Download How Electrons Become Bits

Digital Technology
How Electrons Become Bits
Thursday, September 15, 16
Alternatives
• Fluidics - can use hydraulics to work valves
• Analog - capacitors integrate, inductors
differentiate, etc.
• Optics - hard to control photons with
photons (electro-optics)
• DNA, Quantum
Thursday, September 15, 16
Binary Digital Concept
• On-Off circuit can represent base-2 (binary) digits
(bit) values of 1 or 0
• Parallel circuits represent multi-digit values
• Everything in the world can be digitized (broken
0
1
0
1
1
0
1
0
into discrete units with numerical values)
• Computers can represent and operate on any kind
of data using on-off circuits, through Boolean
algebra, which uses True and False (1 and 0)
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Precursors
• Mechanical - decimal gearing
• Electromechanical
• Binary coded decimal (4 bits for 0-9)
• True binary
• Vacuum tube/transistor repeats designs
• IC transitions to mostly binary
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Words
• Because number of parallel wires is fixed
once a machine is built, the basic numerical
unit of computation is also fixed (called
word size)
1, 4, 8, 12, 16, 18, 24, 32, 36, 48, 60, 64, 68, 72, 80
• Other numerical units are multiples or
integral partitions of word size
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Requisites for Binary
Digital Technology
• Some kind of electronically controlled
switching device
• Rapid switching between on and off
states (no intermediate voltage level)
• Easily wired together, with low
resistance
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Not like this
Materials
• Conductors (electrons flow freely)
• Insulators (electrons do not flow)
• Semiconductors (in between)
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Energy Bands
• Electrons occupy discrete energy levels
around a nucleus
• With multiple atoms, electrons have more
levels, which become bands of energy level
• Valence and Conduction
• Conduction band has free electrons, with
high mobility
• Valence is just below
• Full bands cannot conduct -- need holes
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Conductors
• Valence and conduction band energies
overlap
• Valence band is nearly filled with electrons
• Due to band overlap, electrons can easily
attain conduction band level and move
between atoms
Conduction
Valence
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Insulators
• Valence and conduction bands widely
separate in energy level (band gap)
• No or few electrons in conduction band
• Valence band not fully populated
• High energy needed to lift electrons over
band gap, so resist movement between atoms
Conduction
Valence
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Electrons and Holes
• Electrons carry negative charge
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- - - --
Electrons and Holes
• Moving an electron out of the
Valence band leaves a hole
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- -
- --
Electrons and Holes
- -
- --
• Holes attract electrons and act
like positive charge carriers
-
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Semiconductors
• No overlap in Valence and Conduction
bands but energy gap is small
• Pure form acts as an insulator
• Implanted impurities narrow band gap of
material by providing extra electrons or
holes
Conduction
Valence
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Dopants
• Can be doped with materials to add
electrons or holes
• Boron adds holes (P-type)
• Hole-carrier material
• Phosphorus adds electrons (N-type)
• Electron carrier material
Thursday, September 15, 16
Transistors
• Source, Gate, Drain
• N-type body (pMOS) conducts holes when
negative voltage (gate to source) applied
• P-type body (nMOS) conducts electrons
when positive voltage (gate to source)
applied
• Act as switches
Thursday, September 15, 16
Cross Section View
Thursday, September 15, 16
NMOS
(P semiconductor, N-channel)
-------- Gate -------N Source
Oxide
+++++++++++++
N Drain
P semiconductor body
- charge on gate. Hole carriers in body prevent
flow of electron carriers between source and drain
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NMOS
(P semiconductor, N-channel)
+++++Gate+++++
Oxide
-----------------------N Source
N
Drain
Inversion Layer
+++++++++++++
P semiconductor body
+ charge on gate repels + carriers in body, opening layer
of - carriers so current can flow from source to drain
Thursday, September 15, 16
PMOS
(N semiconductor well, P-channel)
+++++Gate+++++
P Source
Oxide
--------------------------
P Drain
N semiconductor well
P semiconductor body
+ charge on gate. Electron carriers in body prevent
flow of hole carriers between source and drain
Thursday, September 15, 16
PMOS
(N semiconductor, well P-channel)
--------Gate-------Oxide
P Source ++++++++++++++
P
Drain
Inversion Layer
N-------------------------semiconductor well
P semiconductor body
- charge on gate repels - carriers in body, opening layer
of + carriers so current can flow from source to drain
Thursday, September 15, 16
Schematically
P-type
N-type
Complementary Metal Oxide Semiconductor: CMOS
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N-type
Drain
Gate
Source
Switch conducts electrons from source to drain when
+voltage applied to gate, insulates with -voltage
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P-type
Source
Gate
Drain
Switch turns off (insulates) when +voltage applied to gate.
Conducts holes from source to drain when -voltage applied
Thursday, September 15, 16
What does it do?
Vcc
Out
In
Ground
Thursday, September 15, 16
What does it do?
Vcc
Out
In
Ground
Thursday, September 15, 16
What does it do?
Vcc
One
Out
In
Ground
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Zero
What does it do?
Vcc
Out
Zero In
Ground
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One
Inverter
Vcc
Out
In
Note that Vcc and
Ground were never
connected together
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Ground
Schematically
NOT
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What Does it Do?
Vcc
In 2
Out
In 1
In 2
Ground
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In 1=0, In 2=0
Vcc
In 2
Out
In 1
In 2
Ground
Thursday, September 15, 16
In 1=0, In 2=1
Vcc
In 2
Out
In 1
In 2
Ground
Thursday, September 15, 16
In 1=1, In 2=0
Vcc
In 2
Out
In 1
In 2
Ground
Thursday, September 15, 16
In 1=1, In 2=1
Vcc
In 2
Out
In 1
In 2
Ground
Thursday, September 15, 16
Truth Table View
Thursday, September 15, 16
In1
In 2
Out
0
0
1
0
1
1
1
0
1
1
1
0
Compare to AND
Thursday, September 15, 16
In1
In 2
Out AND
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
Compare to AND
NAND
Thursday, September 15, 16
In1
In 2
Out AND
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
Schematically
NAND
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NAND Inverter
NAND
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In1
In 2
Out
0
0
1
0
1
1
1
0
1
1
1
0
NAND Inverter
NAND
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In1
In 2
Out
0
0
1
0
1
1
1
0
1
1
1
0
NAND Inverter
NAND
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In1
In 2
Out
0
0
1
0
1
1
1
0
1
1
1
0
What Does it Do?
Vcc
In 2
In 1
Out
In 2
Ground
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In 1=0, In 2=0
Vcc
In 2
In 1
Out
In 2
Ground
Thursday, September 15, 16
In 1=0, In 2=1
Vcc
In 2
In 1
Out
In 2
Ground
Thursday, September 15, 16
In 1=1, In 2=0
Vcc
In 2
In 1
Out
In 2
Ground
Thursday, September 15, 16
In 1=1, In 2 = 1
Vcc
In 2
In 1
Out
In 2
Ground
Thursday, September 15, 16
Truth Table View
Thursday, September 15, 16
In1
In 2
Out
0
0
1
0
1
0
1
0
0
1
1
0
Compare with OR
Thursday, September 15, 16
In1
In 2
Out
OR
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
1
Compare with OR
NOR
Thursday, September 15, 16
In1
In 2
Out
OR
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
1
Schematically
NOR
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NOR Inverter
NOR
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In1
In 2
Out
0
0
1
0
1
0
1
0
0
1
1
0
NOR Inverter
NOR
Thursday, September 15, 16
In1
In 2
Out
0
0
1
0
1
0
1
0
0
1
1
0
NOR Inverter
NOR
Thursday, September 15, 16
In1
In 2
Out
0
0
1
0
1
0
1
0
0
1
1
0
Universal Boolean
Operators
• AND, OR, NOT can be combined to
express any Boolean expression
• NAND can become NOT with addition of
a wire
• NOT (A NAND B) = A AND B
• Can NAND become OR?
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NAND OR
A
B NAND NOT A NOT B NOT A NAND NOT B
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
Because we can build NOT with NAND,
we can also build OR entirely with NAND circuits
Thursday, September 15, 16
Universal Boolean
Operators
• AND, OR, NOT can be combined to
express any Boolean expression
• NAND can become NOT with addition of
a wire
• NOT (A NAND B) = A AND B
• NOT A NAND NOT B = A OR B
• Thus NAND is universal by itself
Thursday, September 15, 16
Where We Are
• NOR can also be shown to be universal
• We have now seen how transistors can
make circuits that mimic all the Boolean
operators necessary for any expression
• We will see that if we take True = 1 and
False = 0, then Boolean logic is capable of
representing binary (base-2) arithmetic
Thursday, September 15, 16