SOME ASPECTS OF THE VOLTAGE AND FREQUENCY DEPENDENCE OF ELECTROLUMINESCENT ZINC SULPHIDE

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1 R 268 Philips Res. Rep. 10, , 1955 SOME ASPECTS OF THE VOLTAGE AND FREQUENCY DEPENDENCE OF ELECTROLUMINESCENT ZINC SULPHIDE by P. ZALM, G. DIEMER Summary and H. A. KLASENS Experiment shows that the relation between the luminous emittance H of an electroluminescent cell and the applied r.m.s. voltage V is given by H = Ho exp (-cjvi;.). A mechanism is proposed that may explain both the well-known linear frequency dependence at a constant r.m.s. voltage of the emittance and the observed voltage dependence. Résumé L'expérience montre que la relation entre le pouvoir ëmissif lumineux H d'un élément électro-iuminescent et la tension efficace Vappliquée est donnée par la formule H = Ho exp (-cjv!). L'on propose un mécanisme pouvant expliquer en même temps le fait bien connu qu'à une tension efficace constante, le pouvoir émissif est une fonction lineaire de la frequence, ainsi que la dëpendance observëe du pouvoir êmissif de la tension. Zusammenfassung Der Versuch zeigt, daf das Verhältnis zwischen der Luminanz II einer elektrolumineszenten Zelle und der angelegten Effektivspannung gegeben wird durch H = Ilo exp (-cjv!). Ein Mechanismus wird vorgeschlagen, der sowohl die bekannte lineare Frequenzabhängigkeit bei konstanter Effektivspannung der Emittanz als auch die beobachtete Spannungsabhängigkeit erklären könnte : Introduction In a previous paper 1) we have shown that inhomogeneities on the surface of the grains (e.g. a copper- or gold-rich phase) are responsible for the occurrence of electroluminescence of zinc sulphide. Suchinhomogeneities may lead to a non-linear field distribution over the grains, and where the copper-rich phase and the zinc sulphide are in contact with each other they may give rise to a potential barrier of the nature of an exhaustion barrier. The presence of this exhaustion barrier must obviously affect the relation between integrated light output and voltage, frequency, etc. Concerning the mechanism of electroluminescence of zinc sulphide several theories have been formulated, all of ch agree in the conception that the aètivator centres are excited (or ionized) by collision with electrons that are accelerated in the conduction band 1)2)3)4). The fluorescent centres need not be excited directly; just as with cathode-ray excitation the basic

2 206 P. ZALM, G. DIEMER and H. A. KLASENS lattice ions themselves are excited first and the energy is transferred to the activators by hole migration. ' The probability P that a conduction electron gains sufficient energy for impact excitation in an electric field E is 5)6) P= A exp (-c'je), (1) A and c' being constants depending on the specimen involved. We assume the acceleration of an electron to take place in an exhaustion barrier and that relation (1) also holds for an inhomogeneous field distrihution if we put E equal to an adequate average value of the field. In that case the local field E is proportional to V! (V being the applied voltage) and one finds for the' voltage dependence P= AVexp) -bj!). (2) The probability that the activators are directly field-ionized in the exhaustion region and the probability that an electron out of. the copperrich phase penetrates the potential barrier by a tunnel process are, however, also given by expressions of this same form. The foregoing considerations have led us to attempt to represent the observed voltage dependence of the light output of an electroluminescent cell by *) H = Hoexp (-cjp), (3) where V is the root-mean-square value of the applied voltage. 2. Experiments A number of measurements of the voltage dependence of the luminous emittance H of electroluminescent cells with different types of electroluminescent material, suspended in various dielectrics, shows that the relation between H and the applied voltage V is given exactly by eq. (3). The accuracy of this law is so great that over a range of nearly lob in brightness, no significant deviation was found between the experimental points and a curve representing eq. (3). In fig. 1 the results are given for ZnS-10-a Cu Al, ZnS Cu-Cl and ZnS-10-a Cu-10-2 Mn at various frequencies, and for ZnS-10-2 Li 2 S-10-2 Mn at d.c. excitation. Butler, Jerome and Waymouth 7) attribute the strong variation of light output with applied voltage to the increase of the number of particles that becomes luminescing with increasing voltage. :. They conclude from their measurements that the light output of a single spot increases linearly with the applied voltage. *) The same relation was proposed simultaneously by J. B. Taylor and G. F. Alfrey and the authors at the Cambridge Conference on Luminescence 1954.

3 -, VOLTAGE AND FREQUENCY DEPENDENCE OF ELECTROLUMINESCENT ZnS 207 We too estimated the brightness of a single. spot, and our results are in disagreement with the observations of Butler et al. Of course a linear relationship may be found over a small range, but we found eq. (3) to represent the measurements over the whole range of observations. The intensity of a single spot was measured by observing it through a microscope and adjusting the voltage until the spot became just visible. By repeating 10 8 r I I x x x ZnS-Cu-A7 50eps(green «i» \ \1\\. 000 ZnS-Cu-A7500eps(green e.7)... ZnS -Cu-Mn 1500eps(orange e.7.j ZnS-Cu-Cl 250 eps (blue «u ZnS-Li 2 S -Mn ä.c.!\x\. \XO "''''''' 6 \ l',. '\, -. 1\\ 0,,-, "'-0", 1''0" \\\ I'D.\ 10" 10 \ \ 0, 0"" r-, \ 0\ ""'0 \ \ ""'\ \ p\ u\ \. [\ ' I,- VV 5 6 ( volts)-f Fig. 1. The linear relation between the logarithm of the emittance and the inverse square root of the applied voltage..

4 208 P. ZALM, G. DIEMER and H. A. KLASENS these measurements with. various grey filters of known transmission an (H, V) curve is obtained which is rather well reproducible *). Figure 2 gives the experimental results; log H is plotted versus V--!. Curve (a) corresponds to the brightest spot visible in the field, curve (b) to a somewhat diffusely lighting grain in which probably several very small weak spots were contributing to the light emission. Curve (c) gives the average brightness' of the "cell" as measured with a photomultiplier. + \\. \\ \\+ \ 10 1> \0.\ \ \ \ b\ \ c, 1\ \ \ \\ '\ 1 o 0,1 0'2 1 W + d + '\ \ + 1\ \. \ in (7di; Fig. 2. The logarithm of the emittance versus the inverse square root of the applied voltage (500 cis) as measured on: - (a) one single spot, (b) a diffusely luminescent grain, (c) an electroluminescent cell. One might be surprised about the fact that the same relation between emittance and voltage holds both for an electroluminescent cell and for a single spot, since the dimensions of the particles' and their orientation in the applied electric field vary, thereby causing a considerable spread *) This method 'of measuring absolute light intensities at values far below the sensitivity limit of a photocell by means of the human eye was kindly suggested to us by Dr K. W. Böer, Berlin.

5 VOLTAGE AND FREQUENCY DEPENDENCE OF ELECTROLUMINESCENT ZnS 209 in the value of c in eq. (1). A simple analysis as given in the appendix shows, however, that even with a large variationin c-values the average emittance-voltage relation will have nearly the same form as that for a single spot. Destriau 2) has also attributed the voltage dependence of the luminous emittance to the probability P that a conduction electron gains sufficient energy for impact excitation. Destriau arrived. at the expression H = A V2exp (-b'v), (4) by assuming that excitation takes place throughout the zinc-sulphide crystal and that the field is a linear function of the applied voltage. The observed voltage dependence showed, however, a slight but significant deviation from this relation 2).. 3. Discussion It must be emphasized that a straightforward application of the proposed emittance-voltage relation as given in eq. (3) seem to lead to a frequency dependence which is not in accordance with experiment. If the actual potential drop over the exhaustion barrier could be represented by V(t) = Vof(vt), (5) (v = frequency) f being a periodic function of vt, then the integrated light output lover half a cycle would be given by! I c-o f exp [-cd V(t)] d(vt)..0 (6) Accordingly I is proportional to Iv; the luminous emittance is given by 2vI and would be independent of frequency. The experiments, however, show nearly a linear relationship between frequency and emittance at a constant voltage over a rather wide frequency range (see fig. 3). To get round this difficulty one has to construct a physical model for electroluminescence such that the integrated light output over half a cycle is independent of frequency. Piper and Williams 4 ) have developed such a model. They assumed the electrons that are responsible for the excitation of the phosphor to come from field-ionized "deep" donor levels. The strong electric field required for the ionization and excitation is found in an exhaustion layer with a positive space charge. As soon as the local field reaches a certain value all donor levels of a given depth are emptied so that during each half cycle (independently of frequency) a constant charge is displaced. They further

6 210 P. ZALM, G. DIEMER and H. A. KLASENS assume the probability of excitation to be "proportional to the drop in potential experienced by the electron from the point where it is released (from the donor levels) the to point where it reaches the threshold field below which it cannot be succesfully accelerated". The latter assumption would only lead to the observed voltage dependence over such a wide range. if a special distribution of the depths of the deep donors would he assumed. 10' en :!:: e '" :C'" 10 3 ij Jj ; ",.,.-.: 1 V" ; V x ' 00 0 Zns-Cu. At 560 volt s» " ZnS-Cu.AI.200 volt ri ZnS-Cu.CI.200 volt., V ID ' _c;ts Fig. 3. Emittance versus frequency at a constant a.c. voltage. A somewhat wider variation in the donor distru:mtion can be tolerated if one assumes the probability of excitation to be given by eq. (2). Nevertheless we do not believe that the primary electron comes from donor levels in the bulk of the material for the following reasons: (A) To have a constant positive charge density in the exhaustion layer, Piper and Williams assumed the presence of a large number of "shallow" donors which are emptied thermally or at low field strengths. This assumption is not compatible with the presence of empty traps of considerable depth in certain electroluminescent phosphors (e.g., ZnS-Cu-Al-Co, ZnS- Cu-Ga) as shown by the glow spectrum. Moreover one would expect the electroluminescent crystals to be fairly conducting with a large number of donors below 0 5 ev. Such a conductance has not been found. I on the other hand the shallow donors are filled traps which are normally empty (suggestion also made by Piper and Williams) they cannot give rise to a positive space charge when being emptied.

7 VOLTAGE AND FREQUENCY DEPENDENCE OF ELECTROLUMINESCENT ZnS 211 (B) If electron traps are acting as donor levels for the primary electrons, one can calculate the distrihutions of trap depths that can be tolerated to give the observed voltage dependence, assuming the probability of excitation to be given by eq. (2). This calculated distribution of trap depths is not in agreement with the observed glow spectra. We therefore started from the following assumptions: (1) Donor levels are localized in the surface (either in the thin coppersulphide layer or in the zinc-sulphide surface in contact with the copper sulphide). ', (2) Donor levels of a given depth are exhausted instantaneously when the field reaches a certain value. (3) The' probability of excitation is proportional to exp (-bi V!). (4) The positive spaoe-charge density in the barrier.layer is not influenced by the excitation process. The last assumption is most easily explained by assuming that the donors responsible for the positive spaoe-charge density (that is, for the exhaustion barrier) are the ionized activator centres in the barrier region. This space charge is built up during the first fewvoltage cycles (see1),fig. 25). Excitation is then caused by exciting the valence-band electrons (leaving a positive hole in the valence band) due to the injection of the electrons from surface states. Light emission is caused by recombination of conduction electrons and holes via the excited centres. We now represent the distrihution of donor levels by n(e)de = g(v)d V, (7) where E is the depth of the donor levels below the bottom of the conduction band at the surface of the Zns (fig. 4 )and n(e)de is the number of donor, levels between E and E + de. The total photon emission I for one half cycle is then given by I CS! v. Ig(V) exp (-biv!) o dv, where Vo is the amplitude of V. Now v. Ig(V) exp (-bi V!) dv CS! exp (-bivo!) o if g(v)d V CS! V-i d V. Since the critical field strength Fe for field ionization for levels of depth E is given by 8) Fe = const. Ei, (9) and V! CS! F, (10) (8)

8 212 P. ZALM. G. DIEMER and H. A. KLASENS we find.. v cs:>e3 and a donordistribution n(e) de cs:>e-ide. CU2S + Zns (11) Bottom conduction band Top filled band Fig. 4. Assumed energy-band picture of a zinc-sulphide crystal in contact with copper sulphide showing the donor levels n. To investigate the effect of various donor distributions on the voltage dependence we write so that For p = 1we have and v, J g(v) exp(-bjv!)dvcs:> o Vlexp(-bjVo!) (12) g(v) CS> P VP-l + tb VP-i. (13) n(e)de CS> (E2 + tb E!)dE. Since exp (-bjv!) -ei and bjv! 1we may write n(e)de e-c EtdE. If P = -1 we are led to a donor distribution. (1 b ) g(v)dv CS> - V2 + 2Vi dv (17) that approximates to (14) (15) (16). n(e)de c-c E-"I. de. (18) With a similar approximation one finds that for a uniform donor distribution or n(e)de CS> node, the total photon emission for one half cycle is proportional to

9 VOLTAGE AND FREQUENCY DEPENDENCE OF ELECTROLUMINESCENT ZnS 213 Thus the voltage dependence of the emittance is, indeed, rather Insensi-: tive to the donor distribution. However the accuracy with which the experimental points satisfy eq. (3) is so great that ifthe proposed mechanism is accepted, one is forced to believe that the donor distrihution is given approximately by in which q is between -1 and -5. In that case the luminous emittance will show a voltage dependence between V* exp (bjvi) and.v-i exp (-bjv*), which is the maximum variation that can be tolerated with respect to the experiments. The latter relation, however, would only he consistent with the observations if by the statistical fluctuations of b the pre-exponential factor is canceled for the greater part (see appendix). Our measurements of the light output versus voltage of a single spot are not conclusive to decide about the occurrence of a voltage-dependent pre-exponentlal factor since the accuracy and the range of observations were too small. Since the accessible voltage range of experiments is about 30 to 50 times the threshold voltage and from eq. (11) V CS) ES, the range in E about which the donor-distribution function must satisfy the relation mentioned, is between El and 3 to 4 times El' if El is the depth of the donors emptied at the threshold voltage. Concerning the temperature dependence of electroluminescence we want to make a preliminary remark. One may expect that the positive space charge and eonsequently the value of b in eq. (2) will be dependent on temperature since both the number of trapped electrons and of trapped holes (especially if activator levels of various depths are present) may vary with the temperature. We have experimental evidence that the temperature of electroluminescence can be attributed to the variation of b with temperature. This will be discussed in detail in a forthcoming article. 4. Appendix (20) Some evidence concerning the distribution of c-values (c, as discussed, varies from one crystal to the other) was found by counting the number of luminescing spots N on a small area of an electroluminescent cell (observed through a microscope) as a function of voltage V. Figure 5 gives N as a function of V, measured with an a.c. field of 500 cjs. At very high voltages the number of newly arising spots is difficult to estimate because of the background radiation due to the bright spots already present. Therefore only N-values at moderate voltages are given.

10 214 P. ZALlII, G. DIElIIER and H. A. KLASENS By plotting N versus Vi and differentiating with respect to Vi, we get the actual distribution function g(c) of c-values as shown in fig. 6. We see that for the lower, c-values (which are most important for the contrihution to the emittance) this function can be approximated by a straight line. We shall exaggerate the number of particles with high c-values (thus taking unfavourable conditions' for our analysis) if we choose as the distribution function of c-values: 60 N t la o. J 1I la v v V V, v (volts) Fig. 5. The number N of perceptible light spots as a function of voltage at 500 els ,..., <=1:::. - 1 la \ I -, I... _ I I 'L _., V'2 (volts)va Fig. 6. The distribution function g( c).

11 VOLTAGE AND FREQUENCY DEPENDENCE OF ELECTROLUMINESCENT ZnS 215 g(e)=pe-q. (qp=::;;;e<oo). (21) In this case the number of particles with high e-values will increase indefinitely. Now the emittance H will be H C'l J g(e) exp (-ev!) de C'l J (pe - q) exp (-ev!) de qp qp C'l P Vexp (- qp V!). (22) The voltage dependence according to eq. (22) is essentially the same as that for one single spot. The actual shape of g(e) (as shown in fig. 6) makes the difference between the voltage dependence of a single spot and that of a luminescent cell still smaller than it would be according to eq. (22). Eindhoven, November 1954 REFERENCES 1) P. Zalm, G. Diemer and H. A. Klasens, Philips Res. Rep. 9, , ) G. Destriau, Phil. Mag. 38, , ) D. Curie, J. Phys. Radium 13, , ) W. W. Piper and F. E. Williams, Brit J. appl. Phys. suppl. 4, Paper No. 7, Cambridge Conference on Luminescence ) W. Franz, Z. Phys. 113, , ) F. Seitz, Phys. Rev. 76, , ) K. H. Butler, C. W. Jerome nd J. F. Waymouth, Elect. Eng. N.Y. 73, , B) W. Franz, Ann. Phys., Lpz., 11,17-28,1952.