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Time-dependent dielectric breakdown of SiO2 films in a wide electric field range
Microelectronics Reliability 41 (2001) 47±52
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Time-dependent dielectric breakdown of SiO2 ®lms in a wide electric ®eld range A. Teramoto a,*, H. Umeda a, K. Azamawari b, K. Kobayashi c, K. Shiga a, J. Komori a, Y. Ohno a, A. Shigetomi a a
ULSI Development Center, Mitsubishi Electric Corporation, 4-1 Mizuhara, Itami, Hyogo 664-8641, Japan b TADA Electric Corporation, 4-1 Mizuhara, Itami, Hyogo 664-8641, Japan c Memory IC Division, Mitsubishi Electric Corporation, 4-1 Mizuhara, Itami, Hyogo 664-8641, Japan Received 30 March 2000; received in revised form 5 June 2000
Abstract We have performed time dependent dielectric breakdown measurement of SiO2 ®lms in the electric ®eld (EOX ) range 7±13.5 MV/cm and evaluated the electric ®eld dependence of intrinsic lifetime, using both area and temperature dependences of oxide lifetime. We have evaluated the electric ®eld dependence of time to breakdown (tBD ) below 125°C, because the activation energy of intrinsic lifetime changes at 125°C tBD of 7.1 and 9.6 nm oxides is not proportional to exp EOX but proportional to exp 1=EOX . This suggests that the breakdown mechanism of 9.6 and 7.1 nm oxides is the same and adheres to the anode hole injection model. However, the breakdown mechanism of 4.0 nm oxides is not the same as that of 7.1 and 9.6 nm oxides. The slope of log tBD versus 1=EOX plot in 4.0 nm oxide increases with decreasing oxide ®elds. The intrinsic lifetime in the positive gate bias decreases with increasing oxide thicknesses in the range of electric ®elds employed in the present experiment. Ó 2001 Elsevier Science Ltd. All rights reserved.
1. Introduction The time dependent dielectric breakdown (TDDB) of thin gate oxides is one of the most important reliability issues of MOS integrated circuits. For the prediction of oxide reliability, it is crucial to clarify the electric ®eld dependence of time to breakdown (tBD ). Several researchers have proposed many breakdown mechanisms from TDDB measurements [1±17]. According to the anode hole injection model, log tBD is proportional to 1=EOX [1±5,8]. Other researchers have reported that log tBD is proportional to EOX , in accordance with thermodynamic model [9,10]. The correct choice of this model is crucial because lifetime at device working conditions is usually obtained by extrapolating orders of magnitude in time from lifetime at accelerated stress test
*
Corresponding author. Tel.: +81-727-84-7355; fax: +81727-80-2675. E-mail address: [email protected] (A. Teramoto).
conditions. To clarify the ®eld dependence of the oxide lifetime at low electric ®elds, the TDDB measurements at the low electric ®elds are essential. The low electric ®eld measurements at high temperatures were performed by Suehle et al. [17] and McPherson et al. [18]. However, the activation energy of the lifetime changes at 125°C [19]. This suggests that the breakdown mechanism of oxides changes at 125°C. This means that the TDDB measurement at temperatures lower than 125°C is required. In this paper, we perform the TDDB measurement at temperatures lower than 125°C in a wide electric ®eld range in three years.
2. Experiment Fig. 1(A) and (B) shows the test structures of MOSFETs and MOS capacitor. p-Type (1 0 0) substrates with a resistivity of 8.5±11.5 X cm and n-type (1 0 0) substrates with a resistivity of 10±20 X cm were used in this study. MOSFETs in p-type substrate and
0026-2714/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 6 - 2 7 1 4 ( 0 0 ) 0 0 0 9 5 - 0
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A. Teramoto et al. / Microelectronics Reliability 41 (2001) 47±52
Fig. 1. Test structures of MOS capacitor and MOSFET.
n-well and MOS capacitors in n-type substrate were fabricated with standard CMOS technology. Gate oxides with thicknesses ranging from 4.0 to 9.6 nm were grown using pyrogenic oxidation at 750°C. Gate electrodes were formed from in situ phosphorus-doped polysilicon. The gate oxide areas are 0.03, 0.1 and 10 mm2 . The measurement temperatures are 25°C and 125°C. The number of points in each TDDB evaluation are 100± 1000. The measurement oxide electric ®elds ranges from 7.0 to 13.5 MV/cm. The EOX values are de®ned by EOX VG ÿ VFB =TOX
Fig. 2. Weibull plots of 7.1 nm oxide. The sample area is 10 mm2 , and measurement temperature is 125°C.
1
for substrate accumulation and EOX VG ÿ VFB ÿ 2/F =TOX
2
for substrate inversion, respectively, where VG is the voltage applied to the gate electrode, VFB , the ¯at-band voltage, TOX , the gate oxide thickness, and /F , the Fermi potential in the substrate. Patrikar et al. reported that the degradation mechanism is dierent for stressing of ptype capacitors in inversion and that of n-type capacitors in accumulation [20]. However, we used two types test structure, i.e. p-type MOSFETs in inversion and that of n-type capacitors in accumulation, because the tBD s in both stresses are the same in this experiment. For measuring TDDB characteristics for a wide range of electric ®eld, we have taken about three years for testing.
3. Results and discussion 3.1. TDDB data Fig. 2 shows the Weibull plots at constant voltage TDDB measurement for 7.1 nm oxides. The sample area is 10 mm2 and the measurement temperature is 125°C. The distribution seems to be bimodal [21]. However, we are concerned with only the intrinsic breakdown region in this paper. For obtaining the TDDB characteristics at high ®elds, the TDDB measurements are performed for a small oxide area because of a voltage drop caused by series resistance. Current density (JG ) vs. electric ®eld (EOX ) of 7.1 nm oxides were measured for various oxide areas. Fig. 3 shows the Fowler±Nordheim plots for the
Fig. 3. Fowler±Nordheim (F±N) plots for the JG ±EOX data of 7.1 nm oxides.
JG ±EOX data. The F±N plots for 0.03 and 0.1 mm2 oxides show a straight line at EOX below 13.5 MV/cm. The JG ±EOX data above 13.5 MV/cm deviated from a straight line because of in¯uence of a voltage drop caused by series resistance. This indicates that we can evaluate the TDDB characteristics below 13.5 MV/cm without the in¯uence of the series resistance for 0.1 and 0.03 mm2 . Fig. 4(A) and (B) shows the Weibull plot for sample area of 0.03 mm2 , measurement temperature of 125°C, and EOX values of 12.0, 12.5 and 13.0 MV/cm and the Weibull plot for sample area of 0.1 mm2 , measurement temperature of 25°C, and EOX values of 12.5, 13.0 and 13.5 MV/cm, respectively.
A. Teramoto et al. / Microelectronics Reliability 41 (2001) 47±52
49
Fig. 4. (A) Weibull plots of 7.1 nm oxide: The sample area is 0.03 mm2 , and measurement temperature is 125°C. (B) Weibull plots of 7.1 nm oxide: The sample area is 0.1 mm2 , and measurement temperature is 25°C.
3.2. Area dependence Fig. 5 shows the Weibull plots of 6.9 nm oxides for sample areas of 10ÿ2 , 10ÿ4 , 10ÿ5 and 10ÿ6 mm2 . Here, let us make two assumptions that the breakdown of oxide in a wearout failure period occurs in a localized weak spot, and the distribution of the weak spot has a random distribution throughout the oxide area. Relation between the cumulative distribution function (F) and area (A) is expressed by the following equation: 1 ÿ F t expfÿAD tg;
3
where t is the time and D t is cumulative weak spot density at t. The cumulative distribution function, can then be normalized by the following equation: 1 ÿ F1 t f1 ÿ F2 tgA1 =A2 ;
4
where A1 and A2 are oxide areas, and F1 and F2 are the cumulative distribution functions at a stress time t for A1 and A2 , respectively. Fig. 6 shows the plots of the cumulative distribution function versus the stress time,
Fig. 6. The plots of cumulative distribution functions versus the stress time, where Eq. (4) was used to calculate the rate at 10ÿ6 mm2 for those cases featuring dierent oxide areas.
where the rate per 10ÿ6 mm2 was calculated from those for dierent oxide areas using Eq. (4). The rate for 10ÿ6 mm2 which were calculated from those dierent oxide areas using Eq. (4), are unique in the same oxide. This indicates that we can estimate the oxide lifetime for any oxide area by using Eq. (4). This coincides with the results in previous works [22,23]. 3.3. Temperature dependence
Fig. 5. Weibull plots of 6.9 nm oxide for sample area of 10ÿ2 , 10ÿ4 , 10ÿ5 , and 10ÿ6 mm2 .
It has been reported that the temperature dependence of the activation energy changes at 125°C [19]. Fig. 7 shows the Arrhenius plots obtained at electric ®elds of 9.0, 10.0, 11.0 and 12.5 MV/cm for the 7.1 nm oxides. The slopes of 9 and 10 MV/cm data change at 125°C. This means that activation energy changes at 125°C and suggests that the breakdown mechanism changes at 125°C. This means that the limit temperature under which we can discuss the breakdown mechanism is 125°C. In this paper, we study the TDDB characteristics under 125°C. The slope of this ®gure indicates that the
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A. Teramoto et al. / Microelectronics Reliability 41 (2001) 47±52
electric ®eld at the temperatures ranging from 25°C to 125°C. Fig. 8 shows the activation energy as a function of the oxide ®eld. The activation energy (Ea ) is expressed by the following equation with the oxide ®eld: Ea 0:83 ÿ 0:049EOX :
5
3.4. Discussion
Fig. 7. Arrhenius plot obtained at electric ®elds of 9.0, 10.0, 11.0, 12.5, and 13.0 MV/cm for 7.1 nm oxides.
Fig. 8. Activation energy as a function of the oxide electric ®eld.
activation energy decreases with increasing oxide ®elds, i.e., the activation energy has a dependence on the
Fig. 9 shows the Weibull plots of 7.1 nm oxides for the sample area of 0.1 mm2 and the temperature of 125°C, translated from measurement data (shown in Figs. 2 and 4) using Eqs. (4) and (5). The wide electric ®eld range data (7.0±13.5 MV/cm) are shown in Fig. 9. The data at 12.5 and 13.0 MV/cm calculated from the measurement condition (Fig. 4(A)) are in complete agreement with those calculated from other measurement condition (Fig. 4(B)). This supports the view that Eqs. (4) and (5) can be applied to calculate the oxide lifetime. Fig. 10(A) and (B) shows the time to 4% failure of 7.1 nm oxides as a function of electric ®eld for sample areas of 0.1 mm2 and the temperature of 125°C. The log tBD is not proportional to EOX but proportional to 1=EOX . It has been reported that the breakdown mechanism at high ®eld stress is dierent from that at low ®eld stress [24] because the charge to breakdown value changed in a high ®eld region. However, the log tBD ±EOX relationship agrees with the 1=EOX model. This supports that the breakdown mechanism of 7.1 nm oxides in positive gate bias under 125°C adheres to the anode hole injection model [1±5,8]. The electric ®eld dependence of the intrinsic lifetime for positive gate bias of 7.1, 9.6 and 4.0 nm are also shown in Fig. 10(A) and (B). The log tBD of 9.6 nm oxide is also proportional to 1=EOX . This suggests that the breakdown mechanism of 9.6 nm oxide is the same as that of 7.1 nm oxide and adheres to the anode hole injection model. The slope of
Fig. 9. Weibull plots of 7.1 nm oxide for the sample area of 0.1 mm2 and temperature of 125°C, calculated from measurement data (Figs. 2 and 4) using Eqs. (4) and (5).
A. Teramoto et al. / Microelectronics Reliability 41 (2001) 47±52
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4. Conclusions We have evaluated the intrinsic lifetime in a wide electric ®eld range at temperatures lower than 125°C, using the area dependence and temperature dependence on oxide lifetime. For positive gate bias, the log tBD of 7.1 and 9.6 nm oxides is not proportional to the electric ®eld but proportional to 1=EOX . This suggests that the breakdown mechanism of 9.6 nm oxide is the same as that of 7.1 nm oxide and adheres to the anode injection model. The breakdown mechanism of 4.0 nm is not the same as that of 7.1 and 9.6 nm oxides. The slope of log tBD versus 1=EOX plot in 4.0 nm oxide increases with decreasing oxide ®elds. The intrinsic lifetime in the positive gate bias decreases with increasing oxide thicknesses in the present experiment.
Acknowledgements The authors would like to thank Drs. H. Miyoshi and T. Nishimura for their continuous encouragement. The authors also wish to thank Dr. M. Inoue for the valuable discussions throughout this work.
References
Fig. 10. Time to 4% failure of 7.1, 9.6 and 4.0 nm oxides as a function of oxide electric ®eld ± the sample area is 0.1 mm2 , and temperature is 125°C: (A) log tBD ±1=EOX plot, (B) log tBD ± EOX plot.
log tBD versus 1=EOX plot in 4.0 nm oxide increases with decreasing oxide ®elds. It is suggested that the mechanism of 4.0 nm oxide is dierent from that of 7.1 and 9.6 nm oxides. However, more data are needed to discuss the breakdown mechanism of 4.0 nm oxide because the amount of data for 4.0 nm oxides is insucient.
[1] Chen IC, Holland SE, Hu C. IEEE Trans Electron Dev 1985;ED-32(2):413. [2] Chen IC, Holland SE, Hu C. Proceedings of the International Reliability Physics Symposium, IEEE, 1985. p. 24. [3] Chen IC, Hu C. IEEE Electron Dev Lett 1987;EDL8(4):140. [4] Chen IC, Hu C. Proceedings of the International Reliability Physics Symposium IEEE, 1988. p. 131. [5] Lee JC, Chen IC, Hu C. IEEE Trans Electron Dev 1988;ED-35(12):2268. [6] Boyko KC, Gerlach DL. Proceedings of the International Reliability Physics Symposium, IEEE, 1989. p. 1. [7] Shiono N, Itsumi M. Proceedings of the International Reliability Physics Symposium, IEEE, 1993. p. 1. [8] Shuegraf KF, Hu C. Proceedings of the International Reliability Physics Symposium, IEEE, 1993. p. 7. [9] McPherson JW, Baglee DA. Proceedings of the International Reliability Physics Symposium, IEEE, 1985. p. 1. [10] McPherson JW, Baglee DA. J Electrochem Soc 1985; 132:1903. [11] Hokari Y, Baba T, Kawamura N. IEEE Trans Electron Dev 1985;ED-32(11):2485. [12] DiMaria DJ, Cartier E, Arnord D. J Appl Phys 1993; 73:3367. [13] Abadeer WW, Vollertsen R-P, Bolam RJ, DiMaria DJ, Cartier E. Symposium on VLSI Technology Digest of Technical Papers, 1994. p. 43. Proceedings of the International Reliability Physics Symposium, IEEE, 1989. p. 1.
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[14] Dumin DJ, Mopuri S, Vanchinathan S, Scott RS, Subramoniam R, Lewis TG. Proceedings of the International Reliability Physics Symposium, IEEE, 1994. p. 143. [15] Dumin DJ. J Electrochem Soc 1995;142:1272. [16] Matsuda T, Ohzone T, Hori T. Solid-State Electron 1996;39:1427. [17] Suehle JS, Chapaparala P, Messic C, Miller WM, Boyko KC. Proceedings of the International Reliability Physics Symposium, IEEE, 1994. p. 120. [18] McPherson J, Reddy V, Banerjee K, Le H. International Electron Device Meeting Technical Digest, 1998. p. 171. [19] Shiga K, Komori J, Katsumata M, Teramoto A, Sekine M. Proceeding of IEEE 1998 International Conference on
[20] [21] [22] [23] [24]
Microelectronic Test Structures, vol. 11, March 1998. p. 198. Patrikar RM, Lal R, Vasi J. J Appl Phys 1993;74: 4598. Degraeve R, Ogier JL, Bellens R, Roussel Ph, Groeseneken G, Maes HE. Proceedings of the International Reliability Physics Symposium, IEEE, 1996. p. 44. Osburn CM, Ormond DW. J Electrochem Soc 1972; 119:591. Wolters DR, Van Der Schoot JJ. Philips J Res 1985; 40(3):115. Wolters DR, Van Der Schoot JJ. Philips J Res 1985; 40(3):137.
www.elsevier.com/locate/microrel
Time-dependent dielectric breakdown of SiO2 ®lms in a wide electric ®eld range A. Teramoto a,*, H. Umeda a, K. Azamawari b, K. Kobayashi c, K. Shiga a, J. Komori a, Y. Ohno a, A. Shigetomi a a
ULSI Development Center, Mitsubishi Electric Corporation, 4-1 Mizuhara, Itami, Hyogo 664-8641, Japan b TADA Electric Corporation, 4-1 Mizuhara, Itami, Hyogo 664-8641, Japan c Memory IC Division, Mitsubishi Electric Corporation, 4-1 Mizuhara, Itami, Hyogo 664-8641, Japan Received 30 March 2000; received in revised form 5 June 2000
Abstract We have performed time dependent dielectric breakdown measurement of SiO2 ®lms in the electric ®eld (EOX ) range 7±13.5 MV/cm and evaluated the electric ®eld dependence of intrinsic lifetime, using both area and temperature dependences of oxide lifetime. We have evaluated the electric ®eld dependence of time to breakdown (tBD ) below 125°C, because the activation energy of intrinsic lifetime changes at 125°C tBD of 7.1 and 9.6 nm oxides is not proportional to exp EOX but proportional to exp 1=EOX . This suggests that the breakdown mechanism of 9.6 and 7.1 nm oxides is the same and adheres to the anode hole injection model. However, the breakdown mechanism of 4.0 nm oxides is not the same as that of 7.1 and 9.6 nm oxides. The slope of log tBD versus 1=EOX plot in 4.0 nm oxide increases with decreasing oxide ®elds. The intrinsic lifetime in the positive gate bias decreases with increasing oxide thicknesses in the range of electric ®elds employed in the present experiment. Ó 2001 Elsevier Science Ltd. All rights reserved.
1. Introduction The time dependent dielectric breakdown (TDDB) of thin gate oxides is one of the most important reliability issues of MOS integrated circuits. For the prediction of oxide reliability, it is crucial to clarify the electric ®eld dependence of time to breakdown (tBD ). Several researchers have proposed many breakdown mechanisms from TDDB measurements [1±17]. According to the anode hole injection model, log tBD is proportional to 1=EOX [1±5,8]. Other researchers have reported that log tBD is proportional to EOX , in accordance with thermodynamic model [9,10]. The correct choice of this model is crucial because lifetime at device working conditions is usually obtained by extrapolating orders of magnitude in time from lifetime at accelerated stress test
*
Corresponding author. Tel.: +81-727-84-7355; fax: +81727-80-2675. E-mail address: [email protected] (A. Teramoto).
conditions. To clarify the ®eld dependence of the oxide lifetime at low electric ®elds, the TDDB measurements at the low electric ®elds are essential. The low electric ®eld measurements at high temperatures were performed by Suehle et al. [17] and McPherson et al. [18]. However, the activation energy of the lifetime changes at 125°C [19]. This suggests that the breakdown mechanism of oxides changes at 125°C. This means that the TDDB measurement at temperatures lower than 125°C is required. In this paper, we perform the TDDB measurement at temperatures lower than 125°C in a wide electric ®eld range in three years.
2. Experiment Fig. 1(A) and (B) shows the test structures of MOSFETs and MOS capacitor. p-Type (1 0 0) substrates with a resistivity of 8.5±11.5 X cm and n-type (1 0 0) substrates with a resistivity of 10±20 X cm were used in this study. MOSFETs in p-type substrate and
0026-2714/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 6 - 2 7 1 4 ( 0 0 ) 0 0 0 9 5 - 0
48
A. Teramoto et al. / Microelectronics Reliability 41 (2001) 47±52
Fig. 1. Test structures of MOS capacitor and MOSFET.
n-well and MOS capacitors in n-type substrate were fabricated with standard CMOS technology. Gate oxides with thicknesses ranging from 4.0 to 9.6 nm were grown using pyrogenic oxidation at 750°C. Gate electrodes were formed from in situ phosphorus-doped polysilicon. The gate oxide areas are 0.03, 0.1 and 10 mm2 . The measurement temperatures are 25°C and 125°C. The number of points in each TDDB evaluation are 100± 1000. The measurement oxide electric ®elds ranges from 7.0 to 13.5 MV/cm. The EOX values are de®ned by EOX VG ÿ VFB =TOX
Fig. 2. Weibull plots of 7.1 nm oxide. The sample area is 10 mm2 , and measurement temperature is 125°C.
1
for substrate accumulation and EOX VG ÿ VFB ÿ 2/F =TOX
2
for substrate inversion, respectively, where VG is the voltage applied to the gate electrode, VFB , the ¯at-band voltage, TOX , the gate oxide thickness, and /F , the Fermi potential in the substrate. Patrikar et al. reported that the degradation mechanism is dierent for stressing of ptype capacitors in inversion and that of n-type capacitors in accumulation [20]. However, we used two types test structure, i.e. p-type MOSFETs in inversion and that of n-type capacitors in accumulation, because the tBD s in both stresses are the same in this experiment. For measuring TDDB characteristics for a wide range of electric ®eld, we have taken about three years for testing.
3. Results and discussion 3.1. TDDB data Fig. 2 shows the Weibull plots at constant voltage TDDB measurement for 7.1 nm oxides. The sample area is 10 mm2 and the measurement temperature is 125°C. The distribution seems to be bimodal [21]. However, we are concerned with only the intrinsic breakdown region in this paper. For obtaining the TDDB characteristics at high ®elds, the TDDB measurements are performed for a small oxide area because of a voltage drop caused by series resistance. Current density (JG ) vs. electric ®eld (EOX ) of 7.1 nm oxides were measured for various oxide areas. Fig. 3 shows the Fowler±Nordheim plots for the
Fig. 3. Fowler±Nordheim (F±N) plots for the JG ±EOX data of 7.1 nm oxides.
JG ±EOX data. The F±N plots for 0.03 and 0.1 mm2 oxides show a straight line at EOX below 13.5 MV/cm. The JG ±EOX data above 13.5 MV/cm deviated from a straight line because of in¯uence of a voltage drop caused by series resistance. This indicates that we can evaluate the TDDB characteristics below 13.5 MV/cm without the in¯uence of the series resistance for 0.1 and 0.03 mm2 . Fig. 4(A) and (B) shows the Weibull plot for sample area of 0.03 mm2 , measurement temperature of 125°C, and EOX values of 12.0, 12.5 and 13.0 MV/cm and the Weibull plot for sample area of 0.1 mm2 , measurement temperature of 25°C, and EOX values of 12.5, 13.0 and 13.5 MV/cm, respectively.
A. Teramoto et al. / Microelectronics Reliability 41 (2001) 47±52
49
Fig. 4. (A) Weibull plots of 7.1 nm oxide: The sample area is 0.03 mm2 , and measurement temperature is 125°C. (B) Weibull plots of 7.1 nm oxide: The sample area is 0.1 mm2 , and measurement temperature is 25°C.
3.2. Area dependence Fig. 5 shows the Weibull plots of 6.9 nm oxides for sample areas of 10ÿ2 , 10ÿ4 , 10ÿ5 and 10ÿ6 mm2 . Here, let us make two assumptions that the breakdown of oxide in a wearout failure period occurs in a localized weak spot, and the distribution of the weak spot has a random distribution throughout the oxide area. Relation between the cumulative distribution function (F) and area (A) is expressed by the following equation: 1 ÿ F t expfÿAD tg;
3
where t is the time and D t is cumulative weak spot density at t. The cumulative distribution function, can then be normalized by the following equation: 1 ÿ F1 t f1 ÿ F2 tgA1 =A2 ;
4
where A1 and A2 are oxide areas, and F1 and F2 are the cumulative distribution functions at a stress time t for A1 and A2 , respectively. Fig. 6 shows the plots of the cumulative distribution function versus the stress time,
Fig. 6. The plots of cumulative distribution functions versus the stress time, where Eq. (4) was used to calculate the rate at 10ÿ6 mm2 for those cases featuring dierent oxide areas.
where the rate per 10ÿ6 mm2 was calculated from those for dierent oxide areas using Eq. (4). The rate for 10ÿ6 mm2 which were calculated from those dierent oxide areas using Eq. (4), are unique in the same oxide. This indicates that we can estimate the oxide lifetime for any oxide area by using Eq. (4). This coincides with the results in previous works [22,23]. 3.3. Temperature dependence
Fig. 5. Weibull plots of 6.9 nm oxide for sample area of 10ÿ2 , 10ÿ4 , 10ÿ5 , and 10ÿ6 mm2 .
It has been reported that the temperature dependence of the activation energy changes at 125°C [19]. Fig. 7 shows the Arrhenius plots obtained at electric ®elds of 9.0, 10.0, 11.0 and 12.5 MV/cm for the 7.1 nm oxides. The slopes of 9 and 10 MV/cm data change at 125°C. This means that activation energy changes at 125°C and suggests that the breakdown mechanism changes at 125°C. This means that the limit temperature under which we can discuss the breakdown mechanism is 125°C. In this paper, we study the TDDB characteristics under 125°C. The slope of this ®gure indicates that the
50
A. Teramoto et al. / Microelectronics Reliability 41 (2001) 47±52
electric ®eld at the temperatures ranging from 25°C to 125°C. Fig. 8 shows the activation energy as a function of the oxide ®eld. The activation energy (Ea ) is expressed by the following equation with the oxide ®eld: Ea 0:83 ÿ 0:049EOX :
5
3.4. Discussion
Fig. 7. Arrhenius plot obtained at electric ®elds of 9.0, 10.0, 11.0, 12.5, and 13.0 MV/cm for 7.1 nm oxides.
Fig. 8. Activation energy as a function of the oxide electric ®eld.
activation energy decreases with increasing oxide ®elds, i.e., the activation energy has a dependence on the
Fig. 9 shows the Weibull plots of 7.1 nm oxides for the sample area of 0.1 mm2 and the temperature of 125°C, translated from measurement data (shown in Figs. 2 and 4) using Eqs. (4) and (5). The wide electric ®eld range data (7.0±13.5 MV/cm) are shown in Fig. 9. The data at 12.5 and 13.0 MV/cm calculated from the measurement condition (Fig. 4(A)) are in complete agreement with those calculated from other measurement condition (Fig. 4(B)). This supports the view that Eqs. (4) and (5) can be applied to calculate the oxide lifetime. Fig. 10(A) and (B) shows the time to 4% failure of 7.1 nm oxides as a function of electric ®eld for sample areas of 0.1 mm2 and the temperature of 125°C. The log tBD is not proportional to EOX but proportional to 1=EOX . It has been reported that the breakdown mechanism at high ®eld stress is dierent from that at low ®eld stress [24] because the charge to breakdown value changed in a high ®eld region. However, the log tBD ±EOX relationship agrees with the 1=EOX model. This supports that the breakdown mechanism of 7.1 nm oxides in positive gate bias under 125°C adheres to the anode hole injection model [1±5,8]. The electric ®eld dependence of the intrinsic lifetime for positive gate bias of 7.1, 9.6 and 4.0 nm are also shown in Fig. 10(A) and (B). The log tBD of 9.6 nm oxide is also proportional to 1=EOX . This suggests that the breakdown mechanism of 9.6 nm oxide is the same as that of 7.1 nm oxide and adheres to the anode hole injection model. The slope of
Fig. 9. Weibull plots of 7.1 nm oxide for the sample area of 0.1 mm2 and temperature of 125°C, calculated from measurement data (Figs. 2 and 4) using Eqs. (4) and (5).
A. Teramoto et al. / Microelectronics Reliability 41 (2001) 47±52
51
4. Conclusions We have evaluated the intrinsic lifetime in a wide electric ®eld range at temperatures lower than 125°C, using the area dependence and temperature dependence on oxide lifetime. For positive gate bias, the log tBD of 7.1 and 9.6 nm oxides is not proportional to the electric ®eld but proportional to 1=EOX . This suggests that the breakdown mechanism of 9.6 nm oxide is the same as that of 7.1 nm oxide and adheres to the anode injection model. The breakdown mechanism of 4.0 nm is not the same as that of 7.1 and 9.6 nm oxides. The slope of log tBD versus 1=EOX plot in 4.0 nm oxide increases with decreasing oxide ®elds. The intrinsic lifetime in the positive gate bias decreases with increasing oxide thicknesses in the present experiment.
Acknowledgements The authors would like to thank Drs. H. Miyoshi and T. Nishimura for their continuous encouragement. The authors also wish to thank Dr. M. Inoue for the valuable discussions throughout this work.
References
Fig. 10. Time to 4% failure of 7.1, 9.6 and 4.0 nm oxides as a function of oxide electric ®eld ± the sample area is 0.1 mm2 , and temperature is 125°C: (A) log tBD ±1=EOX plot, (B) log tBD ± EOX plot.
log tBD versus 1=EOX plot in 4.0 nm oxide increases with decreasing oxide ®elds. It is suggested that the mechanism of 4.0 nm oxide is dierent from that of 7.1 and 9.6 nm oxides. However, more data are needed to discuss the breakdown mechanism of 4.0 nm oxide because the amount of data for 4.0 nm oxides is insucient.
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