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Theses
2004
Avalanche photodiodes arrays Avalanche photodiodes arrays
Daniel Ma
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Avalanche Photodiodes Arrays
By
Daniel Ma
B.S. College of Engineering, Rochester Institute of Technology (1998)
A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science
in the Chester F. Carlson Center for Imaging Science of the College of Science Rochester Institute of Technology
August 2004
Signature of the Author __ D_a_n_i e_1 _M_a _______ _ Harvey E. Rhody .y/h~~s-
) Accepted by
Coordinator, M.S. Degree Program Date
CHESTERF.CARLSON CENTER FOR IMAGING SCIENCE
COLLEGE OF SCIENCE ROCHESTER INSTITUTE OF TECHNOLOGY
ROCHESTER, NEW YORK
CERTIFICATE OF APPROVAL
M.S. DEGREE THESIS
The M.S. Degree Thesis of Daniel Ma has been examined and approved by the thesis committee as satisfactory for the
thesis requirement for the Master of Science degree
Zoran Ninkov Dr. Zoran Ninkov, Thesis Advisor
Lynn Fuller Dr. Lynn Fuller
Jonathan S. Arney Dr. Jon Arney
Date
ii
THESIS RELEASE PERMISSION
ROCHESTER INSTITUTE OF TECHNOLOGY
COLLEGE OF SCIENCE
CHESTER F. CARLSON
CENTER FOR IMAGING SCIENCE
Title of Thesis: Avalanche Photodiode Arrays
I, Daniel Ma, hereby grant permission to theWallace Memorial Library ofR.I.T. to reproduce my thesis in whole or in part. Any reproduction will not
be for commercial use or profit.
Avalanche Photodiode Arrays
By
Daniel Ma
Submitted to the Chester F. Carlson Center for ImagingScience College of Science in partial fulfillment of the
requirements for the Master of Science Degree at the
Rochester Institute of Technology
Abstract
This research investigates the performance of avalanche photodiode (APD) arrays that
were designed, fabricated, and tested at Rochester Institute of Technology. The APD
devices, based on the"reach-through"
structure, were designed with various array sizes
and dimensions in order to investigate the optimal design. An explanation of the
operating principle and device theory is presented, along with the testing methods used
in determining the performance of the APD arrays. The results and the reasons behind
the performance of the devices are discussed. Suggestions and solutions to problems
found are presented as a guide for any future research.
IV
Table of Contents
1. Introduction 1
1.1. Scope ofWork / Objectives 1
1.2. APD History and Background 1
1 .2.1 Advantages of APDs Compared to Other Detectors 3
1 .3. Thesis Background 5
2. Device Theory and Design 6
2.1 . Device Structure and Operating Principles 6
2.1.1 Depletion Region Concept 7
2.1.2 Absorption Region 12
2.1.2.1 Photon Absorption / Electron-Hole Generation 14
2.1.3 Multiplication Region / P-N Junction 19
2.1.3.1 Avalanche Mechanism 23
2.1.4 Guard Ring 28
2.2. Supporting Electronics 30
2.2.1 Quenching Circuit 30
2.2.2 Transimpedance Amplifier 31
2.3. Problems with Arrays of APDs 33
2.3.1 Cross-Talk 33
2.3.2 Non-Uniformity 34
2.3.3 Pixel Latching 35
3. Implementation 36
3.1. Design 36
3.1.1 Wafer Variations 36
3.1.2 Die Layout 37
3.1.3 Device Cross-Section 40
3.2. Calculations 41
3.2.1 Oxide Thickness 42
3.2.2 Ion Implant 43
3.2.3 Drive-In 44
3.3. Fabrication 46
3.4. Test Set-up 47
3.5. Deviation of Fabricated Devices from Ideal 49
4. Test Results 52
4.1. Figures of Merit 52
4.1.1 Breakdown Voltage 52
4.1.2 Dark Current 54
4.1.3 Gain 56
4.1.4 Responsitivity 57
4.1.5 Crosstalk Plot 58
4.2. Single APD Results and Comparison to Commercial Devices 59
4.2.1 l-V Curve 61
4.2.2 Breakdown Voltage 63
4.2.3 Dark Current 66
4.2.4 Gain 67
4.2.5 Spectral Response 70
4.2.6 Responsitivity 72
4.2.7 Noise Equivalent Power 73
4.3. APD Array Results 74
4.4. Problems of Non-Working Devices 77
4.4.1 No Signal 77
4.4.2 Uncontrolled Voltage Breakdown 79
4.4.3 Low responsitivity 80
4.4.4 Performance Uniformity 83
4.5. Solutions for Improvement 85
4.5.1 Lower Doping Levels / Correct P Layer Doping 85
4.5.2 Fabrication Control and Uniformity 86
5. Conclusion 87
6. Appendix 89
6.1. Oxide Thickness Calculation 89
VI
6.2. Ion Implant and Drive-In Calculation 90
6.3. Fabrication Steps 99
6.4. Third-Order Polynomial Fit Algorithm in Microsoft Visual Basic 6.0 102
6.5. Responsitivity to Quantum Efficiency Conversion Calculation 106
6.6. Depletion Width and Built-in Voltage Calculation 107
6.7. Photodiode Test Data 109
6.7.1 Raw l-V Graphs 109
6.7.2 Raw l-V Data 156
6.7.3 Figures of Merit Analysis of Selected Photodiodes 170
6.7.4 Raw Crosstalk Data 243
6.7.5 Crosstalk Analysis of Selected Photodiodes 256
7. Bibliography 259
VII
Table of Figures
Figure 1 .2.1 : Cross-Section of a PIN Photodiode 3
Figure 2.1.1: Cross-Section of a Reach-Through Avalanche Photodiode and
Corresponding Electric Field Strength 7
Figure 2.1 .2: Doping Profile of a P-N Step Junction 8
Figure 2.1 .3: Charge Density Profile of a P-N Step Junction 8
Figure 2.1 .4: Electric Field Profile of a P-N Step Junction 9
Figure 2.1.5: Layer Profile of a Reach-Through APD 11
Figure 2.1.6: Doping Profile of a Reach-Through APD 11
Figure 2.1.7: Charge Density Profile of a Reach-Through APD 11
Figure 2.1.8: Electric Field Profile of a Reach-Through APD 12
Figure 2.1.9: Carrier Mobilities as a Function of Dopant Concentration in Silicon [Pierret,
1996] 14
Figure 2.1.10: E-k Plots of Recombination of Direct and Indirect Semiconductor 15
Figure 2.1.1 1: Absorption Coefficient as a Function of Wavelength at 300K [Schroder,
1990] 17
Figure 2.1.12: Spectral Response of Silicon P-N Junction Photodiode [Pierret, 1996].... 18
Figure 2.1.13: Doping Profile of a P-N Junction 20
Figure 2.1 .14: Energy Band Diagram of a P-N Junction 21
Figure 2.1 .15: Electrostatic Potential of a P-N Junction 21
Figure 2.1 .16: Electric Field of a P-N Junction 22
Figure 2.1.17: Typical Diode l-V Curve 24
VIII
Figure 2.1.18: Breakdown Voltage Versus Nondegenerate-side Doping Concentration for
Ge, Si, and GaAs semiconductors [Pierret, 1996] 28
Figure 2.1.19: Exaggerated Detail of the Curvature Effect 29
Figure 2.1 .20: Curvature Effect - Implant and Diffusion Spread 29
Figure 2.2.1: Passive Quenching Circuit 31
Figure 2.2.2: Transimpedance Amplifier Circuit 32
Figure 2.2.3: Quench and Transimpedance Amplifier Circuit 33
Figure 2.3.1 : Photocurrent Output of a Diode 35
Figure 3.1.1: Die Layout 38
Figure 3.1 .2: Die Layout with Labeled Areas 39
Figure 3.1 .3: Cross-Section of a Reach-Through APD with Contacts 41
Figure 3.2.1 : Silicon Consumption From Oxide Growth 43
Figure 3.2.2: Ion Implant Range and Straggle - Longitudinal Axis [Cheung, 2003] 44
Figure 3.2.3: Ion Implant Drive-In 46
Figure 3.4.1: Test Set-Up Diagram 47
Figure 3.4.2: Test Set-Up Picture 48
Figure 3.5.1: Doping, Depletion, and Electric Field Diagram of a Standard APD 49
Figure 3.5.2: Doping, Depletion, and Electric Field Diagram of Fabricated Reach-Through
APD 51
Figure 4.1 .1 : Breakdown Voltage via Interpolation Method 53
Figure 4.1 .2: Breakdown Voltage via Threshold Method 54
Figure 4.1 .3: Defined Dark Current 55
Figure 4.1 .4: Theoretical Crosstalk Plots 58
Figure 4.2.1: Acceptable and Unacceptable APD Current-Voltage Curves 59
Figure 4.2.2: l-V Plot (W4 C7,3 D200,20,300,Y) 61
IX
Figure 4.2.3: l-V Plot (Mitsubishi PD8XX2 Series Photodiode) [Mitsubishi, 1997] 62
Figure 4.2.4: l-V Plot (W4 C7,3 D200,30,400,N) 63
Figure 4.2.5: l-V Plot with Breakdown Voltage Interpolation Lines (W4 C7,3
D200,20,300,Y) 64
Figure 4.2.6: l-V Plot with Breakdown Voltage Interpolation Lines (W5 C9.10
D400,20,500,N) 65
Figure 4.2.7: Dark Current (W4 C7,3 D200,30,400,N) 66
Figure 4.2.8: Gain (W4 C7.3 D200,20,300,Y) 67
Figure 4.2.9: Gain (Perkin Elmer) 68
Figure 4.2.10: Gain (W4 C7,3 D200,30,400,N) 69
Figure 4.2.11: Responsitivity vs. Wavelength (W4 C7,3 D200,20,300,Y) 70
Figure 4.2.12: Responsitivity vs. Wavelength (W5 C9,10 D400,20,500,N) 71
Figure 4.2.13: Responsitivity @ M=1 (W4 C7,3 D200,20,300,Y) 72
Figure 4.2.14: Practical Silicon Photodiode Responsitivity [Kruger, 2002] 73
Figure 4.2.15: Noise Equivalent Power (NEP) (W4 C7,3 D200,20,300,Y) 74
Figure 4.3.1 : Crosstalk Plot 76
Figure 4.4.1 : Metal Discontinuity Example A 78
Figure 4.4.2: Metal Discontinuity Example B 78
Figure 4.4.3: Responsitivity @ M=1 (W5 C9.10 D400,20,500,N) (@ 0.01u.m Depletion
Width) 82
Figure 4.4.4: Responsitivity @ M=1 (W5 C9,10 D400,20,500,N) (@ 0.1 ^im Depletion
Width) 83
Figure 4.4.5: [W4 C7,3 D200,20,300,N] and [W4 C10,9 D200,20,300,N] Comparison @
100% Illumination 84
Table 3.1: Wafer Design Variations 36
Table 3.2: Pixel Geometry Variations in Die Design 37
Table 3.3: Photodiode Nomeclature 40
Table 4.1: Tested Photodiodes Results 60
XI
Table of Equations
Equation 2.1: Charge Density Equation [Pierret, 1996] 9
Equation 2.2: Electric Field Equation [Pierret, 1996] 10
Equation 2.3: n-side / p-side Depletion Width [Pierret, 1996] 10
Equation 2.4: Built-in Potential Equation [Pierret, 1996] 10
Equation 2.5: Majority Carrier Mobility Equation [Pierret, 1996] 13
Equation 2.6: Photogeneration Rate [Pierret, 1996] 16
Equation 2.7: Photocurrent Due to Incident Light 17
Equation 2.8: Wavelength Energy at Band Gap Energy 18
Equation 2.9: Depletion Width at Zero Bias [Pierret, 1996] 23
Equation 2.10: Gain, M, Theoretical [Zeghbroeck, 2001] 26
Equation 2.11: Gain, M, Empirical [McKay and Chynoweth, 1956] 26
Equation 2.12: Voltage Breakdown Proportion to Doping 27
Equation 2.13: Transimpedance Amplifier Voltage Output 32
Equation 3.1 : Oxide Thickness Calculation 42
Equation 3.2: Implanted Ion Concentration 43
Equation 3.3: Fick's Second Law of Diffusion 44
Equation 3.4: Impurity Profile after Implant and Diffusion 45
Equation 4.1: Photodiode Gain, M 56
Equation 4.2: Primary Photocurrent, lP 56
Equation 4.3: Responsitivity, R 57
Equation 4.4: Functions of Responsitivity 57
Equation 4.5: Noise Equivalent Power (NEP) 73
Equation 4.6: Reprint of Equation 4.4 80
XII
Equation 4.7: Depletion Width, Linearly Graded Junction 80
Equation 4.8: Built-in Voltage, Linearly Graded Junction 81
XIII
1. Introduction
1 .1 . Scope ofWork / Objectives
The primary objective of this research is to design, fabricate, and test avalanche photodiode
(APD) arrays. The design is an array of planar reach-through APD structures on a single wafer.
The performance of the photodiodes and photodiode arrays are investigated using figures of
merit calculations. The feasibility of fabricating APD arrays in an academic lab environment is
determined by comparing the performance of the devices in this research to other commercially
available APDs. An analysis of improving the devices is discussed. The devices were designed
and fabricated in Rochester Institute of Technology's Microelectronic Department using
semiconductor processes.
1.2.APD History and Background
An avalanche photodiode (APD) is a solid-state photodetector that is typically fabricated using
silicon (Si), germanium (Ge), or combinations of lll-V materials from the periodic table such as
gallium arsenide (GaAs), indium gallium arsenide (InGaAs), and InGaAs/lnP. The device is
commonly described as being similar to a p-n junction photodiode with a multiplication region.
Known as a device that has an own internal gain, caused by operating in high reverse bias and
utilizing the avalanche mechanism within the semiconductor. The internal multiplication gives the
PD a high signal to noise ratio, giving signal amplification without amplification of the noise.
Because of its sensitivity, APDs are used in low light level applications such astronomy, optical
fiber communication, spectrometry, laser radar, orwhere photon counting and/or
correlation
information is needed [MacGregor, 1991]. Also, because an APD's gain is a function of the
reverse bias voltage, it can be gain modulated by adjusting the reverse biasvoltage.
The first publication of avalanche photodiodes was in 1966 by R. J. Mclntyre, using silicon as the
device material [Mclntyre, 1966]. Research into using other materials, such as Ge, GaAs,
InGaAs, and InGaAs/lnP has been performed since. Different structures such as the planar
reach-through and the MESA structure have been studied. Other areas of research include
improving performance and uniformity of APDs. Since APDs have been popular due to their
small size and high sensitivity, APDs of different varieties are also commercially available.
Although avalanche photodetectors (APD) have existed for many years, arrays of APD on a
single chip are not widely commercially available. Arrays of APD present unique problems, such
as preventing cross-talk between pixels and controlling the uniformity of the device. The
applications for APD arrays are similar to single APDs such as astronomy, optical fiber
communication, etc. Its usage can be comparable to CCD arrays, but with a higher sensitivity
due to using APD technology as its photosensing mechanism.
One interesting application in using APD arrays versus a single APD is for the reception of optical
communications from space. Signals suffer degradation of the optical phase front due to
atmospheric turbulence, leading to random fluctuations of the point-spread function in the focal
plane. To simply have a larger detector area to collect the entire signal would also increase
background radiation noise, decreasing the noise to signal ratio. An optical detector array would
be able to adaptively select areas of higher signal while ignoring areas with high background
noises [Mclntyre, 1966].
1.2.1 Advantages of APDs Compared to Other Detectors
Compared to similar devices such as PIN photodiodes and photomultiplier tubes (PMT), APDs
are more sensitive, robust, and compact. APDs are a derivative of PIN diodes and are similar in
structure. PIN diodes have an intrinsic region sandwiched between a heavily doped p+ and n+
layers, creating a depletion region where electron-hole pairs are generated from incident photons:
j n Doped Impurities j j Oxide
\/A p Doped Impurities Metal Contacts
n
n+
^^^^^^^^^^^^^^^^^^^^^^^^^^
Figure 1.2.1: Cross-Section of a PIN Photodiode
The advantages of PINs over most photodetectors are that they are highly customizable in terms
of spectral response and have a greatly enhanced frequency response. Because photons are
absorbed in the intrinsic region (7t-region) of the PIN, the peak wavelength response can be
tailored by changing the thickness of the 7t-region. This is done by making the rc-layer thickness
equal to the inverse of the absorption coefficient (1/a) for the desired wavelength. PINs have a
higher frequency response also due to the 7t-region. The highelectric field within the depleted
tc-
region leads to rapid collection of the photogenerated carriers [Pierret, 1 996]
The major difference between PIN diodes and APDs are that APDs have an additional
avalanching multiplication region. Consequently, PIN diodes are not as sensitive.
There are other devices that are as sensitive to photon detection as APDs. Photomultiplier tubes
(PMT) are very sensitive and have a fast response, but the quantum efficiency drops significantly
at wavelengths longer than 400nm [MacGregor, 1991]. Also, PMTs are susceptible to moisture,
have a high dark current, and delicate, making it unsuitable for portability [Proudfoot, 1 997]. In
addition, trying to collect spatial information by having an array of PMTs is simply not possible or
feasible due to its bulk size. A Multi-Anode MicroChannel Array (MAMA) detector is possibly the
closest equivalent to APD arrays, where MAMA detectors have the high sensitivity and can
collect spatial information. Unfortunately their physical size and operation, where a
photocathode, microchannel plate, anode array, and supporting electronics are needed, is still too
delicate for portability.
Silicon APDs have useable quantum efficiency between wavelengths from around 200nm to
1 100nm and hence, are sensitive between those wavelengths. Other materials have been
investigated, especially lll-V compounds such as GaAs, InGaAs, Ge, etc. which have better
quantum efficiencies at higher wavelengths. Although lll-IV compounds can have a higher
sensitivity beyond 1 100nm up to 1300nm, the advantage of silicon APDs is that it has a much
lower noise due to having only one carrier, namely electrons, which initiate the avalanche
process. The electron/hole ionization rate (a/p) of silicon is around 50, compared to ratios of
near unity for other lll-IV compounds [Ridley, 1985].
1.3.Thesis Background
The original scope of work was to design and fabricate APD arrays along with onboard
discriminator circuits. The array would be read in by a computer via a multi-channel I/O card, with
the intended application is to have this device somewhat portable for in-the-field use. The
devices were to be designed and fabricated at Rochester Institute of Technology's
Microelectronic Department.
In order to achieve that final goal, several successful steps were needed: have working individual
APDs, working APD arrays, working discriminator circuits onboard, and a practical interface to the
computer.
Because avalanche photodiodes have never been fabricated at the Microelectronic Department,
knowledge of the design and fabrication needed to be gained. In doing so, successful individual
APDs, especially with uniform characteristics, were difficult to fabricate. The result is that only a
handful of arrays (array sizes of only four pixels) were able to exhibit successfully working
characteristics.
This thesis will discuss the theory and design of the avalanche photodiode, fabrication process,
and test results. It will also discuss the problems of the devices and provide an analysis of
improving the design and fabrication.
2. Device Theory and Design
APDs are solid-state devices that are fabricated using silicon (Si), germanium (Ge), and
combinations of lll-V materials from the periodic table such as gallium arsenide (GaAs), indium
gallium arsenide (InGaAs), and InGaAs/lnP
APDs are essentially a p-n junction photodiode with a multiplication region. Common tomost
optoelectronic devices, there is a lightly doped layer that serves as a photo absorption region.
What is unique to the avalanche photodiode is an extra multiplication region, giving the device its
internal signal gain.
Ill-V compounds are sensitive up to wavelengths approximately 1600nm versus about 1 100nm
for silicon. But silicon APDs are much less noisy due to the high electron-hole ionization rate of
about 50 versus close to unity for the other materials. This mechanism is important for the device
operation and will be described in detail later. Also, another reason silicon technology is used is
because it is much more widely used and therefore has more advanced fabrication techniques,
which leads to better uniformity and control that is critical to device performance.
2.1. Device Structure and Operating Principles
The standard design of an avalanche photodiode consists of an intrinsically doped region for
photo-absorption, a multiplication region that has a high electric field presence, and a guard ring
to minimize edge breakdown voltage problems. Here is a cross-sectional diagram of the
standard design, and it's known as the planar reach-through structure:
Incoming Light
Multiplication
Region Electric Field
n+
guard
rings
Absorption
Region 71 (intrinsic)
p+ contact
OCD
y
Figure 2.1.1: Cross-Section of a Reach-Through Avalanche Photodiode and
Corresponding Electric Field Strength
The pixel shape of an APD is round, to achieve a uniform edge junction and preventing current
crowding. That can lead to early voltage breakdown.
2.1.1 Depletion Region Concept
Because the planar reach-through APD structure consists of several layers of elements,
combined with the criticalness of the APD of needing a high internal electric field for carrier
multiplication, the doping of the device along with the concept of the depletion region is critical.
Avalanche multiplication of the carriers happens that the point of the highest electric field within
the device. Ideally, this should occur in the designed multiplication area, around the top p-n
junction area. As a review, the following is the conceptual idea of how the electric field is affected
by the charge density and doping profile:
Nd-Na
Nr
-N.
Figure 2.1.2: Doping Profile of a P-N Step Junction
P
i
qND
qN,
Figure 2.1.3: Charge Density Profile of a P-N Step Junction
Figure 2.1.4: Electric Field Profile of a P-N Step Junction
For the purpose of the review, a step junction approximation is used for simplicity.
The following are equations that help form the above graphs. The charge density equation is
given by:
P =
qNA
qND
0
-
xp< x < 0
0<x<xn
x<-x andx>x
Equation 2.1: Charge Density Equation [Pierret, 1996]
Where q is the electron charge, NA and ND are the acceptor and donor doping concentration,
respectively. xn and xp are the n-side and p-side width of the depletion region, respectively.
The electric field is given by:
E(X):
3i^(Xp+x) ...-xp<x<0
qND
Ks 0(xn+x) ... 0<x<xr
Equation 2.2: Electric Field Equation [Pierret, 1996]
Where Ks is the dielectric constant and e0 is the permittivity of freespace. To determine xp and
xn:
*n=
2KS0NAv
qND(NA+ND)b
xp=
2Ksg0ND^
qNA(NA+ND)b
Equation 2.3: n-side / p-side DepletionWidth [Pierret, 1996]
Where Vbi is the built-in potential, determined by:
Vbi=^lnKT . fNA ND
n>
Equation 2.4: Built-in Potential Equation [Pierret, 1996]
Applying the above concept to the structure of the reach-through APD, the doping profile, charge
density, and corresponding electric field is:
10
n+ 71 p+
-* X
Figure 2.1.5: Layer Profile of a Reach-Through APD
ND-NA
Nr
-> x
-N,
Figure 2.1.6: Doping Profile of a Reach-Through APD
qND
-qNA
-> X
Figure 2.1.7: Charge Density Profile of a Reach-Through APD
11
*- X
Figure 2.1.8: Electric Field Profile of a Reach-Through APD
Because of the unique shape of the electric field throughout the device, there are two regions of
interest, the Absorption region, which is essentially the intrinsic (/) region of the device, and the
Multiplication region, which is the p-n junction with the high electric field.
It is also pointed out here that, since it is desired to have the depletion region be extended into
the intrinsic region and stop at the p+ layer, the middle p and i layers should be doped
accordingly.
2.1.2 Absorption Region
As the name implies, the purpose of this region is to absorb the incoming photons. As photons
are collected, electron-hole pairs are generated from the photon energy via photogeneration.
Photogeneration is when electrons in the valence band are directly excited into the conduction
band from the energy of the incoming photon [Pierret, 1 996]. The mechanism of photogeneration
is discussed in detail in Section 2.1 .2.1 . Once electron-hole pairs are generated, the mild electric
field present in this region sweeps one carrier, either holes or electrons depending on device
design, into the multiplication region.
12
Another characteristic of this region is in having a light doping to facilitate high carrier mobility.
Since the goal of the absorption region is to collect photons and generate electron-hole pairs,
recombination of carriers or collisions between the free carriers and the lattice is not desired. At
the weak electric field that is present in the absorption region, any collisions with the lattice would
not result in impact ionization and would in fact, impede the sensitivity of the device by the
scattering of the carriers from the lattice vibration. Instead, this layer is to have a weak electric
field sweep the carriers into the multiplication region, where the high electric field there would
create the desired impact ionization.
The relationship between doping density and mobility is:
M= Mmin+-
Mo
1 +'N
^
Nref
Equation 2.5: Majority Carrier Mobility Equation [Pierret, 1996]
Where:
Parameter
Values at 300K
Electron Carrier Hole Carrier
Nref [cm3] 1.3MO17
2.35MO17
u.mln [cm3A/-sec] 92 54.3
u-o [cm3/V-sec] 1268 406.9
a 0.91 0.88
[Pierret, 1 996]
13
The graph is:
* i--.<{;-a-*<
:
< <....(...*...>.(.<*
( j ^ i V-<".^. i-
Electrons HI!:
-i ^ ; i i.i-4-^
Silicon : ;T;
7=300Khfi
1000
:-. -.- ~
-::t : ;:;
: l ::\'-~-
f--^H44tf:::::q:::4:::p:pf^;:|
' A'a or Nx> (cm-3 . >, fh
-
Holes -i-ffftr...;.n....|.44.ji;
100
1 lxlO'4. ...: 2
:;:::-"t 1 x IOl!....
2
1358 461
1357 460
1352 459
1345 458 ?
1332 455"
1298 448 -.j.
1248 437 :!
1165 419 ?v
986 378
801 331
"~""f~4~f~iTuf1 j~4444J4
''-,"*": ~-.-^j 1 X 10"\...
"'] 2
10
i i x io" ....
1014 10'5 10'6 1017
NAor/VD(cm-3)
10'8
Figure 2.1.9: Carrier Mobilities as a Function of Dopant Concentration in Silicon [Pierret,
1996]
2.1 .2.1 Photon Absorption / Electron-Hole Generation
When light is transmitted into semiconductor material, electron-hole pairs are generated if the
incident photon energy is greater than the band gap energy. These generated electron-hole pairs
in turn generate current. This is known as photogeneration and the current from this process is
the photocurrent.
To understand how an absorbed photon generates electron-hole pairs, E-k plots (electron-energy
band vs. electron crystal momentum) are used to visualize the process. There are two general
categories of E-k plots in regards to semiconductor materials, direct semiconductor and indirect
14
semiconductor. The difference being that direct semiconductors have the minimum conduction
band energy and the maximum valence band energy both at k=0, while indirect semiconductors
have the conduction band minimum shifted off from k=0:
Direct Semiconductor Indirect Semiconductor
Figure 2.1.10: E-k Plots of Recombination of Direct and Indirect Semiconductor
Silicon is an indirect semiconductor. When a photon with certain energy (hv) is absorbed into the
silicon, it is essentially a vertical transition of an electron on the E-k plot, since photons are
massless entities and carry no momentum. In contrast, momentum generated from lattice
vibrations, known as phonons, translate to a horizontal movement on the E-k plot [Pierret, 1996].
To generate an electron-hole pair from an incident photon, the photon need to have energy
greater than the band gap energy and have some assistance from lattice vibrations in order to
make the electron jump from valence to conduction band.
Because of the polarity of the electric field of the absorption region and the depletion region it
creates, the photogenerated electron-hole pairs add a reverse current to the overall reverse
15
current generated from the avalanching mechanism. Hence, the reverse current increase when
light is present.
To determine the current generated from the incident light, the photogeneration rate (GL) needs to
be determined first:
aP,
G, = *-L Ahu
Equation 2.6: Photogeneration Rate [Pierret, 1996]
Where a is the absorption coefficient in [1/cm], P| is the incident optical power in [W], A is the
illuminated area in [cm2], and hv is the photon energy in [eV]. Photogeneration rate GL is in [cm
3*sec"1] units. The absorption coefficient is a function of wavelength and temperature and is
different for each type of semiconductor:
16
105
104r
103
10
1
\ \S1 1 1 1 z
1 { \-
:
GaAs
\ GeV1 \ Si >
~
InP _ \~
: GaP
\\"
1
1 \\, , ,
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
Figure 2.1.11: Absorption Coefficient as a Function ofWavelength at 300K [Schroder,
1990]
Assuming a constant photogeneration rate throughout the semiconductor, the photocurrent due to
incident light (lL) is:
"2
lL =-qA Jgl dx
Equation 2.7: Photocurrent Due to Incident Light
17
Where A is the illuminated area, x, and x2 are the boundary locations of thethickness of the
illuminated area.
The photocurrent generated from a semiconductor is also dependent on the wavelength, or
spectral response. At the same incident optical power across all wavelengths, the photocurrent is
expected to be:
0.8
j 0.6
0.4
02
0
0.4 0.5 0.6 0.7 0.8 OS 1.0 1.1 1.2
Wavelength (/an)
Figure 2.1.12: Spectral Response of Silicon P-N Junction Photodiode [Pierret, 1996]
The decrease in the longer wavelength region of the spectral response graph is due to the band
gap of the silicon material. Since electron-hole pairs are generated only when the incident
photons have more energy than the band gap, the upper wavelength limit essentially cuts off at:
K =
1.24
Equation 2.8: Wavelength Energy at Band Gap Energy
18
Where EG is the energy band gap of the material. For silicon, the EG is 1 .12eV at 300K and the
effective wavelength limit is about 1.1p.m.
The decrease of the spectral response at shorter wavelengths is due to two reasons. First,
photon energy increases at shorter wavelengths. Since the incident optical power is held
constant, the flux of the incident photon decreases as compared to longer wavelengths.
Therefore, the decrease in spectral response is partially due to the decrease of the number of
incident photons absorbed. Second, as shown in Figure 2.1 .1 1,the absorption coefficient
increases rapidly at shorter wavelengths. Taking the inverse of the absorption coefficient (1/a),
the light being absorbed in the material, on average, takes place increasingly closer to the
surface at shorter wavelengths. Since the p-n junction is at a set depth into the material, the
photogenerated carriers from the light absorption recombine before they can diffuse into the
depletion region. It is noted that Figure 2.1.12 is a typical representation of spectral response;
the peak can be tailored by changing the depth of the p-n junction in the device.
2.1.3 Multiplication Region / P-N Junction
The first two layers of the"front"
side of an APD are the n+ and p layers. Together they form a p-
n junction and its characteristics behave exactly as a classical p-n junction diode. In the case of
the APD device, the p-n junction serves as the multiplication region. As photons are collected in
the absorption region and electron-hole pairs are generated, the electron or hole carriers,
depending on the device design, are swept into this multiplication region. The carriers are then
multiplied via the avalanche mechanism, a condition created by applying a high reverse voltage
bias on the p-n junction.
19
As a review, the doping profile, energy band, electrostatic potential, and electric field diagrams of
a p-n junction under equilibrium, forward bias (VA>0), and reverse bias (VA<0) are [Pierret, 1996]:
A
ND
"NA
Figure 2.1.13: Doping Profile of a P-N Junction
20
Equalibrium (VA = 0)
E,
Forward Bias (VA > 0)
Figure 2.1.14: Energy Band Diagram of a P-N Junction
Figure 2.1.15: Electrostatic Potential of a P-N Junction
21
V. > 0
Figure 2.1.16: Electric Field of a P-N Junction
It is noted that the above diagrams are using a step junction profile for simplicity.
Notice in Figure 2.1 .14 the energy band diagrams have a section where the bands are"bent"
,or
band bending. Band bending is due to a connection made between the p-type and n-type
materials. Charge carriers from both materials diffuse from regions of high concentration to low
concentrations. Specifically, holes from the higher p-doped side would diffuse into the n region
and electrons from the heavier n-doped side would diffuse into the p region. When the carriers
diffuse away from their original location, they leave behind an unbalance of charges, or ionization.
The p-side would have ionized acceptors and the n-side would have an equal number of ionized
donors [Torres, et. al., 2002]. This section of the diode, where the p-doped and n-doped layers
meet, is known as the depletion region.
The width of this depletion region is mainly a function of doping concentrations and is calculated
by:
22
w =
2KC (s "-0 NA+NC
NANDVh
Equation 2.9: Depletion Width at Zero Bias [Pierret, 1996]
Where Ks is the semiconductor dielectric constant, e0 is the permittivity of free space (8.85* 10"14
[farad/cm]), q is the electronic charge (1 .6* 10'19
[coul]), NA and ND is the acceptor and donor
doping concentration in [cm-3] respectively, and Vb, is the voltage breakdown in [V]. This equation
is assuming that the junction is a perfect step function and no voltage bias is applied.
As suggested by Figure 2.1 .15 and Figure 2.1.16,
an increase of the electrostatic potential by
having a reverse voltage bias can increase the magnitude of the electric field. As discussed in
Section 2.1 .3.1,a"good"
avalanche mechanism is mainly dependent on having a high electric
field.
2.1.3.1 Avalanche Mechanism
When reverse biasing a p-n junction, where current is flowing from the n-doped region of the
semiconductor to the p-doped region, current flow is limited to a few milliamps and is independent
to the magnitude of the reverse bias. If the reverse bias is continually increased beyond a certain
point, known as the breakdown voltage, a large current will flow. This is a completely reversible
process and does not damage the diode, except for overheating concerns if there is excessive
current flow.
23
4+ I
Voltage
Breakdown
T-l
Figure 2.1.17: Typical Diode l-V Curve
Two processes cause this large current flow occurring beyond the voltage breakdown. One is the
Zener process and the other more predominant process is the avalanche mechanism [Pierret,
1996].
The Zener process is where the particle, instead of gaining enough kinetic energy to overcome
the potential energy barrier to move, tunnels through the barrier without any change in the particle
energy. This phenomenon is rare compared to the avalanche process. It happens when the
width of the potential energy barrier is very thin (less than 100A) and can only happen when there
are filled states on one side of the barrier and empty states on the other side of the barrier
[Pierret, 1996].
24
The dominant process in contributing to the breakdown current is the avalanche process. When
the diode is in reverse bias past the breakdown voltage, the current flow is due to minority
carriers entering the depletion region and accelerated to the other side of the junction. The
movement of the minority carriers is caused by the internal electric field. When minority carriers
cross the depletion region, it collides with the semiconductor lattice. The mean free path is about
~10nm between collisions and depletion widths are around the order of magnitude of microns. At
small reverse biases the energy losses from the collisions are small and only cause lattice
vibrations. The result is just localized heating from friction vibrations.
At high reverse biases, beyond the reverse breakdown voltage, impact ionization occurs. The
minority carriers accelerate through the depletion region with enough energy that when it collides
with the lattice, it ionizes a semiconductor atom, freeing a valence electron from the atom and
giving it enough energy to jump into the conduction band. This creates an electron-hole pair.
Because of the high electric field present, these newly generated carriers are then immediately
accelerated and consequently collide with the lattice for more impact ionization. The result is a
multiplication of carriers and the reverse current essentially peaks off into infinity [Pierret, 1 996].
As a note, the avalanche mechanism does not occur sharply at the breakdown voltage. Because
collisions, mean free path, and energy of each carrier is a random variable distributed around a
mean value, there are avalanching events happening far below breakdown and conversely, not
all free carriers participate in the avalanche effect at voltages beyond breakdown. Below
breakdown, there may be a few free carriers that have enough energy to cause impact ionization
to start, but because of the low electric field, it does not permeate. It is only at higher reverse
biases that this phenomenon becomes significant and leads to high reverse current [Pierret,
1996]. The result of this statistical distribution is that there is not a sharp edge at the voltage
25
breakdown, but a sloping approach and a slightly gentle bend to the curve as depicted in Figure
2.1.17.
When the device is in avalanche breakdown, the increase in current is expressed by a carrier
multiplication factor, or gain:
M = L
1- [ordx
xi
Equation 2.10: Gain, M, Theoretical [Zeghbroeck, 2001]
Where x, and x2 are the boundaries of the depletion layer region and a is the ionization
coefficient. This theoretical equation assumes that the electrical field is constant between the
depletion boundaries.
Empirically, the multiplication factor is expressed as:
M-'
(1-
va
vbr)
Equation 2.11: Gain, M, Empirical [McKay and Chynoweth, 1956]
Where Va is the voltage applied, Vbr is the breakdown voltage, and m is between 3 and 6
depending on the semiconductor material used.
26
As a note, the voltage breakdown value is can be designed by controlling the doping level of the
lighter doped side of the junction. At lighter dopings, approximately below 1017/cm3, the
breakdown voltage is proportional to the doping level:
V,BR
Sp
Equation 2.12: Voltage Breakdown Proportion to Doping
Where NB is the doping concentration on the lighter doped side of the junction [Pierret, 1996].
Figure 2.1.18 shows the VBr and doping relationship for Si, Ge, and GaAs semiconductors [Sze,
1981]. At heavier dopings beyond 1017/cm3, as indicated by the dashed line in the figure, the
relationship does not follow Equation 2.12.
27
1000
10 1015 1016
/VAorWD(cm-3)
1017 10'
Figure 2.1.18: Breakdown Voltage Versus Nondegenerate-side Doping Concentration for
Ge, Si, and GaAs semiconductors [Pierret, 1996]
2.1.4 Guard Ring
The purpose of the guard ring around the main avalanche photodiode structure is to minimize
edge breakdown and achieve a more uniform breakdown across the photodiode [Pierret, 1996].
Because planar reach-through structures are fabricated using diffusion and ion-implantation
through a mask, it always creates a curved edge from the bulk of the substrate to the edge:
28
Impurity after implant
and diffusion ^
71 Bulk Silicon (Intrinsic)
Figure 2.1.19: Exaggerated Detail of the Curvature Effect
This is known as a "curvatureeffect"
[Sze, 1 966]. It is due to the fact that when impurities diffuse,
it diffuses in all direction; vertically and horizontally:
Impurity after implant
Impurity after implant and diffusion
Figure 2.1.20: Curvature Effect - Implant and Diffusion Spread
Since the "curvatureeffect"
presents a non-uniform edge shape between the heavily doped
multiplication region and the lightly doped absorption region, it results in a premature low voltage
breakdown at the junction periphery.
29
One approach to eliminate this problem is to create a guard ring at the junction periphery to
reduce the electric field and minimize edge voltage breakdown. It can be thought of as a buffer
zone between the multiplication and absorption region. The guard ring is lighter doped than the
multiplication region, but is not as light as the absorption region [Matsushima, et. al., 1984].
2.2. Supporting Electronics
A complete APD array system requires supporting electronics in order for it to be functional. The
two major components are a quenching circuit and a transimpedance amplifier.
2.2.1 Quenching Circuit
A quenching circuit is needed in order to prevent pixels to latch indefinitely in the avalanche
mode. There are two main categories of quenching circuits: passive quenching and active
quenching. Both of them operate on a principle based by lowering the bias voltage when extra
current flows and restoring the voltage bias soon after to enable the photodetector to detect
another signal. Passive quenching circuits are easier to implement, but are slow in recovery from
the avalanche pulses [Cova, et. al., 1996].
Passive quenching circuits operate by developing a voltage drop on a high impedance load. It
uses resistors in a voltage divider configuration to prevent latching [Cova, et. al., 1996]:
30
Figure 2.2.1: Passive Quenching Circuit
By selecting the right resistor values, the APD, depicted by the diode symbol in Figure 2.1 .1 , is at
the desired bias in dark conditions (no signal light input).
Because the APD is a current sourcing device, when as incoming photon triggers the APD into
avalanche and extra current is sourced, the biased voltage at the Vbias point drops, changing the
reverse bias level of the APD itself and unlatching the avalanche mechanism. Therefore the
voltage seen at Vout is at first negative (the detector is reverse biased) and spikes in the positive
direction when there is incoming light, and drops back down to starting level when it is dark again.
The passive quenching circuit is best using the APD in Geiger mode, counting photons and
requiring the output to be binary in reporting if photons are present or not.
2.2.2 Transimpedance Amplifier
Since most solid-state devices are essentially current sourcing devices, a transimpedance
amplifier is necessary for the operation of these devices. The role of a transimpedance amplifier
31
is to both amplify the signal of the detector andconvert it from a current to a voltage signal. It
utilizes an operational amplifier (op amp) circuitry with a feedback resistor:
Figure 2.2.2: Transimpedance Amplifier Circuit
The value of the feedback resistor adjusts the voltage gain of the amplifier by using the classic
formula:
Vout ="
'in ^F
Equation 2.13: Transimpedance Amplifier Voltage Output
A common mistake to avoid is in selecting a high gain such that the voltage output is higher than
the +Vcc and -Vee rail voltage used to power the op amp; the output will be clipped.
To utilize the transimpedance amplifier along with the quenching circuit to read from an APD, the
circuit is:
32
Figure 2.2.3: Quench and Transimpedance Amplifier Circuit
2.3. Problems with Arrays of APDs
Due to the nature of how an APD operate, creating an array of APDs has certain obstacles. The
problems involved are in having optical and electrical cross-talk, the significance of non-uniformity
within pixel and from pixel-to-pixel, and the possibility of having a pixel latched in the avalanching
state after photon detection.
2.3.1 Cross-Talk
It was first reported in the 1 950's that photons were emitted from avalanche breakdown in silicon.
During a reverse bias voltage breakdown, photon emission occurs at the p-n junction and is due
to both avalanche and Zener mechanism [McKay and Chynoweth, 1 956]. Optical cross-talk
describes the condition when the diode itself is emitting secondary photons from the avalanche
and Zener mechanism as triggered by the primary incoming photons. These photons can then be
33
detected by surrounding pixels. In an experiment by Franco Zappa et. al., the secondary photons
emitted are proportional to the current flowing through the diode [Zappa, 1996].
Electrical cross-talk can either arise from a readout circuit, consisting of a quenching circuit and
an amplifier, or from the avalanche mechanism. The avalanche source of cross-talk is due to the
relatively high electric field and impact ionization taking place. It is possible for the ionizing carrier
to scatter into adjacent pixel and produce a false trigger. Because this is a random event, as the
pixel-to-pixel distance gets closer, the probability of having a carrier wander into adjacent pixels is
higher. Therefore, to minimize or eliminate electrical cross-talk, pixels need to be spaced out.
The tradeoff of this is that the dead space, the region between pixels where it would not sense
incoming photons, increases.
2.3.2 Non-Uniformity
The gain of an APD is dependent on the strength of the electric field across the depletion region.
The uniformity of the electric field is dictated by the doping uniformity of the n and p regions of the
ADP. Therefore, the gain of the device is dependent on the doping uniformity, which is
dependent on the fabrication process technology.
To illustrate the importance of controlling the fabrication process to control the uniformity of diode
performance, the equation of the photocurrent output of a diode is used:
34
, Poqd-r)(1,e-ad)
Figure 2.3.1: Photocurrent Output of a Diode
Where P0 is the incident optical power, q is the charge, r is the optical reflection loss, hv is the
photon energy, a is the absorption coefficient, and d is the depletion layer width. Since d is an
exponential term, small changes in the depletion width would result in a significant change in the
photocurrent of the diode.
2.3.3 Pixel Latching
There are problems associated with single APDs in general. Besides cross-talk that generates
false triggers, thermally generated electron-hole pairs can also have the same effect. This is
known as the dark current. At relatively higher temperatures, a carrier may be able to receive
enough energy to ionize and cause the avalanche process, since the high electric field is already
present.
A second problem is that when an electron-hole pair is generated, either thermally or optically
from a photon, the device discharges and if it exceeds a certain latch current, would remain in the
avalanche state. A quenching circuit is needed to momentary lower the electric field to stop the
avalanche effect and quickly raise the electric field back in order to detect further photons.
35
3. Implementation
3.1. Design
APD arrays were fabricated at the Rochester Institute of Technology Microelectronics
Department. Several APD array designs were fabricated and tested to see howcertain design
element changes would affect performance.
3.1 .1 Wafer Variations
One wafer was used for each design variation. The variations included using either polysilicon or
aluminum as the metal connection, having a guard ring, or eliminating the middle p layer. There
were five designs:
Wafer ID Description
APD02-01 Regular NiP structure
APD02-02 NiP structure with polysilicon contacts
APD02-03 NiP with no Guard Ring
APD02-04 NPiP Structure with no Guard Ring
APD02-05 NPiP Structure with Guard Ring
Table 3.1 : Wafer Design Variations
To find how pixel dimensions change the performance of the device, several pixel dimensions
were fabricated on the same die. Pixel diameter varied from 100 to 1500um. The guard ring
36
lateral width was from 10 to 50um. Most pixels were replicated and placed in an array fashion at
various distances. The following table shows the different pixel dimensions available in the die:
Pixel (Active
Area) Diameter
Guard RingLateral Width
Pixel to Pixel
Distance (Center
to Center)
Ring Material
100u.m 10u.m 100|im Polysilicon
100u.m 10u.m 200|im Polysilicon
100u.m 10u.m 400u.m Polysilicon
200u.m 10u.m 400|am Polysilicon
200^m 20u.m 250|am Polysilicon
200u.m 20u.m 300u.m Polysilicon
200u.m 20u.m 300|am Aluminum
200u.m 20u.m 400u.m Polysilicon
200u.m 30n.m 400|im Polysilicon
400u.m 20u.m 500u.m Polysilicon
400^m 20u.m 750|im Polysilicon
1 500u.m 50u.m N/A Aluminum
Table 3.2: Pixel Geometry Variations in Die Design
3.1.2 Die Layout
Several pixel sizes along with a few other devices were fabricated in each die. The following
illustration shows the layout of the die:
37
Figure 3.1.1: Die Layout
As a reference to the size of the die, all the contact pads are 100x100 urn. The die layout is
shown again but with labels to indicate each area:
38
-r-*
:;,>j^-;'i
I;-,'. :,-
O?- :
**.<
lil
'!APD with Passive
Quench Circuits,j:i.
j,<Various APD Arrays'
>?r\. i^i -r^, ^X!*?'
W"i!W~
\J }i -1! .-.
? i.v
/<:*?'
ft-- -.1 -4 ,*.,: ;f3
if^ ^ f^ f^v
.- -*- *^ ^=
^F^-->-.
"^^
'4i?J'V^*
<t-:^'
I^ki?1
7]-
ri n q
| D1500,50,0,Y
i iD200,30,400,N i \ D200.1 0,400,N'
D 1100.10 .200,N i ;
'.":
D 1 00,1 0 .400.N
: .- jlI _j. : : -. . i
, , .1
\ ''*. S"i. *"* -i"**. , \-:~\ -A-\ j.-:-\r*~'.
D200.20.300.N'j
u:s' 1 lr :
: 1 Resistors =
:':
"1 ! 111"
-
|j1
ji
! "~*.'
tj
t
I"
t
.1
:'D200.20.306.Y
1
1
1
1
D100.10.100.N:
; D200.20.250.N ;
: ir t: m -j :
- : ^Alignment*
:;..* ->.."
:| ^ Verniers-
iYD200.20.400.N--1:,:
; j ^itPSSh-^ii
D400,20,750,N
ft ED
Figure 3.1.2: Die Layout with Labeled Areas
Photodiodes [Dddd,gg,ppp,Y/N\:
The arrays of photodiodes arranged in sets of fours are labeled with the following designation:
39
ddd Active diameter of the photodiodes.
99 Width of the guard ring.
PPP Pixel to pixel distance measured from center to center.
Y/NIf the guard ring is fabricated of aluminum (Y) or frompolysilicon (N).
Table 3.3: Photodiode Nomeclature
Various APD Arrays:
Various APD arrays in different configurations and connections.
APD with Passive Quench Circuits:
Individual APD pixels with connected resistor as quenching mechanism.
Resistors:
Various resistors with different resist values.
Alignment Verniers:
Used for aligning the Guard Ring, N+ Region, P+ Region, and Aluminum mask levels.
3.1.3 Device Cross-Section
The general device structure used was the planar reach-through structure as described in Section
2.1 . The following figure shows the final cross-section of the device:
40
[ _J n Doped Impurities I j Oxide
^^ p Doped Impurities f:*:j p+ Contact
Poly-Si or Aluminum Interconnectn+ Guard Ring
7t Bulk Silicon (Intrinsic)
Figure 3.1.3: Cross-Section of a Reach-Through APD with Contacts
The type of wafer used was a heavily doped p-type (boron) substrate with a 28u.m thick epitaxial
layer. The substrate had a resistivity of 0.0163 Q-cm while the epitaxial layer was around 18Q-
cm. The substrate served as the p+ contact layer while the remaining device features were in the
epitaxial layer. The impurity layers are fabricated using ion implantation at various species and
doses. The drive-in steps are done via diffusion furnaces. Traditional g-line optical lithography
was used for masking and defining device layouts.
3.2. Calculations
Three specific calculations are needed in order to fabricate the device properly: oxide growth
thickness, ion implant dose, and drive-in time.
41
3.2.1 Oxide Thickness
The following equation is used in order to determine the oxide thickness growth:
A'
x
2h+*-l
Equation 3.1: Oxide Thickness Calculation
Where:
A =K1ekT
B = K2ekT
B/A is known as the linear rate constant and B as the parabolic rate constant. T is the process
temperature in Kelvin, t is the oxidation time in hours, and k is the Boltzmann constant in [eV/K].
Oxide thickness x is in microns. Exact values of K,, K2, E1; and E2 are shown in Appendix 6.1 .
Note that the equation used is for diffusion-rate limited regime in wet oxidation on bare silicon,
which is applicable for the devices in this research. It is also noted that approximately 46% of the
oxide grown is"consumed"
from the silicon:
42
__
Bulk Silicon
_j
Oxide
(original silicon surface)
Oxidation
46% of silicon
"consumed"
when
growing oxide
Figure 3.2.1: Silicon Consumption from Oxide Growth
Algebraic manipulation is all that is needed in order to determine the process parameters for a
desired oxide thickness. Actual oxide calculations performed for this research are shown in
Appendix 6.1.
3.2.2 Ion Implant
To determine the implanted ion concentration as a function of depth into the wafer, the following
formula is used [Wolf and Tauber, 1986]:
N,(X):
2k dRc
Equation 3.2: Implanted Ion Concentration
Where x is the depth into the wafer,N'
is the implant dose, RP is the implant projected range, and
dRP the implant projected straggle. This calculation was needed for the guard ring, n+, and p+
device structures. Graphs and calculations of implant ion concentration are shown in detail in
Appendix 6.2.
43
L o n g itud i n q I P r o ject o n
Projected Range, Rp
Projected Straggle, dRF
Depth -> seaen
Figure 3.2.2: Ion Implant Range and Straggle - Longitudinal Axis [Cheung, 2003]
3.2.3 Drive-In
To determine the doping profile for a diffusion step (drive-in) at a specific process parameter,
Fick's law of diffusion is used [Wolf and Tauber, 1986]:
Q ^
C(x,t) =^=e4Dt
VnDt
Equation 3.3: Fick's Second Law of Diffusion
Where x is the depth into the wafer, t is the time of diffusion, Q0 is the total quantity of impurity
present, and D is the diffusion coefficient.
44
Since all impurity drive-in performed on the devices in this research is after ion implantation, a
simplified equation combining Equation 3.2 and Equation 3.3 can be used:
N' TT^T^"
Nd(X) =e2(dRp-+2Dt)
V2tuydRp2
+ 2 D t
Equation 3.4: Impurity Profile after Implant and Diffusion
Details of this equation are shown in detail in Appendix 6.2.
45
Wafer Depth jam]
Figure 3.2.3: Ion Implant Drive-In
3.3. Fabrication
Appendix 6.3 outlines each step of the fabrication process and show the device profile for that
process. As mentioned in Section 3.1 .1, there were five wafers each with a slightly different
46
design variation. Next to each process description lists the wafers that were used for that
particular step.
3.4.Test Set-up
The following diagram illustrates the test-up:
HP4145B
Light
Source
Diffraction
Grating
Fiber Optic
Microscope
Vacuum
Chuck
Electrical
Cables
-v.
/ i
Needle
Probe
Wafer Under
Test
Figure 3.4.1 : Test Set-Up Diagram
Here is a picture of the set-up:
47
Figure 3.4.2: Test Set-Up Picture
The microscope used featured a shelf for the needle probe to rest on and is capable of moving
independently from the wafer and vacuum chuck. The microscope head also has an independent
range of movement.
A halogen light source is used as illumination, into a diffraction grating with the ability to select the
desired wavelength. The light is piped into the photodiode tested. The fiber optic has an exit
angle of approximately30
FWHM (full width half-maximum intensity).
All l-V measurements were obtained on the HP4145B parametric analyzer.
48
3.5. Deviation of Fabricated Devices from Ideal
As mentioned in Section 2, "Device Theory and Design", of this paper, the main key in designing
a successful APD is to have the doping levels correct for each of the layers such that the
depletion region (and hence, the electric field) extends into the intrinsic layer when under
sufficient reverse bias:
n-i-
Depletion Region
A
71 P+
-> X
ND NA
"> X
-> X
Figure 3.5.1: Doping, Depletion, and Electric Field Diagram of a Standard APD
49
Also, a more appropriate depth for each layer is usually less than 0.5pm for n+, to minimize the
participation of holes in the detection process, and around a few microns for the middle p layer
[Wegrzecka, et. al., 2004]. The depth and thickness of the intrinsic layer can be varied to adjust
the spectral characteristics of the device.
Instead, the devices fabricated in this research had incorrect doping levels. The p layer had too
high of a doping level such that the depletion region existed only between the n and p layers:
50
Depletion Region
nn-71 P+
-* x
ND-NA
-* X
-> X
Figure 3.5.2: Doping, Depletion, and Electric Field Diagram of Fabricated Reach-Through
APD
It is stated again that the above depletion and electric field characteristics are for the device in
reverse bias state.
51
4. Test Results
4.1. Figures of Merit
To compare the performance of the avalanche photodiodes both within this research and with
other manufactured photodiodes, four figures of merit are used: voltage breakdown, dark current,
gain, and spectral responsitivity. Two independent plots of each photodiode are needed in order
to calculate those figures of merit. A third plot is used specifically for photodiode arrays; to
compare cross-talk between photodiodes.
The following explains how each figure of merit is obtained and calculated.
4.1.1 Breakdown Voltage
The breakdown voltage is the reverse voltage at which the current flow increases dramatically
due to avalanche mechanism and Zener process (see Section 2.1.3.1 and Figure 2.1.17).
In the case of the photodiodes that tested here, the"knee"
of where voltage breakdown occurs is
not sharp enough to quote a definite number. Because of that, three definitions that are
commonly practiced within the industry were used. Human judgment was then applied to
determine which method reported the most sensible number, as some methods reported an
erroneous or illogical voltage breakdown number. The three techniques used were:
1 . Third-Order Polynomial Fit Method
2. Interpolation Method
3. Current Threshold Method
52
The Third-Order Polynomial Fit Method defines the voltage breakdown by first fitting a third-order
polynomial to the data, finding the derivative, and determining where the maximum gradient
occurs. This method worked best when the data did not exhibit a very sharp knee at the voltage
breakdown point. Although a higher order polynomial fit would have fit that type of data better,
there were too many inflection points around the linear region of the l-V curve of a photodiode
(area between reverse bias (OV) and breakdown voltage). The computer algorithm performing
the third-order polynomial fit method was coded in Microsoft Visual Basic 6.0. The code is
reprinted in Appendix 6.4.
The Interpolation Method takes the avalanche regime of the photodiode l-V curve and
interpolates a straight line towards the voltage axis. The intercept is the breakdown voltage:
*+ 1
Calculated Voltage
Breakdown
- V + V
v-l
Figure 4.1.1: Breakdown Voltage via Interpolation Method
53
The Current Threshold Method defines the breakdown voltage by setting a certain current
threshold. Because this research deals with different variations of device designs, this method is
only useful if comparing photodiodes that has similar magnitudes on the l-V graph:
Calculated Voltage
Breakdown
^L + v?-
v-l
Figure 4.1.2: Breakdown Voltage via Threshold Method
4.1.2 Dark Current
Dark current is the current that flows in the photodiode when no incident light is present.
Intrinsically, dark current is a function of temperature and the amount of reverse voltage. Dark
current arises due to electrons having enough energy from thermal and lattice vibrations to jump
from the valence band to the conduction band. If the reverse bias is high enough, these jumps
result in a cascading avalanche situation.
54
Dark current can also be controlled using special device designs. One simple way to reduce dark
current is to merely reduce the size of the active area of the photodiode, reducing the number of
electrons jumping bands.
In this research, dark current is determined from the current-voltage (l-V) plot. For the l-V plot of
each photodiode tested, a voltage sweep was done with no incident light. Dark current is usually
specified at a certain reverse voltage, typically at the designed operating voltage. Since this
research consists of different designs and sizes, a dark current number will be quoted at the
defined breakdown voltage.
Figure 4.1.3: Defined Dark Current
55
4.1.3 Gain
The definition of gain for a photodiode is the ratio of the total multiplied output current to the
primary unmultiplied photocurrent:
M = -
Equation 4.1: Photodiode Gain, M
I is the multiplied current that is output from the detector. Ip is the photocurrent that is generated
during the absorption of photons into the device. Where:
(
p ^-Vo[l-e(asW)](1-Rf)yhVj
Equation 4.2: Primary Photocurrent, lP
Where q is the electronic charge in [C], h is Planck's constant [J*s], v is the photon momentum
[Hz], P0 is the incident optical power [W], a is the absorption coefficient of the photodiode
material [1/m], w is the depletion width [m] inside the semiconductor, and Rf is the surface
reflectivity percentage.
In examining Equation 4.2, lP is already taking into account the reflectivity of the photodiode
surface, incident optical power, wavelength, and absorption into the device. Therefore, Equation
4.1, M, only deals with the gain that is produced internally inside the photodiode.
56
Since gain is also a function of bias voltage, the gain at breakdown voltage will be used to quote
a gain specification.
4.1 .4 Responsitivity
Responsitivity is a measure of how well the photodiode converts incident light into current. A
higher responsitivity means that the photodiode is more sensitive to light and would yield a higher
electrical output than one with a lower responsitivity. Responsitivity is defined as:
R-i-
Po
Equation 4.3: Responsitivity, R
Where lP is the primary photocurrent (same as Equation 4.2) and P0 is the incident optical power.
If the equation was written out to the basic properties, responsitivity is a function of photon
energy, absorption coefficient of the material, depletion width of the p-n junction, and the optical
power loss due to reflection:
R = fj-][l-e(asW)](1-Rf)
Equation 4.4: Functions of Responsitivity
Responsitivity is a function of wavelength. As mentioned in Section 2.1 .2.1, different
semiconductor materials would have different absorption coefficients of wavelengths. For silicon,
57
it stops absorbing light beyond 1 100nm due to the incident photons not having enough energy to
excite an electron to jump the 1 .12eV band gap. Responsitivity will be quoted at 600nm.
4.1 .5 Crosstalk Plot
The arrays of four photodiodes were used to test for crosstalk. The first photodiode was
connected to the measurement equipment while each photodiode was individually illuminated one
at a time (i.e. one through four). The current output, defined at a specific voltage bias that is
particular to the arrays tested, was compared at each illumination. Knowing the distance
between the four photodiodes, a signal output versus distance plot was obtained (see Figure
4.3.1). To have the plot meaningful, the output signals are normalized to the first photodiode.
The following figure illustrates how a perfectly isolated crosstalk and a poorly isolated crosstalk
plot should look like:
Perfectly Isolated
1 oo% -
D
Q.
o
I 50%
1_
o
0%
2 3
Pixel
1 00%
D.
O
50%
o
0%
Poorly Isolated
~i 1 r
1 2 3
Pixel
Figure 4.1.4: Theoretical Crosstalk Plots
58
4.2. Single APD Results and Comparison to Commercial Devices
Typical to both research and manufacturing, some of the devices fabricated performed as
expected and some did not. Most of the devices suffered at least one of the following problems:
no signal, uncontrolled voltage breakdown, and low responsitivity. Those issues are discussed in
detail in Section 4.4.
Because of the number of imperfect photodiodes, a judgment needed to be made in order to
determine which photodiodes to test. Ideally, the current-voltage (l-V) plot should look similar to
the one as shown in Figure 4.2.1. That figure also shows how most photodiodes look like, where
the transition into the avalanche breakdown regime is not sharp but a gradual slope:
v-l
Acceptable l-V Curve
t-i
Unacceptable l-V Curve
Figure 4.2.1 : Acceptable and Unacceptable APD Current-Voltage Curves
59
With each wafer containing more than 121 dies, two dies were chosen to be tested. Within each
die, five different photodiode sizes were tested, with each photodiode being randomly selected
within each size.
Of the five different device structure variations (APD02-1 through APD02-5), the fourth wafer
(APD02-4) represents the standard planar reach-through structure. Photodiode [W4 C7,3
D200,20,300,Y] will be used to discuss the analysis in detail. In addition, specifics of other
photodiodes will be shown as appropriate. Appendix 6.5 contains the complete graphs of all 42
photodiodes tested. Using the figures of merit as defined in Section 4.1 as a metric for
comparison, six photodiodes were considered acceptable. Here is the summary of the results:
CellBreakdown
Voltage [V]
Dark Current
[uA]Gain
Responsitivity
[AAV]
NEP
[HW]
W1 C5,6D1500,50,0,Y -1.244 -38.7 1513 0.199 0.195
W2C6,8C1500,50,0,Y -1.346 -73.8 2413 0.199 0.371
W3C11,10D200,20,300,Y -0.451 -3.4 1332 0.199 0.017
W4 C7,3 D200,20,300,Y -7.624 -2484 22677 0.280 8.870
W4 C7,3 D200,30,400,N -5.2 -10.4 188 0.272 0.038
W5C9,10D400,20,500,N -50.43 -63 19053 0.307 0.205
Table 4.1: Tested Photodiodes Results
60
4.2.1 l-V Curve
Photodiode [W4 C7,3 D200,20,300,Y] has a diameter of 200um and a 20u.m width aluminum
guard ring, located on wafer 4 on die 7,3. Its l-V curve is:
I.00 -6.00
Voltage Bias [V]
2.00 0.00
Figure 4.2.2: l-V Plot (W4 C7,3 D200,20,300,Y)
Denoting lo as the full optical power used in the test set-up, it shows the curves at no light (dark),
3% light (0.03 lo), 33% light (0.33 lo), and full power (lo) as described in test set-up in Section
3.4. Full optical power (lo) was approximately 486nW/cm2.
61
Coincidentally, this photodiode exhibited the highest current output of all tested photodiodes. The
high current output is most likely due to non-uniformity issues during fabrication and is not due to
design. This is proven because a similar photodiode on the same wafer with roughly the same
device geometry [W4 C7,3 D200,30,400,N] happen to exhibit the lowest current output of the
group.
The typical output of an APD that is commercially fabricated has the following l-V curve:
<
C
o
<DVI
>
DC
10^
10*
10^
10-'
10-
10"
10"
Input power
Pin=0.3^W
20 40 60 80 100
Reverse voltage Vh(V)
Figure 4.2.3: l-V Plot (Mitsubishi PD8XX2 Series Photodiode) [Mitsubishi, 1997]
Note that this graph shows the reverse voltage and reverse current as a positive scale. Of the
tested photodiodes in this research, one photodiode [W4 C7,3 D200,30,400,N] exhibited the
closest response:
62
-10.00 -6.00 -4.00
Voltage Bias [V]
Figure 4.2.4: l-V Plot (W4 C7,3 D200,30,400,N)
4.2.2 Breakdown Voltage
For [W4 C7,3 D200,30,400,N], the voltage breakdown (Vbr) was determined by using the
Interpolation Method:
63
2000
-2000
-4000
o--6000
3
o
-8000
-10000
-12000
-14000
T
-14.00 -12.00 -10.00 8.00 -6.00
Voltage Bias [V]
-4.00 -2.00
-Dark
-Dark Vbr
-0.03IO
-0.03 lo Vbr
0.33 lo
-0.33 lo Vbr
-lo
-loVbr
0.00
Figure 4.2.5: l-V Plot with Breakdown Voltage Interpolation Lines (W4 C7,3 D200,20,300,Y)
Because Vbr is slightly different depending on the light intensity, the overall Vbr number was
obtained by averaging the four curves. Ideally, Vbr should be the same at all light intensities. The
Vbr for this photodiode is at -7.624V.
As mentioned earlier that a typical diode should have a sharp transition into the avalanche
regime, of all the photodiodes tested [W5 C9.10 D400,20,500,N], showed the most defined
transition:
64
2000
-2000
S -4000
a-6000
3
o
-10000
-12000
'VJJSWK5J.
'/
1 /4
V
)
-Dark
-Dark Vbr
- 0.03 lo
-0.03 lo Vbr
0.33 lo
-0.33 lo Vbr
-lo
-loVbr
-70.00 -60.00 -50.00 -40.00 -30.00 -20.00
Voltage Bias [V]
-10.00 0.00 10.00
Figure 4.2.6: l-V Plot with Breakdown Voltage Interpolation Lines (W5 C9,10 D400,20,500,N)
It's also noted that [W5 C9,10 D400,20,500,N], and wafer 5 in general, showed devices with the
highest breakdown voltage. Although wafer 5 devices do not have the advantage of having a
guard ring, which prevents a premature low voltage breakdown at the junction periphery, it
benefits from having a simpler design. It's also possible that wafer 5 unintentionally had a lower
doping concentration; a result of processingnon-uniformity.
Commercial avalanche photodiode devices have a much higher breakdown voltage, typically over
80V. The devices in this research were designed to have lowbreakdown voltages, but at a
65
tradeoff of making the photodiodes perform more like a Zener diode, which is explained in
Section 4.4.2.
4.2.3 Dark Current
Using the Vbr as the operating voltage, the dark current (ldark) at Vbr is -2484u.A for [W4 C7,3
D200,30,400,N]:
5
-5
1-10
3-153Q.
3
o -20
oo
QO
1 -25
0.
-30
-35
-12.00 -10.00 -8.00 -6.00 -4.00
Voltage Bias [V]
-2.00 0.00 2.00
Figure 4.2.7: Dark Current (W4 C7,3 D200,30,400,N)
66
The expected trend of dark current is that the higher the reverse bias voltage, more dark current
will be present. Since dark current arises from mobile electrons gaining energy from lattice
vibrations, at higher reverse bias voltages, these electrons might initiate a cascading avalanche
situation.
4.2.4 Gain
Quoting gain (M) at Vbr as the operating voltage, the gain of [W4 C7,3 D200,30,400,N] is 22677:
CD
o
o : 1 1 1 1 T 1
-14.00 -12.00 -10.00 -8.00 -6.00
Bias Voltage fV]
-4.00 -2.00 0.00
Figure 4.2.8: Gain (W4 C7,3 D200,20,300,Y)
67
The general trend of this gain curve is similar in all the photodiodes tested. Comparing to gain
curves as released by Perkin Elmer, photodiode [W4 C7,3 D200,30,400,N] comes closest to their
data:
KHMI
ioo
10
I'iliiton ( Jiinliut:
MM)
ioo
"Standard"
Structure At*l>
200 300
ffi*(\)
400 5(10
Figure 4.2.9: Gain (Perkin Elmer)
68
E
c
m
0 -
-12.00 -10.00 i.00 -6.00
Bias Voltage [V]
-4.00 -2.00
Figure 4.2.10: Gain (W4 C7,3 D200,30,400,N)
It is noted here again that Figure 4.2.9 shows the reverse bias voltage as a positive scale while
data generated from this research uses the convention of plotting the reverse bias voltage as a
negative scale.
The fabricated devices have higher gain output than commercial devices. This is due to the high
doping level used, which resulted in a high electric field around the p-n junction region.
69
4.2.5 Spectral Response
Plotting the spectral response curve of photodiode [W4 C7,3 D200,20,300,Y], its peak is around
500nm:
15t>-
>*
>
to
coQ.n
rr
153- i i i i i i i i i i i i i i i i
400 450 500 550 600 650
Wavelength [nm]
700 750 800
Figure 4.2.1 1 : Responsitivity vs.Wavelength (W4 C7,3 D200,20,300,Y)
The peak of this photodiode is lower than typically measured in the rest of the photodiodes
tested. The typical response of the photodiodes are closer to photodiode [W5 C9.10
D400,20,500,N], where the peak is around 600nm:
70
288
400 450 550 600 650
Wavelength [nm]
700 800
Figure 4.2.12: Responsitivity vs.Wavelength (W5 C9,10 D400,20,500,N)
The peak of the spectral response can be tailored by changing the impurity junction depth into the
device. As explained in Section 2.1 .2.1 ,longer wavelengths are absorbed deeper into the silicon.
If the long wavelengths are absorbed beyond the depletion region, the electron-hole pair has a
much higher chance to recombine before it is swept into the depletion region.
In comparing to commercial devices,the fabricated devices in this research tend to have the
spectral peak at a lower wavelength. Most commercial devices are around 800nm.
71
4.2.6 Responsitivity
The responsitivity is calculated at unity gain (M = 1) is 0.2801AAV, which is equivalent to a
quantum efficiency (QE) of 0.580 electrons per photon. See Appendix 6.5 for responsitivity to QE
conversion details. The responsitivity is quoted at 600nm wavelength:
0.70
0.60
0.50
< 0.40
Q. 0.30
o
c
0.10
0.00
^
- ' -
'- 1
r-. *-i.
R@ 1.0QE
R @ 0.9QE
R @ 0.8QE
R @ 0.7QE
R @ 0.6QE
R @ 0.5QE
R @ 0.4QE
- R 0.3QE
R @ 0.2OE
R @ 0.1QE
400 450 500 550 600 650
Wavelength [nm]
700 800
Figure 4.2.13: Responsitivity @ M=1 (W4 C7,3 D200,20,300,Y)
Examining the responsitivity of commercially available photodiodes, the responsitivity should
peak close to 1000nm, near the energy band gap of silicon:
72
1.0
0,8->-
0.6 +
0.4 +c
oQ_CO
(1)
K 0.2+
Theoretical Silicon Photodiode
Practical Silicon Photodiode
Abrupt Break
Linear tnea&&
With Wavelencth -
200 400 600 800
Wavelength (nm)
1000
Figure 4.2.14: Practical Silicon Photodiode Responsitivity [Kruger, 2002]
Section 4.4.3 will discuss the details of why the photodiodes tested have low responsitivity.
4.2.7 Noise Equivalent Power
Noise Equivalent Power (NEP) is defined as the signal power required to achieve a unitysignal-
to-noise ratio within a one second integration. For this research, the equation is:
NEP= dark
Equation 4.5: Noise Equivalent Power (NEP)
Where ldark is the dark current [A] and R is the responsitivity [AMI].
73
The noise equivalent power (NEP) of [W4 C7,3 D200,20,300,Y] at Vbr is 0.00887W. As expected,
note that as the gain of the photodiode increases, the NEP increases somewhat linearly:
5.0E-02
4.5E-02
4.0E-02
3.0E-02
2.5E-02
2.0E-02
1.5E-02
1.0E-02
5.0E-03
O.OE+00
10000 20000 30000 40000 50000
Gain (M)
60000 70000 80000 90000 100000
Figure 4.2.15: Noise Equivalent Power (NEP) (W4 C7,3 D200,20,300,Y)
4.3. APD Array Results
In designing APD arrays, one area of concern is the crosstalk between individual elements.
Because APDs operate on the nature of internal gain, there is a higher chance of crosstalk
between pixels than compared to, as an example, regular PIN photodiode arrays. The random
74
paths of the electrons during the avalanche mechanism may possibly wander into the adjacent
pixel and trigger a signal there instead.
The simplest solution to the problem would be to increase the distance between pixels as far as
possible. Unfortunately, this would decrease the spatial resolution of the array. Another solution,
which is beyond the scope of this research, is to use device structures that would minimize the
lateral fields of a photodiode, possibly by having the same equipotential as the pixels themselves
[Webb and Mclntyre, 1984].
From just spatially spacing the arrays of photodiodes, this research shows that the signal is not
perfectly isolated and that there is a certain level of crosstalk as a function of distance.
Since only a few arrays were found to be fully successful, data was not complete in characterizing
the APD array design. The following arrays were found to be successfully working:
Array 1:[W1 C11,10 D400,20,750,N]
Array 2:[W3 C5,8 D400,20,750,N]
Array 3:[W4 C5,6 D400,20,750,N]
Array 4:[W4 C10.9 D200,20,300,N]
In mapping the crosstalk plot as described in Section 4.1.5, this is the result:
75
-W1 C11,10D400,20,750,N
-W3C5,8D400,20,750,N
W4 C5,6 D400,20,750,N
- W4 C10.9 D200,20,300,N
500 1000 1500
Pixel Distance (Center to Center) [um]
2000 2500
Figure 4.3.1 : Crosstalk Plot
Arrays 1 to 3 have the same pixel to pixel distance, 750u.m. Array 4 has a pixel to pixel distance
of 300u.m. Arrays 1 to 3 exhibit the same general response and are somewhat in agreement at a
distance of 750u.m. The plot also suggests that the guard ring features do lower crosstalk and
minimize lateral fields as Array 4 shows.
76
4.4. Problems of Non-Working Devices
The major challenge of this research was to have working, uniform photodiodes to test. As
discussed in Section 3.5, the basis for the lack of performance from the fabricated devices were
due to wrong doping levels, namely for the p layer. The effect was that, although it performed
somewhat similar to true APDs, it had many"characteristics"
that were not favorable.
Specifically, the avalanche photodiodes did not perform as expected for at least one of the
following reasons:
1. No signal.
2. Low sensitivity.
3. Uncontrolled voltage breakdown.
4. Low responsitivity.
5. Performance uniformity.
4.4.1 No Signal
In order to connect to the photodiodes, the needle probes make contact to the metal pads, which
are 100u.m x 100u.m in size. When trying to connect to some photodiodes, it is apparent that the
connection could not be made, as there was no current flow at any voltage level.
The reason is simple; the metal interconnect from the metal pad to the photodiode has
discontinuities. The most likely places of discontinuities are either along the thin interconnect
from the pad to the photodiode (Figure 4.4.1), or at the junctionnear the photodiode edge (Figure
4.4.2):
77
Figure 4.4.1 : Metal Discontinuity Example Figure 4.4.2: Metal Discontinuity Example
A B
The metal layer, fabricated using aluminum, was wet etched. Although both discontinuities are a
result of overetching, the break in the thin interconnect is a result from having too small of a
geometry in width and the junction break is from step height differences between the layers.
Referring to the cross-section of the device (Figure 3.1.3), there is a large step height from the
top of the oxide to the photodiode edge. When depositing the aluminum layer via sputtering, it is
subject to step coverage problems, where the aspect ratio from the top of the oxide to the top of
the silicon bulk may be too great. This leads to thinning of the aluminum at the edge and it would
be etched faster than the rest of the layer [Wolf and Tauber, 1 986]. The oxide thickness in these
wafers was approximately -4950A thick.
78
4.4.2 Uncontrolled Voltage Breakdown
Most APDs tested exhibited a very soft knee during transition into the avalanche regime, as
illustrated in Figure 4.2.1. This makes determining the breakdown voltage difficult and uncertain.
This characteristic is typically known as"soft"
breakdown and is an indication that there is a
presence of tunneling current occurring [Forrest, et. al., 1980], [Laifer and Gilad, 2002].
Tunneling current occurs in a diode when both sides of the p-n junction are so heavily doped that
the depletion width is less than 10'6cm. To have such small depletion widths, the lighter doped
side of the p-n junction would still be in excess of approximately 1017/cm3. This causes the width
of the potential energy barrier to become very thin. As Section 2.1 .3.1 described, another way for
current to flow in reverse bias besides the avalanche mechanism is by the Zener process, where
the particle tunnels through the energy barrier instead of gaining additional energy to overcome it.
This is a quantum mechanical phenomenon and doesn't have a classical equivalent.
One device that utilizes the tunneling current mechanism is the Zener diode. It was found that
the devices in this research were inadvertently designed similarly to Zener diodes; the p-n
junction was degenerately doped. A low breakdown voltage was desired, which is typical of
Zener diodes. In order to achieve low breakdown voltages, heavily doped p-n junctions are
needed, which triggered the whole tunneling current situation and resulting in the"soft-
breakdown found in the l-V curves of the devices of this research.
79
4.4.3 Low responsitivity
Responsitivity values are obtained indirectly through calculations from measured values of the
photodiodes. Compared to commercial devices, the photodiodes in this research have a much
lower responsitivity, especially at the longer wavelengths.
In this research, the depletion width of the p-n junction is what causes the low responsitivity.
Here is the responsitivity equation reprinted:
R = f-f )[i-e(-a*w)](1-Rf)
Equation 4.6: Reprint of Equation 4.4
The equation used to calculate the depletion width (w) is based on a linearly degraded junction
model:
W =
qa
Equation 4.7: Depletion Width, Linearly Graded Junction
The built-in voltage, Vbi, is solved by iteration using the following equation:
80
.. 2kT .
vki = lnDl n
2a fl2K t VI t-
i\s CQ |hi
2n,v.
qa'bi
Equation 4.8: Built-in Voltage, Linearly Graded Junction
Where a is the grading constant. Details of Equation 4.7 and Equation 4.8 are shown in
Appendix 6.6. With the photodiodes in this research having a peak doping of 2.635*1023/cm3
at a
junction depth of 0.0731 u.m for n+ implant, and a peak doping of 1 .975*1023/cm3
at a junction
depth of 0.2801 u.m for P+ implant (see Section 3.2.2), the typical grading constant is
3.1 88*1 027/cm4. Because of the heavy doping levels of the multiplication region (namely the p
layer that was too heavily doped), the depletion width is a thin 0.00542nm at an applied voltage of
5.2V, making the responsitivity of the devices very low.
A chip designer has only two parameters to control, without changing the material used, in order
to control responsitivity: depletion width and surface reflectivity of light (Rf). A designer can
improve responsitivity by merely getting more light into the silicon. Or rather, decrease the
surface reflectivity of the light. This involves fabricating an anti-reflection coating on top of the
photodiodes and other standard practices that are not concentrated by this research.
The other is to increase the depletion width. As the depletion width is increased in Equation 4.4,
responsitivity increases. The effect is morepronounced at longer wavelengths, due to increased
absorption coefficient, lower reflectivity and higher photon energy at the longer wavelengths.
81
As an example, if diode [W5 C9.10 D400,20,500,N] had a depletion width of 0.108p.m instead of
0.0108|im (biased at the breakdown voltage of -50.43V), the responsitivity would have increased
as such:
0.70-
^
-
'
-
-
"-
_
-
'
-
'
_-
-
~
"
--
*"
~-
~
._
-
"
"
-
-
_.-
-
_-
-
^"^-N^^
-
^^--,^'^_-
*- '
__
_-
--
-
f1-'
_-
-
"""
f-"
_- -
-**
--
-
_-
--
-"
_-
-""
0.00 - 1 1 1 1 1 1 1 1
< Responsitivity
R @ 1.0QE
R @ 0.9QE
R @ 0.8QE
R @ 0.7QE
R @ 0.6QE
R @ 0.5QE
R @ 0.4QE
- - R @ 0.3QE
R @ 0.2QE
R @ 0.1QE
400 450 500 550 600 650
Wavelength [nm]
700 750 800
Figure 4.4.3: Responsitivity @ M=1 (W5 C9.10 D400,20,500,N) (@ 0.01 \im Depletion Width)
82
0.70
0.60
< 0.40
a- 0.30
0.20
0.10
0.00
400 450 500 550 600 650
Wavelength [nm]
700 750
? Responsitivity
R @ 1.0QE
R @ 0.9QE
R @ 0.8QE
R @ 0.7QE
- - R @ 0.6QE
R @ 0.5QE
R @ 0.4QE
R @ 0.3QE
R @ 0.2QE
R @ 0.1QE
800
Figure 4.4.4: Responsitivity @ M=1 (W5 C9,10 D400,20,500,N) (@ 0.1 nm DepletionWidth)
The depletion width is controlled by the amount of doping used.
4.4.4 Performance Uniformity
Even when the devices exhibited a general l-V curve of a photodiode, there was an issue of
having the devices performuniformly. As an example, photodiodes [W4 C7,3 D200, 20, 300, N]
and [W4 C10,9 D200, 20, 300, N] are of the same dimensionson the same wafer. Their l-V
curve is widely different:
83
-16.00 -14.00 -12.00 -10.00 1.00 -6.00 -4.00 -2.00 0.00
-200
-400
-600
-800
-1000
-1200
-1400
1600
-W4C7.3
-W4C10,9
Voltage [V]
Figure 4.4.5: [W4 C7,3 D200,20,300,N] and [W4 C10,9 D200,20,300,N] Comparison @ 100%
Illumination
By just looking at the differences in the breakdown voltage suggests that implant doping levels in
the p-n junction are very different. Figure 2.1 .1 8 shows how doping levels affect the breakdown
voltage. At breakdown voltages of a few volts, as in the case of [W4 C7,3 D200,20,300,N] and
[W4 C10,9 D200,20,300,N], a significant change in doping is needed in order for a small amount
of voltage change.
As previous sections have described, the doping level is an integral part of the device
characteristic as it affects an avalanchephotodiodes'
responsitivity, gain, photon absorption, etc.
84
4.5. Solutions for Improvement
The following are solutions that rectify the problems outlined in the previous sections and improve
on the design. These steps are follow-up suggestions for any future research.
4.5.1 Lower Doping Levels / Correct P Layer Doping
In order to have correct working APDs, the doping levels should be lower. Specifically, the
fabricated devices had too high of a doping for the p layer. As mentioned in Section 3.5, the
highly doped p layer had effectively contained the depletion layer to just between the n+ and p
layers. If the p layer was doped lighter, then the depletion layer could extend into the intrinsic
layer when under sufficient reverse bias. Beyond the incorrect device designed, the high doping
also made the devices exhibit a"soft"
breakdown voltage and have a low responsitivity.
The devices exhibit"soft"
breakdown due to excessive tunneling current taking place. If the
doping levels are lowered, the depletion width would increase and the width of the energy barrier
would be wider, decreasing the chance of tunneling and breakdown would occur more due to
avalanching. A wider depletion width would also increase responsitivity. As discussed in Section
4.4.3, the depletion width would be the only factor that a device designer would have easy control
over.
The original intention of the design was to have an avalanche photodiode with a low breakdown
voltage for portability reasons. In order to have low breakdown voltages high doping levels are
85
needed. Unfortunately, a design tradeoff exists between low voltage breakdown and having the
occurrence of tunneling current.
4.5.2 Fabrication Control and Uniformity
To realize a design of an avalanche photodiode array, good fabrication control is needed. The
performance of the devices in this research was subject to fabrication problems, mainly uniformity
problems. The two fabrication processes that would improve the current devices dramatically
would be the aluminum etch process and implant process.
Devices that did not work because of no signal showed obvious problems with the aluminum
interconnect (see Figure 4.4.1 and Figure 4.4.2). The process used to etch the aluminum was a
wet etch. Because wet etch is an isotropic etch, where it etches uniformly in all directions, sharp
corners of the interconnects erode quicker due to a larger exposed surface area. A more suitable
etch to use in future research is an aluminum etch that is anisotropic.
The design variations between the five wafers are not extreme in differences. As Table 3.1 listed
out, the variations are either to have a guard ring, an extra P layer, or a different metal layer. The
only element that would affect an individual photodiode's performance would be the extra P layer.
In testing the devices, it was found that device characteristics varied widely from wafer to wafer
and even within wafer. As an example,Wafer 5 exhibited the highest breakdown voltages in
general. Yet, with the exception of having a guard ring, it is identical toWafer 4. Figure 4.4.5
illustrates the variability within wafer. The differences in breakdown voltage indicate that the
doping levels are different. The breakdown voltage change between -8V and -12V are
significant, where the doping levels are almost an order of magnitude in difference.
86
5. Conclusion
The original direction of this research was to realize an avalanche photodiode array device with
an onboard discriminator circuit for readouts. The array would be controlled via computer I/O and
possibly be portable for in-the-field use.
To reach that stage, several intermediate steps were needed. The first step is to have working
individual APDs since that has not been designed or fabricated at the RIT Microelectronic Fab.
As this research shows, the first attempt in the design and fabrication needed improvement, as it
has been found that the doping levels were incorrect.
Individual devices did not function mainly due to design error problems. In the pursuit of
designing the devices to be usable in portable applications, low breakdown voltages were
needed. To achieve the low breakdown voltages, high doping levels were needed for the p-n
junction. In doing that, the devices ran into two major problems, current tunneling and low
responsitivity. Both problems are attributed to having too high of a doping for the p layer,
resulting in a too small of a depletion width that didn't extend into the intrinsic region. As the
device is put under increased reverse bias, current tunneling occurs, where reverse current
started trickling before the actual breakdown.This decreased the ability for the device to have a
clear on/off current output. Low responsitivity, especially at higher wavelengths, is also mainly
caused by the small depletion width.
87
Once individual photodiodes are properly designed, fabricating arrays of working photodiodes
present another hurdle. During testing of the photodiodes in this research, it was concluded that
process uniformity, especially within wafer, need to be better controlled. The two main areas to
concentrate for improvement is the aluminum etch and implant processes.
In order to reach the ultimate goal of having an APD array with onboard discriminators, device
design and fabrication control need to be improved. After the design and fabrication issues of the
above are addressed, the next steps of research would be to either integrate the onboard
discriminators and/or enhance the performance of the APD array by increasing the spatial density
of the photodiodes.
88
6. Appendix
6.1.Oxide Thickness Calculation
Oxide Growth Calculation [44](For Diffusion-Rate Limited Regime in Wet Oxidation on Bare Silicon)
Constants are for (100) Process parameters.
silicon in wet oxidation.
Kl := 4.0210"6
[um] t := 1.53 M
El := 1.29 [eV] T := 1273 [K]
K2:=214 [um2/hr]
E2:=0.71 [eV]
k:= 8.6175[eV/K]
El
k TA:=Kle
-E2
k T
B:=K2e
"(t)J 4B )
X = 0.4991 [urn]
89
6.2. Ion Implant and Drive-In Calculation
Guard Ring Impurity Profile
Constants:
eV:=1.610 19J
-5eV
k:= 8.617-103
K
x :=0,0.01- 10_6m.. 1.5 10"6m
Electron Volt
Boltzmann Constant
Depth
Wafer Parameters:
Nb(x):=11014cm3
Background Doping
Implant Parameters:
Rp:= 0.073 10 m
dRp:= 0.0305 10 m
N':=1.61018-cm"2
Projected Range
Projected Straggle
Implant Dose
Diffusion Parameters:
D0:= 03.85^-
s
Ea:=3.66eV
Tl := 1273K
tl := 4.5hr
T2:=1223K
t2 := 2.3hr
Frequency Factor [Boron(0.76), Phos(3.85)]
Activation Energy [Boron(3.46), Phos(3.66)]
Diffusion Temperature 1
Diffusion Time 1
Diffusion Temperature 2
Diffusion Time 2
90
Implant Calculation:
N'
Nxrp:=
V5c-dRp
1%= 2.093x
1023
Peak Concentration [N(x=Rp)]
Ni(x) := N^-e
2dRp2
Impurity Profile After Implant
Drive-in Calculation:
Dl:=DekTl
D2:=D0e
Nd(x) :=-
-E,
kT2
N'
Diffusion Coefficient
2J_dRp2+2(Dltl+D2t2)]
V2~7t->/dRp2+ 2(Dltl + D2t2)
Impurity Profile After Drive-in
Nd(0) = 2.795x1022 Surface Doping Concentration
xj:= i <r- 0m
19 -3
while | Nd(i) -
Nb(i)| >MO1
m
i<-i + MO m
xj= 1.417X 10 mJunction Depth
91
Profile Graph:
Guard Ring Impurity Profile
I 10
610 810Depth 1m]
Implant Profile
Diffusion Profile
Background DopingOverall Impurity Profile
92
N+ / P+ Impurity Profile
Constants:
eV:=1.610"19J Electron Volt
-5eV
k:= 8.617 105
K
Boltzmann Constant
x:=0,0.0110"6m.. 1.5106m Depth
Wafer Parameters:
Nb(x):=11014cm3
Background Doping
Implant Parameters:
Rp, := 0.073 10 m
dRpl:= 0.0305 10 m
N'l:=5.2-1018cm2
Projected Range
Projected Straggle
Implant Dose
Diffusion Parameters:
2cm
Dol :=03.85-
Eai:=3.66eV
Tl := 1223K
Frequency Factor [Boron(0.76), Phos(3.85)]
Activation Energy [Boron(3.46), Phos(3.66)]
Diffusion Temperature
tl := 2.3hrDiffusion Time
93
Implant Calculation:
N'lN.xrpl
^2ridR,Pi
N^^e^xio23-^-
cm
Nil(x) := Nxrpl-e2dRD
Peak Concentration [N(x=Rp)]
Impurity Profile After Implant
Drive-in Calculation:
Dl:=Dole
-Eai
k-Tl
Dl = 3.181x 10
Ndl(x) :=
15 cm
N'l
V^-JdRp?
Diffusion Coefficient
2-(dRpl2+2Dltl)
+ 2-Dl-tl
Ndl(O) = 1.714X1023
xjl:=
cm
i <r- 0m
19 -3
while |Ndl(i) -
Nb(i)| > 110 m
i<-i+ 110 9m
xjl=5.91x 10 m
Impurity Profile After Drive-in
Surface Doping Concentration
Junction Depth
94
P+ Impurity Profile
Implant Parameters:
Rp2:=0.28-10 m
dRp2:= 0.064 10 6m
N'2:=5.2-1018-cm2
Projected Range
Projected Straggle
Implant Dose
Diffusion Parameters:
Do2:=0.76-cm
Frequency Factor [Boron(0.76), Phos(3.85)]
E^:= 3.46 eV Activation Energy [Boron(3.46), Phos(3.66)]
T2 := 1223K Diffusion Temperature
t2 := 2.3hr Diffusion Time
95
Implant Calculation:
N'2N.xip2
V^Tt-dR,P2
Nxrp2 = 3.241xlO23-^
cm
Ni2(x) := Nxrp2-e2dR,P2
Peak Concentration [N(x=Rp)]
Impurity Profile After Implant
Drive-in Calculation:
-Ea2
D2:=Do2ek-T2
D2 = 4.19x10"15cm
Nd2(x) :=N'2
Nd2(0) = 5.658x1021
2(dRp22+2D2t2j
dRp2 + 2D2t2
cm
xj2:= i <- 0m
19 -3
while | Nd2(i) -
Nb(i)| > 110 m
i -H 1- 10 m
xj2=9.66x 10 m
Diffusion Coefficient
Impurity Profile After Drive-in
Surface Doping Concentration
Junction Depth
96
N+ / P+ Profile Calculations
PNJuncDepth := i < Om
while Ndl(i) > (1.001- Nd2(i)) v Ndl(i) < (0.999 Nd2(i))
-10
i < i -H 110 ium
PNJuncDepth = 1.73x 10"7m
Ndl (PNJuncDepth) = 1.176x1029
3m
Nd2(PNJuncDepth) = 1.1 76x1029
NdlPeak:= i^O
while Ndl(i) > Ndl(i- 10T10m)
i <- i + 10 10m
NdlPeak=7.31x 10"8m
Nd2Peak := i<-0
while Nd2(i) > Nd2U - 10"10m)
i+10-10m
Nd2Peak = 2.801 x 10 m
Ndl(NdlPealc) = 2.635x1029
m
Nd2(Nd2Peak) = 1.975x1029
m
(Ndl(NdlPeak)- Nd2(Nd2Peak))
NdlPeak- Nd2Peak
a = -3.188x1035
4m
Grading Constant
97
Profile Graph:
N+ Diffusion Profile
P+ Diffusion Profile
Background DopingOverall Impurity Profile
98
6.3. Fabrication Steps
1 . Scribe (APD02-X)1.1. APD02-1
1.2. APD02-2
1.3. APD02-3
1.4. APD02-4
1.5. APD02-5
2. RCA Clean (APD02-X)
3. Field Oxide (APD02-x)3.1. Target thickness: 5kA
3.2. Recipe #350 on Bruce Furnace
3.2.1. Push @ 800C, 12in/min., N23.2.2. Ramp up to 1 1 00C, dry 023.2.3. Soak 21Omin, wet 023.2.4. Ramp down to 800C, N23.2.5. Pull @ 12in/min.
4. Photolithography - Guard Ring (APD02-1,2,4)
5. Etch - Oxide (APD02-1,2,4)
5.1. Expected oxide thickness to etch: 5kA
5.2. EtchinBHF
5.3. Etch rate: ~1kA/min.
5.4. Etch time: ~5 min.
6. Implant - Guard Ring (APD02-1,2,4)
6.1. Target Xj: 1.4u.m
6.1.1. Energy: 60keV
6.1.2. Dose: 1.6*1018/cm2
6.1.3. Species: P31
7. Resist Strip (APD02- 1,2,4)
8. Diffusion - Guard Ring Drive-In (APD02-1,2,4)
8.1. Temp: 1000C
8.2. Time: 4.5 hours
8.2.1 . (6.5 hours would yield an Xj of 1u.m, but there is a following thermal step of 1 hour
@ 950C)
9. Photolithography- N+ Region (APD02-x)
10. Etch - Oxide (APD02-x)
99
10.1. Expected oxide thickness to etch: 4.5kA
10.2. EtchinBHF
10.3. Etch rate: ~1kA/min.
10.4. Etch time: -4.5 min.
10.4.1. Leave ~500A oxide as sacrificial oxide during implant.
11. Implant -N+(APD02-x)
11.1. Target Xj: 0.5u.m
11.1.1. Energy: 60keV
11.1.2. Dose: 5.2* 1018/cm2
11.1.3. Species: P31
12. Resist Strip (APD02-X)
13. Photolithography- P+ Region (APD02-4,5)
14. Implant - P+ (APD02-4,5)14.1. Target Xj: 1u.m
14.2. Energy: 90keV
14.3. Dose: 5.2* 1018/cm2
14.4. Species: B
15. Resist Strip (APD02-4,5)
16. Diffusion - N+/P+ Drive-In / Anneal (APD02-x)16.1. Temp:950C
16.2. Time: 2.3 hours
17. Etch -Oxide (APD02-X)1 7.1 . Expected oxide thickness to etch: 0.5kA
17.2. Etch in BHF
17.3. Etch rate: ~1kA/min.
17.4. Etch time: -0.5 min.
18. Aluminum Sputter (APD02-1,3,4,5)18.1 . Target thickness: 2kA
18.2. Material: AI/1% Si
18.3. Power: 2kW
18.4. Time: 10min.
19. CVD - Polysilicon (APD02-2)19.1. Target thickness: 1 kA
20. Photolithography - Aluminum (APD02-x)
21. Etch - Aluminum (APD02-1,3,4,5)21.1. Standard procedure
22. Plasma Etch - Polysilicon (APD02-2)
100
22.1 . Gases: SF6 @ 42sccm, 02 @ 7.5sccm
22.2. Pressure: 400mT
22.3. Power: 40W
22.4. Time: 40 sees.
23. Resist Strip (APD02-x)
24. Aluminum Sinter (APD02- 1,3,4,5)24.1. Standard Recipe
24.1.1.Temp:450C
24.1.2. Gas:N2/H2
24.1.3. Time: 15-30min.
101
6.4.Third-Order Polynomial Fit Algorithm in Microsoft Visual Basic 6.0
Option Explicit
Option Base 1
Public sDatal) As Single
Public sCoeffArrO As Variant
Public Function ReadDataFile (strFileName As String)
Dim iFileNum As Integer
Dim strLinelnput As String
Dim iRow As Integer
Dim iCol As Integer
Dim iRowUB As Integer
Dim iColUB As Integer
Dim sTempArrO As Single
Dim i , j
iFileNum FreeFile
ReDim sData(50, 50)
Open strFileName For Input As #iFileNum
iRow 0
Do Until E0F(1)
Line Input ((iFileNum, strLinelnput
iRow iRow + 1
If iRow >= iRowUB Then iRowUB = iRow
'Data file should be a comma delimited file.
'Tagging line with a'
,
'
to make string parsing MUCH easier in next section.
strLinelnput strLinelnput +"
,
"
iCol 0
Do Until strLinelnput
iCol iCol + 1
If iCol >= iColUB Then iColUB iCol
sDatadCol, iRow) - Val (Left (strLinelnput , InStr (strLinelnput ,
"
,
"
) 1))
strLinelnput Mid (strLinelnput, InStr (strLinelnput ,
"
,
"
) + 1)
Loop
Loop
Close liFileNum
'Resize sDataO array to streamline memory. Swap with temp array to keep data.
ReDim Preserve sTempArr (iColUB, iRowUB)
For i 1 To iColUB
For j 1 To iRowUB
sTempArrfi, j) sDatad, j)
Next jNext i
ReDim sDatadColUB, iRowUB)
For i 1 To iColUB
For j 1 To iRowUB
sData ( i , j ) sTempArr ( i , j )
Next jNext i
End Function
Public Function CalcDataO'First col are X values, following cols are Y values for each respective curve.
Dim RegObj As New RegressionObject
Dim sIThres As Single
Dim sCalcI As Single
Dim sPrevCalcI As Single
Dim sVoltStep As Single
102
Dim i , j , k
ReDim sCoef fArr (UBound(sData ( ) , 1), 9)
sCoeffArrd, 1) "Poly Coeff A"
sCoeffArrd, 2) "Poly Coeff B"
sCoeffArrd, 3) "Poly Coeff C"
sCoeffArrd, 4) "Poly Coeff D"
sCoeffArrd, 5) "2nd Deriv Coeff A"
sCoeffArrd, 6) "2nd Deriv Coeff B"
sCoeffArrd, 7) = "Max Grad Vbr"
SCoeffArrd, 8) "ThresVbr"
SCoeffArrd, 9) = "Vbr"
RegObj .Degree 3
'Calculate the coefficients of the 3rd order polynomial.
For i 2 To UBound(sData( ) , 1)
RegObj . Init
For j = 1 To UBound ( sData ( ) , 2)
'Add data to RegObj. When done grab coefficients from it.
RegObj . XYAdd sData ( 1 , j ) , sData ( i , j )
Next j'Grab coefficients from RegObj. will be 4 coefficients.'
[x"3 is SCoeffArrd, 1) or RegObj . Coeff (3 ) ]'[const is sCoeffArrd, 4) or RegObj .Coeff (0) ] , etc.
For k 1 To 4
sCoeffArrd, 1) = RegObj .Coeff (3)
sCoeffArrd, 2) = RegObj .Coeff (2)
sCoeffArrd, 3) = RegObj . Coeff (1)
sCoeffArrd, 4) RegObj . Coeff ( 0)
Next k
Next i
'Calculate the coefficients of 2nd derivative and voltage point of max gradient.
For i 2 To UBound ( sData ( ) , 1 )
sCoeffArrd, 5) 6 *sCoeffArrd, 1)
sCoeffArrd, 6) 2 *
sCoeffArrd, 2)
sCoeffArrd, 7) -sCoeffArrd, 6) / sCoeffArrd, 5)
Next i
End Function
Public Function WriteOutputFile (strOutputFileName As String)
Dim iFileNum As Integer
Dim i, j
iFileNum FreeFile
Open strOutputFileName For Output As #iFileNum
For j 1 To UBound(sCoeffArrl) , 2)
For i = 1 To UBound ( sData () , 1)
Print #iFileNum, sCoeffArrd, j) & ","
;
Next i
Print #iFileNum," "
Next j
Close #iFileNum
End Function
Option Explicit
Private Const MaxOi 2 5
Private GlobalOi' "Ordnung" = degree of the polynom expected
Private Finished As Boolean
Private SumX#(0 To 2 *MaxO)
Private SumYX#(0 To MaxO)
Private M#(0 To MaxO, 0 To MaxO + 1)
Private C#(0 To MaxO) 'coefficients in: Y C(0)*X~0 + C(1]'X"1 + C(2)*X~2 +...
Private Sub GaussSolve (0&)
'gauss algorithm implementation,
103
'followingR.Sedgewick'
s "Algorithms in C", Addison-Wesley, with minor modifications
Dim ii, j&, ki, iMax&, T#, 01#
01 Otl
'first triangulize the matrix
For i = 0 To 0
iMax = i: T Abs(M(iMax, i) )
For j i + 1 To 0 'find the line with the largest absvalue in this row
If T < Abs(M(j, i)) Then iMax j: T AbslMdMax, i))
Next j
If i < iMax Then 'exchange the two lines
For k i To 01
T Md, k)
M(i, k) = M(iMax, k)
MdMax, k) T
Next k
End If
For j i + 1 To 0 'scale all following lines to have a leading zero
T M(j, i) / M(i, i)
M(j, i) 0#
For k : i + 1 To 01
M(j, k) M(j, k) Md, k)* T
Next k
Next jNext i
'then substitute the coefficients
For j 0 To 0 Step -1
T = M(j, 01)
For k = j + 1 To 0
T T M(j, k)*
C(k)
Next k
C(j) T / M(j, j)
Next jFinished True
End Sub
Private Sub BuildMatrix(Oi)
Dim ii, ki, Oli
01 0 + 1
For i = 0 To 0
For k 0 To 0
M(i, k) = SumXd + k)
Next k
M(i, 01) SumYX(i)
Next i
End Sub
Private Sub Final izeMatrix(Oi)Dim i&, Oli
01 0 + 1
For i 0 To 0
Md, 01) SumYX(i)Next i
End Sub
Private Sub SolvedDim 0&
0 GlobalO
If XYCount <= 0 Then 0 = XYCount 1
If 0 < 0 Then Exit Sub
BuildMatrix 0
On Error Resume Next
GaussSolve (0)
While (Err.Number <> 0) And (1 < 0)Err.Clear
CIO) 0#
0-0 1
FinalizeMatrix (0)Wend
On Error GoTo 0
End Sub
Private Sub Class_Initialize ( )
104
Init
GlobalO 2
End Sub
Public Sub Initl)
Dim i&
Finished False
For i = 0 To MaxO
SumX(i) = 0#
SumX(i + MaxO) 0#
SumYX(i) = 0#
C(i) 0#
Next i
End Sub
Public Property Get Coeff # (Exponents.)
Dim Ex&, 0&
If Not Finished Then Solve
Ex Abs (Exponent )
0 = GlobalO
If XYCount <= 0 Then 0 XYCount 1
If 0 < Ex Then Coeff 0# Else Coeff C(Ex)
End Property
Public Property Get Degrees O
Degree GlobalO
End Property
Public Property Let Degree(NewVal&)
If NewVal < 0 Or MaxO < NewVal Then
Err. Raise 6000,"RegressionObject"
, NewVal &"
is an invalid property value! Use 0<= Degree <="
&
MaxO
Exit Property
End If
Init
GlobalO NewVal
End Property
Public Property Get XYCounti ( )
XYCount = CLng ( SumX ( 0 ) )
End Property
Public Function XYAddlByVal NewX# , ByVal NewY#)
Dim ii, j&, TX#, Max20i
Finished - False
Max20 2 * GlobalO
TX 1#
SumX(O) SumX(O) + 1
SumYX(O) = SumYX(O) + NewY
For i 1 To GlobalO
TX TX* NewX
SumXd) SumX(i) + TX
SumYX(i) = SumYXd) + NewY* TX
Next i
For i GlobalO + 1 To Max20
TX TX * NewX
SumXd) SumXd) + TX
Next i
End Function
Public Function RegVal#(X#)
Dim i&, 0&
If Not Finished Then Solve
RegVal 0#
0 = GlobalO
If XYCount <= 0 Then 0 XYCount 1
For i 0 To 0
RegVal RegVal + C(i)* X
"
i
Next i
End Function
105
6.5. Responsitivity to Quantum Efficiency Conversion Calculation
Responsitivity to Electrons / Photon Conversion
Parameters: Constants:
R:= 0.2801
W
X := 60010~9m
eV_per_sec :=R W
eV
eV_per_sec = 1.751x 1018A
h:= 6.626 10 34Js
c := 2.9979245810
eV:= 1.610 19C
E:=he
E=3.311x 10 19J
photons_per_sec :=
E
photons_per_sec =3.021x1018 S
kgm
x:=-eV_per_sec
photons_per_sec
x =0.580
kgm A[electrons / photon]
106
6.6. Depletion Width and Built-in Voltage Calculation
PN Junction Electrostatics of a Linearly Graded Junction
Constants:
eV:=1.610"19J
q:=1.610"'9C
rij:= 110 cm
T := 300K
_5eV
k:= 8.617 105
K
1 cm 1
xn:=M0_6s
up:=331-
cm |
-6
S
Ks:=ll.
-14F
e:=8.8510
Electron Volt
Charge
Intrinsic Carrier Concentration
Temperature
Boltzmann Constant
Electron Mobility (@ Nd = 10A17/cm3)
Electron Minority-Carrier Lifetime (Average)
Hole Mobility (@ Na = 10*17/0713)
Hole Minority-Carrier Lifetime (Average)
Dielectric Constant of Silicon
Permittivity of Free Space
Sub-Calculations:
( k-T^IUn"{.Tj
K
(DP MtJ
Lp =p? tp
Electron Diffusion Coefficient
Electron Diffusion Length
Hole Diffusion Coefficient
Hole Diffusion Length
Device Parameters:
N - l 9391023 Acceptor Concentration
a-
3cm
NH := 2.4841023 Donor Concentration
VA:=-5.2V Applied Voltage
: 3.188lf/W4
Grading Constant
107
Calculations:
Vguess0:=0.5V
2-k-TVguess(f+i):= In
f:=0.. 10
2-nj
'l2-Ks-e0 VVguessf
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Vbi := Vguess 10
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213
qa-(vbi-vA)
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x Electrostatic Potential
Electric Field
Charge Density
108
6.7. Photodiode Test Data
6.7.1 Raw l-V Graphs
The following graphs are the raw l-V test results of the APD arrays constructed for this research.
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The following tables are the raw numerical data from the l-V graphs of Section 6.7.1
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34.55 -32.55 -40.95 -77.51
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6.624 -9.B32 -27.6
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-104 1 -13B-T -51Z.7
-75.6 -252-8
-34.57 -42.87 -161.8
-32.95 39 42 -140
IV DMs - Water s .ti (Pag* 1 ol 2)
-39630
-4637
2457
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4990 5108
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119.6 -1334 166.9 -153 8
-7B12 -83 66 -92 13 -78.SS
-10.31 -55.23 -58 99 -50
-10240 14 10540.65 -10550 12 -13253 91
9171 BS1 9204 117 -12153.61
-7740 142 6079 117
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-83.9617 126 4512 370 4166 -3444 915
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-8 761704 18 05117 -35.2068 -1446.915
3.2S917S -4S7 1147
-02641 417186 -26 7898 -260 7147
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0134532 643903 10 53488 -101 6775
19 27784 -100 6276
43 12811 8.636596 -1B0925 -99 44177
41125754 O 632516 -10 93228
-0120735 0.62B1B3 16 67439 -97 17535
-0.11779 O 6347TB 1841057 -96 00644
-0113962 0 620709 18 24674 95 02074
47111205 O 617081 1799596 S396587
-0106696 0.612105 17 69458 -92 7356
* 103023 -0.609296 1743443 -9143036
-0101355 0 606003 -90 4285
-0 096852 O.6O08SB 16.96496 -89.22125
-0.092916 0.598293
-0 08924 0 59371 16 54676 -86.9797
41067363 0.590S23 1E3G484 -85 85701
-0OB291B 0.586687 16 15534
-0 079922 O.S81B71 IS.84699 -83 66751
4)075985 0 578862 -8237657
O 574901 1 .30926 8143037
O 71668 IS 14198 -B0 17065
41064883 0 566414 14 90162 -79.06724
41062S24 0 563371 14 69568 -77*6703
4)058469 0.559379 14 45541 -76 86365
-0 055033 0 555B35 14.23767 -75 77481
-0 05182B -0 55245 13 947B
-0 048679 0 548712 13.74221 -73 42534
-0 045357 -0.54558 13.51061 -72.24342
-0 041211 13.27738 -7106077
-0 036099 0 536051 13 04821 -70 06621
-0 033565 0.533347 12.B5072 438*6976
0 030042 0S291B7 -12.5652 417*0075
0 027182 0 526159 12.31964 416 5548
4)024273 0 521118
4)01384 4)5178 -11.99 -64 48
0 013O4 -0 5176 11 68 -633
0 013*4 4) SI 76 -1154 -62 16
0134 -0 5176 1126
-0 01384 -0.5178 -59 64
-O013B4 -0.5170 10 92 S7 73
0 01384 0.5176 -10 62 -27 37
-O0I3B4 -0 5176 9 642 9614
-0 013*4 4)5176 3 105 -2.627
4)01384 -0 5178 -0 6459 4)5817
-0 01384 a 01035 0 02591 0 00066
0 01384 0 6543 128 1 179
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-5834 11560 13050
-3019 SO52 -6951
-1200 -3146 -4070
3361 1460
1298
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12 16 -49 31 261 a
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2199
V Data - Wale' 5 IPbqs 2 of 2)
6.7.3 Figures ofMerit Analysis of Selected Photodiodes
The following are figures of merit calculation of selected photodiodes discussed in this research
paper.
170
Cell: W1 C5,6 D1500,50,0,Y
Breakdown Voltage: -1 .244 [V]
Dark Current (@ Vbr): -38.7 [uA]
Gain (@ Vbr): 1513
Responsitivity (@ 600nm, 2V Bias): 0.199 [A/W]
NEP (@ Vbr): 0.000195 [W]
Analysis (W1 C5,6 D1500,50,0,Y).xls (Page 1 of 12)
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Cell 5,6 5, 6 5,6 5,6
Diameter [um] 1500 1500 1500 1500
Guard Ring [um] 50 50 50 50
Pixel Dist [um] 0 0 0 0
Metal Ring Y Y Y Y
Illumination [%] Dark 0.03 lo 0.33 lo lo
Bias Voltage [V] -3.00 -331.9 -343.3 -610.8 -855.4
-1.360 -0.822 -9.8492 -122.109 0.1592
-1.356 -0.0212 -9.04232 -120.918
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-0.950 -0.044
Curve Fit a
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Analysis (W1 C5,6 D1500,50,0,Y).xls (Page 10 of 12)
q=
1.60E-19[C]h = 6.63E-34 [J s]
c = 3.00E+08 [mis]wavel = 6.00E-07 [m]v = 5.00E+14 [Hz]Po @ 600i 4.86E-07 [W]w = 2.69E-06 [m]R @ 600m 0.3538 [%]a@600nr 3.75E+05 [1/m]
lp = 9.65E-08 [A]
QE = 0.4104
Vbias [V] Idark [A] I [A] Inorm [A] M R @ 1 [AA>NEP [W]-3.00 -3.32E-04 -8.55E-04 9.65E-08 8862.437 0.1986 1.67E-03
-2.75 -2.76E-04 -7.12E-04 9.65E-08 7372.586 0.1986 1.39E-03
-2.50 2.26E-04 -5.82E-04 9.65E-08 6034 0.1986 1.14E-03
-2.25 -1.82E-04 -4.67E-04 9.65E-08 4842.533 0.1986 9.15E-04
-2.00 -1.39E-04 -3.68E-04 9.65E-08 3813.728 0.1986 7.00E-04
-1.75 -1.02E-04 -2.84E-04 9.65E-08 2946.548 0.1986 5.16E-04
-1.50 -6.92E-05 -2.12E-04 9.65E-08 2192.298 0.1986 3.48E-04
-1.25 -3.92E-05 -1.47E-04 9.65E-08 1527. 149 0.1986 1.98E-04
-1.00 -1.61E-05 -9.00E-05 9.65E-08 932.0374 0.1986 8.09E-05
-0.75 -3.66E-06 -4.35E-05 9.65E-08 450.6851 0.1986 1.84E-05
-0.50 -1.88E-07 -1.40E-05 9.65E-08 145.2553 0.1986 9.47E-07
-0.25 -1.52E-08 -2.63E-06 9.65E-08 27.26904 0.1986 7.63E-08
0.00 4.45E-09 8.28E-08 9.65E-08 -0.857856 0.1986 2.24E-08
0.25 -9.00E-09 3.37E-08 9.65E-08 -0.349048 0.1986 4.53E-08
0.50 1.12E-08 -3.43E-08 9.65E-08 0.355782 0.1986 -5.64E-08
Analysis (W1 C5,6 D1500,50,0,Y).xls (Page 11 of 12)
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Analysis (W2 C6,8 D1500,50,0,Y).xls (Page 1 of 12)
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Guard Ring [um] 50 50 50 50
Pixel Dist [um] 0 0 0 0
Metal Ring Y Y Y Y
Illumination [%] Dark 0.03 lo 0.33 lo lo
Bias Voltage [V] -3.00 -535.5 -573.2 -897.9 -1336
-1.472 0.16816 -17.5299 -186.189 -46.5192
-1.423 0.12772 -163.437 -5.4278
-1.417 -160.651 -0.3962
-1.071 0.00328
Curve Fit a
b
2nd Derivative
c
d
a
b
VbrMax Gradient
Threshold Vbr
Linear Trend Vbr -1.472 -1.423 -1.071 -1.417
Voltage Breakdown Vbr -1.346 -1 .34575 -1.34575 -1.34575
Analysis (W2 C6,8 D1500,50,0,Y).xls (Page 10 of 12)
q= 1.60E-19 [C]
h = 6.63E-34 [J s]
c = 3.00E+08 [m/s]wavel = 6.00E-07 [m]v = 5.00E+14 [Hz]Po @ 600l 4.86E-07 [W]w = 2.69E-06 [m]R @ 600ni 0.3538 [%]a@600nr 3.75E+05 [1/m]
lp = 9.65E-08 [A]
QE = 0.4104
ias [V] Idark [A] I [A] Inorm [A] M R@ 1 [AAfNEP [W]-3.00 -5.36E-04 -1.34E-03 9.65E-08 13841.73 0.1986 2.70E-03
-2.75 -4.37E-04 -1.11E-03 9.65E-08 11500.24 0.1986 2.20E-03
-2.50 -3.52E-04 -9.01E-04 9.65E-08 9332.807 0.1986 1.77E-03
-2.25 -2.75E-04 -7.07E-04 9.65E-08 7323.891 0.1986 1.38E-03
-2.00 -2.07E-04 -5.41E-04 9.65E-08 5599.892 0.1986 1.04E-03
-1.75 -1.49E-04 -4.01 E-04 9.65E-08 4153.555 0.1986 7.49E-04
-1.50 -9.90E-05 -2.89E-04 9.65E-08 2992.134 0.1986 4.98E-04
-1.25 -5.80E-05 -1.98E-04 9.65E-08 2052.43 0.1986 2.92E-04
-1.00 -2.70E-05 -1.26E-04 9.65E-08 1300.252 0.1986 1.36E-04
-0.75 -7.20E-06 -6.96E-05 9.65E-08 720.8889 0.1986 3.62E-05
-0.50 -1.10E-07 -3.01E-05 9.65E-08 311.5425 0.1986 5.52E-07
-0.25 -3.67E-08 -6.60E-06 9.65E-08 68.36944 0.1986 1.85E-07
0.00 1.48E-08 -8.14E-08 9.65E-08 0.843247 0.1986 -7.46E-08
0.25 -9.71E-09 4.03E-08 9.65E-08 -0.417117 0.1986 4.89E-08
0.50 5.02E-09 -9.40E-09 9.65E-08 0.097389 0. 1986 -2.53E-08
Analysis (W2 C6,8 D1500,50,0,Y).xls (Page 11 of 12)
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NEP (@ Vbr): 1 .7E-05 [W]
Analysis (W3 C11.10 D200,20,300,Y).xls (Page 1 of 12)
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Cell 11, 10 11, 10 11, 10 11, 10
Diameter [um] 200 200 200 200
Guard Ring [um] 20 20 20 20
Pixel Dist [um] 300 300 300 300
Metal Ring Y Y Y Y
Illumination [%] Dark 0.03 lo 0.33 lo lo
Bias Voltage [V] -3.00 -824.7 -866.9 -1198 -1680
-0.796 -0.04044 -31.0136 -291.177 -368.75
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-0.209 -50.1485 -0.11991
-0.087 -0.05407
Curve Fit a
b
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c
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a
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Analysis (W3 C11.10 D200,20,300,Y).xls (Page 10 of 12)
q=
1.60E-19[C]h = 6.63E-34 [J s]
c = 3.00E+08 [m/s]wavel = 6.00E-07 [m]v= 5.00E+14 [Hz]Po @ 600r 4.86E-07 [W]w = 2.69E-06 [m]R @ 600m 0.3538 [%]a @ 600nr 3.75E+05 [1/m]
lp = 9.65E-08 [A]
QE = 0.4104
Vbias [V] Idark [A] I [A] Inorm [A] M R @ 1 [AA/NEP[W]-3.00 -8.25E-04 -1.68E-03 9.65E-08 17405.77 0.1986 4. 15E-03
-2.75 -7.16E-04 -1.57E-03 9.65E-08 16297.19 0.1986 3.61E-03
-2.50 -6.12E-04 -1.46E-03 9.65E-08 15167.88 0. 1986 3.08E-03
-2.25 -5.18E-04 -1.34E-03 9.65E-08 13893.53 0. 1986 2.61E-03
-2.00 -4.16E-04 -1.18E-03 9.65E-08 12246.2 0.1986 2.09E-03
-1.75 -3.26E-04 -1.00E-03 9.65E-08 10356.43 0.1986 1.64E-03
-1.50 -2.45E-04 -8.11E-04 9.65E-08 8405.536 0.1986 1.23E-03
-1.25 -1.71E-04 -6.25E-04 9.65E-08 6478.468 0.1986 8.62E-04
-1.00 -1.04E-04 -4.48E-04 9.65E-08 4636.358 0.1986 5.25E-04
-0.75 -4.56E-05 -2.86E-04 9.65E-08 2967.269 0.1986 2.29E-04
-0.50 -4.21 E-06 -1.50E-04 9.65E-08 1555.123 0.1986 2.12E-05
-0.25 -1.83E-08 -4.00E-05 9.65E-08 414.2158 0.1986 9.20E-08
0.00 -3.13E-08 -5.74E-07 9.65E-08 5.948007 0. 1986 1.58E-07
0.25 -5.29E-08 4.52E-08 9.65E-08 -0.468194 0. 1986 2.66E-07
0.50 -2.88E-08 -4.99E-08 9.65E-08 0.516889 0. 1986 1.45E-07
Analysis (W3 C11.10 D200,20,300,Y).xls (Page 11 of 12)
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Cell: W4 C7,3 D200,20,300,Y
Breakdown Voltage: -7.624 [V]
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Responsitivity (@ 600nm): 0.2801 [A/W]
NEP (@ Vbr): 0.00887 [W]
Analysis (W4 C7,3 D200,20,300,Y).xls (Page 1 of 12)
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Wafer 4 4 4 4
Cell 7, 3 7, 3 7, 3 7, 3
Diameter [um] 200 200 200 200
Guard Ring [um] 20 20 20 20
Pixel Dist [um] 300 300 300 300
Metal Ring Y Y Y Y
Illumination [%] Dark 0.03 lo 0.33 lo lo
Bias Voltage [V] -72.00 -12410 -12460 -12700 -12940
-11.50 -10850 -10910 -11150 -11390
-11.00 -9354 -9398 -9649 -9933
-10.50 -7932 -7986 -8255 -8561
-10.00 -6654 -6685 -7003 -7287
-9.50 -5531 -5545 -5871 -6193
-9.05 -4571 -4573 -4909 -5207
-8.47 -3720 -3722 -4066 -4349
-7.99 -2966 -3002 -3328 -3578
-7.50 -2321 -2353 -2681 -2920
-7.00 -1779 -1814 -2147 -2344
-6.46 -1337 -1374 -1689 -1850
-6.00 -977 -1014 -1303 -1438
-5.50 -697.7 -733.7 -974.3 -1089
-5.00 -483.6 -512.5 -712.8 -804.7
-4.51 -320.7 -346.5 -497 -571.5
-4.00 -222.8 -228.2 -329.4 -389.6
-3.50 -170.4 -166.1 -209 -254.1
-3.00 -126.5 -122 -130.4 -160.4
Analysis (W4 C7,3 D200,20,300,Y).xls (Page 9 of 12)
Wafer4 4 4 4
Cell 7, 3 7, 3 7, 3 7,3
Diameter [um] 200 200 200 200
Guard Ring [um] 30 30 30 30
Pixel Dist [um] 400 400 400 400
Metal Ring N N N N
Illumination [%] Dark Vbr 0.03 lo Vbr0.33 lo Vbr loVbr
Bias Voltage [V] -12.00 -12410 -12460 -12700 -12940
-7.729 0.106 -18.9092 -403.936 -774.883
-7.722 1.3544 -383.932 -755.094
-7.588 -0.9864 -376.276
-7.455 -0.285
Curve Fit a
b
2nd Derivative
c
d
a
b
VbrMax Gradient
Threshold Vbr
Linear Trend Vbr -7.729 -7.722 -7.588 -7.455
Voltage Breakdown Vbr -7.624 -7.624 -7.624 -7.624
Analysis (W4 C7,3 D200,20,300,Y).xls (Page 10 of 12)
q=
h =
c =
wavel =
v =
1.60E-19 [C]
6.63E-34 [J s]
3.00E+08 [m/s]6.00E-07 [m]5.00E+14 [Hz]
Po @ 600i 4.86E-07 [W]w = 6.02E-06 [m]R @ 600m 0.3538 [%]a @ 600nr 3.75E+05 [1/m]
lp = 1 .36E-07 [A]
QE 0.5787
Vbias [V] Idark [A] I [A] Inorm [A] M R @ 1 [AA>NEP [W]-12.00 -1.24E-02 -1.29E-02 1.36E-07 95073.31 0.2801 4.43E-02
-11.50 -1.09E-02 -1.14E-02 1.36E-07 83685.09 0.2801 3.87E-02
-11.00 -9.35E-03 -9.93E-03 1.36E-07 72980.16 0.2801 3.34E-02
-10.50 -7.93E-03 -8.56E-03 1.36E-07 62899.74 0.2801 2.83E-02
-10.00 -6.65E-03 -7.29E-03 1.36E-07 53539.35 0.2801 2.38E-02
-9.50 -5.53E-03 -6.19E-03 1.36E-07 45501.47 0.2801 1.97E-02
-9.05 4.57E-03 -5.21E-03 1.36E-07 38257.09 0.2801 1.63E-02
-8.47 -3.72E-03 -4.35E-03 1.36E-07 31953.16 0.2801 1.33E-02
-7.99 -2.97E-03 -3.58E-03 1.36E-07 26288.43 0.2801 1.06E-02
-7.50 -2.32E-03 -2.92E-03 1.36E-07 21453.95 0.2801 8.29E-03
-7.00 -1.78E-03 -2.34E-03 1.36E-07 17221.94 0.2801 6.35E-03
-6.46 -1.34E-03 -1.85E-03 1.36E-07 13592.4 0.2801 4.77E-03
-6.00 -9.77E-04 -1.44E-03 1.36E-07 10565.33 0.2801 3.49E-03
-5.50 -6.98E-04 -1.09E-03 1.36E-07 8001.147 0.2801 2.49E-03
-5.00 -4.84E-04 -8.05E-04 1.36E-07 5912.326 0.2801 1.73E-03
-4.51 -3.21E-04 -5.72E-04 1.36E-07 4198.949 0.2801 1.15E-03
-4.00 -2.23E-04 -3.90E-04 1.36E-07 2862.486 0.2801 7.96E-04
-3.50 -1.70E-04 -2.54E-04 1.36E-07 1866.934 0.2801 6.08E-04
-3.00 -1.27E-04 -1.60E-04 1.36E-07 1178.498 0.2801 4.52E-04
Analysis (W4 C7,3 D200,20,300,Y).xls (Page 11 of 12)
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Cell: W4 C7,3 D200,30,400,N
Breakdown Voltage: -5.2 [V]
Dark Current (@ Vbr): -10.4 [uA]
Gain (@ Vbr): 188
Responsitivity (@ 600nm): 0.272 [A/W]
NEP (@ Vbr): 3.83E-05 [W]
Analysis (W4 C7,3 D200,30,400,N).xls (Page 1 of 12)
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Cell 7, 3 7, 3 7, 3 7, 3
Diameter [um] 200 200 200 200
Guard Ring [um] 30 30 30 30
Pixel Dist [um] 400 400 400 400
Metal Ring N N N N
Illumination [%] Dark 0.03 lo 0.33 lo lo
Bias Voltage [V] -10.00 -35.9 -37.71 -41.8 -56.1
-9.50 -31 -32.56 -35.9 -50
-9.05 -27.4 -28.7 -31.7 -45.8
-8.47 -23.7 -24.7808 -27.3 -41.8
-7.99 -21 -21.9 -24.2 -38.5
-7.50 -18.82 -19.48 -21.5 -35.6
-7.00 -16.72 -17.48 -19.1 -32.9
-6.46 -14.71 -15.5028 -17 -30.3
-6.00 -13 -13.85 -15.3 -28.1
-5.50 -1 1 .37 -12.14 -13.8 -26.1
-5.00 -9.75 -10.52 -12.3 -23.9
-4.51 -8.42 -9.08 -10.7361 -22.2
-4.00 -7.1 -7.6928 -9.47393 -20.5
-3.50 -5.94 -6.22 -8.3 -18.6
-3.00 -4.973 -5.063 -6.96 -16.7
-2.50 -3.84 -4.033 -5.865 -15.01
-2.00 -2.784 -3.06 -4.64 -13.24
-1.50 -1.757 -1.995 -3.34 -11.3
-1.00 -0.7186 -0.9749 -2.263 -9.723
-0.50 -0.1643 -0.3023 -1.809 -8.701
0.00 0.04135 -0.07548 1.851 5.689
0.50 0.3052 0.728 2.658 6.611
Analysis (W4 C7,3 D200,30,400,N).xls (Page 9 of 12)
Wafer 4 4 4 4
Cell 7, 3 7,3 7, 3 7, 3
Diameter [um] 200 200 200 200
Guard Ring [um] 30 30 30 30
Pixel Dist [um] 400 400 400 400
Metal Ring N N N N
Illumination [%] Dark Vbr 0.03 lo Vbr0.33 lo Vbr loVbr
Bias Voltage [V] -10.00 -35.421 -37.218 -41.2 -55.354
-5.63 -0.70091 -0.38555 -0.0004 -14.7206
-5.59 -0.33455 0.003099 -14.2919
-5.54 -0.00078 -13.9012
-4.05 0.003171
Curve Fit a 2.57E-02 2.95E-02 0.05806 0.100617
b 6.70E-02 0.119131 0.546536 1.382015
c 1.626956 1 .924237 3.85923 9.477178
d 0.18952 0.284974 1.012613 0.922955
2nd Derivative a 0.154212 0.177134 0.34836 0.6037
b 0.133921 0.238261 1 .093072 2.76403
Max Gradient Vbr -0.86842 -1.34509 -3.13777 -4.57848
Threshold Vbr
Linear Trend Vbr -5.63 -5.59 -5.54 -4.048
Voltage Breakdown Vbr -5.2 -5.2 -5.2 -5.2
Analysis (W4 C7,3 D200,30,400,N).xls (Page 10 of 12)
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q= 1.60E-19 [C]
h = 6.63E-34 [J s]
c = 3.00E+08 [m/s]
wavel = 6.00E-07 [m]
v = 5.00E+14 [Hz]
Po @ 600l 4.86E-07 [W]
w = 5.42E-06 [m]
R @ 600ni 0.3538 [%]
a@600nr 3.75E+05 [1/m]
lp = 1 .32E-07 [A]
QE= 0.5615
sM Idark [A] I [A] Inorm [A] M R @ 1 [AA> NEP [W]
10.00 -3.59E-05 -5.61 E-05 1.32E-07 424.77 0.2717 1.32E-04
-9.50 -3.10E-05 -5.00E-05 1.32E-07 378.59 0.2717 1.14E-04
-9.05 -2.74E-05 -4.58E-05 1.32E-07 346.79 0.2717 1.01E-04
-8.47 -2.37E-05 -4.18E-05 1.32E-07 316.50 0.2717 8.72E-05
-7.99 -2.10E-05 -3.85E-05 1.32E-07 291.51 0.2717 7.73E-05
-7.50 -1.88E-05 -3.56E-05 1.32E-07 269.55 0.2717 6.93E-05
-7.00 -1.67E-05 -3.29E-05 1.32E-07 249.11 0.2717 6.15E-05
-6.46 -1.47E-05 -3E-05 1.32E-07 229.42 0.2717 5.41E-05
-6.00 -1.30E-05 -2.8E-05 1.32E-07 212.77 0.2717 4.78E-05
-5.50 -1.14E-05 -2.6E-05 1.32E-07 197.62 0.2717 4.18E-05
-5.00 -9.75E-06 -2.4E-05 1.32E-07 180.96 0.2717 3.59E-05
-4.51 -8.42E-06 -2.2E-05 1.32E-07 168.09 0.2717 3.10E-05
-4.00 -7.10E-06 -2.1 E-05 1.32E-07 155.22 0.2717 2.61E-05
-3.50 -5.94E-06 -1.9E-05 1.32E-07 140.83 0.2717 2.19E-05
-3.00 -4.97E-06 -1.7E-05 1.32E-07 126.45 0.2717 1.83E-05
-2.50 -3.84E-06 -1.5E-05 1.32E-07 113.65 0.2717 1.41E-05
-2.00 -2.78E-06 -1.3E-05 1.32E-07 100.25 0.2717 1.02E-05
-1.50 -1.76E-06 -1.1 E-05 1.32E-07 85.56 0.2717 6.47E-06
-1.00 -7.19E-07 -9.7E-06 1.32E-07 73.62 0.2717 2.64E-06
-0.50 -1.64E-07 -8.7E-06 1.32E-07 65.88 0.2717 6.05E-07
0.00 4.14E-08 5.69E-06 1.32E-07 -43.08 0.2717 -1.52E-07
0.50 3.05E-07 6.61 E-06 1.32E-07 -50.06 0.2717 -1.12E-06
Analysis (W4 C7,3 D200,30,400,N).xls (Page 12 of 12)
Cell: W5C9,10D400,20,500,N
Breakdown Voltage: -50.43 [V]
Dark Current (@ Vbr): -63 [uA]
Gain (@ Vbr): 19053
Responsitivity (@ 600nm, 2V Bias): 0.307 [AMI]
NEP (@ Vbr): 0.000205 [W]
Analysis (W5 C9.10 D400,20,500,N).xls (Page 1 of 12)
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Water 4 4 4 4
Cell 7, 3 7, 3 7, 3 7, 3
Diameter [um] 200 200 200 200
Guard Ring [um] 20 20 20 20
Pixel Dist [um] 300 300 300 300
Metal Ring Y Y Y Y
Illumination [%] Dark 0.03 lo 0 33 lo la
Bias Voltage [V] -60 00 -10240 1 -10540.7 -10550 1 -13253 9
-59 00 4888 14 -9171.65 -9204.12 -12153.9
-56 00 -7740.14 -8039.65 -8079 12 -11043.9
-57 00 -6561 14 -6869.65 -6925.12 -9618.91
-56 00 -5356.14 -5661.65 -5732.12 -8751.91
-55 00 -114614 -4441.65 -4537.12 -7689.91
-54 00 -2970.14 -3234.65 -3376.12 -6618.91
-53 00 -1621.14 -206665 -2251.12 -554831
-52.00 -714.542 -1024 65 1236 12 -448791
-51 00 -83 9617 -126 451 -370.417 -344431
-50 00 -J7.1517 -58.3512 -98.0168 -2393.91
-49 00 4.7617 -18.0512 352068 -144631
-46.00 -0.3786 -125917 -27 327B -457 115
-47 00 -0.2841 -0.7186 -26.7898 -260.715
-4600 -0.1854 -0.6845 -234578 -138.435
-45.00 -0.1417 -0.65117 -20 1168 -103.915
-44 00 -0.13943 -0.64744 -193268 -102.872
43 00 0.13453 -0.6439 -193349 -101.677
4100 0.13185 -0.64046 -192776 -100.628
41 -0.12811 -0.6366 -19.0925 -99.4418
-40 -0.12575 -0.63252 -185323 -98.4024
39 -0.12074 -0.62818 -18.6744 -97.1753
-38 -011779 -0.62472 -184106 -96.0064
-31 -0.11398 -0.62071 -182467 -95.0207
-36 -0.1112 -0.61709 -17.996 -93.8659
-35 -0.1067 -0.6121 -17.6946 -92.7356
34 -010302 -0.6093 -17.4344 -914304
-33 -0.10136 -0 606 -172627 -90 4285
-32 -0.09685 4.60089 -16.985 -892212
31 -0.09292 0.59829 -16.8371 88.D411
-30 -0.08924 -0.59371 -163468 -86 9797
-29 -0.0B736 -0.59082 -16.3648 -85B57
-28 -0.08292 -0.58669 -16.1553 -84 7748
-27 -0.07992 -0.58187 -15.B47 -83.6675
26 -0.D7599 -0.57666 -15.6151 -82.3796
-25 -0JJ72B4 0.5749 -153093 -81.4304
-24 -0.06812 -0.57169 -15.142 -80-1707
-23 -0.06488 -0.56641 -143016 -79.0672
-22 -0.06252 -0.56337 -14.6957 -77.867
-27 -0.05847 -0.55938 -14.4555 -76.6637
-20 -0.05503 -0.55593 -142377 -75.7746
-19 -0.05183 -055245 -133478 -74 4817
16 -0.D4868 -034871 -13.7422 -73 4253
-17 0 04536 -0.54556 -133106 -722434
-16 -0.04121 -0.54004 -132774 -71 0608
15 -0.0361 -0.53605 -13.0482 -70.D862
-14 -0.03356 -0.53335 -123507 -68B898
-13 -0.03004 -032919 -123652 -673008
12 0.02718 -032616 -12.3196 -665548
11 -0.02427 -0.52112 -12.1054 -65.466
-10 -0.01384 -0.5176 -11.99 -64 48
9 -0.01384 -03176 -11 66 -63.3
-e -0.01384 -05176 -11.54 -62.18
-7 0 01384 -0.5176 -1126 -61.08
-6 -0.01384 -05176 -11.1 -59.64
5 -0.01384 -05176 -1092 -5773
4 -0.01384 -0.5176 -10.62 -27 37
3 -0.01384 -0.5176 -9 642 -9614
2 -0J31384 -0.5176 -3.105 -2.827
1 -0.01384 -05176 -0.6459 -05817
0 -0.01384 -0.01035 0.02591 -0.00066
1 -0.01384 0.6543 128 1.179
2 -0.01384 3.53 4 984 5174
MEASUREMENTS ARE DONE AT 600nm
Analyst (W5 C9.10 D4D0,20,500,N).xls (Page 9 of 12)
Wafer 4 4 4 4
Cell 7, 3 7, 3 7, 3 7, 3
Diameter [um] 200 200 200 200
Guard Ring [um] 30 30 30 30
Pixel Dist [um] 400 400 400 400
Metal Ring N N N N
Illumination [%] Dark Vbr 0.03 lo Vbr0.33 lo Vbr loVbr
Bias Voltage [V] -60.00 -10240.1 -10540.7 -10550.1 -13253.9
-51.470 -0.00952 -280.979 -490.077 -3844.69
-51.234 0.05077 -214.973 -3585.55
-51.050 0.00608 -3383.04
-47.967 0.4208
Curve Fit a
b
c
d
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b
Max Gradient Vbr
Threshold Vbr
Linear Trend Vbr
Voltage Breakdown Vbr
-51.470 -51.234 -51.050 -47.967
-50.4303 -50.4303 -50.4303 -50.4303
Analysis (W5 C9.10 D400,20,500,N).xls (Page 10 of 12)
I 60E-19 |C]
6 63E-34 [J 5)
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viutary] dirk [A) [A] Inarm/A] W fi@ IIAAVjNEPfW]
-60 00 -1.02E-O2 -1.33E-02 I 49E-07 88736 64 0 3073 3 33E-02
-69 00 -8 89E-03 -1 22E-02 1 49E-07 81372 0 3073 2 B9E-02
-S8 00 -7 74E-03 -1.10E-02 1 49E-07 73940 41 0 3073 2 52E-02
-57 00 -6 56E-03 -9 B2E-03 1 49E-07 65736 88 0 3073 2 136-02
-56 00 -5.36E4J3 -8.75E-03 1 49E-07 58595 re 0 3073 1 74E-02
-5500 4 1SE-03 -7 69E-03 I 49E-07 51454 95 0 3073 1 35E-02
-54.00 -2.97E-03 -6 62E-03 I 49E-07 44314 47 0 3073 9 666-03
-S3 OO -1 82E-03 -5.55E-03 1 49E-07 37150 69 O3073 5 93(7-03
52.00 -7.15E-04 -1 4ye-03 1 49E-0? 30047 16 0 3073 2 32E-03
-51 00 - 40E-05 -3 44E-03 1 49E-07 23064 74 0 3073 2 73E-04
-50-00 -4.72E-05 -2.39E-03 1 49E-07 16027 56 0 3073 1 5317-04
-49.00 -JJ.76E-06 -1 4SE-03 1 49E-07 9687 277 0 3073 2 856-05
-48.00 -3.79E-07 -4.57E4M 1 49(7-07 3060 441 0 3073 1236-06
41 00 -Z B4E-07 -2.61E-04 1 49E-07 1745 518 0 3073 9 24E-07
-46 00 -1.B5E-07 -1.3BE-04 1 496-07 926 8378 0 3073 6 03E-O7
-4500 -1 42E-07 -1 04E-O4 1 49E-0? 695 7221 D3073 4 616-07
-14 tin -1.39E-07 -1 03E-O4 1 49E-07 688 7391 0 3073 4 54E-07
-13.00 -1.35E-07 -V02E-O4 I 49E-07 680 7436 0 3073 4 38E-07
-42.00 -1.32E-07 -1.01E-04 1 49E-07 673 7158 0 3073 4 29E-07
-41 -1.3E-07 -9.9E-05 1 49E-07 665 7752 0 3073 4 1 7E-07
-411 -tJE-07 -9 BE -05 1 49E-07 658 8162 0 3073 4 09E-O7
-39 -1-2E-07 -9.7E-05 1 49E-07 650 6013 0 3073 3 93E-07
-38 -1.2E-07 -9 6E-05 1 49E-07 642 7753 0 3073 J 63E-07
-37 -1.1E-07 -9.SE-05 I 49E-C7 636 T75S 0 3073 3 7JE-07
-36 -1.1E-07 -9.4E-05 1 49E-07 628 4439 0 3O73 3 62E-07
-35 -1.1E-07 9.3E-05 1 49E-07 620 8766 0 3073 3 47E-07
-34 -1E-07 -9 1E-05 I 49E-07 612 1378 0 3073 3 35E-07
-33 -1E-07 -9E-05 r 49E-07 605 4303 0 3073 3 30(7-07
-32 -9.7E-OB -B.9E-OS 1 49E-07 597 3476 0 3073 3 1SE-07
-31 -9.3E-OB -6 BE -05 1 496-07 589 4465 0 3073 3.026-07
-30 -S9E-08 -8 7E-05 I 496-07 582 3401 0 3073 2 90E-O7
-29 -8.7E4JB -B.6E-05 1 49E-07 574 8236 0 3073 2 84E-07
-28 -B.3E-08 -S 5E-05 1 49E-07 567 5778 0 3073 2 70E-07
-27 -AE-oa -B.4E-05 I 49E-07 560 1646 0 3O73 2 60E-O7
-26 7.6E-0B -8.2E-0S 1 49E-07 551 5417 0 3073 2 476-07
-25 -7.3E-OB -8.1E-05 1 49E-07 545 1867 0 3073 2 37E-07
-24 -6.8E-OB -SE-05 1 49E-07 536 7527 0 3073 2.22E-07
-23 -6.SE-O8 -7.9E-05 1 49E-07 52S 3652 0 3073 2 1 1E-07
-22 -6JE-08 -7.BE-05 1 49(7-07 521 3296 0 3073 2 03E-O7
-21 see -ob -7.7E-05 I 49E-07 514 6119 0 3073 1 906-07
-20 -5 5E-08 -7.BE-0S 1 49E-07 507 322 0 3073 1 79E-07
-1B -57E-OB -7 4E-05 1 49E-C7 406 6644 0 3073 1 60E-C7
-18 -4.9E-0B -7.3E-0S 1 49E-07 491 593 0 3073 1 586-07
-17 -4.5E-0B -7JE-OS 1 49E-07 46J 6789 0 3073 1 486-07
-16 4 1E-0-B -7 1E-05 1 49E-07 475 7609 0 3073 1 34E-07
-IS 3 8E-48 -7E-05 1 49E-07 469 236 0 3073 1 24E-07
-14 -3 4E-OB -6.9E-05 1 49E-07 461 2257 0 3073 I 09E-07
-13 3E-08 -6.BE-DS 1 49E-07 53 9347 0 3073 9 78E-08
-12 2 7E-OB -6 7E-05 1 49E-07 445 5928 0 3073 8B4E-0B
-11 -2.4E-08 -6 5E-05 1 4BE437 438 3031 0 3073 7 90E-OB
-10 -1.4E-0B -6 4E-05 1 49E-07 431 7018 0 3O73 4.50E-O8
-1 -1 4E-0B 6JE-05 1 496-07 423 8015 0 3073 4 5OE-0S
1 -1 4E-0B -6.21: 05 1 496-07 416 303 0 3073 4S0E-08
-7 -1.4E-C* -6 IE-OS 1 49E-07 408 9384 0 3073 4 50E-O8
-6 14E-08 -6E-C5 1 49E-07 399 2874 0 3073 4 SOE-OB
-5 1 4E-0B -5.BE-0S I 496-07 386 5097 0 3073 4 506-08
-4 -1 4E-08 -2.7E-03 1 49E-07 183 2456 0 3073 4 506-08
-: 1 4E-0B -S BE -06 1 49E-07 65 70598 0 3073 4 506-08
-2 -1 4E-06 -2 HE 06 1 49E-07 18 927)2 0 3073 4 50E-08
-1 1 4E-08 -5.BE-07 1 49E-07 3 894555 0 3073 4 506-08
0 -1 4E-0S -6.6E-10 1 49E-07 0 004419 0 3O73 4 506-08
1 -1 4E-0B 1.1BE-06 1 49E-07 -7 89355 0 3073 4 506-08
2 1 4E-0B 5.17E-0* 1 49E-07 -34 6406 0 3073 4 SOE-OB
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6.7.5 Crosstalk Analysis of Selected Photodiodes
The following are crosstalk calculations of selected APD arrays.
256
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Die: W1 C11.10 D400,20,750,N
Vbias: -3.0 [V]
Distance P4 Off P4 On Signal Crt Signal Crosstalk (Normalized)
0 -718.95 -907.5 1.262257 1
750 -718.95 -854.9 1.189095 0.942039
1500 -718.95 -734.8 1.022046 0.809697
2250 -718.95 -693.1 0.964045 0.763747
Die: W3 C5,8 D400,20,750,N
Vbias: -3.0 [V]
Distance P4 Off P4 On Signal Cr< Signal Crosstalk (Normalized)0 -470.575 -794.7 1.688785 1
750 -470.575 -774.4 1.645646 0.974456
1500 -470.575 -357.5 0.759709 0.449855
2250 -470.575 -114.6 0.243532 0.144205
Die: W4 C5,6 D400,20,750,N
Vbias: -9.0 [V]
Distance P4 Off P4 On Signal Cr< Signal Crosstalk (Normalized)0 -807.9 -7112 8.80307 1
750 -807.9 -6619 8.192846 0.930681
1500 -807.9 -519.6 0.643149 0.07306
2250 -807.9 -1208 1.495235 0.169854
Die: W4 C10.9 D200,20,300,N
Vbias: -9.0 [V]
Distance P4 Off P4 On Signal Cr Signal Crosstalk (Normalized)0 -191.1 -398.9 2.087389 1
300 -191.1 -303.96 1.590581 0.761995
600 -191.1 -297 1.55416 0.744548
900 -191.1 -155.6 0.814233 0.390073
Pixel Crosstalk Summary.xls (Page 2 of 2)
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260