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Theses
2004
Avalanche photodiodes arrays
Daniel Ma
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This Thesis is brought to you for free and open access by RIT Scholar Works. It has been accepted for inclusion in Theses by an authorized administrator of RIT Scholar Works. For more information, please contact [email protected]. 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______
Accepted by Harvey E. Rhody .y/h~~s- ) 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 the Wallace Memorial Library of R.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 Imaging Science 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
"reach-through" devices, based on the 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 of Work / 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
of Figure 2.1 .15: Electrostatic Potential 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 of Work / 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. level applications such astronomy, optical Because of its sensitivity, APDs are used in low light
photon and/or correlation fiber communication, spectrometry, laser radar, or where counting
APD's gain is a function of the information is needed [MacGregor, 1991]. Also, because an
reverse bias voltage. reverse bias voltage, it can be gain modulated by adjusting the
silicon as the The first publication of avalanche photodiodes was in 1966 by R. J. Mclntyre, using
device material [Mclntyre, 1966]. Research into using other materials, such as Ge, GaAs,
such as the planar InGaAs, and InGaAs/lnP has been performed since. Different structures
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 have a larger simply detector area to collect the entire signal would also increase
background radiation noise, the noise decreasing 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 tc- electric field within the depleted higher frequency response also due to the 7t-region. The high
1 region leads to rapid collection of the photogenerated carriers [Pierret, 996]
additional The major difference between PIN diodes and APDs are that APDs have an 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
drops (PMT) are very sensitive and have a fast response, but the quantum efficiency 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
beyond 1 100nm sensitivity 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 to most 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
O Absorption CD Region 71 (intrinsic)
p+ contact 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:
- < < qNA xp x 0 P = qND 0
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: -xp Equation 2.2: Electric Field Equation [Pierret, 1996] space. To determine and Where Ks is the dielectric constant and e0 is the permittivity of free xp xn: 2KS0NA = v *n b qND(NA+ND) 2Ksg0ND = ^ xp b qNA(NA+ND) Equation 2.3: n-side / p-side Depletion Width [Pierret, 1996] Where Vbi is the built-in potential, determined by: KT . f Vbi=^ln NA 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 -> X -qNA 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 .2.1 . electron-hole Section 2.1 Once pairs are generated, the mild electric field present in region one either holes or this sweeps carrier, 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: Mo = Mmin+- M ^ 'N 1 + N ref Equation 2.5: Majority Carrier Mobility Equation [Pierret, 1996] Where: Values at 300K Parameter Electron Carrier Hole Carrier MO17 MO17 Nref [cm3] 1.3 2.35 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-*< < *...>.(.<* V- <".^. i- ( j ^ i -i ^ ; i i.i-4-^ : Silicon : ;T; 7=300 Khfi Electrons HI!: 1000 - ~ :-. -. -::t : ;:; :\'-~- : l : :::::q:::4:::p:pf^;:| f--^H44tf - Holes -i-ffftr ...;.n....|.44.ji; (cm-3 fh ' A'a or Nx> . >, 1 lxlO'4. ... 1358 461 : 2 1357 460 100 1352 459 IOl! ? :;:::-"t 1 x .... 1345 458 " 2 1332 455 1298 448 -.j. "~""f~4~f~iTuf ''-,"*": ~-.-^ j 1 X 10"\... 1248 437 :! 1 "'] 2 1165 419 ?v j~4444J4 986 378 io" i i x .... 801 331 10 1014 10'5 10'6 1017 10'8 NAor/VD(cm-3) 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 1 1 1 1 z \ \S 104 r 103 - { \ : GaAs 1 GeV \ 1 \ Si > 10 ~ ~ InP _ \ GaP : " 1 \\ 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 of Wavelength 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 locations of the thickness of the Where A is the illuminated area, x, and x2 are the boundary illuminated area. or The photocurrent generated from a semiconductor is also dependent on the wavelength, photocurrent is spectral response. At the same incident optical power across all wavelengths, the 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: 1.24 K = 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. shown .1 coefficient Second, as in Figure 2.1 1 , the absorption 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 "front" The first two layers of the 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. "bent" .14 section where are or Notice in Figure 2.1 the energy band diagrams have a the bands , 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 2KC ( s "-0 NA+NC w = Vh NAND Equation 2.9: Depletion Width at Zero Bias [Pierret, 1996] * 10"14 Where Ks is the semiconductor dielectric constant, e0 is the permittivity of free space (8.85 * 10'19 [farad/cm]), q is the electronic charge (1 .6 [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. suggested 2.1 .15 and 2.1 an of the electrostatic potential As by Figure Figure .16, increase by having a reverse voltage bias can increase the magnitude of the electric field. As discussed in "good" 2.1 .3.1 a avalanche mechanism dependent on a high electric Section , is mainly having 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 br v ) 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 1017 10' /VAorWD(cm-3) 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 effect" This is known as a "curvature [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 effect" Since the "curvature 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 the right resistor the the symbol .1 at By selecting values, APD, depicted by diode in Figure 2.1 , is 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 convert from a current to a voltage signal. It is to both amplify the signal of the detector and it feedback resistor: utilizes an operational amplifier (op amp) circuitry with a 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 of importance 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 certain design Department. Several APD array designs were fabricated and tested to see how 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 to Pixel Pixel (Active Guard Ring Distance (Center Ring Material Area) Diameter Lateral Width to Center) 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 lil -r -* '! :;,>j^-;'i O?- : APD with Passive D1500,50,0,Y Quench Circuits | **.< ,j:i. ; I -,'. :,- - /<: *?' ,< Arrays' |j j Various APD :s' lr 1 -.1 ft-- -4 ,*.,: ;f3 u 1 : : 1 Resistors = if^ ^ f^ " ji >?r\. i^i -r^, f^ ': v - ^F^ *?' ^X -*- *^ -->-. "^^ ! W~ . ^= : ! "1 111 t W"i! \J 1 N' 1 i iD200,30,400,N i \ D200.1 0,400, :'D200.20.306.Y 1 1 '.": D100.10.100.N: .200,N i .400.N D 1100 . 10 ; D 1 00 , 1 0 .- . : . : jlI _j : -. i - : ^Alignment* , , . 1 " - *"* r*~'. -i"**. \-:~\ :;..* \ ''*. S"i. , -A-\ j.-:-\ ->.. :| ^ Verniers D200.20.250.N D200.20.300 iYD200.20.400.N--1:,: ; ; .N'j : ir t: m -j : ; 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. If the guard is fabricated of aluminum or from Y/N ring (Y) polysilicon (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 the Guard aligning 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 n Doped Impurities I Oxide [ _J j ^^ p Doped Impurities f:*:j p+ Contact n+ Guard Ring Poly-Si or Aluminum Interconnect 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 h+*-l 2 Equation 3.1: Oxide Thickness Calculation Where: K1ekT A = K2ekT B = 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 "consumed" oxide grown is from the silicon: 42 Bulk Silicon __ Oxide _j 46% of silicon (original silicon surface) "consumed" Oxidation 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 N' Where x is the depth into the wafer, 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]: ^ ^=e4DtQ C(x,t) = VnDt Equation 3.3: Fick's Second Law of Diffusion Where x is the depth into the t is the wafer, 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^" e2(dRp-+2Dt) Nd(X) = ydRp2 V2tu + 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 were , there 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: Electrical Microscope Cables HP4145B -v. / i Light Diffraction Source Grating Needle Probe Vacuum Fiber Optic Chuck 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 30 angle of approximately 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: Depletion Region A n-i- 71 P+ -> X ND N A "> 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-N A -* 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). "knee" In the case of the photodiodes that tested here, the 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 + v ^L ?- 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 The definition of gain for a photodiode is the ratio of the total multiplied output current to 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 with gain photodiode. , M, only deals the that is produced internally inside the 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 wavelength. mentioned in Section 2.1 .2.1 different Responsitivity is a function of As , 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 Poorly Isolated 1 oo% - 1 00% D Q. D. o O I 50% 50% 1_ o o 0% 0% ~i 1 r 2 3 1 2 3 Pixel 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 t-i Acceptable l-V Curve 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: Breakdown Dark Current NEP Cell Gain Responsitivity Voltage [V] [uA] [AAV] [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 2.00 0.00 Voltage Bias [V] 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: 10^ Input power Pin=0.3^W 10* < 10^ C 10-' o VI 10- > DC 10" 10" 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 -Dark -4000 -Dark Vbr -0.03IO -0.03 lo Vbr o- -6000 3 0.33 lo o -0.33 lo Vbr -lo -8000 -loVbr -10000 -12000 T -14000 -14.00 -12.00 -10.00 8.00 -6.00 -4.00 -2.00 0.00 Voltage Bias [V] 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 'VJJSWK5J. -2000 -Dark S -4000 -Dark Vbr - 0.03 lo -0.03 lo Vbr a -6000 3 '/ 0.33 lo o -0.33 lo Vbr -lo -loVbr -10000 4 1 / V -12000 ) -70.00 -60.00 -50.00 -40.00 -30.00 -20.00 -10.00 0.00 10.00 Voltage Bias [V] 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 at junction it guard ring, which prevents a premature low voltage breakdown the periphery, benefits from having a simpler design. It's also possible that wafer 5 unintentionally had a lower doping concentration; a result of processing non-uniformity. Commercial avalanche photodiode devices have a much higher breakdown voltage, typically over 80V. The devices in this research were designed to have low breakdown voltages, but at a 65 a Zener which is explained in tradeoff of making the photodiodes perform more like diode, Section 4.4.2. 4.2.3 Dark Current -2484u.A [W4 C7,3 Using the Vbr as the operating voltage, the dark current (ldark) at Vbr is for D200,30,400,N]: 5 -5 1-10 3-15 3 Q. 3 o -20 o o Q O 1 -25 0. -30 -35 -12.00 -10.00 -8.00 -6.00 -4.00 -2.00 0.00 2.00 Voltage Bias [V] 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 -8.00 -6.00 -4.00 -2.00 -14.00 -12.00 -10.00 0.00 Bias Voltage fV] 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 I'iliiton ( Jiinliut: MM) ioo "Standard" Structure At*l> 10 ioo 200 300 400 5(10 ffi*(\) Figure 4.2.9: Gain (Perkin Elmer) 68 E c m 0 - -12.00 -10.00 i.00 -6.00 -4.00 -2.00 Bias Voltage [V] 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 electric field around the p-n junction region. doping level used, which resulted in a high 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 c o Q. n rr 153- i i i i i i i i i i i i i i i i 400 450 500 550 600 650 700 750 800 Wavelength [nm] 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: 70 288 400 450 550 600 650 700 800 Wavelength [nm] Figure 4.2.12: Responsitivity vs. Wavelength (W5 C9,10 D400,20,500,N) the The peak of the spectral response can be tailored by changing the impurity junction depth into absorbed silicon. .2.1 wavelengths are deeper into the device. As explained in Section 2.1 , longer electron-hole pair has a If the long wavelengths are absorbed beyond the depletion region, the region. much higher chance to recombine before it is swept into the depletion the fabricated devices in this research tend to have the In comparing to commercial devices, commercial devices are around 800nm. spectral peak at a lower wavelength. Most 71 4.2.6 Responsitivity The responsitivity is calculated at unity gain (M = 1) is 0.2801 AAV, 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 r-. * -i. R@ 1.0QE R @ 0.9QE ' - < - ' - 1 0.40 ^ R @ 0.8QE R @ 0.7QE R @ 0.6QE R @ 0.5QE Q. 0.30 R @ 0.4QE o c - R 0.3QE R @ 0.2OE R @ 0.1QE 0.10 0.00 400 450 500 550 600 650 700 800 Wavelength [nm] 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 Abrupt Break Theoretical Silicon Photodiode 0,8 ->- Practical Silicon Photodiode 0.6 + Linear tnea&& With Wavelencth - c + o 0.4 Q_ CO (1) K 0.2 + 200 400 600 800 1000 Wavelength (nm) 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 unity signal- 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 60000 70000 80000 90000 100000 Gain (M) 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] this is the result: In mapping the crosstalk plot as described in Section 4.1.5, 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 2000 2500 Pixel Distance (Center to Center) [um] 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 "characteristics" somewhat similar to true APDs, it had many 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 it is apparent that the are 100u.m x 100u.m in size. When trying to connect to some photodiodes, at voltage connection could not be made, as there was no current flow any level. the metal pad to the photodiode has The reason is simple; the metal interconnect from discontinuities. The most likely places of discontinuities are either along the thin interconnect or at the junction near the photodiode edge (Figure from the pad to the photodiode (Figure 4.4.1), 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. to the cross-section of the 3.1 a Referring device (Figure .3), there is 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. "soft" This characteristic is typically known as 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 "soft- needed, which triggered the whole tunneling current situation and resulting in the 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 2 .. 2kT . a I t- fl2Ki\s tCQ V| = ln vki 'bihi Dl n 2n, qa v. 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 023/cm3 Appendix 6.6. With the photodiodes in this research having a peak doping of 2.635*1 at a 023/cm3 junction of u.m depth 0.0731 for n+ implant, and a peak doping of 1 .975*1 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, pronounced at longer responsitivity increases. The effect is more wavelengths, due to increased absorption coefficient, lower reflectivity and higher photon energy at the longer wavelengths. 81 a width of 0.108p.m instead of As an example, if diode [W5 C9.10 D400,20,500,N] had depletion 0.0108|im (biased at the breakdown voltage of -50.43V), the responsitivity would have increased as such: 0.70 - ' - ^ - < Responsitivity R @ 1.0QE R @ 0.9QE " - ' - - _ R @ 0.8QE ' " - ~ - _- R @ 0.7QE *" - - R @ 0.6QE ~ " ~- " - _ . R @ 0.5QE R @ 0.4QE - - - - - _. - _ ^"^-N^^ - - R @ 0.3QE R @ 0.2QE R @ 0.1 QE ' *------_ - ^^--,^'^_ _ _ f1-' "" " - - _ ** " - f- - - _ " ------_ -"" _- 0.00 - 1 1 1 1 1 1 1 1 400 450 500 550 600 650 700 750 800 Wavelength [nm] Figure 4.4.3: Responsitivity @ M=1 (W5 C9.10 D400,20,500,N) (@ 0.01 \im Depletion Width) 82 0.70 0.60 ? Responsitivity R @ 1.0QE R @ 0.9QE < 0.40 R @ 0.8QE R @ 0.7QE - - R @ 0.6QE R @ 0.5QE a- 0.30 R @ 0.4QE R @ 0.3QE R @ 0.2QE R @ 0.1QE 0.20 0.10 0.00 400 450 500 550 600 650 700 750 800 Wavelength [nm] Figure 4.4.4: Responsitivity @ M=1 (W5 C9,10 D400,20,500,N) (@ 0.1 nm Depletion Width) The depletion width is controlled by the amount of doping used. 4.4.4 Performance Uniformity of a there was an issue of Even when the devices exhibited a general l-V curve photodiode, uniformly. As an photodiodes [W4 C7,3 D200, 20, 300, N] having the devices perform example, of the same dimensions on the same wafer. Their l-V and [W4 C10,9 D200, 20, 300, N] are curve is widely different: 83 -10.00 -6.00 -4.00 -2.00 -16.00 -14.00 -12.00 1.00 0.00 -200 -400 -600 -W4C7.3 -800 -W4C10,9 -1000 -1200 -1400 1600 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 photodiodes' as it affects an avalanche 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 "soft" also made the devices exhibit a breakdown voltage and have a low responsitivity. "soft" The devices exhibit 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. an avalanche photodiode with a low The original intention of the design was to have breakdown order to have low breakdown voltages high levels are voltage for portability reasons. In doping 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 to Wafer 4. Figure 4.4.5 illustrates the variability within wafer. The differences in breakdown voltage indicate that the are doping levels 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, didn't extend into the intrinsic region. As the resulting in a too small of a depletion width that device is put under increased reverse bias, current tunneling occurs, where reverse current This decreased the for the device to have a started trickling before the actual breakdown. ability 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. 10"6 Kl := 4.02 [um] t := 1.53 M El := 1.29 [eV] T := 1273 [K] K2:=214 [um2/hr] E2:=0.71 [eV] 5 k:= 8.617 [eV/K] El k T A:=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 Electron Volt -53 eV k:= 8.617-10 Boltzmann Constant K 0.01- x :=0, 10_6m.. 1.5 10"6m Depth Wafer Parameters: 3 Nb(x):=11014cm Background Doping Implant Parameters: Rp:= 0.073 10 m Projected Range dRp:= 0.0305 10 m Projected Straggle N':=1.61018-cm"2 Implant Dose Diffusion Parameters: D0:= 03.85^- Frequency Factor [Boron(0.76), Phos(3.85)] s Ea:=3.66eV Activation Energy [Boron(3.46), Phos(3.66)] Tl := 1273K Diffusion Temperature 1 tl := 4.5hr Diffusion Time 1 T2:=1223K Diffusion Temperature 2 t2 := 2.3hr Diffusion Time 2 90 Implant Calculation: N' Nxrp:= V5c-dRp 1023 1% = 2.093 x Peak Concentration [N(x=Rp)] 2dRp2 Ni(x) := N^-e Impurity Profile After Implant Drive-in Calculation: kTl Dl:=De Diffusion Coefficient -E, kT2 D2:=D0e N' - 2J_dRp2+2(Dltl+D2t2)] Nd(x) := Impurity Profile After Drive-in V2~7t->/dRp2 + 2(Dltl + D2t2) 1022 Concentration Nd(0) = 2.795x Surface Doping xj:= i MO119 -3 while | Nd(i) - Nb(i)| > m i<-i + MO m Junction Depth xj= 1.417X 10 m 91 Profile Graph: Guard Ring Impurity Profile I 10 610 810 Depth 1m] Implant Profile Diffusion Profile Background Doping Overall Impurity Profile 92 N+ / P+ Impurity Profile Constants: eV:=1.610"19J Electron Volt eV -55 k:= 8.617 10 Boltzmann Constant K 6 x:=0,0.0110"6m.. 1.510 m Depth Wafer Parameters: 3 Nb(x):=11014cm Background Doping Implant Parameters: Rp, := 0.073 10 m Projected Range dRpl:= 0.0305 10 m Projected Straggle 2 N'l:=5.2-1018cm Implant Dose Diffusion Parameters: 2 cm 03.85- Factor Dol := Frequency [Boron(0.76), Phos(3.85)] Eai:=3.66eV Activation Energy [Boron(3.46), Phos(3.66)] Diffusion Temperature Tl := 1223K Diffusion Time tl := 2.3hr 93 Implant Calculation: N'l N. xrpl ^2ridR,Pi N^^e^xio23-^- Peak Concentration [N(x=Rp)] cm 2dRD Profile After Implant Nil(x) := Nxrpl-e Impurity Drive-in Calculation: -Eai k-Tl Coefficient Dl:=Dole Diffusion 15 cm Dl = 3.181x 10 N'l 2-(dRpl2+2Dltl) Profile After Drive-in Ndl(x) := Impurity V^-JdRp? + 2-Dl-tl 1023 Concentration Ndl(O) = 1.714X Surface Doping cm xjl:= i 19 -3 while |Ndl(i) - Nb(i)| > 110 m i<-i+ 110 9m xjl=5.91x 10 m Junction Depth 94 P+ Impurity Profile Implant Parameters: Rp2:=0.28-10 m Projected Range dRp2:= 0.064 10 6m Projected Straggle 2 N'2:=5.2-1018-cm Implant Dose Diffusion Parameters: cm Do2:=0.76- 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'2 N. xip2 V^Tt-dR,P2 Concentration = Peak [N(x=Rp)] Nxrp2 3.241 xlO23-^ cm 2dR, P2 Profile After Implant Ni2(x) := Nxrp2-e Impurity Drive-in Calculation: -Ea2 k-T2 D2:=Do2e Diffusion Coefficient 10"15cm D2 = 4.19x N'2 2(dRp22+2D2t2j Profile After Drive-in Nd2(x) := Impurity dRp2 + 2D2t2 1021 Concentration Nd2(0) = 5.658x Surface Doping cm xj2:= i <- 0m 19 -3 while | Nd2(i) - Nb(i)| > 110 m 1- i -H 10 m xj2=9.66x 10 m Junction Depth 96 N+ / P+ Profile Calculations PNJuncDepth := i < Om (1.001- while Ndl(i) > Nd2(i)) v Ndl(i) < (0.999 Nd2(i)) -10 < i i -H 110 ium PNJuncDepth = 1.73x 10"7m 1029 Ndl(PNJuncDepth) = 1.1 76x 3 m 1029 Nd2(PNJuncDepth) = 1.1 76x 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 1029 Ndl(NdlPealc) = 2.635x m 1029 Nd2(Nd2Peak) = 1.975x m (Ndl(NdlPeak) - Nd2(Nd2Peak)) Ndl Peak- Nd2Peak 1035 Constant a = -3.188x Grading 4 m 97 Profile Graph: N+ Diffusion Profile P+ Diffusion Profile Background Doping Overall 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., N2 3.2.2. Ramp up to 1 1 00C, dry 02 3.2.3. Soak 21 Omin, wet 02 3.2.4. Ramp down to 800C, N2 3.2.5. Pull @ 12in/min. 4. - Guard Photolithography 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. - (APD02-1 6. Implant Guard Ring ,2,4) 6.1. Target Xj: 1.4u.m 6.1.1. Energy: 60keV 018/cm2 6.1.2. Dose: 1.6*1 6.1.3. Species: P31 (APD02- 1 7. Resist Strip ,2,4) - Drive-In (APD02-1 8. Diffusion Guard Ring ,2,4) 8.1. Temp: 1000C 8.2. Time: 4.5 hours yield an of but there is a thermal of 8.2.1 . (6.5 hours would Xj 1u.m, following step 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. implant. 10.4.1. Leave ~500A oxide as sacrificial oxide during 11. Implant -N+(APD02-x) 11.1. Target Xj: 0.5u.m 11.1.1. Energy: 60keV * 1018/cm2 11.1.2. Dose: 5.2 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 1018/cm2 14.3. Dose: 5.2 * 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. ' ' with a make MUCH easier in next section. 'Tagging line , to string parsing " " 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 j Next i ReDim sDatadColUB, iRowUB) For i 1 To iColUB For j 1 To iRowUB sData i ( , j ) sTempArr ( i , j ) Next j Next 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) "Thres Vbr" SCoeffArrd, 9) = "Vbr" RegObj .Degree 3 'Calculate the coefficients of the 3rd order polynomial. For i 2 To UBound(sData( ) , 1) RegObj . Init For = 1 To j UBound ( sData ( ) , 2) 'Add data to RegObj. When done grab coefficients from it. . XYAdd sData 1 sData RegObj ( , j ) , ( i , j ) Next j 'Grab coefficients from RegObj. will be 4 coefficients. ' [x"3 is SCoeffArrd, 1) or RegObj . Coeff (3 ) ] '[const is or .Coeff sCoeffArrd, 4) RegObj (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 "Ordnung" Private GlobalOi ' = 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 R.Sedgewick' 'following 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 j Next 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 j Finished 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 FinalizeMatrix(Oi) Dim i&, Oli 01 0 + 1 For i 0 To 0 Md, 01) SumYX(i) Next i End Sub Private Sub Solved Dim 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 "RegressionObject" " " value! 0<= Degree <= & Err. Raise 6000, , NewVal & is an invalid property Use 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 1 If XYCount <= 0 Then 0 XYCount 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 h:= 6.626 10 34Js W c := 2.9979245810 X := 60010~9m eV:= 1.610 19C eV_per_sec :=R W eV eV_per_sec = 1.751 x 1018A he E:= E=3.311x 10 19J photons_per_sec := E 18 S photons_per_sec =3.021x10 kgm eV_per_sec x:=- photons_per_sec kgm A x =0.580 [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 Electron Volt q:=1.610"'9C Charge := Intrinsic Carrier Concentration rij 110 cm T := 300K Temperature _55 eV k:= 8.617 10 Boltzmann Constant K 1 cm 1 Electron Mobility (@ Nd = 10A17/cm3) Minority-Carrier Lifetime xn:=M0_6s Electron (Average) cm | = up:=331- Hole Mobility (@ Na 10*17/0713) -6 Minority-Carrier Lifetime S Hole (Average) Constant of Silicon Ks:=ll. Dielectric F -14 of Free Space e:=8.8510 Permittivity Parameters: Sub-Calculations: Device 1023 Acceptor Concentration - ( k-T^I Electron Diffusion Coefficient Na- l 939 Un 3 cm "{.Tj Length 1023 Electron Diffusion Donor Concentration K NH := 2.484 Coefficient ( Hole Diffusion Applied Voltage DP MtJ VA:=-5.2V Hole Diffusion Length lf/W4 Constant Lp =p? tp : 3.188 Grading 107 Calculations: Vguess0:=0.5V f:=0.. 10 2-k-T 'l2-Ks-e0 V Vguess(f+i):= In Vguessf 2-nj qa ) Vbi := Vguess 10 Built-in Voltage Vbi = 1.2739V 2 13 12-Kse, W:= -(vbi-vA) qa W = 5.4181x 10 m Depletion Width -w f-W W "\ W ' J" 2 2 20 2 K Q-a fw V(x):=-^ [(?)' x- x Electrostatic Potential 6-Kse0 q" S(x):= - Electric Field 2Kse0 >-(!)] p(x) :=q- ax Charge Density 108 6.7. 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IL ** 4" +* + C 0 > J CO W ID 0 > > u X X X X X r_j 1 Oru Xo ru L0a Hni X[J Xru <~* X CD X X X X X X < > >> > oo o o o o o o o o in o ow tu o pi tx i 8 *< b m -. x; 5 ..x: ut u 0 1 4> I n L C XI 0 41 8 0 0 c. aa 4i ti C 8 O 8 8 C U. X X X X >- X o3 d.8 cj-^ Xcu x CD X X X X X X < E Ij- >>> 2: o o o o o o o o O O 10 o O 10 cu o * I + m a i _ < ro M XJ 3 XJ -n 0 a b cj el *> i ft c c XJ 8 41 B e a xl a a + ^ C 8 O 8 B C U. *" 41 4* 41 C 8 > J 0 CO to o > > u X X X OS &Xo al Mai Xa X. cj X CD X X X X X < E > > > > O o o o o oo o o o a o o 30 w o * r - PI CX I 8 vl B PJ ... x: s .. c vl CJ 8 O 8 1 41 J H L C XJ 0 4> 0 b e l. a a + n c 0 o L LL *1 4* +> +1 C 0 > _J CO CO W 5 > X X X u1 o!g CJ L Hni :ru Xru <^ X CD X X X X X X < E >>> > O O C o oo o o O O 10 o OLD W o PI ex 1 8 ti a CO . x: at ..x: vi a e 0 o 8 1 +i i 8 > -1 CO CO CO 3> > X o X' f * 1 J * 3 *>. X .-; l-o > ; - - T3 Xlh \ v-i O L'J o c - 1 > '. I- r 1 XlJ i ! Ux 1 Xro i \ 1 \ \ > --VV- X \ CD j \\ > \I X \W ! 1 > \ - i X . . 1 X W \ j X j o \ 4 X o 1 0 .. X _ a i .. o o W < o iO-ri o J o 1iDX3 in o i a. 1 j > > > > O o o o o oo o O O ID o o to 01 o a l 8 B p> X. * * CJ B 0 O U ] L c XI 0 41 8 8 8 . a. a 41 C 0 O 0 8 C. tl. rt 4*4* +1 C 8 > -J to W til a > > CJ X X X X . xg Xo 01 Xu IX fu X CD X X X x X X < M >>> > o o o o o o o o O O 10 o o to tw o * t P) a ? 8 PI s .. c V.S 8 0 CJ 8 1 4> I L e 8 4> B e c a a 4 c b a B B C1L H+il4> C 8 > _1 CO CO CO o> > CJ X o X - -- T in . . ^ Xg > I \ > < Xo \ O cnQ \ o 1 ID tn Mco' V - V V Xcu X \ j \ v \ X \ LD \ 1 V t > x i \ 1 \ X X ^ X i X 1 \ X w \ X o i o X s J CD j \. X L^ I \ \ j ^ o o> o < o 8 H j > > > > oo o o o o o o O O 10 o a id cw o * * P) a. i 8 vl B m .. XT * vl U 8 b5 8 I 4 1 M C C n 0 4 8 0 0 c a a 4 fi C 8 O 8 8 C U. ** + 41 4) C 8> _a co to co D > > O X X r~ X I2 o> 'NT Cm > H D xg \ OJ i O O tn tn i0 ft CJ Xcu <^ AX X LL CD > 1,X X \ X X \ \\ O X \ 1 A O v. X \ CD X &_. i. O o > OtVJ I < o O E o LOXJ in o > >> > o o o o o o o o o o o o # PS a I 0 Vl 8 PI .. XJ 3t .. c vl O 8 8 U 8 I 4> I n C c X) 8 4> 0 8 8 L. a a 4* f C 8 OB 0 C II * 4 4J 4* C 8 > J CO to co o > > o X o X 1 X -- ' *z ! . ; X _ o> 1 t IT i 1 ; ' ,--: o I lJ ai V 1 > li o \ \ \ !'l ~-\ o o in ~ V v '._J L .. X" - Xcd <3 - s. X IL. CD \ ix \ i V - X ' ;X 1 x\ s. s X 1. tl .J X 1 \ X 1 \ O \ \ o X i to i . X \ v^ \ O < o CVJ < O t o I o ] ID o LL 1 b M I > > > > o o o o o o o o O O ID o O 10 w o CO a. l 8 vi a m .. x: 2t .. xj vi O 0 8 U 8 1 4J 1 rl t c XI 0 4* 8 0 0 l a a *i H C 0 O 0 8 L. U_ Ti + 41 4* C e > _i oo to co O > > u X O X O 1 I m X t in X 1 x> 1 ! i 1 ! 1 1 1 i 1 ! i . . . ( i . \ \ > , - 1 s Xld i \ i o - - \ . _ . 'in \i W Xrj Xru v* X CD X > 'I X i \ \ "s. x s X \ X O X ^\ X o X I CO * X \, S \ a o> C>0J O-rl c1 i < c> o in -a IT1 o 1 Ll. 3 > > o o o o o o o o o SIS o a tn a i vl 8 PI .?XJ % .. XJ vt Q 8 8 CJ 8 I 4> 1 i- C c X> 8 4J 0 8 8 C a a 41 vl C 8 DO 0 C li. 41 4> 4 C 8 > -J CO CO CO o > > u X X X X . * p. CJO- I HUH XG x CD X X X X X X < > > > > o oo o o o o O O O 10 o on o pi a i PI ..XJ s .. x: *0 0 8 U 0 1 4J I -* i. c XI * ** 8 8 f caa 4J> vt c a a e 8 L U- 4J 4 4J C 8 > -J to CO co o> > CJ X o X IK P5 X . X > rn I- - <* ^ \ > v, ^x X o DDU X o v^. in X CJ01 4 \s Mm" Xu \ Xfj <* \ X X CD \ X > \ \ X X- X \ X \ X \ 1= \ X Rx X. o o> MS I < o an O E o UlTJ in o M >>> > o oo o OOP o OOD o OIDN o p) a i rt 0 p> 01 * * n c* J 8 4J 0 4> 8* 8 c a a C 8 O B 0 C U, ** 4* 4J 4 C 8 > J CO C0 CO D> > w X X X X T^J, X to L_J f'l o!s CJ coD (JO) Miff x^] <^ X CD X X X x X X < E Li nt > > > > o o o a o o o o oog o O ID W o PI a I o 0 PI .. JC * ..x: vl CJ 0 BO 0 I 4> I c c a 8 * 0 o O L. O. ti 4> -rl C 8 O 8 0 ** 41 4J 41 C j con co o > o X O . r- X i i 1 m X < i cn *z t X .. xg in -> 1 ^ ^ --_... X o \ O ry V > rl -Jo 11 \, N. Xo o o v cn X - .. tn CJ ^ \ \\ cn Mir w X V X V, Xfj \Is \ \ a: LL (3 \ > I . X \ \ \ \ \\ L X/-TV _..\ O " \ \ O * \ \ 0 ' " . \\ \ ...... j o < o 0-- Gi 1 E o inrj in o ^x vl U. . i-t 1 >>> > o o o o ooo o o o c o O 10 w o PI a i 8 vl 8 CO at .. c 0 BO O I 41 1 rl L XI XI 0 41 8 8 0 i, an. 4* vf C 0 9 0 L. tL *t 41 4* *; 0 > j to t to g> > CJ X X X x x>- *o L-O ^ 8 a. m cna fJ0) XLJ Xfj <^ ir X' x x X X X X < E li. >>> > oo o o oo o o o OID W o ft - V PI a i 8 vi a P) ,, x: x ..XJ vl CJ 8 0 O 8 I 4> I r* C c XI 8 41 8 e x. a. a vt C 8 O 8 C ti. -^ 4 41 4) 8 > J CO CD CO o> > u X X X:z *o X o Xn o L_^J COd ucj Q Q Cfl2 f-U-i 1 G_cn X X X X X X < LL M > > > > oo o o oo o o x>x>jp > o m oj o ... pj a I B fA vl b 5 vtO b 0,9 el fj 1 XI 0 41 0 b b c a a +i v* C 0 O 8 0 L. U. v4l 4 CJ +J Q> B > -J CO tO 0) > o X o X i in x> I- CO X Xo Xf0 o V L_r>.j Oo" > n xS CJ o XX in \ x \\ x AX XX V \ a.rn \\ <:^ \ -s X \l ^ X. lL CD x\ X > \\ \ X ^\ \ X X \ X *r V X J4 8 X \ i CO X ~L & O ocu < o o i E o m o vi I > > > > o o o o o o o o o o c o O ID W o * 4 PI a 1 0 vl 8 CO .. XJ X .. c vl Q D B O 8 1 41 1 rl C c X) 8 41 0 8 8 . Q. a 41 ^t COO* 8 L. Li. vi +1 4J 41 C 8 > _l CO CO CO 0> > u X O X o "1 in Xz ^ CO *d Xo i 1 X^ i i CD i |_rn 1 Go' 'x\. > i rt \x T3 ^ v Xcj I r ~~1 X. o . o rp2 i tn X r i - cn *' X v- Mv! 1 X : "i f V \ \ \ . Xrn \*i i \ i \ <"^ X \ i CD \v \ 1 > i \ i X V, ! - X X \ o X x \ x \ \ X * o o> CCVJ 1 < o c> o tnxj IT\ 3 a t > goo o o o o o ogn o ODAI o P) a j m vl 8 pi ? *. XJ 3E -HO 0 U 01 *i ' XI B 41 8 8 b c a a + r* C 8 O 8 8 . U. vl 41 4? 4" c: a > b > -J to to to X x Xz x - X o x1^ o f\1 Xq o cj XLJ" LLP) w \ <^ a: CD \ > j... x \x \\ \ x \ x x o X V.XJV to X o o> ocvi < o e o int? in w o VI I >>> > O o o o o o o o O O 10 O o to tu o * ft ft PI a i 8 ti g P) -. Xl 3S , jC vl CJ O B CJ 0 1 +11 rl C. C XI 0 4> 0 0 Laa 41 vl C 0 O B B C_ U. -H 4J *J +1 C 0 > J CO CO CO o> X- X X in cn xv X a *0- o> in 1 o rx > rl T3 X IT \ o r- X o \ in XX \ m \\^. \ \ w XtJ \ X \ X \ \ CD \< \ \ X X \- \x X \ 4 X I- \ X \ ]<0 " X IX -4 o one i < o O-rt o E o tn o ^x. Ll vl 1-4 I >>> > O O o o o o o o o oo o * 10 o jo o * a i i vi 8 P vl o 0 0. 9 8i *; XI 0+i 0 0 * c. aa vf c 8 o a o C U. v +1 4 *1 C 8 > ^> in co co a > o X o X X 1 = Sf o Xo t'.l uoa iJ fQ X:j Xt CI' X X X X X X < E >> > > o o o o o o o o o o o o * O ID o Aj . . 1 vi pj a. i i 8 vl o (0 .. x: * .. XJ vl CJ 8 0 u 8 1 4 1 n C c XI 04* 8 0 0 c. a a ** vl C 0 O 0 8 C UL vl 4* 4" 4 C 0 > -1 to to to o> > a >>> > o oo o o oo o o SS8 o PJ a i m vl 8 Pi vl D B 8 U 8i *j > rl r. c XJ 8 41 0 e ncaa * -* C 8 D 8 0 (. U. v 41 4 41 C b > _J to co to o > > o > > > > oo o 0 o o o 0 oo o 0 * K) 0 CO vl vl 0, 1 1 0 vt 8 PI .. XJ JC ..X. ** O 0 BO 0 1 41 1 n C c XI 0 4> 0 0 0 u tx a 41 vl C 8 O 8 8 C U. *l 4 41 4 c 0 > -J CO to CO 0 > > 0 o X o X X X * in 1-0 Org I rig D; CJ n] Mn -p u x n X X X X X X < E li nt O o o o OQfj g O 10 o O * " vl ^ a i i vi 8 " * I vt OB 0 U T ?! - X* B 41 8 8 b c a a v c 8 o 8 0 L li. vi 41 4> 4 C 8 > _i to to n a> X X X x Xv *d 1 03 CJ^ MrC XG X^r X X X X X X X < E ul > > > > o o o o o o o o o oo o . o JO o 01 * 8 8 PI .. XJ vl CJ 8 B U o i 41 I . c 0 4> 0 o c. a a 47 c 8 o 8 0 C li. VI +* + + c 8 > _i to to to o > > a o X o o X w i! X I m !' *z i X 1 i *2 1! 1 > tj 1 1 . E_ . 1 t ^- o CXu u \ > a *- t^ a 8 ll ? 0J Vt o i CDa o tr" o O*5 X M*. ^ X - x^ X^r V \ . Vs\ : X Xk\- i u_ (_D \x > X ^ i X \ \\ NX \\ i X XX \\ X \\ XX V ^N^ x _,. Jo O 1D> O o < E o OT3 Ovl o vl\ - | i-i LL * M 1 > o o o o o oo o o o o 01 ' vi a a t i B * 0 PI viS. -5 8 I ?* I Xt 8 *1 0 8 8 C. a tt 41 vl C 8 O 8 0 f_ It * 41 4 4> C B > -J CO CO CO O > > o X X X x>- *d *3 i o b Xcu o {/la' r 1 . I r-l j-*l? <:s x CD X X X X X X < E LL M > > > > o oo o o oo O o o o *.s o ID O vl vl a I I 0 ^0 CO w x: s .. xj T*OI 0 O 0 1 41 I r* C C X) 041 0 0 0 C Q. O. 41 vf C 8 D 8 0 C U. -^ 41 41 41 C 8 > J to CO co o> > o o X o X X x^ Xd x 'n XrriI X . D COcn C-Jd CLs- a: x X X X X X X < E lL H >>> > o o o o o o o o o o o o * O 10 o AJ . * vl GO a i I PI .. XJ .. XJ * vl CJ 0 0 u 8 1 41 I n C c XI 0 4* 0 0 0 l a ft + vi C 0 O 0 0 > 0 > _i w so to > X X X xz X 0 * rn 5". X-vT CI GDc? ud M.V! I0 Xv X X X X X X 3 >>> > oo o o o o o o O O Q o * O 10 o o ? vl * a i i 0 vf 0 PI ..XJ 3 .. XJ t*0 8 0 u 0 1 41 ] r* t> c XI 041 0 0 0 c a a 41 vt C 8 O 8 0 C.JL v* 41 44 c 8 > J tO CD 00 o > > u X x X X > X x j_Ln Co MiC X-- uDlt r i - *-' o M-i T-'J X X X X X X X X < E LL >>> o o o o o o o o ' o o o o * o o o o vl 0 vl o. i 7 vl 8 ft .. XJ S v*0 0 0O 0 1 fj 1 r4 C C Xi B + " b 0 c a a * v* C 8 O 8 8 (. U. vi 41 41 41 c m > j to to to o > o X o ft X i 1 i -o X 1 CD t i j 1 ] I s^ E . \ X . I 1 t x 1 0 i Ti * > ; M,_: f _ 0 ( r l_J nj 1 1 1 t 1 * 1 -V; j \ Lio i 73 X oj I ) { L o ~CI 00 F Xt o \ o CJN ! X < ft L . ! \ ' cu Mm I xt; Xlf! ^ v. <3 "vj-v ' fT" 1 | X X 1 1 X. \ F Li. LO ' *- r 1 1 1 1 > NX * t "X i X \ 1 1 -X > T ! -. X ^X 1| 1 X X, X. 1 ^ j X 1 X x X. X 1 ^ 1 | , **- X . x -I o o> OO < o o-* 00 E o in "a vl o x. in 1 v 1 > > > > o o o o o o o o o oo o * o o o 0vi a j I 0 vi 8 n .* I .. XJ vl CJ 0 BO 8 1 4 I ri C. C XI 0 41 a O L ft a 4 v* C 0 o 0 8 L U. vl +i C B > .J DO CO to o> > u o X o X X *^ X . xg cn to X f\J uoc CJ^ Sin" Xin <^ a: x x x X X X X < E LL H >>> > o o o o o o o o o o o o . o o o o BID vi ft I i 8 *1 0 p* OO B 41 I r-l XI m ** b 8 b c. o. a 4i i* C 8 O 8 8 C 8 > J cO co to O > > o X o X T X X n? x^ *d M in I I O ; ! t xS u a DO0 o o w i v* X'J -il Xcn <"* \ x x LL r > X \ X X X X X 1 X io o o> o < o O-rl oo E o on ?CD o -\ O I LL C\i Oi H I > > > > oo o 0 oo o 0 oo o 0 . . o 0 co 55 * a i i 8 vl o pi .. X s .. vi CJ 8 0 CJ 8 1 41 1 rl C. C XI 041 0 0 0 c. ft a 4> -rl C 0 O 0 0 C. U. vf 41 4* v> c 0 > _j to to tn s> > o X o X X X > X X m o CJ o X o D. CO CJ 00 o cj-' Men X':j X in < X c n X X X X. X X LL >>> > o oo o o oo o o oo o . o o o o * vl W vl ft I 8 vl 0 CO .. XJ * vlO 0 5 B I 41 1 rl L c Xt 04i 0 0 c ft a v C 8 8 L U. v*4l 4> 41 c m> j so in to a > o X X X X X c X o If M x Xt ? 00 o o- Ma? XCJ Xld <^ X CD X X X X X X < Ll M > > > > oo o o o o o o o o o o o o a 10 ?*t VI 0 vl O p .. XJ 5 ** O 0 0 i 41 | c XJ 8 41 8 o 0 c a a 41 vl C 8 D 8 8 C U. 41 41 41 C B > J tO CO CO O > > O O X O X ft -jin X TT X >- ^ X Xc 1 > o !_ m Oo > .rl x. Q O O O CXH vl XCJ CLiiJ i v v <^ X CD \\ V X I X X X X v X <2 X I JO o _6> o < o O-H otn o OID in o o J LL ?* M i 6.7.2 Raw l-V Data The following tables are the raw numerical data from the l-V graphs of Section 6.7.1 156 SSS2SS200oooi ."2 ZS nnpir-^ooiffloA^Sr-' PSS09<=>ooooo^i-co-s- S? Jona^oJoodmaJdricdiNT-' SS22OOOOh--r-CDCNC0 C^lO^r;0)Cg0)lD^r-SN0)S0) tDiriirirXor^irii^tNv^T^criv^rXcNJ OlCMLOCOCNinOifOCOCOCOrt-r- s-s|2 CN OOOOOOOOOOCOCNCNCOCO WnoDCSj(DCN|inr;^r-^(DO'd;S O 2 r- O ^p rXioXrcdaitricdiriootDC\ioixSo CDCTJCNlOeOCNtOOinoiOCNJ v- CO CDiom^cotntNOJv-T- < OOlCmOiCDCOOv- .(OtqqtNooo * .' t ' _ C) ,, O '-'..' >. m w ! i.'j i i I ,) ::.. > 1 . cotNU^Tfcdv^ocritd-T-v^v^ocSo ^ CMOONW^cOir1 fsj CN CO O OOOOOOOOt-COCNOO'v-Ov- roqrait(D(0(OT-r\iiflrooo iriNtoiriooipgr-V^iiioddd :-ii>l OOOOOOCNTfrCNO-r-O^-CO oii^v-inommh-Ti-^-ooooo cooscdiDoriiDSrooddd" OT-cNnmcov-io-v-' ^- :-8>-s CO in CO IN r- r- i ' OOOOOOv-v-TfrCNOT-T-COvf tDcqcoTtTj-r^tDoovooooo O (-, O ^o 2 s^ cooJu'iiriNcoiritDcrJdddddd o S o ^>- cocooiotN^j-con'1 ^ v- ' ^ CN CO O LO Tf CO CO CN o o o o o OOOOOh-Tl-CO OOO CD t}- tDco 2 .'JCOr'^IDtDtOlfi'tCOtO^ S S T-omcricostoin^cotxiT- T o > OOOOOOOOOOOOCNCOO (NTtv^COCNLpCOOOCNCOO)lOCNin a> o ^CDfOr-'tvi^Nlo'^CDT-'fOCOfsi^ incOfNtDOtKlCMinNOJOCVI < S^Q COSStOCDin^-Tl-fOtN'-T- ' cn t t OOOOOOOOOOt-OOCDtJ- r^cxjv-;r^tDv-;ir)0)if>f---TrrN.cNCDco r-'LO^SLOIDCDOilOCOinX'T-'^CD o> o , vj-r^.T--vj-COtNtDOlf>OLOv- ' - ' s^& r-- cm CDlDtO^COCOCMOJv-v- ' ' ooooooooo^T-mcoTj-co cnrgswono)S'i-riT-s(NNtN rxisrjaisiDN^NddNdtNco tNir>0?CNCDO**01COCOTl- '' CD If) tJ- <^- CO CO CN COCNtNCNCNv-t-v- o o o o o o XI X) ro .a O -D CD -D > > C I T3 > c ra c i > _ ^ > xi 2 m o LL 2 o > O a _ 1 E J; a 2 E o c SOOI5lS = O IfS COCOC0COtt3-cO,^J-'^COCNO) CO N iq LOCNCNCOCO^CMt-v- Oh-CNCOCNlOTrOO -- W v- -r- OSOOJO^^^V^S1" cd LO loTTcmlooT J; co ro r- o lOco-r-Ttr-p^cMOO o o tr'NS.CC)8r:^t,l d d *COT-(OlNT-(Dr-T- 0)COC3)t-0)SNt-t- OJCO-^-COIOCDCOv-t- CD ' t- t- CO O O) CD CN T r ' CO CM O r- v- O Q) CO S CO O) N t O) CO ' '" . 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S n toV 6 6 o ^ - TSrNlNrOr Sn5MOr)inN N N ID IN (N CM " r- iri ri *. ^ = 2 i/ii/i a a a a s o o "-; o o -o S o > ||||Si?sas52llsli?i P> gS O ,-, O . r >" a> n- pi ^ S 2 "Ss< oowcm^^-^-ocoOOVNW-T-0(OT-Cftl^r> >-ioiriminnrN m o m f-. o v o *" )SSi-5m - ^ 2 - 25 o co 5 T o RS "P v o in jintMioooiip'oiri .-SSozJ ^-. c> cn m cm r- cn a n u-i u-j r Jffirir^airoeM'0,^,nr' co o) co to to n "EiniOMnsdioVri v v j t aoi K TiSviNr-efNin^co - * cri 5 cn => v cm cm o co S e V PS P> i- CO CD ' woiomNo i- v- Jir jmifiOlTrOr -w ._: en ot co T7N^N|-ioiflirncv ^ P) CM CO *". 1- O i- m io v- o o v ji-f-ooaiacDr^r^r^coco oin"Y^-mcocvic\iT-^c^ CD 1 CJ "D CD O 5 = I a. | | , 1|5|I | Scjooa.EE m s leg IINOOIiniBtOOIOlSi-lOffl T-MScDOLflS|gg|gJ0 o 8 8 o > s o-wcDnocMcocnuimmw'w- cocoiricDcjopigj^j^^r^ciZ d 8 8 o > g iococnpi3oPF2S!S~c ."gSSzo jnNqn^nT-T-wiDfflfflCMiD ,ReS,* - co s to lf> V CM M-oJr^COinifj toontoinoonooi 7cM'r^^ilr)co^^cl'wa?t,:l,' iSSs^S > 35* t J 3 cn to cn co cn enSS:ioio),ncMCi<::io r- 'oZo T VV V a> to T 3 T toSSSZ rwi-^onmoi-'. >'S2>S in ili cfl to in in o> id cn .,, ,n ,, o^j^oco^jtrr^T-^gJ! S > o oioi-^-koco-op)tomi^ lOmOlfflLnrNWKKJgj^^ 2S$^3cmv-^*s ; fosBrijinoriiri,'n0.p! -(pif^P)CMM^5p^''IN 't^t^- -ipoioiAiaifla'-inniDiNv^ ' 2 O) v CO 'cMrviT^v^ep^,p)cj'^oicp' in^ ooor"-cDP>Tro>iOKt--cnu ',71 -91 -17050 -9 B4 -10940 -6039 -BOSS 4669 -6661 -ST12 -8648 4517 -758-5 3234 -3356 -6515 2066 -2231 -5*45 : -50490 0 -23240 -39190 -4604 497 6 -1695 3342 -1961 -319.7 -1346 -51Z.7 -104 1 -13B-T -75.6 -252-8 -34.57 -42.87 -161.8 -140 -32.95 39 42 3116 -317D -3394 -3212 -2176 -2422 -2310 -1547 1193 125* -1543 9*0.6 -409.3 -504-3 -B34.8 -484.1 -78.96 -82.B1 -325.5 -1B2.9 -54.28 -52.71 -97.8 34.55 -32.55 -40.95 -77.51 -13.5 -12*2 13.55 29.16 6.624 -9.B32 -27.6 -20.77 -7 12 -9J3 12J2 -8 652 -6.762 -11.91 -25.96 IV DMs - Water s .ti (Pag* 1 ol 2) -S732 -5870 5323 -4652 4990 5108 -3955 -4096 -4231 -1517 -3043 3349 267B- 2132 -2262 2475 -1894 -1257 1654 -1163 -10240 14 10540.65 -10550 12 -13253 91 -365.5 538 7 -6607 594 9171 BS1 9204 117 -12153.61 -39630 -1667 -187 -3318 -291 E -7740 142 6079 117 -4637 119.6 -1334 166.9 -153 8 -6561 142 6869 651 41B25117 -B6 18.91 5 2457 -7B12 -83 66 -92 13 -78.SS -5358.142 5661651 -5732.117 4)751.915 -10.31 -55.23 -58 99 -50 -4146 142 4537 117 -7BB9 91S -5834 11560 13050 3234 651 -3019 SO52 -6951 1821 142 2066 651 2251 117 -SS46.915 -1200 -3146 -4070 -714.5417 1236 117 -4487 915 3361 1460 -83.9617 126 4512 370 4166 -3444 915 1298 -47 1517 56 35117 -2393.915 -77.29 -600 6 -8 761704 18 05117 -35.2068 -1446.915 29 39 -105 3 -370 7 3.2S917S -4S7 1147 12 16 -49 31 261 a -02641 417186 -26 7898 -260 7147 11-22 -42 09 -0 1BS4 4)6845 -23 4S7B -10 6 -40 35 -223.9 0141704 &6S1175 10 12 2199 43139428 4.647443 19S2664 102 8717 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 * 01 364 3 S3 4684 5 174 V Data - Wale' 5 IPbqs 2 of 2) 6.7.3 Figures of Merit 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) o o CO CO CO O CO Q o d 2 H T o CM X o m r- Q 2S to w lO in b O oo o i? Q o CO 'co to c < [vn] uajjnQ )nd)no apoipotogd o o o o -3CJ 1_ CO CO CO CO CD CO o o CO CO Q Q d d d d _S .2 | t 1 II | 1 ;: I o in o m Q CO in O 0) c c o m3 O a. w a> + c a> O) to * o > c S o a jc: to 0) L- m o a. > [yn] uiauno indno apoipojoijd > < > o ^r tl) O) CD o m L -. o > in Q c CD tfi L- in 3 O o to Q c < o o O O o LO o LO O LO *~ CN CN CO CO LVn] juejjno jndjno epoipojoijd < 1 O in CD rn to n > CO X m a o CO > o no m b ' > o Q in l/l co CO o o in CO in O Q CO in c O "to O CO CO ^> to c < LO CN o o o o o o o o o o o o o o o o o o * CM o (IN) U!B9 o o co o LO f- o 1> o O o CD m CC Q TO CO co a in O _ to E x io ? o a in c a o > O V a in > to 5Q 5 to in O 3 a 3 CO o CO j>. c to 0) c u. < 3 o [yn] jueuno 2: LLI LU LU LU LU 1X1 LU LU 111 O o a a a OOO c o CO CD LO CO CN t- o o o Q. CO @ (X. ce cr a: a: a: a: a: a: a: o: i ? \ \\ \\\ ' CN \\ o o r-- m CD ro to m CL Q tn co li x in o > O LO CD b ^ m \1 P o> Q <. "5 in > O > CO c \\ 1 o CO Q. CO U) a> CO Qi c < \\\ 11 \\ 1 \ , 1 \\\ 1 o , 1 1 ~t 1 M o 1 1 1 1 1 1 1 1 1 1 1 1 1 Ml 1 1 4 1 * o o d d [/WV] A}!Ai!suodsay \ CN m O t o m O CD 5 to in jo O 8 ^ o f. O a. o S Ui z o in l_ v o o o o CO a in +^ O c to > 3 IT CO LU to O c CO < '5 z o o CN V ' i 1 1 1 1 1 1 1 1 1 1 1 1 i 1 1 ) 1 1 1 1 1 1 1 1 1 1 1 t 1 1 1 1 1 1 1 1 1 ' I CO co CO CO co 3 ct * a o O O o V 9 9 9 9 9 9 + LU LU LU LU LU LU LU LU LU LU CD * CN o O O o o o T_ <- T i- *- 00 CD * CN o [M] (d3N) JSMOd juaiBAinba asjOfg E c o o ID LU Z o Q LU a. < LU or t/> o ^- LO - CO t t * CO CO LO N N CO O) if o> O CO CN CD CO d o N N CO ^ _; CO CD t- o o o CO CO >- LO LO LO LO o .2 Tf CO CM CM d d 5 CD COCOOl(DCOT-T-i-Nf0^i-NlO0J o dio'dNNdNois1,!p!S|tDo"' O '-IO(OSI>-IOCONSCD'-9SSo OO CDLOtS-COCOCNt-t- ' > CO ^ CM H LO LO S I I i III i i t , <- ^CJ O LO $1 3 i o d >. COlO^CDCDCnOJr-STtT-COCMCRCO CO CONNr^ON^tncOCnST-CO^N < T- O ?E5coSioi-:c6d--'ir!Sg35r)^l2 . O > CO 9 51 t CM O t- * C S N CO CO lO CD t- ' o 10 co t- -^r o cm - ID CD O) CM *- CD LO O t- COr^CNCOCOOOOJCD Tf coMt\i'-'-t-con>- 995890 ^s 00 0 O LO O LO o olooloolooloo O N It) N O LO CNOf^lOCNOCNlO CO CM CM CM CM E ;? ? E - E =. b. e = 2> to L. - .2 ~ -a 5 .B o > J!E S=|18 x .2 3 3 5 O Q O 0. E = m Wafer 1 1 1 1 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 YYY 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 -1.311 0.03508 -107.521 -0.950 -0.044 Curve Fit a b c d 2nd Derivative a b Max Gradient Vbr Threshold Vbr Linear Trend Vbr -1.360 -1.356 -1.311 -0.950 Voltage Breakdown Vbr -1.244 -1.244 -1.244 -1.244 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) j), S 3 S 3 5 ^ l K t X c PP PPP o ^ S 3 S S 2 5 S SS 2 fc 3* * *t * p p p p p p p p o p p p d p p p p p p p p p o p p p p p p p p- p p p p p Ul n n o v w io CM O CO CO M- if ^- . CO IT) CO LU lil LU LU LU o o o o o o o O OO o ff d d d d d 7? . 9 r-- r- s. a. CO CO 5 co CO o CO o ,r" m* ,- LO "T a. C cn cn cn 0. O) a CO o M- CO ,_ to CO CM O CO i^ 9 9 9 9 9 M- Oj UJ UJ Ul CO CO UJ HI p CM CM CO CO cn en cn cn cn ID CD u> to CD @ d d d d d cm CM CM CM CM * cc M" CD LO in LO o CO CO CO CM r^ O o o o o r^ uo CM CO LO + + + + + CM CO CO o> in LU UJ LU LU UJ CM CM CO CO M- CO in CM o d d d d d e. 0) CO CO <> CD CO CO CO CO CC CO CO CO CO CO CO ^_ r-^ CM r- r^ a CO CO f^- CO CO CM r-^ to CO CO LO CO CM UO CM CO in - p M- "* CO CO CO CO CM CO CO in o o o o o d d d d d a. ct o o o o o o M- o> in ^ r^ ? t-\ c> m- O) cm in co o , m CO K. CO o> co co o co cm co m- in in CD CO g S I d d d d d *- 1 s. h- r-. r s. O CO O) CO CN o o o o o __ O CM CO CO Mr W CM O CO CO Mr -_ Lil UJ UJ LU 111 *- co m- m- CO o o o o o in co > o o o o o ) d d d d d > io to k oo Cell: W2C6,8C1500,50,0,Y Breakdown Voltage: -1.346 [V] Dark Current (@ Vbr): -73.8 [uA] Gain (@ Vbr): 2413 Responsitivity (@ 600nm, 2V Bias): 0.199 [A/W] NEP (@ Vbr): 0.000371 [W] Analysis (W2 C6,8 D1500,50,0,Y).xls (Page 1 of 12) o o CO CO a d d .2 H ;: o o LO CM O CD U) CO (L o CO o > o !>' T^ o O o w in co CO CO o m o O a> in CM O) T"~ to Q o o cn LO > o CO O CN > CO CO o m o r CM < [yn] juajjno jndjno apoipo)Ol|d o o n o ^ CO CO CO CO CO CO o o CO CO CJ Odd o d -2 Si I Ml l \ l lO O CO CD o o o CN LO d CO 5 CD CD to CD CD a C '_i co X c o o > 'J o ^ > o 1 o o in in a i_ o a> CO o <- a in TO T to * Q a> O) O o oo CO LO > +- CO O o > CNI c S CO o 'lO a >> O m re O a> r t_ CM < CO o 0. > [vn] juajjno jndjnrj apoipojoiid CM M o CD O) CD CL ~ JO Ci X to c~- >- o to co m o a O TO O in CM o in *^ 5 C co L. to 3 O o CN to o CO CD c [yn] )U3Jjno jndjno epojpoioild o m CD O) CD CL > a> %> 3 o I oo CO SO 5 8 O CM Q co c O 're CM O CO CO >. CD c < (W) "ieo o o CO o LO lO O o O CO m cS O CM 5 O i- CD O "1 c 1 o > to sO CD > LO > re 00 > O *- CN 3 Q. 3 CO o 'co > c CD CD c w i_ < 3 o ?h III- o LO o T CO CN LO LO LO [Vn] juajjno Ill LU HI LU LU 111 111 o o OOO OO 05 CO N CD lO CO CM odd LtttLtKirtciririL'ii: \ \ /: \> \\\ ' \ \ / O CD (^ CD m CL o CO >< CO \\ \\ O > O LO CD o CM o r , in E o \\ c o in \\ .c O TO n C CD a CO CO > ( > 5 CN tn 5 c O CO o LO a LO CO tn >. CD CD CC cz < O O \ \ LO li1I O ' 1 t t t-^l - . 1 M 4 1 1 O ? 1 1 1 1 1 1 1 1 1 1 1 1 O o o o CO CM h- LO O O O o o o CM >- m o o o 00 o o o lO CD O) O CD CO CO O ^^ X CM s . * o V o o c o 00 CO o ST in LU o in CD i Q o o rn o a. o CO *- CD n c a> CN re > '5 ty to LU o o CD tD o C to -3- < O z I CO CO CO CO co rf 9 o 9 9 9 9 LU HI HI UJ LU LU LU LO o LO o o O CO CM CM T- T LO d LM] (d3N) JSMOd jueiEAmba asjON E c o < LU z o Q LU < UJ s HI on o => CO o> CD CO CO >- LO CD o CO O) LO O) CO T- LO CO l-~ CX> O) CO tf CO LO O CO CM d d d d CO CO LO o o CO LO o o CO o o O CO o> CM d d LO o o CO O Si LO CM CO CO d p LO LO > T o o d T d d CO T_ O) LO ^ CO 00 CO r- CO CD ^f t CO LO LO o CM CO LO CM r-: CO LO o r~: d LO CO d d 'J- CM "3- LO LO o CO CN r- CO * d d CM o O >- i~- LO CO LO CM 5 O CO CO G d o o LO LO CO ' 1 5 d o d d d ,_ CM ^_ CO CO LO CD CD CD a> CO Ol LO CT> LO o CO CO LO CD CO o 00 csi CM r~: o CO CO CO d o> CM o o r- CM CO CO CO d CO CO o o o r^ CO O > CO LO CO CM o 5 o o LO LO o ? *7 V V d T" c6 d d d d m m lo c O)COC0SNCOINt-CM ^ O)OOOjO)(0COSO -r1 r^ in cd ._ r O CO ^ O) Ifl COCOLONOn-COCOS f- CO t- o o o lOtOCMCM'-OJlOCN 8 o O O O LO LO i I i i i i i '" T H CD ^S o o o o o o c*i csi csi E :? El E .2. E CD TO e (0 w ? .2 13 O | > S = 2 E re I xg e .2 3 5 "5 O Q O 0. 2 = LU 2 2 Wafer 2 2 6,8 6,8 Cell 6,8 6,8 1500 1500 Diameter [um] 1500 1500 50 Guard Ring [um] 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 c d 2nd Derivative a b Max Gradient Vbr 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 [AAf NEP [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 -9.01 E-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 -5.41 E-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 -3.01 E-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 -9.71 E-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) f "* > ? 2 ,00000 UJ UJ UJ UJ UJ co Mr M> f^- co UJ O) ^- co 2 M- -- O) CD O CD "> M- M" CO oi csi co p o CO CO CO N- co M- O M" LO M- to M- lo N. OOOOO OOOOO N. CM O Ol *- ^Tf iti s ti H ^ 1- CM CO CM T- 3 10 lO U} Ul VI UJ co co Mr uo lo O M- 00000 t- CM O CO CD co Mr M- i5 .< eg Lil Ul LU UJ UJ o o o o o o in *o K. Mf co fa) <6 cS c6 <5 <6 Si, iri iri S m 10 Oi O CM 10 0 CM O LO CO M- Oi < M- < CO r-^ CO CD Oi 3 CO 0 CM CO 0 0 0 0 CO CO LO Oi CO UJ 0 M" CJ) CM CO Oi z UJ uj UJ uj uj 0 0 f*. ID ID 0 *~_ d d O d O D 2 CO to LO @ CM 'p- oS 10 Ul Oi. tt a. M" -r- Mr M- M- M- 0 0 CO CO CO < M- Oi CO ID co + + + + CM to Oi CM LO to d CM CM 1 _^ Uj UJ Uj Uj UJ J? Oi O O S N S CO CO DC OOOOO CD O Mr CD CM ="T LU LU UJ UJ UJ x- CM CM CM CO > CO CM CO O O * * r- cm co cm co i 0 d o d d o t- iri -f -r - CJi Oi Oi Oi Oi O co o Mr co *- to co cm o co r*-. 9 9 9 9 9 M- -^ Oi Oi CO CO UJ LU LU LU LU O --- cm CM CO co EO) O) 9) O) 0) CO CO CO co to ) d o d d d 7 N N oi N N CO ID lO LO "* O co co CO CM N. 0 0 0 0 0 LO CM CO LO + + + + CM CO CO Oi LO Ell UJ UJ UJ Lil O CM CM CO CO Mr ~- CO O) lO CM O M" O d d d d CO r-. CO CO CO "- CD CO cc CO CO CO CD CO 0 CO CM 03 t-r- to r>- CO CO CM r-~ CD CO CO ID co CM LO CM CO CO CO CO CO O CM CO CO M- LO , Mr LO CO s CO Oi r^ CD i CC r- r- r-. N. 0 to Oi CO CM 2 M" fc O CM CO CO LO CM O CD CO M- *~ tr- _ UJ LU UJ LU lil c^i -* in CD OOO O O > q q o o q lO O O OO > -t Ul CD S CO Cell: W3 C11,10 D200,20,300,Y Breakdown Voltage: -0.451 [V] Dark Current (@ Vbr): -3.4 [uA] Gain (@ Vbr): 1332 Responsitivity (@ 600nm, 2V Bias): 0.199 [A/W] NEP (@ Vbr): 1 .7E-05 [W] Analysis (W3 C11.10 D200,20,300,Y).xls (Page 1 of 12) o co co co o co ? ci o .2 H T o o fN in o CD a> CO O CL O to to >< > o o o CM o t- O > to o ts CM m o o a CN o O) co a CO o o o 5 LD * > _ T- 4-1 o o a. CO > cn 'cn o >, CD CM C < [vn] juejjno jndjno apoipoioiid o o o o S CO CO CO CO CO CO o o CO CO a Odd o d Si o I IH IH c i : i o o CM o d CM O O to o CD CO l\ D) CO g CL to CD c >< > c o \vT > o S a. \\ m o u. m O a> S, pi re Q CD > t. O) \ re \ o o > K CO c o T3 jc \ CO re > a> tz L- < ffi k o a. \ N > \ ^ \ \ O O O o O O o O O O o O O o O o O CN CO CN CM T CD CO [vn] uajjno jndjno apoipojoiid o LO 1 d > CM o CD o CD o \ CO CO L o tN o ^ o > Jl CM >: O to O 5 O o S -* to to I CM 5 ^ Q 4- c E 3 O o CO L- to o cn O o cn CM >, co r* o o o o O o o o o o o O o o CM CO in CD t". CO CJ) [vn] juejjno jrtdino 3poipo)oi|d to CM CM O o to 5 c "to o LO r- CO O CM CD o CD o LO CM CO O) a CO IX ,-, tn E * O CO o O) o o C CO 5 CD a cn O) tB O c 5o * CN 0) a > re o s LO LO > o CO 3 a. <- 3 tn o cn ^. c CO c < 3 o o o o o o o o o CN CO CM tvn] juejjno LU LU Lil Lil LU LU LU LU LU LU a a a a a a a OOO O) CO co 10 CO CN t- d d d d KLtO: trKQiQrCCirCrrQ: \ \ = I 0 ' LO \ / I- \ \ \\ CN / "5 CO_ \ \ CD O m CM r- CO a CN cn O >< \\ > 0 0 LO 0 O CO CO CM F 5 O O .c CM 4-> Q O n> c CD O y a> > , s O CO tn <> s' c LO o LO cn Q. cn tn >-. CD CO or c < \ \ \ o i\ LO ( 1 1 H -H 1 '1 < 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \ o o iv d d [/liW] AiiAjjisuodsey o o \ CO O CM CO CD O) CM o CO o Q CN CL x o to fg c o 5 5 (3 O CM (L LU o CN a CD o 5 o 0. o c J) CO re > 3 cn IT cn LU CO CD c w O < o O O z 1- " \ o o o CM 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 II 1 l> CO CO CO CO CO CO CO CO * o V 9 9 9 9 9 9 9 o o Lil LU LU LU LU Lil Lil UJ LU Lil o LO o LO o LO o o o *- - -* tf CO CO CN CN LO o [M] (d3N) J3MOd juaieAmbg asiON < 111 z o o UJ a. < w i- LU at o O) t/> CD > o CO d O CO r^cNiconcoiri'tr-co^gjuj CN to r- "=r E5 d in coo0!' co d CD LO t- 10 CJ) ^ O) M co lo cr> K o >- o >- cn co to cn co "i CN J2 V o o i i i o d d COt-COCMCDCDCOCM^" CO CO CO ^- CM ' CD O t- t- o o "ScdiriLricDco'cN'tr-iri O I_ifcOCOCOCOCOCOCOTrCNCO CO OI N CO LO CO CO - o a o >. jo VVo)scciici^nw>-o r- W O O CM CO CO *- o d d ^" O) CO r- CO O) "^ 00 CO *- LO G) CJ) CO ON O ID cocd^co'cd'tdco^ CO ^J CO CN O) O lZ t- LO -tf CM CO > < CM s CO Ps V o p q p 'OOO r*-CO-*-lOC0*-CDCMCOCO f- CO t t- LO O) r-- ^tONSlricD-f^-f1^ o cm to o CN CO i- CM CO T"*- O0 0 ^ CMT-T-^-T-N--SOin- i- O V -: co m cm >- r- CO ^ CO - o S o co CO CD LO ^ CM I II I I I V T o o o o t- ^ I T CN CO O d d d d o o lo o lo O LO O LO O LO O LO o o lO CM O N. LO CN O r^ LO CM O CM LO co'c\ic\ic\ic\i^^^ v- d d d d d d -, E -- "? 5 E =. E i CO = ffli = O) 2> = - to ._ .2 o ri S >- 1 S 5 > 2 = tti "5 5 E Bias Voltage [V] -3.00 -824.7 -866.9 -1198 -1680 -0.796 -0.04044 -31.0136 -291.177 -368.75 -0.712 -0.05032 -256.685 -315.999 -0.209 -50.1485 -0.11991 -0.087 -0.05407 Curve Fit a b c d 2nd Derivative a b Max Gradient Vbr Threshold Vbr Linear Trend Vbr -0.796 -0.712 -0.087 -0.209 Voltage Breakdown Vbr -0.451 -0.451 -0.451 -0.451 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 -8.11 E-04 9.65E-08 8405.536 0.1986 1.23E-03 -1.25 -1.71 E-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) CO CO CO CO CO ,00000 UJ uj Uj Uj Uj CM LO O) lO N. LO CO O *- O CO- CM t^ CM CO 7= Oi M- CO O CO W ^ -jj. CO CM CO CO CM Oi CO CO g >- CM - -r- O w d d o d CM --- O io oi CM CO ID CO CO O CO CO O O CM CO Oi CM CM OI Oi M" Nr *- UO -=. d cm r^ Mr ^ O ^ O) CO -- Mr Mr lo co UJ UJ LD lil LU OOOOO (8 t MO -3- OO O CO CD 1 d d o d d t- W B N CM LO M- Oi CM O LD fr*. CO o> 0 < M- CO O CO CO CM O CO CM O) m LO CO 0 CO CO o> CM M- O ~ ""* ID LO CM O 0 0 > O O d d d d 0 d d O CM UJ @ 0 a: CD N- CO O) Oi O CO O CM Mr CO 111 OOOOO z Uj uj uj Uj uj o ------r- o JlO N IO "O *- -r- i d d o o d a 2". CO CO LD ^J (M * o> LO LU .a. tc C M- M- Mr M- M- O 0 co CO CD *- < M- 01 CO co 10 in ift -j O co CO CO CM N. 0 0 0 r->- LD CM CO LD T- + + + CM CO CO Oi LO E LU LU UJ UJ UJ d CM LN CO CO Mr LO CM 0 M" d d d d O IT. CD @ CO *" CO 0: CO CD CO O -^ . ZL . K. cT o o o o o M- Oi ID 1- N. 00000 O CM ID CO O M- . LO CD r-v CO Oi CO CO O to CM CO M" LO LO tO CD 1 d d d d d r^ CO r-. r- r*- h- k- - CO CO O) CO CM 0 OOO O CM CO CO M^ lo E_ - " CO CO _ UJ UJ LU UJ UJ ^co^^iocS CD OOO OO > O O O O o OOOOO 2 MT ID CO N. CO Cell: W4 C7,3 D200,20,300,Y Breakdown Voltage: -7.624 [V] Dark Current (@ Vbr): -2484 [uA] Gain (@ Vbr): 22677 Responsitivity (@ 600nm): 0.2801 [A/W] NEP (@ Vbr): 0.00887 [W] Analysis (W4 C7,3 D200,20,300,Y).xls (Page 1 of 12) co co co o CO Q d d Si 1 1 1t 1 1 1 1 1 1 1 1 1 1 1 1 t 1 1 1 1 1 1 1 1 H 1 1 " CM o O P CM *f u> CO o tn CO x o > o _ ,-r o > CM 9 o O to m. . \\ to o CO ci O O o > CMS -* to a Q o > CO o *\\ ? O 0. > cn co CD C < ^ o o o o o o o o o o O o o o o CM T CO CO CN [vn] luejjno jndino apoipojoiid -O. > > o o o o CO CO CO CO CD CD O O CO CO Q Q d d d d Si 1 1 1 1 i i y4 i i i i i i i t 1 1 1 1 1 1 1 1 1 1 1 1 I 1 1 1 o CO o CM O CO ' O o CO 1 8 a) T co tn o c tn X c > o o o2 d > co o Q. i_ 0> *- s c ^ K CM a> Q tl) O) CO o t-j\\ > c to o 0) a j*: co co CD V. u. CD ^^ % O 0. %^ > o O o o o O o O o o o O o o o o o O CD CM CM T [Vn] juaxino jndjno apojpoioijd i. n o T CN T M o CD o O) o CO o CO n tn CM 9 > X in , , o to CM > o m o CD o CO O) ro CO o O CN o o > O o | CO CN Q c CO L. 3 o o 1 to o o O tn o tn 1 CO c < o o CM o o o o o o o o o o o O o o o o CM T CD CO o LVn] luajjno jndjno apoipoiond o LO CI) D) CO > o a. o 9 > tn CO " * X 0) ^-C^ O) > 10 o o o CM > CO o to o CM CO o CO o o CO o CN Q CO c O 'to o 5 o o cn o tn CO c < o o o o o o o o o o o o o o o o o o o o o -3- o (W) ujEQ o o CO O LO o CN o CO CM o S O)ft CM CD O CL CO o i Jl T >: O r- o CD 5 C0_ O) m O c > CM o S O tl) 5 o > CM to a CO to > 3 a 3 o CO ^. c co 0) o c l_ o < L_ LO 3 o LO o o s l"vn] uajjno LU Lil LU LU LU LU LU LU o OOO o O n OOO o O) co CO LO * CO CM ^ d d o o o LtLtairKirLttCLtLtLi: >-_ o o o r- CO O o o -* CO "= Is j: o % cm "? Q CO Is" V) c o Q. cn IA 0) CO ce: cz < [/WV] AiiAHisuodsay o o o o O) o o o o CO o o o o o o co o IN CO o CD o o O) CM o CO O o CD CL CO O X | g C O LO CO CL 0 LU o CN o o o CU o CM o Q 5 o o t co_ CL c O to > o o '3 o cr CO LU CD CO 10 c 'o < Z CN CN CM CM CM CN CN CN co O O O 0 o V 9 9 9 9 + LU lil lil Lil LU lil LU LU LU LU O LO O O LO 0 LO OO o LO T- T- rf ^r CO CN CN LO d [M] (d"3N) JSMOd lueieAmbg asiON 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) 4 4 4 Wafer 4 3 Cell 7, 3 7, 3 7, 7,3 200 200 200 Diameter [um] 200 30 30 Guard Ring [um] 30 30 400 400 Pixel Dist [um] 400 400 N Metal Ring 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 c d 2nd Derivative a b Max Gradient Vbr 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 = 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 @ 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 -5.21 E-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 -3.21 E-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) CM CM CO CM CM c^ O O O O O S, ui Uj Uj Uj Uj r- -r- S. N. O) U. lo o co O Is-- g ~ ~ is ~ -; r- ; (J) Ol O J 2 M" ID O CO CO CO M- CO CO CO g t- CM CM CM -r- Co O O O O O _ CO Oi Y- cr> M- O CO co CO LO ID CO CO oS LO O CO CO co CO CM CO r~~. LO "*" T~ LO CO co 5 o O o O O o o> CO Mr CO CO CM CO CO -> cm M1 MJ CO CM 5 ID LO -D LO LO T~ - * "-* - 5. UJ M* Mf M- ** ** o CO CO M- LD ID O O O o o CM O CO CO M- CO M- M- LO CO LU LU UJ UJ UJ d OOOOO CO LO M" CO CO o 5" m LO ID ID @) d d d d CM CO CO O O >d f-~ co Oi o Oi co CM LO CM "* O CO CM Oi O CO Co Oi t- CM LO CO LO M- CM o o o - *- o o O O O @) d O d d d UJ O to Oi Oi Of CO O CM M- CO o o O o O m O -r- ID Oi CO Oi CM M- CO Oi UJ Uj UJ Ul UJ LO CO CO Oi CM CO CM CO IS CM (3)00000 CM --r~ *-1~" o> CM o .a.Q. q: M" M- M- M- M- M- o o CO CO CO M- Oi CO LO CO + + + CM CO O) CM LO Ul UJ Ul Ul LU O T- - * CM CM Oi o o CO LO d d d d d M- o o CM ts r> l< CO ID CO tt r-. r r- CO CO o CO CO o CO CO o O o O o LO CM CM CM CO o Mr CO CM UJ Lil UJ Lil Lil d CM CM CM CO ? CO CM CO o O ' ' r-- CM CO CM CO @ d d O d d o *~ ,~ LO T -T CL or Oi Oi Oi Oi Oi O to o M" CD ,_ o o o o O CO co CM o CO fs Oi M- Oi CO co Lil Lil UJ Lil UJ d CM CM CO to fM CM CM , q q q q| o I o o o o o > CD CO CD CO CD CO ID ID ID t* O co co to cm r-v OOOOO \ LO C\ CO LT) "- + + + + + _ CM CO CO C3i LD E uj uj uj uj uj O cm CM CO CO M- ~- CO O) LO CM O d d d d d ~", O) CO S (O Tf {) it -g CO CO CO CD CO CO CO CD CO CO K n N s CO CO in CO CM LO CM CO LO M- __ CO CO CO CO d CM CO CO M- LO O d o o o L^, @ d O d d d cr or O o o o o o o> IT o o o o o Oi CM LO CO M- o LO CO r-* CO CT) CO CO o CO d CM CO M- ID LO CO CO @ d d d d d -^ CO i cc o CO CO Oi CO CM o o M- 1 q q q o CM CO CO LO CM o CD CO UJ Lil LU LU LU M- M- t CO LO *CD o o o o i s > q q o o o OOOOO > t ift CD S CO 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) 2 O S co co CO O CO Q d d -2 H \ o CM O CO O <* ** o Q. > [yn] ^usjjno indjno apoipojond o CO o CM O O tn tu c c o o a w CD 9> a) to o > c S o TJ JC CO a) L_ CO o CL > [vn] ut*Jjno indjno apoipoioiid o CN 1 o o CM o * CD o cn o CD CL CO tn t -T x o CM Z Q CO CO O a ^ O "? o JS co o > o I CM Q c \\ CO 3 O o XL i to O CO cn >. CO c < LO o CM [yn] juajjno jndjno 9pojpo)OL|d o o d o LO CO 0) CD CL > x o CO to O CO o o O ~ o CM d o o > CO t CO to o O CO o CN o | CO c o 'to O cn cn CO c < O o o LO o LO "3- o o CO o o Tt O CO CO o CD CM CO O CD CL cn o E x c - pO) o o to CO c > m o a> o > CN to Q o 5 lO CO tn > o 3 cn o cn ^> c CO tu c k. L. < 3 o 1 1 1 1 1 1 1 1 Vt i i i 11 1 t 1 1 1 1 1 1 1 ( 1 1 1 ! [vn] juajjno lUJUJLLILULJLULULdLLILU '""SSSPSSoaoo O) CO CD LO -"Cf co CN d d o d icciroiLLifctirLLir o LO CO \ 1 i \ \ i i i i\ \ ^\ \ LO o \\ N CD CO CO \\ m CL o O CM \ o r~. a V cn \ X CO i>r o CJ> o \ ^* CO \ \\ i I o E \f\ i c \ i O \\ .c o \ i \ CN s o Q \ c CO A 0) CO 0) r^- \\ CO O \(\ u 5 * tn o LO s c \\\ LD o \ CO o. cn tfl >. tl) a: CD \\ C O \\\ O < \\ \\ ul \\\ 1 \y 1 1 1 1 ' 1 1 1- -1 1 1 1 1 1 1 1 1 1 \ 1 1 1 1 1 1 1 1 1 1 1 1 1 i\ CM d [M/v] AjjAiiisuodsay o o a- o LO CO z o o o CO CO CO CD O) CM CO o CL CO CN ^ o I .E o to o (3 * CL LU co o CD CM Q o CO 0. O c o to > '3 tn tT cn LU >. co CD c < 2; .J LO LO LO LO O O 0 O O 9 ? 9 9 + LU LU LU LU LU LU LU CM O O O OO O ^ *~ "- CO CD T CM O [Ml (d3N) JSMOd }ua|BAinbg as|ON 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 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) ID LO LD LO ID CD LO - O O O OO O O Ul Ul Ul Ul Ul Ul Ml IT) M- CM CO * O CM CM 1 CM *~ *- *- *- CM CO t^ Oi v. IS ,_ CO S C CM cm Oi Mr CO CO LO CO M- CM CM O CO Oi O) N N CD o> CO *- ID Oi M- CM LO M- o CO CO CM CO M- N. CO LO * O CM CO CO Oi d CM CO d d Uj CO LO ID ID LD LO LO o CM CO CO M- ID LO CO q q O q O q q CO CM O CO CO m- CO CM CO M- M- ID CO CO LU uj UJ UJ Lil LU LU d m- o O O o o o o CM ID CM o CM CO CO O CM CO o o @ d d d d d d o CM CM N. LO T- O CO o LO LO IS CO Oi o ,_ s. s |S CD CM O M- o CO CM Oi s. CO O CO CO O) CM LO CO CO CT> CM CO M- LO to LD CO -f- " d o O o o - d d d d d d d d d d d d d d UJ @ O X CO CO N. S. Oi Oi Oi rs to o CM M- CO S- a m- o o o o o o o CO CO LO Oi CO LO CO Oi CM M- CO Oi o LU LU uj LU LU LU LU d o o CM CO ID CO CM CO CO M- g o CO CM CO o O @ d d d d d d d ^ *" W s. CM Oi CM x M- M- M- M- M- M" M- o Oi o CO CO CO _ CM M- CM o> CO LO CD M- + + + + + CM CO Oi CM LO S- d i- T "n1 UJ LU UJ LU LU LU UJ CM CM CM o O CO LO CO d d d d d d o 5. LO M- o O CM IS LO m M; i. CO K CO LO CO CO x CO S- N- r-- CO CO CO o ^ CO CO o CO CO CO o LO CM CM CM CM q M- M" q q q q q CO o Mr CO CM Lil UJ UJ LU LU LU LU d CM CM CM CO CO O CO CM CO O o O ' ' Oi r CM CO CM CO CM @ d d d d d d d O ,_ M" *" *" CO LO Mr Q_ x CD Oi Oi CT> Oi Oi CD o M- CO o M- CO _ CO CO Oi CO CM O CO S- q q q q q q q CO OI M- CO co LU LU LU UJ Ljj LU LU d M- "H* CM CM CO CO CM CM CM CM CM CM CM T ""* "* o o o o ID ID > LD ID lO ID LO co co m in id t t O CO co co co cm is Oi ooooooo r^. S. L/J CM CO LO 1- Oi Oi CM CO CO Oi ID N- M- E LU LU t- CM CM CO CO Mr - CO CO d d d d d d d r*. o q i- CO CO P) r- CDCO ro co co co co co co ^r CO - CO - N. CM ID cocor--cos.r-.--r LO CO CM IS t- CO CO CM LO CM CD LO -r- M- CM CM CO CO M- ID LO ooooooo i OO O O d O O ^2, or ooooooo t- Mr OS CO - N- O M" Is t- CO O O O O O O ID O CM LO CO O LO *- g CO Mh LD CO Is OQ CO LO Oi CO CO o co CM CM CO M- ID ID CO 4 4 LU ~ i CD CD CD CD CD CD CD CD CO g -On i r s n s. r-. r r- r*- CO = lp 1 .32E-07 [A] QE= 0.5615 [AA> sM Idark [A] I [A] Inorm [A] M R @ 1 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] 1 of Analysis (W5 C9.10 D400,20,500,N).xls (Page 12) 2 2 co CO ra o CO Q d d Si \\ t O CN CD D) CD CL x o IN o o Q lC tn o 5 CM o 01 t3> d O O o co O "? ** m 5 Q 5 5 o O CL m > o f cn cn ^>- CD C < o d CD o O o O o o o o o O o o o o O o O o o CM CN T CD CO o LVn] ;uejjno indino epoipojond J2 > > O -i - co co co co CO CO O O CO CO Q Q d d d d th o m o CM o o o LJ o O CO tn CD o> 5 CD CL V) CD cn c O X O O Z c IN o o in > o CO CN a CO l_ o n CD CO o o <* C o> O 0) o OI o T CO > a> O o > in o c < N 5 to o C/3 a >s j: co CD C ID o o < CD O a. > [vn] luajjno indino apoipojoqj o o 1 I I I 1 I I I 1 I I I 1 I I I _l I I I d o CD o CT1 o CO in CL _. tn CM_ "1 * 5" o 0) O [Q O <""> /,, S> w- to O O) O m -J- 5 Q o c o ID d 3 O o to cn o cn CD c < o o - d CD o o o o o o o o o o o o o o o ? CD o CM LVn] luajjno jndjno apoipojond CN M o in CD O) co Q. CO ^ - CM at Z 3 is co CM O m t ... O) c O '5 in O 5 cn ^. CD c < o d CD o o o o o o o o o o o o o o o o o o o o o o o o o o o o o * o CO (IN) uibo o o CO o o o o m o CM CD CD a> O CO CL , . to O) E x O c . ^ m X. D) O to o O) CN c O O CD > Q to a> O 3 a *^ 3 o CO c CD ID c L. L. < 3 o [vn] juajjno LU LU LU LU LU LU LU LU LU o a a a a a o a o a c O) CO s co in ^r co cm - o d d d d d d d CL to CD LT LtLCLtLtitairirLtLt o o h- m CD O) CO CL tn a X o o o o in m ^ E cm. <=> E cn Q S o O) O to c o cn Q. en j>. to CD co a: c < [M/V] AjjAHisuodsay O o o o o o o o o CO o o o o o l-~ in o CM CO O CD o a> CO O CL tn x o m o o o 5 o n m o ST CM LU z O O o ^* 0) 8 a s o 0. O c J2 to > '5 8 .a cr cn LU ^> co CD c 10 < o o z o o < o o 1 r o o c ' l I CN CN CM CM CN co o o O o o 9 9 9 + LU LU LU LU LU LU o lO O LO o o o CO T T- CN CM LO o LAA] (d3N) JSAAOd juaiEAinbg bsion Water 4 4 4 4 MEASUREMENTS ARE DONE AT 600nm 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 -60 [V] 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 -62.18 -e -0.01384 -05176 -11.54 -61.08 -7 0 01384 -0.5176 -1126 -59.64 -6 -0.01384 -05176 -11.1 5 -0.01384 -05176 -1092 -5773 -27 37 4 -0.01384 -0.5176 -10.62 -9614 3 -0.01384 -0.5176 -9 642 -2.827 2 -0J31384 -0.5176 -3.105 1 -0.01384 -05176 -0.6459 -05817 -0.00066 0 -0.01384 -0.01035 0.02591 1.179 1 -0.01384 0.6543 128 5174 2 -0.01384 3.53 4 984 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 2nd Derivative a b Max Gradient Vbr Threshold Vbr Linear Trend Vbr -51.470 -51.234 -51.050 -47.967 Voltage Breakdown Vbr -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) 3 00E*0B |nUs] 6 OOE-07 H 5 0QE-14 \Hz] Po @ 6OO1 4 B6E-07 JWl 1 0Bt 1)5 [m] R@600n 0 353B |%j @600nrr 3 75E*0S [1fm) > = 1 49E-07 |A] OE = 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 7 4 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 -4 6 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 -1.1 E-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 1 E-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 476-07 -26 7.6E-0B -8.2E-0S 1 49E-07 551 5417 0 3073 2 -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 1E-07 -23 -6.SE-O8 -7.9E-05 1 49E-07 52S 3652 0 3073 2 1 3073 -22 -6JE-08 -7.BE-05 1 49(7-07 521 3296 0 2 03E-O7 906-07 -21 see-ob -7.7E-05 I 49E-07 514 6119 0 3073 1 1 79E-07 -20 -5 5E-08 -7.BE-0S 1 49E-07 507 322 0 3073 3073 1 60E-C7 -1B -57E-OB -7 4E-05 1 49E-C7 406 6644 0 586-07 -18 -4.9E-0B -7.3E-0S 1 49E-07 491 593 0 3073 1 0 3073 1 486-07 -17 -4.5E-0B -7JE-OS 1 49E-07 46J 6789 1 34E-07 -16 4 1E-0-B -7 1E-05 1 49E-07 475 7609 0 3073 3073 1 24E-07 -IS 3 8E-48 -7E-05 1 49E-07 469 236 0 2257 0 3073 I 09E-07 -14 -3 4E-OB -6.9E-05 1 49E-07 461 0 3073 9 78E-08 -13 3E-08 -6.BE-DS 1 49E-07 53 9347 0 3073 8B4E-0B -12 2 7E-OB -6 7E-05 1 49E-07 445 5928 3031 0 3073 7 90E-OB -11 -2.4E-08 -6 5E-05 1 4BE437 438 0 3O73 4.50E-O8 -10 -1.4E-0B -6 4E-05 1 49E-07 431 7018 8015 0 3073 4 5OE-0S -1 -1 4E-0B 6JE-05 1 496-07 423 303 0 3073 4S0E-08 1 -1 4E-0B -6.21: 05 1 496-07 416 9384 0 3073 4 50E-O8 -7 -1.4E-C* -6 IE-OS 1 49E-07 408 4 -6E-C5 49E-07 2874 0 3073 SOE-OB -6 14E-08 1 399 5097 0 3073 4 506-08 -5 1 4E-0B -5.BE-0S I 496-07 386 49E-07 183 2456 0 3073 4 506-08 -4 -1 4E-08 -2.7E-03 1 3073 4 506-08 -06 49E-07 70598 0 -: 1 4E-0B -S BE 1 65 927)2 0 3073 4 50E-08 -2 -1 4E-06 -2 HE 06 1 49E-07 18 49E-07 894555 0 3073 4 506-08 -1 1 4E-08 -5.BE-07 1 3 49E-07 0 004419 0 3O73 4 506-08 0 -1 4E-0S -6.6E-10 1 -7 89355 0 3073 4 506-08 1 -1 4E-0B 1.1BE-06 1 49E-07 49E-07 -34 6406 0 3073 4 SOE-OB 2 1 4E-0B 5.17E-0* 1 1 1 Analysis (W5C9.10 D400.20.500N) ills (PaflB 0(12} >- s s s r_, CD O o o O LU LU LU LU LU Tf- CN LO O CO LO o o Oi CN) 2* CO CM CM CNI Oi co CD CO TT N. s. Oi CO C co ** o o O t- CM CO cn CM co" d d d d d cn v- co co lo T- C\| (\l CO N Oi Csj Oi CO Tfr Oi CN t- *-- -t- O ^ CO O N- Co CD K ^ CM 00 CO CO CO co i cn c\i csj csj csi (O (D (O CO CO ooooo n -q- ^ o UJ UJ LU UJ LU OOOOO ry r- oo ^ n CD CD CD CD CD n a CO CO CO ) S. csi oi csi oi n CM CO CJ LO CM Oi < LU "r" o in <* * s D_ X O co o * co r- CO CO CN O CO N. 09099 _ Oi t> Oi co 50 UJ UJ UJ UJ til O t- CM CM Co CO ECO 00) CO 00 00 d d 0 d d ..OOOOO) 5 cc CO LO UO LO ^r O CO CO CO CN s. 0 O O O 0 r>- LO CM CO LO + + + + + CM CO CO Oi 10 d TJ- E LU LU LU LU LU CM CM CO CO 00 to CM O d O d d O CO CD @ 06 CO *-" CD CO CO CC CO CO CO CD CO O T- CO ^- N. CM CO r- CO r- CO CO CM N. to CO CO LO CO CN LO CN CO LO ---- T CO CO CO CO d CM 00 CO Tr LO OOOOO 1 o o o o o OOOOO 0 TJ- Oi LO OOOOO Oi 0 CN Ui CO O tj- LO CO r^ 00 o> CO CO 0 CO d CM CO Tr LO LO CD CO 0) 0 0 O 0 0 <-: cc 0 CO CO Oi CO CN E o o o o 0 0 CM CO CO Th LO CN O CO O Tj- ~ LULULULULU ' * The following graphs are the raw crosstalk test results of the APD arrays. Only arrays exhibiting promising data were tested for crosstalk. 243 > o OOO o o OO 10 o a i el A ** * * b l a a rt c o 9 4- L. li. *4 + -M C > _J W W OT O > > W *,-: .j x " 19 n' >. haj C" | ' | J i Xlo 1 |-~ >j<^ }s o V !i 1} 1 f\J 1 ! sfc Oc 5 k : o cn2 o - to Ii^ WW X1-1 '^\ 1 \ 1 X. w\ \ 1 v\v- I * % N, '' 1 N * 1 1 *.M^ O (o> o O (D-H oy O iOT3 in * * LU 4. ^ M i >>> > OOO o ooo o OOO o O O 10 o lO ? a i B vl b CO - jC * .. . ^O D * B > _J CO W 3* > * CJ >>> > OOO o OOO o OOO o OOO o JO *t a i B a m 5* B B U 0 I + I r L c A *> B m b c a. a H C B O B 8 I, U. -rt 4-1 + * C i>jnnc4 o > > o -K Tl 1 X O rO * "Z IO -flD * Q.l * f^-. rjj i , "J CJ ^_3 \ *. \ > O _l G. O \W -^ o o \ o :n s-1 \ \ o CJ V m \ \ * . L_ \ \ \ \ V. | \- W \|- Vs. "V LrJ JjL \ WW I > ^r*%' """ *" -i \N % -4- \. \ \ o w\ V \ o IZ ^ ^v.j i*** 0 ^ o < o O-rt ? E O in -a in i o > > > > OOO o O O o o OOO o O O ID o 10 ** a i * v* B cn .. J -*0 N 5 I 4J 3 >i L, C + B *> c a o. * rt C B D B a L LL *4 *- * + c > jmcjffl o > > U *"W O i 1 1 o xz I o no \ i * ^rv \ 6 W i \ UO J > : i ! "D - Q.S W - - O w O oo 2 ; \ O s \ ID i \ \ 0L V i La. CD > i i ; * v\ i w 1 2 i *' 1 i [CD c o> c O-H c < c ci tm-j IT t c i Li. * i J >>> > OOO o OOO o OOO o OOifl o 10 ** a 1 B n b n B U 6 1 +* 1 it L c a +* B e l a a 4J n C B O B B t 11. *i 4* 4A * C b > j 09 a) o S* > ,o 1 o T * t i lO n i ; . \-. r ^ i LIin1 , 1 f - w- .. . L i Oil ^i > i -H w i Li o * 0] \\ O o CD (J to r lLT X':: \\ Q' CD \\ \ \ \\ \ '-. S * \ . ., 1 ED o 1 V I > > > > o o o O OOO O OOO o OOO o {0 -r* O. I B B S .. JC B 8 O B I -M 1 C A 44 m B b c a a ** c a o b m t- LL ** an c j tO Tl a i 9 vt B P) * 5 rl U B IU B 1 4* E r* L. C J3 B ** ft b l a. a +> n C B O B B C tl, -H 4i + 44 C B > -J CO CO CO o> > o Xn" *7 H.," cj 5 Cjna Hifi' Xu [Let. X >< * * < e > > > > OOO o ooo o OOO o O O Q o T * ID * Li? _ o Ucj tXo "5 (l)Q rj ct; LI* "J Q.co X < > > 9 a O OO o O o oo o o Tl a i a rt .$ c c B4> B JO 4* B B C a a r* C B O 0 0 u rl 41 c B _l tfl CO to > -* in 1 f> C3ru Jc; Xo Um LX^ X LD *. X * & * < LL > >> > ooo o OOO O OOO - o o 8 o * t ..ex .. n o a 0 u s 1 4> 1 - e. c 1 0 4* 0 0 a i. a n 4 rl C 0 O B 0 t "i. -rl 4* 4* 4* c 0 > J to to CO o> > o > >> > o OO o o O O o o OO o * oo o o * rl * a I 0 14 Tl 0 .. S .5 Tl O 0 ' 0 P I n C c a 04* 0 (. a a Tt C 0 o B 41 4 c 0 > j to to co o > > o X . Jt- Xo LJ - I- ho XfJ Q.1 <3: X CD X X X X X X E >> > > OOO o OOO o OOO o O O o O d n ti a t 0 Wf PI . J= .. rt o 0 b a 0 ( 4J 1 r t. c J3 0 4> B B v t a a 4T rl C B Q B B t. U. * ? 4J + C B > ^ 0) CO 0) O > > o X*T X j . l-v -"-" 1 iLD ^:J X^T <-* n CD X X x X * X' 6.7.5 Crosstalk Analysis of Selected Photodiodes The following are crosstalk calculations of selected APD arrays. 256 Z- o 4 LO 2 z t^- ( > o o o Lf> lo 1^- S- CN o (_> o CN O CM CM ^r O O fl CJ C 3 CN a o Q T- aj CD 1X1 m u O o o T TO *- tn tn O (P8Z!|bujjon) >(|Bissoj3 |eu6js 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) 7. 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in O >
CO in CO CO + + + + + d CM CO Oi CM tn UJ LU UJ LU LU CM CM o o CO d d d d d I M" o o CM O M: Si S^ CO w CO K
0 0 o p o ] o o o o o 5 'T LfJ CO S OS 6.7.4 Raw Crosstalk Data