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Development of a photomultiplier tube with high quantum efficiency
Nuclear Instruments and Methods in Physics Research A 431 (1999) 185}193
Development of a photomultiplier tube with high quantum e$ciency T. Shima, Y. Nagai* Department of Applied Physics, Tokyo Institute of Technology, O-okayama 2-12-1, Meguro-ku, Tokyo 152-8551, Japan Received 11 January 1999
Abstract We propose a new method to signi"cantly increase the quantum e$ciency of a photomultiplier tube by employing a multi-photocathode and a mirror to produce photoelectrons by reusing photons transmitted by a single photocathode. In order to estimate the expected performance of the new photomultiplier, we studied the spectral responses of the re#ectance, transmittance, and quantum e$ciency of a K CsSb photocathode as a function of the wavelength of incident light. A large enhancement of the quantum e$ciency is expected in the regions between j"280 and 650 nm. 1999 Elsevier Science B.V. All rights reserved. PACS: 29.40.Mc Keywords: Scintillation detectors; Scintillators and photomultipliers
1. Introduction Photomultiplier (PM) tubes have been used as the most common and useful type device for detecting photons in various "elds of science and technology, owing to the special features of good sensitivity and fast response (a few ten ps) to photons. The sensitivity is described in terms of the quantum e$ciency (QE), which is de"ned as the ratio of the number of photoelectrons emitted from the photocathode to that of incident photons. Although QE is as good as about 30%, it would be extremely nice if one could make PM tubes having better e$ciency. In the present work, we proposed * Corresponding author. Tel.: #81-3-5734-2750; fax: #813-5734-2750. E-mail address: nagai.ap.titech.ac.jp (Y. Nagai)
a new method to increase QE of a PM tube and studied the expected performance. So far, several methods have been developed to increase QE, which can be categorized into three types. The "rst concerns a photocathode (cathode) [1]. Currently, semiconducting compounds, such as K CsSb, Na KCsSb (multi-alkali), and GaAs}Cs, are being used as cathode materials because of a good quantum e$ciency of about 30%. They meet the requirements so as to obtain a high QE, such as a small band gap energy (E ) and a small electron a$nity (E ). The second is related to the thickness of the photocathode. In order to achieve a high QE, the thickness of the photocathode should be su$cient to convert a large fraction of the incoming photons into photoelectrons, and thin enough to permit most photoelectrons to escape from the cathode. To meet the
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latter condition the thickness is usually a few ten nm for photons having a wavelength such as 400 nm, and is almost equal to the escape depth of photoelectrons in cathode materials of the alkali}antimonide type. However, the thickness is not enough to absorb most of the incident photons, since the attenuation length for photons is a few thousand nm in the cathode. Hence, incident photons were passed through the cathode many times by means of total internal re#ection, and thus an enhancement of QE was obtained [2,3]. The enhancement depends on the wavelength of the photons: &2 and &4 for a blue light and a red light, respectively, since the cathode absorbs blue light more e$ciently than red. The third is related to the extraction of photoelectrons from the cathode with higher e$ciency using an external electric "eld [4]. A test experiment was performed by applying a high "eld of 7.9;10 V/cm near to the surface of a Na KCsSb cathode; a maximum en hancement of QE was obtained below the threshold energy (&2 eV) of photoemission [4]. An enhancement was achieved, since the potential barrier at the vacuum interface of the cathode was lowered by applying an external "eld; and thus low-energy photoelectrons originating from impurity levels within a forbidden band could escape from the cathode. The simultaneous use of total internal re#ection and a high electric "eld has been studied; and has provided further enhancement of QE [5]. The latter two methods, however, have not been realized for commonly used PM tubes. In the present work, we propose an alternative method to increase QE, where the transmitted photons are utilized several times to produce photoelectrons by means of a multi-cathode and a mirror.
2. A PM tube with a multi-cathode and a mirror A schematic view of a PM tube consisting of two separated cathodes and one mirror is shown in Fig. 1. Here, the photoelectrons are produced at the following stages: "rst, when the incident photons impinge upon the "rst cathode through the photon window; second, when the transmitted photons reach the second cathode through a "eld-shaping grid; third when the photons transmitted through
Fig. 1. Schematic drawing of the new PM tube (cross-sectional side view).
the second cathode are re#ected by the mirror, and enter the second cathode again; and fourth, when the transmitted photons impinge upon the "rst cathode again, respectively. Therefore, the total quantum e$ciency (Q ) of this new PM tube would 2 be higher than that of a conventional one with a single cathode. Here, Q is given as 2 Q "N /N (1) 2 where N and N are the numbers of photo electrons collected at a dynode and of the incident photons entering the "rst cathode, respectively. Here, N is given as N "k N #k N #k N #k N (2) where k (i"1}2) and N (i"1}4) stand for the G G collection e$ciency and numbers of the photoelectrons produced at the above-mentioned stages; k was calculated as described later. The number G N was estimated as follows, where we assume that G the re#ectance (R) and the transmittance (¹) are the same for the "rst and second cathodes, respectively. Since the incident photons are reduced by re#ection at the "rst cathode, N is given using the quantum e$ciency (Q) of a single photocathode as N "Q N . (3) Since the intensity of the transmitted photons through the "rst cathode is reduced by the re#ection at both the second cathode and the
T. Shima, Y. Nagai / Nuclear Instruments and Methods in Physics Research A 431 (1999) 185}193
"eld-shaping grid, respectively, N is given as N "Q ¹ (1!R) ¹N $%
(4)
where ¹ stands for the transmittance of the $% "eld-shaping grid, given as the ratio of apertures between grid wires to the total area of the acceptance for the incident photons. It is estimated to be 0.85. In a similar way, we obtain N and N as N "Q R ¹ ¹(1!R)¹N +0 $%
(5)
and N "Q R (¹ ) ¹(1!R)¹N +0 $%
(6)
where R indicates the re#ectance of the mirror. +0 Consequently, Q is given as 2 Q "Q[k #k ¹ ¹(1!R)#k R ¹ 2 $% +0 $% ;+¹(1!R),#k R (¹ )+¹(1!R), +0 $% (7) Hence, if we collect all of the photoelectrons, we can obtain a large enhancement of QE. In order to estimate the performance of a new PM tube, we studied the spectral response of a K CsSb photo cathode, and calculated the collection e$ciency of the photoelectrons for several con"gurations of the electrodes. Here, the re#ectance (R ) should +0 be mentioned; since an aluminum-evaporated mirror is known to have the highest re#ectance of 0.91}0.92 in the visible region [6]; we used Al.
3. Experimental procedure and results
thickness of the antimony was determined by an X-ray #uorescence analysis, and that of the K CsSb layer was determined within an uncertainty of about 10% by multiplying the antimony thickness by a factor 4.9, which is the ratio of the number density of antimony atoms to that of K CsSb mol ecules. In order to accurately measure the cathode thickness, we used quartz with a thickness of 1.55 mm as a photon window, but not normal borosilicate glass, since it contains antimony. We measured the spectral response using three phototubes with di!erent thickness of the cathode layer as listed in Table 1; two phototubes (A2 and B2) were used to check the tube-to-tube variation of the spectral response, and phototube D was used to study any contributions to the spectral response from materials other than the cathode. Here, two samples (A1 and A2) have cathodes with a `standarda commercial thickness. The photoelectrons emitted from the cathode were collected at an anode, and measured as photocurrents. The anode was made by evaporating aluminum onto a glass window opposite the photon window.
Fig. 2. Structure of the phototube used for the spectral response measurements of the K CsSb photocathode.
3.1. Phototubes The spectral responses of K CsSb were mea sured with the phototube shown in Fig. 2 as a function of the wavelength (j) of unpolarized photons in a vacuum environment at 253C. The phototube had no electron-multiplication stage, and was made by "rst coating a small amount of MnO onto a photon window, and then evaporating antimony on it. A crystal layer of K CsSb was formed by adding potassium and cesium to the antimony layer. The
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Table 1 Speci"cations of the sample photo tubes Phototube
Cathode thickness (nm)
A1 A2 B1 B2 C D
76 76 38 38 152 0 (Not evaporated)
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3.2. Reyectance (R) The re#ectance (R) of the cathode is de"ned as R"I /I (8) P where I and I are the intensities of incident photons onto the cathode layer and re#ected photons from the cathode, respectively. The experimental setup used to measure R is shown in Fig. 3. Photon beams with continuous wavelength of j"190}352 nm and 352}840 nm were produced using a deuterium lamp and a tungsten lamp, respectively. Monochromatic photons were selected with a spectrometer (Hitachi model-340), and were guided so as to impinge upon either the quartz window of a sample phototube or a reference mirror (aluminum-coated #at mirror) by changing the photon path using rotating mirrors. The re#ected photons were detected by a reference PM tube, whose sensitivity was calibrated using a standard calibrated Si-photodiode (Hamamatsu S-13371010BQ). The photon intensity from the reference mirror was measured in order to cancel out the #uctuation of the incident photon intensity. Here, it should be mentioned that since the spectrometer and the reference tube could not be placed on the same axis, they were set at symmetric positions with respect to the normal of the photon window of
Fig. 3. Experimental setup for the re#ectance measurement. The incoming angle and the outgoing angle were adjusted to 53 with respect to the normal of the photon window of the sample tube.
a sample tube. The incidence angle (h ) and the G re#ection angle (h ) of the photons were adjusted to P be 53 against the normal to the window; also according to the Fresnel formulae, R is of the same magnitude as that for h "h " 0 within an uncerG P tainty of 1%. The incident photon intensity (I ) at Q the surface of the window is related to the intensity (I ) at the K CsSb layer as I "¹ (1!R )I (9) Here, ¹ and R stand for the transmittance and re#ectance of the window, respectively, and were measured with sample D (no cathode material), while I was measured without a sample phototube. The measurement of ¹ is discussed later. Since both photons re#ected by the cathode and window surface are detected by the PM tube, the observed photon intensity (I) is given by I"¹ I #R I (10) Consequently, R is obtained by using the measured values of I and I as R"+I/I !R ,/+(¹ )(1!R ), (11) The thus-obtained re#ectance (R) is shown in Fig. 4 as a function of j for each sample; as one expects, R becomes smaller as the thickness of K CsSb becomes thinner. In addition, a broad resonance is observed at around j"460, 540, and 750 nm, which might be due to some speci"c photoemission processes, as discussed in Section 5.2.
Fig. 4. Re#ectance as a function of the photon wavelength. The solid, dotted, and dashed curves are obtained for the phototubes with the cathode thickness of 76, 38 and 152 nm, respectively.
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3.3. Transmittance (¹) The transmittance (¹) is given by ¹"I /I
(12)
where I and I are the intensities of the photons entering the K CsSb layer and the transmitted photons, respectively. Here, I is given using Eq. (9) as I "(1!R) I "(1!R) (1!R ) ¹ I
(13)
Fig. 5. Experimental setup for the transmittance measurement.
The intensity (I ) was measured with a reference PM tube as a function of j using the experimental setup shown in Fig. 5, where the monochromatic photons were divided into two paths using rotating mirrors, and a reference beam was used to monitor the intensity of the incident photon beam. The thus-obtained transmittance (¹) is shown in Fig. 6, where one can clearly see that ¹ is larger for samples B1 and B2 compared to those of A and C, and ¹ increases rapidly above j"450 nm, which is discussed in Section 5.1. 3.4. Quantum ezciency The quantum e$ciency of a K CsSb cathode was measured using the experimental setup shown in Fig. 7, where photoelectrons produced were collected at the anode, and the photocurrent was measured by a digital ammeter (ADVANTEST TR8652). The collection e$ciency was shown to be 100% for an anode voltage above 90 V; we used 100 V. The incident photon intensity was measured before setting a sample phototube with the standard Si-photodiode, as described above, and was stable during measurements. The quantum e$ciency (Q), which is de"ned in Eq (1), is written as Q"(N /N )/[(1!R) (1!R )¹ ]
Fig. 6. Transmittance as a function of the photon wavelength. The solid, dotted, and dashed curves are obtained for the phototubes with the cathode thickness of 76, 38 and 152 nm, respectively.
(14)
where N and N are the numbers of photoelectrons and of the incident photons at the photon window. We obtain Q as shown in Fig. 8, where one can clearly see that Q is approximately constant for j"300}450 nm, and decreases as j increases from 450 nm to 700 nm. Namely, Q is in anti-correlation with the transmittance (¹). Hence, the j depend-
Fig. 7. Experimental setup for the measurement of the quantum e$ciency.
ence of Q is strongly related to the photoabsorption process in the cathode. Here, it is worth noting that the highest Q value was obtained for sample A with the standard thickness.
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Fig. 8. Quantum e$ciency Q as a function of the photon wavelength. The solid, dotted, and dashed curves are obtained for the phototubes with the cathode thickness of 76, 38 and 152 nm, respectively.
Fig. 9. Total quantum e$ciency Q of the proposed PM tube. 2 The solid, dotted, and dashed curves are the estimated values for the PM tubes with the cathode thickness of 76, 38 and 152 nm, respectively.
4. Quantum e7ciency of a new PM tube In order to obtain the maximum quantum e$ciency of the new PM tube, it is important to collect the photoelectrons emitted from the cathode with high e$ciency. Since the e$ciency depends on the con"gurations of both the cathodes and dynodes, we calculated the e$ciency (k) for various con"gurations of the electrodes, as described below. First, the distribution of the electric potential in the PM tube was calculated for several voltages of the electrodes. Next, the trajectories of the photoelectrons were numerically obtained for the calculated electric "eld. Here, for simplicity, we make two assumptions: "rst, the photoelectrons are emitted perpendicularly from the cathode with a constant kinetic energy of 1.2 eV, a typical value for the K CsSb cathode; second, the probability of photo electron emission is uniform over the surface of the cathode. Thus, the collection e$ciencies (k and k ) for the photoelectrons from the "rst and second cathodes were calculated for several con"gurations of the electric "eld, respectively; best values of k " k "0.95 were obtained for the con"guration shown in Fig. 1. Using these values, Q in Eq (8) 2 was calculated as a function of j as shown in Fig. 9. Hence, we obtain quite a large enhancement of the quantum e$ciency (Q /Q ) by a factor of 1.1}2.3 in 2 1 the range of 280 nm(j(650 nm, as shown in Fig. 10. The enhancement is larger for a thinner
Fig. 10. Enhancement of the quantum e$ciency of the proposed PM tube compared to that of the conventional one. The solid, dotted, and dashed curves are the values for the PM tubes with the cathode thickness of 76, 38, and 152 nm, respectively.
cathode as expected, since it is more transparent than the thicker one. However, since a thinner cathode has a smaller Q value, Q is not necessarily 2 the highest, as shown in Fig. 9. Hence, it is necessary to determine an optimum thickness of the cathode so as to obtain a high Q . 2 5. Optical property of a K2CsSb photocathode The above results concerning the spectral response provide important information about the
T. Shima, Y. Nagai / Nuclear Instruments and Methods in Physics Research A 431 (1999) 185}193
optical properties of the K CsSb cathode, such as the photoabsorption and photoelectron emission processes, as discussed below [7]. So far, the properties have been studied by measuring the photoemission, optical absorption, photoconductivity and electric conductivity; a small band gap energy (E ) of !1.0 eV and an electron a$nity (E ) of E ? !1.1 eV have been reported [8]. Furthermore, by measuring the energy distribution of photoelectrons, the photoemissions for photons below 2.5 eV (j'495 nm) and above 4.0 eV (j(309 nm) are claimed to be due to excitations from impurity levels and from the maxima in the valence-band density of states at depths of 2.3 and 2.8 eV below vacuum, respectively [9]. 5.1. Photoabsorption mechanism in K2CsSb From a measurement of the transmittance (¹) of the K CsSb cathode one can extract a photoab
191
sorption coe$cient (a), which is de"ned as (15)
¹"exp(!az),
where z stands for the cathode thickness [10]. In Fig. 11 we show a for three cathodes with di!erent thicknesses. Here, a theoretical value of a is given for a direct interband transition near to an absorption edge as A a" (E !E )L (16) E where A is a normalization constant, and E and E are the incident photon energy and band gap energy, respectively. Also, n stands for the power which characterizes the type of interband transition; n is equal to and for pure allowed and pure forbidden-transitions, respectively. From the present data in the region E "2.1}3.3 eV, E and n were obtained as listed in Table 2; they indicate that the photoabsorption is caused by direct forbidden and direct allowed transitions in the regions E "2.1}2.6 eV and E "2.6}3.3 eV, respective ly. However, in the region E "1.7}2.1 eV we con sider the transition from the impurity levels to the conduction band, since the measured result diverges from the theoretical curve [7]. Here, it should be mentioned that these energy regions, E "1.7}2.1, 2.1}2.6, and 2.6}3.3 eV, correspond to the resonance observed in the spectra of the re#ectance (see Fig. 4). 5.2. Threshold energy of photoemission
Fig. 11. Photoabsorption coe$cient as a function of the photon energy. Circles, crosses and triangles denote the data for the cathode thickness of 76, 38 and 152 nm, respectively. The curves are the results of the "tting with the parameters listed in Table 2.
From a measurement of the quantum e$ciency one can obtain information about the threshold energy (E ) of the photoemission process, as
Table 2 E and n of the photocathode samples at room temperature. The result of the sample B is the average values of the samples B1 and B2 Sample
A B C Average
Thickness (nm)
76 38 152
E "2.1}2.6 eV
E "2.6}3.3 eV
E (ev)
n
E (ev)
n
1.77$0.04 1.87$0.04 1.93$0.07
1.56$0.18 1.28$0.11 1.38$0.28
2.02$0.05 2.28$0.06 2.23$0.06
0.64$0.12 0.49$0.06 0.63$0.16
1.86$0.07
1.4$0.12
2.2$0.1
0.59$0.07
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T. Shima, Y. Nagai / Nuclear Instruments and Methods in Physics Research A 431 (1999) 185}193
described below. The yield of photocurrents (i.e. quantum e$ciency) from the valence band of the cathodes of an alkali}antimonide type is theoretically given as
origin of the di!erence could be found in any process to make the cathode.
6. Summary and discussions Q(E )"+(E !E ) B,/+(E !E ) #c,
(17)
where B and c are constants, or slowly varying functions of E [7]. Hence, by "tting our data of the quantum e$ciency with Eq. (17) in the energy region of E "2.6}3.3 eV we obtain average E values of 2.38$0.05 eV for three samples (A, B and C). In addition, we obtain the electron a$nity (E ) to be 0.52$0.08 eV from the band gap energy (E ) in the region E "2.1}2.6 eV, as given in Table 2 and the relation E "E #E . Here, it should be mentioned that these values of E and E di!er from the previous values of E "1.0 eV and E "1.1 eV [8]. In order to "nd a possible origin of the di!erence, we compare our data of the absorption coe$cient with those by Nathan and Mee [8] and by Timan [11] in Fig. 12. Here, the previously obtained data are plotted relative to our value for the standard cathode thickness at E "3.18 eV, since the cathode thickness was not measured in the old measurements. One can clearly see that our results agree quite well with that by Timan, but not with that by Nathan and Mee. The di!erence is quite large in the region below E &2.5 eV, where the photoabsorption due to the impurity becomes dominant. Hence, a possible
In this paper we proposed a new method to increase the quantum e$ciency of a PM tube using photons transmitted by a cathode, and we considered the spectral response of a K CsSb cathode to estimate the performance of the new PM tube. From the present result, we obtain a large enhancement of the quantum e$ciency by a factor of 1.1}2.3 in the region 280 nm(j(650 nm. Here, it should be mentioned that a larger enhancement can be achieved using a thinner cathode, since it is more transparent. The thinner cathode, however, has a smaller value quantum e$ciency. Therefore, it is necessary to adjust the cathode thickness in order to obtain the highest e$ciency. The principle of the new method can be employed to construct a PM tube with an extended sensitive band using the second cathode which has a di!erent sensitive band from the "rst cathode. In this study we also found that photoabsorption in K CsSb is caused by a direct-allowed transition with E "2.2$0.1 eV, a direct-forbidden transition with E "1.86$0.07 eV and an impu rity photoabsorption process, in the ranges of E '2.6 eV, E "2.1}2.6 eV and E (2.1 eV, respectively. The electron a$nity (E ) was determined to be 0.52$0.07 eV. Finally, it should be mentioned that since this work was aimed at testing the e$ciency of the new method, we designed the structure of the PM tube so as to optimize the quantum e$ciency. The e!ects of the transit-time spread of the photoelectrons and of the quantum e$ciency for photons with various incident angles to the cathode must be studied.
Acknowledgements
Fig. 12. Comparison of the data of the absorption coe$cient: circles, present work; triangles, Nathan and Mee (Ref. [8]); crosses, Timan (Ref. [11]).
We would like to thank Mr. H. Sato for his help in designing the PM tube, and Messrs. S. Suzuki, M. Kinoshita, and T. Okada of Hamamatsu Photonics K.K. for their cooperations in the experiment. This work was supported by a Grant-in-Aid of
T. Shima, Y. Nagai / Nuclear Instruments and Methods in Physics Research A 431 (1999) 185}193
the Japan Ministry of Education, Science, Sports and Culture.
References [1] A.H. Sommer, Photoemissive Materials, Wiley, New York, 1968. [2] W.D. Gunter Jr, E.F. Erickson, G.R. Grant, Appl. Opt. 4 (1965) 512. [3] G.R. Grant, W.D. Gunter Jr., E.F. Erickson, Rev. Sci. Instr. 36 (1965) 1511.
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[4] K.R. Crowe, J.L. Gunnick, Appl. Phys. Lett. 11 (1967) 249. [5] W.D. Gunter Jr, R.J. Jennings, G.R. Grant, Appl. Opt. 7 (1968) 2143. [6] G. Hass, J.E. Waylonis, J. Opt. Soc. Am. 51 (1961) 719. [7] A.H. Sommer, Appl. Phys. Lett. 3 (1963) 62. [8] R. Nathan, C.H.B. Mee, Int. J. Electron. 23 (1967) 349. [9] R. Nathan, C.H.B. Mee, Phys. Stat. Sol. A. 2 (1970) 67. [10] R.H. Bube, in: Photoelectronic Properties of Semiconductors, Cambridge University Press, Cambridge, 1992. [11] H. Timan, Optical characteristics and constants of high e$ciency photoemitters, Revue Tech. Thomson-CSF 8 (1976) 49.
Development of a photomultiplier tube with high quantum e$ciency T. Shima, Y. Nagai* Department of Applied Physics, Tokyo Institute of Technology, O-okayama 2-12-1, Meguro-ku, Tokyo 152-8551, Japan Received 11 January 1999
Abstract We propose a new method to signi"cantly increase the quantum e$ciency of a photomultiplier tube by employing a multi-photocathode and a mirror to produce photoelectrons by reusing photons transmitted by a single photocathode. In order to estimate the expected performance of the new photomultiplier, we studied the spectral responses of the re#ectance, transmittance, and quantum e$ciency of a K CsSb photocathode as a function of the wavelength of incident light. A large enhancement of the quantum e$ciency is expected in the regions between j"280 and 650 nm. 1999 Elsevier Science B.V. All rights reserved. PACS: 29.40.Mc Keywords: Scintillation detectors; Scintillators and photomultipliers
1. Introduction Photomultiplier (PM) tubes have been used as the most common and useful type device for detecting photons in various "elds of science and technology, owing to the special features of good sensitivity and fast response (a few ten ps) to photons. The sensitivity is described in terms of the quantum e$ciency (QE), which is de"ned as the ratio of the number of photoelectrons emitted from the photocathode to that of incident photons. Although QE is as good as about 30%, it would be extremely nice if one could make PM tubes having better e$ciency. In the present work, we proposed * Corresponding author. Tel.: #81-3-5734-2750; fax: #813-5734-2750. E-mail address: nagai.ap.titech.ac.jp (Y. Nagai)
a new method to increase QE of a PM tube and studied the expected performance. So far, several methods have been developed to increase QE, which can be categorized into three types. The "rst concerns a photocathode (cathode) [1]. Currently, semiconducting compounds, such as K CsSb, Na KCsSb (multi-alkali), and GaAs}Cs, are being used as cathode materials because of a good quantum e$ciency of about 30%. They meet the requirements so as to obtain a high QE, such as a small band gap energy (E ) and a small electron a$nity (E ). The second is related to the thickness of the photocathode. In order to achieve a high QE, the thickness of the photocathode should be su$cient to convert a large fraction of the incoming photons into photoelectrons, and thin enough to permit most photoelectrons to escape from the cathode. To meet the
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latter condition the thickness is usually a few ten nm for photons having a wavelength such as 400 nm, and is almost equal to the escape depth of photoelectrons in cathode materials of the alkali}antimonide type. However, the thickness is not enough to absorb most of the incident photons, since the attenuation length for photons is a few thousand nm in the cathode. Hence, incident photons were passed through the cathode many times by means of total internal re#ection, and thus an enhancement of QE was obtained [2,3]. The enhancement depends on the wavelength of the photons: &2 and &4 for a blue light and a red light, respectively, since the cathode absorbs blue light more e$ciently than red. The third is related to the extraction of photoelectrons from the cathode with higher e$ciency using an external electric "eld [4]. A test experiment was performed by applying a high "eld of 7.9;10 V/cm near to the surface of a Na KCsSb cathode; a maximum en hancement of QE was obtained below the threshold energy (&2 eV) of photoemission [4]. An enhancement was achieved, since the potential barrier at the vacuum interface of the cathode was lowered by applying an external "eld; and thus low-energy photoelectrons originating from impurity levels within a forbidden band could escape from the cathode. The simultaneous use of total internal re#ection and a high electric "eld has been studied; and has provided further enhancement of QE [5]. The latter two methods, however, have not been realized for commonly used PM tubes. In the present work, we propose an alternative method to increase QE, where the transmitted photons are utilized several times to produce photoelectrons by means of a multi-cathode and a mirror.
2. A PM tube with a multi-cathode and a mirror A schematic view of a PM tube consisting of two separated cathodes and one mirror is shown in Fig. 1. Here, the photoelectrons are produced at the following stages: "rst, when the incident photons impinge upon the "rst cathode through the photon window; second, when the transmitted photons reach the second cathode through a "eld-shaping grid; third when the photons transmitted through
Fig. 1. Schematic drawing of the new PM tube (cross-sectional side view).
the second cathode are re#ected by the mirror, and enter the second cathode again; and fourth, when the transmitted photons impinge upon the "rst cathode again, respectively. Therefore, the total quantum e$ciency (Q ) of this new PM tube would 2 be higher than that of a conventional one with a single cathode. Here, Q is given as 2 Q "N /N (1) 2 where N and N are the numbers of photo electrons collected at a dynode and of the incident photons entering the "rst cathode, respectively. Here, N is given as N "k N #k N #k N #k N (2) where k (i"1}2) and N (i"1}4) stand for the G G collection e$ciency and numbers of the photoelectrons produced at the above-mentioned stages; k was calculated as described later. The number G N was estimated as follows, where we assume that G the re#ectance (R) and the transmittance (¹) are the same for the "rst and second cathodes, respectively. Since the incident photons are reduced by re#ection at the "rst cathode, N is given using the quantum e$ciency (Q) of a single photocathode as N "Q N . (3) Since the intensity of the transmitted photons through the "rst cathode is reduced by the re#ection at both the second cathode and the
T. Shima, Y. Nagai / Nuclear Instruments and Methods in Physics Research A 431 (1999) 185}193
"eld-shaping grid, respectively, N is given as N "Q ¹ (1!R) ¹N $%
(4)
where ¹ stands for the transmittance of the $% "eld-shaping grid, given as the ratio of apertures between grid wires to the total area of the acceptance for the incident photons. It is estimated to be 0.85. In a similar way, we obtain N and N as N "Q R ¹ ¹(1!R)¹N +0 $%
(5)
and N "Q R (¹ ) ¹(1!R)¹N +0 $%
(6)
where R indicates the re#ectance of the mirror. +0 Consequently, Q is given as 2 Q "Q[k #k ¹ ¹(1!R)#k R ¹ 2 $% +0 $% ;+¹(1!R),#k R (¹ )+¹(1!R), +0 $% (7) Hence, if we collect all of the photoelectrons, we can obtain a large enhancement of QE. In order to estimate the performance of a new PM tube, we studied the spectral response of a K CsSb photo cathode, and calculated the collection e$ciency of the photoelectrons for several con"gurations of the electrodes. Here, the re#ectance (R ) should +0 be mentioned; since an aluminum-evaporated mirror is known to have the highest re#ectance of 0.91}0.92 in the visible region [6]; we used Al.
3. Experimental procedure and results
thickness of the antimony was determined by an X-ray #uorescence analysis, and that of the K CsSb layer was determined within an uncertainty of about 10% by multiplying the antimony thickness by a factor 4.9, which is the ratio of the number density of antimony atoms to that of K CsSb mol ecules. In order to accurately measure the cathode thickness, we used quartz with a thickness of 1.55 mm as a photon window, but not normal borosilicate glass, since it contains antimony. We measured the spectral response using three phototubes with di!erent thickness of the cathode layer as listed in Table 1; two phototubes (A2 and B2) were used to check the tube-to-tube variation of the spectral response, and phototube D was used to study any contributions to the spectral response from materials other than the cathode. Here, two samples (A1 and A2) have cathodes with a `standarda commercial thickness. The photoelectrons emitted from the cathode were collected at an anode, and measured as photocurrents. The anode was made by evaporating aluminum onto a glass window opposite the photon window.
Fig. 2. Structure of the phototube used for the spectral response measurements of the K CsSb photocathode.
3.1. Phototubes The spectral responses of K CsSb were mea sured with the phototube shown in Fig. 2 as a function of the wavelength (j) of unpolarized photons in a vacuum environment at 253C. The phototube had no electron-multiplication stage, and was made by "rst coating a small amount of MnO onto a photon window, and then evaporating antimony on it. A crystal layer of K CsSb was formed by adding potassium and cesium to the antimony layer. The
187
Table 1 Speci"cations of the sample photo tubes Phototube
Cathode thickness (nm)
A1 A2 B1 B2 C D
76 76 38 38 152 0 (Not evaporated)
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3.2. Reyectance (R) The re#ectance (R) of the cathode is de"ned as R"I /I (8) P where I and I are the intensities of incident photons onto the cathode layer and re#ected photons from the cathode, respectively. The experimental setup used to measure R is shown in Fig. 3. Photon beams with continuous wavelength of j"190}352 nm and 352}840 nm were produced using a deuterium lamp and a tungsten lamp, respectively. Monochromatic photons were selected with a spectrometer (Hitachi model-340), and were guided so as to impinge upon either the quartz window of a sample phototube or a reference mirror (aluminum-coated #at mirror) by changing the photon path using rotating mirrors. The re#ected photons were detected by a reference PM tube, whose sensitivity was calibrated using a standard calibrated Si-photodiode (Hamamatsu S-13371010BQ). The photon intensity from the reference mirror was measured in order to cancel out the #uctuation of the incident photon intensity. Here, it should be mentioned that since the spectrometer and the reference tube could not be placed on the same axis, they were set at symmetric positions with respect to the normal of the photon window of
Fig. 3. Experimental setup for the re#ectance measurement. The incoming angle and the outgoing angle were adjusted to 53 with respect to the normal of the photon window of the sample tube.
a sample tube. The incidence angle (h ) and the G re#ection angle (h ) of the photons were adjusted to P be 53 against the normal to the window; also according to the Fresnel formulae, R is of the same magnitude as that for h "h " 0 within an uncerG P tainty of 1%. The incident photon intensity (I ) at Q the surface of the window is related to the intensity (I ) at the K CsSb layer as I "¹ (1!R )I (9) Here, ¹ and R stand for the transmittance and re#ectance of the window, respectively, and were measured with sample D (no cathode material), while I was measured without a sample phototube. The measurement of ¹ is discussed later. Since both photons re#ected by the cathode and window surface are detected by the PM tube, the observed photon intensity (I) is given by I"¹ I #R I (10) Consequently, R is obtained by using the measured values of I and I as R"+I/I !R ,/+(¹ )(1!R ), (11) The thus-obtained re#ectance (R) is shown in Fig. 4 as a function of j for each sample; as one expects, R becomes smaller as the thickness of K CsSb becomes thinner. In addition, a broad resonance is observed at around j"460, 540, and 750 nm, which might be due to some speci"c photoemission processes, as discussed in Section 5.2.
Fig. 4. Re#ectance as a function of the photon wavelength. The solid, dotted, and dashed curves are obtained for the phototubes with the cathode thickness of 76, 38 and 152 nm, respectively.
T. Shima, Y. Nagai / Nuclear Instruments and Methods in Physics Research A 431 (1999) 185}193
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3.3. Transmittance (¹) The transmittance (¹) is given by ¹"I /I
(12)
where I and I are the intensities of the photons entering the K CsSb layer and the transmitted photons, respectively. Here, I is given using Eq. (9) as I "(1!R) I "(1!R) (1!R ) ¹ I
(13)
Fig. 5. Experimental setup for the transmittance measurement.
The intensity (I ) was measured with a reference PM tube as a function of j using the experimental setup shown in Fig. 5, where the monochromatic photons were divided into two paths using rotating mirrors, and a reference beam was used to monitor the intensity of the incident photon beam. The thus-obtained transmittance (¹) is shown in Fig. 6, where one can clearly see that ¹ is larger for samples B1 and B2 compared to those of A and C, and ¹ increases rapidly above j"450 nm, which is discussed in Section 5.1. 3.4. Quantum ezciency The quantum e$ciency of a K CsSb cathode was measured using the experimental setup shown in Fig. 7, where photoelectrons produced were collected at the anode, and the photocurrent was measured by a digital ammeter (ADVANTEST TR8652). The collection e$ciency was shown to be 100% for an anode voltage above 90 V; we used 100 V. The incident photon intensity was measured before setting a sample phototube with the standard Si-photodiode, as described above, and was stable during measurements. The quantum e$ciency (Q), which is de"ned in Eq (1), is written as Q"(N /N )/[(1!R) (1!R )¹ ]
Fig. 6. Transmittance as a function of the photon wavelength. The solid, dotted, and dashed curves are obtained for the phototubes with the cathode thickness of 76, 38 and 152 nm, respectively.
(14)
where N and N are the numbers of photoelectrons and of the incident photons at the photon window. We obtain Q as shown in Fig. 8, where one can clearly see that Q is approximately constant for j"300}450 nm, and decreases as j increases from 450 nm to 700 nm. Namely, Q is in anti-correlation with the transmittance (¹). Hence, the j depend-
Fig. 7. Experimental setup for the measurement of the quantum e$ciency.
ence of Q is strongly related to the photoabsorption process in the cathode. Here, it is worth noting that the highest Q value was obtained for sample A with the standard thickness.
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Fig. 8. Quantum e$ciency Q as a function of the photon wavelength. The solid, dotted, and dashed curves are obtained for the phototubes with the cathode thickness of 76, 38 and 152 nm, respectively.
Fig. 9. Total quantum e$ciency Q of the proposed PM tube. 2 The solid, dotted, and dashed curves are the estimated values for the PM tubes with the cathode thickness of 76, 38 and 152 nm, respectively.
4. Quantum e7ciency of a new PM tube In order to obtain the maximum quantum e$ciency of the new PM tube, it is important to collect the photoelectrons emitted from the cathode with high e$ciency. Since the e$ciency depends on the con"gurations of both the cathodes and dynodes, we calculated the e$ciency (k) for various con"gurations of the electrodes, as described below. First, the distribution of the electric potential in the PM tube was calculated for several voltages of the electrodes. Next, the trajectories of the photoelectrons were numerically obtained for the calculated electric "eld. Here, for simplicity, we make two assumptions: "rst, the photoelectrons are emitted perpendicularly from the cathode with a constant kinetic energy of 1.2 eV, a typical value for the K CsSb cathode; second, the probability of photo electron emission is uniform over the surface of the cathode. Thus, the collection e$ciencies (k and k ) for the photoelectrons from the "rst and second cathodes were calculated for several con"gurations of the electric "eld, respectively; best values of k " k "0.95 were obtained for the con"guration shown in Fig. 1. Using these values, Q in Eq (8) 2 was calculated as a function of j as shown in Fig. 9. Hence, we obtain quite a large enhancement of the quantum e$ciency (Q /Q ) by a factor of 1.1}2.3 in 2 1 the range of 280 nm(j(650 nm, as shown in Fig. 10. The enhancement is larger for a thinner
Fig. 10. Enhancement of the quantum e$ciency of the proposed PM tube compared to that of the conventional one. The solid, dotted, and dashed curves are the values for the PM tubes with the cathode thickness of 76, 38, and 152 nm, respectively.
cathode as expected, since it is more transparent than the thicker one. However, since a thinner cathode has a smaller Q value, Q is not necessarily 2 the highest, as shown in Fig. 9. Hence, it is necessary to determine an optimum thickness of the cathode so as to obtain a high Q . 2 5. Optical property of a K2CsSb photocathode The above results concerning the spectral response provide important information about the
T. Shima, Y. Nagai / Nuclear Instruments and Methods in Physics Research A 431 (1999) 185}193
optical properties of the K CsSb cathode, such as the photoabsorption and photoelectron emission processes, as discussed below [7]. So far, the properties have been studied by measuring the photoemission, optical absorption, photoconductivity and electric conductivity; a small band gap energy (E ) of !1.0 eV and an electron a$nity (E ) of E ? !1.1 eV have been reported [8]. Furthermore, by measuring the energy distribution of photoelectrons, the photoemissions for photons below 2.5 eV (j'495 nm) and above 4.0 eV (j(309 nm) are claimed to be due to excitations from impurity levels and from the maxima in the valence-band density of states at depths of 2.3 and 2.8 eV below vacuum, respectively [9]. 5.1. Photoabsorption mechanism in K2CsSb From a measurement of the transmittance (¹) of the K CsSb cathode one can extract a photoab
191
sorption coe$cient (a), which is de"ned as (15)
¹"exp(!az),
where z stands for the cathode thickness [10]. In Fig. 11 we show a for three cathodes with di!erent thicknesses. Here, a theoretical value of a is given for a direct interband transition near to an absorption edge as A a" (E !E )L (16) E where A is a normalization constant, and E and E are the incident photon energy and band gap energy, respectively. Also, n stands for the power which characterizes the type of interband transition; n is equal to and for pure allowed and pure forbidden-transitions, respectively. From the present data in the region E "2.1}3.3 eV, E and n were obtained as listed in Table 2; they indicate that the photoabsorption is caused by direct forbidden and direct allowed transitions in the regions E "2.1}2.6 eV and E "2.6}3.3 eV, respective ly. However, in the region E "1.7}2.1 eV we con sider the transition from the impurity levels to the conduction band, since the measured result diverges from the theoretical curve [7]. Here, it should be mentioned that these energy regions, E "1.7}2.1, 2.1}2.6, and 2.6}3.3 eV, correspond to the resonance observed in the spectra of the re#ectance (see Fig. 4). 5.2. Threshold energy of photoemission
Fig. 11. Photoabsorption coe$cient as a function of the photon energy. Circles, crosses and triangles denote the data for the cathode thickness of 76, 38 and 152 nm, respectively. The curves are the results of the "tting with the parameters listed in Table 2.
From a measurement of the quantum e$ciency one can obtain information about the threshold energy (E ) of the photoemission process, as
Table 2 E and n of the photocathode samples at room temperature. The result of the sample B is the average values of the samples B1 and B2 Sample
A B C Average
Thickness (nm)
76 38 152
E "2.1}2.6 eV
E "2.6}3.3 eV
E (ev)
n
E (ev)
n
1.77$0.04 1.87$0.04 1.93$0.07
1.56$0.18 1.28$0.11 1.38$0.28
2.02$0.05 2.28$0.06 2.23$0.06
0.64$0.12 0.49$0.06 0.63$0.16
1.86$0.07
1.4$0.12
2.2$0.1
0.59$0.07
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described below. The yield of photocurrents (i.e. quantum e$ciency) from the valence band of the cathodes of an alkali}antimonide type is theoretically given as
origin of the di!erence could be found in any process to make the cathode.
6. Summary and discussions Q(E )"+(E !E ) B,/+(E !E ) #c,
(17)
where B and c are constants, or slowly varying functions of E [7]. Hence, by "tting our data of the quantum e$ciency with Eq. (17) in the energy region of E "2.6}3.3 eV we obtain average E values of 2.38$0.05 eV for three samples (A, B and C). In addition, we obtain the electron a$nity (E ) to be 0.52$0.08 eV from the band gap energy (E ) in the region E "2.1}2.6 eV, as given in Table 2 and the relation E "E #E . Here, it should be mentioned that these values of E and E di!er from the previous values of E "1.0 eV and E "1.1 eV [8]. In order to "nd a possible origin of the di!erence, we compare our data of the absorption coe$cient with those by Nathan and Mee [8] and by Timan [11] in Fig. 12. Here, the previously obtained data are plotted relative to our value for the standard cathode thickness at E "3.18 eV, since the cathode thickness was not measured in the old measurements. One can clearly see that our results agree quite well with that by Timan, but not with that by Nathan and Mee. The di!erence is quite large in the region below E &2.5 eV, where the photoabsorption due to the impurity becomes dominant. Hence, a possible
In this paper we proposed a new method to increase the quantum e$ciency of a PM tube using photons transmitted by a cathode, and we considered the spectral response of a K CsSb cathode to estimate the performance of the new PM tube. From the present result, we obtain a large enhancement of the quantum e$ciency by a factor of 1.1}2.3 in the region 280 nm(j(650 nm. Here, it should be mentioned that a larger enhancement can be achieved using a thinner cathode, since it is more transparent. The thinner cathode, however, has a smaller value quantum e$ciency. Therefore, it is necessary to adjust the cathode thickness in order to obtain the highest e$ciency. The principle of the new method can be employed to construct a PM tube with an extended sensitive band using the second cathode which has a di!erent sensitive band from the "rst cathode. In this study we also found that photoabsorption in K CsSb is caused by a direct-allowed transition with E "2.2$0.1 eV, a direct-forbidden transition with E "1.86$0.07 eV and an impu rity photoabsorption process, in the ranges of E '2.6 eV, E "2.1}2.6 eV and E (2.1 eV, respectively. The electron a$nity (E ) was determined to be 0.52$0.07 eV. Finally, it should be mentioned that since this work was aimed at testing the e$ciency of the new method, we designed the structure of the PM tube so as to optimize the quantum e$ciency. The e!ects of the transit-time spread of the photoelectrons and of the quantum e$ciency for photons with various incident angles to the cathode must be studied.
Acknowledgements
Fig. 12. Comparison of the data of the absorption coe$cient: circles, present work; triangles, Nathan and Mee (Ref. [8]); crosses, Timan (Ref. [11]).
We would like to thank Mr. H. Sato for his help in designing the PM tube, and Messrs. S. Suzuki, M. Kinoshita, and T. Okada of Hamamatsu Photonics K.K. for their cooperations in the experiment. This work was supported by a Grant-in-Aid of
T. Shima, Y. Nagai / Nuclear Instruments and Methods in Physics Research A 431 (1999) 185}193
the Japan Ministry of Education, Science, Sports and Culture.
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[4] K.R. Crowe, J.L. Gunnick, Appl. Phys. Lett. 11 (1967) 249. [5] W.D. Gunter Jr, R.J. Jennings, G.R. Grant, Appl. Opt. 7 (1968) 2143. [6] G. Hass, J.E. Waylonis, J. Opt. Soc. Am. 51 (1961) 719. [7] A.H. Sommer, Appl. Phys. Lett. 3 (1963) 62. [8] R. Nathan, C.H.B. Mee, Int. J. Electron. 23 (1967) 349. [9] R. Nathan, C.H.B. Mee, Phys. Stat. Sol. A. 2 (1970) 67. [10] R.H. Bube, in: Photoelectronic Properties of Semiconductors, Cambridge University Press, Cambridge, 1992. [11] H. Timan, Optical characteristics and constants of high e$ciency photoemitters, Revue Tech. Thomson-CSF 8 (1976) 49.