1. Ingeniería

Diode Review
ROCHESTER INSTITUTE OF TEHNOLOGY
MICROELECTRONIC ENGINEERING
Diode Review
Dr. Lynn Fuller
Webpage: http://people.rit.edu/lffeee
Microelectronic Engineering
Rochester Institute of Technology
82 Lomb Memorial Drive
Rochester, NY 14623-5604
Tel (585) 475-2035
Email: [email protected]
Department webpage: http://www.microe.rit.edu
Rochester Institute of Technology
Microelectronic Engineering
1-28-15 diode_review.ppt
© January 28, 2015 Dr. Lynn Fuller, Professor
Page 1
Diode Review
OUTLINE
Uniform Doped pn Junction
Real pn Junctions
Diode Temperature Sensors
Photodiodes
Other Semiconductors
LEDs
Rochester Institute of Technology
Microelectronic Engineering
© January 28, 2015 Dr. Lynn Fuller, Professor
Page 2
Diode Review
CONSTANTS
Electronic charge
Speed of light in vacuum
Permittivity of vacuum
Free electron Mass
Planck constant
Boltzmann constant
Avogadro’s number
Thermal voltage
q
c
o
mo
h
k
Ao
kT/q
1.602 E -19 Coulomb
2.998E8 m/s
8.854 E -14 F/cm
9.11E-31 Kg
6.625E-34 J s
1.38 E-23 J /°K = 8.625E-5 eV/°K
6.022E23 molecules/gm- mole
@ 300 °K = 0.02586
PLAY
Rochester Institute of Technology
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© January 28, 2015 Dr. Lynn Fuller, Professor
Page 3
Diode Review
1
PERIODIC TABLE OF THE ELEMENTS
1.0079
2
He
H
0.1787
Helium
0.0899
Hydrogen
3
6.914
4
Be
0.53
Lithium
1.85
Beryllium
1122.9898 12
Density
g/cm3
24.305
Na
Mg
0.97
Sodium
1.74
Magnesium
47.90
K
Ca
Sc
Ti
0.86
Potassium
1.55
Calcium
3.0
Scandium
4.50
Titanium
38
87.62
39
88.906
40
91.22
Rb
Sr
Y
Zr
1.53
Rubidium
2.8
Strontium
4.5
Yttrium
6.49
Zirconium
55
132.90
56
137.33
14
20.086
Si
57 138.906 58
178.49
23 50.941 24
V
51.996
Cr
7.19
5.8
Vanadium Chromium
41
92.906
Nb
42
95.94
25
54.938
180.95
183.85
27 58.9332 28
29
63.546
30
65.238
14.0067
8
15.9994
9 18.9984 10
20.179
B
C
N
O
F
Ne
2.34
Boron
2.62
Carbon
1.251
Nitrogen
1.429
Oxygen
1.696
Fluorine
0.901
Neon
13
58.70
7
12.011
26.9815
14
20.086
15 30.97376 16
32.06
17
35.453
18
39.948
Al
Si
P
S
Cl
Ar
2.70
Aluminum
2.33
Silicon
1.82
Phosphorous
2.07
Sulfur
3.17
Clorine
1.784
Argon
31
69.72
32
72.59
33 74.9216 34
78.96
35
79.904
36
83.80
Fe
Co
Ni
Cu
Zn
Ga
Ge
As
Se
Br
Kr
7.43
Manganese
7.86
Iron
8.90
Selenium
8.90
Nickel
8.96
Copper
7.14
Zinc
5.98
Gallium
5.32
Germanium
5.72
Arsenic
4.80
Selenium
3.12
Bromine
3.74
Krypton
43
Mo
60
55.847
6
10.81
Mn
98
44
61
186.207
101.07
45 102.9055 46
47
106.4
107.868
48
112.41
49
114.82
50
118.69
51
121.75
26
55.847
26
127.60
54
131.30
Ru
Rh
Pd
Ag
Cd
In
Sn
Sb
Te
Fe
Xe
12.2
Rhodium
12.4
Rhodium
12.0
Palladium
10.5
Silver
8.65
Cadmium
7.31
Indium
7.30
Tin
6.68
Antimony
6.24
Tellurium
7.86
Tellurium
5.89
Xenon
76
77
78
84
85
Tc
8.55
10.2
11.5
Niobium Molybdenum Technetium
59
26
5
Name
2.33
Silicon
19 39.0983 20 40.08 21 44.9559 22
85.468
Atomic Weight
Symbol
Atomic Number
9.01218
Li
37
4.0026
190.2
192.22
79 196.9665 80
195.09
200.59
81
204.37
82
207.2
83
206.980
209
210
86
222
Cs
Ba
La
Hf
Ta
W
Re
Os
Ir
Pt
Au
Hg
Tl
Pb
Bi
Po
At
Rn
1.87
Cesium
3.5
Barium
6.7
Lanthanum
13.1
Hafnium
16.6
Tantalum
19.3
Tungstem
21.0
Rhenium
22.4
Osmium
27.16
Iridium
21.4
IPlatinum
19.3
Gold
13.53
Mercury
11.85
Thallium
11.4
Lead
9.8
Bismuth
9.4
Polonium
???
Astatine
9.91
Radon
89
104 261 105 262 106 263
87
223
88
226.02
Fr
Ra
???
Francium
5
Radium
227.02
Ac
PLAY
Unq Unp Unh
10.07
????
Unnilpentium
????
Actinium Unnilquadium
Unnilhexium
58 140.12 59 140.91 60
Ce
Pr
144.24
Nd
61 145
Pm
62 150.4 63 151.96 64 157.25
Sm
6.78
6.77
7.00
6.475
7.54
Cerium PraseoymiumNeodymium Promethium Samarium
90 232.0
Th
91 231 92 238.02
Pa
U
93 237
Np
11.7
15.4
18.90
Thorium Protactinium Uranium
94
237
Eu
95 243
Pu Am
20.4
19.8
13.6
Neptunium PlutoniumAmericium
Rochester Institute of Technology
Microelectronic Engineering
Gd
5.26
7.89
Europium Gadolinium
96
247
65 158.92
66
162.5
67 164.93
68 167.26
69 169.93
70
173.04
71
174.97
Tb
Dy
Ho
Er
Tm
Yb
Lu
8.27
Terbium
8.54
Dysprosium
8.90
Holmium
9.06
Erbium
9.33
Thulium
6.98
Ytterbium
9.84
Lutetium
97 247
98
251
99 252
Cm
Bk
Cf
Es
13.511
Curium
????
Berkelium
????
Californium
????
Einsteinium
© January 28, 2015 Dr. Lynn Fuller, Professor
100 257 101
Fm
258
Md
????
????
Fermiumr Mendelevium
Page 4
102
259
103
260
No
Lr
????
Nobelium
????
Lawrencium
Diode Review
MATERIAL PROPERTIES
Symbol
Atoms per unit cell
Atomic Number
Atomic weight
Lattice constant
Atomic density
Density
Energy Gap 300°K
Relative permittivity
Index of refraction
Melting point
Specific heat
Thermal diffusivity
Coefficient expansion
Intrinsic carrier conc
Electron Mobility
Hole Mobility
Density of States conduction
Density of States valance
Breakdown Electric Field
Effective mass electron
Effective mass hole
Electron affinity
Z
MW
ao
No
d
Eg
r
n
Tm
Cp
K
Dth
ni
µn
µp
Nc
Nv
E
mn*/mo
mp*/mo
qX
Units
g/g-mole
nm
cm-3
g cm-3
eV
°C
J (gK)-1
w(cmK)-1
K-1
cm-3
cm2/Vs
cm2/Vs
cm-3
cm-3
V/cm
eV
Si
8
14
28.09
0.54307
5.00E22
2.328
1.124
11.7
3.44
1412
0.70
0.87
2.5E-6
1.45E10
1417
471
2.8E19
1.04E19
3E5
1.08
0.81
4.05
Ge
8
32
72.59
0.56575
4.42E22
5.323
0.67
16.0
3.97
937
0.32
0.36
5.7E-6
2.4E13
3900
1900
1.04E19
6.0E18
8E4
0.55
0.3
4.00
GaAs
8
31/33
144.64
0.56532
2.21E22
5.316
1.42
13.1
3.3
1237
0.35
0.44
5.9E-6
9.0E6
8800
400
4.7E17
7.0E18
3.5E5
0.068
0.5
4.07
GaP
8
31/15
100.70
0.54505
2.47E22
4.13
2.24
10.2
3.3
1467
Si3N4
14/8
60.08
14/7
140.28
0.775
1.48E22
3.44
4.7
7.5
2.0
0.004
5.3E-6
2.20E22
2.19
8~9
3.9
1.46
1700
1.4
0.32
5E-6
300
100
20
10E-8
6~9E6
0.5
0.5
4.3
Rochester Institute of Technology
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© January 28, 2015 Dr. Lynn Fuller, Professor
SiO2
Page 5
1.0
0.17
2.8E-6
Diode Review
UNIFORMLY DOPED PN JUNCTION
P+ Phosphrous donor atom and electron
Space Charge Layer
P+ Ionized Immobile Phosphrous donor atom
BB-
Ionized Immobile Boron acceptor atom
+
n = ND
p = NA
B-
+
B-
B-
+
B-
p-type
Boron acceptor atom and hole

B-
charge density, 
qNA W1 =qND W2
P+
P+
P+ P+
P+
P+
P+
P+
P+
+VR
n-type
+qND
-W1
x
W2
-qNA
Electric Field,

Potential, 
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© January 28, 2015 Dr. Lynn Fuller, Professor
 +VR
Page 6
Diode Review
UNIFORMLY DOPED pn JUNCTION
From Physical Fundamentals:
Potential Barrier - Carrier Concentration:
 = KT/q
ln (NA ND /ni2)
From Electric and Magnetic Fields :
Gauss’s Law, Maxwells 1st eqn:
=
D
Relationship between electric flux D and electric field  : D = 
Poisson’s Equation:
2
 = -  / 
Definition of Electric Field:

= -
V
Rochester Institute of Technology
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© January 28, 2015 Dr. Lynn Fuller, Professor
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
Diode Review
 FROM PHYSICS (FERMI STATISTICS)
q(Vbi) = (Ei - Ef)p-side + (Ef-Ei) n-side
p= ni e(Ei-Ef)/KT/q
ln(p/ni) = ln e(Ei-Ef)/KT/q
KT/q ln(p/ni) = (Ei-Ef)p-side
n= ni e(Ef-Ei)/KT/q
ln(n/ni) = ln e(Ef-Ei)/KT/q
KT/q ln(n/ni) = (Ef-Ei)n-side
 = KT/q ln (NA ND /ni2)
ni = 1.45E10 cm-3 for silicon
Rochester Institute of Technology
Where
NAEngineering
=~p in p-type silicon and ND=~n in n-type silicon
Microelectronic
© January 28, 2015 Dr. Lynn Fuller, Professor
Page 8
Diode Review
UNIFORMLY DOPED PN JUNCTION
Built in Voltage:
 = KT/q
ln (NA ND /ni2)
ni = 1.45E10 cm-3
Width of Space Charge Layer, W: with reverse bias of VR volts
W  W1  W2 
= [ (2 q  +VR) (1/NA  1/ND)]1/2
W1 width on p-side
W1 = W [ND/(NA  ND)]
W2 width on n-side
W2 = W [NA/(NA  ND)]
Maximum Electric Field:
 =
- [(2q/  +VR) (NA ND/(NA  ND))]1/2
Junction Capacitance per unit area:
Cj’   rW
=  r[(2 q  +VR) (1/NA  1/ND)]1/2
Rochester Institute of Technology
Microelectronic Engineering
  o r = 8.85E-12 (11.7) F/m
= 8.85E-14 (11.7) F/cm
© January 28, 2015 Dr. Lynn Fuller, Professor
Page 9
Diode Review
EXAMPLE
Example: If the doping concentrations are Na=1E15 and Nd=3E15
cm-3 and the reverse bias voltage is 0, then find the built in voltage,
width of the space charge layer, width on the n-side, width on the pside, electric field maximum and junction capacitance. Repeat for
reverse bias of 10, 40, and 100 volts.
 = Vbi = KT/q ln (NA ND /ni2) =
W  W1  W2  = [ (2/q) ( +VR) (1/NA  1/ND)]1/2
=
W1 =
W2 =
Emax =
Cj =
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© January 28, 2015 Dr. Lynn Fuller, Professor
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Diode Review
EXAMPLE CALCULATIONS
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Diode Review
REAL JUNCTION
Real pn junctions: The uniformly doped abrupt junction
is rarely obtained in integrated circuit devices. (epi layer
growth is close).
Diffused pn junction:
NA
NBC = ND (x)
x
0
Xj
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© January 28, 2015 Dr. Lynn Fuller, Professor
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Diode Review
REAL pn JUNCTION
Given, Xj, NA (X), ND (X)
Calculate potential V1 from
physical fundamentals:
V1= KT/q ln (NA ND /ni2) + VR
Pick an X1 to the left of Xj.
Calculate the total charge per
unit area in the region
Between X1 and Xj. This
charge is Q1.
Calculate potential V2 from
E & M fields fundamentals:
2
Pick an X2 to the right of Xj.
Calculate the total charge per
unit area in the region between
X2 and Xj. This charge is Q2.
 = -  / 
No
V1 = V2
Yes
No
Calculate W1 = X1, W2 = X2
W = W1 + W2, Cj, other
Q1 = Q2
Rochester Institute of Technology
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Yes
© January 28, 2015 Dr. Lynn Fuller, Professor
Page 13
Diode Review
REAL, UNIFORM DOPED, SINGLE SIDED DIODES
Example: assume that the heavily doped side of a pn junction is
doped at 1E20, calculate the doping necessary on the lightly doped
side such that the space charge layer is ~0.1 µm. With 5 volts reverse
bias.
 = KT/q ln (NA ND /ni2)
guess ~0.9 volts
W  W1  W2 
= [ (2/q) ( +VR) (1/NA  1/ND)]1/2 = 0.1 µm = 0.1E-4 cm
5.9V
0
N  2 11.78.85-145.91.6-190.1-42  7.617 cm-3
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© January 28, 2015 Dr. Lynn Fuller, Professor
Page 14
Diode Review
CURRENTS IN PN JUNCTIONS
Id
VRB = reverse
breakdown voltage
Forward Bias
Is
VD
Reverse Bias
Vbi = turn on voltage
~ 0.7 volts for Si
Id
Ideal diode equation
p
n
+ VD Rochester Institute of Technology
Microelectronic Engineering
Id = Is [EXP (q VD/KT) -1]
Is = qA (Dp/(LpNd) +Dn/(LnNa))ni2
© January 28, 2015 Dr. Lynn Fuller, Professor
Page 15
Diode Review
INTEGRATED DIODES
n+
n-well
p+
p-wafer
p+ means heavily doped p-type
n+ means heavily doped n-type
n-well is an n-region at slightly higher
doping than the p-wafer
Note: there are actually two pn junctions, the well-wafer pn
junction should always be reverse biased
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© January 28, 2015 Dr. Lynn Fuller, Professor
Page 16
Diode Review
REAL DIODES
Series Resistance =1/4.82m=207
Junction Capacitance ~ 2 pF
Is = 3.02E-9 amps
BV = > 100 volts
Size 80µ x 160µ
P
N
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© January 28, 2015 Dr. Lynn Fuller, Professor
Page 17
Diode Review
DIODE SPICE MODEL
DXXX N(anode) N(cathode) Modelname
.model Modelname
D Is=Value Cjo=value Rs=value
Model Parameter
Is reverse saturation current
N emission coefficient
RS series resistance
VJ built-in voltage
CJ0 zero bias junction capacitance
M grading coefficient
BV Breakdown voltage
IBV Reverse current at breakdown
MEMS Diode
Default Value Extracted Value
1e-14 A
3.02E-9 A
1
1
0
207 ohms
1V
0.6
0
2pF
0.5
0.5
infinite
400
1E-10 A
-
.model RITMEMS D IS=3.02E-9 N=1 RS=207
Rochester Institute of Technology
+VJ=0.6 CJ0=2e-12 M-0.5 BV=400
Microelectronic Engineering
© January 28, 2015 Dr. Lynn Fuller, Professor
Page 18
Diode Review
DIODE TEMPERATURE DEPENDENCE
Id = IS [EXP (q VD/KT) -1]
Neglect the –1 in forward bias, Solve for VD
VD = (KT/q) ln (Id/IS) = (KT/q) (ln(Id) – ln(Is))
eq 1
Take dVD/dT: note Id is not a function of T but Is is
dVD/dT = (KT/q) (dln(Id)/dT – dln(Is)/dT) + K/q (ln(Id) – ln(Is))
zero
VD/T from eq 1
Rewritten
dVD/dT = VD/T - (KT/q) ((1/Is) dIs/dT )
eq 2
Now evaluate the second term, recall
Is = qA (Dp/(LpNd) +Dn/(LnNa))ni2
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Note: Dn and Dp are proportional to 1/T
© January 28, 2015 Dr. Lynn Fuller, Professor
Page 19
Diode Review
DIODE TEMPERATURE DEPENDENCE
ni2(T) = A T 3 e - qEg/KT
and
This gives the temperature dependence of Is
Is = C T 2 e - qEg/KT
Now take the natural log
ln Is = ln (C T 2 e - qEg/KT)
Take derivative with respect to T
eq 3
(1/Is) d (Is)/dT = d [ln (C T 2 e -qEg/KT)]/dT = (1/Is) d (CT2e-qEg/KT)dT
= (1/Is) [CT2 e-qEg/KT(qEg/KT2) + (Ce-qEg/KT)2T]
= (1/Is) [Is(qEg/KT2) + (2Is/T)]
Back to eq 2
dVD/dT = VD/T - (KT/q) [(qEg/KT2) + (2/T)])
dVD/dT = VD/T - Eg/T - 2K/q)
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© January 28, 2015 Dr. Lynn Fuller, Professor
Page 20
Diode Review
EXAMPLE: DIODE TEMPERATURE DEPENDENCE
dVD/dT = VD/T - Eg/T - 2K/q
Silicon with Eg ~ 1.2 eV, VD = 0.6 volts, T=300 °K
dVD/dT = .6/300 – 1.2/300) - (2(1.38E-23)/1.6E-19
= -2.2 mV/°
T2
I
T1
T1<T2
V
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© January 28, 2015 Dr. Lynn Fuller, Professor
Page 21
Diode Review
DIODE TEMPERATURE SENSOR RESPONSE
Poly Heater, Buried pn Diode,
N+ Poly to Aluminum Thermocouple
P+
N+
Apply 5 volts (gives ~ 65mA)
P=IV =0.3 watts
Delta Vd = 0.64 -0.48 = 0.16
Delta T = 0.16 / 2.2mV = 72.7 °C
Rochester Institute of Technology
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© January 28, 2015 Dr. Lynn Fuller, Professor
Page 22
Diode Review
PHOTODIODE
space charge layer
+
B-
P+
B-
p-type
B-
B-
B-
B-
-
P+
+
electron
and hole
pair
-
P+
+
P+
P+
P+
B-
+
B-
+
B-
P+
+
P+
P+

P+
I
BP+
B-
-
+
n-type
P+
P+
Phosphrous donor atom and electron
Ionized Immobile Phosphrous donor atom
Ionized Immobile Boron acceptor atom
Boron acceptor atom and hole
Rochester Institute of Technology
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© January 28, 2015 Dr. Lynn Fuller, Professor
Page 23
Diode Review
V
I
p
I
n
I
+
V
-
V
No Light
More Light
Most Light
Adsorption Coefficient, a (1/cm)
ADSORPTION VERSUS DISTANCE
1.00E+06
Adsorption Coefficient vs Wavelength
For Silicon
1.00E+05
1.00E+04
1.00E+03
1.00E+02
1.00E+01
1.00E+00
1.00E-01
1.00E-02
1.00E-03
1.00E-04
1.00E-05
1.00E-06
250
450
650
850
1050
Wavelength (nm)
Rochester Institute of Technology
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f(x) = f(0) exp-a x
Find % adsorbed for Green light
at x=5 µm and Red light at 5 µm
© January 28, 2015 Dr. Lynn Fuller, Professor
Page 24
1250
1450
Diode Review
PHOTO DIODE RESPONSE TO LIGHT
1mm
2mm
42uA
P
N
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© January 28, 2015 Dr. Lynn Fuller, Professor
Page 25
Diode Review
CHARGE GENERATION vs WAVELENGTH
E = h = hc / 
h = 6.625 e-34 j/s
= (6.625 e-34/1.6e-19) eV/s
2
1
E = 1.55 eV (red)
E = 2.50 eV (green)
E = 4.14 eV (blue)
3
+
BP+
B-
B-
B-
BP+
n-type P+
-
+
B-
+
P+
P+
+
4
p-type
P+
P+

P+
B-
P+
II
B-
B-
-
+
P+
P+
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© January 28, 2015 Dr. Lynn Fuller, Professor
Page 26
Diode Review
VARIOUS SEMICONDUCTORS
E = h = hc / 
What wavelengths will not
generate e-h pairs in silicon.
Thus silicon is transparent or
light of this wavelength or
longer is not adsorbed?
h = Plank’s constant
c = speed of light
From: Micromachined Transducers,
Gregory T.A. Kovacs
Rochester Institute of Technology
Microelectronic Engineering
Material
Bandgap
eV @ 300°K
max
(um)
GaN
3.360
0.369
ZnO
3.350
0.370
SiC
2.996
0.414
CdS
2.420
0.512
GaP
2.260
0.549
CdSe
1.700
0.729
GaAs
1.420
0.873
InP
1.350
0.919
Si
1.120
1.107
Ge
0.660
1.879
PbS
0.410
3.024
PbTe
0.310
4.000
InSb
0.170
7.294
© January 28, 2015 Dr. Lynn Fuller, Professor
Page 27
Diode Review
LIGHT EMITTING DIODES (LEDs)
Electron concentration vs distance
Hole concentration vs distnace
Light
Light
Space
charge
Layer
x
x
P-side
N-side
In the forward biased diode current flows and as holes
recombine on the n-side or electrons recombine on the p-side,
energy is given off as light, with wavelength appropriate for the
energy gap for that material.  = h c / E
h = Plank’s constant
Rochester Institute of Technology
c = speed of light
Microelectronic Engineering
© January 28, 2015 Dr. Lynn Fuller, Professor
Page 28
Diode Review
LED
Light Emitting Diode -LED
Flat
n
p
- Va +
Rochester Institute of Technology
Microelectronic Engineering
© January 28, 2015 Dr. Lynn Fuller, Professor
Page 29
Diode Review
OPTICAL LINK CIRCUIT DESIGN
Lets design a LED/Photo Detector circuit for a digital communication link.
Assumptions:
Block Diagram:
Circuit Diagram:
Rochester Institute of Technology
Microelectronic Engineering
© January 28, 2015 Dr. Lynn Fuller, Professor
Page 30
Diode Review
REFERENCES
1. Micromachined Transducers, Gregory T.A. Kovacs, McGrawHill, 1998.
2. Chapter 3 of Microelectronic Circuits, by Sedra and Smith
3. http://www.digikey.com
Rochester Institute of Technology
Microelectronic Engineering
© January 28, 2015 Dr. Lynn Fuller, Professor
Page 31
Diode Review
HOMEWORK: DIODE REVIEW
1. Look up the 1N4448 diode on the Digikey.com webpage, find the
unit price, max current, max reverse voltage, package types, etc.
2. A pn junction has Na=2e16 and Nd=5e17. At 0 volts bias
calculate the Vbi, W, W1, W2, Emax, and Cj.
3. Calculate the reverse breakdown voltage for a pn junction with
Nd=1e19 and Na=2.75e16.
4. Design a pn junction and an amplifier circuit that will make a
good photo detector for red light. State reasonable assumptions.
5. A diode is used to rectify an ac voltage from a transformer and
charge a 1uF capacitor. Estimate how long it will take the capacitor
to discharge from 3 volts to 1.5 volts (once ac voltage is turned off)
Rochester Institute of Technology
a) with no load
b) with a scope probe across the capacitor.
Microelectronic Engineering
© January 28, 2015 Dr. Lynn Fuller, Professor
Page 32
Diode Review
HOMEWORK: DIODE REVIEW
6. Repeat problem 5 but use the largest value 3 volt super capacitor
available from digikey.com.
7. Diodes and capacitors can be used to create a very large dc voltage
from a relatively small ac voltage. These circuits are called voltage
multipliers. Using a 5 volt peak ac voltage estimate the dc output
voltage of this multiplier circuit.
Vin
Vout
Rochester Institute of Technology
Microelectronic Engineering
© January 28, 2015 Dr. Lynn Fuller, Professor
Page 33
Diode Review
OPTICAL LINK CIRCUIT DESIGN
Design a LED/Photo Detector circuit for a digital communication link.
Assumptions: Assume we have +5 and -5 volts available and the
digital signal is 0 or 5 volts.
Block Diagram:
Digital In
LED ….
Photo
Detector
I to V
Amp
Analog V
To
Digital
Circuit Design:
Rochester Institute of Technology
Microelectronic Engineering
© January 28, 2015 Dr. Lynn Fuller, Professor
Page 34
Digital Out