Temperature dependence of dark current in a CCD

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Portlad State Uiversity PDXSholar Physis Faulty Publiatios ad Presetatios Physis 4-1- Temperature depedee of dark urret i a CCD Ralf Widehor Portlad State Uiversity Morley M.

1 Portlad State Uiversity PDXSholar Physis Faulty Publiatios ad Presetatios Physis 4-1- Temperature depedee of dark urret i a CCD Ralf Widehor Portlad State Uiversity Morley M. Blouke Portlad State Uiversity lexader Weber rmi Rest Erik Bodegom Portlad State Uiversity Let us kow how aess to this doumet beefits you. Follow this ad additioal works at: Part of the Physis Commos Citatio Details Ralf Widehor; Morley M. Blouke; lexader Weber; rmi Rest ad Erik Bodegom, "Temperature depedee of dark urret i a CCD," Pro. of SPIE 4669, Sesors ad Camera Systems for Sietifi, Idustrial, ad Digital Photography ppliatios III, Morley M. Blouke; Niti Sampat; Joh Caosa; Niti Sampat, Editors, pp (pril ); DOI: / This rtile is brought to you for free ad ope aess. It has bee aepted for ilusio i Physis Faulty Publiatios ad Presetatios by a authorized admiistrator of PDXSholar. For more iformatio, please otat pdxsholar@pdx.edu.

2 Temperature depedee of dark urret i a CCD Ralf Widehor, Morley M. Blouke, * lexader Weber, rmi Rest, ** Erik Bodegom Departmet of Physis, Portlad State Uiversity, Portlad, OR 977 * Sietifi Imagig Tehologies, Tigard, OR 973, ** stroomy Departmet, Uiversity of Washigto, Seattle, W BSTRCT We preset data for dark urret of a bak-illumiated CCD over the temperature rage of to 91 K. Usig a rrheius law, we foud that the aalysis of the data leads to the relatio betwee the prefator ad the apparet ativatio eergy as desribed by the Meyer-Neldel rule. However, a more detailed aalysis shows that the ativatio eergy for the dark urret hages i the temperature rage ivestigated. This trasitio a be explaied by the larger relative importae at high temperatures of the usio dark urret ad at low temperatures by the depletio dark urret. The usio dark urret, haraterized by the bad gap of silio, is uiform for all pixels. t low temperatures, the depletio dark urret, haraterized by half the bad gap, prevails, but it varies for eret pixels. Dark urret spikes are prooued at low temperatures ad a be explaied by large oetratios of deep level impurities i those partiular pixels. We show that fittig the data with the impurity oetratio as the oly variable a explai the dark urret harateristis of all the pixels o the hip. Keywords: depletio dark urret, usio dark urret, Meyer-Neldel rule 1. INTRODUCTION Sie the ivetio of the Charged-Coupled Devie (CCD) i 1969, by George E. Smith ad Willard S. Boyle at the Bell Telephoe Laboratories, the CCD tehology has ome a log way. State of the art CCDs are able to detet light levels of a few photos. The detetio of photos is doe by apturig the photoeletros, geerated by the photoeletri effet, i a potetial well. For low light level appliatios oly a few sigal eletros are geerated ad the oise limits the resolutio of the CCD. soure of oise itrisi to the CCD is the so-alled dark urret. It is geerated eve though the hip is ot exposed to light. This dark urret is due to the thermal exitatio of eletros ito the odutio bad ad olletio i the CCD wells. The geeratio of dark eletros is a thermally ativated proess ad as suh strogly temperature depedet. Oe way to suppress dark urret is by oolig the CCD-hip to very low temperatures. Dark urret is ot uiform for all pixels. Pixels with a very high dark sigal are referred to as dark urret spikes or hot pixels. They are geerally radomly distributed ad show up as white dots i a dark frame (Fig. 1). Pitures otaiig dark urret a be orreted by subtratig a dark frame of the same exposure time from the image. However, subtratig a dark frame adds the Poiso oise of this frame to the image. We ivestigated the dark urret for a bakside-illumiated CCD housed i SpetraVideo amera (Model: SV51V1) maufatured by Pixelvisio, I.. The hip was a three phase, -buried hael, three-level polysilio bak-thied devie (1.3 mm x 1.3 mm, 51 x 51 pixels, maufatured by SITe I.) with a idividual pixel size of 4 µm x 4 µm. The outer edge ( pixels) was exluded from the aalysis. I order to miimize uertaities due to the readout oise ad the Poiso oise, the dark urret was determied as the average of several pitures. 5 images where take eah for the followig exposure times: 3, 5, 1,, 5, 1 s, images eah for 5 ad 5 s ad 1 images where take for 1 s. Dark frames for all exposure times were take at, 3, 4, 5 ad 6 K, for exposure times up to 5 s at 71 K, for exposure times up to 5 s at 81 K ad for exposure times up to 5 s at 91 K. Noe of the of 47 x 47 pixel subframes showed pixels whih were saturated ad the dark urret ireased liearly with ireasig exposure time. Hee, we ould alulate the dark urret by fittig the umber of eletros olleted versus the exposure time. 1 Eletroi mail: ralfw@pdx.edu Eletroi mail: bodegom@pdx.edu Sesors ad Camera Systems for Sietifi, Idustrial, ad Digital Photography ppliatios III, Morley M. Blouke, Joh Caosa, Niti Sampat, Editors, Proeedigs of SPIE Vol () SPIE X//$

3 FIG. 1. seods dark frame take at 5 K. The white dots represet pixels with high dark urret. They are ofte referred to as hot pixels or dark urret spikes.. THE MEYER-NELDEL RULE FOR DRK CURRENT IN CCD I a first approah the dark urret, as may thermally ativated proesses, was assumed to follow the rrheius law: De De exp b E ktg, (1) where De - is the dark urret i e - /s ad E is the ativatio eergy. ordig to Eq. (1) all data poits i a plot of the logarithm of De - versus the iverse temperature, the so-alled rrheius plot, should lay o a straight lie. The ativatio eergy of the proess is the absolute value of the slope of this lie. Figure shows the rrheius plot ad liear fits to the data poits of four radom pixels. lthough a straight lie fit does ot model the data perfetly, the assumptio of desribig dark urret with Eq. (1) seems reasoable. We fitted all,784 idividual pixels aordig to the rrheius law ad obtaied,784 pairs of expoetial prefators, De, ad ativatio eergies E. These results were aalyzed aordig to the Meyer-Neldel rule (MNR). The MNR is a empirial law first espoused by W. Meyer ad H. Neldel i 1937, ad is observed frequetly for proesses whih follow the rrheius law. The rule states that the logarithm of the expoetial prefator depeds liearly o the ativatio eergy. Hee, for the dark urret: De De expb E E MN g, () where De ad E MN are positive ostats. The MNR is foud i various fields ad for several eret proesses, e.g. for usio 3,4 or the odutivity of semiodutors. 5-7 lthough eret explaatios have bee proposed oe is uiversally aepted ad the disussio as to what auses the MNR is ot settled. It has bee argued that the MNR arises due to a expoetial desity of state distributio that idues a shift i the Fermi level. 8 Others see the origi i the etropy of multiple exitatios. 9,1 The CCD gives the uique possibility to ivestigate the MNR for a set of more tha, samples. Figure 3 shows the plot of the logarithm of the expoetial prefator versus the ativatio eergy for all pixels. The ativatio eergies vary from roughly half the bad-gap of Si to about the bad-gap of Si, with most pixels havig E s of approximately.9 ev to 1 ev. The agreemet of all data poits with the MNR is remarkable. We a dedue the two MNR-ostats 194 Pro. SPIE Vol. 4669

4 as E MN 5.3 mev ad De 1685 e/s. I order to get a better uderstadig of the meaig of these two ostats substitutig Eq. () ito Eq. (1) oe obtais: L NM F HG 1 1 De De exp E (3) E kt Eq. (3) shows that for a harateristi temperature or eergy the dark urret is idepedet of the ativatio eergy. This temperature, also kow as isokieti temperature, is give for our experimet as T MN E MN /k94 K. De is the dark urret at this partiular temperature. The isokieti temperature a also be see i Fig. as the itersetio of the liear fits. The agreemet of the liear fits ad the atual data poits at T MN is ot perfet. t temperatures higher tha the isokieti temperature the MNR predits a iversio of the dark urret. Hee, hot pixels with a high dark urret at low temperature should show a lower dark urret tha other pixels for T>T MN. I order to verify this preditio, the hip was heated to a temperature of 313 K. We foud that the predited iversio did ot our. It ould oly be foud that the dark urret was fairly similar for all pixels. s we will show later this is ot surprisig, but to be expeted for dark urret i a CCD. Thus, the liear relatioship betwee the logarithm of the prefator ad the ativatio eergy for all,784 pixels is remarkable, but the MNR does ot predit the dark urret lose to ad above the isokieti temperature aurately. I fat the apparet rossig i the rrheius plot is atually more a overgee of the dark urrets for eret pixels. loser look at the data-set shows a positive urvature i the rrheius plot. The ativatio eergy is lower at low temperatures tha at high temperatures. We showed that suh a hage i the ativatio eergy a explai the observatio of the MNR. 11 The origi of the shift i the ativatio eergy with hagig temperature for dark urret i a CCD will be disussed i the ext setio. MN IO KJ QP l(de - /s -1 ) /T [K -1 ] FIG. The logarithm of the dark urret vs the iverse temperature ad liear fits for four eret pixels. FIG. 3 The logarithm of the expoetial prefator vs the apparet ativatio eergy for all pixels o the CCD-hip. 3. SOURCES OF DRK CURRENT The dark urret i a CCD is a very importat soure of oise ad has bee studied thoroughly. Geerally three eret soures of dark urret otribute to the total dark urret i a CCD: the depletio or bulk dark urret geerated i the depletio regio, the usio dark urret geerated i the field-free regio ad the surfae dark urret geerated at the Si-SiO iterfae. For a CCD operated i multipied phase (MPP) mode the iterfae is Pro. SPIE Vol

5 iverted with a high hole arrier oetratio ad this soure of dark urret is almost ompletely suppressed. The aalysis of the remaiig usio ad depletio dark urret is very similar to the aalysis of the dark urret i a diode ad a be foud i various books o semiodutors, see for example Grove 1 or Sze. 16 The geeratio or reombiatio of a eletro-hole pair a our either as a bad-to-bad proess (i.e., odutio bad to valee bad) or through a itermediate state. The bad to-bad proess should oly deped o the bad struture of the semiodutor. However, it has bee foud that the geeratio or reombiatio of arriers i Si depeds greatly o the preparatio of the semiodutor. This idiates that the reombiatio ad geeratio proess ivolves impurities or imperfetios. Those imperfetios disrupt the lattie of Si ad itrodue eergy levels ito the bad-gap. The et geeratio-reombiatio rate, U, of arriers through these itermediate eters has bee suessfully desribed by Hall, Shokley ad by Read It a be show that: U σ L NM + exp i F HG σ σ v p N p th i t Et Ei kt d I K JO i L NM F HG Ei E p p i QP + + σ exp kt t I K JO QP, (4) where σ p ad σ are the apture ross-setios for holes ad eletros respetively, v th the thermal veloity, the eletro oetratio, p the hole oetratio, N t the oetratio of bulk geeratio-reombiatio eters at the eergy level E t, E i the itrisi Fermi level ad i the itrisi arrier oetratio whih is give as: i NvN expdeg kti, (5) where E g stads for the bad gap i silio ad N v ad N are the effetive desity of states for the valee ad odutio bad respetively. I thermal equilibrium, p i ad thus the geeratio is equal to the reombiatio ad U. 1. Depletio dark urret CCD, however, is ot operated i equilibrium. I the depletio regio, beeath the CCD wells, the eletri field sweeps holes to the p-type substrate ad eletros to the potetial wells. Thus there is a regio depleted of arriers where ad p << i. ssumig the ross-setios for holes ad eletros are equal (σ σ σ ), Eq. (4) results i: p U dep σv N th t i i osh bei Etg kt τ (6) with: [( E E ) kt] osh i t τ (7) σ v N th t as the effetive geeratio-reombiatio life-time i the depletio regio. The geeratio-reombiatio rate, U, dereases expoetially as the eergy level of the eters moves away from the mid-gap E i. Hee, those eters lose to E i are most effetive for produig dark urret. Those eters lose to the mid-gap are ofte referred to as deep-level impurities. For E E, the arrier lifetime is give as: τ σv N i t b th t g 1 (8) Usig Eq. (6), the dark urret desity per uit area geerated i the depletio regio a be expressed as: I dep qxdepi τ, (9) 196 Pro. SPIE Vol. 4669

6 where q is the eletro harge ad x dep is the width of the depletio regio. The dark urret i eletros per pixel ad per seod, De dep, is give as: where is the area of the pixel. pix De dep x dep pix i τ, (1). Diffusio dark urret The potetial well beeath the gates does ot reah all the way to the bak-surfae ad a part of the CCD remais field-free. I this field-free regio, the equilibrium miority arrier oetratio p is give as: where N is the aeptor oetratio i the p-type substrate, i our ase boro. p i, (11) N We kow from the study of usio urret outside the spae-harge regio of a diode i reversed bias, that the usio urret is proportioal to the gradiet of the eletro oetratio evaluated at the iterfae betwee the depletio ad the eutral or field-free regio: I p qd d dx x, (1) where D is the usivity of eletros ad p is the miority or eletro oetratio. For a diode where the field-free regio, x ff ; is geerally larger tha the usio legth, L, the arrier oetratio i the field free regio is give as: whih leads to 1expbx Lg (13) I p p, diode qdi N L (14) However, it is questioable that the usio urret as see i a diode, desribes the usio urret i a bak-illumiated CCD properly. Bak-illumiated CCDs are thied suh that the field-free regio is oly a few miros. If the field-free regio is smaller tha the usio legth, a arrier distributio whih is ot a futio of the usio legth but of the size of the field-free regio might desribe the system more aurately. ssumig leads to: I qdi x N ff p px x ad ff De D x N pix i ff (15). (16) Pro. SPIE Vol

7 The expressios for the usio urret i Eq. (14) ad Eq. (16) are similar. The oly hage is that for a small field-free regio, x ff is substituted for L. The small field-free regio might also have a impat o the usivity, D. Dark urret, as desribed i Eq. (16), would result i a ireasig usio urret with dereasig field-free regio. This aot be true for very small values of x ff. The miority arrier distributio give i Eq. (15) aot desribe suh a system aurately. The boudary oditio that the equilibrium arrier oetratio is reahed at the bak surfae aot be true i suh a ase. For ow, we will assume that the usio dark urret for our CCD is similar to Eq. (14) ad Eq. (16): where x is a harateristi legth. De D xn pix i (17) 4. DT NLYSIS The total dark urret is give as the sum of the usio dark ad the depletio dark urret as give by Eq. (1) ad Eq (17): D x pix i De De + Dedep + xn dep pix i τ (18) The usio dark urret is proportioal to i ad the depletio dark urret proportioal to i. The temperature depedee of itrisi arrier oetratio is give by: 3 d i d i d i F k i NvN Eg kt me mh T Eg kt T Eg kt H G I exp π h K J exp exp (19) where h is Plak s ostat, m e ad m h are the effetive masses of eletros ad holes, ad E g is the bad-gap for Si. Empirially, the bad gap of Si is give as: T EgbTg 117. ev () T The values of m e ad m h for Si are ot osistet throughout the literature. The values geerally quoted for N v ad N at 3 K are: N m 3 ad N m 3, whih leads to: m 3 K 3 v It follows that the temperature depedee of the dark urret a be expressed by the followig equatio: De D x pix 3 dep pix 3 T exp E kt + g T exp E g kt xn τ b g b g (1) Oe a easily see that the first term ireases i importae as the temperature ireases. The seod term will have a tedey to domiate at lower temperatures. It is ommoly believed that the depletio dark urret is domiat for temperatures lose or smaller tha room temperature. 17,18 Hee, the ativatio eergy for the dark urret should be i the proximity of half the bad-gap. The rrheius plot for the depletio urret oly would show a slight urvature due to the temperature depedee of the bad-gap ad the T 3/ term. However, the urvature i our data is muh stroger ad the alulated ativatio eergies are too high to be aused by the depletio dark urret oly. Figure 5 depits the rrheius plot for the average dark urret (average for all,784 pixels). The ativatio eergy hages from about half the bad gap at low temperatures to approximately the bad gap at high temperatures. This idiates that a 198 Pro. SPIE Vol. 4669

8 trasitio from depletio to usio domiated dark urret ours i the ivestigated temperature rage. The parameters for the usio dark urret are speifi to our partiular amera but should ot hage sigifiatly for eret pixels o the hip. This explais why the dark urret is fairly uiform for all pixels at high temperatures (see Fig. ad Fig. 4). I Fig. 4 the dark urret is ormalized suh that the average dark urret is set to 1 e - /se. The distributio gets wider as the temperature ireases. While the omparatively higher read oise at low temperatures, aused some spread i the distributios, the width ireases maily beause of the ireasig otributio of the depletio dark urret. The dark urret at low temperatures varies osiderably due to the fat that the depletio urret depeds o the ueve impurity distributio. umber of pixels umber of pixels 4 91 K ormalized dark urret [e - /se] 5 K ormalized dark urret [e - /se] umber of pixels K ormalized dark urret [e - /se] 5 3 K 4 umber of pixels ormalized dark urret [e - /se] FIG. 4 Dark urret histograms at 3 K. 5 K, 71 K ad 91 K. The average dark urret is ormalized to 1 e-/s. I order to verify if the dark urret i our CCD a be desribed by Eq. (1), we left both prefators ad ativatio 3 3 eergies as parameters ad fitted the data aordig to: De De T exp E kt + De T exp E kt d i d i,, dep dep These trials showed that ideed the assumptios leadig to Eq. (1) were justified ad aordigly, we fixed the ativatio eergies to E g ad E g / respetively. Usig oly the two prefators as fittig parameters showed that, as expeted, De, was very similar for all pixels. s see i Fig. 6 the data ould be aurately modeled with: d i d i () 3 3 De De T exp E kt + De T exp E kt, g, dep g where E g is the bad gap of Si as give by Eq. (), De, From Eq. (1) ad Eq. () oe gets exp(34.9) e - /K 3 ad De, dep is harateristi for eah pixel. De, pixd ad De xn, dep x dep pix τ (3) Pro. SPIE Vol

9 It is importat to otie that the value for τ will be temperature depedet if the impurity eters are ot loated at midgap. Our aalysis shows that impurities, roughly at mid-gap, are resposible for the depletio urret. Modelig our data required oly the assumptio of eret oetratios of mid-gap impurities. This does ot exlude the possibility that eret impurities loated lose to mid-gap are resposible for the eletro geeratio. Suh impurities ould for example be Ni, Co, u whih are lose to the mid-gap ad to a lesser extet Fe whih is further away from the mid-gap. 19- The harateristi legth, x, derived from Eq. (3) is: x D pix De, N (4) Our CCD was built of 3 Ωm material. This leads to a aeptor impurity oetratio N of approximately 4*1 14 m -3 The usivity, D, whih i reality is temperature depedet, is more iult to estimate tha N. ssumig D 5 m /s results i a harateristi legth x of 7 µm. This was larger tha the field-free regio whih should be of the order of 1 µm or less, but muh smaller tha the usio legth i Si. More researh with various eret sizes of the field-free regios is required to fully uderstad how the size of x ff ifluees the usio urret. We a alulate the eletro lifetime i the depletio regio from Eq. (3) as: τ x dep pix De,dep (5) The size of the depleted regio for a buried-hael CCD a be estimated as desribed by Jaesik. 18 For a oxide thikess of 1 m, a -layer of width 1µm ad door impurity oetratio of *1 16 m -3, the 5 V bias leads to a depleted regio, x 8.6µ m. The values for De dep, dep varied for eret pixels, its average value was give as exp(19) e - /K 3/. This leads to a average lifetime of.5 s. l(de - /s -1 ) 7 6 E1.14 ev E.57eV /T [K -1 ] l(de - /s -1 ) /T [K -1 ] FIG. 5. The average of the logarithm of the dark urret vs the iverse temperature. FIG. 6. The logarithm of the dark urret vs the iverse temperature for four radom pixels. The fits are based o the model assumig eret impurity oetratios. The deep-trap impurity oetratio follows from Eq. (8) as: Nt bσvthτg 1. The arrier veloity, though i reality temperature depedet, was assumed as 1 7 m/s. The ross-setio depeds o the type of the impurity. s a Pro. SPIE Vol. 4669

10 example, the ross-setio of u is equal to 1-15 m -. 1, This results i a average impurity oetratio of approximately *1 9 /m 3 or about 1 impurities/pixel. Hot pixels have a impurity oetratio twie or more of this average value. 5. CONCLUSION I olusio, we showed that aalyzig dark urret aordig to the rrheius law leads to a spread i the apparet ativatio eergies with a mea value of approximately 1 ev. These ativatio eergies ad the orrespodig prefators were related as predited by the MNR. The iversio i the dark urret, for temperatures higher tha the isokieti temperature was ot observed. We foud that with ireasig temperature the dark urret for eret pixels was gettig more uiform. This ould be explaied by a trasitio from the depletio dark urret to usio dark urret with ireasig temperature. The usio dark urret was domiat at lower temperatures tha ommoly assumed. ll dark urret measuremets ould be modeled by eret oetratios of a sigle impurity omplex. It would be of geeral iterest to uderstad how the usio dark urret hages with eret sizes of the field-free regio. 6. REFERENCES 1 R. Widehor, L. Müderma,. Rest, ad E. Bodegom, J. ppl. Phys 89, 8179, 1 W. Meyer ad H. Neldel, Z. Teh. Phys. 1, 588, (1937) 3 D. G. Papageorgiou, G.. Evagelakis, Surfae Siee 461, L543, 4 X. L. Wu, R. Shiar, ad J. Shiar, Phys. Rev. B 44, 6161, Y. Lubiaiker ad I. Balberg, Phys Rev. Lett. 78, 433, K. Shimakawa ad F. bdel-wahab, ppl. Phys. Lett. 7, 65, Y. F. Che ad S. F. Huag, Phys. Rev. B 44, 13775, H. Overhof ad P. Thomas, Eletroi Trasport i Hydrogeated morphous Semiodutors, (Spriger-Verlag, Berli, 1989) 9. Yelo, B. Movaghar ad H.M. Braz, Phys. Rev. B 46, 144, Yelo ad B. Movaghar, ppl. Phys. Lett. 71, 3549, R. Widehor,. Rest, E. Bodegom, The Meyer-Neldel rule for a property determied by two trasport mehaisms, to be published 1. S. Grove, Physis ad Tehology of Semiodutor Devies, (Joh Wiley & Sos, 1967) 13 C. T. Sah, R. N. Noye, ad W. Shokley, Carrier Geeratio ad Reombiatio i p- Jutio ad p- Jutio Charateristis, Pro. IRE, 45, 18, R. N. Hall, Eletro-Hole Reombiatio i Germaium, Phys. Rev. 87, 387, W. Shokley ad W. T. Read, Statistis of the Reombiatio of Holes ad Eletros, Phys. Rev. 87, 835, S.M. Sze, Physis of Semiodutor Devies, seod editio (Joh Wiley & Sos, 1981) 17 M. J. Howes ad D. V. Morga, Charge-Coupled Devies ad Systems, (Joh Wiley & Sos, 1979) p J. R. Jaesik, Sietifi Charge-Coupled Devies, Spie Press, 1 19 R. D. MGraph, J. Doty, G. Lupio, G. Riker, ad J. Vallerga, IEEE Tras. Eletro Devies, vol. ED-34, 555, 1987 W. C. MColgi, J. P. Lavie, J. Kya, D. N. Nihols, ad C. V. Staampiao, Iteratioal Eletro Devie Meetig 199, p. 113, De., W. C. MColgi, J. P. Lavie, ad C. V. Staampiao, Mat. Res. So. Symp. Pro. 378, 713, 1995 W. C. MColgi, J. P. Lavie, C. V. Staampiao, ad J. B. Russell, Mat. Res. So. Symp. Pro. 51, 475, 1998 Pro. SPIE Vol

Chapter MOSFET

Chapter MOSFET Chapter 17-1. MOFET MOFET-based ICs have beome domiat teholog i the semiodutor idustr. We will stud the followig i this hapter: - Qualitative theor of operatio - Quatitative I D -versus-v D harateristis