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Resistor Fabrication
ROCHESTER INSTITUTE OF TECHNOLOGY
MICROELECTRONIC ENGINEERING
Resistors
Dr. Robert Pearson
9-19-05 Resistor fabrication.ppt
Rochester Institute of Technology - MicroE © REP 5/5/2017
Device Fab. 1 page-1
Resistor Fabrication
OUTLINE
Definitions
Resistor I-V Characteristics
The Semiconductor Resistor
Resistivity
Carrier Mobility
The Diffused Semiconductor Resistor
Resistor Design and Cross-Sections
Resistor Fabrication Sequence (micrographs)
Resistor Networks, Terminations
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Resistor Fabrication
DEFINITIONS
Voltage - The force applied between two points causing charged
particles (and hence current) to flow. Units - Volts, and the symbol
used is V. Sometimes called the potential
Current - A measure of the number of charged particles passing a
given point per unit time. Units - Amperes or Coulombs per second.
The symbol I is usually used to denote a current.
Resistance - A measure of the ability of a sample of a material to allow
a current to pass through it when an external force or potential is
applied. The units are Ohms and the symbol R is used for a resistance.
Ohm’s Law V = I (R)
or
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R = V / I or
I=V/R
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Resistor Fabrication
MEASURING RESISTOR I-V CHARACTERISTIC
variable Voltage Supply
5
10
0
control
knob
+ -
resistor
(Volts)
V
Ammeter (measures current)
5
10
0
-
+
Volts
V
-5
-4
-3
-2
-1
0
1
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(Amperes)
I
Amperes
I
-0.005
-0.004
-0.003
-0.002
-0.001
0
0.001
Data Table
Resistance
(V/I) in Ohms
1000
1000
1000
1000
1000
?
1000
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Resistor Fabrication
PLOT OF I-V RESISTOR CHARACTERISTIC
I
R = V/I = 1/slope
V
Resistor a two terminal device that exhibits a
linear I-V characteristic that goes through the
origin. The inverse slope is the value of the
resistance.
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Resistor Fabrication
THE SEMICONDUCTOR RESISTOR
Resistance = R =  L/Area = s L/w
ohms
Resistivity =  1/( qµnn + qµpp)
ohm-cm
Sheet Resistance s = 1/ ( q µ(N) N(x) dx) ~ 1/( qµ Dose) ohms/square
s =  / t
integral
L
Area
w
t
Note: sheet resistance is convenient to
use when the resistors are made of thin
sheet of material, like in integrated
circuits.
R
q = 1.6E-19 coulombs
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Resistor Fabrication
RESISTIVITY OF SILICON
Impurity Concentration, N, cm-3
1021
1/(qµN)
1020
1019
Because the carrier mobility, µ
is a function of N and N is the
doping, the relationship
between resistivity  and N is
given in the figure shown to the
left, or calculated from
equations for µ as a function of
N (see next page)
1018
Boron doped silicon
1017
1016
1015
Phosphorous
Doped silicon
1014
1013
10-4
10-3
10-2
10-1 100
101
102
103
104
Resistivity, ohm-cm
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Resistor Fabrication
ELECTRON AND HOLE MOBILITY
Electron and hole mobilities in silicon at 300 K as functions of the total dopant
concentration (N). The values plotted on the next page are the results of the curve
fitting measurements from several sources. The mobility curves can be generated
using the equation below with the following parameter values:
(µmax-µmin)
µ(N) = µ min +
{1 + (N/Nref)}
Parameter
µmin
µmax
Nref

Arsenic
52.2
1417
9.68X10^16
0.680
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Phosphorous
68.5
1414
9.20X10^16
0.711
Boron
44.9
470.5
2.23X10^17
0.719
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Resistor Fabrication
ELECTRON AND HOLE MOBILITY
Carrier Mobilities versus Doping Concentration
1.60E+03
Carrier Mobility (cm2/V-sec)
1.40E+03
1.20E+03
1.00E+03
mu_n
mu_p
8.00E+02
6.00E+02
4.00E+02
2.00E+02
0.00E+00
1.00E+14 1.00E+15 1.00E+16 1.00E+17 1.00E+18 1.00E+19
Doping Concentration (Na or Nd)
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Resistor Fabrication
DIFFUSED RESISTOR
Aluminum contacts
Silicon dioxide
n-wafer
Diffused p-type region
The n-type wafer is always biased positive with respect to the p-type
diffused region. This ensures that the pn junction that is formed is in
reverse bias, and there is no current leaking to the substrate. Current
will flow through the diffused resistor from one contact to the other.
The I-V characteristic follows Ohm’s Law: I = V/R
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Resistor Fabrication
Layout/Mask Layer 1 - Diffusion (green)
Top View
W
Resistor
termination
L
Side View
P type Diffusion
N wafer
The resistance, R = rhos (L/W)
The sheet resistance rhos, is the resistance of each square
L/W is the number of ‘squares’ long the resistor is said to be.
5 squares in this case
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If rhos is 100 ohms
per square,
R = 500 ohms
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Resistor Fabrication
Layout/Mask Layer 3 - Contacts (gray)
Top View
W
10 by 10 microns
L
Side View
Remember, inside the
green (diagonally shaded)
regions is p type silicon,
outside is n type
contact
openings
Oxide
Diffusion
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N wafer
Device Fab. 1 page-12
Resistor Fabrication
Top View
Layout/Mask Layer 4 - Metal (blue)
10 by 10 microns
W
L
Side View
Metal (Aluminum)
Oxide
Diffusion
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Resistor
Symbol
N wafer
Device Fab. 1 page-13
Resistor Fabrication
Metal (Aluminum) wiring to the Probe Pads
Probes
Aluminum Pads
5 squares
5 squares
resistor 10 squares
rhos for aluminum is
0.01 Ohms per square
rhos for diffusion = 100 Ohms per square
Rtotal = 10(100) + (5+5)(0.01) = 1000.1 Ohms, therefore
Metal “wiring” does not add very much to the resistance
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Resistor Fabrication
Wafer with silicon dioxide, patterned and etched
This end of the resistor loops were cut off in the picture
MASK # 1
20mm
This resistor is
many, many
squares long
Green is oxide
(glass)
Gray is bare
silicon
Diffusion openings
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Resistor Fabrication
After dopants have been diffused in and a new oxide grown
 Purple areas are
diffused and pink
areas are not (the
oxide in this area
did not allow the
dopant to diffuse
into the silicon)
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Device Fab. 1 page-16
Resistor Fabrication
After thin oxide openings have been patterned and etched
 The thin oxide
layer is actually
part of the
transistor
fabrication
sequence
MASK # 2
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Bare Silicon
Device Fab. 1 page-17
Resistor Fabrication
After thin oxide growth (part of the transistor process)
1000Å of SiO2
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Resistor Fabrication
After the contact openings have been patterned and etched
MASK # 3
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Contact opening
To bare silicon
Device Fab. 1 page-19
Resistor Fabrication
After Aluminum has been deposited
 Aluminum short
circuits
everything at
this stage, until
it is patterned
and etched.
Particle on the
microscope
lens
Aluminum
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Device Fab. 1 page-20
Resistor Fabrication
After aluminum is patterned and etched
Contact
Unused
Pad
Aluminum
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Device Fab. 1 page-21
Resistor Fabrication
RESISTOR NETWORK
Desired resistor network
500 W
400
250 W
Layout
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Device Fab. 1 page-22
Resistor Fabrication
VARIATIONS ON THE BASIC RESISTOR LAYOUT
R = s (10+0.5+0.5)
1
2
3
0.5
4 4.5
5.5
6.5
Corner squares count ~ 1/2
7
8
9
10
0.5
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Device Fab. 1 page-23
Resistor Fabrication
RESISTOR TERMINATIONS
Field Mapping
~ 0 squares
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~ 0.5 squares
Device Fab. 1 page-24