- Email: [email protected]
Modeling charge variation during data retention of MLC Flash memories
Microelectronics Reliability 49 (2009) 1060–1063
Contents lists available at ScienceDirect
Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel
Modeling charge variation during data retention of MLC Flash memories J. Postel-Pellerin a,b,*, F. Lalande a,b, P. Canet a,b, R. Bouchakour a,b, F. Jeuland c, L. Morancho c a
Aix-Marseille Université, IM2NP, IMT Technopôle de Château-Gombert, 13451 Marseille, France CNRS IM2NP, Institut Matériaux Microélectronique et Nanosciences de Provence, UMR 6242, IMT Technopôle de Château-Gombert, 13451 Marseille, France c ATMEL Corporation, Device Engineering, ZI de Rousset 13106 Rousset, France b
a r t i c l e
i n f o
Article history: Received 11 June 2009 Available online 26 July 2009
a b s t r a c t In this paper, we propose to model charge variation in Multi-Level Cells in NOR Flash memories. We first define a sensitivity-to-temperature factor to determine the number of involved mechanisms. Then, according to previous studies, we can use the Poole–Frenkel (PF) and/or the Fowler–Nordheim (FN) equations to model every charge loss, which we apply to our cells. We succeed in modeling our data retention measurements by superimposing these two phenomena, being, respectively preponderant at the beginning and at the end of the data retention measurements, as shown by the factor of sensitivity-to-temperature. We have then found a relationship between temperatures to evaluate our cells lifetime. We validate that the classical 1/T Arrhenius law is not the most appropriate and that a T model can be better. We also model a fictive charge gain by using a negative charge front displacement in the tunnel oxide. This study can easily be extended to any floating gate non-volatile memory. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction
2. Determination of the number of involved mechanisms
To increase data stocked in NOR Flash memories, multi-level cells have been developed which save two, or more, bits per cell [1]. In our technology, we can define four levels instead of two, to store two bits per cell. These four levels are read as current levels that is why they have been chosen to be equally distributed in terms of current. These levels correspond to the four cell distributions represented in Fig. 1 as a function of threshold voltage VT. Adding two levels in a conventional Flash memory cell requires to better study data retention in order to ensure a good discrimination of the four levels, especially after cycling and retention phases. Before data retention measurements, we first apply a 100,000 cycling between (0 0) and (1 1) levels to damage the tunnel oxide and to increase the charge loss. The cell distributions become larger and can merge between different levels, causing failure of the cell and a loss of data. Fig. 2 shows the decrease of threshold voltage, i.e. the charge loss, for the four levels at 150 °C for 1200 h. We have chosen to use the Poole–Frenkel (PF) equation, linked to a trap current through the oxide, and the Fowler–Nordheim (FN) equation linked to a tunneling current through the oxide [2–5]. In the continuation of this study, we will use the (0 0) level curve to identify the involved mechanisms.
In order to highlight the number of involved mechanisms, we define the sensitivity U to temperature X of the charge loss during retention, as the ratio of threshold voltage shifts DVT between temperature X °C and 25 °C, formulated as follows:
* Corresponding author. Address: CNRS IM2NP, Institut Matériaux Microélectronique et Nanosciences de Provence, UMR 6242, IMT Technopôle de ChâteauGombert, 13451 Marseille, France. Tel.: +33 491 054 783; fax: +33 491 054 782. E-mail address: [email protected] (J. Postel-Pellerin).
BðTÞ IFN ¼ AðTÞ S E2ox exp Eox
0026-2714/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.microrel.2009.06.034
CðX CÞ ðtÞ ¼
DV TðX CÞ ðtÞ DV Tð25 CÞ ðtÞ
ð1Þ
Fig. 3 highlights two phenomena occurring before 200 h and after 200 h. The first mechanism is strongly amplified with temperature, by a factor 2.5–4 before 200 h. Then a second mechanism occurs after 200 h, less amplified with temperature by a factor 1.9– 2.5. After having shown the presence of two charge loss mechanisms, we have to identify them, what will be done in the following of this paper.
3. Modeling charge loss using PF and FN equations When plotting the measured (0 0) charge loss in the Fowler– Nordheim plot, i.e. lnðIFN =SE2ox Þ vs. 1/Eox, there should be a straight line if the phenomenon fits a Fowler–Nordheim equation as follows [6,7]:
ð2Þ
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J. Postel-Pellerin et al. / Microelectronics Reliability 49 (2009) 1060–1063
where Eox is the electric field across tunnel oxide, S is the cell area, A(T) and B(T) are the fitting parameters depending on temperature T.
We can notice in Fig. 4 that measurement fits a FN equation for high 1/E, i.e. low electric fields E, but not for high electric fields. Fig. 5 shows the modeling of the measured (0 0) curve using only FN equation. We can see that we have to use a second phenomenon to model the first part of the curve. We succeeded in fitting this part by using a PF equation, added to the previously determined FN equation. This PF equation is presented as follows:
IPF ¼ A0 ðTÞ S Eox exp q bPF ðTÞ
Fig. 1. The four cell distributions in our Multi-Level Cells.
Fig. 2. Variation of threshold voltage for the four levels at a 150 °C temperature for 1200 h.
E1=2 ox kT
! ð3Þ
where Eox is the electric field across tunnel oxide, S is the cell area, q is the elementary charge, k is the Boltzmann constant, A0 (T) and bPF(T) are the fitting parameters depending on temperature T. Fig. 6 shows the modeling of the measured (0 0) curve using both PF and FN equations. The whole (0 0) curve cannot be fitted neither by using only a FN equation nor using only a PF equation. PF equation is preponderant in the first 200 h whereas FN equation is preponderant for longer times. This shows that the first important charge loss corresponds to the detrapping of charges stocked in tunnel oxide during cycling. When all these charges are detrapped, the leaking current is a tunneling current type, through thin tunnel oxide. This result has also been validated for the three other levels (0 1), (1 0) and (1 1) stored in the memory cell. We also reproduce the same results for different retention temperatures from 25 °C to 150 °C. In every case, we can model the charge loss by a PF phenomenon superimposed to a FN mechanism. By erasing cells after cycling, using Ultraviolet radiation, all the charges stored in the floating gate and in the oxide are detrapped. When detrapping charges before data retention, we can model the whole charge loss by a single FN equation, available for any time as shown in Fig. 7.
Fig. 3. Sensitivity factor U, extracted at 150 °C temperature, showing two distinct mechanisms.
Fig. 5. Modeling charge loss using only FN equation.
Fig. 4. Fowler–Nordheim plot of the (0 0) level data retention curve.
Fig. 6. Modeling charge loss using both PF and FN equations.
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J. Postel-Pellerin et al. / Microelectronics Reliability 49 (2009) 1060–1063
Fig. 9. Modeling a fictive charge gain during data retention, using a negative front charge displacement from tunnel oxide to substrate. Fig. 7. Modeling charge loss of an UV erased cell, using only a FN equation.
T tretention ¼ t 0 exp T0
4. Relationship between temperatures After modeling the charge loss, the aim is to find a relationship between temperatures to extrapolate a retention lifetime at room temperature, based on a 15% charge loss. The classical law used to evaluate retention lifetime tretention is the Arrhenius law, defined as follows [8–11]:
t retention ¼ A exp
EA kT
ð4Þ
where A is an exponential prefactor, EA is the activation energy, k is the Boltzmann constant and T is the temperature. Some studies have shown that the 1/T Arrhenius law is not the most appropriate law because it is not physical and propose an alternative law [12–14]. We have chosen to check the relevance of these laws to extrapolate the cell lifetime and to compare results from the 1/T Arrhenius law and the T law proposed by DeSalvo et al., defined as follows [14]:
ð5Þ
where t0 is the lifetime at 0 K and T0 a characteristic temperature. Fig. 8 shows the 1/T Arrhenius law and the T law proposed by DeSalvo, applied to our multi-level cells data retention for (0 0), (0 1), (1 0) and (1 1) levels at four different temperatures, 25 °C, 85 °C, 125 °C and 150 °C. We can notice that the T law proposed by DeSalvo fits our extracted lifetimes better than the classical Arrhenius law. For the four levels, we extracted T0 10 K, which is close to the extracted value, T0 21 K, in [14]. 5. Modeling a fictive charge gain using a front charge model Another part in modeling the charge variation during retention measurements is that, when zooming the first hours of data retention, a fictive charge gain sometimes occurs, as represented in Fig. 9. We have chosen to use a negative front charge displacement to model this phenomenon [15].
Fig. 8. 1/T and T laws applied to our multi-level cells to estimate their lifetime.
J. Postel-Pellerin et al. / Microelectronics Reliability 49 (2009) 1060–1063
Using the kinetics described in (5), we can model this fictive charge gain, represented in Fig. 9.
xðtÞ ¼ ð2BÞ1 ln
ts t0
ð6Þ
with B = 3 109 m; s = 4 h; t0 = 1010 s and x(0) = tox/2. Our fictive charge gain corresponds to a front charge moving from the middle of tunnel oxide (x(0) = tox/2), with a 4-h-activation-delay s and a characteristic time t0 = 1010 s. When the negative charges come near the substrate, their impact on the threshold voltage screen decreases and this threshold voltage increases as if a charge gain were occurring. When the negative charges are out of the oxide the data retention measurement joins the typical data retention curve with a classical charge loss. 6. Conclusions When trying to store two bits per cell, data retention must be carefully studied to guarantee a good discrimination of the four logical levels. We first succeed in highlighting the number of involved mechanisms by defining a sensitivity-to-temperature factor. After having shown the presence of two mechanisms, we have developed a modeling of charge loss during data retention by superimposing a Poole–Frenkel (PF) and a Fowler–Nordheim (FN) equation, each being preponderant for low and for long times. This shows that we first detrap charges stocked in tunnel oxide during cycling and then a tunneling current is responsible for the slower charge loss. Then we demonstrate that the classical 1/T Arrhenius law is not the most appropriate one to evaluate the cell lifetime in retention and that a T model is more accurate. We also succeed in modeling a fictive charge gain, sometimes occurring in data retention measurements, by considering a negative front charge, moving from the middle of tunnel oxide to substrate.
1063
References [1] Dan R, Wong D, Enabling MLC NAND Flash for cost-effective, high-capacity data storage. In: IEEE Proceedings of NVMTS; 2002. [2] Bhattacharyya A. Modeling of write/erase and charge retention characteristics of floating gate EEPROM devices. Solid-State Electron 1984;27(10):899–906. [3] Kameyama H et al. A new data retention mechanism after endurance stress on flash memory. In: IEEE Proceedings of IRPS; 2000. [4] Ielmini D, Spinelli AS, Lacaita AL. Recent developments on flash memory reliability. Microelectron Eng 2005;80:321–8. [5] Cheng XR, Liu BY, Cheng YC. Electrical conduction in thin thermally nitrided SiO2. Appl Surf Sci 1987;30:237–43. [6] Fowler RH, Nordheim L. Electron emission in intense electric fields. Proc Soc London Ser A 1928;119(781):173–81. [7] Pananakakis G, Ghibaudo G, Kies R, Papadas C. Temperature dependence of the Fowler–Nordheim current in metal-oxide-degenerate semiconductor structures. J Appl Phys 1995;78:2635. [8] Pic D, Goguenheim D, Ogier JL. Assessment of temperature and voltage accelerating factors for 2.3–3.2 nm SiO2 thin oxides stressed to hard breakdown. Microelectron Reliab 2008;48:335–41. [9] Goguenheim D, Pic D, Ogier JL. Oxide reliability below 3 nm for advanced CMOS: issues, characterization and solutions. Microelectron Reliab 2007;47:1322–9. [10] Pic D, Goguenheim D, Ogier JL. A comprehensive study of stress induced leakage current using a floating gate structure for direct applications in EEPROM memories. Microelectron Reliab 2007;47:1373–7. [11] Foucher B, Boullié J, Meslet B, Das D. A review of reliability prediction methods for electronic devices. Microelectron Reliab 2002;42:1155–62. [12] Cheung KP. Thin gate oxide reliability – the current status:. [13] Dimaria DJ, Stathis JH. Non-Arrhenius temperature dependence of reliability in ultrathin silicon dioxide films. Appl Phys Lett 1999;74:1752–8. [14] DeSalvo B, Ghibaudo G, Pananakakis G, Reimbold G, Mondond F, Guillaumond B, et al. Experimental and theoretical investigation of non-volatile memory data retention. Trans Electron Dev 1999;46(7):1518. [15] Dumin DJ, Maddux JR, Scott RS, Subramoniam R. A model relating wearout induced physical changes in thin oxides to the statistical description of breakdown. In: IEEE proceedings of IRPS; 1993. p. 285.
Contents lists available at ScienceDirect
Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel
Modeling charge variation during data retention of MLC Flash memories J. Postel-Pellerin a,b,*, F. Lalande a,b, P. Canet a,b, R. Bouchakour a,b, F. Jeuland c, L. Morancho c a
Aix-Marseille Université, IM2NP, IMT Technopôle de Château-Gombert, 13451 Marseille, France CNRS IM2NP, Institut Matériaux Microélectronique et Nanosciences de Provence, UMR 6242, IMT Technopôle de Château-Gombert, 13451 Marseille, France c ATMEL Corporation, Device Engineering, ZI de Rousset 13106 Rousset, France b
a r t i c l e
i n f o
Article history: Received 11 June 2009 Available online 26 July 2009
a b s t r a c t In this paper, we propose to model charge variation in Multi-Level Cells in NOR Flash memories. We first define a sensitivity-to-temperature factor to determine the number of involved mechanisms. Then, according to previous studies, we can use the Poole–Frenkel (PF) and/or the Fowler–Nordheim (FN) equations to model every charge loss, which we apply to our cells. We succeed in modeling our data retention measurements by superimposing these two phenomena, being, respectively preponderant at the beginning and at the end of the data retention measurements, as shown by the factor of sensitivity-to-temperature. We have then found a relationship between temperatures to evaluate our cells lifetime. We validate that the classical 1/T Arrhenius law is not the most appropriate and that a T model can be better. We also model a fictive charge gain by using a negative charge front displacement in the tunnel oxide. This study can easily be extended to any floating gate non-volatile memory. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction
2. Determination of the number of involved mechanisms
To increase data stocked in NOR Flash memories, multi-level cells have been developed which save two, or more, bits per cell [1]. In our technology, we can define four levels instead of two, to store two bits per cell. These four levels are read as current levels that is why they have been chosen to be equally distributed in terms of current. These levels correspond to the four cell distributions represented in Fig. 1 as a function of threshold voltage VT. Adding two levels in a conventional Flash memory cell requires to better study data retention in order to ensure a good discrimination of the four levels, especially after cycling and retention phases. Before data retention measurements, we first apply a 100,000 cycling between (0 0) and (1 1) levels to damage the tunnel oxide and to increase the charge loss. The cell distributions become larger and can merge between different levels, causing failure of the cell and a loss of data. Fig. 2 shows the decrease of threshold voltage, i.e. the charge loss, for the four levels at 150 °C for 1200 h. We have chosen to use the Poole–Frenkel (PF) equation, linked to a trap current through the oxide, and the Fowler–Nordheim (FN) equation linked to a tunneling current through the oxide [2–5]. In the continuation of this study, we will use the (0 0) level curve to identify the involved mechanisms.
In order to highlight the number of involved mechanisms, we define the sensitivity U to temperature X of the charge loss during retention, as the ratio of threshold voltage shifts DVT between temperature X °C and 25 °C, formulated as follows:
* Corresponding author. Address: CNRS IM2NP, Institut Matériaux Microélectronique et Nanosciences de Provence, UMR 6242, IMT Technopôle de ChâteauGombert, 13451 Marseille, France. Tel.: +33 491 054 783; fax: +33 491 054 782. E-mail address: [email protected] (J. Postel-Pellerin).
BðTÞ IFN ¼ AðTÞ S E2ox exp Eox
0026-2714/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.microrel.2009.06.034
CðX CÞ ðtÞ ¼
DV TðX CÞ ðtÞ DV Tð25 CÞ ðtÞ
ð1Þ
Fig. 3 highlights two phenomena occurring before 200 h and after 200 h. The first mechanism is strongly amplified with temperature, by a factor 2.5–4 before 200 h. Then a second mechanism occurs after 200 h, less amplified with temperature by a factor 1.9– 2.5. After having shown the presence of two charge loss mechanisms, we have to identify them, what will be done in the following of this paper.
3. Modeling charge loss using PF and FN equations When plotting the measured (0 0) charge loss in the Fowler– Nordheim plot, i.e. lnðIFN =SE2ox Þ vs. 1/Eox, there should be a straight line if the phenomenon fits a Fowler–Nordheim equation as follows [6,7]:
ð2Þ
1061
J. Postel-Pellerin et al. / Microelectronics Reliability 49 (2009) 1060–1063
where Eox is the electric field across tunnel oxide, S is the cell area, A(T) and B(T) are the fitting parameters depending on temperature T.
We can notice in Fig. 4 that measurement fits a FN equation for high 1/E, i.e. low electric fields E, but not for high electric fields. Fig. 5 shows the modeling of the measured (0 0) curve using only FN equation. We can see that we have to use a second phenomenon to model the first part of the curve. We succeeded in fitting this part by using a PF equation, added to the previously determined FN equation. This PF equation is presented as follows:
IPF ¼ A0 ðTÞ S Eox exp q bPF ðTÞ
Fig. 1. The four cell distributions in our Multi-Level Cells.
Fig. 2. Variation of threshold voltage for the four levels at a 150 °C temperature for 1200 h.
E1=2 ox kT
! ð3Þ
where Eox is the electric field across tunnel oxide, S is the cell area, q is the elementary charge, k is the Boltzmann constant, A0 (T) and bPF(T) are the fitting parameters depending on temperature T. Fig. 6 shows the modeling of the measured (0 0) curve using both PF and FN equations. The whole (0 0) curve cannot be fitted neither by using only a FN equation nor using only a PF equation. PF equation is preponderant in the first 200 h whereas FN equation is preponderant for longer times. This shows that the first important charge loss corresponds to the detrapping of charges stocked in tunnel oxide during cycling. When all these charges are detrapped, the leaking current is a tunneling current type, through thin tunnel oxide. This result has also been validated for the three other levels (0 1), (1 0) and (1 1) stored in the memory cell. We also reproduce the same results for different retention temperatures from 25 °C to 150 °C. In every case, we can model the charge loss by a PF phenomenon superimposed to a FN mechanism. By erasing cells after cycling, using Ultraviolet radiation, all the charges stored in the floating gate and in the oxide are detrapped. When detrapping charges before data retention, we can model the whole charge loss by a single FN equation, available for any time as shown in Fig. 7.
Fig. 3. Sensitivity factor U, extracted at 150 °C temperature, showing two distinct mechanisms.
Fig. 5. Modeling charge loss using only FN equation.
Fig. 4. Fowler–Nordheim plot of the (0 0) level data retention curve.
Fig. 6. Modeling charge loss using both PF and FN equations.
1062
J. Postel-Pellerin et al. / Microelectronics Reliability 49 (2009) 1060–1063
Fig. 9. Modeling a fictive charge gain during data retention, using a negative front charge displacement from tunnel oxide to substrate. Fig. 7. Modeling charge loss of an UV erased cell, using only a FN equation.
T tretention ¼ t 0 exp T0
4. Relationship between temperatures After modeling the charge loss, the aim is to find a relationship between temperatures to extrapolate a retention lifetime at room temperature, based on a 15% charge loss. The classical law used to evaluate retention lifetime tretention is the Arrhenius law, defined as follows [8–11]:
t retention ¼ A exp
EA kT
ð4Þ
where A is an exponential prefactor, EA is the activation energy, k is the Boltzmann constant and T is the temperature. Some studies have shown that the 1/T Arrhenius law is not the most appropriate law because it is not physical and propose an alternative law [12–14]. We have chosen to check the relevance of these laws to extrapolate the cell lifetime and to compare results from the 1/T Arrhenius law and the T law proposed by DeSalvo et al., defined as follows [14]:
ð5Þ
where t0 is the lifetime at 0 K and T0 a characteristic temperature. Fig. 8 shows the 1/T Arrhenius law and the T law proposed by DeSalvo, applied to our multi-level cells data retention for (0 0), (0 1), (1 0) and (1 1) levels at four different temperatures, 25 °C, 85 °C, 125 °C and 150 °C. We can notice that the T law proposed by DeSalvo fits our extracted lifetimes better than the classical Arrhenius law. For the four levels, we extracted T0 10 K, which is close to the extracted value, T0 21 K, in [14]. 5. Modeling a fictive charge gain using a front charge model Another part in modeling the charge variation during retention measurements is that, when zooming the first hours of data retention, a fictive charge gain sometimes occurs, as represented in Fig. 9. We have chosen to use a negative front charge displacement to model this phenomenon [15].
Fig. 8. 1/T and T laws applied to our multi-level cells to estimate their lifetime.
J. Postel-Pellerin et al. / Microelectronics Reliability 49 (2009) 1060–1063
Using the kinetics described in (5), we can model this fictive charge gain, represented in Fig. 9.
xðtÞ ¼ ð2BÞ1 ln
ts t0
ð6Þ
with B = 3 109 m; s = 4 h; t0 = 1010 s and x(0) = tox/2. Our fictive charge gain corresponds to a front charge moving from the middle of tunnel oxide (x(0) = tox/2), with a 4-h-activation-delay s and a characteristic time t0 = 1010 s. When the negative charges come near the substrate, their impact on the threshold voltage screen decreases and this threshold voltage increases as if a charge gain were occurring. When the negative charges are out of the oxide the data retention measurement joins the typical data retention curve with a classical charge loss. 6. Conclusions When trying to store two bits per cell, data retention must be carefully studied to guarantee a good discrimination of the four logical levels. We first succeed in highlighting the number of involved mechanisms by defining a sensitivity-to-temperature factor. After having shown the presence of two mechanisms, we have developed a modeling of charge loss during data retention by superimposing a Poole–Frenkel (PF) and a Fowler–Nordheim (FN) equation, each being preponderant for low and for long times. This shows that we first detrap charges stocked in tunnel oxide during cycling and then a tunneling current is responsible for the slower charge loss. Then we demonstrate that the classical 1/T Arrhenius law is not the most appropriate one to evaluate the cell lifetime in retention and that a T model is more accurate. We also succeed in modeling a fictive charge gain, sometimes occurring in data retention measurements, by considering a negative front charge, moving from the middle of tunnel oxide to substrate.
1063
References [1] Dan R, Wong D, Enabling MLC NAND Flash for cost-effective, high-capacity data storage. In: IEEE Proceedings of NVMTS; 2002. [2] Bhattacharyya A. Modeling of write/erase and charge retention characteristics of floating gate EEPROM devices. Solid-State Electron 1984;27(10):899–906. [3] Kameyama H et al. A new data retention mechanism after endurance stress on flash memory. In: IEEE Proceedings of IRPS; 2000. [4] Ielmini D, Spinelli AS, Lacaita AL. Recent developments on flash memory reliability. Microelectron Eng 2005;80:321–8. [5] Cheng XR, Liu BY, Cheng YC. Electrical conduction in thin thermally nitrided SiO2. Appl Surf Sci 1987;30:237–43. [6] Fowler RH, Nordheim L. Electron emission in intense electric fields. Proc Soc London Ser A 1928;119(781):173–81. [7] Pananakakis G, Ghibaudo G, Kies R, Papadas C. Temperature dependence of the Fowler–Nordheim current in metal-oxide-degenerate semiconductor structures. J Appl Phys 1995;78:2635. [8] Pic D, Goguenheim D, Ogier JL. Assessment of temperature and voltage accelerating factors for 2.3–3.2 nm SiO2 thin oxides stressed to hard breakdown. Microelectron Reliab 2008;48:335–41. [9] Goguenheim D, Pic D, Ogier JL. Oxide reliability below 3 nm for advanced CMOS: issues, characterization and solutions. Microelectron Reliab 2007;47:1322–9. [10] Pic D, Goguenheim D, Ogier JL. A comprehensive study of stress induced leakage current using a floating gate structure for direct applications in EEPROM memories. Microelectron Reliab 2007;47:1373–7. [11] Foucher B, Boullié J, Meslet B, Das D. A review of reliability prediction methods for electronic devices. Microelectron Reliab 2002;42:1155–62. [12] Cheung KP. Thin gate oxide reliability – the current status: