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JO URNAL OF RESEARCH of the National Bureau of Standards-A. Physics a nd Chemistry Vol. 64A, No.4, July- August 1960 Photovoltaic Effect Produced in Silicon Solar Cells
by x- and Gamma Rays J Karl Scharf
(J anuary 25, 1960) T he open-circuit voltage a nd photocur-rcnt produced in a silicon sola r cell by X- a nd gamma rays we re measured as a function of exposure dose ra te, cell temperature, angle of l incidence of radiation, a nd p hoton energy. This photore ponse was stable a nd propor tional to t he exposure dose rate, which was appli ed up to a maximum of J.8 X lOo roentgen per minute for X -rays a nd 4 X 10 2 roentgen per minute for C060 gamma rays. At a n expo I sure dose rate of 1. roentgen per mi n ute t he response was of the order of 10- 5 vol t for t he open-circuit voltage a nd 10- 8 a mpere for the photocurrent. At high exposure dose rates of Cooo gam ma rays, radiation damage became apparent. The temperature dependence of the photoresponse was controll ed by the te mpera ture dependence of t he cell resistance. The directional dependence of t he photoresponse vari ed wit h t he quality of radiation a nd for Cooo gamma rays was very small for a ngles from 0° to 70 °. The photoresponse decreased with increasin g p hoton energy but cha nged onl y litt le between 200 a nd 1,250 kilo electron vo lts. The ratio of the re ponse to X-rays of 38 k ilo electron volts effe ctive energy a nd t ha t to CoGO ga mma rays was approx im a tel." 6:1. An approxi mate value of t he thi ckness of the effec tive p- n jUllction layer is deduced from the energy dependence.
1. Introduction would be less dependent on incident photon cncrgy than t hat of other photovolta ie cells. ~ The investigation reported in this paper was :Measurements are reported of the response of -carried out in order to test t he suitability of silico n silicon solar cells to X- and gamma-rays as a function s olar p hotocells for dosimetry of X- (t ll d gamllHt rays. of (1) the exposure dose rate of t he radiation, (2) Silico n solar cells are photovoltaic cell s of t he p- n the cell temperature, (3) t he fl, ngle of incidence of junction type. ·VVhen ilTadi,tted with photons of (tn the radiation, a nd (4) the incident photon energy. energy sufficient to produce electron-hole pairs in s ilicon, a photocurrent is produced without appJic(t 2 . General Considerations t ion of an external electrical power uppl~- . The photocLirrent or the photovoltage developed between A silicon solar cell co nsists of a large arca n -type silicon disk with a very thin p-type layer on its t he two ide of t he junction CILtl be uscd as 11 measure -of tb e intensity of t he incident mdiation. surface [8] . In bfl,la ncing a n equilibrium between PllOtovoltaic cells are frequentl)' used for measm e the differe nt carrier con centrations in th e p-t~ ' pe ments of the intensity of visible light. Only few a nd n -type silicon , fl, strong electrostatic field is establish ed in the transition zone (fig . ] ). The I quantitative investigations have been l1Htde of t he response of photovoltaic cells to X- a nd gamm (t rays. electric junction field is due to a potential difl"erence :Morc detailed investigations were carried out on with Lh e higher potential on t he side of th e n-type -c uprous-oxide [1, 2] 2 a nd selenium [1 , 3, 4] cells of l a~T e r. This potent ial difference, sometim es call ed t he metal-semiconductor co ntact type a nd on the "difl"u sion potential," is of t he order of 1 v in germanium [5] a nd gallium arsenide [6] p- n junction silicon . This can be seen from t h e configuration photocells. L arge area selenium cells had the great of the electron energy bands in t he p- n junction as est overall sensitivity but showed a very slow photo shown in figure l. In the equilibrium state, the response to X-rays, similar to t hat observed in Fermi level EF is co nstant throughout the p- and photoconducti ve cells. Photovoltaic p-n junction n -type layers and t he barrier height t"1E is sligh tly ). cells were less sensitive th an selenium cells but h ad smaller than the energy gfl,P E a, which is l.1 ev for response t itTl es of t he order of milliseconds [6]. silico n. No detailed investigation of the response of silico n The p-n junction h as a current -vol tage charac solar cells to X- a nd gamma rays has been reported. teristic of an electric rectifier with the forward rfhe investigation of t hese cells seem ed to be prom current flowing from the p-type to the n -type layer. ising for different reasons. The silico n solar cell If t he p-n junction is irradiated with photons of an energy larger tha n Ea, electron-hole pairs are pro is a large area photovoltaic cell which has a high duced which are separated by tbe j u netion fi eld . current output and a short response time [7]. I t Electrons are driven to the n-type and holes to the I was also expected that due to the low atomic num ber p -type layer . In this way fl, voltage difference is of silicon (Z 81 = 14), th e response of silico n solar cells produced between the two sides of the junction, the p-side becoming positive and the n-side n egative. p-n 1 Supported in part by the U.S . Atomic En c r ~y Commiss ion. This photovoltage biases the junction in tbe , Figures in brackets indicate the literature references at the end of this paper. forward direetion and opposes the diffusion voltage. 297 COLL ECTING VOLUME Vc the forward direction and RL is the load resistance. (SH AD ED PART) I t may be assulll ed that t h e series cell resistance R .• a nd shunt resistance RS/i need not b e considered if I R s< < RL< < RS/i, a condition usu ally- fulfilled. According to the th eory of the p- n jUll etion [9] , one obtains - I j=I o [exp (I[ T//kT) - 1]. (1) - 10 is the s,1t umtion curren t of the j un ction in th e - rever se direction, q t he electronic charge, k t he Bolt z m an constant, T th e absolute temperature, and V dn---l th e photovoltage. The pllOtocurrent I measured in thc external load is then ( 0) I = I s-I j= I s- I o[exp (I[V/kT)-l]. (2)
From t his eq uflt ion one obtains for th e photoyoltflge Illeasured across t he cell terminals V= ~T 111(18-; 1+ 1}
Two special cases are us ually considered : (b) (a) Opell circui t co ndition :
FIGl' R E I . (a) Geomel1'Y of p- n j unction photocell showing the RL = ro; 1= 0; I s= I j photoelectric eJIective collecting volume V c determin ed by the minority carrier diffusion lengths Ln and . Lp. ( ~ ) E~ Ut librill1n config uration of electron ener gy bands tn a p- nJli1lctwn. (4)
The CUlTCllt carriers produced b.,- tll C l'Hdi flt ioll For (1 s/l o) < < 1, one obtains a nd scparat ed by the junction fi eld represent th e gellerated photocurl'ent in the r everse direction of the junction. In restoring t he equilibrium sl,1te, (4a) t h e photovoltage produces a current through the junction in the forward direction. Provided that (b) Short circuil co ndition: no extel'nalload is co nn ected to t he cell , the open circuit voltage (photoelectromot ive for ce) reachcs a steady vH lue at which t he genemted photoculTenl equals the junction curren t produced by the photo The open-circuit vol tage Vo a nd th e generated eul' voltage. If a, load resistance is connected across reut I s, u s uall~ ' called the short-circuit clilTent , nre the junction, pflrt of t his current flows t hrough lhe co nsidered as characteristic m easures for the pholo extcrnal load and t he photovoltage is reduced. response of the cell. The elecLrical characteristic of a p- n junction The theOl'~ ' of the photovoltaie eft'ect assumes th :lt , photovoltaic cell can be derived by co nsidcring the in ,1ddition to carriers produced inside the junction , equivalellt circuit shown in figure 2. The photocell all minority ca rriers produced outside it but able to is represen ted as a constant current generator. r each the junction by difl'usion, are co ntribut ing to The generated photocul'l'ent I s divides into the t he photocurrent. The photoelectric effec live area jUllction current I j and t he extenlalload current I . is therefore determined by the diffusion lengths of I Hj is the voltage dependen t j unction res istance in the minol'i t ~· carriers, the 'diffusion length being de fin ed as the average distance th at carriers diffuse ~ before recombining. If the mean free path of the rad.ia tion (equ"l to t he reciprocal of t he absorption coefficient m easured in cm - I ) is large compared with th e diffusion lengths CURRENT one obtains for the width L of the eft'ect iv e Hrea GEN. (6)
L" is the diffusion length of electrons in the p-type layer, L1' the diJrusion length of holes in the n -type l a~- er, a nd Ttl ' is t he width of the junction (fig. 1). FIG L' RE 2. Equivalent circuit of p- n j unction photocell . Usually Ttl? is vcr} slllHll compared with L v and Ln 29.8 a nd can be neglected. In solar cell d p< L ", if dp is High-energy electrons, which pass the p- n junction the thickness of the p-layer. The value of L is are negligibly influe ll ced by the low potential r therefore approximately barrier of approximately 1 ev. Only low-energy carriers are acted upon by the junction fwlcl in sueh (6a) a way that tbey co ntribute to the photocurrent. Equations ( ) and (9) are, therefore, also applicable Tbe gener~L l e d CUlTcn t I s will compri e all minorit? in the case of Jligh-energymdiat,ion , provided that carriers produced by radiation in the collecting go rcf'ers to the gellemtion rate of low-energy canier volume produced by the hi O' h-energy electrons. The col (7) lectin g volume Vc wilY be the same as in the case of visible light. provided that the whole junction clrea A is being irradiated. It has also been sbown that Hie satura 3 . Experimental Procedure tion current 10 will comprise all minority carriers thermally generated in the same collecting volume The photocells investigated were commercial 1'0 uncI 3 2• Vc· silicon solar cclls with a sensitive area of 7.9 cm Considering eqs (2) and (3) one obtains [10] The silicon disk of the cell was ~lpp roxiJ\1~Ltely 0.7 mm thick and was encapsul nted in It m etell casin g. Tho I = qAgoL - qAgL' [exp (qVlIcT ) - 1] (8) front of the cell was closed with a glass window and 1.25 mm thick. The wbole cell was 'Happed in black insulation tape in order to prevent t he access. V = IcT ln (qAgoL - I + 1) (9) q qAgL' of light. if The X-ray OLll'ces were a 250-kv Machlett tube with an inherent filtration of 3-mm Al and a 50-lev gL' = gpLp+ gndp (10) '. Machlett beryllium window-type tube with all , where go is the mte of generation of electron-hole inherent filtrcLtion of l-1111ll Be. The t ubes were l tungsten target tubes operated by a sta,bilizecL pair due to radiation ~lnd i equal to t heir number produced by the radiation per cubic ce ntimeter per constant voltage supply. A calibraLed 100-curie second. and gp and gn are the tiJennal generation CS 137 and a calibrated 200-curie C0 60 SOUl'ce wcre rates of holes in the n-Iayer and eleclrons in t he used as gamma ray sources. U lIless othenvi e stated, exposure dose rates were l p -Iayer, respectively. r From eqs (8) and (9) one obtains for tilC generated measured with Victoreen I'-JII eters which had bee n I or shorL circuit current calibmted for each investigated type of radiation against the NB ' standard free a il' cham bers.4 All (11 ) measurements were c~Ll'ri e d out with a ll irradiation of the whole se nsitive cell area. a nd for the open-circui t voltage The open circuit voltage was m easured by tLil elec tric compensation method. The pi1otoeuJ'l'en t ( L2 ) was determined either directly with a microaml1letel" Vo = k~'1 n (~t + l) or se nsitive galvanometer or by m easuring the voltage drop across a known load r esistance with a For (goL /gL' )« l , the approximation ca ll be made po tentiometel'.
v. _ KT . YoLo (12a) 4. Results and Discussion 0 - q gL' 4.1 Exposure Dose Rate Dependence The nbove relations were derived for tb e photo voltaic effect produced by visible li gh t but arc also Figure 3 shows the open-circuit voltage 110 nnd the >9 valid for irradiation with X- and gamma rays. In photo current I as a fun ction of the exposure close the case of visible light each absorbed photon excites rate for 250 kv unfiltered X-rays (fig. 3 0 3 5 x 10- 1 4 0 a. W- :t W- E (9 0 (9 « 5 ~2 « 1-- ~ W ~ z 3 0 a:: 3 0 W > a:: > a:: ::J a:: 4 !::: U I- ::J ::J 0 ::J U U f- U ~ 0 ~ I 29;; 2 3 U 0 '-? 0- I Z ~ 0- W W a. 0- 2 0 0 EX POSUR E DO SE RATE , r/min EXPOSURE DOSE RATE , r/mln (a) (b) FIGURE 3. Dependence oj open-cil'clLit voltage V 0 and photocll1'1'enl I on exposw'e dose l'ate measlLl'ed at 1'00111 tempel'atw'e (a) with 250-kv lLnfiltel'ed X -rays (load l'es'istance R L = 890 ohms), and (b) with 0060 gamma rays (R L = 532 ohms). Open circuit voltage and photocurrent produced The values of the photocurrent I shown in figure " by X - and gamma ra)TS were proportioJl T = 332 0 K Rc = 2 .95 x 102 ohm a. T=291° K E o Rc= 1. 23 x 103 0hm f f---" 1.5 Z W T = 2230 K 3 I ~ 1. 0 Rc=9.75 x 10 ohm i.. <.) 1 2.5 - 4 2.0 1. 5 1.0 0 . 5 1.0 1. 5 2.0 2.5 - 4 x 10 x 10 VOLTAGE, v 2 .0 FIGU RE 4. Clirrent-voltage characteristics of the investigated s'ilicon solar cell meawred at di.O·erent cell temperatures T , with indicat'ion of res pective cell resistance R c. time of irradiation. S Lluultaneously with the decay of the photoresponse the electrical resistance of the 80 cell decreased. Such transient response, apparently I.) o PHOTOCURRENT • OPEN-CIRCUIT vOLTAGE due t o radiation damage, was not observed in i m ea urement with gamma rays at low exposure 60 dose rates and is also not in agreement wi th m easure m ents reported by other authors. Moody et al. [11] o "- found a constant response of silicon solar cells to C060 ,.: z gamma rays at an exposure dose rate of approxi ~40 a: m ately 105 r/h!'. Lofer ki and R appaport [12] found ::J u 5 that the photoresponse of silicon solar cells to visible il: light remained unaff ected by simultaneous irradiation ::, 20 - with 750 lev and 2 M ev X-rays. The response of 5000 silicon solar cells to high-energ:v radiation at high 1000 exposure dose rates is bein g further investigated by , I the author. 1. 5 2.0 2,5 r EXPOSURE DOSE RATE , rlmln 4.2. Temperature Dependence f I GUR E 5. E xposure do se rate dependence of open-circuit l voltage and photo current measured at room temperatuTe with 'Vo and I produced by C S1 37 gamma rays were m eas di:O'erent load resistances at high exposure do se rates of 50-kv Ul'ed for different cell t emperatures between - 50° C lmfiltered X -rays obtained fTom a beryllium-window-type tube. and 60 ° C. The silicon solar cell was placed inside a wooden box in wmch the t emperature could be The maximum photocurrent observed at these high regulated by m eans of a thermostat. Dry ice was posure dose rates remained constant during irradia used for obtaining temperatures below room tempera 'n over several hours, The open-circuit voltage t ure. The gamma-ray source was placed outside Jwed a slow decrease in time of irradiation, wmch the box. as apparently due to an increase of the cell tempera The results of these measurements are shown in ure. When the radiation was shut off and t be cell figure 6. Vo decreased nearly exponentially with 'lowed to cool down, the open-circuit voltage increasing temperature. The photo current I meas Jcovered to the original value at a subsequent ured with a load resistance of RL = 532 ohms was .cradiation. approximately constant up to 10 ° C and deer·eased Open-circuit voltage and photocurrent produced then with increa ing temperature. The temperature by gamma rays obtained from a water-s bielded 2,000 dependence of Vo and I will, according to eqs (13) > curie C060 source at an exposure dose rate of approxi and (14), be determined by the temperature depend 5 I mately 6 X 10 r/h1", showed a considerable decay with ence of R j • The generated current I s m ay be 548228- 60--3 301 200 , lOG 1.0 150 150 f- , 8 Z w' w ~ II: I '" II: 1-' '::J'" OJ Z a u w > J il' 100 - 100 f- ~6 OJ 0 u OJ I a u "- I a: a U w I z > 0.. w 0.. ~.4 5000 a --' 50 - 50 w a: ,2 0 L-_~4ko --L-~' 2~6 --L--0~--~2~0~~' ~4~0~---6~6~ 0 TEMPERATURE, • C 0 ~20~~~3~0--~~40~-L--~5 0~-L--6~0~-L~70 F I GURE 6. Temperature dependence of open-circuil voltage V 0 TEMPERATURE , ·C and photocurrenl I (R L = 532 ohms) produced by Cs 137 gamma rays, FIGU R E 7. Re l a t i ~e change of pholocurrenl with cell tempera lure measured wzlh 250-kv unfiltered X -rays for di.D'erent load _, assumed to be independent of temperature, because resistances. I the generation ra te go and the diffusion length Lp (eq (11)) remain approximately constan t over a limited range of temperature. R j decreases nearly exponen tially with in creasing temper ature causing 4 .3. Directional Dependence the exponen tial decrease of V o (eq (14)). The tem perature dependence of I is determined by the ratio The directional dependence of Vo and I measured 4c Rd Rj (eq (13)). Rd Rj increases with in creasing fo r differen t qualities of radiation is shown in figure 8. I temperature and the photocurrent therefore de The photocell was turned at differen t angles 8 around creases. With decreasing temperature the ratio an axis going through the cen tel' of the cell perpen Rd Rj decreases and the photo current increases ap dicular to th e direction of the inciden t radiation. proaching the value of Is. However, at lower tem Vo and I changed in the same way with ch anging 8. peratures the series resistan ce R., originally assumed The relative values shown in figure 8 therefore apply as negligibly small, increases too and eq (13) has to to both . be modified as, The directional dependence measured with 50-kv unfiltered X -rays from a beryllium-window-type tube approximately follows a cosine law. There is (13a) less directional dependence fo r 250-lev unfiltered X-rays and th e response to 0 060 gamma rays is prac The temperature dependence of I is now determined tically independent of 8 up to 70 °. At larger angles by th e ratio (RL+ R,)/Rj. The rate of increase of I the attenuation in the metal casing becomes appar with decreasing temperature is redu ced and I reach es en t . For more penetrating radiation, a response is a maximum a t low temperatures as seen in figure 6. also observed with irradiation of the backside of the _ The temperature dependence of I with different cell. The di,Tectional dependence for backside irradi- '~ load resistances RL was measured with 250 lev ation is similar to that fo r frontside irradiation. unfiltered X-rays. The relative values of I are The directional dependence of the photoresponse shown in figure 7, the photocurrent at 25 ° 0 being can be explained by considering the energy absorbed in the effective lJ-n junction layer. The inciden t normalized to unity. With RL = 50 ohms, the photocurrent remained constant from 25 ° 0 up to energy flux density will be proportional to cos 8, approximately 50° 0 and th en decreased slowly at while the path length of the radiation inside th e effective layer will be d/cos 8, if d is the thiclmess of (: high er temperatures. With increasing RL , the temperature dependence becomes stronger . For th e effective layer. The energy Ea absorbed in this layer will th erefo re show a directional dependence, very large RL , th e photovoltage V = IRL approaches th e value of V o and the photocurren t shows a tem perature dependen ce similar to that of V o. The influence of the load resistance on th e temperature Eact:. cos 8[I - exp (- t-td/cos 8)], dependence of the photo curren t can in the same way, as shown above, be explained by th e temper wh ere t-t is th e absorption coefficient of silicon. For c; ature dependence of R j • large valu es of t-td/cos 8, th e directional dependence 302 4.4. Energy Dependence The photoresponse of the silicon solar cell to radi ations of clillerent photon energies was measured with heavily filtered X-ray and CS137 and C0 60 gamma rays. ?-,ube voltages, fil trations, half value layer (HVL) ill copper, and corresponding effective energies for the difl"erent inves tigated radiations are shown in table 1. The applied exposure do e rates were be tween 0.5 and 5 r/min. ?-,he open-cu:cuit voltage and photocurrent per umt exposure do e rate showed the same energy de pendence. Their relative values, normalized to unity for IOO-kv X-rays, are the same for both. They are shown in figure 9 as a function of the ef fective photon energy. The absorption of the radi ation in the glass window, measured after di mantling T A B LE 1. Qualiti es of investigated m diati ons Approximate Constan t F iltration • Approximate effective X-ray tu be (mm) half-value photon voltage layer (IlVL) energy (hp.lI) X-rays kv C u Sn P b mmCu kev 50 ------0. 125 0. 16 38 60 0. 32 ------. 125 . 26 46 65 . 32 ------.-- . 125 .31 49 75 .81 ------. 125 . 47 58 80 ------.52 .55 62 100 ------.52 .72 70 ~ FIGURE. Relative values of photoresponse (open-circuit volt- 150 4. 00 1. 53 --.------2. 4 122 age V 0, photoc1lrrent I and genemted photo current I.) fo r dij)"er 200 .59 4. 00 . 69 4.1 170 ent angles of incidence of (a) 50-kv unfiltered X-mys from a 250 . 62 1. 00 2.67 5. 4 210 beryllium-window-lype tube, (b) 250-kv 1m jiltered X-rays, and (c) C060 gamma rays. Gamma rays 661 8~~~7::_ ~:~ ~::::::::: : :::::::::::::::::::: ::: ::::: : ::::::: : ::::::: : I 1250 of Ea approaches a cosine Jaw. For }.td/cos 0< < I • Additional to inherent tube fil tra tiou of 3 mm A I. one can make the approximation T and Ea becomes independen t of O. For large values of 0 one has to consider that the silicon di sk has a fini te diameter D and the radiation will enter the w 304 1.5 1. 2 w <./l 75 oZ Q. 8 0 1.1 ~ 1.0 0 .8 F I GU1~E 10. R elation between photoresponse and radiation 0 . 7 ~IO,---....L-...L.....L....L.L.Ll.LIO.l..,2;---....L-...L.....L....L...L..L.L..LI..L03"'--....J en er gy absorbed per unit exposw 'e do se rate in the photoeleetTie e.8"eetive silicon layer. EFFECT IVE PHOT ON ENERGY, k ev i r l ~ hi s e nergy is <1. func tion of 'f', the ratio o f the m ass energy absorption coe 01 - F I e: UHE 11 . EneTgy dependence of Telative ionization co cicnts of silicon [",d Hir. VHl ucs of J wcrc ca lcul ated by taking into account the spectr;:l l distribution o f the rad iations. N umbe rs nca r the measured po ints e.fFci ent K/K 100. indicate t ho operating voltages fo r (mcreel X -rays, as referred to in table 1. {('co is the ioni za tion coeffi cien t fo r 100-k v filtered X -rays (hp.If= 70 kcv). L (19a) T A BLE 2. A vemge energies of pTi1l1aTY eiectTons prodticed by mdi ation in silicon in sinrJle interaction s The ioni"ation coeffi cient K is energy dependen t ftS can be deduced fron1 t he gmph in fi gure ] O. The Fraction of energy A vcrage elec tron energy rclfLt ive v nlu e of the generated current is, according a bsorlleel to eq (1 9H ), Photon energy ]]p T oial of Photo- Com pion- P hoto- Corn pto ll- phow- anel 18 K j electrons elec t rOil S cicc i rO ilS elec trons Com pion- (2l ) eleci ro ns (18) 100 K lOO jlOO kel ) % % kcv kel! kcv 30 99.3 0.7 28.2 1. 5 24. G if the indcx 100 refers to the values for the ] OO-kv 40 97. (j 2. 4 38.2 2. G 28. 0.5 5. Conclusions The stable and linear response of silicon solar cells o~o ------~------+------+----~ to X-rays and low-level gamma rays makes it possible to use such cells for quantitative measure men ts of such radiations. The maximum exposure F I GURE 12. R elative ionization coefficients, K/K tOo, as a func dose rates applied in this investigation were l.8X 106 tion of (us/ }L ,n) Si, the ratio of energy scattered by Compton photons and energy tmnsferred to electrons (photoelectrons rfhr for unfiltered SO lev X -rays from a beryllium and Com pton recoil electrons) . window-type tube, 6X 10 4 r/hr for unfiltered 2S0-kv 2 For the calculation of values of (U'/I'.n)Si, t he spectral d istributions of the X-rays, and 4X I0 rfhr fOJ' C0 60 gamma rays. The radiations were taken into account. N umbers shown ncar the poin ts indicate t he operating voltages for X .rays (table 1). relatively low electron energy threshold ("-' 14S ]wv) for radiation damage in silicon [22] may pu t a limit on the use of silicon solar cells for gamma radiations For lower energies, the values of K /K lOoshow a linear of photon en ergies above ilpproximately 400 kev. dependence on (fY s/ J.L en)S I which has a maximum value The limit for a measurable response at low exposure a t approximately hv = I SO kev. For the linear par t dose rate levels is determined by the sensitivity of the of the graph a t lower energies, one can assume measuring instrumen ts. The response observed in th e relation this investiga tion for an exposure dose rate of 1 r/min K /K lOO = a[l +{3 (rTs/ Jl en)S I] (23) was of the order of 10- 5 volts for the open-drcu it voltage and 10- 8 amp for the photocurren t.. Because with a = 0.71 and {3= 0.29. For higher en ergies the of the great tempera ture dependence of the open K /K lOO values are lower tha n those given by relation circuit voltage, it is preferable to use the pho to curren t (23). Assuming that for very low photon energies for radiation measurements. However , it will be K = l , one obtains by linear extrapolation to difficult to r educe th e load resistan ce suffi cien tly to (fY s/Jl en)sI= O: make th e photocurrent temperature independent because of the usual high impedance of sensitive current measuring instruments. The response of the silicon solar cell showed a From th e value of ex one obtains K lOO= 1.41. With smaller directional dependence for X- and gamma this value, one can calculate K for all investigated rays than for visible ligh t which follows a cosine radiations from th e lmown values of K /K IOO • They law [7] . For C060 gamma rays, th e photoresponse increase from 1.09 for th e SO-lev X-rays to a maximum remained constan t over a wide angle of incidence of value of 1.79 for the I S0-kv X -rays and fall off to radiation. 1.21 for CS137 gamma rays. The value of ,8=0.29 The silicon solar cells show a better energy depen indicates that for the investigated low-energy X-rays, dence than oth er solid state devices used for meas 29 percent of the energy of Compton pho tons uremen t of high-energy radiation. The ratio scattered in all directions are reabsorbed in the between the response to SO-kv X -rays (hve!l=38 key) collecting volume Vc. and that to C0 60 gamma rays was approximately 6 :1 The collecting volume Vc and th e thickness L of the compared wi th a,n approximate value of 2S:1 for th e effective layer can be calculated by introduci.:ng same ratio r eported for cadmium sulfide photocon th e values of K in eq (19a) and calculating I s from ductive cells [23 ] and photographic films [I S]. B e eq (13). The energy requi.:red to produce one cause of their high-atomic number, a high ratio may electron-hole pair is assumed as e= 2.25 ev, a value also be eA'Pected fo r germanium (Zae = 32) and found by Chynoweth and M cK ay [1 9] for the selenium (Zs.= 34) photocells. Il_ _ 306 Silicon solar cell of the arne manufacture and of 6. References the sam e type showed different electrical character- [1] IC. Sc harf and O. vVeinbaum, Z. Physik 80, 465 (1933) . ~ i tics and accol'cLmgly different sensitivity with the [2] H. F elsin ger, An n. Physik 29,81 (1937) . sam e measuring etup. The m eaS1Jl"em ents r eported [3] G. BJet, J . Phys. Radiu m 14, 368 (1953). in this in vestiaaLion wer e all canied ou t on one and [4] R. Feinberg, Nature 181, 1057 (1958). the same cell. [5] J . Drahokoupil, M. Malkowska and J . T a uc, Czech . J. Phys. 7, 57 (1957). The response of ilicon olar cell to X- and gamma [6] H . ])fi ster, Z. Naturfor ch . 11a, 434 (1956) . rays could be improved by making certain adjust [7] M . B. Prince a nd M . WoU , J . Brit. I.R.E . 18, 583 (1958) . m ents to the cell, which is actually designed for use [8 ] M . B. P rince, J. Appl. Phys. 26, 534 (1955). with visible light. In high energy radiation cells, [9] W. Shockley, Bell ystem T ech. J. 28, 435 (1949) . [10] R. L . Cummerow, Phys. Rev. 95, 16 (1954). the p-type and n-type layers should be larger than [11] J . W . Moody, G. L. K endall and R . IC. Willardson, the diffusion lengths by an amount which is equal to Nucleonics 16, No. 10, 101 (1958). the range of the mos t energetic electron produced by [12] J . J . Loferski and P. Rappaport, R CA Review 19, 536 the radiation. In this way clectronicequilibriumcon (1958) . [13] Report of t he International Commission on Radiological dition could be approached. The ionization coefficient Units a nd Measurements (ICRU), N BS Handb. 62 and the collecti.n g volume would thus be increased p. 11 , (1956). ~( and the cell would become more sensitive for high [1 4] H . A. Kra mers, Phi!. Mag. 46, 836 (1923) . energy radiation. A special design of the cell casing [15] M. Ehrlich and S. H . Fitch, N ucleo nics 9, No.3, 5 (1951). [16] G. H ettinger and N. Starfelt, Acta Radio!. 50, 3 1 (1958). could improve the directional and energy dependence [17] G. White Grodsteio , NBS Circ. 583 (1957) . of the photoresponse. The overall sensitivity could [18] A. T. Nelms, NBS Circ. 542 (1952). b e increased by using multicell arrangements and [19] A. G. Chynoweth aod K. G. McKay, Phys. R ev. 108,29 stacking of cell in case of irradiation with high (1957) . [20] P. Happaport, HCA R eview 20, 373 (1958) . energy gamma rays. The silicon solar cell co uld be [21] R. Gremmelmaier, Proc. I.H.E. 46, 1045 (1958). specially useful in monitoring and relative measure- [22] J . J . Loferski and P. Happapor t, Phys. R ev. 111, 432 "- ments of radiation, having also the advantage of (1958) . being independent of an external electric power [23] L. E. Hollander, Nucleonic 14, No. 10,68 (1956) . supply. W ASHINGTON, D .O. (Paper 64A4- 52) F 307