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Energy bands and charge carriersin semiconductors
2
Bonding Forces & Energy Bands in Solids In Isolated Atoms In Solid Materials
3rd Band2nd Band
1st Band
Core
3
Bonding Forces in Solids
Na (Z=11) [Ne]3s1
Cl (Z=17) [Ne]3s1 3p5
Na+ Cl_
4
Bonding Forces in Solids
e_
Na+
5
Bonding Forces in Solids
6
Bonding Forces in Solids
Si<100>
7
Energy Bands
Pauli Exclusion Principle
C (Z=6) 1s2 2s2 2p2
2 states for 1s level
2 states for 2s level
6 states for 2p level
For N atoms, there will be 2N, 2N, and 6N states of type 1s, 2s, and 2p, respectively.
8
3-1-2. Energy Bands
Atomic separation
Diamond lattice
spacing
En
erg
y
1s
2s
2p
Valence band
Conduction band
2p
2s
2s-2p
4N States
4N States
Eg
1s
9
Metals, Semiconductors & Insulators
For electrons to experience acceleration in an applied electric field, they must be able to move into new energy states. This implies there must be empty states (allowed energy states which are not already occupied by electrons) available to the electrons.
The diamond structure is such that the valence band is completely filled with electrons at 0ºK and the conduction band is empty. There can be no charge transport within the valence band, since no empty states are available into which electrons can move.
10
Metals, Semiconductors & Insulators
The difference bet-ween insulators and semiconductor mat-erials lies in the size of the band gap Eg, which is much small-er in semiconductors than in insulators.
Insulator Semiconductor
Filled
Filled
Empty
Empty
Eg
Eg
11
Metals, Semiconductors & Insulators
Metal
Filled
Partially Filled
Overlap
In metals the bands either overlap or are only partially filled. Thus electrons and empty energy states
Metal
are intermixed with-in the bands so that electrons can move freely under the infl-uence of an electric field.
12
3-2-3. Intrinsic Material
A perfect semiconductor crystal with
no impurities or lattice defects is
called an Intrinsic semiconductor.
In such material there are no charge
carriers at 0ºK, since the valence
band is filled with electrons and the
conduction band is empty.
13
3-2-3. Intrinsic Material
SiEgh+
e-
n=p=ni
14
3-2-3. Intrinsic Material If we denote the generation rate of EHPs
as and the recombination rate
as equilibrium requires that:
)(Tgi
)( 3scmEHPri
ii gr Each of these rates is temperature
depe-ndent. For example,
increases when the temperature is
raised.
)( 3scmEHPgi
iirri gnpnr 200
15
3-2-4. Extrinsic Material
In addition to the intrinsic carriers generated thermally, it is possible to create carriers in semiconductors by purposely introducing impurities into the crystal. This process, called doping, is the most common technique for varying the conductivity of semiconductors.
When a crystal is doped such that the equilibrium carrier concentrations n0 and p0
are different from the intrinsic carrier concentration ni , the material is said to be
extrinsic.
16
3-2-4. Extrinsic Material
0ºK3ºK2ºK4ºK5ºK1ºK6ºK7ºK8ºK9ºK10ºK11ºK12ºK13ºK14ºK50ºK15ºK16ºK17ºK18ºK19ºK20ºK
Ec
Ev
Ed
Donor
V
P
As
Sb
17
3-2-4. Extrinsic Material
0ºK3ºK2ºK4ºK5ºK1ºK6ºK7ºK8ºK9ºK10ºK11ºK12ºK13ºK14ºK50ºK15ºK16ºK17ºK18ºK19ºK20ºK
Ec
Ev
Ea
Acceptor
ш
B
Al
Ga
In
18
3-2-4. Extrinsic Material
h+
Al
e- Sb
Si
19
3-2-4. Extrinsic Material
We can calculate the binding energy by using the Bohr model results, consider-ing the loosely bound electron as ranging about the tightly bound “core” electrons in a hydrogen-like orbit.
rKnhK
mqE 022
4
4, 1;2
20
3-2-4. Extrinsic Material
Example 3-3: Calculate the approximate donor binding energy for Ge(εr=16, mn
*=0.12m0).
21
3-2-4. Extrinsic Material
eVJ
h
qmE
r
n
0064.01002.1
)1063.6()161085.8(8
)106.1)(1011.9(12.0
)(8
21
234212
41931
220
4*
Answer:
Thus the energy to excite the donor electron from n=1 state to the free state (n=∞) is ≈6meV.
22
3-2-4. Extrinsic Material
When a ш-V material is doped with Si or Ge, from column IV, these impurities are called amphoteric.
In Si, the intrinsic carrier concentration ni is about 1010cm-3 at
room tempera-ture. If we dope Si with 1015 Sb Atoms/cm3, the conduction electron concentration changes by five order of magnitude.