Tuesday, October 8, 2024
Intrinsic Semiconductors (Pure)
1. Semiconductors are materials whose conductivity lies between that of conductors,
and insulators.
2. There are two kinds of semiconductors: o Single element (Germanium & Silicon)
a. Compound semiconductors
b. (Gallium-arsenide) → used for LEDs
3. In pure silicon:
a. At low temperatures, (0𝐾), all the covalent bonds are intact and no free
electrons o
b. Thus, the intrinsic silicon behaves as an insulator
c. At room temperature, thermal energy breaks some covalent bonds, (Thermal
Generation) o Free electron can wander away from its atom, → current if an e-
field is applied
Intrinsic Semiconductors
1. As electron leaves its atom, it leaves behind a net positive charge, (Hole Generation).
2. Hole may attract an electron from a neighboring atom (Recombination)
3. This process may repeat itself, → free Electrons and free Holes
4. As temperature increases, more bonds are broken and electron– hole pairs are
generated, → increase silicon conductivity.
5. In thermal equilibrium, the recombination rate = generation rate, and the
concentration of free electrons n/cm3 is equal concentration of holes p/cm 3
−Eg
2
n=p=n i=B T 1.5 e 2 kT & p ×n=ni
a. Where the temperature T is in kelvin
b. B: is the material – depended parameter which is always the same constant as
15 −3 −1.5
7.3 ×10 cm K for silicon and any other material he will be giving u the B.
c. E g : Bandgap energy (minimum energy required to brake covalent bond) =
1.12 eV for silicon.
d. k : Boltzmann’s constant = 8.62 ×10−5eV/K
ni 100 ×ni
6. The fraction of ionized atoms ( f ion ¿ :f ion = & f ion %=
natoms / cm
3 natoms /cm
3
Extrinsic Semiconductors (Doped)
1. Doping involves introducing impurity atoms into the silicon crystal.
𝒏 −type semiconductor
2. Silicon doped with a pentavalent atom. (5-electrons, e.g., phosphorus), Resulting in →
4. (3-electrons, e.g., boron), Resulting in → 𝒑 −type semiconductor
3. Silicon doped with a trivalent atom.
𝑵 −type semiconductor
Each phosphorus atom donates a free electron to the silicon crystal, (Donor).
a. n n ≅ N D , 𝑛: −𝑣e semiconductor
1. Doping concentration (Electrons):
2. Holes from thermal ionization have:
i. pn ≪ n n
2
ii. pn nn=ni
2 2
ni ni
iii. pn = ≅
nn N D
3. In N-types semiconductors:
a. Electrons are said to be the majority carriers
b. Holes are the majority carriers
P-type semiconductors
Each boron atom accepts a free electron from the silicon crystal, (Acceptor):
a. p p ≅ N A , 𝑝: +𝑣e semiconductor
1. Doping concentration (Holes):
2. Holes from thermal ionization have:
a. p p ≫ n p
2
i. p p n p=ni
2 2
ni ni
ii. n p = ≅
pp N A
3. In P-type semiconductors:
a. Electrons are said to be minority carriers
b. Hole are the majority carriers
Current Flow in Semiconductors (Drift &
Diffusion)
Drift Current: When electrical field 𝑬 is established in a semiconductor crystal:
a. Holes are accelerated in the direction of 𝐸.
1. For holes:
b. Electrons are accelerated in the opposite direction.
c. Holes acquire a velocity: v p−drift =μ p E
2
i. For intrinsic Silicon: μ p=480 cm /V . s
a. μ p : hole mobility (degree of ease by which holes move)
d. For 𝒒: 𝒆 −charge, 𝒑: holes density, 𝑨: area, the hole current flowing through
the bar is:
i. I p=qp ( A v p−drift ) =Aqp μ p E
Ip
ii. Current density: J p= =qp μ p
A
2. For electrons:
a. Holes are accelerated in the direction of 𝐸.
b. Electrons are accelerated in the opposite direction.
c. Holes acquire a velocity: v n−drift =−μ n E
2
i. For intrinsic Silicon: μn=1350 cm /V . s ; NB: μn ≅ 2.5 μ p
a. μn : electron mobility (degree of ease by which electrons
d. For 𝒒: 𝒆 −charge, 𝒑: holes density, 𝑨: area, the hole current flowing through
move)
the bar is:
i. I n=qp ( A v n−drift ) =Aqp μn E
In
ii. Current density: J n= =qp μn
A
3. The total drift current density is: J=J n+ J p=q ( p μn +n μ p ) E
Ip In
a. J p= =qp μ p & J n= =qp μn
A A
1
b. J= E Ω cm or J=σ E Ω −1 cm−1
ρ
