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

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 (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

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 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.

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 -- I __ _ I - I - I

0 0.5 1 1.5 2 2.5VOx Thickness(X)

27

Figure 3-2: Data Points and Bulk Model

0.OOE+00 1- T

0.5 11. -

1.5

VOx Thickness(X)

IX Resistivity F2L PixelsVOx Thickness

0.50.5

1.51.52

Sqrt Thickness0.7071067810.707106781

11

1.2247448711.2247448711.414213562

VnN1.25E-061.25E-068.81 E-079.61E-079.66E-077.55E-077.22E-07

Vn/V1.25E-061.25E-068.81 E-079.61 E-079.66E-077.55E-077.22E-07

Approximation1.19E-061.19E-061.02E-061.02E-068.46E-078.46E-076.75E-07

Approximation1.21 E-061.21E-069.98E-079.98E-078.34E-078.34E-076.96E-07

Table 3-4: Bulk vs. Surface Model

28

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 2 2.5

Error4.88%4.73%15.52%5.90%12.33%12.18%6.43%

8.85%

Error3.12%2.97%13.25%3.82%13.62%10.54%3.53%

7.26%

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:

N Post-Baking0 Pre-BakingM Twice-Baked

8.95E-07 9.43E-07 9.90E-07 1.04E-06

VnN

Histogram of Baking ExperimentsPre mean = 1.13e-6Pre std = 2.38e-7

Post mean = 9.44e-7Post std = 2.84e-8

Twice mean = 9.349-7Twice std = 3.93e-8

1.09E-06 1.13E-06

Figure 3-4 Plot by Part

X Pre Baking+ Post Baking0 Twice Baked

X

XxXt

x

XXX X.0 off*~ *

20 25

12

10

8

4)CrU.

6

4

2

0 t I-More

2.50E-06

2.OOE-06 -

1.50E-06

'p

1.OOE-06 -

5.OOE-07

X X X

0.OOE+000 5 10 15

Part index

30

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 Weidemann-

Franz 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 -

30.0030 35 40 45 50 55 60 65 70 75 80

Measured Responsivity (counts/dog C)

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

00.00 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

Meas R. VnN46.8 5.84E-0735.5 8.06E-0745.3 4.49E-0724 1.06E-06

31.1 1.17E-0631.1 1.22E-0631.1 1.15E-0626.6 9.92E-0726.6 1.09E-0628.7 1.06E-0628.7 1.14E-0626.6 1.08E-0628.7 1.09E-0624.8 9.93E-0723.3 1.02E-0624.8 1.03E-0624.8 9.84E-0723.3 1.01E-0621.9 9.84E-0723.3 1.04E-06

Mean 28.85 9.96E-07

Bias(X)1.501.251.251.001.001.001.001.001.001.251.001.001.001.001.001.001.001.001.001.001.06

Responsivity56.3551.8

51.8758.5549.5552.1350.4851.1350.1652.2953.5649.5549.3657.3555.5758.5454.2158.9

60.3858.0653.99

ModelReasp71.1240.5742.0057.9850.0159.6655.1356.4051.3762.1256.2842.2855.3758.4055.1258.2758.9761.2059.6762.7955.73

Error TNETD26.21%-21.69%-19.03%-0.98%0.92%

14.45%9.20%

10.31%2.41%18.80%5.09%

-14.68%12.17%1.83%-0.81%-0.46%8.78%3.90%-1.18%8.14%3.17%

67.4482.4878.5978.3587.6085.8087.7390.0690.6890.8485.5190.4592.1782.6679.9676.5488.1483.3276.4081.8083.83

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

ModelTNETD54.0288.6178.9283.8998.987.389.3

83.2994

84.8288.61102.8185.32

8288.7385.9683.6582.8784.0983.7485.54

Error-19.90%7.43%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%

Figure 4-3: Responsivity Check, Thicker Wafers

80

70

60

50

40

30

20

10

060 70 80

Figure 4-4: TNETD Check, Thicker Wafers

50 60 700 10 20 30 40

Measured TNETO (mK)

45

0 10 20 30 40 50Measured Responsivity (counts/deg C)

V.I

aI-wzI-

70

60

50

40

30

20

10

0

00000

Meas R. Vn/V Bias (X)27 4.88E-07 1.25

26.2 4.25E-07 1

26 3.57E-07 1

28.1 3.81E-07 1.25

Mean 26.825 4.13E-07 1.125

Resp. Resp Error TNETD TNETD Error67.57 70.06 3.69% 54.16 51.86 -4.25%55.32 54.57 -1.34% 62.81 59.29 -5.60%53.12 61.51 15.81% 65.74 55.85 -15.040%53.85 54.46 1.15% 63.99 63.31 -1.06%

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

Model Model

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 ExperimentMeasurements

Lot Wafer Die

99.199.199.199.199.199.199.199.199.199.199.199.199.199.199.199.199.199.199.199.199.199.199.199.199.199.199.199.1104.1104.1104.1104.1104.1

Part Meas R. Dep.Time2525

22.422.422.422.422.522.521.521.521.521.521.521.521.521.521.521.521.421.421.421.421.521.521.421.42121

20.120.118.818.8

19

404040404040404040404040404040404040404040404040404040404040404040

Vhigh

0.1630.0820.1520.0760.1520.0760.1520.0760.1470.0740.1470.0740.1470.0740.0910.0450.0980.0490.1470.0740.1470.0740.1470.0740.1470.0740.1470.0740.1470.0740.1360.0680.14

b VnN

9.16E-085.06E-086.78E-083.76E-086.72E-083.96E-087.21 E-083.63E-082.85E-081.60E-086.76E-083.24E-086.69E-083.07E-088.51 E-083.47E-084.58E-082.59E-087.31 E-084.41 E-087.42E-084.64E-089.41 E-084.51E-086.47E-083.35E-087.83E-084.05E-086.09E-082.88E-085.17E-082.80E-085.60E-08

5.53E-075.83E-074.31 E-074.39E-074.27E-074.69E-074.70E-074.59E-071.84E-071.80E-074.56E-074.21 E-074.52E-074.03E-079.25E-077.18E-074.49E-074.61 E-074.95E-075.87E-074.97E-076.03E-076.37E-076.OOE-074.37E-074.40E-075.31 E-075.41 E-074.13E-073.84E-073.74E-073.90E-073.88E-07

49

Lot Wafer Die

104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1

Part Meas R.

F2F2F2F2F2F2F2F2F2F2F2

F2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2L

192020

20.420.420.220.220.420.42020

19.619.619.619.618.618.618.618.619.619.646.846.820.720.720.720.720.720.721.921.921.921.920.720.720.720.720.720.720.720.721.921.920.720.7

Dep.Time

404040404040404040404040404040404040404040404040404040404040404040404040404040404040404040

Vhigh

0.070.1430.0720.1430.0720.1430.0720.1430.0720.1430.0720.140.070.140.07

0.1360.0680.1360.0680.140.07

0.2140.1070.1430.0720.1430.0710.1430.0720.1470.0740.1470.0740.1430.0720.1430.0720.1430.0720.1430.0720.1470.0740.1430.072

b VnN

2.91 E-086.44E-083.23E-087.32E-083.70E-086.40E-083.17E-086.74E-083.47E-085.62E-082.98E-085.1 OE-082.85E-085.57E-082.81 E-084.94E-082.63E-084.76E-082.27E-086.28E-083.09E-088.26E-084.45E-085.89E-082.85E-086.31 E-083.32E-086.62E-083.65E-081.30E-076.36E-087.80E-084.33E-086.51 E-083.07E-087.25E-083.49E-086.66E-083.38E-085.94E-083.28E-089.99E-085.35E-086.64E-083.15E-08

3.68E-074.42E-074.13E-075.07E-074.93E-074.42E-074.20E-074.67E-074.64E-073.92E-074.09E-073.61 E-073.96E-073.92E-073.77E-073.59E-073.74E-073.48E-073.25E-074.43E-074.18E-073.81 E-073.97E-074.09E-073.83E-074.36E-074.47E-074.56E-074.84E-078.84E-078.57E-075.28E-075.74E-074.41 E-073.65E-075.01 E-074.60E-074.56E-074.30E-074.01 E-074.02E-076.76E-077.1OE-074.58E-074.09E-07

50

Lot Wafer Die

104.1104.199.199.199.199.199.199.199.199.199.199.199.199.199.199.199.199.199.199.199.199.199.199.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.199.199.199.199.199.199.199.1

161613131313131313132020202020202020202020202020999999

1717171717171717131313131313

Part Meas R. e

F2LF2LF2F2F2F2F2F2F2F2F2F2F2F2F2F2F2F2F2F2F2F2F2F2F2F2F2F2F2F2F2F2F2F2F2F2F2F2

F2LF2LF2LF2LF2LF2L

13 10 F2L

19.619.610.510.510.510.510.410.410.110.112.112.112.112.112.112.1

12121212

11.711.711.411.412.412.411.811.811.611.612.512.517.217.212.512.512.212.225.325.326.626.624.124.125.3

404060606060606060606060606060606060606060606060606060606060606060606060606060606060606060

Vhigh

0.140.07

0.1050.0530.1050.0530.1050.0530.1040.0520.1110.0550.1110.0550.1110.0550.11

0.0550.1110.0550.1090.0540.1090.0550.1130.0560.1150.0580.1080.0540.1130.0560.1160.0580.1140.0570.1120.0560.1620.0810.1630.0820.1570.0790.162

b Vn/V

5.52E-082.96E-083.37E-071.79E-073.13E-071.73E-072.84E-081.62E-083.04E-081.66E-083.83E-071.89E-073.72E-071.84E-073.99E-071.81 E-073.70E-082.17E-083.23E-081.93E-083.23E-081.88E-083.21 E-081.67E-084.OOE-082.22E-083.84E-081.74E-082.78E-081.76E-085.05E-082.67E-089.99E-074.41 E-073.54E-081.91 E-083.39E-081.89E-084.58E-082.42E-085.16E-082.86E-084.04E-082.11 E-084.29E-08

3.81 E-073.73E-073.21 E-063.37E-062.98E-063.25E-062.57E-072.56E-072.76E-072.56E-073.44E-063.42E-063.35E-063.34E-063.60E-063.29E-063.27E-073.60E-072.76E-072.97E-072.85E-073.05E-072.89E-072.81 E-073.48E-073.76E-073.30E-072.84E-072.37E-072.55E-074.45E-074.69E-078.61 E-067.60E-062.92E-072.62E-072.90E-072.89E-072.77E-072.80E-073.14E-073.40E-072.53E-072.47E-072.60E-07

51

Lot Wafer Die

99.199.199.199.199.199.199.199.199.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1104.1

Da r Mfa .R Dep.

F2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2L

25.334.634.636.836.831.531.528.928.912.912.91212

12.412.412.912.928.328.328282828282828282828

13.313.313.313.313.313.313.813.813.313.311.211.213.813.813.313.3

. VhIgh b VnNTime606060606060606060606060606060606060606060606060606060606060606060606060606060606060606060

0.0810.180.090.190.1

0.1750.0880.1690.0850.1120.0560.1090.0540.1110.0550.1130.0560.1690.0850.1680.0840.1690.0850.1690.0840.1680.0850.1690.0840.1140.0570.1140.0570.1140.0570.1160.0580.1140.0570.1120.0560.1160.0580.1140.057

1.99E-087.51 E-083.92E-087.59E-083.85E-087.14E-083.72E-086.96E-084.17E-084.04E-082.40E-083.09E-081.71 E-082.88E-081.68E-083.43E-081.76E-088.79E-084.32E-085.02E-082.91 E-084.37E-082.20E-084.80E-082.63E-084.35E-082.60E-084.82E-082.71 E-084.82E-082.62E-083.29E-081.81E-083.42E-081.62E-084.91 E-082.55E-084.29E-081.94E-083.25E-081.69E-083.62E-081.75E-083.50E-081.92E-08

52

2.22E-074.16E-074.33E-073.85E-073.28E-074.01 E-073.97E-074.02E-074.57E-073.51E-073.96E-072.69E-072.61 E-072.46E-072.55E-072.90E-072.58E-075.1OE-074.65E-072.82E-072.86E-072.47E-072.08E-072.82E-073.08E-072.43E-072.52E-072.79E-072.99E-074.21 E-074.54E-072.72E-072.51 E-072.93E-072.52E-074.11E-073.93E-073.69E-073.05E-072.84E-072.79E-073.09E-072.90E-073.01E-073.13E-07

Lot Wafer Die Part Meas R. Dep. Vhigh b Vn/VTime104.1 17 6 F2L 13.3 60 0.114 4.30E-08 3.70E-07104.1 17 6 F2L 13.3 60 0.057 2.13E-08 3.43E-07104.1 17 7 F2L 34.3 60 0.184 6.73E-08 3.64E-07104.1 17 7 F2L 34.3 60 0.092 3.25E-08 3.46E-07104.1 17 7 F2L 34.3 60 0.184 7.72E-08 4.18E-07104.1 17 7 F2L 34.3 60 0.092 3.72E-08 3.98E-07104.1 17 9 F2L 33.9 60 0.183 1.57E-07 8.54E-07104.1 17 9 F2L 33.9 60 0.092 8.31 E-08 8.83E-07104.1 17 9 F2L 33.9 60 0.183 1.99E-07 1.08E-06104.1 17 9 F2L 33.9 60 0.092 8.27E-08 8.84E-07104.1 17 10 F2L 29.6 60 0.175 7.51E-08 4.21E-07104.1 17 10 F2L 29.6 60 0.088 3.54E-08 3.69E-07104.1 17 11 F2L 10.6 60 0.109 3.44E-08 3.01E-07104.1 17 11 F2L 10.6 60 0.054 1.98E-08 3.15E-07104.1 17 12 F2L 12.8 60 0.113 4.94E-08 4.31E-07104.1 17 12 F2L 12.8 60 0.056 2.55E-08 4.31E-07104.1 17 13 F2L 13.8 60 0.116 3.43E-08 2.76E-07104.1 17 13 F2L 13.8 60 0.058 1.75E-08 2.14E-07104.1 17 14 F2L 13.8 60 0.116 4.24E-08 3.52E-07104.1 17 14 F2L 13.8 60 0.058 2.32E-08 3.47E-07104.1 17 15 F2L 12.4 60 0.111 3.46E-08 3.1OE-07104.1 17 15 F2L 12.4 60 0.055 2.14E-08 3.82E-07104.1 17 16 F2L 11.6 60 0.107 7.54E-08 7.03E-07104.1 17 16 F2L 11.6 60 0.054 3.1OE-08 5.63E-07

53

54

Appendix B

Annealing Experiment Measurements

Before BakingLot Wafer Die Part R Vhigh b VnN54 10 5 F2L 41.4 0.202 2.35E-07 1.16E-0654 10 5 F2L 41.4 0.101 1.22E-07 1.20E-0654 10 7 F2L 37.2 0.192 2.51E-07 1.31E-0654 10 7 F2L 37.2 0.096 1.22E-07 1.26E-0654 10 8 F2L 41.4 0.202 2.17E-07 1.07E-0654 10 8 F2L 41.4 0.102 1.09E-07 1.05E-0654 10 10 F2L 46.6 0.214 2.27E-07 1.06E-0654 10 10 F2L 46.6 0.107 1.13E-07 1.05E-0654 10 10 F2L 41.4 0.202 2.18E-07 1.08E-0654 10 10 F2L 41.4 0.102 1.05E-07 1.03E-0654 10 13 F2L 41.4 0.202 3.22E-07 1.59E-0654 10 13 F2L 41.4 0.101 1.55E-07 1.53E-0654 10 15 F2L 41.4 0.202 2.26E-07 1.12E-0654 10 15 F2L 41.4 0.101 1.11E-07 1.1OE-0688 21 1 F2L 41.4 0.202 2.26E-07 1.12E-0688 21 1 F2L 41.4 0.101 1.11E-07 1.09E-0688 21 5 F2L 41.4 0.202 2.15E-07 1.05E-0688 21 5 F2L 41.4 0.101 1.1OE-07 1.06E-0688 21 7 F2L 41.4 0.202 2.11E-07 1.04E-0688 21 7 F2L 41.4 0.101 1.08E-07 1.06E-0688 21 8 F2L 41.4 0.202 2.32E-07 1.15E-0688 21 8 F2L 41.4 0.102 1.16E-07 1.13E-0688 21 10 F2L 41.4 0.202 2.22E-07 1.1OE-0688 21 10 F2L 41.4 0.101 1.09E-07 1.07E-0688 21 13 F2L 41.4 0.202 2.22E-07 1.1OE-06

55

Lot Wafer Die Part R Vhigh b Vn/V88 21 13 F2L 41.4 0.101 1.1OE-07 1.07E-0688 21 15 F2L 46.6 0.215 2.26E-07 1.05E-0688 21 15 F2L 46.6 0.107 1.04E-07 9.63E-07

106 11 1 F2L 28.7 0.169 1.63E-07 9.61E-07106 11 1 F2L 28.7 0.085 8.03E-08 9.31E-07106 11 1 F2L 28.7 0.169 1.76E-07 1.04E-06106 11 1 F2L 28.7 0.085 8.39E-08 9.74E-07106 11 5 F2L 28.7 0.169 1.48E-07 8.71E-07106 11 5 F2L 28.7 0.084 7.13E-08 8.31E-07106 11 5 F2L 28.7 0.169 1.81E-07 1.07E-06106 11 5 F2L 28.7 0.085 9.06E-08 1.05E-06106 11 7 F2L 28.7 0.168 3.67E-07 2.18E-06106 11 7 F2L 28.7 0.084 1.54E-07 1.83E-06106 11 8 F2L 26.6 0.162 1.73E-07 1.07E-06106 11 8 F2L 26.6 0.081 8.91E-08 1.1OE-06106 11 9 F2L 28.7 0.169 1.85E-07 1.09E-06106 11 9 F2L 28.7 0.085 8.68E-08 1.01E-06106 11 10 F2L 26.6 0.162 1.59E-07 9.80E-07106 11 10 F2L 26.6 0.081 7.87E-08 9.65E-07106 11 13 F2L 26.6 0.162 1.60E-07 9.86E-07106 11 13 F2L 26.6 0.081 8.36E-08 1.01E-06106 11 15 F2L 28.7 0.168 1.70E-07 1.01E-06106 11 15 F2L 28.7 0.084 8.93E-08 1.05E-06

Once Baked54 10 1 F2L 21.9 0.147 1.45E-07 9.86E-0754 10 1 F2L 21.9 0.074 6.78E-08 9.14E-0754 10 5 F2L 21.9 0.148 1.36E-07 9.19E-0754 10 5 F2L 21.9 0.074 6.94E-08 9.26E-0754 10 7 F2L 20.7 0.143 1.35E-07 9.45E-0754 10 7 F2L 20.7 0.072 7.02E-08 9.69E-0754 10 8 F2L 21.9 0.147 1.37E-07 9.31E-0754 10 8 F2L 21.9 0.074 6.89E-08 9.27E-0754 10 9 F2L 21.9 0.147 1.48E-07 1.OOE-0654 10 9 F2L 21.9 0.074 7.30E-08 9.70E-0754 10 10 F2L 23.3 0.152 1.43E-07 9.37E-0754 10 10 F2L 23.3 0.076 6.98E-08 9.02E-0754 10 13 F2L 21.9 0.147 1.33E-07 9.OOE-0754 10 13 F2L 21.9 0.073 6.57E-08 8.90E-0788 21 1 F2L 26.6 0.162 1.56E-07 9.63E-0788 21 1 F2L 26.6 0.081 8.02E-08 9.89E-0788 21 5 F2L 24.8 0.157 1.53E-07 9.69E-0788 21 5 F2L 24.8 0.079 7.77E-08 9.72E-0788 21 7 F2L 24.8 0.157 1.49E-07 9.47E-0788 21 7 F2L 24.8 0.079 7.1OE-08 8.94E-0788 21 8 F2L 24.8 0.157 1.54E-07 9.77E-0788 21 8 F2L 24.8 0.079 7.65E-08 9.61 E-07

56

Lot888888888888106106106106106106106106106106106106

54545454545454545454545454545454106106106106106106106106888888

Wafer212121212121111111111111111111111111

101010101010101010101010101010101111111111111111212121

Die99

1010151511558899

10101313

9910

10101313557788

151511

1313151599998

PartF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2L

F2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2L

R24.824.824.824.826.626.619.619.620.720.719.619.620.720.718.618.619.619.6

Twice21.921.921.921.99.569.5621.921.921.921.921.921.921.921.921.921.919.619.618.618.619.619.619.619.626.626.624.8

Vhigh0.1570.0790.1570.0790.1620.0810.1390.07

0.1430.0720.1390.07

0.1430.0710.1360.0680.1390.07

Baked0.1480.0740.1480.0740.0980.0490.1480.0740.1480.0740.1480.0740.1480.0740.1480.0740.140.07

0.1360.0680.140.070.140.070.1620.0820.157

b1.53E-077.47E-081.54E-078.02E-081.54E-078.16E-081.30E-076.53E-081.37E-076.83E-081.32E-076.41E-081.37E-076.81 E-081.23E-076.28E-081.32E-076.18E-08

1.41E-077.57E-081.40E-077.16E-088.35E-084.23E-081.38E-077.44E-081.38E-076.76E-081.58E-077.31 E-081.35E-076.79E-081.31 E-077.27E-081.22E-076.16E-081.24E-076.35E-081.33E-076.91 E-081.24E-076.74E-081.58E-077.60E-081.50E-07

VnN9.72E-079.36E-079.81 E-071.01 E-069.47E-079.99E-079.34E-079.29E-079.53E-079.42E-079.44E-079.01 E-079.58E-079.53E-079.02E-079.12E-079.46E-078.72E-07

9.53E-071.01E-069.42E-079.48E-078.47E-078.43E-079.27E-079.75E-079.25E-078.93E-071.06E-069.83E-079.09E-079.02E-078.82E-079.61 E-078.69E-078.76E-079.11E-079.23E-079.46E-079.59E-078.87E-079.59E-079.71 E-079.16E-079.49E-07

57

Lot88888888888888888888888888

Wafer21212121212121212121212121

Die87755

13131515101011

PartF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2LF2L

R24.824.824.824.824.824.824.824.824.823.323.324.824.8

Vhigh0.0780.1570.0780.1570.0780.1570.0790.1570.0780.1520.0760.1570.079

b8.05E-081.51 E-077.40E-081.50E-077.87E-081.43E-077.32E-081.47E-077.18E-081.43E-077.23E-081.44E-077.36E-08

VnN1.02E-069.59E-079.30E-079.49E-079.94E-079.13E-079.23E-079.32E-079.03E-079.35E-079.42E-079.15E-079.18E-07

58

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