WEBVTT - generated by Videoportal Universität Freiburg

1
00:00:13.080 --> 00:00:13.840
Welcome to

2
00:00:13.840 --> 00:00:17.640
the PV online course, in this chapter,

3
00:00:17.800 --> 00:00:21.440
we cover the topic of how a solar cell works.

4
00:00:21.760 --> 00:00:26.640
In this teaching unit, we deal with the doping
of semiconductors.

5
00:00:27.920 --> 00:00:29.920
Semiconductors generally

6
00:00:29.920 --> 00:00:32.520
have a relatively low conductivity.

7
00:00:33.440 --> 00:00:35.720
By doping semiconductors,

8
00:00:35.720 --> 00:00:38.760
their conductivity can be changed or improved.

9
00:00:39.920 --> 00:00:42.760
This is done by selective contamination

10
00:00:43.200 --> 00:00:48.240
with impurity atoms of the otherwise very pure
crystal.

11
00:00:49.440 --> 00:00:53.400
Why is it necessary to dope silicon?

12
00:00:53.400 --> 00:00:55.240
The covalent

13
00:00:55.240 --> 00:01:00.000
bonds, here circled in red, represent a very
stable connection,

14
00:01:00.000 --> 00:01:03.000
thus the contained electrons are locally bound
/ fixed.

15
00:01:04.000 --> 00:01:07.000
Therefore an intrinsic (pure)

16
00:01:07.000 --> 00:01:11.000
Silicone crystal has a very poor

17
00:01:12.000 --> 00:01:13.000
conductivity.

18
00:01:15.000 --> 00:01:16.000
As previously

19
00:01:16.000 --> 00:01:21.000
mentioned in a Silicon crystal lattice only
a few electrons break free

20
00:01:21.000 --> 00:01:24.000
from their bonds, leaving a hole behind.

21
00:01:27.000 --> 00:01:31.000
This process is strongly dependent on temperature.

22
00:01:31.000 --> 00:01:34.000
The higher the temperature, the more FREE moving

23
00:01:34.000 --> 00:01:38.000
electrons and holes are in the intrinsic crystal.

24
00:01:38.000 --> 00:01:42.000
As an example, the values for silicon are displayed.

25
00:01:42.000 --> 00:01:45.000
n: Electron density,

26
00:01:45.000 --> 00:01:50.000
p: Hole density, Ni is called the intrinsic
charge carrier density

27
00:01:50.000 --> 00:01:53.000
k: Boltzmann constant

28
00:01:54.000 --> 00:01:57.000
and T the temperature in Kelvin.

29
00:01:57.000 --> 00:02:02.000
At any temperature, the product of electron
density and hole

30
00:02:02.000 --> 00:02:09.000
density equals the intrinsic carrier density
squared.

31
00:02:10.000 --> 00:02:15.000
For a better understanding, let us first look
at the distribution

32
00:02:15.000 --> 00:02:17.000
of energy states in a metal.

33
00:02:18.000 --> 00:02:21.000
On the y-axis the energy is plotted,

34
00:02:21.000 --> 00:02:24.000
on the x-axis the probability F

35
00:02:25.000 --> 00:02:29.000
with which an energy state is occupied is plotted

36
00:02:30.000 --> 00:02:34.000
The red curve describes the occupation probability

37
00:02:35.000 --> 00:02:37.000
as a function of the energy.

38
00:02:38.000 --> 00:02:41.000
This function is called Fermi-Dirac-function.

39
00:02:41.000 --> 00:02:44.000
At low energies

40
00:02:44.000 --> 00:02:47.000
ALL states are occupied,

41
00:02:47.000 --> 00:02:53.000
the Fermi-Dirac function has the value 1.

42
00:02:53.000 --> 00:02:55.000
At high energies, none of the states is occupied

43
00:02:55.000 --> 00:02:59.000
by an electron, the Fermi-Dirac-function has
the value 0.

44
00:02:59.000 --> 00:03:04.000
The Fermi energy is the ENERGY

45
00:03:04.000 --> 00:03:08.000
at which the occupation probability is exactly
50%.

46
00:03:10.000 --> 00:03:13.000
At a temperature of 0K,

47
00:03:13.000 --> 00:03:17.000
at absolute zero, the Fermi-Dirac-function
assumes a jump function.

48
00:03:18.000 --> 00:03:21.000
All electrons are in the energetically

49
00:03:22.000 --> 00:03:24.000
most favorable state.

50
00:03:25.000 --> 00:03:31.000
In the conduction band, all energy states are
occupied

51
00:03:31.000 --> 00:03:34.000
with low energy state, are occupied

52
00:03:35.000 --> 00:03:37.000
so the occupation probability is 1.

53
00:03:38.000 --> 00:03:40.000
Above the Fermi level,

54
00:03:40.000 --> 00:03:42.000
the occupation probability jumps to 0.

55
00:03:43.000 --> 00:03:47.000
Thus, the Fermi energy corresponds to the highest
occupied energy level

56
00:03:47.000 --> 00:03:49.000
in a METAL at zero Kelvin.

57
00:03:52.000 --> 00:03:54.000
With increasing temperature,

58
00:03:54.000 --> 00:03:59.000
the electrons also assume states with higher
energy.

59
00:03:59.000 --> 00:04:03.000
Thus the Fermi-Dirac-function runs more continuously.

60
00:04:04.000 --> 00:04:08.000
The electrons distribute themselves around
the Fermi level.

61
00:04:08.000 --> 00:04:12.000
As mentioned before: the Fermi energy is the
ENERGY

62
00:04:12.000 --> 00:04:16.000
where the occupation probability is exactly
50%.

63
00:04:18.000 --> 00:04:21.000
With increasing temperature, the Fermi-Dirac-function
changes

64
00:04:21.000 --> 00:04:23.000
accordingly.

65
00:04:24.000 --> 00:04:26.000
We now consider the band

66
00:04:26.000 --> 00:04:29.000
model in an intrinsic semiconductor.

67
00:04:30.000 --> 00:04:33.000
The Fermi level is in the middle

68
00:04:33.000 --> 00:04:35.000
of the forbidden zone, the band gap.

69
00:04:36.000 --> 00:04:40.000
Therefore, no states exist in the region of
the Fermi level.

70
00:04:41.000 --> 00:04:44.000
The occupation of the states in the conduction
band

71
00:04:44.000 --> 00:04:48.000
depends on the temperature.

72
00:04:48.000 --> 00:04:53.000
This then leads to the fact that at 0 Kelvin,
the valence band is fully occupied

73
00:04:54.000 --> 00:04:58.000
and the conduction band is not occupied at
all.

74
00:04:59.000 --> 00:05:00.000
But also

75
00:05:00.000 --> 00:05:04.000
at increasing temperature, there are only a
few electrons

76
00:05:04.000 --> 00:05:09.000
in the conduction band and correspondingly
few holes in the valence band.

77
00:05:11.000 --> 00:05:13.000
The missing electrons in the valence band,

78
00:05:13.000 --> 00:05:18.000
the holes, were shown with purple circles.

79
00:05:18.000 --> 00:05:22.000
For better representation, the other electrons
in the valence band

80
00:05:22.000 --> 00:05:25.000
have now been removed.

81
00:05:25.000 --> 00:05:28.000
The red curve again describes the Fermi-Dirac-function

82
00:05:28.000 --> 00:05:33.000
meaning the probability with which an electron
is encountered

83
00:05:34.000 --> 00:05:37.000
in the corresponding energy state.

84
00:05:37.000 --> 00:05:41.000
The gray curve is 1 MINUS the Fermi-Dirac-function

85
00:05:42.000 --> 00:05:47.000
meaning the probability with which a hole can
be encountered in the valence band

86
00:05:47.000 --> 00:05:50.000
depending on the energy.

87
00:05:52.000 --> 00:05:53.000
Doping, as already

88
00:05:53.000 --> 00:05:56.000
mentioned, can have a significant effect

89
00:05:56.000 --> 00:06:01.000
on the conductivity of an semiconductor.

90
00:06:01.000 --> 00:06:05.000
To do this, let's first look at the periodic
table of elements.

91
00:06:06.000 --> 00:06:09.000
Silicone is in the fourth main group

92
00:06:09.000 --> 00:06:12.000
and has 4 valence electrons, meaning

93
00:06:12.000 --> 00:06:15.000
4 electrons in the outer shell.

94
00:06:15.000 --> 00:06:20.000
Next to it, in the 5th main group, is phosphorus

95
00:06:20.000 --> 00:06:23.000
with 5 valence electrons.

96
00:06:23.000 --> 00:06:26.000
So 1 electron more than silicone.

97
00:06:28.000 --> 00:06:28.000
In the

98
00:06:28.000 --> 00:06:33.000
3rd main group there is boron with 3 electrons
in the outer shell.

99
00:06:33.000 --> 00:06:36.000
So 1 electron less

100
00:06:36.000 --> 00:06:39.000
in the outer shell than in the case of silicone.

101
00:06:40.000 --> 00:06:44.000
If the base material, in this case a silicone
crystal,

102
00:06:44.000 --> 00:06:47.000
is mixed with elements

103
00:06:47.000 --> 00:06:51.000
that each have one electron more in the outer
shell,

104
00:06:52.000 --> 00:06:54.000
this is called negative doping.

105
00:06:55.000 --> 00:06:57.000
Phosphorus has 5

106
00:06:57.000 --> 00:07:01.000
valence electrons, 1 electron more than the
silicone

107
00:07:01.000 --> 00:07:04.000
in the surrounding silicone crystal lattice.

108
00:07:06.000 --> 00:07:09.000
This extra electron can move

109
00:07:09.000 --> 00:07:11.000
freely in the Si crystal lattice.

110
00:07:13.000 --> 00:07:14.000
The conductivity of the

111
00:07:14.000 --> 00:07:17.000
semiconductor crystal increases.

112
00:07:18.000 --> 00:07:20.000
After the spatial representation,

113
00:07:20.000 --> 00:07:23.000
we now want to understand the energetic representation.

114
00:07:24.000 --> 00:07:28.000
We consider the band diagram of a silicon crystal

115
00:07:28.000 --> 00:07:33.000
which has been contaminated with donors (e.g.
phosphorus).

116
00:07:33.000 --> 00:07:36.000
These free electrons of the donors

117
00:07:36.000 --> 00:07:39.000
are energetically at the donor level.

118
00:07:40.000 --> 00:07:44.000
This energy level is much closer to the conduction
band than to the valence band.

119
00:07:46.000 --> 00:07:48.000
Very little thermal energy is required

120
00:07:49.000 --> 00:07:52.000
to lift electrons from the donor level to the
conduction band.

121
00:07:53.000 --> 00:07:57.000
As a result, almost as many electrons enter

122
00:07:57.000 --> 00:08:01.000
the conduction band of the silicone as dopant

123
00:08:01.000 --> 00:08:05.000
atoms have been incorporated into the crystal
lattice.

124
00:08:05.000 --> 00:08:09.000
n-doping leads to an increase in the charge
carrier

125
00:08:09.000 --> 00:08:12.000
concentration in the conduction band.

126
00:08:12.000 --> 00:08:15.000
This also increases the Fermi energy.

127
00:08:15.000 --> 00:08:18.000
Accordingly, the Fermi level is very close

128
00:08:18.000 --> 00:08:20.000
to the conduction band.

129
00:08:21.000 --> 00:08:23.000
In this way, there are

130
00:08:23.000 --> 00:08:28.000
then many more electrons in the conduction
band than holes in the valence band.

131
00:08:28.000 --> 00:08:31.000
The electrons are in the majority,

132
00:08:32.000 --> 00:08:35.000
therefore they are also called majority charge
carriers.

133
00:08:36.000 --> 00:08:39.000
The free-moving holes in the valence

134
00:08:39.000 --> 00:08:41.000
band, on the other hand, are outnumbered

135
00:08:42.000 --> 00:08:46.000
in the n region and are called minority charge
carriers.

136
00:08:47.000 --> 00:08:49.000
Accordingly, p n

137
00:08:49.000 --> 00:08:55.000
is the hole concentration in the n-doped region.

138
00:08:55.000 --> 00:08:59.000
To calculate the conductivity of the semiconductor,

139
00:09:00.000 --> 00:09:05.000
we need the electron concentration nn in the
n-doped region.

140
00:09:06.000 --> 00:09:09.000
This is approximately

141
00:09:09.000 --> 00:09:13.000
equal to the concentration of ionized donor
atoms,

142
00:09:13.000 --> 00:09:16.000
and this in turn is approximately equal

143
00:09:16.000 --> 00:09:19.000
to the concentration of donor atoms.

144
00:09:20.000 --> 00:09:23.000
The semiconductor is n-conducting.

145
00:09:24.000 --> 00:09:27.000
Thus, its conductivity is approximately

146
00:09:27.000 --> 00:09:30.000
proportional to the donor density.

147
00:09:31.000 --> 00:09:33.000
E is the elementary charge

148
00:09:34.000 --> 00:09:37.000
and µ_n the mobility of the electrons.

149
00:09:40.000 --> 00:09:44.000
If the basic material, here again our silicone
crystal,

150
00:09:44.000 --> 00:09:49.000
is mixed with elements, each of which has one
electron

151
00:09:49.000 --> 00:09:54.000
less in the outer shell, this is called positive
doping.

152
00:09:55.000 --> 00:10:00.000
Boron has 3 valence electrons, that is 1 electron

153
00:10:00.000 --> 00:10:04.000
less than the silicone atoms in the silicone
crystal lattice

154
00:10:07.000 --> 00:10:11.000
This missing electrons or holes

155
00:10:11.000 --> 00:10:14.000
can move freely in the silicone crystal lattice.

156
00:10:15.000 --> 00:10:18.000
The conductivity of the semiconductor crystal
increases.

157
00:10:19.000 --> 00:10:21.000
However, the conductivity is lower

158
00:10:22.000 --> 00:10:25.000
than in the n-doped semiconductor.

159
00:10:28.000 --> 00:10:30.000
We also want to look

160
00:10:30.000 --> 00:10:33.000
at the p-doping in the energetic representation.

161
00:10:34.000 --> 00:10:38.000
You can see here the band diagram of a silicon
crystal

162
00:10:38.000 --> 00:10:42.000
which has been contaminated with acceptors
(e.g. boron)

163
00:10:43.000 --> 00:10:45.000
This results in an acceptor level.

164
00:10:47.000 --> 00:10:50.000
This level is much closer to the valence band

165
00:10:50.000 --> 00:10:53.000
than to the conduction band.

166
00:10:53.000 --> 00:10:56.000
Very little thermal energy is required to lift
electrons

167
00:10:56.000 --> 00:10:59.000
from the fully occupied valence band to the
acceptor level.

168
00:11:00.000 --> 00:11:03.000
Remember the fully occupied parking deck

169
00:11:03.000 --> 00:11:07.000
where parking spaces are created?

170
00:11:07.000 --> 00:11:10.000
There are almost as many holes in the valence

171
00:11:10.000 --> 00:11:17.000
band of the semiconductor as there are doping
atoms in the crystal lattice.

172
00:11:17.000 --> 00:11:20.000
p-Doping leads to an increase of the carrier

173
00:11:20.000 --> 00:11:24.000
concentration in the valence band.

174
00:11:24.000 --> 00:11:26.000
This also decreases the Fermi energy.

175
00:11:27.000 --> 00:11:30.000
The Fermi level is very close to the valence
band.

176
00:11:31.000 --> 00:11:33.000
There are many more holes in

177
00:11:33.000 --> 00:11:36.000
the valence band than electrons in the conduction
band.

178
00:11:37.000 --> 00:11:40.000
The holes outnumber the electrons,

179
00:11:40.000 --> 00:11:43.000
so they are called majority charge carriers.

180
00:11:43.000 --> 00:11:48.000
Pp is the hole concentration in the p-doped
region.

181
00:11:48.000 --> 00:11:54.000
In contrast, the free-moving electrons in the
conduction band are outnumbered

182
00:11:54.000 --> 00:11:57.000
in the p-doped region and are called

183
00:11:57.000 --> 00:12:00.000
minority charge carriers.

184
00:12:01.000 --> 00:12:03.000
Accordingly, n p

185
00:12:04.000 --> 00:12:07.000
is the electron concentration in the p-doped
region.

186
00:12:09.000 --> 00:12:12.000
The concentration of the majority charge carriers

187
00:12:12.000 --> 00:12:16.000
(holes) is approximately equal to the concentration

188
00:12:16.000 --> 00:12:21.000
of the ionized acceptor atoms, and these in
turn are approximately equal

189
00:12:21.000 --> 00:12:24.000
to the concentration of the acceptor atoms.

190
00:12:25.000 --> 00:12:28.000
The semiconductor is p-type.

191
00:12:28.000 --> 00:12:31.000
So its conductivity is approximately proportional

192
00:12:32.000 --> 00:12:35.000
to the acceptor density.

193
00:12:35.000 --> 00:12:38.000
E is the elementary charge and µ_p

194
00:12:38.000 --> 00:12:40.000
the mobility of the holes.

195
00:12:45.000 --> 00:12:47.000
We now summarize this teaching unit.

196
00:12:48.000 --> 00:12:49.000
In intrinsic

197
00:12:49.000 --> 00:12:53.000
semiconductors, the total number of negative
charge carriers

198
00:12:53.000 --> 00:12:57.000
equals the total number of positive charge
carriers.

199
00:12:58.000 --> 00:13:02.000
In n-doped semiconductors a large number of
free electrons is present.

200
00:13:03.000 --> 00:13:06.000
Electrons are the majority charge carriers.

201
00:13:06.000 --> 00:13:12.000
In n-doped semiconductors a large number of
holes is present.

202
00:13:13.000 --> 00:13:15.000
Holes are the majority charge carriers.

203
00:13:16.000 --> 00:13:19.000
In both cases, the charge carrier density

204
00:13:19.000 --> 00:13:23.000
can be estimated equal to the dopant concentration.