A study on time-resolved CMOS image sensors with draining-only modulation pixels for fluorescence lifetime imaging microscopy

A study on time‑resolved CMOS image sensors with draining‑only modulation pixels for fluorescence lifetime imaging microscopy

著者 Li Zhuo

year 2013‑01

出版者 Shizuoka University

URL http://doi.org/10.14945/00008283

DOCttORAL THESIS

A Study on Time-Resolved GMOS lmage Sensors with Draining-Only Modulation Pixels for Fluorescence Lifetime lmaging

Microscopy

Zhuo Li

Nanovision Technology

Graduate School of Science and Technology Shizuoka University

January 2013

静岡大学   ^博士論文

A Study on Time-resolved CMOS lmage Sensors with Draining-Only Modulation Pixels for Fluorescence Lifetime lmaging

Microscopy

蛍光寿命イメージング顕微鏡のための

電荷 J卜 出変調画素を用いた CMOS時 間分解型 センサに関する研究

李 卓

静岡大学   ^{自然科学系教育部}

ナノビジ ョンエ学専攻

2013年 1月

A Study on Time-resolved CMOS lmage Sensor with

Drai

n

in g-On ly Mod

u

lation Pixels for ^Fl uorescence Lifetime lmaging Microscopy

by Zhuo Li

Submitted for the degree of Doctor of Engineering January 2013

Abstract

This thesis ^presents a time-resolved CMOS image sensor with draining only modulation (DOM) ^pixels, for time domain fluoresc,ence lifetime

imaging.

ln the DOM pixels using pinned photo-diode technology, a time-windowed signal charge transfer

from a

pinned photo-diode (PPD)

to a

pinned storage

diode

(PSD) is controlled by a draining gate only, without a transfer gate between the two diodes.

This structure allows

a

potential barrier-less and trap-less charge transfer from the PPD to PSD, which is suitable to transfer 1 electron at high speed.

A 256

x

256 pixel time-resolved CMOS imager with 7 .\p,rn

x

7.5pm DOM pix- els has been implemented using 0.18pm CMOS image senor process technology with pinned photo-diode

option. The

PPD

and

PSD are layout in a symmetrical shape, thus sensitivity of PPD to incident of light is increased and full well capacity is increased. The barrier between PSD to PPD is chosen large enough to prevent leakage during charge draining time. The prototype demonstrates high sensitivity

ficr weak signal of less than ¹ electron per light pulse, and accurate measurement of fluorescence decay ^process with sub-nanosecond time resolution. Measured fluorescence decaying is

a

convolution of the target fluorescence decaying and

the time

response

of the

DOM

pixel. The time

response

of the

DOM

pixel

is measured

to

be 2ns, and

the

resulting target fluorescence decaying and the re-

sulting target lifetime can be estimated by

the

proposed deconvolution method.

The ^prototype sensor is useful for a compact low-cost camera for FLIM in biolog- ical measurements. Fluorescence from cells under microscope are observed by the sensor, and its related lifetime is successfully measured.

Dark electrons generated by a scooping effect of the draining gate (TD) clock-

ing

cause

offset to the

signal

detection. An

improved version

of

sensor chip

was

designed and fabricated

for

reducing

dark

offset,

and the

reduction effect is proved by the measurement result.

Declaration

The work in this thesis is based on research carried out at the lmaging Devices Laboratory, Research lnstitute of Electronics, Shizuoka University. No part of this thesis has been submitted elsewhere fur any other degree or qualification and it all my own work unless referenced to the contrary in the text.

Copyright(D 2013 by Zhuo Li

The oopyright Ofthis thesis rests with the authon No quotations from it should be published without the author's prior written∞ nsent and information derived from it should be acknow!edged".

「本論文の著作権は、国立大学法人静岡大学 自然科学系教育部ナノビジョンエ学 専攻李卓が所有 しています。本論文の記事 。図面の無断複写、複製および無断転載 を禁 じます。ただ し、著者は本論文の複写権を国立大学法人静岡大学に唯一許諾 し ます」。

V

Gontents

Abstract Declaration

1 lntroduction

Fluorescence lifetime measurement methods

2.1

Overview of fluorescence

libtime

measurements 2.1

.1

Concept of fluorescence

lifttime

2.1.2

Comparison of lifutime measurements in frequency domain and time domain

2.1.3

Time-resolved fluorescence lifetime measurement

in

time domain

2.2

Relationshipbetween ^potential

2.3

Estimation on optical system

2.4

Estimation on time resolution

barrier and current through

banier

1

10 10 10

12

14 18 25 26 Design of

time-resolved

CMOS image

sensor using draining-only mod-

ulation

(DOM)

technique

³⁴

3.1

FLIM using conventional 4 transistor type CMOS image

sensor

³⁴

3.2

^{DOM pixel}

design

³⁹

3.2.1

Pixel

structure ...

³⁹

3.2.2 D0Mmechanism

⁴²

3.2.3

Windowing by draining-only

modulation

⁴⁴

3.3

^lmager

architecture

⁴⁶

Contents

^V‖

3.4 Device simulalon of DOM pixel

4 lmplementation and application of time-resolved

CMOS

image sen.

sor w■h DOM pixeis 41  :rnplemented chip

4.2

Measurement on basic characteristics

4.3

Lifetime measurement results

4.4

Summary of chip perficrmances

lmprovement of time-resolved

CMOS image

sensor with

DOM

pixels

5.1

New structure for reducing scooped dark electrons in DOM pixels .

5.1.1

Design of pixels on reducing charge injection

5.1

.2

Measurement on reduction effect of charge

injection . . .

^.

5.2

Deconvolution method to improve lifetime measurement accuracy

5.2.1

Deconvolution

method

^.

5.2.2

Applying deconvolution method to measured

data . . . .

^.

6 Summary and conclusions

List of publications Acknowledgements

48

58 58 59 70

80 83 83 83 85 87

87 92

100

i

1

Ghapter ¹

lntroduction

Background

Nowadays, image sensor

is widely used in

mobile phone camera

and

dig-

ital still

camera,

and

become

a

consumer product

near us.

^lmage

^sensor

^is

mainly divided into two categories, CCD (Charge Coupled ^Devices) image sen- sors

and

CMOS (Complementary Metal-Oxide Semiconductor) image ^sensor6.

Unlike CCD image sensor which need special process in manufacturing, CMOS image sensor can be designed and manufactured in the same process ^like that

of

CMOS

LSl.

Therefore, processing circuit ficr functional operation

can be

in- tegrated into CMOS image sensors, making

it

^high functional, compact and ^low cost. The large noise problem which is a disadvantage in CMOS image sensors motivates many kinds of researches on noise reduction. Pinned diode structures originally developed for CCD image sensors for both charge generation and stor- age has the advantages of low dark cunent and no image lag [1]. ^Now the pinned photo-diode technologies are applied for CMOS image sensor

[2].

^{As the report} of [3], the CMOS image sensors are dramatically improved the image quality and the interest of CMOS image sensors has increased in various electronic cameras.

One kind

of

high functional applications in CMOS image sensor is

the

fluo- rescen@

imaging.

Fluorescence imaging is

a

^powerful

tool

in biology. Fluores- cence has two ^physical quantities; intensity and lifetime of decaying. Qualitative imaging of fluorescence intensity

can

reveal

the

location

or

distribution of fluo-

Chapter

1,

lntroduction

rophores. The fluorescence intensity measurement has difficulty in quantitative measurement because the fluorescence intensity is influenced by many factors, such as fluorophore concentration, degradation of fluorophore, wavelength and intensity

of

excitation

flux,

sensitivity

of

detectors, and transmittance

of

optical system. To address these difficulties and to ^provide additional novel information, fluorescence lifetime measurement has been becoming important technology in biological imaging

[4].

Fluorescence lifetime measurement uses intensity decay rate rather than the absolute value of intensity, and therefore the quantification is not influenced by degradation of fluorescence intensity. The fluorescence lifetime imaging microscopy (FLIM) has a variety of applications. It can be used to quan- tifo physical parameters such

as

microviscosity, and chemical parameters such as pH and ion concentration. lt can also be a ^powerful tool in DNA sequencing.

Motivation

Streak camera can measure two dimensional dishibution of fluorescence life- time. Optical pulses anive at a slit at photocathode with varying intensities which

vary

slightly in terms

of

time

and space. As the

corresponding photoelectrons generated from photocathode pass between

a

^pair of sweep electrodes, the ap- plied sweep voltage steers the electron paths away from the horizontal direction at different angles depending on their arrival time at the electrodes. The amplified electrons reach

the

phosphor screen forming

an

image

of

three optical ^pulses arranged in vertical direction according

to the

time

of

their arrival at the sweep

electrodes. The

earliest

pulse is ananged in the upper most

position and the latest pulse is in

the

bottom most portion of

the

^phosphor

image.

The resulting streak image has spac,e as the x-axis and time as the y-axis. Two galvano mirrors in the optics are used f,cr scanning the pulsed excitation light spatially in the two dimensional object.

Time-correlated single photon counting (TCSPC) method _{[5] is} a typical method used in FLIM systems. A typical TCSPC system uses

a

photomultiplier tube _[6]

for detecting fluorescence emission and an expensive mechanical scanning mir- ror and optical systems are necessary for two-dimensional imaging, resulting in a

Chapter

^1.

lntrcduction

bulky and expensive system.

lnstead of FLIM systems using the photomultiplier tube, semiconductor FLIM systems such as time-resolved CMOS imagers have been paid much ^attention to implementing a compact and low-cost FLIM system. Single photon avalanche diodes (SPADs) are known as devices for time-resolved lifetime measurement _[7].

ln SPADs, when a p-n junction _biased above breakdotitrn voltage absorbs

a

^pho- ton, a large current is generated and then rapidly quenched by a load resistiance, causing an electric ^pulse per photon

[8,9]. A

SPAD-based time-resolved imager consists of an SPAD detector anay with sensing electronics in each pixel,

time{o-

digital converters (TDCs), digitral integrators to intensify the signals and readout

electronics.

For high photon counting rate,

a

large number of TDCs and digital integrators are necessary. These features make the SPAD-based time-resolved imagers complicated and limit

the

spatial resolution.

A

differential ^pixel circuitry with an active reset technique using standard CMOS photodiode is ^proposed

for

time-resolved fluorescence detection [4]; ^however, the minimum light level is lim- ited by the large circuit noise of

l80e-.

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Figure

1.1:

Comparison of

cunent

study fur time-resolved fluorescence ^lifutime imaging among companies and universities

Recent studies for the time-resolved fluorescence

lifttime

measurements based

on ^pulse

lif,atime measurements

are

represented

clearly in Figure

^1.1

,

^which

shows

time

resolution

of the

order

of

picosecond

is the

most basic necessary

Chapter

1.

lntroduction

condition for the fluorescence lifetime measurement system by company

or

uni- versity

or

even any other

group.

lnterestingly,

the

main difference between the systems

by

companies _[10, 11]

and

universities

[1-4]

(included institute) is the pixel

size. lt

may show

that

supporting

visual

information is

one

of

the

current claims postulated fur commercially available fluorescence

libtime

measurement

system.

On the other hands, even

the

pixel size

of

university systems is vastly insufficient compared with company's work, the frame speed is obviously

hster

than company's

work.

lt may show that real time fluorescence lifetime image pro- cessing

is the

near future trend

of

fluorescence

lifttime

measurement system.

The final goal of this

work

is

a

low noise real-time CMOS image sensor

br

the time-resolved FLIM with sub-nanosecond time resolution.

ln

video

imaging devices, the time resolution which is

about

10 ms is deter- mined by frame rate. ln high frame rate imaging devices for special scientific mea- surement, time resolution is from 100 ns

to

1ps. However, in the case of imaging object such as same repeated phenomenon, by synchronizing the trigger signal of the repeated light source which causes the phenomenon and repeated signal accumulation in the imager, time resolution of less than 1 ns can be achieved.

lf

the detection of the pixel is synchronized with the light source, such kind of pixel _is usually called lock-in pixel. Yoon et al. _[5] from our laboratory proposed a CMOS time-resolved imager using two-stage charge transfer technique in pinned diode

for the

measurement

of

fluorescence

lifttime. ln the

previous structure, using

a fully

depleted pinned photo-diode, fluorescence lifetime

of

nano-second time scales has been measured. Because of the simple structure, a high spatial reso- lution fluorescence lifetime imager can be realized. The time resolution of 160ps has been achieved in the liEtime measurements. However, the implemented fluo- rescent lifetime imager has a problem of the pixel-to-pixel variation of sensitivity at very low light level. To address this ^problem, this paper presents _a time+esolved CMOS image sensor with a draining only modulation (DOM) pixel structure. The draining only modulation (DOM) structure [1] removes the transfer gate between

the

pinned photo-diode (PPD) and

the

pinned storage diode ^(PSD). This allows us

to

realize

a

barrier-less charge transfer between

the

PPD

and

PSD, leading

Chapter

1.

lntrcduction

to

high sensitivity of weak fluorescent signals

with

high time resolution. Using a monotonic positive lateral elec'tric field, high-speed charge transfer from the PPD to PSD in the time scales of nano-second is possible [18,19]. ^{The time windowing} is done by draining the charges with a draining gate (TD) only, which is attached beside

the canier

^path

from the

PPD

to

PSD.

A

256

x

256 pixel time-resolved CMOS image sensor chip has been implemented for the ^proof of concept of the DOM pixel.

Thesis organization

This work is subdivided into six chapters.

Chapter 2 gives a short overview of fluorescence libtime measurements meth- ods

with

detailed concepts

of

fluorescence

libtime. As

mentioned above, this chapter roughly compares 'phase and modulation measurements in the frequency domain' and 'pulse lifetime measurements in the time

domain'.

ln addition, two techniques

of 'pulse

lifetime measurements',

such as

'pulse sampling method'

and

'single photon counting method',

are also described. A

short overview

of

modern analytical needs and techniques fur fluorescence lifetime measurements is followed. Through the comparison

with

modern analytical needs and modern techniques, the goal of this work is represented.

Chapter 3 gives the method of this

work

how

to

^realize the fluorescence life- time imaging using time resolved CMOS image sensor with Draining-only modu- lation techniques. Firstly, the imager architecture for time-resolved liEtime mea- surement explained. After the short overview of pinned diode structure, the con- cept

and

principle of the

drainingonly

modulation technique which

is

^proposed

to

realize

the

^real-time fluorescence

li€time

measurement based on CMOS ^im-

age

sensor

with fast

sivitching operation

are described. ln a

standard ^pinned photo-diode CMOS image sensor technology,

the

attempt

of

different impurity concentrations on same layer

is

not available for

the

device

design.

^Therefore, the pixel optimization for the twc.stage charge transfur technique is done by ma- nipulating the size of parameters in the ^pixel. The procedure of pixel optimization is described with simulation results.

Chapter

^1.

lntroduction

Chapter

4

describes

the

application

of

time-resolved

CMOS

image sensor with draining-only modulation pixels. For fluorescence

libtime

measurement and image display,

an

user-friendly delay timing generator

with

high

time

^precision and

a

low noise readout circuitry have been introduced

to

implement

a

CMOS FLIM sensor having 256(Row)

x

256(Column)

pixels. The

delay time generator can resolve the decaying of fluorescence with Sps time resolution. A double-stage

noise

canceller

with high

readout

gain and

correlated double sampling (CDS) operation is used for the low noise readout circuitry of the CMOS FLIM sensor.

The

result

of

photo-conversion characteristic shows

the

linearity, sensitivity, for detecting weak fluorescent

signal.

Lifetimes

of

four kinds

of

fluorophores were successfully

measured.

Fluorescence

from

cells under microscope is observed by the sensor, and its related lifetime is successfully measured.

Chapter 5 describes the improvement

forthe

proposed imager. To obtain more accurate lifietime result, c,onvolution calculation was developed, and

the

linearity

of

deconvoluted lifetime

is discussed.

Even

the CMOS

FLIM sensor

has

suc- cessful results of lifetime measurements, dark electrons generated by a scooping effect of the draining gate ^(TD) clocking cause offset to the signal detection and reduces the SNR, causing it not qualified

br

more accurate lifetime measurement.

lmprovement method of dark offset of the prototype image sensor was proposed, and the new structure of drained-only modulation pixel was designed and imple- mented

in a

sensor chip,

to

reduce

the dark offset.

Simulated

and

^measured results demonstrate the availability of the improvements.

Finally, this thesis finishes with a brief summary and conclusions.

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Ghapter ²

Fluorescence lifetime measurement methods

2.1 Overviewof fluorescence lifetime measurements 2.1.1 ^Goncept of fluorescence lifetime

The fluorophore excitation and emission was first described by Jablonski. Fig- ure 2.1 is a simplified Jabolonski diagram, considering only the singlet electronic state

(S).

Firstly, the fluorescent substance

which

is called fluorophore absorbs the excitation photon energy hz6, and the electron is excited from ground state ⁵⁶ to higher energy state 52. Secondly, the electron relaxes to lower energy state 51,

this ^process is called internal conversion. Thirdly, the electron returns from lower state 51

to

ground state,96,

while

releasing energy

in

radiative fluorescent part

(hzr) and

non-radiative part,

which

have

the

decay rate

I

^and

^k",

respectively.

The radiative decay rate

I

indicates the fluorophore

species. The

non-radiative decay rate

k*

indicates fluorophore environment

[1].

The fluorescence ^quantum yield is the ratio of the number of photons emitted to the number absorbed. The rate constants

I

^and

k*

both depopulate

the

excited

state.

The fraction of flu- orophores that decay through emission,

and

hence

the

quantum yield, is ^given by

10

2.'1.

Overview of fluorescence lifutime measurements

^ｌ

in r

8y3Lm

｀ tT̲L

:Radiat陥 :Omi38:On

iヽ

^卜P ウ /

FluoraBccnce Phocphorrrcanco

Figure

2.1:

Simplified Jablonski Diagram to illustrate energy state of electron ex- citation and emission

彙■●●ゝｈｒＯｒｕ

9=「 _+塩

r

(2.1)

Fluorescence liEtime which is the average time a fluorophore stays in the excita- tion state, is defined as

「 十硫r (22)

Electrons in the Sl state can also undergO a spin conversion to the nrst triplet electЮnic state Tl Emission from Tl is termed phosphorescence with energy of hゅ,and is genera‖ y shifted to longer wavelengths re:ative to the luorescence Conversion of Sl to Tlis ca‖ ed intersystem cЮ ssing ln this research!we obtain luorescent‖fetirne to distinguish difFerent species ofluoЮphores,and to observe the interaction of rnolecu!e with luorescent pЮ

be

Energy difFerence beh″ een gЮund state So and higher state S2 0fthe luo‐

Юphore is too large fbrthermal population;therefore,we use light and not heatto induce luorescence Figure 2 1 shows the luoЮ phore lrstly absorbs the shorter wavelength‖ght,such as ultraviolet‖ght pulse,and then emits longer wavelength luorescence ln luorescence experiment we do not observe number of excited molecules,but rather luorescence intensity A(o,whiCh iS propOrJonal to pOp‐

ulaJon of luoЮ phores n(0,in the excited state According to the physicallaw 90Verning the process of radiaJon in natureithe rate of change in intendじ

ギツ

^,

2,1.

Overview

of

fluorescence lifetime measurements

¹²

as

is inversely proportional to intensity, A(t):

Ψ ^{=一 :Jの}

^(2.3)

By deriving Equation 2.3, the single exponential decay of intensity is expressed

用 ^=れ u― ゎ

⁽²⁴⁾

where, -4s is the initial intensity of fluorescence emission. Equation 2.4 shows

after the

exciting light pulse,

the

fluorescent

light

pulse fullows

an

exponential decay. The average time a fluorophore remains in the excited

state,

is calculated by Equation(2.5) reveals

the

average time

a

fluorophore remains in the excited state is equal to the

libtime r,

which is typically near 10-8 second _[2].

τ _=争 轟事 ^=牛 環鴇多 ^=ギ 〒 「

⁽²⁵⁾

Fluoreacgnca omlaalon

2.1.2 Comparison of lifetime measurements in frequency do- main and time domain

Excltslon by llght pulso Excltalon by

slnusoldally

Fluolaacence

modulated

llght

^embsion

#ffi ^-:0 * _,ifi"

fluorophore

Tlme sample

^Tlmo

姉 =語

L ttli L

Tlme   Samp:●      T:me

O  τ_l

(a) Frequency domain lifetime measurements (b)Tlme domaln llletlme measurcments

Figure

2.2:

General fluorescence liEtime measurements. (a) Frequency domain lifetime measurement and (b) Time domain lifiatime measurements.

There are two general methods

to

measure fluorescence

lifetime.

ln the fre- quency domain method, as shown in Figure 2.2, a fluorophore sample is excited

Timo

む0 C

僣

2.1.

Overview of fluorescence lifutime measurements

with light in which the intensity is modulated sinusoidally. The fluorescence emis- sion

is

modulated at

the

same circular frequency ^(u,,) as the excitation because the emission is a forced response

to

the

excitation.

^However, the fluorescence emission has

a

delay

of

^phase

(Ad;

phase angle)

and a

reduction

of

relative amplitude modulation

(m=\Esf ElFs;

demodulation

factor).

Through both mea- suring

A/ ^{and m,}

phase and modulation lifetimes (16 and

r^,

respectively) are obtained as

(26) (27) The phase and modulation lifetimes are generally equal for a singular molecule having single exponential decay

[3].

Fluorescence lifetime imaging ^(FLIM) in fre- quency domain can be achieved by

the

modulated image intensifiers and wide- field microscopes or by modulating single channel deteclors used in laser scan- ning microscopes

[4].

^On

^the

other hand, time domain lifetime measurements use pulsed excitation

fur

exciting

a

fluorophore sample

and

record

the

fluores- cence decay

directly. As

^shourn

in

Figure 2.2(b),

the

fluorescence lifetime ^(r1) is defined as the time

when

intensity decay becomes Anf e where,46 is

the

ini-

tial

intensity

of the

fluorescence

decay.

FLIM in time domain

can be

^achieved by gated image intensifiers, by directly gated CCDs, by counting

the

^{photons in} several parallel time gates,

or

by time-conelated photon counting

[5].

^Because

the time domain and the frequency domain are theoretically equivalent, it is very hard to judge _simply which domain is superior for achieving FLIM. Here, there is a good report to deserve consideration ^for the

comparison. ln

_[6], while in their practical implementation for the fluorescence

libtime

measurement the time do- main measurement provides a better signal-to-noise ratio (SNR) for low-intensity images, the frequency domain measurement is

hster and

provides less distor- tion for bright

samples.

Moreover,

a

remarkable development of CMOS ^process in recent can help

to

integrate various functions on a same chip, that makes in- creasing total system speed and reducing distortion by

crosstalk.

These reasons show obviously why

cunent

studies including this work are focused on the time domain lifetime measurements.

13

%=ω

 ^ltan△

^φ

^,

… ‐ 77

2.1,

Overview of fluorescence lifetime measurements

2.1.3 Time-resolved fluorescence Iifetime measurement in time domain

Single photon counting method

14

Excitaion

by

Fluorescence lifetlme

lightpulse

detection

lnputpulse

B-l--l ^oo _Il Ar -,to _|x--E

outputputse

V

4 ^Avalanche

lluorophore ii

^dlod'

sampre Monitoringclock

(clock 3p€ed;Mck)

lnputpulse(l.r) Output pulse(l.t)

lnputpuls.(znd) Output puls.(2nd)

lnputpuls€(3d) Output puli.(3d)

lnputpuls€(Nrh) Outputpulse(Nh)

Figure 2.3: Simple principle of single photon counting method.

Figure 2.3 shows a simple principle of the single photon counting method. The decaying measurement by the single ^photon counting method is started with the pulse input fur exciting

a

fluorophore

sample.

The excitation light is weakened

to count

^photon

one at a time. The time

interval between

the pulse

input and

the

pulse outputs detected

with

photomultiplier

tubes

(PMTs)

or single

^photon avalanche photodiodes (SPADs) is measured with a

timeto-amplitude

converter

Time

*Detected time(TD)

=(#olclks)x ^1/Mck

Detected time(TD)

2.1.

Overview of fluorescence lifetime measurements

(TAC) or a time-to-digital converter (TDC). A periodical pulse input is used for de- tecting a large number of photons and measuring a time-histogram of the fluores- cence emission. This time-histogram represents the time-resolved decay, which shows the lifetime of the fluorescence emission because fluorescence emission is

a

random event and its lifetime is an averaged value.

At

^present the electron- ics are not fast enough to measure multiple photons at each excitation when the lifetimes

are

in

the

nanosecond

range.

To avoid pileup effect in whieh multiple photons are excited at each excitation, excitation frequency is limited under 5%

of

photon counting

rate.

This limits the dynamic range of the fluorescence ^lifetime measurements.

Pulse

sampling method

Figure 2.4 shows

a

simple principle of

the

pulse sampling

method.

The ob- jective of the pulse sampling method is the same as the single photon counting method, which is

to

measure

the

time-resolved

decay. And the

decaying mea- surement is also started with

the

^pulse input for exciting

a fuorophore

^sample- However,

the

fluorescence

emission is

sampled sequentially

by

moving time- window having different delay

times. After a

large number

of

repetitive ^pulses, the time-resolved decay has been sampled for

a

number of delay times and the decay can be analyzed.

Time domain lifetime measurement method

ⁱⁿ

this research

When a very short pulse (typically less than 100ps) excitation light irradiates

a

specimen which carries fluorescent probes,

the

^probes

will

emit fluorescence

with

rapid exponential decaying, typically nano-second

to

several tens

of

nano- seconds, as shown in Figure

2.5 (a).

When the fluorescence intensity becomes

l/e

of the initial intensity A0 at

t : r,

the time

r

is defined as

the libtime

^of the

fluorescence. The

fluorescence intensity

A(t) is

proportional

to

population

of

fluorophores in the excited

state.

The fluorescence decaying is detected in ^the system shown in the block diagram

of

Figure 2.5

(b).

Fluorescence incidents on 15

2.1.

Overview

of

fluorescence lifetime measurements

¹⁶

Excltalon by light pulse

l!E !

Pulsein

Fluorescence llfietlme detection

aD

-* ⁰ -,to'JJ*uon"o"or,

lluorophore

vtl !

⁺

sample

ヽ●Ｅ●一Ｃ¨

Pulsein Gatlng(18t)

Pulseln Gating(2nd)

Pulseln Gatlng(3rd)

Pulseln Gatlng(Nth)

Figure 2.4: Principle of pulse sampling method,

the photo detector and generates photo electrons. ldeally, the electron generation in

the

photo detector follows the fluorescence decay.

The

number of ^generated electrons per unit time can be expressed as

ち●ｏｏ０＞

n(t) : no."rpet

i'o)

^(2.8)

for

t >

0, where n6 is the initial electron number per unit time, to the delay of photo electron generation and

r"

the apparent or measured lifetime.

ln

order

to

measure

the

fluorescence lifiatime,

a part of

fluorescence signal electrons is detected and collected during the time windows. The detection time

Tlme TIme

2.1.

Overview

of

fluorescence lifetime measurements

¹⁷

驀＋

ー

ｍ ｍ

∝  ハ

Ｓ

Fluorescence lntensily decay a(t)= Aoexp(-! )

80ps'

Excitation light ,/' FluorqscencePhoto+lectronFlux

n(t)=ro.rpG

t;*n

)

VDrah

(1●1く tくtdl+T)

VDram (lυ く^tくtd2+T)

Collecled

El●ctrons iogoN(td)

tor+

T

_{1o,+ T}

Figure 2.5: Collection of fluorescence signal electrons

window is set by a gate voltage Vo.ui" at the charge draining gate of photodiode.

The

detection

time

windows

in

Figure

2.5 are

indicated

by the

duration when

Vo.,:, is

low

level.

Generated photo electrons are accumulated by

an

electron collector every period

T

of the time window. The starting point of time window is delayed by a delay generator and the electrons are collected from the time of ta to td

+ T.

lf t6 is assumed

to

be zero for simplicity,

the

number of accumulated electrons N(rd) by the charge collector is expressed as

ｉｍｅ 詢 ｔｄ

Ｄ Ｔ

２ 

＾． り

卜は ^T→ 撻

Ercitarion Light

嘲≪認 に

{糀 ,uり 難 同

⁽²⁹⁾

2,2.

Relationship between potential barrier and current through barrier

¹⁸

if T

is chosen large enough so that the

term

of

exp(-(ta + T)/(2.))

is negli-

gible.

As the fluorescence from an actual biological specimen is very weak, the average number of collected photo-electrons for each excitation light is often less than

one.

To intensify the signal,

the

excitation

is

repeated

br

many times and the photo-electrons are repeatedly collected by the same window. The resulting

total

number

of

photo-electrons by

the

repeated process also follows Equation (2.9). The dependency of the collected photon electrons during the time window as a function of td is illustrated in Figure 2.5 (c), together with fluorescence photo electrons and time

window. The

number of collected electrons

first

decays ex- ponentially, followed by a long low level tail which is caused by noise fluctuation.

Fluorescence lifetime is obtained from the gradient of the exponentially decaying region of the number of collected electrons,

dUnN(td))

dta (2.1o)

2.2 Relationship between potential _{barrier and cur-} rent through barrier

1

dimensional potential distribution of barrier

Current in n type semiconductor includes drift current ^(Ja,irt ₎ and diffusion cur- rent J66o"1o,,. Hence,

Jn

:

Ja,t,!t

- ^Jai

^lo"ion

Drift velosity za,is is given _by

(2.11)

ud,ri.lt:

ptu'E: tt"'Yd

Drift current J6;6 is given by

(2.12)

Jaafi

: _Q.

udrnfi

:

_Q.

n. F". ^Vd

Diffusion flux is given _by

(2.13)

F": _-D"'Vn

^(2.14)

Ta

2.2.

Relationship between potential barrier and current through barrier

¹⁹

Diffusion current is given by

Jai1u"t-,: q. Fn: -q. D".Vn

Therefure, total current is given by

(2.15)

Jn: Ja,fil Ja$f."t-": e.n. ltn.Vd- q.Dn.Yn

^(2.16)

Potential of intrinsic level is given by

o: -8, 'q ^(2.17)

Fermi potential is given by

,b: 'q -E'n ^(2.18)

Goncentration of n-type semiconductor is given by

,:no.opl#@-,Dl e.$)

Diffusivity of electron is given _by

D":

KT

i.p^

^(2.201

Vector-valued differential form of concentration is given _by

"" : ":'"ffir--^r"#'or-'r'

(2'21) Total cunent is given by

J* : _s. nqnVd-

_o.

". #. (vd-vrD.ffu"

:

q.

npn. Vd -

^q.

^n.

^p,".

^(Vd - ^Vt!)

--q.n.p".VlL,

^(2.22)

ln the case of

one-dimensional, current

is

continuous

and

concentration

of

electron is invariable along time _[7].

▽ψ =#

{2.23)

2.2.Relationship between potential barier and current through barrier 20

Pos:tion Position

poten‖ al φ ^potential d

Figure

2.6:

Potential distribution using broken line approximation (80, (E1 and E3

are absolute values of each elechical field). (a) Normal barrier; (b) Barrier around storage diode.

ln area where no current is generated, Jn is contiant. Equation

2.22

can be written as f,cllows,

﹇●ン●コ

¨ 暉

︐ ＥＯ■ＯＬ

︐ ¨ ０コ一●ｇＬ●●目Ｏ

(a)

/」

^{L・ e―}

券φ

_Jα

 = /9  _μπ η

̀ 

▽ψθ

^静

ψα″

=/9  μ η 物 併 ^Cホ ψ

dZ

   =/9.μ η ・ 物 ・

^{e み}

ψ

dψ

=9  μ π ・ し← 等

^{)・ e ttψ tt} 

θ

=―

^ん

T 

_μη

 Q c+ψ

 ^tt 0

r3xo

―

El(

―″

_{o)+φo,″o≦}

″≦

⁰¹

φ

^{l, ωl≦ ≦″2}

fu(c-r2) ⁺ fi,

⁰²

1t 1a,

φ

^3,

0saa

As shown in Figure 2.6 (a), the potential distribution of barrier ficllows

φ

^O,

(224)

(2.25)

and Equation 2.24 can be solved in the following three conditions:

Xl  X2 X̀ X2

2.2.

Relationship between potential barrier and current through barrier

²¹

(1) When:16

( _x (

_{x1, the current is constant,}

/Jn e― 滞φ

d″

 = /島

^{.e 静}

^φ

 ^dφ

  」 菫

₍₂₂₆₎

hence,

When

x: xr,

(2)When Xl

=幕 寺 ← 等

^)イ

ル φ

=島 告・ λ

^{Tg・ C 静}

φ

From Equation 2.24 and Equation 2 26,

=霧 _{￢ 乳}

λト ル

J「

^{静ψ― 励 句}

=等 _<「

力φ一 ご 的

Ii

島 =―

ltn. u

^.

^Er

^.

^{q(e #+} - _"- ^#h)

e ttφ ̲e―力術

"#@r'!t) : - ^{島 「} _Fn' ^― _ni' ^C券 _Et

^{(φl ・}_' ^o河

^a

^s#@t-'to)

Q

島・ ^C#φ

^d″

 =  ―λ

^Tμn・

π _{,c 静} ψ

 _tt 

θ

_l洗 (2.29)

島 =―

̲         =e f2・

^ψ

l̲e静

仇

―

¨

=θ^静(φl―ψ

l)̲e券

(φl―ψo)

(2.27)

(2.28)

(2.30)

(231)

(2.32)

(233)

(234)

(235)

(2.36)

(2.37)

(238)

≦

^{X≦ X2,φ}

=φ

l iS COnstant,

/43・ ^e―

+φ_d″

 =  _ム

 e 静

φ ・″

: J^' s-#h ',

2.2.

Relationship between potential barrier and current through bawier

22 From Equation 2.22 and Equation 2.32,

ガ島 計φ 伽=抑 rに 静 ψ _+q挽  2η

= 

島 ^{c 券}φ^l・ ″菫

1         (240)

hence,

―λ7・ μη

 

^η.(θ 券ψ―C―券ψ

l)=島

.θ 滞φl(″ ―″

1)     (2.41) 島 =― _魃 ^{場 ψ}   _σ滲り

φl(α 一 ″₁₎

=       00

From Equalion 2 42,

cポ← ω   θ 急に の =場   00

(3)When X21≦ X≦ ^X3,e燈Ct口c lett E3=撃 ,dm‖ arto Equalon 2 32,

島 =‑      2竹

When x=x2,Sim‖

arto EquaJon 2 36,

計 ゆ初 =饉 ^脚 _"の   20

Using Equation 2 43,Equation 2 36‐ Equation 2.45 obtains,

cポ仇■0̲θ が "の =覇

鳥 卜生 二

審 竺 里 一生三

餐 竺 2ト

θ静

^(a―

力 )̲e芸

(●

― ψ 3)      (246) 鼎 =「 _{れ 卜些 宰} ^霊 _く ^:[ユ

l十

θ券^(φ

l力 )̲e静

^(φl ψ

3)       (247)

Therefore,

島 ⁼

⁽²⁴⁸⁾

When  ψ ^o≪ 化

^,仇

一φ l≫ 号

^,φ

^{3 φl≫} ギ

,the concentra‖ on of dectЮnsin the area of x≦ xO is nO.Assuming 

φ

O〜

ψ

^o,

島 〜  N    _田

2.2.

Relationship between potential barrier

and

current through barrier

²³

1

dimensiona! potential distribution of barrier around storage diode

As shown in

Figure

2.6 (b), the

potential distribution

of banier

around the storage diode follows

φ

(・

)=

d", t 3r"

Es(r-r")+$", r"ar3ro

-Et(r-ro)*do, roar!rr

(2.50)

φ

^l,

rtSr3xz

E3(″ ″_2)十

φ l,  ^″

2≦

″≦″

3

佑^,

lDs3x

Assuming floating capacitanG€ Cso exists at x0, $s and Sl vary along time.

lnitial

curent

J6 is

(251)

s

is

cross-section

area of

current, and d is distance that charges travel.

, ud,ift.t.S.no.q

tn: T : _{lln. b.} J 'rh ^.q

lnitial electric field is given by

E= 

^ツT

″2  πl

λ

T

9 

^″

2

1

(252)

(253)

(255)

JO=た Tμ

_・ ・η

O S

(254) 12-fil

when

E1

,, + ^E+

^and E3 >>

+ -,*'

^{Equation 2.49} can be rewritten as

几 =考 _争 =CsD等 _{「 〜}

^1生

^」 _篭ご」 ^竺型生

^N JOセ

^券

^0「

^●

^ol

んT

Also assume capacitance

Cr

exists between xo ond

xr,

and capacitance ^C2 exists between x1 olld x3,

△ 01=0△ ^佑

⁽²⁵⁶⁾

2.2.

Relationship between potential barrier

and

current through banier

²⁴

And,

△ 0=(α  tt C)△ φ

^l

△ 0=△ ⁰¹

λ Tの _D(1+a)

9.ι

扮 ^+」 四

(257)

(2.58)

(259)

(260)

(2.61)

(262)

(2.63)

(264)

(265)

(266)

that is

△φ

l=乱

△φ。

From Equalon 2.55,

θ

sD e券

^{(φo φl)dφ}

O=島

^.読

From Equalon 2.59

d(φo―φ

l)=dφ

o一^dφ

l=dφ

o―

乱 ^dあ

=乱

αφ0

GD e静 ^。∝φ l)∵

 

《φ

^O―

φl)=島

^dι

五 懲 ^{)の D謡} 。 ¨ ω ≒ヂ《 φ

^O―

ω ^=10島 効

の D⊆ _寿 2等

_C滞

^°

^Oφ

^。

_1雛

_{舞 =0=島 ・}

t憶=0

When t=0,φ 。=φ

l,SO

ι  = (bD  _トホ●°

^{φll― ll(え +6ち}

^笙

=  ^洗

=鱚 _{∵ 十榊¨―} 」

and,

φ

^o―

φ ^l=lFれ

^[肩

義讐ギ響 ^t,十 」

=等 れ 〔

wheЮ ,Cl=̀3,C2=̀翡 :△Vl=El.(xl Xo),and△ V2=E3(X3 Xl).

Assume El=E3,then t=会 普 ^=等 瑞

傷 ― 仇 ^=lF・ ltt       rll tt ll

_(2.68)

2.3.

Estimation on optical system 25

2.3 Estimation on optical system

An estimation [8] ^of the intensity of the emitted light from the fluorescence dye spots can be derived from Beer-Lambert's law given by

T=1=10‑dM

where

T

is the transmissivity of light traveling through a medium.

lt

is defined as the ratio of

the

intensities of incident excitation light ¹⁶ to the transmitted excita- tion light

I.

^e denotes the absorption coefiicient ^of the medium,

I

is the distance traveled through the medium, and

M

is its molar concentration in moles per unit volume. ln the proposed setup, where planar fluorophore spots are deposited on the surfiace of a glass slide, the medium length I is negligible.

The fraction

of

excitration light intensity absorbed by

the

planar spot

can

be expressed as

4=1‑T=1‑10(S

(2.70)

where S

:

I

x M

is the concentration of fluorophores on the ^planar spot in moles per unit area.

The fluorophore

emib

^photons

at a

longer wavelength

with

an efficiency

of

r;noo. The amount of ^photons

Nrr

incident on the photodetector can be calculated by

(269)

(2.71)

(272)

where 461o()"-) is the filter

transmission

at the

fluorescence emission ^wave- length,

4*

^is

^the

collection efficiency

of the

non-collimated light from

the

fluo- rescing spot, and Epr is the photon energy of the excitration, given by

月 ρλ=モ

‰ ^=Ъ ・ η μ セ ^rp師

^)η

″ ι 。 ス ・ 豊

雉 ≪

¹

where h is

planck's constant,

c is the

speed

of light, and .\o ^{is the}

^excitation

wavelength.

^Equation 2.72 assumes that the amount of excitation ^reaching the photodetector is negligible compared to the

emission.

The filter requirement for this assumption to be valid is

(2.73)

2.4.

Estimation

on

time resolution 26

The photodetector current can be expressed as

Ipo:npo.rlfi.u,Npn

(274)

where _?pD is the photocurrent collection efficiency of the photodetector, and ₄₆₁ is the fill factor

ofthe

pixel. The voltage developed on the photodetector at the end of the integration time can be expressed as

where Tint is the integration tirne of the photodiOde,and CPD iS the photodiOde capac:tance

yP,==貯

2.4 Estimation on time resolution

Lifigtime

can be

calculated

using

number

of

photo charges detected different delay time of time windows _141,

Tr

and 72.

Tz

-Tt ^LTp - -w ^- I;E*,

where, number of photo charges N1 and

N,

are presented as,

川

2=

^0(T2)

9

∂τ

∂Ⅳ_l

△■2

『η

^(鍔

】

²

△T12

『π

(捲

】

²

銚 △T12

(2.75)

at mO

(276)

(277)

(2.78)

(279)

(280)

鋼 一 ９

蝸

∂

7     1

5△

〒 再 ^面 可 顕

1  1     △

T12

再 °

再 ^{= 『} π持】

²

１

蝸一 ^r2

一

針 一

処 童← 鋳 ^)=デ 澄争 ^.島 =洗

⁽²⁸¹⁾

2.4.

Estimation

on

time resolution 27

The deviation fbr presenting accuracy is

ゲ ^=(轟

_5ア

σ

l・

2+(品 ア ■ ^+(乱 ルσ L

七 脳 ^{2Httμ tt・} 洗 跳

Neglecting the read noise, the fluctuation of

Nr

and Ir2 is determined by shot noise

41=Ⅳ

^l

42=乃

Number of charges can be ca!culated by

(2.84)

(285)

手 ^=(箭 ア ^+(豊 ア轟 ^+喘 ア

=(各 甍 号 ^)2+(品 ア 喘十 寺

θ η (:)酢 =1 7  ^θ η (:】

_1+△^T

θ η (:)洸 =卜 ^{7  θ} η (:】

1+△

T

72

鳩

(282)

(283)

(2.86)

(287)

７           ７

△            

△

＋            

＋

ｆ ｆ

一一         既

馬

島

一既

一ア

eaズ

・

^+△

r)+7 eη (子

⁾

―

^r eqズ

ー等 )+7  ^θ η (手

⁾

=̀傾 雫 ^)=θ 颯等 ^)2町

両

=可

・θη(―埋

￨)       289)

△T12 iS the difFerence between h″ o delay tirno of tirne面ndows lts deviation is caused by the itter k Ofthe delay generaton

ん =(箭 ソ

⁽²⁹⁰⁾

2.4.

Estimation

on

time resolution 28

Herel we ignore this tem and assume  λ==o Set A= ^△T12

Then,

o2 IIt.1

u:f:k* _Ar' ^(r, *n,'erpA):k+ Ar.Nt.fl+expA)

The minimum of A can be calculated at

島 ^=― 島 一 留 +轟 判

(2.91)

(292)

(293) Hence,

A. ecpA:2(1 +

erpA) (294)

Set a function fto be

f : A.

ecpA

-

^2(1.

⁺ expA)

^(2.95)

Equation 2.95

can

be calculated using Newton Method

as

shown

in

Figure 2.7 . The procedures are as follows:

(1) Find the minimum value of function

t

^{which is Ao.}

(2) Choose another value

Ar

to be different from A6, and plot the tangent line G(A1) of the function

f

at

Ar.

The crossing point of the tangent line G(A1) and A-axis is A2.

(3)

Find

the

crossing point

of the

tangent

line

G(A2)

and the A-axis at

A3.

Compared with Az, A3 is nearer to the solution

A*

of the function

I

^{which is the}

crossing point of the function f and the A-axis,

(4) Then find the next crossing point at A4. A4 is nearer to

A*

than A3.

The

more

the

above procedure repeats,

the

more

the

crossing point

A"

be- comes nearer to the solution A*.

The gradient of Equation 2.95 can be calculated as

∫ ′

=(И

‑1)eapA

_(2.96)

2.4.

Estimation

on

time resolution 29

∠´ )‐ ^{´ ´} _〜

when,

Figure 2.7'. lllustration of Newton Method fior Solving Function

θ

_(■

o)=∫ ′

(■

o)=(A‑1)・

^Cηp五

=0

→ ス

=1

G′

(4ol=∫

^″

(A=五 ^C"メ =̀〜 27>0     (299)

So A=l is the minimum vaiue offunction i Setinlial value ofス to beス

1=11>

0,C(■.)iS the gradient of function f at九 ^.

(297) (298)

(2100) (2101)

愕 =α _句

→ 五

2= 酬 +■ 1=16757