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OK we're going to do problem 3
now on exam 2 from the fall

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00:00:27,140 --> 00:00:29,840
2009 class.

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00:00:29,840 --> 00:00:33,720
Let's talk a little bit about
what the problem concept is.

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00:00:33,720 --> 00:00:35,170
This is doping.

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00:00:35,170 --> 00:00:37,230
We're going to talk all about
doping semiconductors.

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00:00:37,230 --> 00:00:41,220
As we say chemistry, where
doping is legal.

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00:00:41,220 --> 00:00:44,620
So we're going to look at the
things we should probably know

15
00:00:44,620 --> 00:00:46,810
before attempting the problem.

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00:00:46,810 --> 00:00:48,930
You want to review your
doping principles.

17
00:00:48,930 --> 00:00:49,770
How does doping works.

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00:00:49,770 --> 00:00:52,730
What are the mechanisms, your
conduction mechanisms?

19
00:00:52,730 --> 00:00:54,680
So why does the material
conduct?

20
00:00:54,680 --> 00:00:56,590
What's actually happening?

21
00:00:56,590 --> 00:00:58,800
Your donor and acceptor levels,

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00:00:58,800 --> 00:01:00,590
understanding which is which.

23
00:01:00,590 --> 00:01:03,130
And your p versus your
n type doping.

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00:01:03,130 --> 00:01:04,510
What those mean.

25
00:01:04,510 --> 00:01:07,960
So look at those real quick
and do the problem.

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00:01:07,960 --> 00:01:09,720
Let's go on.

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00:01:09,720 --> 00:01:10,960
I wrote down the information
that we're

28
00:01:10,960 --> 00:01:13,300
given in the problem.

29
00:01:13,300 --> 00:01:19,330
The problem part a asks us to
find specifically how much

30
00:01:19,330 --> 00:01:24,070
gallium is needed to reach a
certain carrier concentration

31
00:01:24,070 --> 00:01:25,060
in our germanium.

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00:01:25,060 --> 00:01:28,490
So we're doping gallium
into germanium.

33
00:01:28,490 --> 00:01:32,670
We're given the fact that the
germanium band gap is 0.7

34
00:01:32,670 --> 00:01:34,160
electron volts.

35
00:01:34,160 --> 00:01:37,280
We know that we want to
achieve a carrier

36
00:01:37,280 --> 00:01:41,670
concentration of 3.091 times
10 to the 17 carriers per

37
00:01:41,670 --> 00:01:43,920
centimeter cubed.

38
00:01:43,920 --> 00:01:46,640
And we're working with 1
kilogram of germanium.

39
00:01:46,640 --> 00:01:48,900
So we need to achieve this
density or this carrier

40
00:01:48,900 --> 00:01:52,640
concentration in one kilogram
of germanium.

41
00:01:52,640 --> 00:01:55,080
I've drawn schematically-- now
remember the germanium

42
00:01:55,080 --> 00:01:58,550
crystals are in 3-D so the bonds
don't actually look 90

43
00:01:58,550 --> 00:02:02,250
degrees like this-- but I've
drawn just for visual a

44
00:02:02,250 --> 00:02:03,055
germanium crystal.

45
00:02:03,055 --> 00:02:04,630
So this is what a
pure germanium

46
00:02:04,630 --> 00:02:05,810
crystal would look like.

47
00:02:05,810 --> 00:02:07,840
I'm going to draw the band
structure for the pure

48
00:02:07,840 --> 00:02:10,060
germanium crystal now as well.

49
00:02:10,060 --> 00:02:13,520
When you see a problem that
gives you your band gap and it

50
00:02:13,520 --> 00:02:15,790
tells you this is about doping,
the first thing you

51
00:02:15,790 --> 00:02:17,540
want to do is just
get some points.

52
00:02:17,540 --> 00:02:19,630
Put some stuff on the paper
that you know to be true.

53
00:02:19,630 --> 00:02:20,880
So let's draw the
band structure.

54
00:02:25,770 --> 00:02:28,290
I'm going to abbreviate
conduction band with cb and

55
00:02:28,290 --> 00:02:30,410
valence band with vb.

56
00:02:30,410 --> 00:02:34,970
So here's my conduction band,
here's my valence band.

57
00:02:34,970 --> 00:02:39,480
We're told that this is here.

58
00:02:39,480 --> 00:02:42,810
We know our band gap
energy is 0.7.

59
00:02:42,810 --> 00:02:49,580
OK and I'm going to use
this blue to show

60
00:02:49,580 --> 00:02:50,870
where electrons are.

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00:02:50,870 --> 00:02:53,080
This just shows that there's
electrons in the valence band

62
00:02:53,080 --> 00:02:54,930
going all the way up to the
top of the valence band.

63
00:02:54,930 --> 00:02:58,090
That's how the valence band
level is defined.

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00:02:58,090 --> 00:03:00,630
So this easy points.

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00:03:00,630 --> 00:03:03,350
You've got this on the paper,
we're good to go.

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00:03:03,350 --> 00:03:05,460
Now what we're talking
about is putting

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00:03:05,460 --> 00:03:07,630
gallium into germanium.

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00:03:07,630 --> 00:03:08,880
So let's do that.

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00:03:14,960 --> 00:03:17,800
Let's take out this germanium.

70
00:03:17,800 --> 00:03:21,345
And let's put a gallium
in its place.

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00:03:21,345 --> 00:03:24,560
We'll put it in red.

72
00:03:24,560 --> 00:03:27,380
OK so this isn't exactly
correct yet.

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00:03:27,380 --> 00:03:28,660
Germanium makes 4 bonds.

74
00:03:28,660 --> 00:03:30,710
If you look at the periodic
table you'll see that it has 4

75
00:03:30,710 --> 00:03:32,110
valence electrons
to make bonds.

76
00:03:32,110 --> 00:03:33,200
But gallium does not.

77
00:03:33,200 --> 00:03:34,462
Gallium only has 3.

78
00:03:34,462 --> 00:03:38,430
So what that means is that one
of these bonds can't exist

79
00:03:38,430 --> 00:03:40,570
like this anymore.

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00:03:40,570 --> 00:03:43,750
So the way I like to draw it,
is we still have an electron

81
00:03:43,750 --> 00:03:47,720
from this germanium but we're
missing one for this gallium.

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00:03:47,720 --> 00:03:50,160
And this is what a hole
basically is,

83
00:03:50,160 --> 00:03:52,930
schematically, in doping.

84
00:03:52,930 --> 00:03:55,820
So we're going to write
this as hole plus.

85
00:03:55,820 --> 00:03:57,860
And the reason it has a positive
charge associated

86
00:03:57,860 --> 00:04:00,360
with it is because in our
neutral crystal with no

87
00:04:00,360 --> 00:04:02,750
charges you having an
electron there.

88
00:04:02,750 --> 00:04:04,750
And you've just removed an
electron and now it's

89
00:04:04,750 --> 00:04:05,780
positively charged.

90
00:04:05,780 --> 00:04:07,980
You have a positive charge in
this region of the crystal,

91
00:04:07,980 --> 00:04:11,000
which corresponds to
a missing electron.

92
00:04:11,000 --> 00:04:12,770
So we just created a hole.

93
00:04:12,770 --> 00:04:14,860
We have a hole here and
then it's going to

94
00:04:14,860 --> 00:04:16,840
result in what we call--

95
00:04:16,840 --> 00:04:19,350
I'll use red again--

96
00:04:19,350 --> 00:04:20,600
an acceptor level.

97
00:04:23,690 --> 00:04:28,530
And remember this band diagram
is an analogy for, these are

98
00:04:28,530 --> 00:04:32,330
the energy levels where your
electrons can exist. So we

99
00:04:32,330 --> 00:04:35,010
have these energy levels and the
valence band and we've got

100
00:04:35,010 --> 00:04:36,440
energy levels up in the
conduction band.

101
00:04:36,440 --> 00:04:39,580
What's just happened is that
this dopant has created an

102
00:04:39,580 --> 00:04:43,070
energy level slightly above
the valence band.

103
00:04:43,070 --> 00:04:46,180
If you have a donor level from
a different type of doping--

104
00:04:46,180 --> 00:04:47,490
which we'll talk about
in a second--

105
00:04:47,490 --> 00:04:52,780
you'll create a level right
below the conduction bands.

106
00:04:52,780 --> 00:04:54,040
So we've got some points.

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00:04:54,040 --> 00:04:56,190
We understand the system now.

108
00:04:56,190 --> 00:04:56,880
It's just going well.

109
00:04:56,880 --> 00:04:58,370
So let's try to do a.

110
00:05:01,430 --> 00:05:04,440
So a, as I said before is asking
us to figure out the

111
00:05:04,440 --> 00:05:05,650
actual amount.

112
00:05:05,650 --> 00:05:09,130
We're looking for grams. This
is what we're looking for.

113
00:05:09,130 --> 00:05:10,540
Grams of gallium.

114
00:05:10,540 --> 00:05:14,040
That we need to put into a
kilogram of germanium to

115
00:05:14,040 --> 00:05:18,670
create a carrier concentration
of 3.091 times 10 to the 17

116
00:05:18,670 --> 00:05:21,010
carriers per centimeter cubed.

117
00:05:21,010 --> 00:05:23,400
Not too bad of a problem.

118
00:05:23,400 --> 00:05:25,500
This is basically just
stoichiometry.

119
00:05:25,500 --> 00:05:27,350
Dimensional analysis.

120
00:05:27,350 --> 00:05:30,540
Here's how I did it and many
people did it this way.

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00:05:30,540 --> 00:05:31,790
I start off.

122
00:05:35,000 --> 00:05:37,380
times 10 to the 17.

123
00:05:37,380 --> 00:05:38,830
And I always keep my units.

124
00:05:38,830 --> 00:05:40,130
That's really important.

125
00:05:40,130 --> 00:05:43,620
So we're going to write
this as carriers

126
00:05:43,620 --> 00:05:44,870
per centimeter cubed.

127
00:05:49,490 --> 00:05:50,910
Now we're also told in the
problem, we have the

128
00:05:50,910 --> 00:05:54,230
additional information that the
temperature is high enough

129
00:05:54,230 --> 00:05:57,030
that all of the sites
are ionized.

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00:05:57,030 --> 00:05:58,820
What that means is that--
let's take a look

131
00:05:58,820 --> 00:06:01,150
at this band diagram--

132
00:06:01,150 --> 00:06:03,780
we have electrons existing
in the valence

133
00:06:03,780 --> 00:06:06,190
bands up to that level.

134
00:06:06,190 --> 00:06:08,190
We've doped and now the
temperature's high enough that

135
00:06:08,190 --> 00:06:11,730
these electrons can be excited,
one of them in this

136
00:06:11,730 --> 00:06:16,520
case can be excited to this
level here, the acceptor

137
00:06:16,520 --> 00:06:20,570
level, creating, of course, a
hole in the valence band.

138
00:06:23,350 --> 00:06:25,690
That's what it means that
it can be fully ionized.

139
00:06:25,690 --> 00:06:28,470
So basically every gallium
atom that we put into our

140
00:06:28,470 --> 00:06:31,310
material creates a carrier.

141
00:06:31,310 --> 00:06:32,540
And why do I say that?

142
00:06:32,540 --> 00:06:37,770
Because conduction is either,
the movement of electrons in

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00:06:37,770 --> 00:06:40,590
the conduction bands, which
we don't have. Or it's the

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00:06:40,590 --> 00:06:43,790
movement of holes in the valence
band, which we now

145
00:06:43,790 --> 00:06:46,040
have. So we're talking
about conduction.

146
00:06:46,040 --> 00:06:51,670
And so for every gallium atom
we put in, we're creating an

147
00:06:51,670 --> 00:06:55,440
acceptor level, which takes an
electron up, which creates

148
00:06:55,440 --> 00:06:57,970
some conduction in
the valence band.

149
00:06:57,970 --> 00:07:00,610
Now if we add lots and lots
of gallium atoms--

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00:07:00,610 --> 00:07:02,670
there's a lot more gallium
atoms in here--

151
00:07:02,670 --> 00:07:06,370
we're going to actually see
many more of these levels

152
00:07:06,370 --> 00:07:08,090
showing up.

153
00:07:08,090 --> 00:07:11,610
And you're going to get what
almost looks like very thin

154
00:07:11,610 --> 00:07:15,070
bands, an acceptor band or
acceptor level there.

155
00:07:15,070 --> 00:07:16,850
So we start off like this.

156
00:07:16,850 --> 00:07:18,510
And I went into that's
digression because now I'm

157
00:07:18,510 --> 00:07:22,760
just going to say that
for every atom we

158
00:07:22,760 --> 00:07:24,445
put in we get 1 carrier.

159
00:07:29,020 --> 00:07:30,270
And then we're going to say--

160
00:07:38,305 --> 00:07:40,230
I want to be sure I
get this right--

161
00:07:48,590 --> 00:08:03,440
we have 6.02 times 10 to
the 23 atoms per mole.

162
00:08:03,440 --> 00:08:04,540
That's right.

163
00:08:04,540 --> 00:08:07,730
And then we have 1 mole.

164
00:08:07,730 --> 00:08:11,060
And notice how I'm being very
careful about the dimensional

165
00:08:11,060 --> 00:08:11,600
analysis here.

166
00:08:11,600 --> 00:08:14,550
Because if you put something
in the wrong top or bottom

167
00:08:14,550 --> 00:08:18,620
you're off by 46 powers.

168
00:08:18,620 --> 00:08:20,235
So don't make that mistake.

169
00:08:20,235 --> 00:08:22,030
We saw that a lot on the exam.

170
00:08:30,320 --> 00:08:31,360
So we're good here.

171
00:08:31,360 --> 00:08:32,540
Let's do our dimensional
analysis.

172
00:08:32,540 --> 00:08:34,900
We start off, we're looking
for this particular

173
00:08:34,900 --> 00:08:37,630
concentration carriers
per centimeter cubed.

174
00:08:37,630 --> 00:08:43,370
We have 1 atom creates
1 carrier.

175
00:08:43,370 --> 00:08:46,740
1 mole has this many atoms.
And one mole of-- we're

176
00:08:46,740 --> 00:08:48,830
talking about in this case--

177
00:08:48,830 --> 00:08:50,080
gallium.

178
00:08:52,650 --> 00:08:56,380
I'll put Gallium here
to be clear.

179
00:08:56,380 --> 00:09:00,120
1 mole of gallium has
this much mass.

180
00:09:00,120 --> 00:09:02,350
And you're left with something
like this.

181
00:09:02,350 --> 00:09:12,740
You're left with 3.58 times 10
to the negative 5 grams per

182
00:09:12,740 --> 00:09:13,270
centimeter.

183
00:09:13,270 --> 00:09:16,560
Grams gallium per centimeter
cubed.

184
00:09:16,560 --> 00:09:18,880
So we're looking good.

185
00:09:18,880 --> 00:09:20,960
We're pretty close to the answer
but we don't actually

186
00:09:20,960 --> 00:09:21,630
have the answer yet.

187
00:09:21,630 --> 00:09:24,680
Remember we're looking for
total grams of gallium.

188
00:09:24,680 --> 00:09:27,520
Not how many grams per
centimeter cubed.

189
00:09:27,520 --> 00:09:29,830
That's pretty easy because
we're told the we have 1

190
00:09:29,830 --> 00:09:32,820
kilogram of germanium and we
know the density of germanium

191
00:09:32,820 --> 00:09:34,400
from our periodic table.

192
00:09:34,400 --> 00:09:37,540
So looking at our periodic
table we can look up

193
00:09:37,540 --> 00:09:41,280
germanium's density and we can
then back out how many

194
00:09:41,280 --> 00:09:44,460
centimeters cubed of germanium
we have. We'll

195
00:09:44,460 --> 00:09:46,140
do that right here.

196
00:09:46,140 --> 00:09:50,830
So 1 kilogram of germanium
is 1,000 grams, times--

197
00:09:50,830 --> 00:09:56,250
we have the density, which is
going to be times 1 over the

198
00:09:56,250 --> 00:09:58,120
density, rather--

199
00:09:58,120 --> 00:10:00,326
grams per centimeter cubed.

200
00:10:00,326 --> 00:10:08,500
And that's going to give us
187 centimeters cubed.

201
00:10:08,500 --> 00:10:09,290
And now we're good.

202
00:10:09,290 --> 00:10:15,240
Because we know here we have
3.58 times 10 to the negative

203
00:10:15,240 --> 00:10:18,900
5 grams of gallium per
centimeter cubed of germanium.

204
00:10:18,900 --> 00:10:22,400
We have this many centimeters
cubed of germanium.

205
00:10:22,400 --> 00:10:29,370
Multiply them together and you
get the answer, which is 6.69

206
00:10:29,370 --> 00:10:34,975
times 10 to the negative
3 grams of gallium.

207
00:10:34,975 --> 00:10:36,860
So that's part a.

208
00:10:36,860 --> 00:10:38,820
Just dimensional analysis
and stoichiometry.

209
00:10:38,820 --> 00:10:41,910
But I stress, be careful about
the way these things are.

210
00:10:41,910 --> 00:10:43,790
Even I pause to make sure
they're correct because if you

211
00:10:43,790 --> 00:10:45,730
get this wrong, the whole
problem's wrong.

212
00:10:45,730 --> 00:10:48,650
You're off orders of 46.

213
00:10:48,650 --> 00:10:51,905
You're off by orders of 1,000
here, so just be careful.

214
00:10:54,680 --> 00:10:56,310
Part b.

215
00:10:56,310 --> 00:10:58,740
We've actually already answered
when we drew it up,

216
00:10:58,740 --> 00:11:00,270
we threw down the
things we knew.

217
00:11:00,270 --> 00:11:02,550
We knew that we were
creating a hole.

218
00:11:02,550 --> 00:11:05,150
And a hole corresponds
to p type doping.

219
00:11:05,150 --> 00:11:06,480
How do I remember p and n?

220
00:11:06,480 --> 00:11:08,790
It's easy. p means positive.

221
00:11:08,790 --> 00:11:11,420
We've created a hole, which
has a positive charge.

222
00:11:11,420 --> 00:11:13,300
n, I think of as negative.

223
00:11:13,300 --> 00:11:16,830
So if you had put something else
in there like arsenic,

224
00:11:16,830 --> 00:11:19,160
arsenic would've had an extra
electron compared to

225
00:11:19,160 --> 00:11:21,590
germanium, which means you
have a negative charge.

226
00:11:21,590 --> 00:11:23,190
So n negative.

227
00:11:23,190 --> 00:11:24,410
So we have p type doping.

228
00:11:24,410 --> 00:11:25,380
We're done with part b.

229
00:11:25,380 --> 00:11:26,330
Easy.

230
00:11:26,330 --> 00:11:28,170
Part c.

231
00:11:28,170 --> 00:11:29,760
I'm just going to erase some of
this stuff here and we're

232
00:11:29,760 --> 00:11:47,580
going to draw a couple more
of these band diagrams. So

233
00:11:47,580 --> 00:11:50,490
basically what we're asked to do
now is to think about, what

234
00:11:50,490 --> 00:11:52,520
does this band diagram look
like at different

235
00:11:52,520 --> 00:11:53,690
temperatures?

236
00:11:53,690 --> 00:11:55,420
Because it actually looks
slightly different.

237
00:11:55,420 --> 00:11:58,600
I've drawn it here
schematically.

238
00:11:58,600 --> 00:11:59,840
But let's actually think
about what it looks

239
00:11:59,840 --> 00:12:01,730
like in real life.

240
00:12:01,730 --> 00:12:07,080
So let's do 2 more of these.

241
00:12:07,080 --> 00:12:10,440
And we'll use that one
as well for part c.

242
00:12:10,440 --> 00:12:12,540
OK so I'm drawing my
conduction bands.

243
00:12:12,540 --> 00:12:13,790
These are my conduction bands.

244
00:12:18,060 --> 00:12:19,310
These are my valence bands.

245
00:12:21,720 --> 00:12:23,570
I have the same band gap
for all of them.

246
00:12:23,570 --> 00:12:25,780
So you know band gap here,
here's the band gap.

247
00:12:29,084 --> 00:12:30,630
It's always worth
putting down.

248
00:12:30,630 --> 00:12:32,840
If you know it's true,
put it down.

249
00:12:32,840 --> 00:12:34,840
And we know that
in both cases--

250
00:12:34,840 --> 00:12:36,790
let me just get rid of this
thing here; we're going to

251
00:12:36,790 --> 00:12:41,600
start from the beginning;
put our electron back--

252
00:12:41,600 --> 00:12:46,480
we've created all these
acceptor levels.

253
00:12:46,480 --> 00:12:48,700
Because we've doped with more
than one gallium atom.

254
00:12:48,700 --> 00:12:53,150
We have many, many, 10 to the 17
gallium atoms. Which sounds

255
00:12:53,150 --> 00:12:57,364
like a lot, but in a mole we
have 10 to the 23 spots in a

256
00:12:57,364 --> 00:12:58,070
mole of material.

257
00:12:58,070 --> 00:13:02,270
So it's 6 orders of
magnitude less.

258
00:13:02,270 --> 00:13:05,120
So we have these systems and
we're asked to do them at--

259
00:13:05,120 --> 00:13:08,130
I'm going to keep going
back and forth--

260
00:13:08,130 --> 00:13:14,745
300 k, 4.2 k and 1200 k.

261
00:13:14,745 --> 00:13:15,995
That's Kelvin.

262
00:13:18,490 --> 00:13:21,590
Let's go with the extremes
first. And we'll do the middle

263
00:13:21,590 --> 00:13:24,700
one, 300 k, once we have an
idea of what's happening.

264
00:13:24,700 --> 00:13:28,400
So basically, in the very
beginning when we to dope in a

265
00:13:28,400 --> 00:13:39,330
material, time t equals 0 and no
electrons have had a chance

266
00:13:39,330 --> 00:13:40,780
to move around.

267
00:13:40,780 --> 00:13:43,040
You have all your electrons in
the valence band, you have

268
00:13:43,040 --> 00:13:45,670
these open holes in your
acceptor levels.

269
00:13:50,600 --> 00:13:53,660
And the reason that electrons
would move between levels is

270
00:13:53,660 --> 00:13:55,730
if they have some energy
associated with them.

271
00:13:55,730 --> 00:13:58,020
Now why would something have
energy in a crystal?

272
00:13:58,020 --> 00:14:00,100
Well that's because of
thermal vibrations.

273
00:14:00,100 --> 00:14:02,660
It's a thermal energy they have.
So it's completely based

274
00:14:02,660 --> 00:14:04,580
on the temperature at which
the crystal exists.

275
00:14:04,580 --> 00:14:06,105
So at a very low temperature--

276
00:14:08,690 --> 00:14:11,320
let me write that up
there for you, this

277
00:14:11,320 --> 00:14:13,370
is our basic equation--

278
00:14:13,370 --> 00:14:15,330
at a very low temperature we
have a very low thermal

279
00:14:15,330 --> 00:14:18,020
energy. kBT: this is the
Boltzman's Constant.

280
00:14:18,020 --> 00:14:19,800
At a very high temperature, we
have a very high thermal

281
00:14:19,800 --> 00:14:22,640
energy, which means that these
electrons have the ability to

282
00:14:22,640 --> 00:14:24,750
move between levels
more easily.

283
00:14:24,750 --> 00:14:28,390
So here's our very
low temperature.

284
00:14:28,390 --> 00:14:30,710
At a very low temperature
we can actually

285
00:14:30,710 --> 00:14:32,100
calculate the energy.

286
00:14:32,100 --> 00:14:36,030
We'll find that the energy
here is about--

287
00:14:36,030 --> 00:14:37,550
just so you have a scale--

288
00:14:37,550 --> 00:14:44,050
it's about 0.00036
electron volts.

289
00:14:44,050 --> 00:14:47,180
Now you say to yourself, wow
that is a lot less than 0.7

290
00:14:47,180 --> 00:14:51,670
electron volts, which is
the energy of this gap.

291
00:14:51,670 --> 00:14:54,120
So there's no way these
electrons here can even make

292
00:14:54,120 --> 00:14:55,980
it up to this acceptor level.

293
00:14:55,980 --> 00:14:58,550
That's not exactly true.

294
00:14:58,550 --> 00:15:03,400
This is best thought of as an
average thermal energy that an

295
00:15:03,400 --> 00:15:05,380
electron will have. It's
based off of a

296
00:15:05,380 --> 00:15:07,140
distribution, if you will.

297
00:15:07,140 --> 00:15:10,650
So most electrons will have
around this energy.

298
00:15:10,650 --> 00:15:12,500
But some will have a little bit
more and some will have a

299
00:15:12,500 --> 00:15:13,530
little bit less.

300
00:15:13,530 --> 00:15:16,250
And very, very, very few at the
tail of that distribution

301
00:15:16,250 --> 00:15:18,740
will have enough energy to
actually make it up to one of

302
00:15:18,740 --> 00:15:19,690
these levels.

303
00:15:19,690 --> 00:15:22,640
So the way to do this problem,
to be actually fully correct,

304
00:15:22,640 --> 00:15:24,330
is to say that and explain it.

305
00:15:24,330 --> 00:15:27,530
I actually, when I did this
problem on the answer key, I

306
00:15:27,530 --> 00:15:31,160
have an electron, one electron
going up into one of these

307
00:15:31,160 --> 00:15:34,770
spots and the rest
are all empty.

308
00:15:34,770 --> 00:15:37,610
I denote that with a little
bit of blue here.

309
00:15:37,610 --> 00:15:39,970
But everything else is empty.

310
00:15:39,970 --> 00:15:41,630
We've got a hole here.

311
00:15:41,630 --> 00:15:44,520
So there is a finite, very
small, amount of conduction.

312
00:15:44,520 --> 00:15:46,760
But it's extremely small.

313
00:15:46,760 --> 00:15:49,760
And it's extremely unlikely to
have electrons moving around

314
00:15:49,760 --> 00:15:52,060
but probabilistically
it will happen.

315
00:15:52,060 --> 00:15:53,430
That's 4.2 Kelvin.

316
00:15:53,430 --> 00:15:55,670
Very, very low.

317
00:15:55,670 --> 00:15:58,280
Let's go to very, very high.

318
00:15:58,280 --> 00:16:00,030
Starting at the beginning again,
we know all of our

319
00:16:00,030 --> 00:16:02,150
electrons are in the
valence bands.

320
00:16:02,150 --> 00:16:11,010
At 1,200 we have an energy
of about 0.1 eV.

321
00:16:11,010 --> 00:16:13,060
Still less than 0.7.

322
00:16:13,060 --> 00:16:17,700
We have a significantly larger
proportion electrons in that

323
00:16:17,700 --> 00:16:21,040
distribution, which
are at 0.7.

324
00:16:21,040 --> 00:16:23,810
So we actually do have electrons
that will move up

325
00:16:23,810 --> 00:16:24,910
into the spots.

326
00:16:24,910 --> 00:16:29,410
And even many that'll move
up here as well.

327
00:16:29,410 --> 00:16:32,310
Because they can overcome
this 0.7 eV.

328
00:16:32,310 --> 00:16:35,510
So we've got some electrons,
they're going to move here,

329
00:16:35,510 --> 00:16:37,780
they're going to fill
up most of these.

330
00:16:37,780 --> 00:16:41,250
Because this delta here, the
difference between our

331
00:16:41,250 --> 00:16:44,320
acceptor level and our valence
band, is actually quite small.

332
00:16:44,320 --> 00:16:46,310
It's extremely small.

333
00:16:46,310 --> 00:16:47,880
That's another reason why
we have an electron

334
00:16:47,880 --> 00:16:49,872
moving up at 4.2.

335
00:16:49,872 --> 00:16:51,880
I should have mentioned that.

336
00:16:51,880 --> 00:16:52,540
This is very small.

337
00:16:52,540 --> 00:16:55,110
This gets pretty much
completely filled.

338
00:16:55,110 --> 00:16:59,990
And I'll denote that with
a blue line here.

339
00:16:59,990 --> 00:17:03,160
And we have some electrons,
even going up into here.

340
00:17:06,510 --> 00:17:09,210
What that means, that that has
to correspond to electrons

341
00:17:09,210 --> 00:17:14,160
being depleted out of
the valence band.

342
00:17:14,160 --> 00:17:15,600
This is the way you would
draw this picture.

343
00:17:20,850 --> 00:17:23,290
So we lose these electrons
from the valence band.

344
00:17:23,290 --> 00:17:27,240
Some jump up to the acceptor
levels and the rest will go up

345
00:17:27,240 --> 00:17:29,430
to the conduction band.

346
00:17:29,430 --> 00:17:30,980
So this is 1,200.

347
00:17:30,980 --> 00:17:33,200
We have more than enough energy
to reach this acceptor

348
00:17:33,200 --> 00:17:35,670
level and we have
probabilistically some

349
00:17:35,670 --> 00:17:39,350
electrons will make it up
to the conduction bands.

350
00:17:39,350 --> 00:17:40,790
That's the best way
to think about it.

351
00:17:40,790 --> 00:17:42,655
Now let's go back to our
middle temperature.

352
00:17:45,360 --> 00:17:47,940
I think the best way to do
this one is to just go

353
00:17:47,940 --> 00:17:49,200
somewhere in the middle.

354
00:17:49,200 --> 00:17:50,630
That's the safest play, right?

355
00:17:50,630 --> 00:17:52,200
So we're at a temperature
which corresponds

356
00:17:52,200 --> 00:17:59,280
to about 0.025 eV.

357
00:17:59,280 --> 00:18:01,850
Now that is obviously smaller
than the gap.

358
00:18:01,850 --> 00:18:04,690
Probabilistically we'll still
get some electrons in the gap.

359
00:18:04,690 --> 00:18:06,060
Diminishingly small.

360
00:18:06,060 --> 00:18:07,500
But we'll put one up there.

361
00:18:07,500 --> 00:18:09,420
OK maybe one goes up there.

362
00:18:09,420 --> 00:18:15,160
And it's still much bigger than
the delta here between

363
00:18:15,160 --> 00:18:18,440
the acceptor level and
the valence band top.

364
00:18:18,440 --> 00:18:22,680
So these electrons will still
pretty easily make their way

365
00:18:22,680 --> 00:18:24,980
into the acceptor level.

366
00:18:24,980 --> 00:18:27,020
Now I'll put a little
bit here.

367
00:18:27,020 --> 00:18:32,445
We're going to lose electrons
very slightly.

368
00:18:37,750 --> 00:18:38,990
That's how I would have
done that problem.

369
00:18:38,990 --> 00:18:41,070
It sort of looks like that
on the answer key.

370
00:18:41,070 --> 00:18:42,990
Now I want to emphasize that,
what is what's the

371
00:18:42,990 --> 00:18:44,390
importance of this?

372
00:18:44,390 --> 00:18:47,050
Well when you dope, you're
creating conduction.

373
00:18:47,050 --> 00:18:47,660
Why is that?

374
00:18:47,660 --> 00:18:51,080
Because the more we dope, the
more holes we have that can be

375
00:18:51,080 --> 00:18:51,810
played around with.

376
00:18:51,810 --> 00:18:54,770
So we have more and more
of these acceptor

377
00:18:54,770 --> 00:18:56,570
level energy levels.

378
00:18:56,570 --> 00:18:58,590
And what happens is these
electrons at finite

379
00:18:58,590 --> 00:18:59,270
temperatures--

380
00:18:59,270 --> 00:19:02,230
temperatures above 0 Kelvin--
will move into those levels.

381
00:19:02,230 --> 00:19:05,660
And they will cause conduction
in the valence band.

382
00:19:05,660 --> 00:19:08,600
And you know at high
temperatures, back over here,

383
00:19:08,600 --> 00:19:10,730
we have electrons moving to the
conduction band, which is

384
00:19:10,730 --> 00:19:12,680
traditionally what we think of
when we think of conduction,

385
00:19:12,680 --> 00:19:14,400
electrons moving around.

386
00:19:14,400 --> 00:19:16,740
So we have in this case
conduction in the conductor

387
00:19:16,740 --> 00:19:19,830
band as well as in
the valence band.

388
00:19:19,830 --> 00:19:21,440
So that's this problem.

389
00:19:21,440 --> 00:19:23,210
This problem was generally
pretty easy; many

390
00:19:23,210 --> 00:19:24,550
students got it right.

391
00:19:24,550 --> 00:19:26,350
The learning goals and
objectives we had from this

392
00:19:26,350 --> 00:19:31,700
problem were, number 1, to
understand doping principles.

393
00:19:31,700 --> 00:19:34,100
What it means to n
and p type dope.

394
00:19:34,100 --> 00:19:36,150
Holes versus electrons
and how you get them.

395
00:19:36,150 --> 00:19:38,990
So if you have germanium or
silicon, those are very common

396
00:19:38,990 --> 00:19:41,720
examples and you dope
things into them.

397
00:19:41,720 --> 00:19:47,000
So gallium or arsenic or
aluminum, for example.

398
00:19:47,000 --> 00:19:48,850
We talked about conduction
mechanisms--

399
00:19:48,850 --> 00:19:50,090
just like here--

400
00:19:50,090 --> 00:19:53,520
and we also talked about the
donor and acceptor levels.

401
00:19:53,520 --> 00:19:57,120
So the donor levels are just
slightly below the conduction

402
00:19:57,120 --> 00:19:58,840
band and are full
of electrons.

403
00:19:58,840 --> 00:20:01,190
And the acceptor levels are
just slightly above the

404
00:20:01,190 --> 00:20:04,010
valence band and initially
holes.

405
00:20:04,010 --> 00:20:08,480
So that's probablem 3 and I hope
you had good luck at It.