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Model of ageing process of electroluminescent structures at a temperature of +40°C and a relative humidity of 98%. The results of the test are shown in Fig. 5. Fig. 3. Results of exploitation tests at constant frequency of supply voltage. Rys. 3. Wyniki badań eksploatacyjnych przy stałej częstotliwości napięcia zasilającego. Fig. 4. Results of exploitation tests at constant supply voltage. Rys. 4. Wyniki badań eksploatacyjnych przy stałym napięciu zasilania. Fig. 5. Changes of luminance during humidity tests. Rys. 5. Zmiany luminancji podczas prób odporności na wilgoć. 120
Z. Porada, M. Cieź, W. Prochwicz The results of the tests conducted indicate that one of the most important factors that cause the deterioration of the electroluminescent structures is humidity, which penetrates the luminophore grains and performs the role of an ion conducting medium, and causes the decomposition of ZnS [2] so that it loses its semiconductor properties. The process is particularly intensive in the presence of electric field. 4. A GENERALISED MATHEMATICAL MODEL FOR AGEING PROCESSES Several independent phenomenons take place in the general ageing process, two of which play an important role: the decomposition of luminescence centres under the impact of moisture and the other much slower process — the decomposition of the ZnS grains due to the reaction with copper and consequently the precipitation of metallic zinc according to the reaction : ZnS + Cu = CuS + Zn In both the processes, the concentration of luminescence centres n decreases what can be written in the form of the following equation: dn dt = − where τ is a time constant of the process. The solution to the equation (1) has a general form: n τ (1) n ( t ) = n ( 0 ) e x p ( − t / τ ) (2) As the luminance B of an electroluminescent film is directly proportional to concentration of active luminance centres [1], the following formula can be written: B( t) / B0 = a1 exp( −t / τ 1) + a2 exp( −t / τ 2 ) where: B(t) is the instantaneous value of luminance, B 0 is the luminance at the initial moment of time and a 1 is a numerical coefficient connected with the luminance centre deterioration process under the impact of moisture, τ 1 – is a time constant of this process, while a 2 is an analogous to a 1 coefficient connected with the decomposition of the ZnS grains, and τ 2 is a time constant of this process, in which: a 1 + a 2 = 1 The values of the τ 1 and τ 2 time constants decrease with increasing applied voltage U and increasing temperature (ΔT – the increase in temperature against the room temperature), because the structure ageing process accelerates the increase in operating temperature. This can written in a simplified form: (3) (4) 121
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