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A new technique to characterize endurance of EEPROM tunnel oxides
Journal of Non-Crystalline Solids 351 (2005) 1890–1896 www.elsevier.com/locate/jnoncrysol
A new technique to characterize endurance of EEPROM tunnel oxides N. Baboux a
a,*
, C. Plossu a, P. Boivin
b
Laboratoire de Physique de la Matie`re, UMR CNRS 5511, Baˆt. Blaise Pascal, INSA de Lyon, 7 av. Jean Capelle, 69621 Villeurbanne cedex, France b STMicroelectronics, ZI Rousset, BP2, 13106 Rousset cedex, France Available online 31 May 2005
Abstract In this study, the critical parameters relevant to endurance of EEPROM memory cells are theoretically determined from cells geometrical design and programming pulses temporal shape. A new experimental technique is then proposed to realize realistic current pulsed stresses on dedicated large area cell test structures. The influence of the different relevant pulses parameters is finally experimentally studied and discussed. 2005 Elsevier B.V. All rights reserved. PACS: 85.30.De
1. Introduction It is well established [1,2] that the progressive closure of Electrically Erasable Programmable Read Only Memory (EEPROM) cells programming window is due to a negative charge trapping inside the tunnel oxide. This negative charge trapping induces a shift of the Fowler–Nordheim (FN) [3] tunneling law to larger voltages which affects FN electron injection into the floating gate during write and erase operations. In a previous work [2], these FN shifts have been quantitatively linked to threshold voltages variations of a memory cell in both written and erase states. To achieve a complete master of endurance reliability issue, that is to predict the programming window closure from intrinsic properties of the tunnel oxide, FN voltage shifts kinetics must be experimentally studied and parameterized for realistic device stress conditions.
Actually, FN voltage shifts kinetics was already studied in the case of constant current stress conditions [4], and a general model was established. Nevertheless, the stress suffered by EEPROM memory cells is essentially bipolar and thus the latter model is a priori not applicable. This fact was demonstrated in Ref. [5], whose authors compared oxide degradation in the case of constant voltage stress, unipolar and bipolar voltage pulse stresses. Unfortunately, the experimental setup used in that latter work did not allow to quantify the charge injected during pulse stress. In this work, we propose an original technique allowing to study quantitatively the endurance of tunnel oxide for realistic device stress conditions. Beforehand we are required to be able to describe precisely the tunnel oxide specific stress conditions during EEPROM programming operations.
2. Real device stress analysis *
Corresponding author. Tel.: +33 4 7243 8267; fax: +33 4 7243 6081. E-mail address: [email protected] (N. Baboux).
0022-3093/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2005.04.033
A schematic cross-section of a FLOating gate Thin OXide (FLOTOX) EEPROM memory [6] is given in
N. Baboux et al. / Journal of Non-Crystalline Solids 351 (2005) 1890–1896
Fig. 1. The floating gate (F) is capacitively coupled to the control gate (C) by the interpoly capacitance, CCF, to the bulk (B) through a Low Voltage (LV) oxide capacitance, CFB. Coupling to the drain (D) arises both through a LV capacitance, CFD,LV, and through a thin tunnel oxide capacitance, CFD,TUN. The most simple representation of this coupling is illustrated in Fig. 2 [7]. A variable resistor is added in parallel to the capacitance CFD,TUN to represent the path of electrons during cell programming. This electron flow is induced by Fowler–Nordheim tunneling injection to/from the floating gate through the tunnel oxide, and modulates the floating gate charge QF. High electric fields necessary for FN injection are obtained by application of a voltage pulse whose typical temporal shape is given in Fig. 3 [7], where
LV oxide
F (floating gate)
S
D (drain)
(source) B (bulk) Fig. 1. Schematic cross-section of a FLOTOX EEPROM cell.
C
QF,C F QF,D QF,B IFD
CFD,TUN
B
CFD,LV
D
Pulse voltage amplitude
Fig. 2. EEPROM cell electrical equivalent circuit.
Vpp
tpl
0
tr
QF ¼ AD V FD þ AC V FC þ AB V FB CT
ð1Þ
I FD dV FD dV FC dV FB þ AC þ AB ; ¼ AD CT dt dt dt
ð2Þ
QF represents the total floating gate charge given by the sum of elementary charges QFC, QFB and QFD associated to each coupling capacitance as illustrated in Fig. 2. IFD is the FN injected current, VFX the potential difference between the floating gate (F) and another terminal (X) and CT the total capacitance of the device (CT = CCF + CFB + CFD,TUN + CFD,LV). AX denotes the capacitive coupling coefficient between the floating gate (F) and terminal (X), defined by AX = CFX/CT. 2.1. Stress intensity
CCF
CFB
tr is the pulse rising time and Vpp the maximum voltage during plateau duration tpl. To erase the cell, the pulse is applied to the control gate (C) while other terminals are grounded. During the write operation, the same signal is applied to drain (D), while (B) and (C) are grounded and source (S) left floating. In the following and when appropriate, exponents ÔeÕ and ÔwÕ will be used to refer to these two programming operations. Considering all capacitances lossless and neglecting the work function differences between the constituent materials, the equations governing the state and time evolutions of the system can be deduced from the electrical equivalent circuit of Fig. 2. These are [7]
and
C (control gate) « tunnel » oxide
1891
time
tp
Fig. 3. Programming pulses temporal shape.
During both write and erase programming operations, the potential drop through the tunnel oxide satisfies the following equation, obtained by rearranging the terms of (2): dV FD dV CD I FD ¼ AP ; dt dt CT
ð3Þ
where AP stands for the ÔprogrammingÕ coupling coefficient. In the case of the erase operation during which the programming pulse is applied on the control gate, we have AP = AC while during the write operation, the voltage pulse is applied on the drain so that AP = 1 AD. By numerically solving Eq. (3) or by dedicated measurements [7], it can be shown that the FN current pulse induced during the programming phases has the typical temporal shape shown in Fig. 4: it mainly consists in a quasi-constant maximum current step until t = tr, followed by a decreasing current transient until t = tr + tpl. As the FN law is monotonic, the maximum injected current Imax occurs when the potential drop through the tunnel oxide reaches its maximum value Vmax. From (3), Imax value is then obtained by
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Fig. 4. Typical temporal shape of FN injected current during one programming cycle. Time integrations of current before and after tr represent DQmax and DQpl, respectively.
V FD ¼ V max
V pp . tr
ð4Þ
To discuss about the reliability of the tunnel oxide, the maximum current density, Jmax, is more appropriate. Introducing C STUN , the tunnel oxide capacitance per unit area, and AD,TUN, the floating gate to drain coupling coefficient through the tunnel oxide (AD,TUN = CFD,TUN/CT), we get J max ¼ C STUN
AP V pp . AD;TUN tr
ð5Þ
2.2. Stress progression The most evident parameter to discuss the total amount of stress is the number of write–erase cycles to which a particular memory cell has been subjected to. Actually the amount of charge that flows through the tunnel oxide in one semi-cycle (write or erase), whatever the injected electron direction, can be expressed as DQtot ¼ QwF QeF ;
ð6Þ
where QeF and QwF are the floating gate charges in erased and written states, which are directly related to the corresponding threshold voltages of the cell, V eth and V wth . Actually these threshold voltages correspond to the same floating gate potential, we have from (1) QwF QeF ¼ AC ðV eth V wth Þ ¼ AC PWtot ; CT
ð7Þ
where PWtot stands for the total programming window width. From (6) and (7), DQtot can be derived, but once again, an expression per unit area, DQStot is preferable DQStot ¼ C STUN
AC AD;TUN
PWtot .
DQSmax ¼ C STUN
AC PWmax ; AD;TUN
ð9Þ
where PWmax is the programming window corresponding to a pulse such that tpl = 0.
dV FD ¼0 () dt
) I max ¼ ðI FD ÞjV FD ¼V max ¼ C CF
programming cycle. Actually as shown in Fig. 4, for t > tr, the injected current features a rapid decrease. Whether the corresponding injected charge (referred hereafter as ÔplateauÕ charge), DQSpl , is negligible or not, compared to injected charge DQSmax before time tr, depends both on geometrical parameters via the capacitive coupling coefficients and on pulse plateau duration tpl. Whether this charge has an impact or not on the tunnel oxide degradation is also questionable. Therefore, it appears necessary to distinguish the amount of injected charge density at maximum current density, DQSmax , for t < tr. By analogy with (8), it comes
ð8Þ
Nevertheless, DQStot is given by the time integration of injected current, which intensity is not constant during a
3. Experimental An experimental study of endurance characteristics could be performed directly on a real memory cell. However, one would have to face with additional and specific problems arising from the miniaturization of the devices, namely a size optimized topology of the tunnel oxide, that renders cells behavior statistical. Moreover, at this scale, the coupling of the floating gate is complex and definition and validation of effective coupling coefficients are consequent tasks deserving a dedicated study [8]. To circumvent these potential issues, and as we are mainly interested in the intrinsic properties of the tunnel oxide, we have used a ÔmacroscopicÕ cell test structure, implemented in the scribe lines of a standard product wafer manufactured by STMicroelectronics, Rousset (France). It basically consists in a large area doublepolysilicon capacitive stack: N+ implanted drain (D) (doping level of 1.5 · 1025 m3); thin (8 nm) tunnel oxide surrounded by a thick (25 nm) gate oxide; polysilicon floating gate (F) (doping level of 4.5 · 1025 m3); ONO (SiO2/Si3N4/SiO2) interpoly dielectric; polysilicon control gate (C). The area of the tunnel oxide is 19 360 lm2, the total capacitance of the structure is 245 pF, the tunnel oxide areal capacitance is C STUN ¼ 4 107 F cm2, and the coupling coefficients are AC = 1 AD = 0.45 and AD,TUN = 0.33. Moreover the floating gate of the structure is connected to the gate of a NMOS transistor, which dimensions (W/L (lm) = 20/1.2) are negligible compared to those of the capacitive stack. This transistor called Ôsense transistorÕ is used to monitor indirectly the floating gate potential transients during programming operations as already shown in a previous work [2]. Thanks to the capacitive coupling of the floating gate with other terminals, these test structures allow to reproduce similar stress current pulses than in real memory cells.
N. Baboux et al. / Journal of Non-Crystalline Solids 351 (2005) 1890–1896
0.000
0.002
0.000
25
0.002
VCD (V)
-5 -10 -15 -20 -25 -30 -1 -2 -3 -4 -5 0
1
2
3
Time from pulse start (ms) Fig. 6. Programming current, IC, during write operations. Negative voltage pulses, VCD, are applied on the control gate, with three different values of tr (0.65, 1.3, 2.6 ms) and fixed Vpp (Vpp = 27 V).
e=w
DV þ= ¼ AC DV th .
ð10Þ
Furthermore, the total FN voltage shift can be defined as DVtot = DV+ DV. Each test structure was stressed by the application of N write–erase cycles in the range 106–107. The cycling was periodically interrupted and threshold voltage measurements were subsequently performed to determine programming windows, and corresponding amounts of elementary floating gate charges. Cumulated injected charge was evaluated using the relation: QS ðN Þ ¼ 2C STUN
30
VCD (V)
0
IC (µA)
The maximum current density of the current pulses, Jmax, was varied by modulating the ramp speed (Vpp/ tr) of applied voltage pulses. For a fixed ramp speed, different maximum amplitudes Vpp led to different amounts of injected charge density at maximum current density, DQSmax . In this work, different combinations of these parameters were tested, corresponding to Jmax ranging from 5.6 to 22.4 mA cm2. Owing to the large area of the test structures, direct measurements of the programming current IC have been achieved using a current–voltage converter and a digital scanning oscilloscope. An example of such recordings for three different values of tr (0.65, 1.3, 2.6 ms) at fixed Vpp (Vpp = 27 V) is given in Fig. 5, in the case of the erase operation. The two steps of the current signals IC correspond respectively to a displacement current and to the FN injected current through the tunnel oxide. It is observed that the maximum injected current increases with the voltage ramp speed. Moreover, values of these current maxima are in very good agreement with Eq. (4). Fig. 6 presents analog measurements in the case of the write operation, and the same remarks can be formulated. In addition, it is noted that for the fastest ramp speed, a current spike appears at the beginning of FN injection, which can be attributed to the occurrence of a deep depletion effect at the tunnel oxide–drain interface [4]. We will refer to this particularity in next section. FN law shifts DV+ and DV for positive and negative floating gate polarities respectively were monitored indirectly using the sense transistor of the test structure. They are related to threshold voltage shifts by [2]
1893
AC
N X
AD;TUN
n¼1
PWðnÞ.
ð11Þ
20 15
4. Results and discussion
10 5
4.1. General features
0
IC (µA)
4 3 2 1 0 0
1
2
3
Time from pulse start (ms) Fig. 5. Programming current, IC, during erase operations. Positive voltage pulses, VCD, are applied on the control gate, with three different values of tr (0.65, 1.3, 2.6 ms) and fixed Vpp (Vpp = 27 V).
A typical example of endurance characteristics is given in Fig. 7. FN voltage shifts DV+, DV and DVtot, have been plotted as a function of cumulated charge at maximum current. It is observed that positive and negative FN voltage shifts have comparable magnitudes, and that their evolution can be decomposed into two regimes: a fast transient followed by an almost linear variation. This behavior is frequently observed in the case of constant current stresses (CCS) (see e.g. [9]) and is usually interpreted as follows: the transient regime corresponds to the filling of native electron traps into the bulk oxide, whereas the linear regime results from the
1.0 ∆Vtot ∆V+ -∆V-
0.8 0.6 0.4
Jmax = 22.4 mA.cm-2
0.2
∆QSmax= 3.2µC.cm-2
0.0 0
10
20
30
40
50
60
70
total FN voltage shifts (V)
N. Baboux et al. / Journal of Non-Crystalline Solids 351 (2005) 1890–1896
FN voltage shifts (V)
1894
1.2
∆QSmax = 7.4 µC.cm-2
0.9 0.6
S
∆Qpl (µC.cm-2): 0 1.4 2 3.25
0.3 0.0
-2
cumulated charge @ max. current (C.cm )
0
25
50
75
100
125
150
cumulated charge @ max. current (C.cm-2)
Fig. 7. Typical endurance characteristics.
Fig. 9. Total FN voltage shifts as a function of cumulated injected charge at maximum current, QSmax , for different pulse plateau durations.
total FN voltage shifts (V)
instantaneous filling of newly generated traps whose creation rate would be proportional to injected charge. Since both the positive and negative FN shifts feature analog evolutions, DVtot, which is the sum of these two components shows also a quasi-linear increase. This simply linear behavior could be very interesting from the point of view of reliability prediction. Fig. 8 depicts a comparison between realistic alternative current stress and the more commonly used constant current stresses (CCS), for both positive and negative polarities. It is clear that these later are far more degrading than current pulsed stress, as already noted in the case of alternative voltage pulse stresses [5]. In particular, whereas the tunnel oxide breakdown occurs around a few tens of C cm2 in the case of CCS, it is not observed in the case of alternative current pulses, until at least 150 C cm2.
Jmax = 5.6 mA.cm-2
1.2
Jmax = 5.6 mA.cm-2 ∆QSmax= 7.4 µC.cm-2
0.9 0.6
∆QSpl (µC.cm-2) : 0 1.4 2 3.25
0.3 0.0 0
50
100
150
cumulated total charge
200
250
(C.cm-2)
Fig. 10. Total FN voltage shifts as a function of total cumulated injected charge, QStot , for different pulse plateau durations.
4.2. Influence of tpl
total FN voltage shifts (V)
In a first stage, the eventual influence of tpl, and thus of the corresponding injected charge during the plateau, DQSpl , was considered. To this aim, many cycling experiments were performed, fixing the maximum current density at Jmax = 5.6 mA cm2 and the amount of injected charge at maximum current density at DQSmax ¼ 5.4 lC cm2, while the plateau duration was varied between 0 and 10 ms, corresponding to amounts
1.2 1.0 0.8 0.6 0.4 0.2
breakdown breakdown Jmax = 10 mA.cm-2 Positive CCS Negative CCS Alternative stress
0.0 -20 0
20 40 60 80 100 120 140 160
cumulated charge @ max. current (C.cm-2) Fig. 8. Comparison of alternative current stress with constant positive and negative current stresses.
of injected charge during the plateau DQSpl ranging from 0 to 3.25 lC cm2. In Fig. 9, total FN voltages shifts are plotted versus accumulated charge at maximum current. As a dispersion of the different characteristics is observed, it can be concluded that the contribution of DQSpl to the degradation is not negligible at all. A dispersion is still noted when the characteristics are plotted as a function of the total cumulated charge density QStot , as illustrated in Fig. 10. It can therefore be stated that the DQSpl induced degradation is not strictly comparable to that induced by DQSmax . Finally, the characteristics were plotted as the function of the cumulated ÔplateauÕ charge QSpl in Fig. 11. In this case, the characteristics appear to converge towards a single curve, suggesting that degradation induced by injected charge during the pulses plateau could be described by only one function of a single parameter, the cumulated plateau charge QSpl . 4.3. Influence of DQSmax In a second step, we looked at the influence of DQSmax , whereas Jmax was kept constant. According to previous section, it was also mandatory to keep DQSpl constant by fixing tpl, and since QStot is not the only indicator of the
1.5
Jmax = 5.6 mA.cm-2
1.2
∆QSmax = 7.4 µC.cm-2
0.9 ∆QSpl (µC.cm-2) :
0.6
1.4 2 3.25
0.3 0.0 0
10
20
30
40
50
60
70
80
negative FN voltage shifts (V)
total FN voltage shifts (V)
N. Baboux et al. / Journal of Non-Crystalline Solids 351 (2005) 1890–1896
0.0
-0.1
∆QSmax (µC.cm-2) : 3.2 , 4.8 , 6.4 -0.2
0.6
∆V+
0.4 0.2
∆Q Smax(µC.cm-2) :
0.0
2.3 , 3.9 , 7.5
-0.2
∆V -
-0.4
FN voltage shifts (V)
-0.6 0.6
Jmax = 11.2 mA.cm-2
0.2
∆Q Smax (µC.cm-2) :
0.0
4.25 , 7.4
-0.2 -0.4 -0.6 0.6
∆V -
Jmax = 5.6 mA.cm-2 ∆V+
0.4 0.2
∆Q Smax(µC.cm-2) :
0.0
3.2 , 4.8 , 6.4
-0.2
0.1
1
10
Fig. 13. Negative FN voltage shifts data from Fig. 12, bottom, plotted in linear–logarithmic axis system.
the tunnel oxide negative charging begins. Moreover, for the greatest DQSmax , a positive charging is pointed out. Therefore, one should not obviously ascribe the dispersion to a modification of negative charging kinetics, but rather to the additional contribution of a varying positive charging phenomenon.
Finally, the potential effect of the maximum injected current density Jmax on the degradation process was investigated. Data of Fig. 12 suggest that the magnitude of FN voltages shifts depends on Jmax. This is better evidenced in Fig. 14, where the data are regrouped according to similar DQSmax . As the same trends were noted for both positive and negative voltage shifts, only the total FN shifts DVtot are plotted here. It is observed that only the characteristic corresponding to the highest Jmax
∆V -
-0.4 -0.6
1E-4 1E-3 0.01
cumulated charge @ max. current (C.cm-2)
4.4. Influence of Jmax
∆V+
0.4
∆V -
Jmax = 22.4 mA.cm-2
cumulated "plateau" charge (C.cm-2) Fig. 11. Total FN voltage shifts as a function of cumulated injected charge during the plateau, QSpl , for different pulse plateau durations.
1895
-2
Jmax = 22.4 mA.cm 0
25
50
75
1.2
100
cumulated charge @ max. current (C.cm-2)
stress progression, the FN voltage shifts characteristics were plotted versus QSmax . The results are given in Fig. 12, for three different maximum current densities. First, it is noted that the influence of DQSmax is asymmetric. Actually whereas positive FN voltage shifts seem not to be affected, a dispersion is observed in the case of negative FN voltage shifts. Furthermore, it is noted that this dispersion is due to a vertical translation of the linear parts of these negative characteristics. To clarify the origin of this effect, some of the above data were replotted in a linear–logarithmic axes system, as illustrated in Fig. 13. Here, it is noted that the greater DQSmax , the later
∆QSmax≈ 3.75 µC.cm-2
0.8
total FN voltages shifts (V)
Fig. 12. Evolution of endurance characteristics with the amount of cumulated injected charge at maximum current. From top to bottom, data are grouped according to increasing maximum injection current density.
1.0
0.6 0.4 0.2 0.0 1.2 1.0
Jmax = 5,6 mA.cm-2 Jmax = 11,2 mA.cm-2 Jmax = 22,4 mA.cm-2
∆QSmax≈ 7 µC.cm-2
0.8 0.6 0.4 0.2 0.0
Jmax = 5,6 mA.cm-2 Jmax = 11,2 mA.cm-2 Jmax = 22,4 mA.cm-2
-20 0 20 40 60 80 100 120 140 160
cumulated charge @ max. current (C.cm-2)
Fig. 14. Evolution of endurance characteristics with the maximum injected current. From top to bottom, data are grouped according to increasing constant charge amount at maximum current, DQSmax .
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N. Baboux et al. / Journal of Non-Crystalline Solids 351 (2005) 1890–1896
differs from the others, featuring a threshold phenomenon in the degradation process. Although this effect could be an intrinsic property of the degradation process, it is tempting to attribute it to the deep depletion effect observed during transient recordings (cf. Fig. 6) and that precisely occurs for the same maximum current density. Actually it is known that such current spikes can lead to an supplemental enhancement of the tunnel oxide degradation [10]. However, a clarification of this topic requires accumulation of more specific data.
5. Conclusion With the guideline of the prediction of memory cell endurance from the knowledge of the intrinsic properties of their constituent tunnel oxide, an analysis of the real device stress conditions has been carried out. It has been shown that during write–erase cycles, the tunnel oxide stress is better represented by alternative current pulses rather than by voltage pulses. Potential key parameters of this alternative current pulsed stress have been pointed out and linked to cell geometrical design, programming pulses temporal shape and measurable threshold voltages. The critical parameters are the maximum current density Jmax, the amount of injected charge DQSmax at maximum current density, and the amount of injected charge during the pulse plateau DQSpl . An experimental study was then conducted on a macroscopic cell. The main conclusions are the following ones: cumulated injected charge QSpl during pulses plateau has a non-negligible effect on the tunnel oxide charging phenomenon and therefore QStot is not a suffi-
cient parameter to assess the progression of the degradation. After a rapid transient, endurance characteristics feature a linear behavior. The slope of this linear increase depends only on Jmax, while its intercept would depend on DQSmax in the case of negative FN shifts. In view of these results, parametrization of the intrinsic endurance characteristics appears quite simple and thus prediction of real cell endurance seems feasible. However, due to the direct dependence of the cell endurance on coupling coefficients, a precise knowledge of the cell geometry is a mandatory step. As this task is not straightforward in the context of extreme device miniaturization, the extrapolation of our results obtained on macroscopic structures to real size memory cells deserves a dedicated study.
References [1] C. Papadas, G. Ghibaudo, G. Pananakakis, C. Riva, P. Ghezzi, IEEE Electron Dev. Lett. 13 (1992) 89. [2] N. Baboux, C. Busseret, C. Plossu, S. Burignat, B. Balland, P. Boivin, J. Non-Cryst. Solids 322 (2003) 240. [3] M. Lenzlinger, E. Snow, J. Appl. Phys. 40 (1969) 278. [4] G. Pananakakis, G. Ghibaudo, C. Papadas, E. Vincent, R. Kies, J. Appl. Phys. 82 (1997) 2548. [5] R. Rodrı´guez, M. Nafrı´a, J. Su˜ne´, X. Aymerich, IEEE Trans. Electron. Dev. 45 (1998) 881. [6] W.D. Brown, J. Brewer, Nonvolatile Semiconductor Memory Technology, IEEE, New York, 1998. [7] R. Bez, D. Cantarelli, P. Cappelletti, IEEE Trans. Electron. Dev. 37 (1990) 1081. [8] R. Duane, A. Concannon, P. OÕSullivan, M. OÕShea, A. Mathewson, Solid-State Electron. 45 (2001) 235. [9] C. Busseret, N. Baboux, C. Plossu, S. Burignat, P. Boivin, J. Non-Cryst. Solids 322 (2003) 191. [10] F. Pio, E. Gomiero, Solid-State Electron. 45 (2001) 1279.
A new technique to characterize endurance of EEPROM tunnel oxides N. Baboux a
a,*
, C. Plossu a, P. Boivin
b
Laboratoire de Physique de la Matie`re, UMR CNRS 5511, Baˆt. Blaise Pascal, INSA de Lyon, 7 av. Jean Capelle, 69621 Villeurbanne cedex, France b STMicroelectronics, ZI Rousset, BP2, 13106 Rousset cedex, France Available online 31 May 2005
Abstract In this study, the critical parameters relevant to endurance of EEPROM memory cells are theoretically determined from cells geometrical design and programming pulses temporal shape. A new experimental technique is then proposed to realize realistic current pulsed stresses on dedicated large area cell test structures. The influence of the different relevant pulses parameters is finally experimentally studied and discussed. 2005 Elsevier B.V. All rights reserved. PACS: 85.30.De
1. Introduction It is well established [1,2] that the progressive closure of Electrically Erasable Programmable Read Only Memory (EEPROM) cells programming window is due to a negative charge trapping inside the tunnel oxide. This negative charge trapping induces a shift of the Fowler–Nordheim (FN) [3] tunneling law to larger voltages which affects FN electron injection into the floating gate during write and erase operations. In a previous work [2], these FN shifts have been quantitatively linked to threshold voltages variations of a memory cell in both written and erase states. To achieve a complete master of endurance reliability issue, that is to predict the programming window closure from intrinsic properties of the tunnel oxide, FN voltage shifts kinetics must be experimentally studied and parameterized for realistic device stress conditions.
Actually, FN voltage shifts kinetics was already studied in the case of constant current stress conditions [4], and a general model was established. Nevertheless, the stress suffered by EEPROM memory cells is essentially bipolar and thus the latter model is a priori not applicable. This fact was demonstrated in Ref. [5], whose authors compared oxide degradation in the case of constant voltage stress, unipolar and bipolar voltage pulse stresses. Unfortunately, the experimental setup used in that latter work did not allow to quantify the charge injected during pulse stress. In this work, we propose an original technique allowing to study quantitatively the endurance of tunnel oxide for realistic device stress conditions. Beforehand we are required to be able to describe precisely the tunnel oxide specific stress conditions during EEPROM programming operations.
2. Real device stress analysis *
Corresponding author. Tel.: +33 4 7243 8267; fax: +33 4 7243 6081. E-mail address: [email protected] (N. Baboux).
0022-3093/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2005.04.033
A schematic cross-section of a FLOating gate Thin OXide (FLOTOX) EEPROM memory [6] is given in
N. Baboux et al. / Journal of Non-Crystalline Solids 351 (2005) 1890–1896
Fig. 1. The floating gate (F) is capacitively coupled to the control gate (C) by the interpoly capacitance, CCF, to the bulk (B) through a Low Voltage (LV) oxide capacitance, CFB. Coupling to the drain (D) arises both through a LV capacitance, CFD,LV, and through a thin tunnel oxide capacitance, CFD,TUN. The most simple representation of this coupling is illustrated in Fig. 2 [7]. A variable resistor is added in parallel to the capacitance CFD,TUN to represent the path of electrons during cell programming. This electron flow is induced by Fowler–Nordheim tunneling injection to/from the floating gate through the tunnel oxide, and modulates the floating gate charge QF. High electric fields necessary for FN injection are obtained by application of a voltage pulse whose typical temporal shape is given in Fig. 3 [7], where
LV oxide
F (floating gate)
S
D (drain)
(source) B (bulk) Fig. 1. Schematic cross-section of a FLOTOX EEPROM cell.
C
QF,C F QF,D QF,B IFD
CFD,TUN
B
CFD,LV
D
Pulse voltage amplitude
Fig. 2. EEPROM cell electrical equivalent circuit.
Vpp
tpl
0
tr
QF ¼ AD V FD þ AC V FC þ AB V FB CT
ð1Þ
I FD dV FD dV FC dV FB þ AC þ AB ; ¼ AD CT dt dt dt
ð2Þ
QF represents the total floating gate charge given by the sum of elementary charges QFC, QFB and QFD associated to each coupling capacitance as illustrated in Fig. 2. IFD is the FN injected current, VFX the potential difference between the floating gate (F) and another terminal (X) and CT the total capacitance of the device (CT = CCF + CFB + CFD,TUN + CFD,LV). AX denotes the capacitive coupling coefficient between the floating gate (F) and terminal (X), defined by AX = CFX/CT. 2.1. Stress intensity
CCF
CFB
tr is the pulse rising time and Vpp the maximum voltage during plateau duration tpl. To erase the cell, the pulse is applied to the control gate (C) while other terminals are grounded. During the write operation, the same signal is applied to drain (D), while (B) and (C) are grounded and source (S) left floating. In the following and when appropriate, exponents ÔeÕ and ÔwÕ will be used to refer to these two programming operations. Considering all capacitances lossless and neglecting the work function differences between the constituent materials, the equations governing the state and time evolutions of the system can be deduced from the electrical equivalent circuit of Fig. 2. These are [7]
and
C (control gate) « tunnel » oxide
1891
time
tp
Fig. 3. Programming pulses temporal shape.
During both write and erase programming operations, the potential drop through the tunnel oxide satisfies the following equation, obtained by rearranging the terms of (2): dV FD dV CD I FD ¼ AP ; dt dt CT
ð3Þ
where AP stands for the ÔprogrammingÕ coupling coefficient. In the case of the erase operation during which the programming pulse is applied on the control gate, we have AP = AC while during the write operation, the voltage pulse is applied on the drain so that AP = 1 AD. By numerically solving Eq. (3) or by dedicated measurements [7], it can be shown that the FN current pulse induced during the programming phases has the typical temporal shape shown in Fig. 4: it mainly consists in a quasi-constant maximum current step until t = tr, followed by a decreasing current transient until t = tr + tpl. As the FN law is monotonic, the maximum injected current Imax occurs when the potential drop through the tunnel oxide reaches its maximum value Vmax. From (3), Imax value is then obtained by
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Fig. 4. Typical temporal shape of FN injected current during one programming cycle. Time integrations of current before and after tr represent DQmax and DQpl, respectively.
V FD ¼ V max
V pp . tr
ð4Þ
To discuss about the reliability of the tunnel oxide, the maximum current density, Jmax, is more appropriate. Introducing C STUN , the tunnel oxide capacitance per unit area, and AD,TUN, the floating gate to drain coupling coefficient through the tunnel oxide (AD,TUN = CFD,TUN/CT), we get J max ¼ C STUN
AP V pp . AD;TUN tr
ð5Þ
2.2. Stress progression The most evident parameter to discuss the total amount of stress is the number of write–erase cycles to which a particular memory cell has been subjected to. Actually the amount of charge that flows through the tunnel oxide in one semi-cycle (write or erase), whatever the injected electron direction, can be expressed as DQtot ¼ QwF QeF ;
ð6Þ
where QeF and QwF are the floating gate charges in erased and written states, which are directly related to the corresponding threshold voltages of the cell, V eth and V wth . Actually these threshold voltages correspond to the same floating gate potential, we have from (1) QwF QeF ¼ AC ðV eth V wth Þ ¼ AC PWtot ; CT
ð7Þ
where PWtot stands for the total programming window width. From (6) and (7), DQtot can be derived, but once again, an expression per unit area, DQStot is preferable DQStot ¼ C STUN
AC AD;TUN
PWtot .
DQSmax ¼ C STUN
AC PWmax ; AD;TUN
ð9Þ
where PWmax is the programming window corresponding to a pulse such that tpl = 0.
dV FD ¼0 () dt
) I max ¼ ðI FD ÞjV FD ¼V max ¼ C CF
programming cycle. Actually as shown in Fig. 4, for t > tr, the injected current features a rapid decrease. Whether the corresponding injected charge (referred hereafter as ÔplateauÕ charge), DQSpl , is negligible or not, compared to injected charge DQSmax before time tr, depends both on geometrical parameters via the capacitive coupling coefficients and on pulse plateau duration tpl. Whether this charge has an impact or not on the tunnel oxide degradation is also questionable. Therefore, it appears necessary to distinguish the amount of injected charge density at maximum current density, DQSmax , for t < tr. By analogy with (8), it comes
ð8Þ
Nevertheless, DQStot is given by the time integration of injected current, which intensity is not constant during a
3. Experimental An experimental study of endurance characteristics could be performed directly on a real memory cell. However, one would have to face with additional and specific problems arising from the miniaturization of the devices, namely a size optimized topology of the tunnel oxide, that renders cells behavior statistical. Moreover, at this scale, the coupling of the floating gate is complex and definition and validation of effective coupling coefficients are consequent tasks deserving a dedicated study [8]. To circumvent these potential issues, and as we are mainly interested in the intrinsic properties of the tunnel oxide, we have used a ÔmacroscopicÕ cell test structure, implemented in the scribe lines of a standard product wafer manufactured by STMicroelectronics, Rousset (France). It basically consists in a large area doublepolysilicon capacitive stack: N+ implanted drain (D) (doping level of 1.5 · 1025 m3); thin (8 nm) tunnel oxide surrounded by a thick (25 nm) gate oxide; polysilicon floating gate (F) (doping level of 4.5 · 1025 m3); ONO (SiO2/Si3N4/SiO2) interpoly dielectric; polysilicon control gate (C). The area of the tunnel oxide is 19 360 lm2, the total capacitance of the structure is 245 pF, the tunnel oxide areal capacitance is C STUN ¼ 4 107 F cm2, and the coupling coefficients are AC = 1 AD = 0.45 and AD,TUN = 0.33. Moreover the floating gate of the structure is connected to the gate of a NMOS transistor, which dimensions (W/L (lm) = 20/1.2) are negligible compared to those of the capacitive stack. This transistor called Ôsense transistorÕ is used to monitor indirectly the floating gate potential transients during programming operations as already shown in a previous work [2]. Thanks to the capacitive coupling of the floating gate with other terminals, these test structures allow to reproduce similar stress current pulses than in real memory cells.
N. Baboux et al. / Journal of Non-Crystalline Solids 351 (2005) 1890–1896
0.000
0.002
0.000
25
0.002
VCD (V)
-5 -10 -15 -20 -25 -30 -1 -2 -3 -4 -5 0
1
2
3
Time from pulse start (ms) Fig. 6. Programming current, IC, during write operations. Negative voltage pulses, VCD, are applied on the control gate, with three different values of tr (0.65, 1.3, 2.6 ms) and fixed Vpp (Vpp = 27 V).
e=w
DV þ= ¼ AC DV th .
ð10Þ
Furthermore, the total FN voltage shift can be defined as DVtot = DV+ DV. Each test structure was stressed by the application of N write–erase cycles in the range 106–107. The cycling was periodically interrupted and threshold voltage measurements were subsequently performed to determine programming windows, and corresponding amounts of elementary floating gate charges. Cumulated injected charge was evaluated using the relation: QS ðN Þ ¼ 2C STUN
30
VCD (V)
0
IC (µA)
The maximum current density of the current pulses, Jmax, was varied by modulating the ramp speed (Vpp/ tr) of applied voltage pulses. For a fixed ramp speed, different maximum amplitudes Vpp led to different amounts of injected charge density at maximum current density, DQSmax . In this work, different combinations of these parameters were tested, corresponding to Jmax ranging from 5.6 to 22.4 mA cm2. Owing to the large area of the test structures, direct measurements of the programming current IC have been achieved using a current–voltage converter and a digital scanning oscilloscope. An example of such recordings for three different values of tr (0.65, 1.3, 2.6 ms) at fixed Vpp (Vpp = 27 V) is given in Fig. 5, in the case of the erase operation. The two steps of the current signals IC correspond respectively to a displacement current and to the FN injected current through the tunnel oxide. It is observed that the maximum injected current increases with the voltage ramp speed. Moreover, values of these current maxima are in very good agreement with Eq. (4). Fig. 6 presents analog measurements in the case of the write operation, and the same remarks can be formulated. In addition, it is noted that for the fastest ramp speed, a current spike appears at the beginning of FN injection, which can be attributed to the occurrence of a deep depletion effect at the tunnel oxide–drain interface [4]. We will refer to this particularity in next section. FN law shifts DV+ and DV for positive and negative floating gate polarities respectively were monitored indirectly using the sense transistor of the test structure. They are related to threshold voltage shifts by [2]
1893
AC
N X
AD;TUN
n¼1
PWðnÞ.
ð11Þ
20 15
4. Results and discussion
10 5
4.1. General features
0
IC (µA)
4 3 2 1 0 0
1
2
3
Time from pulse start (ms) Fig. 5. Programming current, IC, during erase operations. Positive voltage pulses, VCD, are applied on the control gate, with three different values of tr (0.65, 1.3, 2.6 ms) and fixed Vpp (Vpp = 27 V).
A typical example of endurance characteristics is given in Fig. 7. FN voltage shifts DV+, DV and DVtot, have been plotted as a function of cumulated charge at maximum current. It is observed that positive and negative FN voltage shifts have comparable magnitudes, and that their evolution can be decomposed into two regimes: a fast transient followed by an almost linear variation. This behavior is frequently observed in the case of constant current stresses (CCS) (see e.g. [9]) and is usually interpreted as follows: the transient regime corresponds to the filling of native electron traps into the bulk oxide, whereas the linear regime results from the
1.0 ∆Vtot ∆V+ -∆V-
0.8 0.6 0.4
Jmax = 22.4 mA.cm-2
0.2
∆QSmax= 3.2µC.cm-2
0.0 0
10
20
30
40
50
60
70
total FN voltage shifts (V)
N. Baboux et al. / Journal of Non-Crystalline Solids 351 (2005) 1890–1896
FN voltage shifts (V)
1894
1.2
∆QSmax = 7.4 µC.cm-2
0.9 0.6
S
∆Qpl (µC.cm-2): 0 1.4 2 3.25
0.3 0.0
-2
cumulated charge @ max. current (C.cm )
0
25
50
75
100
125
150
cumulated charge @ max. current (C.cm-2)
Fig. 7. Typical endurance characteristics.
Fig. 9. Total FN voltage shifts as a function of cumulated injected charge at maximum current, QSmax , for different pulse plateau durations.
total FN voltage shifts (V)
instantaneous filling of newly generated traps whose creation rate would be proportional to injected charge. Since both the positive and negative FN shifts feature analog evolutions, DVtot, which is the sum of these two components shows also a quasi-linear increase. This simply linear behavior could be very interesting from the point of view of reliability prediction. Fig. 8 depicts a comparison between realistic alternative current stress and the more commonly used constant current stresses (CCS), for both positive and negative polarities. It is clear that these later are far more degrading than current pulsed stress, as already noted in the case of alternative voltage pulse stresses [5]. In particular, whereas the tunnel oxide breakdown occurs around a few tens of C cm2 in the case of CCS, it is not observed in the case of alternative current pulses, until at least 150 C cm2.
Jmax = 5.6 mA.cm-2
1.2
Jmax = 5.6 mA.cm-2 ∆QSmax= 7.4 µC.cm-2
0.9 0.6
∆QSpl (µC.cm-2) : 0 1.4 2 3.25
0.3 0.0 0
50
100
150
cumulated total charge
200
250
(C.cm-2)
Fig. 10. Total FN voltage shifts as a function of total cumulated injected charge, QStot , for different pulse plateau durations.
4.2. Influence of tpl
total FN voltage shifts (V)
In a first stage, the eventual influence of tpl, and thus of the corresponding injected charge during the plateau, DQSpl , was considered. To this aim, many cycling experiments were performed, fixing the maximum current density at Jmax = 5.6 mA cm2 and the amount of injected charge at maximum current density at DQSmax ¼ 5.4 lC cm2, while the plateau duration was varied between 0 and 10 ms, corresponding to amounts
1.2 1.0 0.8 0.6 0.4 0.2
breakdown breakdown Jmax = 10 mA.cm-2 Positive CCS Negative CCS Alternative stress
0.0 -20 0
20 40 60 80 100 120 140 160
cumulated charge @ max. current (C.cm-2) Fig. 8. Comparison of alternative current stress with constant positive and negative current stresses.
of injected charge during the plateau DQSpl ranging from 0 to 3.25 lC cm2. In Fig. 9, total FN voltages shifts are plotted versus accumulated charge at maximum current. As a dispersion of the different characteristics is observed, it can be concluded that the contribution of DQSpl to the degradation is not negligible at all. A dispersion is still noted when the characteristics are plotted as a function of the total cumulated charge density QStot , as illustrated in Fig. 10. It can therefore be stated that the DQSpl induced degradation is not strictly comparable to that induced by DQSmax . Finally, the characteristics were plotted as the function of the cumulated ÔplateauÕ charge QSpl in Fig. 11. In this case, the characteristics appear to converge towards a single curve, suggesting that degradation induced by injected charge during the pulses plateau could be described by only one function of a single parameter, the cumulated plateau charge QSpl . 4.3. Influence of DQSmax In a second step, we looked at the influence of DQSmax , whereas Jmax was kept constant. According to previous section, it was also mandatory to keep DQSpl constant by fixing tpl, and since QStot is not the only indicator of the
1.5
Jmax = 5.6 mA.cm-2
1.2
∆QSmax = 7.4 µC.cm-2
0.9 ∆QSpl (µC.cm-2) :
0.6
1.4 2 3.25
0.3 0.0 0
10
20
30
40
50
60
70
80
negative FN voltage shifts (V)
total FN voltage shifts (V)
N. Baboux et al. / Journal of Non-Crystalline Solids 351 (2005) 1890–1896
0.0
-0.1
∆QSmax (µC.cm-2) : 3.2 , 4.8 , 6.4 -0.2
0.6
∆V+
0.4 0.2
∆Q Smax(µC.cm-2) :
0.0
2.3 , 3.9 , 7.5
-0.2
∆V -
-0.4
FN voltage shifts (V)
-0.6 0.6
Jmax = 11.2 mA.cm-2
0.2
∆Q Smax (µC.cm-2) :
0.0
4.25 , 7.4
-0.2 -0.4 -0.6 0.6
∆V -
Jmax = 5.6 mA.cm-2 ∆V+
0.4 0.2
∆Q Smax(µC.cm-2) :
0.0
3.2 , 4.8 , 6.4
-0.2
0.1
1
10
Fig. 13. Negative FN voltage shifts data from Fig. 12, bottom, plotted in linear–logarithmic axis system.
the tunnel oxide negative charging begins. Moreover, for the greatest DQSmax , a positive charging is pointed out. Therefore, one should not obviously ascribe the dispersion to a modification of negative charging kinetics, but rather to the additional contribution of a varying positive charging phenomenon.
Finally, the potential effect of the maximum injected current density Jmax on the degradation process was investigated. Data of Fig. 12 suggest that the magnitude of FN voltages shifts depends on Jmax. This is better evidenced in Fig. 14, where the data are regrouped according to similar DQSmax . As the same trends were noted for both positive and negative voltage shifts, only the total FN shifts DVtot are plotted here. It is observed that only the characteristic corresponding to the highest Jmax
∆V -
-0.4 -0.6
1E-4 1E-3 0.01
cumulated charge @ max. current (C.cm-2)
4.4. Influence of Jmax
∆V+
0.4
∆V -
Jmax = 22.4 mA.cm-2
cumulated "plateau" charge (C.cm-2) Fig. 11. Total FN voltage shifts as a function of cumulated injected charge during the plateau, QSpl , for different pulse plateau durations.
1895
-2
Jmax = 22.4 mA.cm 0
25
50
75
1.2
100
cumulated charge @ max. current (C.cm-2)
stress progression, the FN voltage shifts characteristics were plotted versus QSmax . The results are given in Fig. 12, for three different maximum current densities. First, it is noted that the influence of DQSmax is asymmetric. Actually whereas positive FN voltage shifts seem not to be affected, a dispersion is observed in the case of negative FN voltage shifts. Furthermore, it is noted that this dispersion is due to a vertical translation of the linear parts of these negative characteristics. To clarify the origin of this effect, some of the above data were replotted in a linear–logarithmic axes system, as illustrated in Fig. 13. Here, it is noted that the greater DQSmax , the later
∆QSmax≈ 3.75 µC.cm-2
0.8
total FN voltages shifts (V)
Fig. 12. Evolution of endurance characteristics with the amount of cumulated injected charge at maximum current. From top to bottom, data are grouped according to increasing maximum injection current density.
1.0
0.6 0.4 0.2 0.0 1.2 1.0
Jmax = 5,6 mA.cm-2 Jmax = 11,2 mA.cm-2 Jmax = 22,4 mA.cm-2
∆QSmax≈ 7 µC.cm-2
0.8 0.6 0.4 0.2 0.0
Jmax = 5,6 mA.cm-2 Jmax = 11,2 mA.cm-2 Jmax = 22,4 mA.cm-2
-20 0 20 40 60 80 100 120 140 160
cumulated charge @ max. current (C.cm-2)
Fig. 14. Evolution of endurance characteristics with the maximum injected current. From top to bottom, data are grouped according to increasing constant charge amount at maximum current, DQSmax .
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differs from the others, featuring a threshold phenomenon in the degradation process. Although this effect could be an intrinsic property of the degradation process, it is tempting to attribute it to the deep depletion effect observed during transient recordings (cf. Fig. 6) and that precisely occurs for the same maximum current density. Actually it is known that such current spikes can lead to an supplemental enhancement of the tunnel oxide degradation [10]. However, a clarification of this topic requires accumulation of more specific data.
5. Conclusion With the guideline of the prediction of memory cell endurance from the knowledge of the intrinsic properties of their constituent tunnel oxide, an analysis of the real device stress conditions has been carried out. It has been shown that during write–erase cycles, the tunnel oxide stress is better represented by alternative current pulses rather than by voltage pulses. Potential key parameters of this alternative current pulsed stress have been pointed out and linked to cell geometrical design, programming pulses temporal shape and measurable threshold voltages. The critical parameters are the maximum current density Jmax, the amount of injected charge DQSmax at maximum current density, and the amount of injected charge during the pulse plateau DQSpl . An experimental study was then conducted on a macroscopic cell. The main conclusions are the following ones: cumulated injected charge QSpl during pulses plateau has a non-negligible effect on the tunnel oxide charging phenomenon and therefore QStot is not a suffi-
cient parameter to assess the progression of the degradation. After a rapid transient, endurance characteristics feature a linear behavior. The slope of this linear increase depends only on Jmax, while its intercept would depend on DQSmax in the case of negative FN shifts. In view of these results, parametrization of the intrinsic endurance characteristics appears quite simple and thus prediction of real cell endurance seems feasible. However, due to the direct dependence of the cell endurance on coupling coefficients, a precise knowledge of the cell geometry is a mandatory step. As this task is not straightforward in the context of extreme device miniaturization, the extrapolation of our results obtained on macroscopic structures to real size memory cells deserves a dedicated study.
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