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
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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 anddistribute publicly paper and electronic copies of this thesis
and to grant others the right to do so.
AuthorDepArtment of Electrical Engineering and Computer Science
May 22, 2000
Certified by_ igHQing Hu
TOsis Spervisor
Accepted byA Irthur C. Smith
Chairman, Department Committee on Graduate Theses
MASSACHUSETTS INSTITUTEOF TECHNOLOGY
JUL 3 12002
LIBRARIES
1
Measurement and Analysis of 1/f Noise in Uncooled Microbolometersby
Jason T. Timpe
Submitted to theDepartment of Electrical Engineering and Computer Science
May 22, 2000
In Partial Fulfillment of the Requirements for the Degree ofMaster of Engineering in Electrical Engineering and Computer Science
ABSTRACT
A method for measuring the 1/f noise in bolometers was developed that would be mostconducive to a production environment. Several experiments were performed to discoverhow best to reduce the 1/f noise through processing changes. A model was developed topredict the performance of an infrared camera based on the 1/f noise measurement andother measurements made on the unpackaged wafers.
Thesis Supervisor: Qing HuTitle: 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, low-
cost 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
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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 (2.1)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
1p = 1 (2.2)
q( uMnn+ p,p)
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.
1kFigure -: wk Vs sg bias monitor
L M399
500k=RcRa= I k +9V(2)
04 ~~~hihi io +10
Rb=lk Rd-9V(3)
- ..MOut
+ 10k
-9 V(3)
Figure 2-1: Two stages of 1/f noise test circuit.
8
-77 50k
62.5k _/ L2
L I LO
50k 20k
10k -_
12.5k S2
SS
S6
Figure 2-2: Resistor network for adjustable Rc.
High
BolometerLow
Bias Monitor
TestBox
High Node
I HP 3458A Multimeter
HP 3478AMultimeter
Out
7
Model 113Pre-amp
Input A and Filter
Out
HP 3561ADynamic Signal
Analyzer
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:
Vmas, = II-.Viu W -R, (2.3)
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=a2 +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 2 of 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
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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 w -b1 , (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+000.1 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 -
I. OOE-07 -CL
8.OOE-08 -
6.OOE-08 -
4.OOE-08 -
2.00E-08 -
0.OOE+000.1 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 100k 100k 100k
20k 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 pW. If this
14
00
0
00
+9V 2)
+ 5V 2 k
lo p +9V(2)
+15V 619kk
15 p 10k
.01 U
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 X OVlp (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
R I = ER R I= E/R
R/2 ) 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
R/2 I= Et/Rs
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.
1 Not all of the test station improvements described in Chapter 2 had been made at the time this experimentwas done.2 A complete listing of all of the data from the thickness experiments is shown in Appendix A. Only thosemeasurements within 3a were considered for the statistical measurements. This is to prevent atypicalpixels from influencing the statistics.
24
Lot Part Dep. Time Mean VnN Std. Dev.99.1 F2 40 min 4.79E-07 1.15E-0799.1 F2 60 min 2.89E-07 3.08E-08
104.1 F2 40 min 4.23E-07 4.24E-08104.1 F2 60 min 3.23E-07 7.39E-0899.1 F2L 60 min 3.38E-07 7.56E-08
104.1 F2L 40 min 4.46E-07 1.1OE-07104.1 F2L 60 min 3.30E-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 Mean Bulk Bulk Err Surface Surface Err99.1 F2 2.89E-07 3.91E-07 -35.34% 3.19E-07 -10.51%104.1 F2 3.23E-07 3.45E-07 -6.87% 2.82E-07 12.74%104.1 F2L 3.30E-07 3.64E-07 -10.43% 2.97E-07 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 Bulk Model Bulk Err Surface Surface ErrF2 40 min 4.83E-07F2 60 min 3.06E-07 3.94E-07 -28.93% 3.22E-07 -5.27%F2L 40 min 4.96E-07F2L 60 min 3.32E-07 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 3-
1 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.