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Noise and transport characterisation of tantalum capacitors
Microelectronics Reliability 42 (2002) 841–847 www.elsevier.com/locate/microrel
Noise and transport characterisation of tantalum capacitors q Jan Pavelka a, Josef Sikula a,*, Petr Vasina a, Vlasta Sedlakova a, Munecazu Tacano b, Sumihisa Hashiguchi c a
Czech Noise Research Laboratory, Brno University of Technology, Technicka 8, 616 00 Brno, Czech Republic b Meisei University, Hino, Tokyo 191-8506, Japan c Yamanashi University, Kofu 400-8511, Japan Received 3 December 2001; received in revised form 24 December 2001
Abstract A low frequency noise and charge carrier transport mechanisms were investigated on tantalum capacitors made by various producers. The model of Ta–Ta2 O5 –MnO2 MIS structure was used to give physical interpretation of I–V characteristics in normal and reverse modes. The noise in time and frequency domain was examined and noise sources were identified. We evaluated correlation between leakage current and noise spectral density and discussed corresponding quality and reliability indicators. Ó 2002 Elsevier Science Ltd. All rights reserved.
1. Introduction A tantalum capacitor consists of metallic Ta anode, insulator-Ta2 O5 film, semiconductor-MnO2 cathode and contacting carbon and silver layers. The ideal metal– insulator–semiconductor (MIS) structure theory [1] to be considered in this paper serves as a basis for understanding the real tantalum capacitor characteristics. Charge carrier transport through amorphous layers is a main source of current fluctuations. They are result of stochastic processes as charge carrier trapping, free charge carriers avalanche, thermal instabilities, regenerative microbreaks, isolation layer thickness variation etc. We concerned our studies on charge carrier transport and current noise spectral density to identify the sources of these fluctuations. Noise spectral density in low frequency range may be considered as a superposition of 1=f a noise, burst noise, shot noise and thermal noise. Fluctuation of polarisation and fluctuation of mechanical strain may cause
q An earlier version of this paper was published in Proceedings of the 15th Annual European Passive Components Conference (CARTS-EUROPE 2001), Copenhagen, 15–19 October 2001, pp. 81–84. * Corresponding author. Tel./Fax: +4205-4114-3398. E-mail address: [email protected] (J. Sikula).
another kind of noise, which may be of importance. Finally the contact resistance noise component also makes some structures being noisy. Two kinds of burst noise can be distinguished: Partial discharges in high electric field and regenerative microbreaks cause two state impulse like noise, whereas charge transport and polarisation fluctuation bring continuous noise spectrum. Irreversible processes, due to crystallisation of amorphous layer, oxide reduction and electric field inhomogenities, are responsible for thin insulating film structure degradation. It was found, that for the same value of DC component of leakage current identical samples have different value of dispersion or current noise spectral density. This feature was used as a quality and in some cases also as reliability indicator. For a good technology the current fluctuation is stationary, ergodic and Markovian and then the current noise spectral density is proportional to the square of DC current component. Normalised noise spectral density given by current noise spectral density divided by a square of the current can be used as a quality indicator. 1.1. Tantalum pentoxide It is very well known that Ta2 O5 films show high dielectric constant, low leakage current, high transmittance in the soft UV radiation, ion conducting, piezoelectric and electrochromic properties. The main
0026-2714/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 6 - 2 7 1 4 ( 0 2 ) 0 0 0 1 3 - 6
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J. Pavelka et al. / Microelectronics Reliability 42 (2002) 841–847
Fig. 1. Reflectivity of tantalum pentoxide thin layer. Fig. 2. Temperature dependence of resistance of MnO2 layer on alumina substrate.
deposition technique of Ta2 O5 thin films used in capacitor industry is electrolytic oxidation of pure tantalum metal. There are different modifications of Ta2 O5 : amorphous (low temperature film preparation methods) and polycrystalline (thermal annealing at about 700 °C is necessary) from which the orthorhombic b-Ta2 O5 is used for microelectronic applications in MOS devices. Electrical conductivity is usually P-type due to nonstoichiometry, oxygen vacancies create acceptors states. Leakage current is mainly given by defects and its density is of the order of 1 nA/cm2 , relative permittivity er 24–27, energy gap EG from 4 to 4.5 eV [2]. The result of our energy gap measurement from optical reflectance is shown in Fig. 1. 1.2. Manganese dioxide The cathode of tantalum capacitor is based on manganese dioxide and b–MnO2 layer is obtained practically always by thermal decomposition of Mn(NO3 )2 H2 O. Wiley and Knight [3] shows, that the resistivity and density of b-MnO2 depends strongly on the sample production. The samples prepared by pyrolytic decomposition of chemically pure Mn(NO3 )2 had resistivities of approximately 1 X cm. The b-MnO2 modification has a band gap of 0.26 eV and the c-MnO2 modification of 0.58–0.7 eV [4]. Our measurements of the temperature dependence of the resistance of a MnO2 layer deposited on alumina with special surface treatment give values in the range of 0.3–0.5 eV. In Fig. 2 two activation energies are found: 0.40 and 0.33 eV. Manganese dioxide is a N-type semiconductor where the conduction process is due to oxygen forming a donor level at 44 meV. Hall mobility depends on the resistivity and is of the order of l ¼ 10 cm2 /Vs. Impurity scattering is the process dominating carrier mobility. MnO2 shows
ohmic behaviour for fields from 10 mV/cm to 100 V/cm and an exponential relationship for higher fields [5]. In high resistivity N-type MnO2 the Seebeck coefficient was found to be 0.6 mV/K.
2. Energy band diagram The band diagram for N-type MnO2 semiconductor and P-type Ta2 O5 insulator, using standard notation [1], is shown in Fig. 3. The electron affinity of manganese dioxide v1 is of 5.3 eV [6] and for tantalum pentoxide the value of v2 is about 1.5 eV [6]. When MnO2 and Ta2 O5 are in contact, the Fermi level must be constant and interface energy conditions cause the energy band bending (see Fig. 4). Conduction and valence energy levels are discontinuous at the interface and due to that
Fig. 3. Ideal heterostructure band diagram.
J. Pavelka et al. / Microelectronics Reliability 42 (2002) 841–847
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2.2. Band diagram for bias in reverse mode When this ideal heterostructure is biased with negative voltage on Ta electrode (reverse mode), energy levels in manganese-dioxide are shifted down, as is shown in Fig. 5. A dipole layer with negative charge in MnO2 and positive charge in Ta2 O5 is formed at the interface and causes the band bending, which create a barrier for electrons. 3. Charge carrier transport
Fig. 4. Band diagram of MnO2 –Ta2 O5 in contact.
the sample forms a heterostructure. Transport phenomena are influenced by DEC and DEV energy discontinuities. In normal mode energy shift DEC decreases the probability of electron transition from MnO2 to Ta2 O5 . Electron waves are reflected on this interface and the macroscopic quantity––resistance––increases with increasing DEC . 2.1. Band diagram for bias in normal mode When this ideal heterostructure is biased with positive voltage on Ta electrode (normal mode), energy levels in manganese-dioxide are shifted up and the probability of electron transition increases. Charge transport is given by Poole–Frenkel mechanism mainly by hopping of electrons between localised states in Ta2 O5 .
Fig. 5. Band diagram of MnO2 –Ta2 O5 heterostructure in reverse mode.
Leakage current in normal mode is described by three components: ohmic conduction, ionic conduction and current given by defects [7]. There are two types of defects: vacancies and non-stoichiometric defects in amorphous Ta2 O5 and technology defects, as cracks and crystals in Ta2 O5 layer. The I–V characteristic in normal mode can be approximated by Poole–Frenkel emission, which is field-enhanced thermal excitation of trapped electrons into the conduction band. This bulk process is described as I ¼ aU expðbU 1=2 Þ þ GU þ I0r
ð1Þ
where second term GU describes ohmic conductivity and I0r is current component generated by redistribution of fixed charge and dipole decay. The constant b is given by b ¼ ðe=pe0 er dÞ1=2 =kT
ð2Þ
with tantalum capacitor’s insulating layer thickness d about 80 nm for 10 V rated voltage. In Fig. 6 the I–V characteristic in normal mode is shown with fitted curve plotted according to this approximation. The I–V characteristic in reverse mode for low voltage is exponential
Fig. 6. Current–voltage characteristic in normal mode.
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J. Pavelka et al. / Microelectronics Reliability 42 (2002) 841–847
4. Temperature dependencies and activation energy The temperature dependence of the leakage current in normal mode was measured for capacitors made by different manufacturers at rated voltage. The temperature dependence can be described by I ¼ I0t expðDE=kT Þ
ð5Þ
with an activation energy DE. In Fig. 9 a typical dependence for a capacitor of 150 lF is given with an activation energy DE ¼ 0:43 eV. An Ohmic current component of 40 nA was subtracted in this case. In reverse mode for voltage less than 1 V the same dependency with similar activation energy was observed (see Fig. 10).
Fig. 7. Current–voltage characteristic in reverse mode.
I ¼ I0b expðbU Þ
ð3Þ
because the current is controlled by the barrier near the MnO2 –Ta2 O5 interface (see Fig. 4). For increasing voltage in reverse mode the energy level of the MnO2 conduction band EC1 will coincide with the energy level of Ta2 O5 valence band EV2 and the tunnelling process becomes dominant charge transport mechanism. After reaching this threshold voltage, the current value markedly increases (see Fig. 7) and the I–V characteristic can be approximated by I ¼ I0m expðm=U Þ
ð4Þ
as is shown in Fig. 8.
Fig. 9. Temperature dependence of leakage current in normal mode.
Fig. 8. Current–voltage characteristic in reverse mode after contacting layers resistance subtraction.
Fig. 10. Temperature dependence of leakage current in reverse mode.
J. Pavelka et al. / Microelectronics Reliability 42 (2002) 841–847
Fig. 11. Temperature dependence of voltage on capacitor for constant reverse current I ¼ 160 lA.
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Fig. 12. Normalised current noise spectral density in reverse mode.
For reverse voltage higher than 1 V tunnelling process is dominant and for constant current the voltage on capacitor slightly decreases from room temperature to 150 °C (see Fig. 11). 5. Noise Noise characteristics can be explained on the basis of these noise sources: 1=f noise, burst noise and hot carrier noise. The noise spectral density is 1=f type in the whole measured frequency range for the main part of samples both in normal and reverse mode (see Fig. 12). For the higher frequencies thermal noise of the load resistance is superposed yielding constant value of noise spectral density. Due to defects in Ta2 O5 layer the metal semiconductor (MS) diodes of Ta–Mn2 O3 contacts are created during self-healing. Burst noise is experimentally observed if one elementary MS diode burst noise source is dominant. In Fig. 13 the typical burst noise voltage signal in time domain is given, showing bistable fluctuation of current driven by carrier capture and emission processes at the defect spot. The structure of the insulating film is very poor and we can expect a large number of randomly distributed localised states in the forbidden band and at the interfaces. Then 1=f noise spectral density can be generated as a superposition of Lorentzians with exponentially distributed relaxation time constant. We are surprised, that 1=f noise component has frequency exponent strictly equal to 1. The frequency dependence of noise spectral density is affected by the changing value of load impedance. In Fig. 14 the experimental circuit is shown. The voltage
Fig. 13. Burst noise voltage time dependence.
fluctuation of battery source UV is filtered by capacitor CF . The preamplifier input is shunted by the parallel combination of the sample capacitance CX and load resistance RL and then the measured signal UN is attenuated with the frequency. In the frequency region, where x 1=RL CX the noise spectral density is proportional to 1=f , while for frequency x > 1=RL CX it decreases as f 3 , as is shown in Fig. 15. The background thermal noise of load resistance RL ¼ 1 kX for zero applied voltage is also decreasing for higher frequencies until it reaches the value of amplifier background noise. To obtain undistorted results, numerical correction according to following equation should be done SI ¼
SU ð1 þ x2 R2L CX2 Þ R2L
ð6Þ
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J. Pavelka et al. / Microelectronics Reliability 42 (2002) 841–847
Fig. 14. Noise voltage measurement set-up with capacitor equivalent circuit.
Fig. 16. Noise spectral density value at 1 Hz versus leakage current for one sample at various applied voltages.
Fig. 15. Noise spectral density frequency dependence.
where SU is a measurable quantity – the voltage noise spectral density on the amplifier input. In Fig. 15 the theoretical circuit characteristic is fitted in the experimental data, using parameters RL ¼ 1 kX, CX ¼ 1 lF and amplifier background noise SU B ¼ 4 1019 V2 s. The noise spectral density is proportional to the square of the current for low and medium value of electric field intensity both in normal (see Fig. 16) and reverse operation modes. For high electric field intensity normalised noise spectral density increases with increasing field intensity in normal mode probably due to avalanche process. In contrast, the normalised noise spectral density decreases in reverse mode (see Fig. 12) probably due to formation of hot conducting channels, which change the transport mechanism due to temperature dependence of the electrical conductivity. A feedback between Joule heating and electron transport exists. In this reverse mode I–V characteristic, a negative resistance region was observed. The leakage current is given mainly by defects and then its value is used to estimate dielectric layer quality. We observed that the current noise spectral density is also related to technology and it constitutes the reliability indicator of capacitors. In Fig. 17 the correlation between leakage current at rated voltage and noise spectral density value at a frequency of 1 Hz (in the 1=f region) is shown for ensemble of 80 samples. The ma-
Fig. 17. Noise spectral density value at 1 Hz versus leakage current for ensemble of 80 samples at rated voltage.
jority of samples follow the quadratic law, although there are also some samples characterised by low noise and high leakage current. We suppose, that DC current is a sum of at least two independent current flow mechanisms, which have not the same noise intensity.
6. Conclusion We considered a model of tantalum capacitor as a metal–insulator–semiconductor heterostructure. This model can give physical interpretation of the leakage current’s electric field and temperature dependencies. In normal mode the main charge carrier transport mechanism is given by the Poole–Frenkel effect. In reverse
J. Pavelka et al. / Microelectronics Reliability 42 (2002) 841–847
mode, when the applied voltage is higher than a critical voltage, current transport is given by field assisted tunnelling and the I–V characteristic is very similar to that of a Zener diode. Charge carrier transport in the thin insulating layer generates excess noise, which is a superposition of 1=f and burst noise. The frequency dependence of noise spectral density in low frequency region gives information on slow processes of layer degradation.
Acknowledgements This research was partially supported by Czech Grant Agency GACR 102/99/0953 and GACR 102/99/ 1088.
847
References [1] Sze SM. Physics of semiconductor devices. 2nd ed. New York: Wiley Interscience; 1981. [2] Porqueras I, Marti J, Bertran E. Optical and electrical characterisation of Ta2 O5 thin films for ionic conduction application. Thin Solid Films 1999;343-344:449–52. [3] Wiley JS, Knight HT. The electrical resistivity of pyrolytic beta MnO2 . J Electrochem Soc 1964;111:656–60. [4] Bhide VG, Damle RV. Dielectric properties of manganese dioxide. Physica 1960;26:33–42. [5] Klose PH. Electrical properties of manganese dioxide and manganese sesquioxide. J Electrochem Soc 1970;117: 854–8. [6] Langer HD. Festk€ orper-elektrolytkondensatoren. Berlin: Akademie-Verlag; 1982. [7] Mead CA. Electron transport mechanisms in thin insulating films. Phys Rev 1962;128:2088–93.
Noise and transport characterisation of tantalum capacitors q Jan Pavelka a, Josef Sikula a,*, Petr Vasina a, Vlasta Sedlakova a, Munecazu Tacano b, Sumihisa Hashiguchi c a
Czech Noise Research Laboratory, Brno University of Technology, Technicka 8, 616 00 Brno, Czech Republic b Meisei University, Hino, Tokyo 191-8506, Japan c Yamanashi University, Kofu 400-8511, Japan Received 3 December 2001; received in revised form 24 December 2001
Abstract A low frequency noise and charge carrier transport mechanisms were investigated on tantalum capacitors made by various producers. The model of Ta–Ta2 O5 –MnO2 MIS structure was used to give physical interpretation of I–V characteristics in normal and reverse modes. The noise in time and frequency domain was examined and noise sources were identified. We evaluated correlation between leakage current and noise spectral density and discussed corresponding quality and reliability indicators. Ó 2002 Elsevier Science Ltd. All rights reserved.
1. Introduction A tantalum capacitor consists of metallic Ta anode, insulator-Ta2 O5 film, semiconductor-MnO2 cathode and contacting carbon and silver layers. The ideal metal– insulator–semiconductor (MIS) structure theory [1] to be considered in this paper serves as a basis for understanding the real tantalum capacitor characteristics. Charge carrier transport through amorphous layers is a main source of current fluctuations. They are result of stochastic processes as charge carrier trapping, free charge carriers avalanche, thermal instabilities, regenerative microbreaks, isolation layer thickness variation etc. We concerned our studies on charge carrier transport and current noise spectral density to identify the sources of these fluctuations. Noise spectral density in low frequency range may be considered as a superposition of 1=f a noise, burst noise, shot noise and thermal noise. Fluctuation of polarisation and fluctuation of mechanical strain may cause
q An earlier version of this paper was published in Proceedings of the 15th Annual European Passive Components Conference (CARTS-EUROPE 2001), Copenhagen, 15–19 October 2001, pp. 81–84. * Corresponding author. Tel./Fax: +4205-4114-3398. E-mail address: [email protected] (J. Sikula).
another kind of noise, which may be of importance. Finally the contact resistance noise component also makes some structures being noisy. Two kinds of burst noise can be distinguished: Partial discharges in high electric field and regenerative microbreaks cause two state impulse like noise, whereas charge transport and polarisation fluctuation bring continuous noise spectrum. Irreversible processes, due to crystallisation of amorphous layer, oxide reduction and electric field inhomogenities, are responsible for thin insulating film structure degradation. It was found, that for the same value of DC component of leakage current identical samples have different value of dispersion or current noise spectral density. This feature was used as a quality and in some cases also as reliability indicator. For a good technology the current fluctuation is stationary, ergodic and Markovian and then the current noise spectral density is proportional to the square of DC current component. Normalised noise spectral density given by current noise spectral density divided by a square of the current can be used as a quality indicator. 1.1. Tantalum pentoxide It is very well known that Ta2 O5 films show high dielectric constant, low leakage current, high transmittance in the soft UV radiation, ion conducting, piezoelectric and electrochromic properties. The main
0026-2714/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 6 - 2 7 1 4 ( 0 2 ) 0 0 0 1 3 - 6
842
J. Pavelka et al. / Microelectronics Reliability 42 (2002) 841–847
Fig. 1. Reflectivity of tantalum pentoxide thin layer. Fig. 2. Temperature dependence of resistance of MnO2 layer on alumina substrate.
deposition technique of Ta2 O5 thin films used in capacitor industry is electrolytic oxidation of pure tantalum metal. There are different modifications of Ta2 O5 : amorphous (low temperature film preparation methods) and polycrystalline (thermal annealing at about 700 °C is necessary) from which the orthorhombic b-Ta2 O5 is used for microelectronic applications in MOS devices. Electrical conductivity is usually P-type due to nonstoichiometry, oxygen vacancies create acceptors states. Leakage current is mainly given by defects and its density is of the order of 1 nA/cm2 , relative permittivity er 24–27, energy gap EG from 4 to 4.5 eV [2]. The result of our energy gap measurement from optical reflectance is shown in Fig. 1. 1.2. Manganese dioxide The cathode of tantalum capacitor is based on manganese dioxide and b–MnO2 layer is obtained practically always by thermal decomposition of Mn(NO3 )2 H2 O. Wiley and Knight [3] shows, that the resistivity and density of b-MnO2 depends strongly on the sample production. The samples prepared by pyrolytic decomposition of chemically pure Mn(NO3 )2 had resistivities of approximately 1 X cm. The b-MnO2 modification has a band gap of 0.26 eV and the c-MnO2 modification of 0.58–0.7 eV [4]. Our measurements of the temperature dependence of the resistance of a MnO2 layer deposited on alumina with special surface treatment give values in the range of 0.3–0.5 eV. In Fig. 2 two activation energies are found: 0.40 and 0.33 eV. Manganese dioxide is a N-type semiconductor where the conduction process is due to oxygen forming a donor level at 44 meV. Hall mobility depends on the resistivity and is of the order of l ¼ 10 cm2 /Vs. Impurity scattering is the process dominating carrier mobility. MnO2 shows
ohmic behaviour for fields from 10 mV/cm to 100 V/cm and an exponential relationship for higher fields [5]. In high resistivity N-type MnO2 the Seebeck coefficient was found to be 0.6 mV/K.
2. Energy band diagram The band diagram for N-type MnO2 semiconductor and P-type Ta2 O5 insulator, using standard notation [1], is shown in Fig. 3. The electron affinity of manganese dioxide v1 is of 5.3 eV [6] and for tantalum pentoxide the value of v2 is about 1.5 eV [6]. When MnO2 and Ta2 O5 are in contact, the Fermi level must be constant and interface energy conditions cause the energy band bending (see Fig. 4). Conduction and valence energy levels are discontinuous at the interface and due to that
Fig. 3. Ideal heterostructure band diagram.
J. Pavelka et al. / Microelectronics Reliability 42 (2002) 841–847
843
2.2. Band diagram for bias in reverse mode When this ideal heterostructure is biased with negative voltage on Ta electrode (reverse mode), energy levels in manganese-dioxide are shifted down, as is shown in Fig. 5. A dipole layer with negative charge in MnO2 and positive charge in Ta2 O5 is formed at the interface and causes the band bending, which create a barrier for electrons. 3. Charge carrier transport
Fig. 4. Band diagram of MnO2 –Ta2 O5 in contact.
the sample forms a heterostructure. Transport phenomena are influenced by DEC and DEV energy discontinuities. In normal mode energy shift DEC decreases the probability of electron transition from MnO2 to Ta2 O5 . Electron waves are reflected on this interface and the macroscopic quantity––resistance––increases with increasing DEC . 2.1. Band diagram for bias in normal mode When this ideal heterostructure is biased with positive voltage on Ta electrode (normal mode), energy levels in manganese-dioxide are shifted up and the probability of electron transition increases. Charge transport is given by Poole–Frenkel mechanism mainly by hopping of electrons between localised states in Ta2 O5 .
Fig. 5. Band diagram of MnO2 –Ta2 O5 heterostructure in reverse mode.
Leakage current in normal mode is described by three components: ohmic conduction, ionic conduction and current given by defects [7]. There are two types of defects: vacancies and non-stoichiometric defects in amorphous Ta2 O5 and technology defects, as cracks and crystals in Ta2 O5 layer. The I–V characteristic in normal mode can be approximated by Poole–Frenkel emission, which is field-enhanced thermal excitation of trapped electrons into the conduction band. This bulk process is described as I ¼ aU expðbU 1=2 Þ þ GU þ I0r
ð1Þ
where second term GU describes ohmic conductivity and I0r is current component generated by redistribution of fixed charge and dipole decay. The constant b is given by b ¼ ðe=pe0 er dÞ1=2 =kT
ð2Þ
with tantalum capacitor’s insulating layer thickness d about 80 nm for 10 V rated voltage. In Fig. 6 the I–V characteristic in normal mode is shown with fitted curve plotted according to this approximation. The I–V characteristic in reverse mode for low voltage is exponential
Fig. 6. Current–voltage characteristic in normal mode.
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J. Pavelka et al. / Microelectronics Reliability 42 (2002) 841–847
4. Temperature dependencies and activation energy The temperature dependence of the leakage current in normal mode was measured for capacitors made by different manufacturers at rated voltage. The temperature dependence can be described by I ¼ I0t expðDE=kT Þ
ð5Þ
with an activation energy DE. In Fig. 9 a typical dependence for a capacitor of 150 lF is given with an activation energy DE ¼ 0:43 eV. An Ohmic current component of 40 nA was subtracted in this case. In reverse mode for voltage less than 1 V the same dependency with similar activation energy was observed (see Fig. 10).
Fig. 7. Current–voltage characteristic in reverse mode.
I ¼ I0b expðbU Þ
ð3Þ
because the current is controlled by the barrier near the MnO2 –Ta2 O5 interface (see Fig. 4). For increasing voltage in reverse mode the energy level of the MnO2 conduction band EC1 will coincide with the energy level of Ta2 O5 valence band EV2 and the tunnelling process becomes dominant charge transport mechanism. After reaching this threshold voltage, the current value markedly increases (see Fig. 7) and the I–V characteristic can be approximated by I ¼ I0m expðm=U Þ
ð4Þ
as is shown in Fig. 8.
Fig. 9. Temperature dependence of leakage current in normal mode.
Fig. 8. Current–voltage characteristic in reverse mode after contacting layers resistance subtraction.
Fig. 10. Temperature dependence of leakage current in reverse mode.
J. Pavelka et al. / Microelectronics Reliability 42 (2002) 841–847
Fig. 11. Temperature dependence of voltage on capacitor for constant reverse current I ¼ 160 lA.
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Fig. 12. Normalised current noise spectral density in reverse mode.
For reverse voltage higher than 1 V tunnelling process is dominant and for constant current the voltage on capacitor slightly decreases from room temperature to 150 °C (see Fig. 11). 5. Noise Noise characteristics can be explained on the basis of these noise sources: 1=f noise, burst noise and hot carrier noise. The noise spectral density is 1=f type in the whole measured frequency range for the main part of samples both in normal and reverse mode (see Fig. 12). For the higher frequencies thermal noise of the load resistance is superposed yielding constant value of noise spectral density. Due to defects in Ta2 O5 layer the metal semiconductor (MS) diodes of Ta–Mn2 O3 contacts are created during self-healing. Burst noise is experimentally observed if one elementary MS diode burst noise source is dominant. In Fig. 13 the typical burst noise voltage signal in time domain is given, showing bistable fluctuation of current driven by carrier capture and emission processes at the defect spot. The structure of the insulating film is very poor and we can expect a large number of randomly distributed localised states in the forbidden band and at the interfaces. Then 1=f noise spectral density can be generated as a superposition of Lorentzians with exponentially distributed relaxation time constant. We are surprised, that 1=f noise component has frequency exponent strictly equal to 1. The frequency dependence of noise spectral density is affected by the changing value of load impedance. In Fig. 14 the experimental circuit is shown. The voltage
Fig. 13. Burst noise voltage time dependence.
fluctuation of battery source UV is filtered by capacitor CF . The preamplifier input is shunted by the parallel combination of the sample capacitance CX and load resistance RL and then the measured signal UN is attenuated with the frequency. In the frequency region, where x 1=RL CX the noise spectral density is proportional to 1=f , while for frequency x > 1=RL CX it decreases as f 3 , as is shown in Fig. 15. The background thermal noise of load resistance RL ¼ 1 kX for zero applied voltage is also decreasing for higher frequencies until it reaches the value of amplifier background noise. To obtain undistorted results, numerical correction according to following equation should be done SI ¼
SU ð1 þ x2 R2L CX2 Þ R2L
ð6Þ
846
J. Pavelka et al. / Microelectronics Reliability 42 (2002) 841–847
Fig. 14. Noise voltage measurement set-up with capacitor equivalent circuit.
Fig. 16. Noise spectral density value at 1 Hz versus leakage current for one sample at various applied voltages.
Fig. 15. Noise spectral density frequency dependence.
where SU is a measurable quantity – the voltage noise spectral density on the amplifier input. In Fig. 15 the theoretical circuit characteristic is fitted in the experimental data, using parameters RL ¼ 1 kX, CX ¼ 1 lF and amplifier background noise SU B ¼ 4 1019 V2 s. The noise spectral density is proportional to the square of the current for low and medium value of electric field intensity both in normal (see Fig. 16) and reverse operation modes. For high electric field intensity normalised noise spectral density increases with increasing field intensity in normal mode probably due to avalanche process. In contrast, the normalised noise spectral density decreases in reverse mode (see Fig. 12) probably due to formation of hot conducting channels, which change the transport mechanism due to temperature dependence of the electrical conductivity. A feedback between Joule heating and electron transport exists. In this reverse mode I–V characteristic, a negative resistance region was observed. The leakage current is given mainly by defects and then its value is used to estimate dielectric layer quality. We observed that the current noise spectral density is also related to technology and it constitutes the reliability indicator of capacitors. In Fig. 17 the correlation between leakage current at rated voltage and noise spectral density value at a frequency of 1 Hz (in the 1=f region) is shown for ensemble of 80 samples. The ma-
Fig. 17. Noise spectral density value at 1 Hz versus leakage current for ensemble of 80 samples at rated voltage.
jority of samples follow the quadratic law, although there are also some samples characterised by low noise and high leakage current. We suppose, that DC current is a sum of at least two independent current flow mechanisms, which have not the same noise intensity.
6. Conclusion We considered a model of tantalum capacitor as a metal–insulator–semiconductor heterostructure. This model can give physical interpretation of the leakage current’s electric field and temperature dependencies. In normal mode the main charge carrier transport mechanism is given by the Poole–Frenkel effect. In reverse
J. Pavelka et al. / Microelectronics Reliability 42 (2002) 841–847
mode, when the applied voltage is higher than a critical voltage, current transport is given by field assisted tunnelling and the I–V characteristic is very similar to that of a Zener diode. Charge carrier transport in the thin insulating layer generates excess noise, which is a superposition of 1=f and burst noise. The frequency dependence of noise spectral density in low frequency region gives information on slow processes of layer degradation.
Acknowledgements This research was partially supported by Czech Grant Agency GACR 102/99/0953 and GACR 102/99/ 1088.
847
References [1] Sze SM. Physics of semiconductor devices. 2nd ed. New York: Wiley Interscience; 1981. [2] Porqueras I, Marti J, Bertran E. Optical and electrical characterisation of Ta2 O5 thin films for ionic conduction application. Thin Solid Films 1999;343-344:449–52. [3] Wiley JS, Knight HT. The electrical resistivity of pyrolytic beta MnO2 . J Electrochem Soc 1964;111:656–60. [4] Bhide VG, Damle RV. Dielectric properties of manganese dioxide. Physica 1960;26:33–42. [5] Klose PH. Electrical properties of manganese dioxide and manganese sesquioxide. J Electrochem Soc 1970;117: 854–8. [6] Langer HD. Festk€ orper-elektrolytkondensatoren. Berlin: Akademie-Verlag; 1982. [7] Mead CA. Electron transport mechanisms in thin insulating films. Phys Rev 1962;128:2088–93.