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First Task: What is the mobility the material (= semiconductor) must have?
Discuss the result in considering the following points - Transistor speed = device speed ???
- Mobility range for a given material ??
- Could we have powerful PCs without micro- or nanotechnology ??
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The essential equation is
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tSD = |
lSD2 µ · USD |
≈ |
1 fmax |
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The necessary mobility thus is given by |
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µ = |
lSD2
tSD · USD | = |
fmax · lSD2
USD | = |
4 · 109 · 2.5 · 10–13
3 | · |
m2 s · V |
= 0.33 · 10–3 |
m2 s · V |
= 3.3 |
cm2 s · V |
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What is the mobility of typical semiconductors? Finding values in the Net is not too difficult;
if you just turn to the Hyperscript "Semiconductors"
you should find this link |
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Well, all "useful" semiconductors seem to be OK, their mobilities are much larger than what we
need. But perhaps we are a little naive? |
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Yes, we are! If a device combining some 10.000.000 transistors is to have a limit frequency of 4
Ghz, an individual transistor "obviously" must be much faster. If you don't see the obvious, think about the
routing of many letters by the mail through a few million post offices (with different routes for every letter) and compare
the individual and (average) total processing times. |
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Bearing this in mind, mobilities of about a factor of 100 larger than the one we calculated do not
look all that good anymore! |
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The mobility table in the link shows large variations in mobility for a given material - obviously
µ is not really a material constant but somehow depends on the detailed structure. |
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We do not need to understand the intricacies of that table - we
already know that µ is directly proportional to the mean free path length l and thus somehow
inversely proportional to defect densities. |
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It is very clear, then, that for high-speed devices we need rather perfect crystals! So let's try to have
single crystals, with no dislocations (or at least only small densities, meaning that the crystal must never
plastically), and the minimum number of extrinsic and intrinsic point defects. |
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Quite clear - but do you see the intrinsic problem? A more or less
perfect crystal is not a device! To make a device from a crystal, we must do something
to the crystal. And whatever you do to a perfect crystal - the result can only be a
less perfect crystal! |
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In other words: Making a device means to start with very good crystals and only induce the minimum of defects
that is absolutely necessary. |
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Could we have 4 GHz without microelectronics? |
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Well, take for lSD a value 100 times larger, and your highest frequency
will be 10.000 times smaller - 400 kHz in the example. Of course, the 4 GHz of modern processors is
not only determined by mobility values of the materials used, but the argument is nevertheless valid. |
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So, without microelectronics (or by now nanoelectronics) life would by much different, because you can
just about forget everything you do as a direct (and indirect!) present-day "user" of electronics. But would it
be worse? The answer is a definite: Yes - it would be worse! Trust me - I have been there! It's not that long ago that 400
kHz was considered a pretty high frequency. |
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