320
06 EECS Carrier Modeling Carrier Density
(chapter 2.3.3 2.3.5)
Carriers
Carriers are electrons or holes that can
conduct (carry) current
conduct (carry) current
Notation:
n = number of (conducting) electrons/cm3
p = number of (conducting) holes/cm3
room temperature
Intrinsic (i.e. pure) silicon has 4N valence electrons which fill the entire valence
band at 0 K.
But at room temperature, some electrons can acquire thermal energy to
generate n and p carriers.
n = p = ni ~ 11010 / cm3
Ku/EECS 320
How conducting are those intrinsic
carriers?
In silicon, there are 5 x 1022 atoms/cm3 (how to get this?)
There are 4 valence electrons per silicon atom.
2 x 1023 valence electrons/cm3
At room temperature, only 1 out of 1013 electrons
becomes carriers.
1 m2
silicon
For every mm, the resistance
is 108 !
Ku/EECS 320
Diode Again
Positive voltage: current flows
Negative voltage: current stops
P-silicon
I
V
N-silicon
Ku/EECS 320
Doping toy model review
Silicon is a semiconductor and has 4 valence
electrons/atom.
Phosphor has 5 valence electrons/atom.
bandgap
4
3
2
1
Si--Si--Si--Si--Si--Si--Si--Si
B
P
Terminology: We call phosphor-doped silicon N-type silicon
& Boron-doped silicon P-type silicon.
P is donor
B is acceptor
Ku/EECS more 320
Doping realistic picture
When phosphor atom replaces one of silicon atoms in the
crystal, the fifth valence electron is still bound to the
phosphor atom.
To set free this extra electron and make it become a
carrier, it must absorb enough thermal energy.
Silicon lattice
lattice
P+
How much is enough?
thermal
energy
Ku/EECS 320
Donor binding energy
Silicon lattice
P+
Like a hydrogen atom except that both the nucleus and the electron
are now in the silicon lattice.
*
mn q 4
~ 0.1eV
From quantum mechanics (eq 2.1 & 2.5): EB ~
2
2(4 K S 0 )
= h / 2
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Energy band diagram with donors
EC
EC
EV
EV
EB
x
x
One donor added
Intrinsic silicon
How long should I draw this line?
Silicon lattice
R
P+
Eq (A.4):
4 K S 0
R~
*
mn q 2
2
o
~ 5.3
Electron stays within 2R ~ 1 nm
There are ~ 4 x 4 x 4 silicon atoms
within that space.
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Carrier concentration with doping
Typical donor or acceptor concentration ~ 1018 /cm3.
1 donor or acceptor every 50000 silicon atoms.
EC
EB
Dashed line used.
EV
1018
/cm3
x
donor added
added
At 0 K, extra electrons from the donors in silicon do
not hop from one donor site to the other.
Exercise: How about donors in GaAs?
Ku/EECS 320