The Effect of Recombination on the Primary Photo-Electric Current From a Crystal Citation Wise, Willis Howard (1926) The Effect of Recombination on the Primary Photo-Electric Current From a Crystal. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/3WHW-8N13. https://resolver.caltech.edu/CaltechETD:etd-11292004-140941 Abstract No abstract. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: Physics Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Unknown, Unknown Thesis Committee: Unknown, Unknown Defense Date: 1 January 1926 Record Number: CaltechETD:etd-11292004-140941 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-11292004-140941 DOI: 10.7907/3WHW-8N13 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 4679 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 29 Nov 2004 Last Modified: 03 Oct 2019 23:37 Thesis Files Preview PDF (Wise_wh_1926.pdf) - Final Version See Usage Policy. 1MB Repository Staff Only: item control page

THE EFFECT OF RECOMBINATION ON THE PRIMARY PHOTO-ELECTRIC CURRENT FROM A CRYSTAL by W. Howard Wise A thesis presented to the faculty of the California Institute of Technology in partial fulfillment of the requirements for the degree of Dector of Philosophy June 1926 The Effect of Recombination on the Primary Photo-electric Current from a Crystal. Many crystals that are very good insulators in the dark show an appreciable conductance when illuminated. The crystals exhibiting thie phenomenon have been the subject of numerous researches. Of the facts reported by the workera in this field those that are most important in connection with this investigation are: There is a particular wavelength to which the crystal is photo-electrically most sensitive. Often the sensitivity curve shows more than one peak. The sharpness of a maximum is increased by an increase in the applied voltage, (fig. |! ). A decrease in temperature usually shifts the peak towards the ultraviolet. Only crystale with a high index of refraction ( ~>2) are photo-electrically active. However, a high index of refraction does not necessarily mean conductance, there are exceptions, and some crystals with low index of refraction can be made conducting by exposing them to X rays. Rock salt is an example of such a crystal. The photoelectric current is of two kinds, (a) the primary current consisting of electrons liberated by the light; (b) the secondary current representing the motion of the positive ions towards the cathode. Under suitable experimental conditions the current is all of the firat or primary kind. As ione naturally move mach slower than electrons, if short illumination periods are used only a negligible portion of the positive ions formed have time to reach the cathode. Heat or infrared radiation hastens the motion of ions. If, therefore, only ultraviolet light is used for excitation Coulomb | cal. ie = \ 'sloo0 \V/em iA \\ 2 A \\ | 16|00 iN 200 400 sys 600 sudden and Pohl Zeitsenrift fur Physik pase 349, vol.c, 1920 Amp. a a Gs ta fig.2 10° Ag,S OC [a A=LIIEM ua 2 > Dark 0.5 L\ { l 20\ Yo 60 sec. So O 0.5 $%F.0 Se@C. Ww. WS. Coblentz Sudden and Pohl Bureau of Standards Naturwisgsenschaften @ 855, vol.is, ieeu ve ca ga 1, 1923 tm pase 34S, vol. and the temperature is kept low enough, no positive current should flow. The latter method was used by Gudden and Pohl in their rock salt experiments Quantitative measurements of the light absorbed and primary current obtained show that within experimental error each 4 V absorbed gives rise to one electron if the wavelength of the absorbed light is greater than and not too near to that of the light most strongly absorbed. On approaching the critical frequency from the long wavelensth side the primary current drops rapidly and almost vanishes just as the critical frequency is reached (fig. /I ) The total photo-electric current changes with time in various ways depending upon the crystal and the experimental conditions. If the mobility of the electrons is rather low it starts from zero and rises to a maximum, as showm in fig. 2 . If the mobility of the electrons is high it starts with the initial value of the primary current and the secondary current is added on more gradually, (fig. 3). Tf there is no secondary current the primary current starts to decrease immediately on account of the positive space ghar ge left behind (fie. ¥ ). When there is no dark current and no positive current electrons mist accumulate on the cathode and neutralize the space charge so far as the applied voltage is concerned. Dus to the fact that the erystal is not an infinite plane this condition is never fully realized. In the ideal case of an infinite plane orystal the net effect of the space charge would be to accelerate the progress of the electrons towards the anode, the additional accelerating force being a maximum at the cathode and decreasing to zero at the anode. When, however, an electron gets close enough to an ion it . #*¥ : must racospbine. The icns ~ - Pena Me & 1 the apace? enarces therefore rei ee bs cs Q Ler) ct of primary current Sy ca:turins electrconse pa on their way te the anode. It is the purpose of this investisation to caleulate to what extent reconbination may reduce the trivary current. T, Tre axcerinents are of tro classes; in the Firat, the light is perpendicular to the electric field ‘fig. 4 lisht is parallel and op Sal > If the licht is. parallel ts the electric field the effect cof lateral diffusion is to flatten cut the orisinal density distritution ax. . 43 re T.. Vant 3309 5 r 4 e given by the light. Trose elactrons iiffuein: frou re ions of greater electron density etn : t . 7 : regions cf lesser electron censity (and acnseyuart lester ion sty 1 avin. mplhy dae any vt - density) have a better chance cf escavin, recembination vith soue ion and reachine the anode than these electrons which dc not diffuse. On the other hand these electrons which dco not diffuse have a smell ler chance of reaching the anode than they would have, did not some others diffuse, tacause they mst now esoare not only the icons normally in their path but alse these icns which the diffusin. electrons.sscave. The effect cf? Jiffusion is thus somewhat eslf comengating and quite a chanse in the jistribution of slectrons from this cause neei net, s> far as can be seen without actually cr gD ey ele 3 ces jue or te nto account in the salevlations, cause a miterial chance in the orimary current. As it is not an easy matter to take iiffusicn into account in caleulatin,; the current to te exyectel it will be shown instead that, fer the experiments to whieh the exoression jJerive2t for the current is tc te o ot wa g 3 a fe aw a] ea ge = oF oO “3 Fe) > QD fy +a ys rn ip re fee ode a ct i} Ree lon ¢ ct ts a rs en be tr oO pte " cr Be & «4 cc a} wa w& mf oO fs" Fh erystal and he distributed accor “ ' ' “MX ' | / to the law @° which is the _£ , LA -t-4-} / Ye . . 7 Lf law by which they are phote- yan Ad ; / : SV Sthanate? : electrically liberate?. is x the ghsorztion ocnstant for the fig. 4¥ lisht used. Suprese now that the electrons are uniformly distributed in a unit layer wider +? MX en. The problem before us is te find cut hew much diffysion has flattered out thie ori, imal distribution @ be the time the field E has polled the unit layer cover to the anode. waked Tas te diffesion each element of volume ¢€ AX in the 2 unit layer will in time assume the distribution x € were & and a are. determined tbr the condition. -au’ bf. e€ “au = aren under the elementary crotability curve OO Since an electron cannot diffuse from the surface of ths erystel into the air the srebsahility curve must be folded back at the surface of the crvstal. The contri aay of an element of vol une e “ho to the e electrons o4 any cther point in the same unit layer after the ' ! redistribution is ths from tive ° z parts of the Little probability curve distant 22% apart. The nurher of electrons at a point =z aue te the diffusion of e€ Ax electrons startin. from t oint x is therefore. Z ene P " -a(x-z)* -42(X+Z) Apz ke +#he But from (1) we have it that -~uUX « and consequently that , la ~a(x-z)* -42(xX+z)* : ~4AX ; aApzye(e + @ Je aX The total number of electrons between Z and z}/ is then 5, ax~z)” -u(xrz)*) SAX é i fe 2 j (6 + @ / e ax -- + (2) This new distribution P satisfies the differential equation z* =u p-2nf® @ -- + (3) Zz x2 The yroperties of © are not apparent from (2) but (3) shows that does have the characteristics to be expected from the nature of the problem: for if @=a& meaning that there is no 2 diffusion, (3) reduces to ze of which the solution is Poe which is the original distribution 2 law; as Z becomes very large (3) again reduces to GEE = uy ad -4U4z Zz with the solution Poe which means that if the original distribution is quite wiiform, as it is for large values of x , then diffusion does not affect it. The expression {2) has yet to be put in a form suitable for comoutation. more -4(X-Z 2 2B (xex)* AX o o T 2 eo 2 2 2 MM 2 +A Zz / f{ -ax*-a(x+F£-%) ralien -4X —a( K+ x +Z) + ZG tZ) pax e + é o e- [eee € 2 + Mia” ae <5 | , a a 2 M Ga) -28 crag) J 4s ] -a|& fe ae pa = al (3 Trl) é a5) + @ (Heth, a5) Z 24 7 a A+Ez z 4 ~AZ{A# ~-a3°) AZ (AW 425°, = ef | ead ux -f# (e , é $+ e e as} | Oo z . At At A ZF -~-a — Zz 2a zZ Z—- 24 2 Ppiae [cord wz -1# (2 [ @ a$-@ , e a3} (#) If the electron can be looked upon 4s having a mean free path l then yg? i a = 7 n2* where #% is the number of collisions it has made mobility cf the electron } A=- tur = Vow = £ Ei . velocity with which it proceeds through 2M? the crystal “= eff , = ratio of forward progress to total 2mvr random motion aaa é 22a 2 o Pay . teens :... navey =- Eq? mu m2 wumber of collisions made in advancing CEL a distance & a2# 1.2.42 28 g ek ~ H* p72 7 *% ye 27 DEF E #L ehinmr wed « K 7 8 _ 4. #77910 Ey 278 - 3/30 Fy wd, 328 S621 aio * T Ta where E,, is the electric field in volts per om..and T is the absolute temperature. T= 306 ; take of =./5 om. = helf the crystal thickness; assume Fy = 1/7.5 and then @2= £/00. SHAK As A only affects the abscissa scale when ¢ is plotted let 4 =]. i é t 2+ Z-ssmz ae <* 76200 2 16200 2 _ 452400 90 =f -2s - f -2$ Pp=e feos Fle e 45 -€ J} e as) hea — “e 7a ~ i = _ et goS=t and then if $ = Z + 7355 t=90Z47 z [ weg -Z 1f0 _4 = 66 — : P= cothe #le f e at re } e dt) a2. The sreatest change due to diffusion must occur at the origin SAX z=o for it is here that the slope of the curve € is sreatest ( % positive). Placing therefore Z=9O we calculate 1 2 7 a k= Ie f e dt =/--0062 = .993F “10 or that the average maximum change in an ordinate, under the conditions stated, is 0.8% er less; less because the average electron travels less than half the crystal thiclmess. From these considerations it is seen to be permissible to assume ““Y in the mathematical work of deriving the expression for the primary current that the dectrons move only in the direction of the electric field. III It is assumed that an electron reaches the anode unless it recombines with an ion and that the radiation emitted when recombination occurs does not liberate another electron before it reacnes the surface of the erystal and escapes. Were this condition not completely fulfilled the effect would merely be that diffusion and the distance between ions would both appear to be greater than normal for the disappearance of an electron in one place and its appearance in another could be looked upon as diffusion and by this process one collision with an ion has been lost. | The mean free path of the electrons, referred to ions, is taken to be A =— 1, where is the number of ions per c.c., Nave $e o ie the radius of an ion and + may be a function of the mobility of the electrons, of the field, and consequently a function of the concentration of ions but is assumed to be a constant. This point will be brought up again. A is thus so defined that the chance that an electron will collide with an ion in going a distance % 2° is 4? The chance that an electron will go a distance S and then collide with an ion in the distance - is 5 e* .e | where A is the mean free path, provided A is a constant. If \ is not a constant it is easily seen that we must have meco & © CRS Svea © = anne a ye A Aw Then the chance that an electron &% YoUZ 7 liberated a distance =z from the b 1 , zight cathode will go to a point distant / . 7 ,--- 2 fig-6 from the cathode and recombine in the distance <y is (7 2s | z AG) “Ly ec As 5 h provided we may neglect the change in \ at any point during the time it takes an electron to go from z to ¥ . If this is not permissible we must write instead ene A where “4 is the mobility, or velocity in a unit field. The rate at which electrons are being liberated is a function of X only, F(X) . ‘Then from the element of volume 4 2x Lz there are liberated -4 42 LLPFAX electrons per sec. of which the number recombining in the element of volume 4.4, / 3g is at the time / if © 2 WZ If there are » electrons per sq. cm. per sec. leaving the cathode, the number of these which combine with ions in the element of volume -A A » y is per sec. at the time “ . In the experiments to which this work is to be applied ==. but it will be retained for the present. Zz Daring the time 2 < 43 the total number of liberated electrons which recombine in -< va vy i8 ; 2 ety A j : ny i : 4 ARS OED ~ ALG Per sec. So up.to the time ¢ =y/4f the total number of electrons recombining per sec. in Ady Zy is _[* as ¥-5 ¥ [ #&y 5 MEt ACS, 0 ae Le YCs,t- FS Adyady aalee Fi f e* AES Az GD | ymet ] while the number being produced per sec. is Ady. dy. FX) The difference must be the net rate of increase of ions which is . ; IN _ fy + af ; eo. 1 ALK LY FE SAK AY Tey I TGs) and hence we have A ds ¥ hat A y -f & det =F -4 [ne +Fof e* “ dz] woe at } a “yuEb as the defining equation for A= A(x, yt ) upto = x/4k The second term on the right has the lower limit ¥y-4£2 for the integral because the chance that the mh 2X electrons reach the point Yy-MEL is 1 if faiy/we£ . Ie b> ¥/AE we must write instead of ( / ) x _ = Fw-t{ ne ° + FY J é Mz 2x] (2) y aS | F dbs ~hevet ra f L A +d ese Zz | --* (3) where A= [027d FO) and B= a/ F(x y y, a obS a aie a Z y+ or “Ag. ‘gr=)h-[Be ty E & x | 71+ (4) Now let A = i/ 2 Log uv(s,0- z ) under the integral signs = | & 4o4- v(y,t) outside the integral signs where S52 ¥ Since A= wot =o UV (Y,0) = nad. = With thie change of variable equ. ( 4% ) becomes | ” lvr Vv V3 | ¥-Z -A(L 28 )- ~-p% - v(z,t-£2)dz wat avr ayat av a AE ag" ay OY MEL or A(x v ae v B vz ob, ee ee eee = LD wr ~ . ff ae oe at) tS , + (z,t- £2 bz at ay YMEb »+{5) If we differentiate ( J ) with respect to ¥ and 7 and then add the results we get the following differential equation oy Pica a gave v rae 3, [A (x "ae ogee * Be lta #[ AG at ay ay which must be solved for vY if we are to know how the current rises when the light is turned on The current passing any point. The part of the Ad Xa z: Fi (xX) electrons liberated per A second from the element of volume Ax WZ that reaches the point y¥ is 4 ds Als o- a) J, A.dx.axz-Flx) e€ Of the % electrons passing 1 sq. cm. per sec. at the point Y-HEL at the time Z=0 the number passing 1 sq. om. per sec. at the point y at the time 7 g as _ #2, ne vue M3) b- FE is up to the time £ = y/wE Then the total number of electrons passing 1 sq. cm. per sec. at time 2% at the point y is y S ex [tees ly A(S)t- y-MEt AG t- $ly =™ eed e an +n e “ e ‘Yy-MEt Placing now =1/% oF a(S, t- +) as before we get rw Ye + a (2)b- TP) az } YAEL or ¥ Mz {Bx J viyt-# dxt=sfL fA(Qe_z v | het rede b= ASS ae aya) * ar f° (7) ae ¥ ay From ( 6) then we have it that Cl Mr - J 2. Me =v sg Fo) te EG or 2 2 a (Mr)_ ave ta (Mr) _ 1 av sal) ay ~ nw 2 opel) AE 9 -(f) In all the experiments of Gudden and Pohl the current leaps immediately to a maximum and then decreases. This indicates that AE is very large and consequently that the time taken for an electron to cross the crystal is small compared to the time required for the distribution of ions to change sensibly. We have then to deal with ( 2 ) and with ( 6 ) rewritten as 2. Ie a oa yw] . Lan 4, | an =V Fy] ( a9¢ av ay38) ge ; ay 4 a o- 9 (A gear we (ASE 4) 2 2 (ALE -v)] <0 ayat } aylL Quer ayat ) ¥ or gv =a vere T2Z ane #F(x)t “+ (9) IYIT A Following the suggestion of ( f ) that 2 and ¥ may enter into 1 in the same way, we assume =v] (r+o(yr4t)| and find that ( 7 ) reduces to the total differential equation (the other simple and most obvious assumtion t= 7(7T+y) does not yield a suitable form of solution): (THA gtk) Ve wae Letting (reply rh) =- this becomes v+riv +4 =0 v= J (a) = J (2iVvittre)lyreé) Using now the fact that «-2 ami «Ff is large we may rewrite ( 3 ) in the following form (~ 45 A2. 4 =)- +f eo Ax at ra” Pp | aaa or gu - J v¥lz,7) zz ++ (0) where we have used ( 9 ) and + = 2. fry \ ‘ 4 Xr aY¥ ea The condition Aa1/Z- Leg i = a Lf a makes ¢ = 0 for only then will 1 be independent of ¥ when ~2=5 . Substi- tuting Benin into ( /0 ) we find that #=0. Substituting ( 9g )in( 7 ) we find $I, = -€ 12 =e 2 yseh ag ~ Tet 4 Ot ey Lire 9 t= ehkif” od Fay £4 Wherein we have taken account of the facts that the crystal is 4 cm. high and that the current is measured at the anode where y="d. The ratio = way be expanded into a power series and then UW I= hil fi TAT re (TY ra(riyr Fo dx Ir @, ergs of energy enter 1 sq. em. of the surface each second the energy remaining in this square beam at a depth X in the crystél is @ = Q, en Of the energy remaining in the beam when it reaches the rear face a fraction f is reflected. The . “Uw reflected energy ( ¢€ = contributes an amount QQ, = Zz aM (wrx @re é ) at the depth X . Obviously the total energy at any point is an infinite series @ = 2 Q,. 4 x -Z 4 Ur pdx 2 T2Z4U Aur 3 -$4Ur ux @=Qe +Qre e°+Qre € +Ore eA. a, (er OE EON = -(€ +Pre tre 2Aur =Q A coek {uy (x-w) + Log Vp } where Az2 ype /()-p Ee”) The rate at which electrons are being liberated at the depth is 7 22 __ @M A yt _ Lo. Fo =a = - Set A sink £4 (x w) + Log YP J pee 2 2 so I-e4 é} {i TALE ETE + alo bs2) Fir tr b Fada fp ALB, +3. 9A 3, 4 OA) Bg t te eneTs) where @nz wok £1 Goa ‘by B= f oO ur 4 ge. . ! (-I) AHA {AC x-#} > m ao 7p dr t AL AX ; ~4 A 4 TA If FP is negligible then Q=Q e€ and Fix = 42" « “fin tf and ( // ) becomes oy Be AU Aur Tseaie f{(i-¢ d+g4ydu-e yee “++ (72) © Lag J,(2ive) ; 0.5 fig. 7 10 i) If most of the light is absorbed on the first trip across the erystal and f is small, it will be sufficiently accurate to correct for the light passing clear through by making uw infinite. With + infinite ( /2 ) becomes where fie) = j +d, +o Pon, te oe bs p+ = ar a4 Sa Pe ; + « boy” _ 4 . 42 2 3 7 g T r iN a * (rla)/ v1 be =p 43 vl) - -! “ ‘5! —_ 3 “ bes Zed, w $(8) = fim, “EUG = fim. “T8) ~ gsa i{o J, (22a) for J (2é49) 2 J (2é4 9) The theory thus says that, / and @, being constant, the current should drop with time as shown in fig. 7 : for O is. a& linear function of the time. This is just what Gadden and Pohl have observed in NaCl#, with intense illumination they got a drop such as shown. With weak illumination they got very little drop in the same length of time and this is to be expected from the formof 9 . If @, is small it takes a long time for 4 to become large. If the experimental conditions were such that most of the light was absorbed in the rock salt it is permissible to compare Ff () with the experimental curves, otherwise it would be necessary to use the more exact expression for I. As t& is not known the test of the theory will consist of seeing if a constant t& can be 80 chosen that the theoretical curve will lie along the experimental curve. The following figure shows how closely +(8) can fit the experimental curve. it x12 Amp.. In view of the approximations 60 ; 33 introduced in deriving #(9) and h - in applying it to the experiments \| the fit seema very good and Ss - appears to warrant the conclusion === that recombination is sufficient to account for the decrease in the o 700" 200" current with time and that the fe. x assumtion = cat. was practically correct. If current per unit intensity of entering light is plotted against wavelength a sensitivity curve having a peak is always obtained. The low current on the red side of the peak is accounted for by the small amount of light absorbed. A possible explanation of the low current on the violet side is furnished by the relation bom, $@ =0 .» On the violet side of the peak is large, consequently § is large and therefore /(4) is small. However, 88 is shown in the next section, this is only a partial explanation and there is some other phenomenon which also reduces the current on the violet side of the peak. IV. In the experiments on diamond, ZnS and HgS the light was, as shown in the accompanying figure, parallel and opposite to the electric field.. The rate of production of electrons is now not a function of x but of ¥ we ow AIRY) We gorz FC(y) - hp é fig Z ra 4 4 SS Reflection at the rear face of x ___4 “ ur the crystal is neglected. It having been found possible and necessary to neglect the change in the density of ions while an electron is crossing the erystal, that simplification is now made at the start. The total number of electrons recombining in the element o volume Adydy is got by integrating hand zF (4 et A dy from Z=0 to Z=yY and so is | y as 4 -yl-z) -L te eC oO y. LA _! phn Ad xd ye iw) Az flr te. The nunber of electrons liberated per sec. in the same element “A(L-¥, of volume is A dx a y Gee e 4 and taking the difference we get, as before, the net rate of production to be ¥ _ aft- yx) -¥ _ yf _ a Adudy Gale XZ 4 / oe Zz) a 22] —_ v A ~o which must equal or —ae where T= not Gott et defines A asa function of ¢ and ¥ . This last equation may also be written a . : vy 3, -2Z.44=dE -j,e “7 aT Differentiating once with respect to we have 7h. a ¥ ws 2 MY, ae aco | = ee = , aA —if ++: « “ze Ay Ly ~ 3yoT gAZzE ‘ gt 4A) 5 rer z ; =e” dA i - AH HS gy 144) OF ah : Let e “ c 22 23. u a and get TPF ar Bae RA Oe ee a Qe ri ue OA -~-2 MS Sey ep ds oo SE FMA) mF GR 2 or Po erp A a tO Le IA LQ) a8 aT 42 OF AS? 4E ’ -2 /. _2)' Placing Aze , -o=5 , faa this takes the standard form ~-2%u2 2-27 -id ef 2 & of which the solution is known to be g 2 x they ow E tA 2 UY where vu and & must satisfy the equations au GV av=afe and “=m aT A a or gS = 37 and GE ae x : Zi On 2 uv where 7, = T/4 AY If we place e€ = § in the original integral equation 4 | ) it becomes | 3 ue CL AEX 2 ghous—-tf e% 4 aR MAM a Ae eli eae. 1 8 Lug | Now Ke av/as ss Ot BER A=DE oy whence by . substitution » a ee Oe ST a Ud wat uar awry (TZ) / ek, ha as or & ow ’ i Pa We need then a solution of a = = For, that satisfies i the conditions IM =) vit 2,) 42, and Azw c& Fz0 97; ! Pas It has already been found that a solution of urs 3557, is =) rsa) + opeth ra) SHA) RH Obviously the second condition is satisfied by taking +=. and. the first by taking “i =-} » we then have Azl/ as oe J, (225-07 ) Ae I a ney, ° aA mot Fo #2 : : mee g wr 2a oe fares Ymos Kj, Xs, FES we & tA j 5) at But JV / oO tL of yer oh. , -}) 7 Di mete Te NR 7 rte TEL TS IF oJ, (2548-7) oe” . ~~ £R Ur gy - “T= a Se) fe ema, (2by¢e NT) v] pe ao / es ~* cA BT Y vT 4b gris JER o(C2i ce yh) 2, Qo sey ky ; a -~eky t-e JS J, (2676, ++ (2) Zi | Zo, °F o( ') where 6s no $ Bo (1-e )t a! AY or T= @ 4. ue Qe (j-€ ) J, (2+F6) a ad Jy (2é73,) £78, Tae b,= fig. l? 2 ACP PP RES ~ U eo T t—~> KN 2) eo oe Pe i 4 la os+!"W+}+"YJ | _ BS a 5 4, 10 1¢ This shows how recombination should make the current drop with time when the light is parallel and opposite to the electric field. The quantity of electricity passing to the anode between the times t= 0 and t= is -{ tit. [ Awd aiden) \ol t c-[ I4t =] ae oF «wg J, (2ivle 1) da _6€AW Tiss SW. 24 Qe = ohe fog JS, (2ifu- E"') nats Be ) , —ue . ; = Chur 2-6 jet 1 og F274.) ---(3) For short observation periods ( ¢ small) the quantity Cc is thus seen to be proportional to ¢ for f(o)=! . This is in agreement with the measurements of Gudden and Pohi*, If recombination is neglected, 1. e. if fia) is made equal toons, Cre Aw oe t which is a straight line when -H4 plotted against - . The factor (/-@ ) is left off to ‘correct for the light that goes clear through and is lost. It is this C which Gudden and Pohl measured in their experiments on diamond, HgS, and ZnS. | The dotted curve in fig. // gives the results of the experiments on ZnS in terms of C/Q@, . The dashed straight line is the C/Q, which would have been obtained had every Ap libe- rated one electron which also reached the anode. It was located 7 by maltiplying the ordinate at 477 44 by SEF - Neglecting , , -27 recombination, the experimental value of -42 is here 7 x /J ~27 instead of 6-53 x /0 . The discrepancy is said to be within experimental error. tT he ae > a ae — a a Z §> of Zeitschrift fiir Physik, sto / o a pf als —— i . Vol. 17, page 345. 8 I od / . w ! bg. fl Rg OS / fig a / 3 / < ; / 350 400 HA 450 F00 The full curve is the C/a, given by equ. ( 3 ). It was calculated with the aid of the curves given by Gudden and Pohl™, for AA in 2ns, taking ( =.é mw. and 80 choosing ¢# as to make the two curves coincide at A= 400 4 4 . It represents then the "Ausbeute" to be expected if recombination were the only phenomenon tending to reduce the current, and provided the phenomenon other than recombination which causes the large drop at 25244 is inoperative at and beyond 70044 . Judging from the shape of the dotted curve this is the case. ‘The peculiar drop is such as would be caused by @ rapid increase in #& between 77) and 377 “u , this does not seem at all likely. If it is caused by initial recombination or Some other reason amounting to the same thing it is equivalent to a decrease in @, , and we mst have v= 7(/) . This does not affect the validity of equations ( 2 ) and ( 3 ) because the integrations were only with respect to space and time. The effect of the unknown process causing the peculiar drop in current when the light is most strongly absorbed is thus seen to be less than it would seem to be were recombination neglected. By determining «+ where the effect is inappreciable we see how big the effect is at the shorter wave lengths. Recombination is able to explain qualitatively some. otherwise unintelligible current-line curves published by W. W. Coblentz. This is a sample. The curve is superposed on the dark . Ag,$ oc current which is the axis of sl (Fou abscissas. Along a the M mere “Tl, \_ Dark current rises because it ae 20.4 4O 69 36e, takes an electron an appreciable time to cross the crystal so that up to the time required for an electron to cross the crystal the anode is receiving electrons from increasingly greater distances from the anode. Along b the current drops because of the formation of a space charge. Along c the current drops because the supply of photo-electrons is cut off when the light is and in the time required for an electron to cross the crystal they cease arriving at the anode. The current drops below the dark current because part of the dark current must go to neutra- lizing the space charge. When the space charge has been all neutralized the dark current will have returned to its original value. It does not seem possible, however, to get a quantitative explanation of these curves because the differential equations representing the different portions of the curves, for example II 6 , are quite unmanageable. ** Physikalische Zeitschrift, vol. 26, page 481. * 'Naturwissenschaften, vol. 11, page 354. # Zeitechrift ft Physik, vol. 17, page 331.