154 IEEE TRANSAC‘rIONS ON ELECTRON DEVICES, VOL. ED-25, NO. 2, FEBRUARY 1978

Solidi, vol. A-20, pp. 675-685,1973. [16] S. B. Campana and D. F. Barbe, “Tradeoffs between aliasing and [13] C. Anagnostopoulos and G. Sadasiv, “Transmittance of Air/SiOz/ MTF,” International Conf. on Tech. and Applications of Charge-

polysilicon/SiOz/Si structures,” ZEEE J . Solid-State Circuits, vol. Coupled Devices, Edinburgh, Scotland, Sept. 1974. SC-10, pp. 177-179, June 1975. [17] D. H. Harper, “The modulation transfer function of front illumi-

[14] B. P. Lathi, Communication Systems. New York Wiley, 1968. nated charge-coupled imaging systems,” M.A.Sc. Thesis, University [ E ] J. W. Coltman, “The specification of imaging properties by response of Waterloo, Waterloo, Ontario, Canada, pp. 1-142, Mar. 1976.

to sine wave input,” J . Opt. SOC. Am., vol. 44, pp. 468-471, June, [18] S. B. Campana, “Techniques for evaluating charge-coupled imag- 1954. ers,” Optical Engineering, vol. 16, pp. 267-274, May-June 1977.

Photosensing Arrays with Irnproved Spatial Resolution THEODORE I. KAMINS, MEMBER, IEEE, .AND GODFREY T. FONG, MEMBER, IEEE

Abstract-The spatial resolution obtainable in a photosensing array used for optical imaging may be limited by the diffusion of photogenerated carriers within a uniformly doped semiconductor even if other components of the optical system are optimized and scattered light is reduced. A technique has been developed to im- prove the spatial resolution for critical applications by incorpo- rating subsurface electric fields that accelerate the photogenerated carriers toward or away from the surface so that the carriers are prevented from diffusing to distant photosensing elements. The subsurface fields are obtained by incorporating suitable dopant concentration gradients into the structure. In one structure fab- ricated the subsurface field was formed by using a heavily doped buried layer and a lightly doped epitaxial film over a lightly doped substrate, all of the same conductivity type. This structure is compatible with the incorporation of other semiconductor devices in the same monolithic substrate. The technique has been applied to an array of photodiodes in a silicon integrated circuit, but the principle is directly applicable to other types of photosensing ar- rays, such as charge-coupled devices (CCD’s), and other semicon- ductor materials.

I INTRODUCTION

N RECENT years, arrays of photosensors have been used for optical imaging applications. Both phol-

todiodes [l] and charge-coupled devices [2] have been employed to collect the photogenerated carriers. In both types of devices, however, the spatial resolution obtainable may be limited by diffusion of the photogenerated carrier: within the semiconductor itself [3], even if other compo. nents of the optical system are optimized and Scattered. light is reduced. A carrier photogenerated under one sensor can diffuse a significant distance in the underlying semi,, conductor substrate to be collected in the space-chargc region of a distant sensor, giving a spurious signal and

Manuscript received July 14,1977; revised November 1,1977. The authors are with the Hewlett-Packard Laboratories, Palo Alto.

CA 94304.

io

Photogenerated Hales Random Motion

Fig. 1. Cross section of conventional photodiode array with uniformly doped substrate, showing that photogenerated minority carriers can diffuse a significant distance in the semiconductor substrate to be collected tt a distant diode (A), where they contribute to the “optical crosstalk.

degrading the spatial resolving power of the array. This type of interaction may be termed “crosstalk” by analogy with the unwanted interactions encountered in commu- nication systems.

During the development of a high-resolution photo- sensing array, this “optical crosstalk” between photosen- sing elements became a limit on the spatial resolution of the array; and a technique was developed to greatly reduce the optical crosstalk by incorporating subsurface electric fields that accelerate the photogenerated carriers toward or away from the surface. The technique is described in this paper. It has been applied to an array of photodiodes fabricated by integrated-circuit technology in a silicon substrate, but the principle is directly applicable to other types of photosensing arrays, such as charge-coupled de- vices (CCD’s), and other semiconductor materials.

SPATIAL RESOLUTION Fig. 1 schematically illustrates the cross section of a

conventional photodiode array, formed by diffusing do- pant impurities through a Si02 masking layer into a uni- formly doped substrate of the opposite conductivity type. When light strikes the region above one photosensor (C in Fig, l), the electron-hole pairs photogenerated in the

0018-9383/78/0200-01.54$00.75 0 1978 IEEE

KAMINS AND FONG: PHOTOSENSING ARRAYS 155

Holes

&G;.;L; - - _ _ - _ _ _ __-_----- - ,-- 1

n - Type Substrate ’ /’ Fig. 2. Cross section of “buried-layer” structure which incorporates

motion of the photogenerated carriers. The carriers are accelerated subsurface electric fields to superpose a drift component on the random

toward or away from the surface, and their probability of collection by a distant diode is reduced.

neutral, uniformly doped, semiconductor substrate move by random thermal diffusion since the fields are negligible. While some arrive at the depletion-region edge of the nearest sensor (C in Fig. l), others diffuse to distant sen- sors ( A ) before recombining and may be collected. This diffusion degrades the spatial resolution of the array since the electrical signal from a carrier collected a t A appears to be caused by light incident a t position A rather than at C. The crosstalk is greater for penetrating long-wavelength light since carriers created deep within the semiconductor have a greater probability of diffusing to distant sensors than do carriers generated close to the surface.

The crosstalk may be significantly reduced by incor- porating built-in fields into the structure so that a drift motion is superposed on the random thermal diffusion, and the light-generated carriers are accelerated either toward the nearest photosensor or away from the surface. In either case, the probability of a carrier reaching a distant sensor is reduced. The field also leads to more rapid col- lection of photogenerated carriers, thus improving the frequency response of the array.

Fig. 2 illustrates a photosensing structure in which such subsurface electric fields are incorporated by means of suitable dopant concentration gradients. A highly doped region of the same conductivity type as the substrate (n- type in this case) is selectively introduced into the sub- strate either by diffusion or by ion implantation. An epi- taxial layer of the same resistivity as the substrate is then grown so that a buried n+ layer is formed beneath the photosensing areas of the wafer, while only a lightly doped, n-type region is located in areas in which other semicon- ductor devices may be fabricated. The structure is then subjected to a long, high-temperature heat cycle to redis- tribute the buried-layer dopant through a substantial fraction of the epitaxial layer. The nonuniform dopant concentration in the epitaxial layer creates an electric field in the photosensing area. The structure is then completed in the conventional manner by fabrication of photodiodes or other photosensing elements and the associated inte- grated-circuit structures.

A more controllable electric field can be built into the epitaxial layer by grading the dopant concentration during the epitaxial growth. However, this method is not as straightforward as the method previously described and creates the field over the entire wafer rather than in se-

Fig. 3. Representation of geometry used in analysis. The surface of the semiconductor is covered by collecting regions. Light is incident at a distance x from the edge of a collecting region of width w. This col- lecting region subtends an angle 02 - 01 at the point of carrier genera- tion a t a depth y beneath the surface.

lected regions. Consequently, it is somewhat less com- patible with the fabrication of other semiconductor devices in the same structure.

ANALYSIS

An accurate analysis of the influence of the subsurface electric field on the carrier collection quickly becomes mathematically complicated, and these complications obscure the physics of the device behavior. Therefore, a simplified, semiquantitative model will be used here to investigate the essential aspects of the optical crosstalk.

To start our analysis, we first consider a uniform semi- conductor totally covered by collecting regions, as shown in Fig. 3. We assume that light is incident on the surface at a distance x from the edge of a collecting region of width w and is absorbed at a depth y beneath the semiconductor surface, creating hole-electron pairs at the point (x,y). We then consider the probability that the minority carriers are collected at a given collecting region. We find the number of carriers reaching a collecting region because of light striking the surface at a distance x from the collecting re- gion by multiplying the number of carriers created within a thickness d y times the probability of collection of these carriers and integrating over the relevant depth. Our as- sumption that the surface of the semiconductor is com- pletely covered by collecting regions implies that any mi- nority carrier which reaches the surface is collected and that none are reflected from the surface.

The number of minority carriers dN created per unit time within a thickness d y at a depth y beneath the surface is given by

dN = &qoi exp ( -ay )dy (1)

where & is the photon flux, 17 is the quantum efficiency for carrier creation, and a is the absorption coefficient of the light. These three parameters are all functions of the wavelength of the incident light.

As an approximation we assume that the fraction of the created carriers that are collected a t one collecting region is given by the probability exp (-r/LD) that a minority carrier has not recombined by the time it reaches the col- lecting region integrated over the angle subtended by the collecting region and normalized by the total angle 2 ~ :

P = J1R2&exp (- 6) dB

where r is the distance from the si.te where the carrier is

IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-25, NO. 2, FEBRUARY 1978

INFRARED

1

\ 4

I ' ~ , ! ' ! \ ' ! ' ! " ? < ' 1 0 20 40 60 80 100 120 140

x ( u r n 1

Fig. 4. Semilogarithmic plot of the calculated, normalized photocurrent collected as an infrared light spot ( a = 0.10 Wm-l) is moved away frcrrl the edge of a collecting region. The upper solid curve corresponds LO a uniformly doped substrate while the lower solid curve was calculatc!d for a "buried-layer" structure with a maximum dopant Concentration 10 pm from the surface, and a characteristic time T of 10 ps. The dashd curve neglects the contribution of the field and considers only .tire termination of collection of carriers generated beyond the maximum dopant concentration.

created to the point where it is collected, and LD is t:hci! minority-carrier diffusion length. (The dependence of t :he collection probability on the angle subtended has belen confirmed by a Green's function calculation [4].)

In our analysis we are primarily concerned with CO:. lecting regions which are relatively far removed from the! point of carrier creation so that the distance r does not vary greatly within one collecting region. For mathematiaL simplicity, we may then approximate r in ( 2 ) by an average value F = within the collecting region and r e . move it from the integral. Then

1 - - exp (- ') (tan-1 - - tan-1 -) . (2 :I

x + w -__ X 27r L D Y Y

From (1) and (3) we may write an approximate expressio (1

for the number of carriers collected per unit time resultinl; from light striking the semiconductor at a distance x from the collecting region:

N = S p d N

tan-1 ') dy. Y Y

The photocurrent I is given by the product of the e1ectro::l charge q and N found from (4) .

Fig. 4 shows the calculated decrease in the photocurrent as the incident light spot moves away from the edge of the collecting region. (For convenience, the photocurrent I hi3ei been normalized by I O , the photocurrent collected whel:, the incident light strikes the semiconductor at x = 0.) T h ? curves have been calculated for a collecting region 74 WE].

wide, a minority-carrier diffusion length of 50 pm, and monochromatic light with a wavelength of 0.80 pm-just into the infrared region; the corresponding absorption coefficient is 0.10 pm-l [5]. The upper curve corresponds to the case of a uniformly doped substrate considered here. The photocurrent decreases by approximately three orders of magnitude as the light spot moves 140 pm from the edge of the collecting region.

The subsurface electric field introduced by the structure of Fig. 2 reduces the optical crosstalk in two ways. First, any carriers generated beyond the peak in the dopant concentration experience a force directed away from the surface, so that they are accelerated into the substrate where they recombine without contributing to the col- lected photocurrent. This effect can be incorporated into our simplified model by terminating the integration in (4) at the depth of maximum dopant concentration yp. While this reduces the photocurrent for all positions of the inci- dent light spot, the reduction becomes greater as the light spot moves away from the collecting region, as shown by the dashed curve of Fig. 4. The termination of the inte- gration in (4) at y = y p reduces the photocurrent by a factor of 4 when the light spot is at x = 100 pm.

The electric field also accelerates carriers created above the dopant concentration peak ( y < y p ) toward the surface, thereby reducing the effective time that they are free to diffuse within the semiconductor before they are collected. We may obtain some indication of the importance of this effect by considering the time T for an electric field to sweep a carrier generated near y = y p to the surface: T = yp /v = yp/p&. We then model the effect of the electric field by multiplying the collection probability found in (3) times the probability that a carrier diffuses more than the dis- tance F to the collecting region in the time T since carriers which diffuse less than F in time T are swept to the surface by the field and do not contribute to the photocurrent in the collecting region under consideration. The probability that a carrier diffuses more than a distance T; in time T is approximated by the expression [6]

1 m

~ 1 exp (-r2/4DT)dr = erfc r

mi: Inserting (5) into the integral of (4), we find the number of carriers collected per unit time to be approximately

- - exp ( -ay - -) (tan-1 - - tan-1 "> dy. (6) r x + w

LD Y Y The integration is terminated at y = y p in order to include the first effect of the field discussed above.

The lower curve of Fig. 4 shows the photocurrent pre- dicted by (6) as the light spot moves away from the col- lecting region. This curve corresponds to a time T = s and a peak in the dopant concentration 10 pm beneath the surface. Fig. 5 shows that the photocurrent is a strong function of the magnitude of the electric field through T.

KAMINS AND FONG: PHOTOSENSING ARRAYS 157

6 1

10 - 6 10 i 4 l d lb2 1i-1

T ( s e c

Fig. 5. Normalized photocurrent as a function of the characteristic time

edge of the collecting region. T, calculated for visible light incident on the structure 74 ym from the

For very low fields (large T ) few carriers are accelerated toward the surface before they diffuse to the collecting region of interest and erfc ( F / 2 m ) = 1. At high fields (small T) , most of the carriers are accelerated to the surface before they diffuse to the collecting region, and the com- plementary error function in (6) becomes small. Because of the random nature of scattering processes, this model may predict a more abrupt decrease in the optical crosstalk with increasing electric field than actually occurs.

For geometries consistent with semiconductor fabrica- tion, only a very small electric field is necessary to reduce the optical crosstalk significantly. A field of only a few volts per centimeter should markedly reduce the crosstalk a t a distance of 100 pm from the edge of the collecting region; consequently, any reasonable dopant concentration gra- dient should have a marked effect on reducing the optical crosstalk.

Fig. 6 shows calculations similar to those of Fig. 4 for a visible light spot with wavelength h = 0.68 pm, corre- sponding to CY = 0.25 pm-' [ 5 ] . Comparing the curves of Fig. 6 to those of Fig. 4, we see that the optical crosstalk is more significant in a uniformly doped substrate for the longer wavelength light (upper curves) since the carriers are generated at a greater depth, but that the dependence on wavelength is diminished in the buried-layer structure (lower curves).

EXPERIMENTAL STRUCTURE

In order to confirm the effectiveness of a subsurface electric field in reducing optical crosstalk, a series of dif- fused p+-n photodiodes were fabricated both on uniformly doped, n-type silicon substrates and on n-type epitaxial films grown over n+ regions diffused into n-type wafers (Fig. 2). The device geometry consisted of five parallel diffusions, each 32 pm wide and 200 pm long, with 74-pm spacing between the centers of adjacent diodes.

The starting substrates were n-type, (100)-oriented silicon wafers doped to 2 X 1015 with phosphorus. A dose of 3 X cmU2 phosphorus ions was implanted to form the buried layer. After the implanted phosphorus was diffused several miorons into the silicon substrate, a lightly doped silane epitaxial film about 8 pm thick was grown.

VISIBLE LIGHT a : 0.25prn-'

0 20 40 60 80 100 123 i40

x ( u . m )

Fig. 6. Calculated photocurrent as a function of position of the light spot for visible light (a = 0.25 ym-'); otherwise, similar to Fig. 4.

A subsequent 10-h diffusion at llOO°C served to redistri- bute the phosphorus buried layer over much of the epi- taxial film in order to provide a subsurface electric field extending through most of the epitaxial film. If the bur- ied-layer doping is assumed to have a Gaussian distribu- tion, the electric field in the quasi-neutral region can be calculated to be 460 V/cm near the surface, decreasing to 60 V/cm at 1 pm above the maximum dopant concentra- tion. As we have seen, fields of this magnitude are sufficient to cause a substantial decrease in the optical crosstalk.

After the buried-layer structure was formed, uniformly doped wafers were added. The two groups were processed through additional fabrication steps together so that the diffused photodiodes in both the standard and buried- layer structures were identical. . The photosensing p-n junctions were formed by conventional boron diffusion.

EXPERIMENTAL RESULTS AND nISCUSSION

After assembly the devices were mounted in an optical test fixture, in which a light spot could be automatically scanned across the set of five parallel photodiodes. All photodiodes were reverse biased, and the photocurrent through the end diode was monitored by a Keithley 616 Electrometer and recorded using a Hewlett-Packard 9820 calculator and plotter. A tungsten lamp with appropriate filters was used as the light source. In one case visible light with a peak wavelength of 0.68 pm (CY = 0.25 purn-l) was incident on the sample. Another incident spectral distri- bution corresponded to near infrared radiation and was obtained by placing a filter that eliminated wavelengths shorter than 0.72 pm in front of the tungsten lamp.

Fig, 7 is a semilogarithmic plot of the photocurrent in the end photodiode as an infrared light spot was scanned across the device. The solid curve corresponds to the structure containing the subsurface electric field, while the dashed curve corresponds to the uniformly doped sub- strate. The sketch above the experimental curves indicates the locations of the diffused regions on the x-axis. (Note that the zero of the x-axis corresponds to the center of the

158 IEEE TRANSPCTIONS ON ELECTRON DEVICES, YOL. ED-26, NO. 2, FEBRUARY lY’l8

P

‘t i

Burisd-layer , structure

x (pm)

Fig. 7. Normalized photocurrent experimentally observed for infrr ~ e d radiation incident on both conventional (uniformly doped substr,tice)

spot. The sketch above the plot shows the locations of the reverse- and buried-layer structures as a function of the position of the 1 ght

monitored biased photodiodes. The photocurrent in the diode at the left end was

leftmost diffused region in this figure, rather than to ?[,he edge.) To the right of the diode being monitored, them is a significant difference between the responses of the two structures when the light spot is near the second and tnird diodes. Beyond the third diode, the photocurrent is d.rrrost four orders of magnitude below its peak value and becc’mes limited by the background stray light in the measurer:rent apparatus. These results are consistent with the expected effect of the buried layer: photogenerated carriers art? ac- celerated toward the surface by the subsurface field and are collected by a nearby diode rather than diffus.ng a significant distance to contribute to optical crosstalk.

To the left of the monitored photodiode, less diffl, :” rnce is seen between the responses of the two structures eince there are no intermediate diffusions to serve as colk cting regions. Photogenerated carriers reflected from the xugion near the Si-Si02 interface may then continue diffusing in both the uniform substrate and the buried-layer structure so that less improvement is expected.

Fig, 8 shows the normalized photocurrent observed. when a visible light spot (X = 0.68 p m ) was scanned acrcss the series of photodiodes. As in the case of infrared lighl,, little difference is seen to the left of the monitored photcsdiode, while a significant difference is seen to the right wE.m the light spot is near the second and third diodes.

The shoulder seen in the data for the uniform s1i:rstrate corresponds to the region between diffusions and occurs since carriers generated within a diffused region. m d its associated depletion zone cannot contribute to optical crosstalk. Thus, beneath the diffused regions, the el’fective zone which can contribute to optical crosstalk s t n t s a t a depth corresponding to the junction depth plus the width of the depletion region, and the integration in (4 I begins at different depths near the diffused regions and hetween diffusions. This effect has been seen more clearly in structures with different diffused-region width:;. Com- paring the experimental data of Figs. 7 and 8, we :!lee that this effect is more pronounced for visible light Lhan for infrared radiation, as expected, since visible light is ab- sorbed closer to the surface.

x (ILml Fig. 8. Experimental results similar to those in Fig. 7 but for visible light

incident on the samples.

Fig. 9. “Shaped” buried-layer structure. (a) Representation of cross section, showing lateral components of built-in electric field. (b) Photomicrograph of beveled and stained section, showing highly doped

The center-to-center spacing is 74 pm, and the maximum dopant buried layer (light-colored regions) embedded in lightly doped material.

concentration occurs approximately 8 &rn beneath the surface.

ADVANCED~TRUCTURE

As a refinement of the basic technique described in this paper, the structure may be fabricated with a lateral component of the subsurface electric field, as well as a vertical component, so that the photogenerated carriers are accelerated toward the closest collecting region. A sketch of the more complex structure is shown in Fig. 9(a), and Fig. 9(b) is a photomicrograph of an angle-beveled section of such a “shaped” buried layer. As can be seen, the n+ region extends closer to the surface between diffusions than it does directly beneath a diffusion. Thus, the force from the built-in field accelerates the photogenerated carriers more directly toward the diffusion.

This “shaped” buried layer can be formed by successive implantation of two species that diffuse at different rates as the buried layer dopants. The more rapidly diffusing impurity [phosphorus in the structure of Fig. 9(b)] is

KAMINS AND FONG PHOTOSENSING ARRAYS 159

placed only between photosensing elements, while the slowly diffusing species (arsenic in this case) is placed beneath the entire photosensing array. After a suitable redistribution diffusion, the resulting fields tend to ac- celerate the photogenerated minority carriers laterally toward the nearest diode, as well as vertically toward the surface.

SUMMARY

A technique has been developed that can be used in a photosensing array to improve the spatial resolution sig- nificantly by incorporating subsurface electric fields that accelerate the photogenerated minority carriers toward or away from the surface. The carriers are thus prevented from diffusing to distant photosensing elements. An ap- proximate analysis has shown that, the optical crosstalk is more significant for penetrating longer wavelength light, and consequently the influence of the electric field is greater for longer wavelength light. The analysis shows that the field both restricts the region from which the carriers are collected and accelerates them toward the surface for more rapid collection.

An experimental structure containing an array of pho- todiodes has been constructed in which the field was ob- tained by incorporating a heavily doped “buried layer” between a lightly doped substrate and a lightly doped epitaxial film, all of the same conductivity type. A signif-

icant reduction in the “optical crosstalk” was observed in this structure, in qualitative agreement with the approx- imate analysis. Other possible techniques for obtaining subsurface fields include the use of a “shaped” buried layer or an epitaxial layer with a graded dopant distribution.

ACKNOWLEDGMENT

The authors would like to thank J. Moll for many helpful discussions and C. Bryson, T. Polowyk, J. Lazier, and F. Schwartz for designing the measurement apparatus and measuring the spatial response of the experimental structures.

REFERENCES [l] R. H. Dyck and G. P. Weckler, “Integrated arrays of silicon photo-

detectors for image sensing,” IEEE Trans. Electron Deuices, vol. ED-15, pp. 196-201, Apr. 1968.

[2] D. F. Barbe, “Imaging devices using the charge-coupled concept,” Proc. IEEE, vol. 63, pp. 38-67, Jan. 1975.

[3] D. H. Seib, “Carrier diffusion degradation of modulation transfer function in charge coupled imagers,” IEEE Trans. Electron Deuices, vol. ED-21, pp. 210-217, Mar. 1974.

[4] J. L. Moll, private communication. [5] W. C. Dash and R. Newman, “Intrinsic optical absorption in single-

crystal germanium and silicon at 77’K and 300’K,” Phys. Reu., vol.

[6] J. P. McKelvey, Solid State and Semiconductor Physics. New York 99, pp. 1151-1155, Aug. 15,1955.

Harper and Row, 1966, p. 340. (By integration of equation (10-3-321, which is derived for the spreading of a minority-carrier packet in time.)