Advances in Photodiodes Part 5 ppt

Front surface of array is irradiated by photon flux hν δ-shaped light beam or uniform flux or spotlight that is absorbed and generates photocurrent in pixel.. Dependence of one-sided sid

concentration in zero point (t = ) is always equal to zero i.e 0 n bgr(0)=0 As the result concentration profile of photogenerated charge carriers nearby to point t = is formed 0preferably by their photogeneration with subsequent extraction into SCR On the other hand due to disparity LP<<L n extraction of dark minority carriers into SCR takes place from

whole thickness of p base where they have existed initially (at V b=0) Furthermore value of concentration n d(0)= Δn(0) 0< is fixed according to expression (34) by applied bias and algebraic value (n LP ≤ d ) 0 grows with increasing of S In other words ratio ( n LP d ) / (0)n d

is raised This entire means that gradient of concentration of non-equilibrium dark minority

charge carriers along axis t grows with increasing of S (Fig 8a)

minimum photocurrent values

5 Photocurrent generation and collection in small-pitch high-density IRFPA

Theoretical approach was developed for the case of front-side illuminated IRFPA based on

regular structure of n+− junctions enlaced by p n gr+ - guard ring around, Fig 10

5.1 PV IRFPA design model

Cross-section of model PD array fragment (pixel) is shown on Fig 10

5.2 Photocurrent generated by sideways δ-shaped light beam

For estimation purpose let’s consider one-dimensional (along line A) n gr+ − −p n m+ − −p n gr+

fragment (Fig 10) of model PD array illuminated by δ-shaped light beam perpendicularly

to surface of array, where n m+ is n+- region of n+− junction, p n gr+ is n+- guard ring

around n+− junction and p is layer (substrate) common for all pixels of PD array Pixel is p area including n+− junction and limited by guard ring (Fig 11) Model array fragment is p

symmetrical regarding n m+ - region (Fig 11) For simplicity word photocurrent will mean further photocurrent generated by pixel illuminated by proper light Photocurrent generated

in pixel is calculated at short-circuit between lead V and Ground (Fig 11)

Fig 10 Cross-section of model PD array fragment (pixel) 1 - n m+ is n+- region of n+− p

junction with width W0; 2 - n gr+ is n+- guard ring with width W ; 3 - p is thin layer gr (substrate) common for all pixels of PD array Spacing between periphery of n+− junction p and guard ring is marked as W Front surface of array is irradiated by photon flux hν (δ-shaped light beam or uniform flux or spotlight) that is absorbed and generates photocurrent

Fig 11 Front view of model PD array fragment 1 - n m+ is n+- region of n+− junction with p

width W0; 2 - n gr+ is n+- guard ring with width W ; 3 - p is thin layer (substrate) gr

common for all pixels of PD array Spacing between periphery of n+− junction and guard p ring is marked as W Front surface of array is irradiated by photon flux hν (δ-shaped light beam or uniform flux or spotlight) that is absorbed and generates photocurrent in pixel One-dimensional consideration is developed along line A (illumination moves along

that line) Common p thin layer and n gr+ - guard ring grid are grounded Photocurrent generated in pixel is calculated between Ground and V diode lead connected to n m+ - region

of n+− junction p

Where: R n and R - recombination rates, n p Δ - concentration and τ- lifetime of excess

electrons and holes

Drift of excess charge carriers in electric field in p - region is negligible

Band-to-band photogeneration of charge carriers at point y y= g, i.e specific rate of

photogeneration is described by formula:

Where: (δ y y− g)- delta-function and Gδ- total photogeneration rate of charge carriers

In analyzed conditions distribution of Δn y( ) in p - region is defined by diffusion equation:

Where: D - coefficient of ambipolar diffusion

Do solve equation (45) in intervals W o/ 2< ≤y y g and y g≤ ≤y y7≡W0/ 2+W assuming

Where: n p - concentration of equilibrium minority charge carriers (electrons) in p - region

Condition (46) means continuity of excess charge carriers’ concentration, and condition (47)

is derived relation resulted from integration of equation (45) in neighborhood of point

Graph of K versus normalized distance d W between δ-shaped light beam and periphery

of n m+- region of n+− junction is presented on Fig 12 p

If sideways δ-shaped light beam illumination is symmetrical in relation to n+- region of

n+− junction (i.e junction is illuminated from left and right sides, Fig 10) then total p

photocurrent value will be two times higher than got from expression (48)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Fig 12 Dependence of one-sided sideways photoelectric conversion coefficient K on

normalized distance d W between δ-shaped light beam and periphery of n m+ - region

5.3 Photocurrent generated by uniform sideways and front illumination

To calculate photocurrent value lat

ph

I under symmetrical regarding n m+ - region sideways

illumination we need integrate expression (48) with respect to y between W o/ 2 and

Wand than multiply result by coefficient 2

In the case of uniform illumination (G xδ( )=const) we get:

2

Where: G 2W- total sideways photogeneration rate (taking into account both left and right

sides) is defined as:

Assuming that photoelectric conversion coefficient is equal to 1 under front-side

illumination we can write photocurrent value I ph frin this case as follows:

0

fr ph

As it follows from expressions (50) - (53) ratio of photocurrents generated by n+− junction p

under uniform sideways and front-side illumination is defined by:

lat ph fr

o ph

5.4 Photocurrent generated by moving small-diameter uniform spotlight

Basic relation (48) allows estimating of photocurrent I variation when small diameter ph

(D spot) uniform spotlight is moving along surface of PD array

To calculate photocurrent value we need integrate expression (48) with respect to y within

uniformly illuminated region except guard ring region (W ) Further we will limit gr

consideration by condition (57):

Within uniform spotlight area dependence of photocurrent I on spot center position ph y c

will be described by formulae given further

Case (a): Gap between n m+ - region border and n gr+ - guard ring is higher than spot diameter:

Generation of photocurrent when spot illuminates right half of central pixel

Let’s mark I( )ph c photocurrent generated in central pixel when spot moves within interval

Spot light is appearing on the side of n m+- region and aty c>y2get it away

In the interval (61) we get:

2

c

spot c

Spotlight gets away gradually from considered central pixel Photocurrents generated in

central pixel and neighbor right side pixel will be equal to each other when y c will coincide

to mid y4of right side guard ring (68):

c

c c

Generation of photocurrent when spot illuminates left half of neighbor right side pixel

Photocurrent generation in right side pixel I ph> will take place when edge of spotlight

appears in that pixel, i.e at condition (72):

10а1 y12≤y c≤y8; I ph( )y c D spot

q Gδ

>

=

× (79)

Where distance between centers of n m+- regions of central and right side pixels: 8 0 2 gr y =W + W W+ (80) Generation of photocurrent when spot illuminates left half of central pixel Let’s mark photocurrent at negative and positive coordinate y c as I ph−( )y c and I ph( )y c properly Values I ph−( )y c and I ph( )y are the same in respect to zero point c y = c 0, i.e ( ) ( ) ph c ph c I − y =I −y (81) Therefore we do have the following cases: 11a −y1≤y c≤ ; 0 I ph−( )y c = ×q Gδ×D spot (82)

12а −y2≤y c≤ − ; y1 I ph−( )y c = ×q Gδ×F y1( 2+y y c, 3+y c) (83)

13а −y3≤y c≤ − ; y2 I ph−( )y c = ×q Gδ×F y2( 7+y c) (84) 14а −y5≤y c≤ − ; y3 I ph−( )y c = ×q Gδ×F y3( 5+y c) (85) 15a y c≤ − ; y5 I ph−( ) 0y c = (86)

Generation of photocurrent when spot illuminates right half of neighbor left side pixel 16a −y6≤y c≤ ; ( ) 00 I ph− y c = (87)

17а1 −y11≤y c≤ − ; y6 I ph−( )y c = ×q Gδ×F3(− −y c y6) (88)

18а1 −y10≤y c≤ −y11; I ph−( )y c = ×q Gδ×F2(− −y c y9) (89)

19а1 −y12≤y c≤ −y10; I ph−( )y c = ×q Gδ×F1(− −y c y10,− −y c y11) (90)

20а1 −y8≤y c≤ −y12; ( )I ph− y c = ×q Gδ×D spot (91)

Case (b): Gap between n m+- region border and n+- guard ring is less than spot diameter: / 2W D≤ spot (92)

Generation of photocurrent when spot illuminates right half of central pixel 21b 0≤y c≤y1; ( )c fr spot ph ph I =I = ×q Gδ×D (93)

22b y1≤y c≤y3; ( ) 1( 2 3 )

( )

,

c c ph

⋅ (94)

In interval (96) part of spot is located in n m+- region but spot edge does not reach guard ring Case (b1): Let’s impose some condition: b1 W gr 2 (≤ D spot/ 2−W) (95)

23b1 y3≤y c≤y2; ( ) 4( 2 ) 2 ( ) 2 c c ph c c I y W F y y y y L th q Gδ L ⎛ ⎞ = − ≡ − + × ⎜ ⎟ ⋅ ⎝ ⎠ (96)

24b1 y2≤y c≤y5; ( ) 3( 5 ) ( ) c c ph c I y F y y q Gδ = − ⋅ (97)

25 y5≤y c≤y8; I( )ph c = 0 (98)

Generation of photocurrent when spot illuminates left half of neighbor right side pixel 26 0≤y c≤y6; ( ) 0I ph> y c = (99)

27b1 y6≤y c≤y10; 3( 6) ( ) ph c c I y F y y q Gδ > = − × (100) 28b1 y10≤y c≤y11; 4( 10) ( ) ph c c I y F y y q Gδ > = − × (101)

29b1 y11≤y c≤y12; 1( 10 11) ( ) , ph c c c I y F y y y y q Gδ > = − − × (102)

30b1 y12≤y c≤y8; I ph( )y c D spot q Gδ > = ⋅ (103)

Generation of photocurrent when spot illuminates left half of central pixel 31 − ≤y1 y c≤ ; 0 I ph−( )y c = ×q Gδ×D spot (104)

32b −y3≤y c≤ − ; y1 I ph−( )y c = ×q Gδ×F y1( 2+y y c, 3+y c) (105)

33b1 −y2≤y c≤ − ; y3 I ph−( )y c = ×q Gδ×F y4( 2+y c) (106)

34b1 −y5≤y c≤ − ; y2 I ph−( )y c = ×q Gδ×F y3( 5+y c) (107)

5.5 LWIR PD array: calculation of photocurrent collection profiles

Data used in calculation of photocurrent generated in small-pitch high-density

Hg0.776Cd0.224Te PD array are given in Table 2 Junction regions thickness t was taken t(n+) =

0.5 μm and t(p-absorber) = 6 μm Surface recombination rate 102 cm/sec

Developed approach (57) - (113) was applied to calculate photocurrent generated in

small-pitch Hg0.776Cd0.224Te PD array Calculated dependences of photocurrent I generated by ph

spotlight in Hg1-xCdxTe (x=0.224) PD array are shown on Fig 14 and ratio of photocurrents

generated at uniform frontal and sideways illumination can be estimated easily from Fig 14

It is seen clearly that developed approach allows analytical estimation of photocurrent

generation in different close-packed PD arrays Following to dependence presented on Fig

13 contribution of photocurrent generated by sideways uniform illumination to total

photocurrent of pixel can be too much high at not reasonable ratios between L , W and W0

Dependences of photocurrent value I are calculated as function of spot center position ph

coordinate y c for central and neighbor pixels of array Condition y = c 0 means that in start

position Zero of coordinate system and spot center are matched Length (distance) is given

in units D spot (spot diameter) Photocurrent is calculated in units q G× δ×D spot It is accepted

in calculation that width of n m+ - region of n+− junction p W o= 20 µm; width of n gr+ - guard

ring W = 5 µm; spot diameter gr D spot= 15 µm; operating temperature T op=77K; ambipolar

diffusion length in p layer L = 48 µm Spacing between periphery of n+− junction and p

guard ring W = 20 µm (a) and W = 5 µm (b) Photocurrent in central, neighbor right-side

and neighbor left-side pixels are presented on graphs by solid curves, dashed curves and

dash-and-dot curves properly

6 Conclusion

We have attempted to develop some general approach for simulation MWIR and LWIR PD

IRFPA including estimation of major electro-optical parameters Estimations have shown

that extended LWIR Hg1-xCdxTe PD with p-n junction will be potentially of 4-5 times lower

dark current value than PD with n+-p junction at T=77 K and 2 times lower at T=100 K

Additionally extended LWIR Hg1-xCdxTe PD with p-n junction will be seriously lower

sensitive to operating temperature increasing than PD with traditional n+-p junction We

have shown that surface recombination rate value at back surface of thin p absorber can

have serious effect on dark current in small-size LWIR Hg1-xCdxTe PD We have developed analytical expressions describing collection of photogenerated charge carriers in small-pitch IRFPA for practical cases: uniform and small-size spotlight illumination

0 0.2 0.4 0.6 0.8 1

Whicker, S (1992) “New technologies for FPA dewars”, Proceedings of SPIE, 1683, pp

102-112, ISBN 9780819408488, August 1992, SPIE Press, Bellingham, Washington Triboulet, P & Chatard, J.-P (2000) “From research to production: ten years of success”,

Proceedings SPIE 4130, pp 422-440, ISBN 9780819437754, December 2000, SPIE

Press, Bellingham, Washington

Baker, I & Maxey, C (2001) “Summary of HgCdTe 2D array technology in the UK”, Journal

of Electronic Materials, Vol 30, No 6, (June 2001) 682-689, ISSN 0361-5235

Norton, P (2002) “HgCdTe infrared detectors”, Opto-Electronics Review, Vol 10, No 3,

(September 2002) 159-174, ISSN 1230-3402

Kinch, M (2007) Fundamentals of Infrared Detector Materials, SPIE Press, ISBN

978-0-8194-6731-7, Bellingham, Washington

Glozman, A.; Harush, E.; Jacobsohn, E.; Klin, O.; Klipstein, Ph.; Markovitz, T.; Nahum, V.;

Saguy, E.; Oiknine-Schlesinger, J.; Shtrichman, I.; Yassen, M.; Yofis, B & Weiss, E (2006) “High performance InAlSb MWIR detectors operating at 100 K and

beyond”, Proceedings SPIE 6206, pp 6206M, ISBN 9780819462602, May 2006, SPIE

Press, Bellingham, Washington

Kinch, M.; Brau, M & Simmons, A (1973) “Recombination mechanisms in 8-14 μ HgCdTe”,

J Appl Phys., Vol 44, No 4, (April 1973) 1649-1663, ISSN 0021-8979

Gelmont, B (1980) “Auger recombination in narrow band-gap semiconductors”, Sov

Semicond Phys & Tech., Vol 14, No 11, (November 1980) 1913-1917, ISSN

1063-7826

Gelmont, B (1981) “Auger recombination in narrow band-gap p-type semiconductors”, Sov

Semicond Phys & Tech., Vol 15, No 9, (September 1981) 1316-1319, ISSN 1063-7826 Blue, M (1964) “Optical Absorption in HgTe and HgCdTe”, Physical Review A, Vol 134, No

1, (January 1964) 226-234, ISSN 1050-2947

Laurenti, J.; Camassel, J.; Buchemadou, A.; Toulouse, B.; Legros, R & Lusson, A., (1990)

“Temperature dependence of the fundamental absorption edge of mercury

cadmium telluride”, J Appl Phys., Vol 67, No 10, (May 1990) 6454-6460, ISSN

0021-8979

Schmit J., (1970) “Intrinsic carrier concentration of Hg1-xCdxTe as a function of x and T using

k-p calculations, J Appl Phys., Vol 41, No 7, (June 1970) 2876-2879, ISSN 0021-8979 Blakemore, J (1962) Semiconductor Statistics, Pergamon Press, ISBN 0-486-49502-7, New

York, New York

Silicon Devices

Methodology for Design, Measurements and

Characterization of Optical Devices on

Integrated Circuits

Mexico

1 Introduction

The main application of optical devices is image processing which is a research field still in study for a wide variety of applications, such as video digital cameras for entertainment use, pattern recognition based in artificial neural networks, real time object tracking, clinical uses for repair by stimulation parts of visual system and artificial vision for application in silicon retinas, among others So, it is important to evaluate the performance of available integrated photo-sensor devices used in these applications, considering issues as noise, resolution, processing time, colour, etc Actually, there are several technologies available for integration

of photo devices, commonly CCD, BiCMOS and GaAs Although all of them are usually applied in image acquisition systems, there are still some performance aspects that should

be optimised, as voltage levels, leakage currents, high fabrication costs, etc., so research is still being done to overcome these limitations Standard CMOS integrated circuit technology

is also an attractive alternative, since devices like phototransistors and photodiodes can be implemented as well The foremost advantage of CMOS devices is its availability in standard technology It should be mentioned that this technology has also some limitations but since fabrication of CMOS integrated circuits has low costs, exploration of the potential

of new technologies for image processing is still an interesting field Besides, algorithms can

be implemented along for tasks such as border detection (space vision), movement detection (space-time vision), image enhancement (image processing vision) and pattern classification

or recognition (neuro-fuzzy vision)

Considering the state of the art (Aw & Wooley 1996; Storm & Henderson, 2006; Theuwissen, 2008), as well as clinic approaches (Zaghloul, & Boahen, 2004), in this work, a chip was

designed and fabricated, with two possible photo-sensor structures: p+/N-well/p-substrate, for phototransistors and N-well/p-substrate, for photodiodes, through the standard 1.5µm AMI’s- , N-Well technology In the future, it is the intention to design a second chip that

must include electronics for image processing with pulse frequency modulation (PFM), once the characterization gives enough information about the performance of the stages studied

A complete description is given