Electroluminescence of the Er3+ ion and electric conduction in polycrystalline ZnO:Mn,Bi,Er sintered pellets

Journal of Physics and Chemistry of Solids 62 (2001) 565±578

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Electroluminescence of the Er 31 ion and electric conduction in polycrystalline ZnO:Mn,Bi,Er sintered pellets J.C. Ronfard-Haret a,*, J. Kossanyi a, J.L. Pastol b b

a Laboratoire des MateÂriaux MoleÂculaires, CNRS, 2-6, rue H. Dunant, 94320 Thiais, France Groupe des Laboratoires de Vitry-Thiais, CECM, B.P. 28, 2-6, rue H. Dunant, F 94320 Thiais, France

Received 8 February 2000; accepted 18 July 2000

Abstract The structure and the electrical and luminescence properties of polycrystalline sintered ZnO pellets containing small amounts of Bi, Mn and Er oxides have been studied. The electric behaviour of the pellets not containing Bi2O3 is ohmic or nearly ohmic, whereas the pellets containing Bi2O3 show a strong increase in their conductivity with the applied voltage. Compared to the Er2O3-free pellets, the pellets containing Er2O3 are highly conducting. The photoluminescence spectrum of all the pellets is the broad classical spectrum of ZnO. The pellets containing Er2O3 are electroluminescent and show mainly the emission spectrum of the Er 31 ion. The electroluminescence intensity increases with the applied voltage and follows a power law, whereas the relative intensity of the different bands of the electroluminescence spectrum of the Er 31 ion is independent of the applied voltage. The ®eld inhomogeneities predicted by the classical model of varistors are unable to account for the observed electroluminescence results. It is concluded that the excitation of the Er 31 ions results either from an indirect process such as a hot electron impact-ionisation of Er2O3 in the boundaries or from a direct impact by hot electrons, the energy of which is controlled by the material. q 2001 Elsevier Science Ltd. All rights reserved.

1. Introduction Zinc oxide varistors are highly non-ohmic resistors. They are made of semiconducting polycrystalline ceramics fabricated by sintering ZnO powders with small quantities of additives, mainly other metal oxides. Since the discovery of the non-ohmicity of polycrystalline sintered ZnO:Bi [1], a considerable amount of theoretical and experimental work has been performed in order to improve the performance of the varistors, mainly their non-ohmicity, as well as to elucidate their electrical conduction mechanism [2±5]. It is now commonly accepted that the non-linearity of the current±voltage curves of the varistors results from the activation of the grain boundaries of the polycrystalline material. In ZnO:Bi sinters, the Bi atoms segregate to the grain boundaries during the sintering. They allow the trapping of excess electrons at the ZnO surface states leading to the formation of back-to-back double Schottky barriers. Polycrystalline ZnO is usually approximated as a stacking of * Corresponding author. Fax: 133-5-4978-1323.

cubic ZnO grains separated by intergranular material so that a varistor corresponds to a succession of grain boundary barriers separated by good conducting ZnO grains. The electrical properties of ZnO grain boundaries have been reviewed [6]. In order to improve the performance of the varistors (nonohmicity, reliability, resistance to the electrical stress, etc.), numerous additives are added to the ZnO powder before sintering. It was found that large sized atoms other than Bi, such as Ba or Sr, or even rare earth (RE) atoms, also act as grain boundary activators, but with performances lower than Bi. It was also found that divalent cations such as Co 21 or Mn 21, which substitute for Zn 21 ions in the semiconducting lattice, are non-linearity improvement agents. But, despite the large number and quantities of additives used to make the varistors, the basic model of a succession of grain boundary barriers separated by good conducting ZnO grains remains unchanged. In a series of papers [7±9] we used this model to account for the electroluminescent properties of RE 31 ions inserted in sintered poly-crystalline ZnO. But, in a more recent paper

0022-3697/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S 0022-369 7(00)00216-X

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Table 1 Chemical composition of the powders, zero-®eld resistance R0, average grain size kll, number of consecutive grains or grain boundaries nG, barrier height under zero bias F B0 from conductivity measurements and theoretical breakdown voltage Vbk of the sintered pellets Designation

Composition (at.%)

R0 (V)

ZnO:Mn(1) ZnO:Mn(2) ZnO:Mn(3) ZnO:Mn(4) ZnO:Mn(5) ZnO:Mn,Er(1) ZnO:Mn,Er(2) ZnO:Mn,Bi ZnO:Mn,Bi,Er

0.01 Mn 0.05 Mn 0.1 Mn 0.5 Mn 1.0 Mn 0.1 Mn 1 0.1 Er 0.1 Mn 1 0.7 Er 0.1 Mn 1 0.6 Bi 0.1 Mn 1 0.6 Bi 1 0.1 Er

5.0 £ 10 3 5.0 £ 10 5 8.0 £ 10 9 7.0 £ 10 9 10 10 10 4 10 4 7.0 £ 10 11 2.0 £ 10 7

dealing with the electroluminescence of polycrystalline ZnO:Tm,Li sintered pellets [10], this model was unable to satisfactorily interpret the experimental results. A mechanism involving the electric conduction along the grain boundaries in Tm-rich regions has been found to agree better with the observations. However, both the chemical composition and the electrical properties of the ZnO:RE and ZnO:Tm,Li electroluminescent ceramics are by far different from those of the varistors. As compared to the Bi-doped sintered polycrystalline ZnO discs, the current±voltage curves of the RE-doped sintered polycrystalline ZnO discs are only weakly nonohmic, and except Pr6O11, the other RE oxides as well as Li, are not commonly used in the manufacture of varistors. For this reason, we have prepared sintered polycrystalline ZnO pellets having a chemical composition close to that of a classical varistor in order to observe the electroluminescence of a RE 31 ion in a material that presents a highly non-ohmic behaviour. The pellets contain one RE element (Er), the usual Bi grain boundaries activator and Mn as a non-ohmicity improvement agent.

kll (mm)

nG

12.2

82

3.6 2.8 26 22

83 280 360 38 45

F B0 (eV)

Vbk (V)

260 0.57 0.56 1.09 0.82

900 1150 120 145

in a Bakelite holder where the electric contacts are achieved by means of copper wires and are slightly abraded in order to obtain a planar rectangular (1 £ 8 mm) face on their edge. The light arising from this abraded edge is observed using a Perkin MPF 44 spectro¯uorimeter where the Bakelite holder is put in the place of the usual quartz cell. The voltage, current and luminescence intensities were recorded simultaneously. The contact capacitances were measured with a HP 4192 A LF impedance analyser operating in the rc parallel circuit mode at frequencies between 10 Hz and 10 MHz. The photoluminescence spectra were recorded from the ¯at surfaces of the sintered pellets using the front surface accessory attached to the spectro¯uorimeter. All the measurements were performed under air at room temperature. The scanning electron micrographs were recorded using a LEO 1530 apparatus at the CECM, CNRS (Vitry, France), on fracture free surfaces of broken pellets.

3. Results and discussion 2. Experimental

3.1. Scanning electron micrography

Mixtures of powdered ZnO, Bi2O3 (Aldrich), MnO2 (Prolabo) and Er2O3 (RhoÃne-Poulenc) were ground carefully in an agate mortar in the presence of a small amount of ethanol. The chemical composition of these mixtures is reported in Table 1. Cylindrical pellets were prepared by pressing 0.5 g of the mixture of oxides at 10 MPa and by sintering the tablets in a muf¯e Vecstar furnace under air for 5 h at 11008C. After sintering, the diameter of the pellets is 11.0 ^ 0.1 mm and their thickness is 1.0 ^ 0.1 mm. For electroluminescence measurements, both the opposite planar faces of the pellets are covered with InGa alloy in order to obtain ohmic contacts. The pellets are then mounted

A scanning electron micrographic analysis has been performed on the samples containing 0.1 at.% Mn and Bi and/or Er oxides. The scanning electron micrographs (Fig. 1) show the usual features already reported widely for such materials [2±6,8±10]. The samples present a compact granular structure with polycrystalline-like irregular grains. The size of the grains is not uniform. The apparent grain diameter ranges from less than 1 mm to more than 40 mm, depending upon the sample. The average grain diameter kll has been determined using the classical method [11] and the classical correction coef®cient, equal to 1.56, between the apparent and the actual grain diameter [12]. The values are

Fig. 1. Scanning electron micrographs of fracture free surfaces of the sintered pellets: (a) ZnO:Mn,Bi,Er; (b) ZnO:Mn,Er(2); (c) ZnO:Mn,Er(1); (d) ZnO:Mn,Bi(2).

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reported in Table 1. They allow a determination of nG, the number of grains, or grains boundaries, in series through the thickness of the pellets. The nG values are reported in Table 1. All the kll values reported in Table 1 are in good agreement with literature data [2±6,8±10,13±15]. The grains of the ZnO:Mn,Er(1) and (2) pellets are the smallest (3.6 and 2.8 mm). The grains of the Bi-doped pellets are the largest (22 and 26 mm). The grain-growth inhibiting effect of the RE oxides, already reported in previous publications, is con®rmed in the present case [8±10,13], but it appears that this effect is overwhelmed by the presence of Bi2O3 which is a known liquid phase sintering aid. The grains of the ZnO:Mn(3) pellet (12.2 mm) are smaller than those of the ZnO:Mn,Bi and ZnO:Mn,Bi,Er pellets, but larger than that of the ZnO:Mn,Er(1) and (2) pellets. It has been reported that ªIn simpli®ed systems containing only Zn, Mn and Co oxides, the grain size is unaffected by Mn and Co valenceº [14] and a grain size equal to 10 mm has been reported for a 0.1 at.% Mn-doped ZnO pellet sintered at 14008C for 1 h [15]. 3.2. Current±voltage characteristics The electric properties of varistors are dominated by the grain boundaries [2±6]. The current±voltage characteristics of the varistors are assumed to result from the presence of back-to-back double Schottky barriers at the grain boundaries. ZnO-based varistors are usually approximated as a succession of good conducting ZnO grains separated by grain boundary barriers. Then, a polarisation V applied to a macroscopic sample is sustained across narrow regions at the grain boundaries, and is divided into nG individual potential drops U, each corresponding to one grain boundary barrier: V ˆ nG U

…1†

where nG is precisely the number of grains or grain boundaries in series through the thickness of the sample, measured by scanning electron micrographic analysis. The current±voltage characteristics of the varistors are usually separated into three regions, pre-breakdown, breakdown and upturn regions corresponding to low, intermediate and high applied voltages, respectively. In the pre-breakdown region, the relationship between the current density J through a grain boundary and the potential U applied to this grain boundary is given by: J ˆ Ap T 2 exp‰2…F B 1 z†=kTŠ…1 2 exp‰2qU=kTŠ†

…2†

p

where A is the Richardson constant, T the temperature, F B the height of the grain boundary potential barrier, z the energy difference between the Fermi level and the conduction band outside the depletion layers, q the charge of the electron, and k the Boltzmann constant. For the lowest applied voltages, when qU p kT; Eq. (2) reduces to: J ˆ …A p TqU=k† exp‰2…F B0 1 z†=kTŠ

…3†

Fig. 2. Current±voltage characteristics of the pellets: j , ZnO:Mn(1); B, ZnO:Mn(2); £ , ZnO:Mn(3); A, ZnO:Mn(4); 1, ZnO:Mn(5); P, ZnO:Mn,Er(1); O, ZnO:Mn,Er(2); W, ZnO:Mn,Bi; V, ZnO:Mn,Bi,Er.

where F B0 is the height of the potential barrier under zero bias. For ZnO:Bi composites and for varistors, the non-ohmicity of the I±V curves is explained by the voltage dependence of the barrier. F B decreases rapidly with the polarisation U until the breakdown occurs when U reaches values corresponding to the ZnO band-gap energy. A set of theoretical breakdown voltages Vbk, corresponding to individual polarisations equal to the ZnO band-gap energy (3.2 eV), can be calculated. They are reported in Table 1. The current±voltage characteristics (I±V curves) of a series of sintered pellets prepared from ZnO powder containing different amounts of Mn, Er and Bi oxides are presented in Fig. 2. The electric behaviour of the Bi-free pellets is ohmic or nearly ohmic, whereas the electric behaviour of the pellets containing Bi is strongly non-ohmic. The pellets which contain more than 0.05 at.% Mn show an ohmic behaviour up to 300 V. Clearly, the strong non-ohmicity is related to the presence of Bi. All the pellets can be characterised by their zero-®eld resistance R0 reported in Table 1. The resistance of the pellets containing both Mn and Bi is the highest …7:0 £ 10 11 V†; while the resistance of the pellets which contain the lowest Mn amount (0.01 at.%), and the resistance of the pellets which contain both Er and Mn are the lowest (5:0 £ 10 3 and 10 4 V, respectively). The zero-®eld resistance of the pellets that contain only Mn atoms increases with the Mn content up to a critical concentration, close to 0.1 at.% (Fig. 3). Above this concentration, the pellets become highly resistive and their zero®eld resistance remains constant close to 10 10 V. It is known from numerous studies on varistors that the Mn atoms are dispersed inside the ZnO grains. Mn 21 ions substitute for Zn 21 ions in the semiconducting lattice [2±5]. The Zn12xMnxO phase diagram shows complete solubility of Mn in ZnO up to x ˆ 20% [16]. However, the conduction mechanism inside these pellets is unknown. The resistivity

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of ZnO doped with a small amount of Mn (ca. to 0.1%) depends strongly upon the sintering conditions. For a low sintering temperature (9008C), ªMn-doped ZnO samples have such high resistance that they may be considered insulatorsº [17]. For a high sintering temperature (14008C), the conductivity of Mn-doped ZnO (1.15 V 21 cm 21) is higher than that of pure ZnO (0.72 V 21 cm 21) [15]. In the present case, the high resistance of the Mn 21-doped ZnO pellets above 0.1 at.% lies between the in®nite value of an insulator and the low value of a sample sintered at 14008C. It is not the goal of the present paper to study the conduction mechanism of sintered polycrystalline Mn-doped ZnO. However, the nearly ohmic behaviour in the 0±300 V range of the pellets containing more than 0.05 at.% Mn, observed in this study and already reported for pellets with a higher Mn content [14], and the absence of breakdown at a voltage lower than 300 V, seem to indicate an absence of activated grain boundary barriers. The grains of the ZnO:Mn(3) pellet (12.2 mm) are not small enough to locate an hypothetical breakdown at a voltage higher than 300 V. In contrast with Bi, Mn is not considered as a grain boundary activator but rather as a non-linearity enhancement agent [4]. The low concentration of Mn atoms and their dispersion inside the ZnO grains according to the Zn12xMnxO phase diagram does not allows a segregation of Mn to the boundaries between the grains. Then, the high resistivity of the ZnO:Mn pellets above 0.1 at.% results likely from a high bulk resistivity. But, the possibility of an electric conduction along the boundaries at the surface of the grains does not allow an accurate determination of the intrinsic resistivity of the bulk and, therefore only a minimum value (10 11 V cm) can be extrapolated from the data of Fig. 2 for the ZnO:Mn pellets containing more than 0.1 at.% Mn. Such a mechanism of parallel conduction along the boundaries has already been proposed to explain the leakage current in varistors without the knowledge of the grain resistance [18,19]. Compared to the ZnO:Mn(3) pellet which contains the same amount of Mn (0.1 at.%), the ZnO:Mn,Er(1) and ZnO:Mn,Er(2) pellets show a dramatic lowering of their resistance owing to the presence of Er2O3. This is surprising since, in contrast with Mn, the RE atoms are considered as ZnO grain boundary activators [4]. Four hypotheses can be put forward to explain this result depending upon the bulk resistivity of Mn-doped ZnO and upon the effects of the Er 31 ions. (i) In the case where the bulk resistivity of Mn-doped ZnO is high, some Er 31 ions are dispersed inside the ZnO grains as a result of the sintering. Their presence counteracts that of the Mn 21 ions. The ZnO grains containing both Er and Mn become highly conductive. The remaining Er atoms, located in the grain boundaries between the grains, act as grain boundary activators and make the potential barriers. The classical picture of the varistors represented by Eqs. (1) and (2) is valid and the total applied voltage is sustained in the depletion regions at

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the grain±grain contact. The ®eld is intense in the space charge regions and zero elsewhere. (ii) In the case where the bulk resistivity of Mn-doped ZnO is high, some Er 31 ions are dispersed inside the ZnO grains as a result of the sintering, but their presence counteracts only partially that of the Mn 21 ions. The ZnO grains containing both Mn and Er are moderately conducting and, in order to obtain a low resistance, there is no activation of the grain boundaries. The classical picture of the varistors does not hold and the pellets can be considered as homogeneous resistors. The total applied voltage is sustained by the grains and the current is controlled by the resistivity of the bulk. The ®eld inside the pellets is uniform. The classical model of the varistors does not hold. (iii) Always in the case where the bulk resistivity of Mndoped ZnO is high, and even if some Er 31 ions are dispersed inside the ZnO grains, the grain resistance remains high because of the presence of Mn. The minimum value of the resistivity of the bulk can be approximated by that of the pellets that contain the same amount of Mn. The pellets correspond to a stacking of insulating grains separated by a network of good conducting grain boundaries. The classical model of the varistors does not hold as for the previous case. (iv) In the case where the bulk resistivity of Mn-doped ZnO is low and where the high resistivity of the Mn-doped ZnO pellets results from activated grain boundary barriers, the presence of Er 31 ions in the boundaries lowers the grain boundary barriers. As in case (i), the total applied voltage is sustained in the depletion regions at the grain±grain contact and the classical picture of the varistors represented by Eqs. (1) and (2) is valid. The ®eld is intense in the space charge regions and zero elsewhere. In addition, some Er 31 ions can be dispersed inside the ZnO grains as a result of the sintering. This case leads to a model identical to that in case (i). In cases (ii) and (iii), a direct application of Eqs. (1)±(3) to the ZnO:Mn,Er(1) and ZnO:Mn,Er(2) pellets must be seriously questioned. It is known from numerous studies on varistors that the RE (and Bi) atoms remain located in the boundaries of the polycrystalline matrix [2±5]. Also, it has been stated in the case of binary chalcogenides that the incorporated RE does not exceed 0.02 at.% whatever the growth technique used [20]. The trivalent RE 31 ions (and the Bi 31 ions) do not substitute for Zn 21 ions into the semiconducting lattice due to their charge and their size. This favours cases (iii) and (iv) compared to cases (i) and (ii). It is known also that some RE atoms such as Pr or La or even Sm are used in the manufacture of varistors [2,4,5] where they act as grain boundary activators. This does not favour case (iv) where they should act as grain boundary deactivators in order to lower the barrier height compared to ZnO:Mn. The zero-®eld resistance of the ZnO:Mn,Bi pellet is approximately 100 times higher, and that of the

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Fig. 3. Dependence of the zero-®eld resistance R0 of the ZnO:Mn pellets upon the Mn content.

ZnO:Mn,Bi,Er pellet 100 times lower than the one of the ZnO:Mn(3) pellet, the three pellets containing the same amount of Mn. Then, the grain resistance can be neglected with regard to the barrier height for the ZnO:Mn,Bi pellet. The comparison of the zero-®eld resistance of the ZnO:Mn,Bi pellet with the one of the zero-®eld resistance of the ZnO:Mn,Bi,Er pellet shows that the presence of Er2O3 also induces a strong decrease of R0. Then, despite the high non-linearity of its I±V curve, a direct application of Eqs. (1)±(3) to the ZnO:Mn,Bi,Er pellet can also be questioned. However within the frame of cases (i) or (iv) formulated above, the F B0 values can be calculated from the R0 and nG values in Table 1 using Eq. (3) and neglecting z because of its low value (0.067 eV) [6]. The results are reported in Table 1 for the samples containing Bi and/or Er oxides. Other attempts to determine the barrier heights in sintered polycrystalline ZnO, for instance from the activation energy of the leakage current or from capacitance±voltage measurements, usually fail. The activation energy of the leakage current contains both the barrier height and its temperature dependence [21], and it is known for a long time that the voltage dependence of the contact capacitance can lead to unrealistic values [22] (for instance F B0 < 6 eV was reported for polycrystalline sintered ZnO:Mn,Co,Sb,Cr,Bi [23]). As expected from the I±V curves, the highest F B0 value is obtained for the ZnO:Mn,Bi pellet and the lowest values for the ZnO:Mn,Er(1) and ZnO:Mn,Er(2) pellets. The I±V curves of Fig. 2 show that a breakdown occurs for both the ZnO:Mn,Bi and the ZnO:Mn,Bi,Er pellets at voltages between 100 and 200 V, in reasonable agreement with the theoretical values of Table 1. The large number of consecutive grains or grain boundaries in the ZnO:Mn,Er(1) and ZnO:Mn,Er(2) pellets excludes to observe such a breakdown in these pellets for the relatively low applied voltages used here. The high currents reported in Fig. 1 for these pellets correspond approximately to individual polarisations

Fig. 4. Equivalent circuits representing the pellets. RG is the grain resistance, CGB and RGB are the capacitance and the resistance of the grain boundary and RP represents the resistance corresponding to the current along the grain boundary parallel to the ®eld.

close to 150 mV by grain boundary. They cannot be taken as breakdown currents that need individual polarisations corresponding to the ZnO band-gap energy. They are the consequence of an intrinsic high conductivity of the material (for instance, enhanced grain boundary conduction and/or low barrier heights and highly conducting grains). The degree of non-ohmic property of the I±V curves of the varistors is usually expressed by a non-ohmic exponent a I de®ned by:

a I ˆ d…ln I†=d…ln V†

…4†

a I increases with the applied voltage. Its value starts from 1 when the behaviour of the pellets is ohmic and reaches 16 and 10 under the highest applied voltages corresponding to currents close to 5 and 10 24 mA, for ZnO:Mn,Bi,Er and ZnO:Mn,Bi pellets, respectively. 3.3. Capacitance measurements Capacitance measurements have been performed on the ZnO:Mn,Bi pellet for comparison with previous results obtained on varistors and on both the ZnO:Mn,Er(1) and (2) pellets.

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The presence of Schottky barriers in polycrystalline ZnO is usually inferred from capacitance±voltage measurements. In order to analyse the capacitance measurements, an electrical circuit, equivalent to the succession of grains and grain boundaries, must be proposed. Three circuits are presented in Fig. 4. The most complicated (4a) takes into account the grain resistance RG, the capacitance CGB and resistance RGB of the grain boundary and a parallel resistance RP corresponding to the current along the grain boundary. In this circuit, an important current ¯ow along the grain boundaries (case (iii)) would imply a low value of RP compared to RG and RGB. The circuit (4b) corresponds to an in®nite value of RP (no current along the grain boundaries). The circuit (4c) neglects the grain resistance compared to the grain boundary resistance and capacitance. This last circuit is the most widely used. It corresponds to the classical picture of a varistor: a succession of good conducting ZnO grains separated by intergranular Schottky type barriers. But, it must be pointed out that, in this case, an electric conduction along the grain boundaries parallel to the ®eld cannot be separated from the conduction across the boundaries. For each equivalent circuit of Fig. 4, a set of two equations relating the microscopic parameters (RG, RGB, CGB and/ or RP) to the measured resistance r and capacitance c at a given test frequency n ˆ v=2p can be readily obtained. For the equivalent circuit (4c): r ˆ nG RGB ;

…5a†

c ˆ CGB =nG :

…5b†

For the equivalent circuit (4b): r=…1 1 r 2 c2 v2 † ˆ nG ‰RGB 1 RG …1 1 …RGB CGB v†2 †Š=‰1 1 …RGB CGB v†2 Š;

…6a†

r 2 c=…1 1 r 2 c2 v2 † ˆ nGB ‰R2GB CGB Š=‰1 1 …RGB CGB v†2 Š: …6b† For the equivalent circuit (4a), RP is neglected compared to RG 1 RGB in order to take into account the preferential conduction along the grain boundaries. Then, the following relations are obtained: r=…1 1 r 2 c2 v2 † ˆ nG RP ; 2

2 2

2

r c=…1 1 r c v † ˆ

nG ‰R2P R2GB CGB Š=‰…RG 1 …RG RGB CGB v†2 Š:

…7a† 1 RGB †

2

…7b†

From theoretical calculations [6,24], the grain boundary capacitance CGB varies with the test frequency. CGB decreases with the reciprocal of v 2, but the exact dependence of CGB upon v 2 is not simple because the distribution of grain boundary states can affect the shape of the CGB ± v curve. Then, in addition to the test frequency dependence of CGB, both circuits (4a) and (4b) lead to frequency dependent r and c values, even if the other microscoscopic parameters RGB, RG and/or RP do not change with this frequency. In the

571

case of circuit (4c), a variation of r and/or c with the test frequency can only arise from a dependence of RGB and/or CGB with this frequency. The grain boundary capacitance varies also with the applied voltage and with the energy distribution of the grain boundary trap states [24]. Typically, the variation of the grain boundary capacitance with the voltage follows a bell shaped curve whose pro®le is a function of both the density of the trap states and the test frequency. The grain boundary capacitance increases with the applied voltage up to a maximum value and then decreases. Only the capacitance measured at high test frequency decreases continuously when the applied voltage increases. For ZnO:Bi and ZnO:RE composites, the applied voltage dependence of the grain boundary capacitance is often approximated as [23,25]: …1=cGB 2 1=2cGB;…Uˆ0† †2 ˆ 2…F B0 1 qU†=q2 1Nd

…8†

where cGB and cGB,(Uˆ0) are the capacitance per unit area of a grain boundary biased with U and zero volts, respectively, 1 is the dielectric constant of the ZnO grains …1 ˆ 8:5† and Nd the donor concentration. Nd is given by the slope of the c±V plot according to Eq. (8), whereas the abscissa axis intercept leads often to unreallistic F B0 values. 3.3.1. The ZnO:Mn,Bi pellet The capacitance c and the resistance r of this pellet depend upon the test frequency and even at low frequency …n ˆ 10 Hz†; r is far from its dc value (Fig. 5). The frequency dependence of the capacitance is weak while that of the resistance is strong but far from a v 22 law. A similar result has been reported for a ZnO-based commercial varistor [26]. Clearly, Eqs. (5a) and (5b) are unable to account for the observed frequency dependence of r and c unless RGB is strongly frequency dependent. For the whole test frequency range r 2 c2 v2 is large compared to 1. Assuming either …RGB CGB v†2 q 1 or …RGB CGB v†2 p 1; Eqs. (6a) and (6b) are readily reduced to: c ˆ CGB =nG ;

…9a†

2 r ˆ nG RGB =…1 1 RG RGB CGB v2 †

ˆ nG RGB =…1 1 n2G RG RGB c2 v2 †;

…9b†

or to: c ˆ 1=nG R2GB CGB v2 ;

…10a†

r ˆ nG R4GB CGB v2 =…RG 1 RGB † ˆ 1=nG …RG 1 RGB †c2 v2 ; …10b† respectively. A frequency dependence of r is thus possible even when RG and RGB are constant. However, correlations between the experimental and the predicted r values using Eqs. (9b) or (10b) are bad because the frequency dependence of r is

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Fig. 5. Frequency dependence of the resistance r (W) and capacitance c (X) of the ZnO:Mn,Bi pellet in the rc parallel circuit mode.

closer to v 21 than to v 22. A good correlation would imply a frequency dependence of RGB and/or RG. Surprisingly, no voltage dependence of the capacitance of this pellet has been found for test frequencies lower than 10 4 Hz. However, at 10 5 Hz the capacitance of the pellet decreases weakly but signi®cantly when the applied voltage increases. At 10 5 Hz, the capacitance of the pellet under zero bias (c(Uˆ0)) is equal to 9 £ 10211 F; its resistance r is equal to 5 £ 104 V the product cv being equal to 5:7 £ 10 25 V 21 : The decrease of the capacitance of the pellet with the applied voltage seems to indicate that Eq. (9a) does apply. This leads to CGB ˆ 3:4 £ 1029 F and RGB q 470 V in order to satisfy …R GB CGB v†2 q 1; but both RG and RGB remain unknown since Eq. (9b) cannot be solved. The analysis of the dependence of c upon V according to Eq. (8) leads to Nd ˆ 1:9 £ 1015 cm23 and to the unrealistic value F B0 ˆ 2:4 eV: 3.3.2. The two ZnO:Mn,Er(1) and (2) pellets Since the results obtained with these pellets are similar, only the ZnO:Mn,Er(2) pellet will be discussed in detail. The frequency dependence of both the resistance r and the capacitance c of this pellet under an applied dc voltage equal to 0.0 V are reported in Fig. 6. The capacitance decreases when the frequency increases but at low frequency, the capacitance depends strongly upon the level of the oscillating test signal and it seems likely that its value, extrapolated at zero level test signal, is constant, close to 0.6 nF. The voltage dependence of the capacitance is reported in Fig. 7. The rms value of the oscillating test signal is added to the continuous applied voltage, on the abscissa axis scale, in

order to take into account its effect on the measure of c. At low test frequencies (,10 4 Hz) c increases with the applied voltage, and more for the low frequencies and the low applied voltages, whereas at high frequencies (.10 4 Hz) c decreases weakly or remains constant when the applied voltage increases. The number nG of consecutive grain boundaries found in the ZnO:Mr,Er(2) pellet is 360. Thus, the upper limit of the voltage U applied to one grain boundary, corresponding to a V ˆ 30 V total bias, is close to 100 mV. For such a low applied voltage and at a low test frequency, theoretical calculations for a grain boundary with a monoenergetic density of trap states predict a frequency independent grain boundary capacitance and a strong increase of its value with the applied voltage [24]. Then, the observed variation of the capacitance c with both the test frequency and the applied voltage agrees qualitatively with the theoretical predictions and indicates that the measured capacitance c is proportional to the grain boundary capacitance CGB. Eqs. (5a) and (5b) can apply; the grain boundary capacitance per unit area cGB under zero bias, calculated from the data of Fig. 7 using Eq. (5b), for a test frequency equal to 10 Hz, is close to 0.2 mF cm 22 whereas the theoretical calculations with parameters appropriate to grain boundaries in ZnO varistors (1 ˆ 8:5; Nd ˆ 3 £ 1017 cm23 and grain boundary trap states located 0.6 V below the conduction band) predict a value close to 0.1 mF cm 22 [24]. The theoretical calculations for a monoenergetic density of grain-boundary trap states predict also a grain boundary barrier F B0 close to 0.5 eV, not far from the values reported in Table 1. This barrier decreases weakly when the

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573

Fig. 6. Frequency dependence of the resistance r (K) and capacitance c (O) of the ZnO:Mn,Er(2) pellet in the rc parallel circuit mode. Test oscillating signal level: 1 V (Ð); 0.5 V (Ð Ð); 0.1 V (± ± ±); 0.05 V(- - -).

individual bias U increases from 0 to 2 V. Such U values correspond to a total applied voltage between 0 and 550 or 700 V for the ZnO:Mn,Er(1) or (2) pellets, respectively. Then, in these pellets the barrier height remains quite constant for moderate applied voltage.

However, the other circuits of Fig. 4 cannot be excluded. r 2c 2v 2 is negligible compared to 1 for test frequencies lower than 10 4 Hz. Eqs. (6a)±(7b) lead to relations similar to Eqs. (5a) and (5b), provided that …R GB CGB v†2 p 1 in the circuit (4b) and …RGB CGB v†2 p 1 or …RG CGB v†2 p 1 in the circuit

Fig. 7. Voltage dependence of the capacitance of the ZnO:Mn,Er(2) pellet at different test frequencies.

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Fig. 8. Photoluminescence spectrum of the ZnO:Mn,Bi,Er pellet under ZnO band-to-band excitation at 365 nm.

(4a). The following relations are obtained: r ˆ nG RP

…11a†

for the circuit (4a), or r ˆ nG ‰RGB 1 RG Š

…11b†

for the circuit (4b), and c ˆ CGB ‰1=nG Š‰RGB =…RGB 1 RG †Š2

…11c†

for both circuits. In both cases the measured capacitance c is proportional to the grain boundary capacitance CGB. In the case of circuit (4b), the product rc is: rc ˆ CGB …RGB 1 RG †;

…12†

Fig. 9. Electroluminescence spectrum of the ZnO:Mn,Er(2) pellet (lower spectrum) recorded under an applied polarisation of 35 V corresponding to a current of 6 mA and electroluminescence spectrum of the ZnO:MnBi,Er pellet (upper spectrum) recorded under an applied polarisation of 130 V corresponding to a current of 1.2 mA.

broad pattern was already reported for polycrystalline sintered ZnO:Bi [27]. The band-to-band photochemical excitation of ZnO promotes electrons from the valence band to the conduction band leaving holes in the valence band. The recombinations occur between electrons from either the conduction band [28] or shallow donor levels [29] and trapped holes on deep levels, close to the surface of the ZnO grains [28]. 3.5. Electroluminescence spectra

and the condition r 2 c2 v2 p 1 implies …RGB CGB v†2 p 1 which justi®es the approximation leading to Eq. (11a). For a test frequency equal to 10 5 Hz, the capacitance of the ZnO:Mn,Er(1) and (2) pellets decreases continuously with the applied voltage. An analysis of this decay following Eq. (8) leads to F B0 ˆ 0:31 and 0.06 eV and to Nd ˆ 1:4 £ 1016 and 4 £ 1016 cm23 for the ZnO:Mn,Er(1) and (2) pellets, respectively. At this point, the results obtained from capacitance measurements are disappointing. They seem to indicate the presence of Schottky barriers in the ZnO:Mn,Er pellets although the equivalent circuits and consequently the microscopic parameters (RG, RGB, CGB and/or RP) cannot be determined. However, among the three hypotheses put forward in the current±voltage characteristics section, the second one (a grain core conductivity controlled conduction) can be disregarded since it corresponds to unactivated grain boundaries.

The pellets that contain Er2O3 are electroluminescent (Fig. 9). The electroluminescence spectra of both ZnO:Mn,Er(1) and ZnO:Mn,Er(2) pellets are identical. They show only the transitions between the 4f levels of the Er 31 ion

3.4. Photoluminescence spectra and mechanism

Fig. 10. Dependence of the Er 31 electroluminescence intensity upon voltage for the: ZnO:Mn,Er(1), P; ZnO:Mn,Er(2), O and K; and ZnO:Mn,Bi,Er, V and S pellets. Open symbols: luminescence from the 4S3/2 level at 560 nm; ®lled symbols: luminescence from the 4F9/2 level at 660 nm.

All the pellets are photoluminescent with identical photoluminescence spectra (Fig. 8) constituted of a broad pattern centred around 550 nm and characteristic of ZnO. Such a

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575

Fig. 11. Energy band diagram of a grain boundary submitted to an applied polarisation U, showing the electron impact excitation of an Er 31 ion in the depletion layer of the positively biased grain.

(2 H11=2 ! 4 I15=2 at 535 nm, 4 S3=2 ! 4 I15=2 at 560 nm and 4 F9=2 ! 4 I15=2 at 670 nm), whereas the spectrum of the Zn:Mn,Bi,Er pellet presents an additional broad pattern between 550 and 850 nm, which can be attributed to ZnO itself. The voltage dependence of the luminescence intensity Bn corresponding to the n different transitions of the Er 31 ion is reported in Fig. 10 (n ˆ 4 S3=2 ! 4 I15=2 at 560 nm or 4 F9=2 ! 4 I15=2 at 670 nm). The Bn ±V curves are not linear and for all the pellets, the degree of non-linearity can be expressed by a non-linear coef®cient a B similar to a I of Eq. (3):

aB ˆ d…ln B†=d…ln V†:

…13†

Contrary to a I, a B does not depend upon the applied voltage. Its values lie close to 6 for all the studied pellets and for all the observed transitions of the Er 31 ion. The comparison of Fig. 2 with Fig. 10, and of a I with a B, shows clearly that the non-linearity of the B±V curves is not correlated with the non-linearity of the I±V curves of the electroluminescent pellets. Furthermore, the electroluminescence of the Er 31 ion is observed for applied voltages well below the theoretical breakdown voltage Vbk of Table 1, specially for the ZnO:Mn,Er(1) and (2) pellets. 3.6. Er 31 electroluminescence mechanism The difference between the electro- and photoluminescence spectra excludes an energy transfer from the semiconductor to the Er 31 ions. Then, the Er 31 electroluminescence must be a consequence of an excitation process that is not related to the presence of holes in the valence band. Conversely, the absence of the characteristic ZnO luminescence in the electroluminescence spectra of both ZnO:Mn,Er(1) and (2) pellets indicates that no hole is produced in the valence band of ZnO for the voltages used to record the spectra. This

is another indication for the absence of breakdown currents in these pellets. The excitation of the Er 31 ions in ZnS:Er 31 electroluminescent thin ®lms results from a direct impact-excitation (i.e. direct exchange of energy between the hot carriers and the 4f electrons) by hot electrons accelerated in the conduction band of ZnS [30,31]. For (Zn,Cd)S:Er sintered phosphors, the mechanism changes gradually from the direct ®eld-ionisation of Er 31 ions to the acceleration±collision as the Er concentration increases [32]. Other excitation processes have also been proposed for ZnS:RE systems [33]. For instance (i) an impact-excitation (or ionisation) which involves impurity states outside the 4f shell, with subsequent energy transfer to this shell, or (ii) an impact-ionisation of the host lattice followed by the capture of the free carriers into impurity states. This last process is excluded in the present case owing to the absence of the ZnO pattern in the electroluminescence spectra. All these excitation mechanisms are related to the presence of intense electric ®elds. In our case, all the pellets are 1 mm thick and the Er 31 luminescence is observed for 10±150 V applied voltages corresponding to average ®elds between 10 2 and 1:5 £ 103 V cm21 : Clearly, in ZnO these ®elds are too low to enable the presence of hot electrons which needs electric ®elds higher than 5:0 £ 105 V cm21 [6]. This high ®eld condition allows to disregard the second hypothesis (a grain core conductivity controlled conduction) formulated in Section 3.2 for the ZnO:Mn,Er(1) and (2) pellets. A grain core conductivity controlled conduction would lead to an homogeneous constant ®eld inside the pellets with a value close to 300 V cm 21 when the total applied voltage is close to 30 V. Then, in addition to the capacitance measurements, the Er 31 electroluminescence itself allows to disregard this hypothesis. However, the ®eld is inhomogeneous in ZnO varistors.

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The applied voltage is entirely sustained across narrow regions, in the depletion layers of the positively biased grains, adjacent to the boundaries, where the ®eld is intense and allows the presence of hot electrons able to impactexcite the luminescent centres. The problem of hot electrons in the depletion layers of the positively biased grains at the ZnO grain boundaries has been discussed in detail in Ref. [6]. Roughly, the presence of hot electrons is restricted to Ê ) when they are the narrow depletion layers ( < 1000 A submitted to strong individual applied voltages ( < 3 V). During the breakdown of varistors, electrons generated at the boundaries are accelerated in the conduction band of the depletion region of the positively biased grains where they impact-ionise ZnO, leaving holes in the valence band. These holes move back to the boundary where, either they recombine with the conduction band electrons giving rise to the characteristic ZnO band-to-band luminescence, or they detrap the trapped electrons resulting in an enhanced decrease of the barrier [34]. Fig. 11, taken from Ref. [6] shows the band diagram of a grain boundary submitted to a polarisation U and its application to the excitation of the Er 31 ions. This model corresponds strictly to the ®rst (case (i)) or to the fourth (case (iv)) hypothesis put forward in Section 3.2. In any case, the direct application of this model to the electroluminescence of the Er 31 ions in the ZnO:Mn,Er(1), ZnO:Mn,Er(2) and ZnO:Mn,Bi,Er pellets needs to ful®l several conditions: (i) Some Er 31 ions do incorporate inside the ZnO grains during the sintering. However, the charge and the size of the Er 31 ions as well as the melting point of Er2O3 (.23008C), for a sintering temperature of 11008C do not favour this hypothesis. Furthermore, numerous analyses on RE-doped ZnO (X-rays, EDS) conclude to the segregation of the RE to the boundaries [2±5]. (ii) The ®eld in the depletion region of the positively biased grain must be intense. This ®eld depends upon the width of the depletion region that is a function of both the donor density Nd and the sum of the barrier height and the polarisation applied to one boundary F B 1 qU: F B 1 qU can be calculated from the current±voltage curves. (iii) The energy gained by the hot electrons in the depletion region of the positively biased grains must be high enough to impact-excite the Er 31 ion into its 2H11/2 and 4 S3/2 emitting levels. This energy gained by the hot electrons depends directly upon F B 1 qU but remains lower than F B 1 qU owing to a strong cooling by emission of longitudinal optical phonons [6]. The last two conditions imply a low grain resistivity. RG must be negligible compared to the equivalent resistance of the grain boundary barrier RGB. For a given total applied voltage, an increase of the grain resistivity induces a decrease of the individual polarisation U and lowers F B 1 qU: The application of Eqs. (1) and (2) to the I±V curves of

Fig. 2, using the average grain diameter reported in Table 1, leads to 0:6 , F B 1 qU , 0:7 eV for the observation of the electroluminescence of the Er 31 ion in ZnO:Mn,Er(1) and (2) pellets. Clearly, such value of F B 1 qU is too low to enable both the presence of hot electrons and a direct impact-excitation of the Er 31 ion to its 2H11/2, 4S3/2 or 2F9/2 levels, the energies of which are 2.3, 2.2 and 1.85 eV, respectively. The excitation of the Er 31 ion to its 2H11/2, 4 S3/2 or 2F9/2 levels needs hot electrons possessing an energy at least equal to the energy of the emitting levels [30,31]. This energy, close to 2 eV, cannot be reached with a polarisation close to 0.7 eV even when neglecting the strong cooling of the hot electrons which does occur in ZnO [6]. Furthermore, following the model of Fig. 11, the luminescence intensity arising from the Er 31 ions depends directly upon the number of hot electrons able to impact-excite the Er 31 ion in its luminescent levels. This number depends exponentially upon the average energy of the hot electrons, which is directly related to, but lower than F B 1 qU: Then, the observed increase of the luminescence intensity by almost three orders of magnitude (Fig. 10) indicates an increase of U close to 7 V. This corresponds to an unrealistic total applied voltage V higher than 2000 V. The grain boundary model of Fig. 11 fails to give an accurate explanation for the electroluminescence of the Er 31 ions. This electroluminescence cannot arise from an impact excitation of Er 31 ions incorporated inside the ZnO grains in the depletion layer close to the boundaries. Other excitation mechanisms such as a ®eld ionisation of Er2O3 particles followed by the capture of an electron leading to Er 31 excited states depend also upon intense electric ®elds and strong polarisations. Their occurrence inside the depletion layers of the ZnO grains can be ruled out on the basis of the same considerations than for the impact excitation mechanism. In any case, the excitation of the Er 31 ion in its visible emitting levels needs intense ®elds and strong polarisations, which are not present in the depletion layers of the positively biased grains. Among the three hypotheses formulated in the current± voltage characteristics section to explain the high conductivity of the ZnO:Mn,Er(1) and (2) pellets compared to the ZnO:Mn(3) pellet, three of them (cases (i), (ii) and (iv)) are unable to account for the electroluminescence of the Er 31 ions. The energy considerations exclude the ®rst and fourth hypotheses and the ®eld conditions exclude the second hypothesis. So, the electroluminescence of the Er 31 ions in the ZnO:Mn,Er pellets can be taken as an indication for another conduction mechanism occurring inside the pellets. This mechanism is accompanied by ®eld inhomogeneities whatever the value of RG. The electroluminescence of the Er 31 ion shows that an intense electric ®eld and a strong polarisation occur simultaneously in Er 31 rich regions. In order to account for the electroluminescence of the Er 31 ion, the classical ªgrain boundary barrierº model does locate Er 31 ions in regions where the intense ®eld allows the presence of hot electrons.

J.C. Ronfard-Haret et al. / Journal of Physics and Chemistry of Solids 62 (2001) 565±578 31

In that case, the electroluminescence of the Er ions is taken as an indication for their presence inside the ZnO grains, in the depletion layers, despite their charge, their size and the high melting point of the sesquioxide [8,9]. But, in polycrystalline sintered ZnO containing rare earth ions, the rare earth ions are mainly located in the boundary between the grains and they act as grain growth inhibitors. Conversely, since the location of Er 31 ions in the depletion layers inside the ZnO grains (leading to the ªclassical grain boundary barrierº model) fails to account for the electroluminescent properties of the Er 31 ion, it seems more likely to locate intense ®elds, strong polarisations, and consequently current ¯ows, inside the boundaries where the Er 31 ion concentration is known to be high. This leads to the third case put forward in Section 3.2. The electroluminescence of the Er 31 ion would be an indication for an electric conduction along the boundaries. In ZnO-based varistors, the microstructures at the grain boundaries are classi®ed into three types depending upon their thickness and their chemical composition [4,6]. A Birich phase is present between the ZnO grains in type I or II structures where the intergranular layers are thick whereas ªtype III structure has almost no intergranular layer except for excess amount of Bi, Co, O ionsº [4]. The grain boundary barriers, consecutive to the presence of trapped electrons at the surface of the ZnO grains and responsible for the electrical properties of ZnO varistors, correspond to type III structures. Schwing and Hoffmann have studied the electric behaviour of an individual grain boundary in a model varistor [35]. They have shown that a 5 mm thick Bi2O3based intergranular material layer, present between two ZnO grains, could sustain an intense electric ®eld corresponding to a strong voltage drop, at its junction with a ZnO grain. These results indicate that both material and ®eld inhomogeneities can occur inside the intergranular material but in the absence of additional experiments, any attempt to propose a complete mechanism for the generation of hot electrons would be highly speculative. For the ZnO:Mn,Bi,Er pellet, the electroluminescence of the Er 31 ion is observed for applied voltages corresponding to F B 1 qU between 1.7 and 3.5 eV, not far from the energy of the emitting levels of the Er 31 ion (1.85, 2.2 and 2.3 eV, respectively). Then, the model of Fig. 11 could account for the electroluminescence of the Er 31 ion in the ZnO:Mn,Bi,Er sinters, but cannot exclude an excitation of Er 31 ions inside the boundaries at the surface of the ZnO grains. Nevertheless, the Er 31 electroluminescence is observed for an applied voltage as low as 50 V, lower than the breakdown voltage close to 150 V. This low voltage corresponds to F B 1 qU ˆ 1:7 eV: It indicates that the presence of intense electric ®elds and strong polarisations is not restricted to the breakdown region. For all the pellets containing Er 31 ions, Fig. 10 shows that the intensity of all the transitions arising from the Er 31 ion follows the same power law. In other words, the intensity ratio r between two transitions (e.g. r560=660 ˆ B‰4 S3=2

4

4

577

4

! I15=2 Š=B‰ F9=2 ! I15=2 Š) does not depend upon the applied voltage. In ZnS:CuCl,Er thin ®lms, where a direct impact of the 4f electrons occurs, the energy distribution function of the hot electrons has been shown to determine the intensity of the electroluminescence emissions corresponding to the different Er 31 transitions leading to voltage dependent ratios r [30,31]. In the present case, for both ZnO:Mn,Bi,Er and ZnO:Mn,Er pellets, the lack of voltage dependence of r can indicate either that the characteristic energy of the hot electrons remains constant whatever the applied voltage or that the luminescence of the Er 31 ions is not consecutive to a direct electron-impact of the 4f electrons. Since the photoluminescence and electroluminescence spectra are different, an impact-ionisation of the host lattice followed by an energy transfer to the 4f shell is excluded. 3.7. ZnO electroluminescence mechanism The broad pattern attributed to ZnO in the electroluminescence spectrum of the ZnO:Mn,Bi,Er pellet is red-shifted as compared to the photoluminescence spectrum. Its maximum lies around 640 nm, while the wavelength of the maximum of the photoluminescence spectra lies around 550 nm. Such a bathochromic shift implies that the two emissions involve different excitation mechanisms. Since the ZnO photoluminescence is related to the presence of holes in the valence band, the electroluminescence cannot follow a process that involves the presence of holes in the valence band. The excitation is rather related to a direct process (®eld or electron-impact ionisation), which can only correspond to the promotion of an electron trapped on a deep level into the conduction band leaving a hole in this deep level. The broadness of the photoluminescence spectrum indicates that the energy of the deep levels is widely distributed. The transitions of high energy, at the shortest wavelengths, correspond to deep levels located at low energies and the transitions of low energy, at the longest wavelengths, correspond to deep levels located at high energies. The excitation of the ZnO electroluminescence corresponds to the ionisation of a deep level. It depends upon both the characteristic energy of the electrical excitation and the ionisation energy of the deep levels (energy difference between the deep level and the conduction band). Then, the deep levels which can be electrically excited and which luminescence are those whose energy is higher than the difference between the ZnO band-gap energy and the electrical excitation energy. Only the higher energy deep levels corresponding to the longest emission wavelengths are involved in the electroluminescence of ZnO. This explains the red-shift of the luminescence spectrum. The photoluminescence of polycrystalline ZnO arises from regions close to the surface of the ZnO grains [15]. These can be proposed for the electroluminescence since ®eld inhomogeneities are located in the depletion layer of

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the grains close to the boundaries or in the grain boundaries. The ZnO electroluminescence is not contradictory to an electrical conduction along the grain boundaries. 4. Conclusions The electrical conduction in sintered polycrystalline ZnO containing small amounts of Mn and Er oxides cannot be simply described using the grain boundaries barrier model proposed for varistors. The electric properties of these ceramics are dominated by the grain boundaries as in the case of varistors. But, in contrast to varistors, the grain boundaries form a lattice of preferential conduction pathway where the electroluminescence of the Er 31 ions between the grains act as a probe which evidence the presence of hot electrons. The additional presence of Bi oxide in the sintered pellets containing small amounts of Mn and Er oxides results in the classical non-linear current±voltage characteristics of the varistors. But, in that case also, the Er 31 ion electroluminescence can indicate grain boundaries conductivity. References [1] M. Matsuoka, Jpn J. Appl. Phys. 10 (1971) 736. [2] L.M. Levinson (Ed.), Ceramic Transactions Advances in Varistor Technology, vol. 3, American Ceramic Society, Westerville, OH, 1989. [3] L.M. Levinson, H.R. Philipp, Ceram. Bull. 65 (1986) 639. [4] K. Eda, IEEE Electrical Insulation Mag. 5 (1989) 28. [5] T.K. Gupta, J. Am. Ceram. Soc. 73 (1990) 1817. [6] F. Greuter, G. Blatter, Semicond. Sci. Technol. 5 (1990) 111. [7] S. Bachir, J. Kossanyi, J.C. Ronfard-Haret, Solid State Commun. 89 (1994) 859. [8] S. Bachir, J. Kossanyi, C. Sandouly, P. Valat, J.C. RonfardHaret, J. Phys. Chem. 99 (1995) 5674. [9] S. Bachir, C. Sandouly, J. Kossanyi, J.C. Ronfard-Haret, J. Phys. Chem. Solids 57 (1996) 1869. [10] J.C. Ronfard-Haret, J. Kossanyi, Chem. Phys. 241 (1999) 339.

[11] R.T. Howard, M. Cohen, Trans. AIME 172 (1947) 413. [12] M.I. Mendelson, J. Am. Ceram. Soc. 52 (1969) 443. [13] D. KouyateÂ, J.C. Ronfard-Haret, J. Kossanyi, J. Mater. Chem. 2 (1992) 727. [14] J.M. Driear, J.P. Guertin, T.O. Sokoly, L.B. Hackney, Adv. Ceram. (Grain Boundary Phenom. Electron. Ceram.) 1 (1981) 316. [15] A. Smith, J.F. Baumard, P. Abelard, M.F. Denenot, J. Appl. Phys. 65 (1989) 5119. [16] W.B. White, K.E. McIlvred, Trans. Br. Ceram. Soc. 64 (1965) 521. [17] M. Liu, A.H. Kitai, P. Mascher, J. Lumin. 54 (1992) 35. [18] L.M. Levinson, H.R. Philipp, G.D. Mahan, in: L.M. Levinson (Ed.), Ceramic Transactions, Advances in Varistor Technology, vol. 3, American Ceramic Society, Westerville, OH, 1989, p. 145. [19] P.R. Emtage, J. Appl. Phys. 50 (1979) 6833. [20] M.R. Brown, A.F.J. Cox, W.A. Shand, J.M. Williams, Adv. Quantum Electron. 2 (1974) 69. [21] G.E. Pike, C.H. Seager, J. Appl. Phys. 50 (1979) 3414. [22] W.G. Morris, J. Vac. Sci. Technol. 13 (1976) 926. [23] S.N. Bai, T.Y. Tseng, J. Appl. Phys. 74 (1993) 695. [24] G.E. Pike, Phys. Rev. B 30 (1984) 795. [25] K. Mukae, K. Tsuda, J. Nagasawa, J. Appl. Phys. 50 (1979) 4475. [26] L.M. Levinson, H.R. Philipp, J. Appl. Phys. 47 (1976) 1117. [27] J.A. Garcia, A. Ramon, J. Piqueras, J. Appl. Phys. 62 (1987) 3058. [28] M. Anpo, Y. Kubokawa, J. Phys. Chem. 88 (1984) 5556. [29] D.C. Reynolds, D.C. Look, B. Joogai, J.E. Van Nostrand, R. Jones, J. Jenny, Solid State Commun. 106 (1998) 701. [30] A. Krier, F. Bryant, Phys. Stat. Sol. (a) 83 (1984) 315. [31] F.J. Bryant, W.E. Hagston, A. Krier, J. Phys. C: Solid State Phys. 19 (1986) L375. [32] P.K. Patil, J.K. Nandgave, R.D. Lawangar-Pawar, Solid State Commun. 76 (1990) 571. [33] R. Boyn, Phys. Stat. Sol. (b) 148 (1988) 11. [34] G.E. Pike, S.R. Kurtz, P.L. Gourley, H.R. Philipp, L.M. Levinson, J. Appl. Phys. 57 (1985) 5512. [35] U. Schwing, B. Hoffmann, J. Appl. Phys. 57 (1985) 3058.