ELEKTRONIKOS PAGRINDAI
1
2008
Repetition 1
1. A silicon specimen is dopes with phosphorus and boron.
Their densities are 3·1015 cm-3 ir 2·1016 cm-3. Find
densities of charge carriers and Fermi level at normal
temperature.
VGTU EF ESK
[email protected]
ELEKTRONIKOS PAGRINDAI
2
2008
Densities of charge carriers. Fermi level
Semiconductors: germanium, silicon, ...
Donor impurities: phosphorus (P), arsenic (As), antimony (Sb).
Acceptor impurities: boron (B), aliuminum (Al), galium (Ga), indium (In).
N a ' > N d ':
N d ' > N a ':
Electrons – majority carriers.
p p = N a ≅ N a '− N d '
nn = N d ≅ N d '− N a '
Holes – minority carriers.
pn = ni2 / N d
Holes – majority carriers.
ni – from table.
Fermi level:
Electrons – minority carriers.
np = ni2 / N a
Fermi level:
N
Wc − WF = kT ln c
Nd
WF − Wv = kT ln
3/ 2
Nc =
2(2 πmn kT )
h
3
≅ 2,5 ⋅10 25 m −3
Nc ir Nd – same dimensions!!!
VGTU EF ESK
ni – from table.
Nv =
(
2 2πmp kT
h3
Nv
Na
)3 / 2 ≅ 2,5 ⋅10 25 m −3
Nv ir Na – same dimensions!!!
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ELEKTRONIKOS PAGRINDAI
3
2008
Repetition 1
1. A germanium specimen is doped with phosphorus and boron. Their
densities are 3·1016 cm-3 and 2·1015 cm-3. Find:
•
carrier densities and position of the Fermi level at temperature 300 K;
•
how many times densities of electrons and holes will change with
temperature increasing from 300 to 350 K.
2. Silicon, doped with acceptor impurity (1016 cm-3), is doped with donor impurity
(1015 cm-3). Find:
•
density of majority carriers before compensation doping;
•
density of majority carriers after compensation doping;
•
how density of majority carriers and conductivity type will change after
additional doping with donor impurity (1017 cm-3).
VGTU EF ESK
[email protected]
ELEKTRONIKOS PAGRINDAI
4
2008
Repetition 1
3. Gallium (Ga – 33) is acceptor impurity. Find its electronic structure
4. Oxygen molecule moves at 0 0C. Its velocity equals the most probable
velocity. Find the length of the de Broglie wave corresponding to the
molecule. Oxygen’s atomic mass is 16.
5. The constant of the silicon lattice is 0,542 nm. Find the density of valence
electrons.
6. Sketch planes with indices (211) and (110).
VGTU EF ESK
[email protected]
ELEKTRONIKOS PAGRINDAI
5
2008
Densities of charge carriers. Fermi level
Semiconductors: germanium, silicon, ...
Donor impurities: phosphorus (P), arsenic (As), antimony (Sb).
Acceptor impurities: boron (B), aliuminum (Al), galium (Ga), indium (In).
N d ' > N a ':
N a ' > N d ':
Electrons – majority carriers.
p p = N a ≅ N a '− N d '
nn = N d ≅ N d '− N a '
Holes – minority carriers.
pn = ni2 / N d
Holes – majority carriers.
ni – from table.
Fermi level:
Electrons – minority carriers.
np = ni2 / N a
Fermi level:
N
Wc − WF = kT ln c
Nd
WF − Wv = kT ln
3/ 2
Nc =
2(2 πmn kT )
h
3
≅ 2,5 ⋅10 25 m −3
Nc ir Nd – same dimensions!!!
VGTU EF ESK
ni – from table.
Nv =
(
2 2πmp kT
h3
Nv
Na
)3 / 2 ≅ 2,5 ⋅10 25 m −3
Nv ir Na – same dimensions!!!
[email protected]