Measuring Electron Work Function in Metal

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1 n experiment of the Electron topic Mesuring Electron Work Function in Metl Instructor: 梁生 Office: Emil: Purposes 1. To understnd the concept of electron work function in metl nd the method of mesuring electron work function by thermionic emission; 2. To lern nd mster the method of liner fitting nd extrpoltion for dt processing; 3. To lern different methods for mesuring temperture. Apprtus Idel diode, opticl pyrometer, work function mesuring instrument, DC voltge meter (0~150V), DC current meter (0~1A) nd digitl multi-meter. Principle The course tht electrons re emitted from the heted metl is known s thermionic emission. The performnce of thermionic emission is relted with the electron work function of metl. The electron work function of metl is the function which is done when electron escpes from the metl. An importnt physicl prmeter is the work 1

2 function for selecting cthode mteril to fbricte the electric vcuum devices (such s cthode ry tube). By investigting the principle of thermionic emission, this experiment is utilized to determine the electron work function of cthode mteril nd provide the reference for selecting pproprite cthode mteril. 1. The electron work function According to the metl electron theory of solid physics, the distribution of conduction electrons with kinetic energy between E to E+dE cn be expressed s: 3 1 dn 4π E E 2 f ( E) ( 2m) f = = 2 E exp de h kt where E is the Fermi level, m is the mss of electron, k is the Boltzmnn constnt nd h is the Plnck constnt. At the bsolute zero temperture, the electron energy distribution dn/de is shown in Fig. 1 s the curve (1). The mximum energy is E f.when the temperture is higher (T>0 K), the curves of electron energy distribution is shown in Fig. 1 s curve (2) nd (3). Only few of electrons hve higher energy thn E f. And the distribution of these electrons will reduce exponentilly with the incresing of energy. 1 (1) Fig. 1. Distribution of electron energy of metl In the cse of norml temperture, there is n electron-positive chrge electric double lyer which is bout m thick on the surfce of metl, or clled brrier E b. E b exists between the metl surfce nd outside (vcuum), which prevents the electrons 2

3 to escpe from the metl. Therefore, electrons need to hve t lest the kinetic energy of E 0 to escpe from the metl. As is shown in Fig. 1, t the temperture of bsolute zero, this energy is: E 0 =E b E f =eφ (2) where E 0 (or eφ) is the electron work function of metl nd its common unit is electron volts (ev). The electron work function describes the energy tht the electron hs mximum energy in the metl under the temperture of bsolute zero needed to escpe the metl. φ is clled the runwy potentil, its vlue is equl to the electron work function which is in unit of electron volts. 2. Principle of mesuring electron work function of metl by thermionic emission method In the high vcuum tube, there is current through the externl circuit which connecting the two electrodes when the cthode K mde by the mesured metl is heted by current, with positive voltge on the node, s shown in Fig. 2, which is known s the thermionic emission. Thermionic emission is to chnge the electron energy distribution by incresing the cthode temperture, so tht prt of the electrons will hve greter energy thn E b, then, these electrons cn escpe from the metl. Therefore, the vlue of work function eφ hs determintive role for the strength of thermionic emission. The intensity of thermionic emission cn be expressed by the lw of Richrdson-Duximn formul: I 2 eϕ = AST exp kt (3) where I is the thermionic emission current intensity, A is the coefficient which is relted to the chemicl purity of cthode surfce, S is the effective emission re of cthode, T is the bsolute temperture of heted cthode nd k is the Boltzmnn constnt (k= J K -1 ). 3

4 In principle, when obtining I, A, S nd T, we cn clculte the work function of cthode mteril by formul (3). However, these two coefficients A nd S re difficult to be mesured directly, so, we utilize the Richrdson method to solve this problem for mesuring the electron work function. Formul (3) on both sides re divided by T 2 of the sme, nd then tke the logrithm, we hve: I eϕ 1 lg lg lg T 2.30κT T T nd 1 T re in liner reltionship. Let lg I be the Y xis, 2 T nd 1 be the X xis to plot, then, we cn get the slope of the line, nmely, the T electron runwy potentil, without mesuring A nd S. This method is clled the then, it is founded tht lg I 2 Richrdson method. 3 = AS = AS ϕ (4) 2 Fig. 2. Circuit for the thermionic emission 3. The idel (stndrd) diode nd the thermionic emission The diode used in the experiment is direct heted idel diode, the cthode is mde by Tungsten line, nd the node is designed s cylinder coxil with the cthode, s shown in Fig. 3. The so clled idel is to be limited the cthode emitting surfce to be mesured to certin length which is in uniform temperture, nd similr the electrodes s infinitely long, or clled the idel stte without edge effects. In order to void both ends of the cthode K of lower temperture nd the electric field uneven edge effects. Ech end of the node A will be mounted to protective electrode B. 4

5 Two protective electrodes will be cited in the pipe nd then diverted to the tube, but the node is insulted with them. Therefore, lthough the protective electrode nd the node hve voltge, this current is not included in the mesured thermionic electron emission current. Through the smll hole of the node, you cn see the cthode to obtin the cthode temperture by the opticl pyrometer. Fig. 3. Idel diode Becuse the cthode nd node re fbricted coxilly, the effect of spce chrge, contct potentil nd other fctors cn be ignored. We cn get the ccelerting electric field between the cthode nd the node s follow: E U = (5) r2 r1 ln r 1 where r 1 nd r 2 re the cthode rdius nd node rdius, U is the ccelerting voltge. The movement of electrons emitted from the cthode by the effect of ccelerting electric field will generte current. 4. The determintion of thermionic emission current I The current I in the formul (4) is the thermionic emission current in cse of there is 5

6 no ccelerting electric field between the cthode nd the node. However, in order to mintin constnt current between the node nd cthode, we need dd n ccelerting electric field E between the node nd cthode. And E will reduce the cthode surfce potentil brrier E b, resulting in the reduction of work function nd the increse of emission current, which is clled the Schottky Effect. Due to the Schottky Effect we cn not determinte the current I directly. It cn be proved tht by the effect of ccelerting electric field, the cthode emission current hs reltionship with I nd E s follow: ( ) I = Iexp E T (6) tke the logrithm of formul (6), we cn get: lg I = lg I + E (7) 2.30T Tke formul (5) into (7): lg I U = lg I + (8) 2.30T r ln r r ( ) Formul (8) shows tht, when the cthode temperture is constnt, lgi nd in liner reltionship for certin length of the diode. Let lgi be the Y xis, U re U be the X xis (Fig. 4), nd extrpolte this line to Y xis, we cn get lgi. Then tke the ntilog, we cn get the emission current I in the cse of the ccelerting electric field is zero t certin temperture. In summry, in order to determinte the metl work function, firstly the mesured mteril should be mde s the cthode of diode. When we mesured the cthode temperture T, the node voltge U nd the node current I, by the Richrdson method bove, we cn get lgi by the zero field vlue of current I. Then ccording to formul (4), we cn find the work function eφ (or the runwy potentil φ). 6

7 Fig. 4. Extrpolting for zero field current Fig. 5. Reltionship between log(i/t 2 ) nd (1/T) Procedures 1. Be fmilir with the instlling the experimentl setup, connect the circuit s shown in Fig. 6, turn on the power, wrm up for 10 minutes. 2. Chnge the idel diode filment current I f between 0.55 ~ 0.80 A, ccording to the dt tble of filment current nd temperture to select the current to mesure temperture. 3. Corresponding to ech of the cthode current (T should be constnt nd cn be obtined by the tble produced by the lb), operte the voltge of 25 V, 36 V, 49 V,, 144 V t the node, respectively, mesure the node current I under different ccelerting voltge U. Plot curve of lgi nd U by the dt mesured, find out the intercept of lgi by dt processing, nd then get I. 7

8 4. Bsed on the vlues of I nd T, plot curve of lg(1/t 2 ) nd 1/T, find the work function vlue from the curve nd compred it with the recognized vlue (4.54 ev). Fig. 6. Circuit for experimentl mesuring the work function Tble 1. The reltionship between I f nd T (Produced by the lb ) I f (A) T (10 3 K) Tbles for dt processing (for Reference) I (10-6 A) I f (A) U (V)

9 lgi T (10 3 K) U T (10 3 K) lg I I lg T 2 1 T Min experimentl results: Slope of the line m= Work function eφ= ev Recognized work function eφ=4.45 ev Reltive error E= % Bsic Requirements 1. Mesure the cthode temperture; 2. Mesure the thermionic emission current intensity; 3. Mesure the electron work function by the method of Richrdson method. Discussions 1. Wht is the method of Richrdson for dt processing? How to mesure the work function by this method? Wht is the technicl dvntge of it? 9

10 2. How to mesure zero emission current ccurtely? 3. Compre the similrities nd differences between thermionic electron emission nd photonic electron emission. Cn mesuring the metl electron work function be relized by photoelectric effect? Attentions 1. The experimentl report need to be chieved in English. 2. Py ttentions to the dynmic rnge of the electric instruments (current nd voltge meters) used in this experiment. 3. It is necessry to operte wrm up process before every mesurement of the diode filment current I f. Elective Reding The mesurement of cthode (filment) temperture T Two methods to mesure cthode temperture T re described s follow. 1. by Tble According to the idel diode filment (cthode) current I f which hs been clibrted, we cn look up tble (produced by the lb) to get the cthode temperture T. In contrst, the result of this method is reltively stble. But the determintion of filment current meter should be used in higher level. 2. by Opticl Method 2.1 Principle The temperture cn be directly mesured by the opticl pyrometer through the hole in the node of idel diode. In the experiment of metl work function mesurement, 10

11 we need to mesure the temperture of the idel diode filment (Tungsten filment). Since the Tungsten hs high temperture (bout 2000 K) with smll size, nd is seled inside the tube, it cn not be contcted directly. Therefore, it is difficult to mesure its temperture with conventionl method. Here we use the opticl pyrometer which is mking use of the principle of rdition. The principle of opticl pyrometer is: the monochromtic brightness of n object is proportionl to its rdition energy density. By compring the brightness of the Tungsten filment with stndrd object whose temperture hs been known, the brightness temperture T L cn be obtined, then, ccording to the known monochromtic rdition coefficient ε λt, we cn get the ctul temperture T. If the rditions of blckbody nd the mesured substnce re with the sme wvelength, they hve the sme brightness (or the sme rdition energy), so, the temperture of blckbody is just the brightness temperture of the object mesured. When the blckbody hs the sme brightness with the object mesured, we hve: ( λ ) ε exp ( λ ) exp C T = C T 2 L λt 2 (9) tke the logrithm, we hve: 1 1 λ = + ln ε T T C L 2 λ T (10) tke λ= m, then tke C 2 /λ= into (10), nd use common logrithm, we hve: 1 1 = + T T L ln ε λt (11) Becuse ε λt <1, it is obvious tht the object temperture T is lwys higher thn the brightness temperture T L. For Tungsten, when λ= m, T=2000 K, ε λt =0.44, we cn trnslte the formul bove into: T (12) L T = T L 11

12 According to (12), we cn clculte the ctul temperture of Tungsten by the brightness temperture of opticl pyrometer. 2.2 Opticl Pyrometer An opticl pyrometer is n instrument bsed on the principle of opticl method to mesure temperture. Since the Tungsten filment of the mesured object is very thin, in this experiment, we designed the opticl pyrometer s micrometry opticl pyrometer which cn mplify the mesured object, which mkes the mesurement esier. The opticl pyrometer is minly composed by telescope, red light filter nd set of circuit with smll light bulb, current meter nd vrible resistor. When using the opticl pyrometer, firstly we should djust the oculr to focus the pyrometer lmp filment, then djust the distnce between the opticl pyrometer nd the mesured object (idel diode cthode), to mke the object imged in the sme plne s the pyrometer lmp filment. Then, it cn be seen tht the diode (filment) nd the pyrometer lmp filment (the brightness of the stndrd) re both in the oculr. Adjust the temperture control tunble resistnce to chnge the current of pyrometer lmp. If the current is smller, the filment of pyrometer lmp will pper drk, if the current is lrger, it will seem bright. Only when the current is pproprite, the brightness of the two filments will seem to be the sme. Then the reding in the tunble resistnce indictor bord is the brightness temperture of mesured object. The bsorbing glss is utilized in pyrometer to control the brightness of mesured object round the 1600 K~2100 K in the pproprite rnge of observtion for humn s eyes, only the light ner λ=655 nm cn pss through the red filter. The center of filter is engrved with circle with dimeter of 1 mm, which is employed to operte the diode cthode nd the light bulb filment of pyrometer to be both t the opticl xis of the opticl pyrometer. The temperture mesurement circuit of opticl pyrometer is designed bsed on the principle of unblnced electric bridge, when chnging the filment current of opticl 12

13 pyrometer, the filment resistnce R x, the temperture T L nd the current I G flow through the glvnometer G will chnge, so the indictor dil of glvnometer cn be clibrted brightness temperture. 13

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