles
Module 2: Transistor Design and Manufacturing Overview
Module 3: Semiconductor Manufacturing Processes
Module 4: Semiconductor Economics
In this third module, we will review the key semiconductor processes, materials and equipment used to fabricate devices, and discuss process conditions and chemistry. 1 1 1
_________________
_________
_________
F (EF) = = =
1 + exp (EF – EF) / kT
1 + exp (0)
1 + 1
Praxair Semiconductor Manufacturing Technology, Module 3: Semiconductor Manufacturing Processes 1

9. DISTRIBUTION FUNCTION VS ENERGY
LET T = 0K AND E < EF 1 1
_________________
_________________ =
= 1
1 + exp (E – EF) / kT
1 + exp (-∞)
F (E < EF) = 1
LET T = 0K AND E > EF
Semiconductor Manufacturing Technology
It has been fifty years since the invention of the transistor. The technology behind this topic cannot be addressed adequately in a single presentation, but has been separated into four modules:
Module 1: Basic Principles
Module 2: Transistor Design and Manufacturing Overview
Module 3: Semiconductor Manufacturing Processes
Module 4: Semiconductor Economics
In this third module, we will review the key semiconductor processes, materials and equipment used to fabricate devices, and discuss process conditions and chemistry. 1 1
_________________
_________________ =
= 0
1 + exp (E – EF) / kT
1 + exp (+∞)
F (E > EF) = 0
Praxair Semiconductor Manufacturing Technology, Module 3: Semiconductor Manufacturing Processes 1

10. a quantum states being occupied in energy levels E1 through E4 is
Consider a system of 13 electrons with discrete energy levels as below;
At T = 0 K E5 E4 E3 E2 E1
Semiconductor Manufacturing Technology
It has been fifty years since the invention of the transistor. The technology behind this topic cannot be addressed adequately in a single presentation, but has been separated into four modules:
Module 1: Basic Principles
Module 2: Transistor Design and Manufacturing Overview
Module 3: Semiconductor Manufacturing Processes
Module 4: Semiconductor Economics
In this third module, we will review the key semiconductor processes, materials and equipment used to fabricate devices, and discuss process conditions and chemistry.
The electrons will be in the lowest energy states, so the probability of
a quantum states being occupied in energy levels E1 through E4 is
unity.
The probability of quantum states to be occupied in energy level E5 is zero
In this case, Fermi energy must be above E4 but less than E5
Praxair Semiconductor Manufacturing Technology, Module 3: Semiconductor Manufacturing Processes 1

11. Consider a system of 13 electrons with discrete energy levels as below;
At T > 0 K, E = EF E5 E4 E3 E2 E1
Semiconductor Manufacturing Technology
It has been fifty years since the invention of the transistor. The technology behind this topic cannot be addressed adequately in a single presentation, but has been separated into four modules:
Module 1: Basic Principles
Module 2: Transistor Design and Manufacturing Overview
Module 3: Semiconductor Manufacturing Processes
Module 4: Semiconductor Economics
In this third module, we will review the key semiconductor processes, materials and equipment used to fabricate devices, and discuss process conditions and chemistry.
Electrons gain certain amount of thermal energy so that some can jump to
higher energy levels.
As the temperature change, the distribution of electrons vs energy changes 1 1 1
_________________
_________
_________
F (EF) = = =
= 0.5
1 + exp (EF – EF) / kT
1 + exp (0)
1 + 1
Praxair Semiconductor Manufacturing Technology, Module 3: Semiconductor Manufacturing Processes 1

12. Let T = 300K. Determine the probability that an energy level 3kT above
Example
Let T = 300K. Determine the probability that an energy level 3kT above
the Fermi energy is occupied by an electron. 1
_________________
F (E) =
1 + exp (E – EF) / kT 1
_________________ =
1 + exp (3kT / kT) 1
Semiconductor Manufacturing Technology
It has been fifty years since the invention of the transistor. The technology behind this topic cannot be addressed adequately in a single presentation, but has been separated into four modules:
Module 1: Basic Principles
Module 2: Transistor Design and Manufacturing Overview
Module 3: Semiconductor Manufacturing Processes
Module 4: Semiconductor Economics
In this third module, we will review the key semiconductor processes, materials and equipment used to fabricate devices, and discuss process conditions and chemistry.
_________ =
= 4.74 %
Praxair Semiconductor Manufacturing Technology, Module 3: Semiconductor Manufacturing Processes 1

13. CONSIDERING A GENERAL CRYSTAL AND APPLYING
SUMMARY
CONSIDERING A GENERAL CRYSTAL AND APPLYING
THE CONCEPT OF QUANTUM MECHANICS TO
DETERMINE THE CHARACTERISTICS OF ELECTRON
IN SINGLE-CRYSTAL LATTICE.
TO APPLY THOSE CONCEPT TO A SEMICONDUCTOR
MATERIALS IN THERMAL EQUILIBRIUM
DENSITY OF STATES IN CONDUCTION AND VALENCE
BANDS TO BE APPLIED WITH FERMI-DIRAC FUNCTION
TO DETERMINE THE CONCENTRATIONS OF ELECTRONS
AND HOLES IN THE RESPECTIVE BANDS.
Semiconductor Manufacturing Technology
It has been fifty years since the invention of the transistor. The technology behind this topic cannot be addressed adequately in a single presentation, but has been separated into four modules:
Module 1: Basic Principles
Module 2: Transistor Design and Manufacturing Overview
Module 3: Semiconductor Manufacturing Processes
Module 4: Semiconductor Economics
In this third module, we will review the key semiconductor processes, materials and equipment used to fabricate devices, and discuss process conditions and chemistry.
Praxair Semiconductor Manufacturing Technology, Module 3: Semiconductor Manufacturing Processes 1

14. ELECTRONS AND HOLES DISTRIBUTION IN EQUILIBRIUM
THE ELECTRONS DISTRIBUTION IN CONDUCTION BAND IS GIVEN
BY;
n (E) = gc (E) F (E)
….. (3)
Where
gc (E) is density of states in the conduction band
F (E) Fermi-Dirac distribution function
Semiconductor Manufacturing Technology
It has been fifty years since the invention of the transistor. The technology behind this topic cannot be addressed adequately in a single presentation, but has been separated into four modules:
Module 1: Basic Principles
Module 2: Transistor Design and Manufacturing Overview
Module 3: Semiconductor Manufacturing Processes
Module 4: Semiconductor Economics
In this third module, we will review the key semiconductor processes, materials and equipment used to fabricate devices, and discuss process conditions and chemistry.
Total electron concentration per unit volume in the conduction band
can be calculated by integrating Equation (3) over entire conduction
band energy.
Praxair Semiconductor Manufacturing Technology, Module 3: Semiconductor Manufacturing Processes 1

15. THE HOLE DISTRIBUTION IN VALENCE BAND IS GIVEN BY;
p (E) = gv (E) [ 1- F (E)]
….. (4)
Where
gv (E) is density of states in the valence band
[1-F (E)] the probability of states not occupied by electron
Semiconductor Manufacturing Technology
It has been fifty years since the invention of the transistor. The technology behind this topic cannot be addressed adequately in a single presentation, but has been separated into four modules:
Module 1: Basic Principles
Module 2: Transistor Design and Manufacturing Overview
Module 3: Semiconductor Manufacturing Processes
Module 4: Semiconductor Economics
In this third module, we will review the key semiconductor processes, materials and equipment used to fabricate devices, and discuss process conditions and chemistry.
Total hole concentration per unit volume in the valence band
can be calculated by integrating Equation (4) over entire valence
band energy.
Praxair Semiconductor Manufacturing Technology, Module 3: Semiconductor Manufacturing Processes 1

16. INTRINSIC SEMICONDUCTOR
pure s/c material with no impurity atoms and no lattice defect
At T = 0 K, all states in valence band are filled with electrons, states
in conduction band are empty.
Fermi energy is between Ec and Ev
As the temperature increase above 0 K, few electrons will get enough
energy to jump to conduction band and creating holes in the valence
band.
In intrinsic material, electrons and holes are created in pairs by thermal
energy. So the number of electrons in conduction band is equal to the
number of holes in the valence band
Semiconductor Manufacturing Technology
It has been fifty years since the invention of the transistor. The technology behind this topic cannot be addressed adequately in a single presentation, but has been separated into four modules:
Module 1: Basic Principles
Module 2: Transistor Design and Manufacturing Overview
Module 3: Semiconductor Manufacturing Processes
Module 4: Semiconductor Economics
In this third module, we will review the key semiconductor processes, materials and equipment used to fabricate devices, and discuss process conditions and chemistry.
Praxair Semiconductor Manufacturing Technology, Module 3: Semiconductor Manufacturing Processes 1

17. gc gv Semiconductor Manufacturing Technology
It has been fifty years since the invention of the transistor. The technology behind this topic cannot be addressed adequately in a single presentation, but has been separated into four modules:
Module 1: Basic Principles
Module 2: Transistor Design and Manufacturing Overview
Module 3: Semiconductor Manufacturing Processes
Module 4: Semiconductor Economics
In this third module, we will review the key semiconductor processes, materials and equipment used to fabricate devices, and discuss process conditions and chemistry.
Praxair Semiconductor Manufacturing Technology, Module 3: Semiconductor Manufacturing Processes 1

18. [ ] ∫ Electron concentration at thermal equilibrium given by; ∞ ni =
gc (E) F (E) dE Ec [
-(Ec – EFi ) ]
_________
……….. (5)
ni =
Nc exp kT
Semiconductor Manufacturing Technology
It has been fifty years since the invention of the transistor. The technology behind this topic cannot be addressed adequately in a single presentation, but has been separated into four modules:
Module 1: Basic Principles
Module 2: Transistor Design and Manufacturing Overview
Module 3: Semiconductor Manufacturing Processes
Module 4: Semiconductor Economics
In this third module, we will review the key semiconductor processes, materials and equipment used to fabricate devices, and discuss process conditions and chemistry.
Where Nc effective density of states in the conduction band Nc
at T = 300K Si
GaAs Ge
2.8 x 1019 cm-3
4.7 x 1017 cm-3
1.04 x 1019 cm-3
Praxair Semiconductor Manufacturing Technology, Module 3: Semiconductor Manufacturing Processes 1

19. [ ] ∫ Holes concentration at thermal equilibrium given by; pi =Ev ∫
pi =
gv (E) [1 - F (E)] dE
- ∞
-(EFI – Ev ) [ ]
_________
……….. (6)
pi =
Nv exp kT
Semiconductor Manufacturing Technology
It has been fifty years since the invention of the transistor. The technology behind this topic cannot be addressed adequately in a single presentation, but has been separated into four modules:
Module 1: Basic Principles
Module 2: Transistor Design and Manufacturing Overview
Module 3: Semiconductor Manufacturing Processes
Module 4: Semiconductor Economics
In this third module, we will review the key semiconductor processes, materials and equipment used to fabricate devices, and discuss process conditions and chemistry.
Where Nv effective density of states in the valence band Nv
at T = 300K Si
GaAs Ge
1.04 x 1019 cm-3
7.0 x 1018 cm-3
6.0 x 1018 cm-3
Praxair Semiconductor Manufacturing Technology, Module 3: Semiconductor Manufacturing Processes 1

20. In intrinsic semiconductor, electron concentration is equal to the
hole concentration, thus
ni = pi and
nipi = ni2 (MASS ACTION LAW) – the product of n p is always
a constant for a given semiconductor material at given temperature
If we take the product of Equation 5 and 6, [
-(Ec – EFi )
-(EFI – Ev ) ] [ ]
_________
_________
ni2 =
Nc Nv exp
. exp kT kT
Semiconductor Manufacturing Technology
It has been fifty years since the invention of the transistor. The technology behind this topic cannot be addressed adequately in a single presentation, but has been separated into four modules:
Module 1: Basic Principles
Module 2: Transistor Design and Manufacturing Overview
Module 3: Semiconductor Manufacturing Processes
Module 4: Semiconductor Economics
In this third module, we will review the key semiconductor processes, materials and equipment used to fabricate devices, and discuss process conditions and chemistry. [ ]
-(Ec – Ev ) =
Nc Nv exp
_________ kT
-Eg =
______
Nc Nv exp
….. (7) kT
Nc and Nv vary at T3/2
Praxair Semiconductor Manufacturing Technology, Module 3: Semiconductor Manufacturing Processes 1

21. band. The value of Nc for silicon at T=300K is Nc = 2.8 x 1019 cm-3
Example
Calculate the probability that a state in the conduction band is occupied by
an electron and calculate the thermal equilibrium electron concentration
in silicon at T=300K. Assume Fermi Energy is 0.25eV below the conduction
band. The value of Nc for silicon at T=300K is Nc = 2.8 x 1019 cm-3
The probability that an energy state at E = Ec is occupied by electron is
given by Fermi-Dirac probability function 1
[- (Ec – EF) ]
_________________
_________
F (Ec) =
exp
Semiconductor Manufacturing Technology
It has been fifty years since the invention of the transistor. The technology behind this topic cannot be addressed adequately in a single presentation, but has been separated into four modules:
Module 1: Basic Principles
Module 2: Transistor Design and Manufacturing Overview
Module 3: Semiconductor Manufacturing Processes
Module 4: Semiconductor Economics
In this third module, we will review the key semiconductor processes, materials and equipment used to fabricate devices, and discuss process conditions and chemistry.
1 + exp (Ec – EF) / kT kT
For electrons in the conduction band, E > Ec. If (Ec – EF) >> kT, then
(E – EF) >> kT. So the Fermi function can be reduced to Boltzman
Approximation
Praxair Semiconductor Manufacturing Technology, Module 3: Semiconductor Manufacturing Processes 1

22. [- (Ec – EF) ] _______ F (Ec) = exp kT
kT = 1.38 x J/K . 300K = 4.14 x J
kT = 4.14 x / 1.6 x eV = eV
Semiconductor Manufacturing Technology
It has been fifty years since the invention of the transistor. The technology behind this topic cannot be addressed adequately in a single presentation, but has been separated into four modules:
Module 1: Basic Principles
Module 2: Transistor Design and Manufacturing Overview
Module 3: Semiconductor Manufacturing Processes
Module 4: Semiconductor Economics
In this third module, we will review the key semiconductor processes, materials and equipment used to fabricate devices, and discuss process conditions and chemistry.
[ ]
_______
F (Ec) =
exp
= 6.43 x 10-5
0.0259
Praxair Semiconductor Manufacturing Technology, Module 3: Semiconductor Manufacturing Processes 1

23. [ ] The electron concentration is given by -(Ec – EFi ) _________
Nc exp kT
= (2.8 x 1019) exp (-0.25 / )
= 1.8 x 1015 cm-3
Semiconductor Manufacturing Technology
It has been fifty years since the invention of the transistor. The technology behind this topic cannot be addressed adequately in a single presentation, but has been separated into four modules:
Module 1: Basic Principles
Module 2: Transistor Design and Manufacturing Overview
Module 3: Semiconductor Manufacturing Processes
Module 4: Semiconductor Economics
In this third module, we will review the key semiconductor processes, materials and equipment used to fabricate devices, and discuss process conditions and chemistry.
Praxair Semiconductor Manufacturing Technology, Module 3: Semiconductor Manufacturing Processes 1

24. at T = 400K. Assume Fermi level is 0.27 eV above the valence band. The
Example
Calculate the thermal equilibrium hole concentration in intrinsic silicon
at T = 400K. Assume Fermi level is 0.27 eV above the valence band. The
value of Nv for silicon at T=300K is Nv = 1.04 x 1019cm-3
At T = 400K
kT = (400/300)
= eV
Nv = (1.04 x 1019) (400/300)3/2 = 1.60 x 1019 cm-3
Semiconductor Manufacturing Technology
It has been fifty years since the invention of the transistor. The technology behind this topic cannot be addressed adequately in a single presentation, but has been separated into four modules:
Module 1: Basic Principles
Module 2: Transistor Design and Manufacturing Overview
Module 3: Semiconductor Manufacturing Processes
Module 4: Semiconductor Economics
In this third module, we will review the key semiconductor processes, materials and equipment used to fabricate devices, and discuss process conditions and chemistry.
pi = (1.6 x 1019) exp ( -0.27/ ) = 6.43 x 1015 cm-3
Praxair Semiconductor Manufacturing Technology, Module 3: Semiconductor Manufacturing Processes 1