Measurement and Analysis of 1/f Noise
in Uncooled Microbolometers
by
Jason T. Timpe
Submitted to the Department of Electrical Engineering and Computer Science
in Partial Fulfillment of the Requirements for the Degree
Master of Engineering in Electrical Engineering and Computer Science
at the Massachusetts Institute of Technology
May 22, 2000
Copyright 2000 Jason T. Timpe. All rights reserved.
The author hereby grants to M.I.T. permission to reproduce and
distribute publicly paper and electronic copies of this thesis
and to grant others the right to do so.
Author
DepArtment of Electrical Engineering and Computer Science
May 22, 2000
Certified by_
igH
Qing
Hu
TOsis Spervisor
Accepted by
A Irthur C. Smith
Chairman, Department Committee on Graduate Theses
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
JUL 3 12002
LIBRARIES
1
Measurement and Analysis of 1/f Noise in Uncooled Microbolometers
by
Jason T. Timpe
Submitted to the
Department of Electrical Engineering and Computer Science
May 22, 2000
In Partial Fulfillment of the Requirements for the Degree of
Master of Engineering in Electrical Engineering and Computer Science
ABSTRACT
A method for measuring the 1/f noise in bolometers was developed that would be most
conducive to a production environment. Several experiments were performed to discover
how best to reduce the 1/f noise through processing changes. A model was developed to
predict the performance of an infrared camera based on the 1/f noise measurement and
other measurements made on the unpackaged wafers.
Thesis Supervisor: Qing Hu
Title: Associate Professor of Electrical Engineering and Computer Science
2
Chapter 1
Introduction
Infrared (IR) imaging systems have the potential to make a dramatic impact on
our way of life. They already perform several useful functions for military applications
including weapons sights and targeting systems. In the commercial market, night-vision
systems could be put into cars and planes to allow drivers and pilots to navigate more
safely at night. Fire fighters could use them to see through smoke and to identify
hazardous floors and walls.
Unfortunately, the cost of producing and maintaining cryogenically cooled IR
imaging systems has prevented them from achieving this potential. Only recently have
room-temperature microbolometers opened up the possibility of high-performance, lowcost IR imaging systems. However, as with any new technology, microbolometer IR
focal plane arrays are a long way from reaching their theoretical limits of performance. It
is important that manufacturers continue to study how to increase the sensitivity and
reduce the noise of these devices.
3
Previous studies indicate that the noise in an IR imaging system is dominated by
the 1/f noise in the microbolometers themselves. The goal of this thesis was to develop
an efficient way to measure 1/f noise, to use this measurement technique to perform
experiments that might indicate a way to reduce the noise, and to prove that this
measurement was valid by developing a model that could predict the performance of an
IR imaging system.
Chapter 2 describes the 1/f measurement system and the improvements made to
make the system fit better into a production environment. It includes background on 1/f
noise.
Chapter 3 describes the experiments performed in an attempt to find a way to
reduce the 1/f noise. It includes a description of how the microbolometers work and the
results of the experiments as well as suggestions for further experiments.
Chapter 4 describes the model used to predict system performance and the results
of comparing these predictions to actual performance. It includes a description of the rest
of the IR imaging system.
4
Chapter 2
1/f Measurement System
2.1
Overview
It is extremely helpful, from a production standpoint, for noise measurements to
be made as early in the manufacturing process as possible. This way potentially bad
wafers or die can be removed from the line before more time and money is spent building
a product that will not perform up to specifications. Furthermore, it is easier to identify
both the causes of and the solutions to problems when the measurement is done at the
detector level since the effects from the signal processor and the readout circuitry are not
included. Finally, it decreases turnaround time for experiments since parts do not have to
be packaged into systems before they can be tested.
It is also important, from a production standpoint, for a test station to be both
efficient and easy to operate. A test station that has a long test time or requires large
amounts of operator intervention is a waste of time and money. It is best to make a test
station as automatic as possible. However, there can often be a tradeoff between
5
automation and reliability unless self-checks are implemented so that the computer can
handle unusual situations.
A 1/f noise test station was constructed based on the procedure described by
Lentz [1]. Several improvements were made in an attempt to make the station more
productive.
2.2
1/f Noise
1/f noise or low frequency noise is distinguished by a power density spectrum
(PSD) that is proportional to 1/f. This means that the spectral density of the noise
increases without limit as the frequency decreases. 1/f noise is ubiquitous, appearing in
everything from transistors and resistors to the fluctuations of a membrane potential in a
biological system.
The 1/f noise in the detectors can be observed as a voltage fluctuation, but it is
actually due to a change in resistance. This means that a change in the bias voltage
across the detector causes an equivalent change in the magnitude of the 1/f noise voltage.
This fact is important for separating the 1/f noise from the other types of noise in the
detector. It also suggests some interesting things about the source of the 1/f noise. The
resistance of the detector is determined by:
R =
Wt
1
(2.1)
where R is resistance, p is resistivity, w is width, t is thickness and 1 is length. Since the
physical size of the detector cannot fluctuate that much, the change in resistance must be
due to a change in resistivity. The resistivity of a semiconductor is given by:
6
p =
1
1
q( uMnn+ p,p)
(2.2)
where q is the charge of an electron, n and p are the number of negative and positive
carriers respectively, and p is the mobility of the carriers. Since the charge of an electron
is a physical constant, the 1/f noise must be due to fluctuations in either mobility or the
number of carriers. The exact mechanism that causes such fluctuations is unknown but
they may be due to traps and other defects in the material. The question is where such
defects occur and how they can be removed.
2.3
Other Noise Sources
There are other kinds of noise in the microbolometers besides I/f noise. Like
every resistive element, they have Johnson noise. At thermal equilibrium the random
motion of charge carriers in a resistive element generates a random electrical voltage
across the element. This noise is white, which means that its PSD is flat across all
bandwidths. Johnson noise is dependent on resistance and temperature (because an
increase in temperature causes an increase in the mean kinetic energy of the carriers), but
not on bias voltage.
Another type of noise is thermal fluctuation noise. This is due to the fluctuations
in temperature of the detector due to radiative exchange with the background. This is
also a white noise although it is band limited by the thermal time constant of the detector.
Finally there is noise due to the drift of the microbolometer temperature over
time. These low-frequency artifacts show up as a 1/f 2 PSD. This noise is particularly
7
troublesome because it can overwhelm the 1/f noise if care is not taken to reduce this
component.
2.4
Test Circuit
To measure the 1/f noise it is necessary to have a very low-noise amplifier that
will operate at low frequencies. The original circuit designed by Lentz is an 8-stage
parallel bridge circuit. Two of the eight stages are shown in Figure 2-1. The device
under test is labeled R in the circuit diagram. Rc is the resistor network shown in Figure
2-2 in series with two 10 kM wire-wound mechanical potentiometers. During testing, its
value is adjusted so that it is 10 times the value of R. The entire circuit is placed in a test
box and connected via BNC connectors to the device under test and to the rest of the test
equipment as shown in Figure 2-3.
1k
LM399
sg
monitor
-: biaswk
Figure Vs
500k=Rc
Ra= I k
+9V(2)
04
~~~hihi
io
Rb=lk
+10
Rd
-9V(3)
-
MOut
10k
+
-9V(3)
Figure 2-1: Two stages of 1/f noise test circuit.
8
..
50k
-77
62.5k
_/
LI
L2
LO
50k
20k
-_
10k
12.5k
S2
SS
S6
Figure 2-2: Resistor network for adjustable Rc.
High
HP 3478A
Multimeter
Bolometer
Low
Model 113
Test
Input A
Out
Box
Pre-amp
and Filter
Bias Monitor
Out
High Node
I
HP 3458A Multimeter
HP 3561A
Dynamic Signal
Analyzer
7
Figure 2-3: 1/f noise test station setup.
The test station operates as follows. The bias is adjusted via a 10 ko wire-wound
mechanical potentiometer until the bridge is biased at .41 V. This means that there is
about .04 V across the detector itself. This voltage is high enough to allow the resistance
to be measured but low enough that heating effects are relatively insignificant. After the
bridge is balanced, the resistance of the detector can be calculated by measuring the
9
current through the 'hi node'. The resistance is measured so that all parts can be tested at
the same power level rather than at the same voltage level.
The voltage is then adjusted to bias the detector at 1 ptW. The voltage necessary
for this can be calculated using the following equation:
(2.3)
Vmas, = II-.Viu W - R,
The spectrum analyzer then averages 16 periodograms of 400 frequency points each from
0.1 Hz to 40 Hz. Each periodogram is a noisy estimate of the PSD of interest, thus
averaging them improves the estimate. This estimated PSD contains all of the noise
sources described above as well as noise from the test station itself. These components
must be separated from each other to give an accurate measure of the 1/f noise.
The first step is to isolate the 1/f noise from the white noise and 1/f
2 noise.
This
can be done by fitting the data to a curve of the form:
S=a 2 +b
+b
2
(2.4)
where f is frequency. Once this is done, the parameter b gives the 1/f noise voltage at 1
Hz. However this value still contains the noise from the test station as well as that of the
detector. Ideally, the test box would have no 1/f noise, however this is not true in
practice.
In order to separate the detector noise from the test box noise, the measurement is
repeated at bias levels of % ptW and 0 pW. The % piW test serves as a check on the test
system. If the system is working properly the 1/f noise voltage from the detector at %
ptW should be 2of the noise voltage at 1 pW. At 0 pW, since the detector is unbiased, it
should have only Johnson noise. Therefore, there should be no 1/f noise from the
10
detector, so any 1/f noise measured at this bias is due to the test station alone. This
means that the 1/f noise voltage can be calculated as follows:
V = b 1 w -b ,
(2.5)
where V. is the noise voltage.
For modeling purposes, it would be better to have a noise figure of merit that was
independent of bias. This is done by dividing V,, by Vb.. This VN/V can then be used to
calculate the noise voltage at whatever bias the system is running at.
2.5
Test Station Improvements
There were several problems with the test station designed by Lentz, particularly
from a production standpoint. Several improvements were made to the test station that
increased reliability and efficiency.
Lentz describes many environmental sources of noise including air currents, light,
and EML Placing the DUT within a light tight enclosure solved most of these problems.
A light tight enclosure is a large metal box that can be closed to prevent light from
entering. This also removes any air currents that could be caused by people walking past
the test station or other activity in the lab. Grounding the casing would also reduce EMI.
The test box is run using batteries to prevent ground loops, however there were
still occasions when spurious noise signals suggested EMI. In the original circuit, two
BNC connectors were used to connect to the device under test. One was attached to the
'hi' node and one to the 'low' node. Since the 'low' node is at ground, this BNC can be
eliminated. This improved the reliability of the test setup by removing another ground
loop. It is also helpful to keep the BNC connectors as short as possible.
11
Despite these improvements to the testing environment, some spurious signals did
appear occasionally. An example of this is shown in Figures 2-4 and 2-5. This plots two
different tests performed on the same pixel. On the second plot there is a large peak that
interrupts the normally smooth curve. This could be due to vibrations caused by other
machinery that was running in the lab. The best solution to this problem would be to
place the setup on an isolation table that would reduce these vibrations. However, since
there was none available at the time, this theory could not be tested.
Figure 2-4: Typical Noise Plot
1.80E-07
1.60E-07
1.40E-07 1.20E-07
e
1.OOE-07 -
8.OOE-08 6.OOE-08 4.OOE-08 2.OOE-08 O.OOE+00
0.1
1
10
100
Frequency (H)
Another problem with the test circuit is that it was designed to measure detectors
with a resistance smaller than 50 kO. Unfortunately, detectors occasionally have a larger
resistance than this. To fix this problem the resistor network shown in Figure 2-2 was
12
Figure 2-5: Spurious Noise Signal
2.00E-07 1.80E-07
1.60E-07 1.40E-07 1.20E-07 CL
I.OOE-07 8.OOE-08 6.OOE-08 4.OOE-08 2.00E-08 -
0.OOE+00
0.1
1
10
100
Frequency (Hz)
changed to that shown in Figure 2-6. This not only made the circuit more robust, it also
made the switching pattern more straightforward. This would make it easier for
technicians to run the test station.
200k
20k
100k
100k
100k
20k
20k
20k
Figure 2-6: New resistor network.
13
Much of the original test station required manual operation. Balancing the bridge,
adjusting the bias, and even operating the dynamic analyzer were all done manually. A
few circuit changes and a software program remedy this situation. The first step was to
write a program that could operate the dynamic analyzer over a GPIB interface. This
reduces a complicated measurement device down to a simple point and click user
interface and removes the necessity of having an operator who understands how the
dynamic analyzer works.
The next step was to replace the potentiometer that adjusts the bias with a circuit
that uses a digital potentiometer to perform the same function. This circuit is shown in
Figure 2-7. With this circuit in place, the software can now control the bias of the circuit
through a digital I/O card. This means that the majority of the test can now be performed
automatically. Only the resistance measurement and the balancing of the bridge need to
be performed by the operator. This makes the test station much more efficient since the
operator can now be freed up to perform other tasks while the test is running, and need
not constantly monitor the testing. Furthermore, since resistance is usually measured
earlier in production, the software was configured to allow the user to input the resistance
directly rather than measuring it. This means that the only operator intervention is the
balancing of the resistors.
The original test station also performed data collection and analysis in two
different steps. This means that the operator of the test station would not be able to get
any real time feedback about whether or not the test station appeared to be working
properly. For example, the 1/f noise at 1 ptW should be about twice that at
14
pW. If this
+9V 2)
+ 5V
2k
00
lo p
0
+15V
+9V(2)
.01 U
619kk
00
15 p
10k
10k
Figure 2-7: Digital Potentiometer Bias Circuit
is not true, it is likely that there was some problem in one or the other of the
measurements. For example, bumping the table could cause a large jump in the noise, or
could cause the probes to slide off the pads. Furthermore, there are times when the
curve-fitting algorithm chooses negative coefficients. This also indicates a problem with
the data, most likely a low frequency artifact that is exaggerating the 1 /fQ noise. With the
original test station, it is impossible to determine this until all of the data has been
collected and then analyzed. This means that time is wasted collecting data that is
erroneous. This problem is also solved in software. The computer that performs the data
collection can also perform the analysis of the data. This means that information can be
15
provided after each set of 16 periodograms. Specifically, the coefficients from the curve
fitting can be displayed along with plots of both the original data and the approximation.
This information can then be used, either by the operator in a manual setting, or by the
computer in an automatic one, to determine whether or not it is worthwhile to take the
next set of data or whether there is some problem with the data.
A final improvement that could be made is to replace the two mechanical 10 kQ
potentiometers in the bridge with digital potentiometers. This would allow the entire
circuit to be placed under computer control, and fully automate the test. This is probably
the most risky of the changes made to the circuit since the noise measurement is
extremely sensitive to noise in the bridge resistors. The original reason for using a
switched resistor network rather than a large potentiometer was because such
potentiometers had too much noise. Unfortunately, time constraints prevented this
change from being implemented.
The problem with computer control is that the computer can only handle
situations that are preprogrammed. Unlike a human operator, it cannot adapt to unusual
situations. It is important, therefore, to make the computer program as robust as possible,
so that it can handle typical problems that may arise.
One typical problem that can arise is due to artifacts that show up as 1/f, noise.
Such spurious noise can drown out the 1/f noise of interest resulting in erroneous data or
even no data at all. This happens most frequently when the measurement is taken too
soon after a change in bias. Probably because of the changing temperature of the
detector, measurements taken immediately after the bias changed have large 1/f noise.
16
This problem was overcome by implementing a one-minute delay between the change in
bias and the beginning of the measurements.
Another problem results from averaging the periodograms. If one of the
periodograms is much different from the others, this can throw off the average and
change the measurement. To prevent this, the dynamic analyzer is set in single auto
range mode. This means that it sets its range at the beginning of each measurement and
then rejects any periodogram that is outside of this range. Unfortunately, the range could
be set too low, so that too many of the periodograms are rejected. To prevent this, a time
limit was placed on the measurement. Typically it takes a little less than three minutes
for the dynamic analyzer to complete an average of sixteen periodograms. The software
has a time limit of four minutes, after which it will record that it timed-out, and will begin
the measurement again.
Spurious noise signals are easiest to spot if the 1/f noise is not proportional to the
bias voltage. To take advantage of this, the software can compare the noise voltage at 1
pW and at
ptW. If the later is not approximately half the former, there is a problem and
the measurement should be repeated.
All instances where the computer assumes that data is bad should be logged along
with the assumed erroneous data. This way a human operator can examine the data
afterwards in an attempt to find what caused the problems.
2.6
Conclusions
The improvements made to the test station drastically reduced the amount of user
intervention required in the test station without reducing the validity of the
17
measurements. Further improvements in this circuit would help little. Changing the
adjustable bridge resistance to digital pots will allow the computer to take over the entire
test, but since the user is already required to set up the test, there is little benefit gained
from this step. The next large step in improving the efficiency of the test procedure will
come from an ability to probe all of the test pixels on a single wafer in parallel. This will
remove the necessity of the user having to change the probes after every test and will
allow an entire wafer to be run without user intervention.
18
Chapter 3
1/f Noise Experiments
3.0
Overview
With a reliable test station, there are a number of experiments that can be done in
an attempt to discover the source of the 1/f noise and how to reduce it. According to Sze
[41 the origin of 1/f noise in most semiconductor devices is due to the surface effect and
carrier recombination at traps. It is possible that the 1/f noise in the microbolometers is
due to similar effects. This immediately suggests a path of experimentation. First,
testing parts with different thicknesses can determine whether or not it is a surface effect.
Secondly, parts can be annealed in different atmospheres and at different temperatures.
Annealing has a dramatic improvement on the 1/f noise of other devices and may prove
equally effective here.
19
3.1
Microbolometer Overview
A bolometer is a resistor with a high thermal coefficient of resistance (TCR). The
microbolometers in these experiments consist of a thin layer of vanadium oxide (VO")
between encapsulating layers of silicon nitride (Si 3N4). The VOx is the temperature
sensitive material. The incoming infrared radiation strikes the microbolometer, and the
energy from this radiation heats up the VOx causing a change in resistance. This
resistance change is related to the power of the radiation and so to the infrared energy
being emitted by the scene the imager is looking at. A short voltage pulse across the
microbolometer measures this change in resistance through an integration capacitor.
Thus an effective measurement is made of the infrared radiation being emitted by the
scene.
Ideally, all of the energy from the incoming radiation would be used to heat up the
vanadium oxide. In reality, some of the energy is lost through the thermal connection to
the substrate. To minimize this effect, the microbolometer is suspended above the
substrate on two thin metal legs. Other losses include those due to imperfect optics and
the fact that the microbolometer does not cover the entire pixel area.
On every production die there are eight different test pixels that can be tested.
Pixels in the actual array cannot be tested because they do not have the metal contacts
and so there is nowhere to connect the probes. These eight test pixels are of various
geometries and may or may not be suspended above the substrate.
There were two main types of pixels used in this testing, called F2 and F2L
pixels. Both are suspended above the substrate. The F2 pixels are approximately 15 pLm
long and 38 pm wide. The F2L pixels are approximately 27 pm long and 19 pm wide. It
20
is important, when comparing different pixel shapes to take these differences into
account. The F2L pixel geometry is most closely matched to the geometry of the pixels
in the array.
3.2
Surface and Bulk Effects
The first experiment run on the microbolometers was to vary the thickness of the
vanadium oxide and determine what effect, if any this had on the 1/f noise. This
experiment would determine whether or not the phenomenon that causes the 1/f noise is a
surface effect or a bulk effect.
The difference between a surface effect and a bulk effect is as follows. In the
case of a bulk effect, the phenomenon is evenly distributed throughout the volume of the
material. This means that the equation for the noise can be written as
V
XOVlp
(3.1)
Since the length and width of the microbolometers is the same for all pixels of a
particular geometry, the noise voltage is inversely proportional to the square root of the
thickness.
The bulk effect equation can be understood by thinking of the detector as a noisy
resistor. When the thickness is doubled, it is the same as putting two equivalent noisy
resistors in parallel. This means that the equivalent circuit shown in Figure 3-1 can
represent the thicker detector. Adding the resistances in parallel gives an equivalent of
2R. Adding the noise currents gives and equivalent of I*12. This means that the
equivalent noise voltage is Vn/42.
21
I = ER
R
R
)
R/2
I= E/R
I = sqrt(2)*Et/R
R/2
XK
E = Et/sqrt(2)
Figure 3-1: Equivalent Circuit for Bulk Effect
A surface effect occurs when the phenomenon that causes the noise is
concentrated near the surface of the detector. In this case, the equivalent circuit is that
shown in Figure 3-2, where RB is a noiseless resistor that represents the bulk and Rs is a
noisy resistor in parallel that represents the surface. In this case, doubling the thickness
of the detector cuts the resistance in half while the noise remains constant. This means
that the noise voltage is inversely proportional to the thickness of the detector. This
assumes that the resistivity of the surface layer and the bulk layer are the same and that
22
the surface effects extend at most to a depth equivalent to the thickness of the original
detector.
X
I=E/Rs
RB+Rs= R
I= Et/Rs
R/2
R/2
E =Et/2
Figure 3-2: Equivalent Circuit for Surface Effect
Because of the different behaviors of the surface and bulk effects, it should be
possible to determine whether or not the effect is bulk or surface by increasing the
thickness. This is important because it will determine how effective it is to reduce the 1/f
noise by increasing the thickness. Increasing the thickness has some negative effects
such as increasing the thermal time constant. Thus, it is important to characterize the
23
benefits properly so designers can make the proper choice when developing the next
generation of pixel.
3.3
Thickness Experiments
The thickness variation experiment was run on four wafers from two different
lots, two from each lot. These wafers were run through the standard process with the rest
of the lot, except at the vanadium deposition step. At this step, the experimental wafers
had a deposition time of 60 minutes rather than the standard 40 minutes. Since the
deposition time controls the amount of vanadium oxide deposited on the wafer, the
thickness should be proportional to time. This means that the thickness of the vanadium
should be 1.5 times greater in the experimental wafers. After processing the wafers were
measured using the 1/f measurement station described earlier. Both F2 and F2L pixels
were tested. Unfortunately, the resistance was greater than 50 kQ on some of the F2L
pixels, so the test station was inadequate for their measurement .
Initially the measurements from the experimental wafers were compared to wafers
from the same lot that had been run at the standard deposition time. Using wafers from
the same lot should minimize the number of uncontrolled variables, since there could be
lot to lot variation. The lot comparison is shown in Table 3-12.
1Not
all of the test station improvements described in Chapter 2 had been made at the time this experiment
was done.
2 A complete listing of all of the data from the thickness experiments is shown
in Appendix A. Only those
measurements within 3a were considered for the statistical measurements. This is to prevent atypical
pixels from influencing the statistics.
24
Lot
99.1
99.1
104.1
104.1
99.1
104.1
104.1
Part
F2
F2
F2
F2
F2L
F2L
F2L
Dep. Time Mean VnN
4.79E-07
40 min
2.89E-07
60 min
4.23E-07
40 min
60 min
3.23E-07
3.38E-07
60 min
4.46E-07
40 min
60 min
3.30E-07
Std. Dev.
1.15E-07
3.08E-08
4.24E-08
7.39E-08
7.56E-08
1.1OE-07
7.60E-08
Table 3-1: Thickness Experiment Lots
The lot comparison data should support one of the above theories of 1/f noise,
either the surface model or the bulk model. If it is assumed that the measurement of the
standard wafers is accurate, then it is possible to predict the behavior of the experimental
wafers. The mean of the measurement should be reduced by a factor of either 1.5 or
41.5, due to the surface model and the bulk model respectively. These predictions, along
with the errors of the predictions are shown in Table 3-2.
Lot
Part
99.1
104.1
104.1
F2
F2
F2L
Mean
Bulk
Bulk Err Surface Surface Err
2.89E-07 3.91E-07 -35.34% 3.19E-07
3.23E-07 3.45E-07 -6.87% 2.82E-07
3.30E-07 3.64E-07 -10.43% 2.97E-07
-10.51%
12.74%
9.84%
Table 3-2 Bulk and Surface Predictions and Errors
These results seem to indicate a surface effect, but are rather unsatisfying,
particularly since the results from the F2 pixels from Lot 104.1 seem to indicate a bulk
effect. In addition, due to the large resistance of the F2L pixels from Lot 99.1, there is no
data for that lot. The error in the predictions could be due to an error in the models, but it
seems more likely that the problem lies in the amount of data taken. More measurements
would increase the statistical certainty of the predictions.
25
The wafers were packaged into systems so that comparisons could be made at the
system level. This meant that no further measurements could be taken on the wafers.
To get further data for the comparisons, it was possible to test other wafers that
came from different lots, but were produced around the same time as the lots of interest.
This has the advantage of giving a greater sampling, but it also adds in the variables from
lot to lot variation. In this case, we are comparing all F2 pixels run at the standard
deposition time to those run at the longer deposition time, and likewise with the F2L
pixels. These comparisons as well as the model predictions are shown in Table 3-3.
Part
Dep. Time
Mean
F2
40 min
4.83E-07
F2
F2L
F2L
60 min
40 min
60 min
3.06E-07
4.96E-07
3.32E-07
Bulk Model Bulk Err Surface Surface Err
3.94E-07
-28.93% 3.22E-07
-5.27%
4.05E-07
-22.19% 3.31E-07
0.23%
Table 3-3: Model Comparison with All Lots
These results clearly show a strong support of the surface model, particularly with
the F2L pixels. The F2L pixels are those that most closely resemble the pixels that are in
the actual array, so it seems fairly certain that the improvements seen at the detector level
will be borne out at the system level. This potential will be explored further in Chapter 4.
Although there was not time to make any more fully functional wafers with
thickness variation, an experimental lot was made that had thickness variations between
.5 times and 2 times the typical thickness. There was no intention to package these
wafers, nor were the pixels suspended, so the measurements done could not be confirmed
at the system level.
The plot of the variation of Vn/V with vanadium thickness is shown in Figures 31 and 3-2. In Figure 3-1 a linear approximation is plotted. The closer the data points are
26
to this line, the greater the chance of a surface effect. In Figure 3-2 a square root
approximation is plotted. The closer the data points are to this line, the greater the chance
of a bulk effect. It is difficult to tell just by looking at the plots, which of the graphs most
closely approximates the data, but Table 3-4 shows that the square-root approximation is
actually closer to the measured data points. This is unfortunate since it actually goes
against what we measured earlier.
This seeming contradiction can be explained by realizing that it is possible for the
surface to extend throughout the whole bulk. In the IX to 2X range, where the first
experiments were done, the high noise region of the vanadium is in fact smaller than the
entire thickness, so the noise goes down proportionally to the thickness, just as a surface
effect should. However, at thicknesses less than IX, the high noise region extends
throughout the entire thickness of the material. Thus, the noise looks like a bulk effect,
and the noise goes as the square root of the thickness.
Figure 3-1: Data Points and Surface Model
1.60E-06
1.40E-06
1.20E-06
1.OOE-06
8.OOE-07
6.OOE-07 4.OOE-07 -
2.OOE-07 -
O.OOE+00
--
0
I
0.5
__ _
I
-
I
1
1.5
VOx Thickness(X)
27
-
2
I
2.5
Figure 3-2: Data Points and Bulk Model
1.60E-06 -
1.40E-06 1.20E-06 -
1.OOE-06 8.OOE-07 6.OOE-07 4.OOE-07 -
2.OOE-07 0.OOE+00 10
0.5
T
1.
1
1.5
-
2
VOx Thickness(X)
IX Resistivity F2L Pixels
Approximation Error
VnN
VOx Thickness
4.88%
1.19E-06
1.25E-06
0.5
4.73%
1.19E-06
1.25E-06
0.5
15.52%
1.02E-06
8.81 E-07
5.90%
1.02E-06
9.61E-07
12.33%
8.46E-07
9.66E-07
1.5
12.18%
7.55E-07
8.46E-07
1.5
6.43%
7.22E-07
6.75E-07
2
8.85%
Sqrt Thickness
0.707106781
0.707106781
1
1
1.224744871
1.224744871
1.414213562
Approximation Error
Vn/V
3.12%
1.21 E-06
1.25E-06
2.97%
1.25E-06
1.21E-06
13.25%
8.81 E-07
9.98E-07
3.82%
9.98E-07
9.61 E-07
13.62%
8.34E-07
9.66E-07
10.54%
8.34E-07
7.55E-07
3.53%
7.22E-07
6.96E-07
7.26%
Table 3-4: Bulk vs. Surface Model
28
2.5
In other words, it appears that the thickness of the high noise region is almost
exactly that of a standard pixel, approximately 600 angstroms. In the cases where the
pixel is thicker than IX, there is an additional low noise region that causes the 1/f noise to
go down proportionally to the volume. If the pixel is made thinner, however, there is no
low noise region at all, and so the noise goes down to proportionally to the square root of
the volume because the high noise region extends throughout the entire bulk.
The fact that the standard thickness lies right at the crux of these two regions
could also explain variations in the noise measurements in production wafers. If some
production technique can slightly vary the thickness of the surface layer, it could produce
occasional good pixels when the surface is made thinner and there is a low noise region.
Furthermore, since the thickness of the vanadium slightly varies from lot to lot, some of
these wafers could have exceeded the thickness of the high noise region.
3.4
Annealing Experiments
The characterization of the phenomenon that causes the I/f noise in the
microbolometers is extremely useful, but it is still necessary to find a way to reduce the
I/f noise. As seen above, the I/f noise is inversely proportional to the thickness of the
detector, so increasing the thickness can reduce the 1/f noise. There is, however, a
practical limit to this solution. First of all, increasing the volume of vanadium oxide
increases the thermal mass of the detector, thereby increasing the thermal time constant.
This has the undesired effect of slowing down the response of the detector. Furthermore,
increasing the thickness increases the thermal conductivity. This means more of the
energy will be conducted to the substrate, thus decreasing the sensitivity.
29
Figure 3-3: Histogram of Baking Experiments
Pre mean = 1.13e-6
Pre std = 2.38e-7
Post mean = 9.44e-7
Post std = 2.84e-8
Twice mean = 9.349-7
Twice std = 3.93e-8
N Post-Baking
0 Pre-Baking
M Twice-Baked
12
10
8
4)
Cr
U.
6
4
2
I-
t
0
8.95E-07
9.90E-07
9.43E-07
1.04E-06
1.09E-06
1.13E-06
More
VnN
Figure 3-4 Plot by Part
2.50E-06
2.OOE-06
X Pre Baking
+ Post Baking
0 Twice Baked
X
-
x
1.50E-06
xX
XXX X
Xt
'p
1.OOE-06
-
X X
X
off*~ *
.0
5.OOE-07
0.OOE+00
0
5
15
10
Part index
30
20
25
The fact that the 1/f noise seems to be a surface effect supports the theory that it is
caused by traps. Traps are usually due to impurity atoms or lattice defects. Since the
surface of a material undergoes a rougher treatment than the bulk, it seems likely that
most impurities and defects would be concentrated at the surface. It is possible that
annealing may removes some of these defects. The thermal energy will give the
molecules in the material enough energy to move around and fix the defects. In other
devices, it has been shown that low-temperature hydrogen annealing can remove most of
the interface traps [4].
Because of the previous successes with other devices and annealing, an
experiment was tried in which the wafers were annealed in a vacuum at 250* for one
hour. They were tested both before and after the annealing. The results of this
experiment are charted in Figure 3-33. It appears that there is some improvement in the
1/f noise after the annealing, however the overlap in the histograms makes it uncertain
whether the improvement is real or merely an anomaly due to changes in the
measurement environment. One encouraging fact is that there is less variation after
baking.
Each part is plotted separately in Figure 3-4. Here it is apparent that every pixel
showed some improvement, although this improvement is not uniform. This could be
due to the fact that some pixels had a greater number of defects to begin with, and yet
there is a limit to the improvements that can be made with the annealing. Thus, annealing
appears to bring all pixels down to the same level of noise. These results are
encouraging, but the improvement is not nearly large enough.
31
The next step was to anneal the wafers for even longer. The same wafers were
annealed for 2500 for another six hours. These are the 'twice baked' wafers shown in the
above figures. It appears that the additional annealing had little or no effect on the pixels.
It appears that the initial annealing brought the pixels to some plateau of noise level.
3.5
Conclusions
As with any experiment, the results of both the thickness and annealing
experiments were mixed. Certainly the thickness experiment seems to strongly indicate a
surface effect, but it would be better to have more data points. Further experiments at
greater thickness extremes, both lower and higher, could help to confirm the theory that
the surface effect begins somewhere around IX thickness.
The annealing experiment shows some improvement, but not enough to be
satisfying. It definitely seems to show that at least part of the 1/f noise is due to traps in
the surface. Annealing brings those pixels with a large number of surface defects back
into range. Thus annealing can improve reliability and uniformity. The next step would
be to try annealing at higher temperatures and in different atmospheres. Unfortunately, it
will be difficult to reach higher temperatures without damaging the readout circuitry
underneath the pixels. The aluminum metalization in the CMOS can be damaged at
temperatures much higher than this. One possibility is to use a rapid thermal anneal.
Because the detectors are thermally isolated from the substrate, this may heat the
detectors to a high temperature while keeping the readout circuitry safe. It is also
3 A complete listing of all of the data from the baking experiments is shown in Appendix B.
32
unfortunate that the equipment was not available to anneal the wafers in different
atmospheres, at least not at the temperatures of interest.
33
34
Chapter 4
System Modeling
4.0
Overview
The results of the experiments described in the previous chapter are interesting,
but they are only useful if they actually have some relation to the performance of the
entire system. It would be helpful if the 1/f noise measurements could be used to predict
the performance of the system. In this way, bad die can be removed from the line early
on, since it can be predicted whether or not their system performance will be adequate.
Furthermore, noise reduction experiments will take less time since they can be tested at
the wafer level, rather than at the system level. Finally, a good model is a valuable
design tool, since hypothetical designs can be modeled to determine their performance
before time and money is spent actually building them. And different parameter curves
can be plotted to help designers determine the relative effects of different variables.
A good model can be developed from the theoretical performance of the system,
but it can only be proven through experimental evidence. That is, the predictions of the
35
model must be borne out by actual system performance. No model can ever be perfect,
since it is impossible to take into account all of the variables that can affect system
performance. Throughout the time of these experiments, a model was developed and
continuously modified as new results became available.
4.1
Model
The model contained a number of sections. The first section consisted of an area
where pixel parameters could be input. Some of these are physical constants or material
properties that the designer has no control over. Both the electrical and thermal
properties of the material are important. The material property of the greatest interest for
this thesis is the 1/f noise figure of merit, labeled 'Vnove,'. This is the 1/f noise parameter
that is measured by the test station. Hopefully, with this value as well as other measured
values input, the model will accurately reflect the performance of the system. The pixel
layout parameters also need to be input. These are the parameters over which the
designer has the most control. They are determined by the size and shape of the pixel
itself. For the most part they are limited by the layout technology available to the
designer. They can also be limited by mechanical considerations since the bolometer is
essentially a bridge. Making the parameters too extreme can cause bridges to collapse or
to become detached during processing.
The model also needs the ROIC parameters. These describe the behavior of the
readout circuitry and its effects on the noise. One of the most important of these is Vbias.
This is the amplitude of the bias pulse sent across the detector to measure the change in
resistance. This is typically .7 V, but may be higher than this. As described in Chapter 3,
36
1/f noise varies with bias. Therefore, it is important to match the modeled bias voltage
to the voltage that the system was tested at. The other ROIC parameters that are
important are those involved in the integration of the current caused by the bias pulse,
and the A/D conversion of this voltage.
Finally, the other parts of the system are included in system parameters. Most
important of these are the frequencies of interest. The type of test that the system will
undergo determines the frequency band that the model must look at. The acceptance test
used in this case looks at two different kinds of noise, spatial and temporal. The temporal
noise is the variation of the pixels over a number of frames. The spatial noise is the
variation of the pixels from the neighboring pixels. Since only one pixel is modeled,
these tests must be converted to equivalent bandwidths. The temporal noise is considered
to be the noise between 1 Hz and the upper limit set by the frame rate. The spatial noise
is considered to be the noise between .01 Hz and 1 Hz. Any other bandwidths could be
used in the model. For example, a lower frequency could be used for to model the
amount of noise that would be observed by a human eye.
The first important value that needs to be calculated is the effective fill factor.
The fill factor is that percentage of the pixel area that is actually covered by the
bolometer and therefore absorbing radiation.
The atmosphere, the optics, the
absorptance of the vanadium oxide, and the physical size of the detector all play a part in
how efficient the detector is at absorbing the incoming radiation. Since many of these
factors vary with wavelength, they can be entered as vectors of values within the
wavelengths of interest (7 - 14 pm) and then a weighted average is taken. It is important
when using the model as a design tool to edit this section carefully. Clearly, altering the
37
size of the pixel changes the fill factor, but changing the thickness can have an effect on
the absorptance and thereby change the fill factor as well.
The noise sources from the read out circuitry need to be measured independently
and entered as factors into the model in a 'Noise Measurements/Estimates' section. It is
in this section that one would normalize the 1/f noise with volume if the surface effect is
assumed, or with the square root of the volume if the bulk effect is assumed. Throughout
the time of using the model, the bulk effect was assumed since this would provide a more
pessimistic estimate of the noise.
The thermal time constant of the detector needs to be calculated from the thermal
properties of the materials that make up the pixel. This is an important parameter
because it determines the response time of the system to changes in the scene. A rapid
thermal time constant can prevent unwanted visual effects when panning the imager
across a scene, or when there is a rapidly moving object in the field of view. The thermal
conductance and thermal capacitance of the pixel is calculated using the physical
parameters of the metal, silicon nitride, and vanadium oxide, as well as the structure of
the pixel. These two parameters than provide the thermal time constant.
Like electrical conductivity, thermal conductivity is proportional to the thickness
and the width and inversely proportional to the length of the material. However it is
important to realize that the two legs of the bridge are electrically in series, while they are
thermally in parallel. It is also important to consider that energy can be lost through
radiation of the pixel.
Next the responsivity of the pixel in counts per degree Kelvin needs to be
calculated. This must take into account not only the efficiency of the pixel in absorbing
38
energy and converting this energy into a resistance change, but also the effectiveness of
the readout circuitry in converting that resistance change in to a digital signal. The
calculation proceeds as follows:
1) eff*size*I/4FA2 is the power of the incoming radiation
2) Dividing this by G gives the temperature change when this power is converted
from radiative to thermal energy.
3) Multiplying by TCR and R then gives the change in resistance due to the
incoming radiation.
4) Dividing by R then gives the fractional change in resistance. This is
proportional to the fractional change in the current through the detector.
5) Multiplying by the original current is Vbias/R, gives the fractional change in
the current through the detector.
6) The current than charges up the integration capacitor. Multiplying by
Tint/Cap gives the change in the voltage on the capacitor.
7) Dividing by the slope of the A/D converter gives the responsivity of the pixel.
Although the resistance of the pixel can be calculated from the sheet resistance of
the VOx, the model will put a lower limit on the resistance based on the WeidemannFranz ratio. This is the ratio between the electrical and thermal conductivity of a
material. Essentially, if a material has a specific thermal conductivity, there is a
maximum electrical conductivity. The ideal material for the legs of the bridge would be
something that had infinite electrical conductivity and zero thermal conductivity.
Weidemann-Franz shows not only that this is impossible, but also exactly how close it is
possible to get to such an ideal.
39
Another important calculation is the pixel TCR. This is not the same as the TCR
of the vanadium oxide, because the legs are a part of the pixel. In other words, the legs
contribute to the total resistance of the pixel, but have a very low TCR compared to the
VOx. The effect of the legs on the TCR can be minimized by keeping the resistance of
the legs small compared to the resistance of the bridge.
Finally, the noise in various bandwidths is calculated. Each of these sections are
the same, with only the bandwidths changed.
First a high and low alias point is calculated. Some practical limit has to be set on
the bandwidth of the 1/f noise so that the model can calculate the amount of noise that is
alliased back into the bandwidth of interest. In this case it was assumed that there was no
noise after 10/2nr, where
t
is the thermal time constant.
Next, the thermal fluctuation noise is calculated. This noise is white, but it is
bandlimited by the thermal time constant, and so the aliasing effects have to be taken into
account. It is also useful to calculate the radiation limited NETD. This is the ideal noise.
The noise of the pixel will be equal to this value when all other noise is removed except
for the thermal fluctuation noise caused by radiative exchange between the pixel and its
environment. This is what is known as background limited.
Johnson noise is white, so it only has to be limited by the bandwidth of interest.
The 1/f noise is calculated in two sections. One calculates the aliased 1/f noise,
and another calculates the 1/f noise without aliasing. Then these are added in quadrature
to give the total 1/f noise. Note that the 1/f noise parameter must be properly scaled with
the square root of the volume because of the assumption that the 1/f noise is a bulk effect.
40
The remaining terms are ROIC noise and are mostly measured independently
during ROIC design and development. All of the noise terms are then added in
quadrature to give a total noise.
4.2
Model Confirmation
Ideally, the model would accurately predict the behavior of any given system
based on measurements made on the die. Practically, there are not only variations in the
measurements that add error, but also problems with the model that cause inaccuracies in
the predictions. It is important then to determine how reliable the model is.
A number of production die were tested over the time of these experiments.
These die were eventually packaged into systems, and this gave an ideal opportunity to
test the model. Several parameters were used as input into the model. The most
important of these was the Vn/V, since this would help to confirm not only the model, but
the test station as well. The bias voltage was of course important, since some systems are
run at higher biases than others and this can have a dramatic effect on the 1/f noise. The
mean resistance of the detectors in the array is measured at wafer probe, so this was used
as a resistance rather than calculating the resistance from the sheet resistance of the VOx.
41
Figure 4-1: Responsivity Check
80.00 75.00 70.00
65.00
60.00
55.00 -
50.00
-
45.00 40.00 35.00 30.00
30
35
40
45
50
55
60
Measured Responsivity (counts/dog C)
65
70
75
80
The model was run using the input parameters above and the results were
compared to the measurements made at the system test station. The comparison is shown
in Figures 4-1, and 4-2, and in Table 4-1. Figure 4-1 shows modeled versus measured
responsivities. Ideally, all of the data points would lie on the line, and in fact they are
quite close, except for a few outliers. Table 4-1 shows that the average error is about 3%.
Of course the ± errors are canceling each other out, but even the absolute values of the
errors average out to 9%.
42
Figure 4-2: TNETD Check
120
100
-I
40
20
0
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Measured TNETD (mK)
Figure 4-2 shows modeled versus measured temporal NETD. Again, the data
points appear to be quite close to the ideal line. And in fact, the Table shows that these
predictions are even better. The average magnitude of the error is only 6.8%.
These results are quite promising. They show that the model, despite being based
on only one pixel seems quite capable of predicting system performance, at least for
responsivity and TNETD. The problem with this conclusion is that it is based on only
one type of pixel, without any major difference that will cause changes in noise levels
that the model should be able to predict.
Fortunately, this experiment was made using the wafers from the original
thickness experiment. These wafers have 1.5 times the VOx and so should have a
significant difference in noise from the standard production wafers. The results from this
43
Bias
Meas R. VnN
46.8 5.84E-07
35.5 8.06E-07
45.3 4.49E-07
24
1.06E-06
31.1 1.17E-06
31.1 1.22E-06
31.1 1.15E-06
26.6 9.92E-07
26.6 1.09E-06
28.7 1.06E-06
28.7 1.14E-06
26.6 1.08E-06
28.7 1.09E-06
24.8 9.93E-07
23.3 1.02E-06
24.8 1.03E-06
24.8 9.84E-07
23.3 1.01E-06
21.9 9.84E-07
23.3 1.04E-06
Mean 28.85 9.96E-07
(X)
1.50
1.25
1.25
1.00
1.00
1.00
1.00
1.00
1.00
1.25
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.06
Model
Reasp
71.12
40.57
Responsivity
56.35
51.8
51.87
58.55
49.55
52.13
50.48
51.13
50.16
52.29
53.56
49.55
49.36
57.35
55.57
42.00
57.98
50.01
59.66
55.13
56.40
51.37
62.12
56.28
42.28
55.37
58.40
55.12
58.27
58.97
61.20
59.67
62.79
55.73
58.54
54.21
58.9
60.38
58.06
53.99
Error TNETD
26.21% 67.44
-21.69% 82.48
-19.03% 78.59
-0.98% 78.35
0.92% 87.60
14.45% 85.80
9.20% 87.73
10.31% 90.06
2.41% 90.68
18.80% 90.84
5.09% 85.51
-14.68% 90.45
12.17% 92.17
1.83% 82.66
-0.81% 79.96
-0.46% 76.54
8.78% 88.14
3.90% 83.32
-1.18% 76.40
8.14% 81.80
3.17% 83.83
Model
TNETD
54.02
88.61
78.92
83.89
98.9
87.3
89.3
83.29
Error
-19.90%
7.43%
94
84.82
88.61
102.81
85.32
82
88.73
85.96
83.65
82.87
84.09
83.74
85.54
0.42%
7.07%
12.90%
1.75%
1.79%
-7.52%
3.66%
-6.63%
3.63%
13.67%
-7.43%
-0.80%
10.97%
12.31%
-5.09%
-0.54%
10.07%
2.37%
2.01%
Table 4-1: Model and Measurement Results
experiment are shown in Figures 4-3, and 4-4 and in Table 4-2. Again the results are
very good with the average magnitude of the error at 6.49% for TNETD and 5.50% for
responsivity. The only unusual thing is that almost all of the modeled TNETD results are
below what was measured. This seems to indicate that there is some source of noise that
the model is not taking into account.
44
Figure 4-3: Responsivity Check, Thicker Wafers
80
70
60
50
I
V.
40
30
20
10
0
0
10
50
40
30
20
60
70
80
Measured Responsivity (counts/deg C)
Figure 4-4: TNETD Check, Thicker Wafers
70
60
00000
50
a
I- 40
w
zI-
30
20
10
0
0
10
20
40
30
Measured TNETO (mK)
45
50
60
70
Mean
Model
Meas R.
Vn/V
Bias (X)
27
26.2
26
28.1
4.88E-07
4.25E-07
3.57E-07
3.81E-07
26.825 4.13E-07
Model
1.25
1
1
1.25
Resp.
67.57
55.32
53.12
53.85
Resp
70.06
54.57
61.51
54.46
Error TNETD TNETD Error
3.69% 54.16
51.86 -4.25%
-1.34% 62.81
59.29 -5.60%
15.81% 65.74
55.85 -15.040%
1.15% 63.99
63.31 -1.06%
1.125
57.465
60.15
4.83%
61.675 57.5775 -6.49%
Table 4-2: Thicker Wafer Model and Measurements
4.3
Conclusions
The model seems to work quite well. It seems to accurately predict system
responsivity and TNETD. It is also capable of predicting these values when the design of
the pixel is changed. Certainly improvements could be made to the model. The results
are not shown here, but the modeled results for SNETD are dramatically different from
what is measured at the system test station. This could be due to certain effects caused by
the shutter of the camera that are not taken into account by the model. Despite this
deficiency, the model is still a powerful design tool.
46
Chapter 5
Conclusions
The results of this work provide a number of powerful tools for the manufacturers
and designers of infrared imaging systems based on uncooled microbolometer
technology. There is now a more efficient, highly automated system for measuring 1/f
noise at the wafer level. Furthermore, there is a greater understanding of what can be
done to reduce this noise so that it no longer dominates the system. Most importantly,
there is a model that can be used to predict performance based on many different design
parameters. This is a valuable design tool for any engineer. It allows an easy way to try
out new designs. Plus it can be used to develop parametric curves that will show relative
effects of various parameters. Finally, it can be used to develop intuition about how the
imaging system and microbolometers function.
Certainly there is further work that needs to be done to bring uncooled infrared
systems closer to the theoretical limits of their performance. There is still no clear
understanding of what exactly causes the 1/f noise, nor, more importantly, how to
47
improve it. The model is an excellent tool, but still cannot adequately predict spatial
noise. The test station is highly automated, but still can only test one pixel every twenty
minutes, and with 128 test pixels on a wafer, this hardly allows for thorough testing of
every wafer. Despite these challenges, the utility of uncooled technology and the wide
variety of applications open to infrared solutions is sure to encourage engineers to
continue to investigate these detectors and push the envelope of performance.
48
Appendix A
VOx Thickness Experiment
Measurements
Lot
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
104.1
104.1
104.1
104.1
104.1
Wafer
Die
Part
Dep.
Vhigh
25
25
22.4
22.4
22.4
22.4
22.5
22.5
21.5
21.5
21.5
21.5
40
40
40
0.163
0.082
9.16E-08 5.53E-07
5.06E-08 5.83E-07
0.152
6.78E-08 4.31 E-07
40
21.5
40
40
0.076
0.152
0.076
0.152
0.076
0.147
0.074
0.147
0.074
0.147
0.074
0.091
0.045
0.098
3.76E-08
6.72E-08
3.96E-08
7.21 E-08
3.63E-08
2.85E-08
1.60E-08
6.76E-08
3.24E-08
6.69E-08
3.07E-08
8.51 E-08
3.47E-08
4.58E-08
2.59E-08
7.31 E-08
4.41 E-08
7.42E-08
Meas R.
21.5
21.5
21.5
21.5
21.5
21.4
21.4
21.4
21.4
21.5
21.5
21.4
21.4
21
21
20.1
20.1
18.8
18.8
19
49
Time
40
40
40
40
40
40
40
40
40
40
40
40
40
0.049
0.147
40
0.074
40
40
0.147
0.074
0.147
0.074
40
40
40
40
40
40
40
40
40
0.147
0.074
0.147
0.074
0.147
0.074
40
0.136
0.068
40
0.14
b
VnN
4.39E-07
4.27E-07
4.69E-07
4.70E-07
4.59E-07
1.84E-07
1.80E-07
4.56E-07
4.21 E-07
4.52E-07
4.03E-07
9.25E-07
7.18E-07
4.49E-07
4.61 E-07
4.95E-07
5.87E-07
4.97E-07
4.64E-08 6.03E-07
9.41 E-08 6.37E-07
4.51E-08 6.OOE-07
6.47E-08 4.37E-07
3.35E-08 4.40E-07
7.83E-08 5.31 E-07
4.05E-08 5.41 E-07
6.09E-08 4.13E-07
2.88E-08 3.84E-07
5.17E-08 3.74E-07
2.80E-08 3.90E-07
5.60E-08 3.88E-07
Lot
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
Wafer
Die
Part
Meas R.
F2
F2
F2
F2
F2
F2
F2
F2
F2
F2
F2
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
19
20
20
20.4
Dep.
Time
40
40
40
40
20.4
20.2
20.2
40
40
20.4
20.4
40
20
20
19.6
19.6
19.6
19.6
18.6
18.6
18.6
18.6
40
40
40
19.6
40
40
19.6
46.8
46.8
20.7
20.7
20.7
20.7
20.7
20.7
21.9
21.9
21.9
21.9
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
Vhigh
b
VnN
0.07
0.143
0.072
0.143
2.91 E-08
6.44E-08
3.23E-08
7.32E-08
3.70E-08
6.40E-08
3.17E-08
6.74E-08
3.47E-08
5.62E-08
2.98E-08
5.1 OE-08
2.85E-08
5.57E-08
2.81 E-08
4.94E-08
2.63E-08
4.76E-08
2.27E-08
6.28E-08
3.09E-08
8.26E-08
4.45E-08
5.89E-08
2.85E-08
6.31 E-08
3.32E-08
6.62E-08
3.65E-08
1.30E-07
6.36E-08
7.80E-08
4.33E-08
6.51 E-08
3.07E-08
7.25E-08
3.49E-08
6.66E-08
3.38E-08
5.94E-08
3.28E-08
9.99E-08
5.35E-08
6.64E-08
3.15E-08
3.68E-07
4.42E-07
4.13E-07
5.07E-07
4.93E-07
4.42E-07
4.20E-07
4.67E-07
4.64E-07
3.92E-07
4.09E-07
3.61 E-07
3.96E-07
3.92E-07
3.77E-07
3.59E-07
3.74E-07
3.48E-07
3.25E-07
4.43E-07
4.18E-07
3.81 E-07
3.97E-07
4.09E-07
3.83E-07
4.36E-07
4.47E-07
4.56E-07
4.84E-07
8.84E-07
8.57E-07
5.28E-07
5.74E-07
4.41 E-07
3.65E-07
5.01 E-07
4.60E-07
4.56E-07
4.30E-07
4.01 E-07
4.02E-07
6.76E-07
7.1OE-07
4.58E-07
0.072
0.143
0.072
0.143
0.072
0.143
0.072
0.14
0.07
0.14
0.07
0.136
0.068
0.136
0.068
0.14
0.07
0.214
0.107
0.143
0.072
0.143
0.071
0.143
0.072
0.147
0.074
0.147
40
0.074
20.7
40
20.7
20.7
40
0.143
0.072
0.143
0.072
0.143
0.072
0.143
0.072
0.147
20.7
20.7
20.7
20.7
40
40
40
20.7
40
40
40
21.9
21.9
40
40
20.7
40
20.7
40
50
0.074
0.143
0.072
4.09E-07
Lot
Wafer
104.1
104.1
16
16
13
13
13
13
13
13
13
13
20
20
20
20
20
20
20
20
20
20
20
20
20
20
9
9
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
Die
Meas R.
F2L
F2L
F2
F2
F2
F2
F2
F2
F2
F2
F2
F2
F2
F2
19.6
19.6
10.5
10.5
10.5
10.5
F2
9
9
9
9
17
17
17
17
17
17
17
17
13
13
13
13
13
13
13
Part
10
F2
F2
F2
F2
F2
F2
F2
F2
F2
F2
F2
F2
F2
F2
F2
F2
F2
F2
F2
F2
F2
F2
F2
F2L
F2L
F2L
F2L
F2L
F2L
F2L
10.4
10.4
10.1
10.1
12.1
12.1
12.1
12.1
12.1
12.1
12
12
12
12
11.7
11.7
11.4
11.4
12.4
12.4
11.8
11.8
11.6
11.6
12.5
12.5
17.2
17.2
12.5
12.5
12.2
12.2
25.3
25.3
26.6
26.6
24.1
24.1
25.3
51
e
40
40
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
Vhigh
b
Vn/V
0.14
0.07
0.105
0.053
0.105
0.053
0.105
0.053
5.52E-08
2.96E-08
3.37E-07
1.79E-07
3.13E-07
1.73E-07
2.84E-08
1.62E-08
3.04E-08
1.66E-08
3.83E-07
1.89E-07
3.72E-07
1.84E-07
3.99E-07
1.81 E-07
3.70E-08
2.17E-08
3.23E-08
1.93E-08
3.23E-08
1.88E-08
3.21 E-08
1.67E-08
4.OOE-08
2.22E-08
3.84E-08
1.74E-08
2.78E-08
1.76E-08
5.05E-08
2.67E-08
9.99E-07
4.41 E-07
3.54E-08
1.91 E-08
3.39E-08
1.89E-08
4.58E-08
2.42E-08
5.16E-08
2.86E-08
4.04E-08
2.11 E-08
4.29E-08
3.81 E-07
3.73E-07
3.21 E-06
3.37E-06
2.98E-06
3.25E-06
2.57E-07
2.56E-07
2.76E-07
2.56E-07
3.44E-06
3.42E-06
3.35E-06
3.34E-06
0.104
0.052
0.111
0.055
0.111
0.055
0.111
0.055
0.11
0.055
0.111
0.055
0.109
0.054
0.109
0.055
0.113
0.056
0.115
0.058
0.108
0.054
0.113
0.056
0.116
0.058
0.114
0.057
0.112
0.056
0.162
0.081
0.163
0.082
0.157
0.079
0.162
3.60E-06
3.29E-06
3.27E-07
3.60E-07
2.76E-07
2.97E-07
2.85E-07
3.05E-07
2.89E-07
2.81 E-07
3.48E-07
3.76E-07
3.30E-07
2.84E-07
2.37E-07
2.55E-07
4.45E-07
4.69E-07
8.61 E-06
7.60E-06
2.92E-07
2.62E-07
2.90E-07
2.89E-07
2.77E-07
2.80E-07
3.14E-07
3.40E-07
2.53E-07
2.47E-07
2.60E-07
Lot
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
99.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
Wafer
Die
Da r
Mfa . R .
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
25.3
34.6
34.6
36.8
36.8
31.5
31.5
28.9
28.9
12.9
12.9
12
12
12.4
12.4
12.9
12.9
28.3
28.3
28
28
28
28
28
28
28
28
28
28
13.3
13.3
13.3
13.3
13.3
13.3
13.8
13.8
13.3
13.3
11.2
11.2
13.8
13.8
13.3
13.3
52
Dep.
VhIgh
b
VnN
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
0.081
0.18
0.09
1.99E-08
7.51 E-08
3.92E-08
7.59E-08
3.85E-08
7.14E-08
3.72E-08
6.96E-08
4.17E-08
4.04E-08
2.40E-08
3.09E-08
1.71 E-08
2.88E-08
1.68E-08
3.43E-08
1.76E-08
8.79E-08
4.32E-08
5.02E-08
2.91 E-08
4.37E-08
2.20E-08
4.80E-08
2.63E-08
4.35E-08
2.60E-08
4.82E-08
2.71 E-08
4.82E-08
2.62E-08
3.29E-08
1.81E-08
3.42E-08
1.62E-08
4.91 E-08
2.55E-08
4.29E-08
1.94E-08
3.25E-08
1.69E-08
3.62E-08
1.75E-08
3.50E-08
1.92E-08
2.22E-07
Time
0.19
0.1
0.175
0.088
0.169
0.085
0.112
0.056
0.109
0.054
0.111
0.055
0.113
0.056
0.169
0.085
0.168
0.084
0.169
0.085
0.169
0.084
0.168
0.085
0.169
0.084
0.114
0.057
0.114
0.057
0.114
0.057
0.116
0.058
0.114
0.057
0.112
0.056
0.116
0.058
0.114
0.057
4.16E-07
4.33E-07
3.85E-07
3.28E-07
4.01 E-07
3.97E-07
4.02E-07
4.57E-07
3.51E-07
3.96E-07
2.69E-07
2.61 E-07
2.46E-07
2.55E-07
2.90E-07
2.58E-07
5.1OE-07
4.65E-07
2.82E-07
2.86E-07
2.47E-07
2.08E-07
2.82E-07
3.08E-07
2.43E-07
2.52E-07
2.79E-07
2.99E-07
4.21 E-07
4.54E-07
2.72E-07
2.51 E-07
2.93E-07
2.52E-07
4.11E-07
3.93E-07
3.69E-07
3.05E-07
2.84E-07
2.79E-07
3.09E-07
2.90E-07
3.01E-07
3.13E-07
Lot
Wafer
Die
Part
Meas R.
Dep.
Time
Vhigh
b
Vn/V
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
17
17
17
17
17
17
17
17
17
17
17
17
17
17
6
6
7
7
7
7
9
9
9
9
10
10
11
11
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
13.3
13.3
34.3
34.3
34.3
34.3
33.9
33.9
33.9
33.9
29.6
29.6
10.6
10.6
60
60
60
60
60
60
60
60
60
60
60
60
60
60
0.114
0.057
0.184
0.092
0.184
0.092
0.183
0.092
0.183
0.092
0.175
0.088
0.109
0.054
4.30E-08
2.13E-08
6.73E-08
3.25E-08
7.72E-08
3.72E-08
1.57E-07
8.31 E-08
1.99E-07
8.27E-08
7.51E-08
3.54E-08
3.44E-08
1.98E-08
3.70E-07
3.43E-07
3.64E-07
3.46E-07
4.18E-07
3.98E-07
8.54E-07
8.83E-07
1.08E-06
8.84E-07
4.21E-07
3.69E-07
3.01E-07
3.15E-07
104.1
17
12
F2L
12.8
60
0.113
4.94E-08 4.31E-07
60
60
60
60
60
60
60
60
60
0.056
0.116
0.058
0.116
0.058
0.111
0.055
0.107
0.054
2.55E-08
3.43E-08
1.75E-08
4.24E-08
2.32E-08
3.46E-08
2.14E-08
7.54E-08
3.1OE-08
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
104.1
17
17
17
17
17
17
17
17
17
12
13
13
14
14
15
15
16
16
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
12.8
13.8
13.8
13.8
13.8
12.4
12.4
11.6
11.6
53
4.31E-07
2.76E-07
2.14E-07
3.52E-07
3.47E-07
3.1OE-07
3.82E-07
7.03E-07
5.63E-07
54
Appendix B
Annealing Experiment Measurements
Before Baking
Lot
54
54
54
54
54
54
54
54
54
54
54
54
54
54
88
88
88
88
88
88
88
88
88
88
88
Wafer
10
10
10
10
10
10
10
10
10
10
10
10
10
10
21
21
21
21
21
21
21
21
21
21
21
Die
5
5
7
7
8
8
10
10
10
10
13
13
15
15
1
1
5
5
7
7
8
8
10
10
13
Part
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
R
41.4
41.4
37.2
37.2
41.4
41.4
46.6
46.6
41.4
41.4
41.4
41.4
41.4
41.4
41.4
41.4
41.4
41.4
41.4
41.4
41.4
41.4
41.4
41.4
41.4
Vhigh
0.202
0.101
0.192
0.096
0.202
0.102
0.214
0.107
0.202
0.102
0.202
0.101
0.202
0.101
0.202
0.101
0.202
0.101
0.202
0.101
0.202
0.102
0.202
0.101
0.202
55
b
2.35E-07
1.22E-07
2.51E-07
1.22E-07
2.17E-07
1.09E-07
2.27E-07
1.13E-07
2.18E-07
1.05E-07
3.22E-07
1.55E-07
2.26E-07
1.11E-07
2.26E-07
1.11E-07
2.15E-07
1.1OE-07
2.11E-07
1.08E-07
2.32E-07
1.16E-07
2.22E-07
1.09E-07
2.22E-07
VnN
1.16E-06
1.20E-06
1.31E-06
1.26E-06
1.07E-06
1.05E-06
1.06E-06
1.05E-06
1.08E-06
1.03E-06
1.59E-06
1.53E-06
1.12E-06
1.1OE-06
1.12E-06
1.09E-06
1.05E-06
1.06E-06
1.04E-06
1.06E-06
1.15E-06
1.13E-06
1.1OE-06
1.07E-06
1.1OE-06
Lot
88
88
88
106
106
106
106
106
106
106
106
106
106
106
106
106
106
106
106
106
106
106
106
Wafer
21
21
21
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
Die
13
15
15
1
1
1
1
5
5
5
5
7
7
8
8
9
9
10
10
13
13
15
15
Part
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
R
41.4
46.6
46.6
28.7
28.7
28.7
28.7
28.7
28.7
28.7
28.7
28.7
28.7
26.6
26.6
28.7
28.7
26.6
26.6
26.6
26.6
28.7
28.7
Vhigh
0.101
0.215
0.107
0.169
0.085
0.169
0.085
0.169
0.084
0.169
0.085
0.168
0.084
0.162
0.081
0.169
0.085
0.162
0.081
0.162
0.081
0.168
0.084
b
1.1OE-07
2.26E-07
1.04E-07
1.63E-07
8.03E-08
1.76E-07
8.39E-08
1.48E-07
7.13E-08
1.81E-07
9.06E-08
3.67E-07
1.54E-07
1.73E-07
8.91E-08
1.85E-07
8.68E-08
1.59E-07
7.87E-08
1.60E-07
8.36E-08
1.70E-07
8.93E-08
Vn/V
1.07E-06
1.05E-06
9.63E-07
9.61E-07
9.31E-07
1.04E-06
9.74E-07
8.71E-07
8.31E-07
1.07E-06
1.05E-06
2.18E-06
1.83E-06
1.07E-06
1.1OE-06
1.09E-06
1.01E-06
9.80E-07
9.65E-07
9.86E-07
1.01E-06
1.01E-06
1.05E-06
1.45E-07
6.78E-08
1.36E-07
6.94E-08
1.35E-07
7.02E-08
1.37E-07
6.89E-08
1.48E-07
7.30E-08
1.43E-07
6.98E-08
1.33E-07
6.57E-08
1.56E-07
8.02E-08
1.53E-07
7.77E-08
1.49E-07
7.1OE-08
1.54E-07
7.65E-08
9.86E-07
9.14E-07
9.19E-07
9.26E-07
9.45E-07
9.69E-07
9.31E-07
9.27E-07
1.OOE-06
9.70E-07
9.37E-07
9.02E-07
9.OOE-07
8.90E-07
9.63E-07
9.89E-07
9.69E-07
9.72E-07
9.47E-07
8.94E-07
9.77E-07
9.61 E-07
Once Baked
54
54
54
54
54
54
54
54
54
54
54
54
54
54
88
88
88
88
88
88
88
88
10
10
10
10
10
10
10
10
10
10
10
10
10
10
21
21
21
21
21
21
21
21
1
1
5
5
7
7
8
8
9
9
10
10
13
13
1
1
5
5
7
7
8
8
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
21.9
21.9
21.9
21.9
20.7
20.7
21.9
21.9
21.9
21.9
23.3
23.3
21.9
21.9
26.6
26.6
24.8
24.8
24.8
24.8
24.8
24.8
0.147
0.074
0.148
0.074
0.143
0.072
0.147
0.074
0.147
0.074
0.152
0.076
0.147
0.073
0.162
0.081
0.157
0.079
0.157
0.079
0.157
0.079
56
Lot
88
88
88
88
88
88
106
106
106
106
106
106
106
106
Wafer
21
21
21
21
21
21
11
11
11
11
11
11
11
Die
9
9
10
10
15
15
1
1
5
5
8
8
9
9
10
10
106
106
11
11
11
106
11
106
11
54
54
54
54
10
10
10
10
9
9
10
54
10
10
54
10
54
54
54
10
10
13
13
5
5
7
7
8
8
15
15
1
1
13
13
13
13
Part
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
R
24.8
24.8
24.8
24.8
26.6
26.6
19.6
19.6
20.7
20.7
19.6
19.6
20.7
20.7
Vhigh
0.157
0.079
0.157
0.079
0.162
0.081
0.139
0.07
0.143
0.072
0.139
0.07
0.143
18.6
0.071
0.136
18.6
19.6
0.068
0.139
19.6
0.07
b
1.53E-07
7.47E-08
1.54E-07
8.02E-08
1.54E-07
8.16E-08
1.30E-07
6.53E-08
1.37E-07
6.83E-08
1.32E-07
6.41E-08
1.37E-07
6.81 E-08
1.23E-07
6.28E-08
1.32E-07
6.18E-08
VnN
9.72E-07
9.36E-07
9.81 E-07
1.01 E-06
9.47E-07
9.99E-07
9.34E-07
9.29E-07
9.53E-07
9.42E-07
9.44E-07
9.01 E-07
9.58E-07
9.53E-07
9.02E-07
9.12E-07
9.46E-07
8.72E-07
1.41E-07
7.57E-08
1.40E-07
7.16E-08
8.35E-08
4.23E-08
1.38E-07
7.44E-08
1.38E-07
6.76E-08
1.58E-07
7.31 E-08
1.35E-07
6.79E-08
1.31 E-07
7.27E-08
1.22E-07
6.16E-08
1.24E-07
6.35E-08
1.33E-07
6.91 E-08
1.24E-07
6.74E-08
1.58E-07
7.60E-08
1.50E-07
9.53E-07
1.01E-06
9.42E-07
9.48E-07
8.47E-07
8.43E-07
9.27E-07
9.75E-07
9.25E-07
8.93E-07
1.06E-06
9.83E-07
9.09E-07
9.02E-07
8.82E-07
9.61 E-07
8.69E-07
8.76E-07
9.11E-07
9.23E-07
9.46E-07
9.59E-07
8.87E-07
9.59E-07
Twice Baked
54
54
54
54
54
54
54
106
106
106
106
106
106
106
106
88
88
88
10
10
10
10
10
10
10
10
10
11
11
11
11
11
11
11
11
21
21
21
15
15
9
9
9
9
8
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
21.9
21.9
21.9
21.9
9.56
9.56
21.9
21.9
21.9
21.9
21.9
21.9
21.9
21.9
21.9
21.9
19.6
19.6
18.6
18.6
19.6
19.6
19.6
19.6
26.6
26.6
24.8
0.148
0.074
0.148
0.074
0.098
0.049
0.148
0.074
0.148
0.074
0.148
0.074
0.148
0.074
0.148
0.074
0.14
0.07
0.136
0.068
0.14
0.07
0.14
0.07
0.162
0.082
0.157
57
9.71 E-07
9.16E-07
9.49E-07
Lot
88
88
88
88
88
88
88
88
88
88
88
88
88
Wafer
21
Die
8
Part
F2L
21
21
21
21
7
7
F2L
21
21
21
5
5
13
13
15
21
21
15
10
21
21
21
10
1
1
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
F2L
R
24.8
24.8
24.8
24.8
24.8
24.8
24.8
24.8
24.8
23.3
23.3
24.8
24.8
Vhigh
0.078
0.157
0.078
0.157
0.078
0.157
0.079
0.157
0.078
0.152
0.076
0.157
0.079
58
b
8.05E-08
1.51 E-07
7.40E-08
1.50E-07
7.87E-08
1.43E-07
7.32E-08
1.47E-07
7.18E-08
1.43E-07
7.23E-08
1.44E-07
7.36E-08
VnN
1.02E-06
9.59E-07
9.30E-07
9.49E-07
9.94E-07
9.13E-07
9.23E-07
9.32E-07
9.03E-07
9.35E-07
9.42E-07
9.15E-07
9.18E-07
Bibliography
[1]
W. Lentz.
Characterization of Noise in Uncooled IR Bolometer Arrays.
Massachusetts Institute of Technology, Cambridge MA, 1998.
[2]
C. D. Motchenbacher and J. A. Connelly. Low-Noise Electronic System Design.
J. Wiley and Sons, New York, 1993.
[3]
R. F. Pierret. Semiconductor Fundamentals. Addison-Wesley Modular Series on
Solid State Devices. Addison-Wesley, Reading MA, 1988.
[4]
S. M. Sze. Physics of Semiconductor Devices, Second Edition. J. Wiley and
Sons, New York, 1981.
[5]
W. L. Wolfe and G. J. Zissis, editors. The Infrared Handbook. Environmental
Research Institute of Michigan, Ann Arbor, Michigan, 1985.
59