A study of trapezoidal programming waveform for the FLOTOX EEPROM

Solid-Stare Eleclronics Vol. 36,No. 8,pp. 1093-1100, 1993 Printed in Great Britain. All rights reserved

0038-1101/93$6.00+ 0.00 Copyright C 1993 Pergamon Press Ltd

A STUDY OF TRAPEZOIDAL PROGRAMMING FOR THE FLOTOX EEPROM

WAVEFORM

SIK ON KONG and CHEE YEE KWOK School

of Electrical

Engineering,

University of New South Australia 2033

(Received 30 November

Wales,

PO Box 1, Kensington

1992; in revised form 6 February

NSW,

1993)

Abstract-An analysis of the effect of some different programming waveforms on the tunneling current and threshold voltage of the FLOTOX EEPROM is presented. Four waveforms have been considered: square, linear ramping, exponential and, a new proposal, trapezoidal. It is shown that the trapezoidal programming waveform is the only one which can produce a constant tunneling current, and therefore it is possible to optimize programming time and achieve tunneling field and current levels consistent with the objective of improving and long term reliability of FLOTOX EEPROM.

INTRODUCTION

It is widely acknowledged that programming window degradation in EEPROM devices is attributable to the build-up of bulk oxide charge in the thermal oxide[l,2]. This effect can occur even in high quality oxides, and depends on the field across and the current through an oxide. The field and current characteristics in the oxide depend on the shape of the programming waveform and the amount of charge residing in the floating gate as a result of Fowler-Nordheim (FN) tunneling. The traditional square programming waveform previously applied to EEPROM devices either produces a very large tunneling current spike at the start which degrades the oxide, in the case of high programming voltage, or an undesirable long programming time if the programming voltage is lowered. Bez[3], Yaron[4] and Wu[5] have proposed the use of a linear ramp, an exponential-rising or a triangular programming waveform as ways to reduce the peak field across the tunnel oxide in order to achieve long term reliability and minimize threshold voltage overshoot. However for those three waveforms, significant tunneling current occurs only after a delay when the programming voltage is sufficient to establish the field across the oxide required for FN tunneling. The higher the ramp rate, the shorter the delay but the higher the peak tunneling current. There is ample evidence that, high field stress and high level current injection, lead to trap generation in tunnel oxides, which result in programming window degradation. Hence, there is a trade-off between programming time and maintaining field/current levels commensurate with the desired long term reliability. In this paper, we focus on the effect of various types of programming waveforms on the shape of the tunneling current in the FLOTOX EEPROM for

both the write and erase operations. We propose a new trapezoidal waveform, and show that it has the advantage of optimizing the programming time and peak current. The results are based on a new computer simulation mode1 which will be presented in a future publication[6]. Earler models[7-91 have all assumed the application of a constant programming voltage pulse which enabled convenient explicit solutions to be obtained. Some work has been done to simulate other waveforms by numerical analysis[ IO]. Recently, the tunneling current with the linear ramping waveform has been measured experimentally[3]. A anomalous new current peak during the erase operation has been discovered, which cannot be explained by the previous models. The new model is developed to account for this phenomenon. Electron trapping in the tunnel oxide has not been included in this analysis. Four programming waveforms: the square, the linear-ramping, the exponential-rising and the proposed trapezoidal waveforms are considered in the computer simulations, of which the trapezoidal programming waveform is shown to be the preferred waveform to use because it can produce a constant tunneling current. The EEPROM parameters for simulation are listed in the Appendix. WRITE OPERATION

The simplified device structure and its corresponding capacitive equivalent circuit for the write operation is depicted in Fig. 1. During the write operation ( Vd = Vsub= 0), the tunneling current is described by the FN equation: I,,, = A,,,

c( . E2 exp

where c( and p are characteristic constants, A,,, is the tunneling area, and E is the electric field across the

SIK ON KONG and CHEE YEE KWOK

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gate oxide \

contro’ gate poly oxide

, field oxide

floatlng gate

Fig. 1. (a) Schematic structure of a FLOTOX EEPROM, (b) write operation equivalent circuit, (c) erase operation equivalent circuit. Cp,: poly to poly capacitance, C,: poly to drain overlap capacitance, C,““: tunnel window capacitance, C,,: poly to channel capacitance, Cpl: poly to source overlap capacitance and C,,: poly to field oxide overlap capacitance.

tunnel oxide. Using charge conversion, the tunnel voltage V,,, across the oxide at any given time t is [9]: Vt,,(t) = IL V&) + q

= EX,,,,

(2)

T

where k, denotes the write coupling ratio, (equal to C,,/C,) CT is the total capacitance, Q, is the floating gate charge, V,(t) is the write programming voltage, and X,,, is the tunnel oxide thickness. The rate of charge build-up in the floating-gate is defined in terms of the tunneling current Z,,, by:

In addition, the variation in the threshold voltage (V,,) seen from the control gate as a function of time is related to the amount of charge on the floating gate by t91: Vt,(t) =

vtiPr(r) )

(4)

LPP

where V, is the zero charge threshold voltage of the device, and C,, is the inter poly capacitanace. For the case where the programming waveform is a square pulse, V8is a constant, and eqns (l)-(4) can then be solved analytically to obtain an expression for vt,(t)[91: Kwlt) = Ki + vg

(5) For the cases of the linear ramp, exponential and trapezoidal programming waveforms, solutions for

the tunneling current and threshold voltage can only be obtained by numerical computation of eqns (l)-(4). Figure 2 shows the results of such a computation. The waveforms for the square, linear and exponential cases (Rl, R2 and R3 respectively in Fig. 2) have the same pulse width but the voltage levels have been chosen such that the change in V,, is the same. The parameters governing the shape of the trapezoidal programming waveform stem from the value chosen for the tunneling current, from which the field E required to sustain such a current is then obtained by the numerical solution of eqn (1). The initial programming voltage is then given by:

EL,

Vg’,(O) =-

k

+ [vtw(o)-

vtil,

w

The ramp rate of the trapezoidal waveform is chosen such that the tunneling current is kept constant. This can only occur if E is constant which means dV,,,ldt = 0. Applying this condition to eqns (1) and (2) gives the ramp rate R,:

R_+$

(7) PP This is similar to the equation for obtaining the peak tunneling current for a ramp programming waveform[3]. With the ramp rate given in eqn (7), the rate of increase in gate voltage compensates for the buildup of charge in the floating gate such that the tunnel field is kept constant. The pulse width of the trapezoidal waveform (t,) is determined from the required change in threshold voltage AV, by:

Trapezoidal programming waveform for EEPROM

1095

20 z

15

p

10 5

ta) 0.06 F * 0.04 s 3 5 0.02 s

4 2 E 3 5

0 -2 -4

0

1

2 Time (msec)

3

Fig. 2. (a) The four programming waveforms during the write operation: Vr = 13.2; Rl--square-pulse, Ve = 10,OOOt max. 13.44; RZ-linear ramp towards a constant value, Vg = 14[1 - exp( - f /0.0007)]; R3_exponentially-rising, Vg = 8.955 + (7096r), R&trapezoidal, (b) tunneling current density response (JtUnW)and (c) write threshold voltage response to the waveforms in (a).

The value of t, in R4 of Fig. 2 is chosen to give the same AV,, as in programming waveforms Rl-R3.

F++;, 4 =

ERASE OPERATION

The erase operation in FLOTOX EEPROM cells requires the control gate and substrate to be grounded, the source floated and a positive erasure pulse applied at the drain as shown in Fig. l(c). This transfers electrons from the floating gate to the drain by FN tunneling. The programming waveforms with the same ramping parameters as in Fig. 2(a) are applied to the drain. For the case of the trapezoidal waveform, the initial voltage [ Vd(0)], trapezoidal ramp rate (R,) and pulse width (t,) can be derived from the simple capacitive equivalent circuit model in Fig. l(c), that is:

(10)

PP

e

7AKe

c,, I

,“”

,

(11)

I

where k, is the erase coupling constant [equal to (C,, + C,, + C,, + C,,)/C,], and AV, is the threshold voltage change during the erase operation. However, the actual erasure process is far more complicated than that depicted in the simple equivalent circuit in Fig. l(c) and the simulation program takes into account the following additional mechanisms[3,9,11]: depletion in the n + drain below the tunnel oxide, generation of holes at the n + surface due to bandto-band tunneling, and generation of holes from the electron-hole pairs due to impact ionization arising from energetic tunneling electrons entering the silicon. The potential difference between the floating gate and the drain consists of the sum of the voltage across the tunnel oxide and the voltage drop across the depletion region in the n + drain.

SIK ON KONG and CHE

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RESULTS AND DISCUSSION

Examination of Fig. 2 reveals that the constant voltage in the square programming waveform (Rl) produces very large initial currents, and is strongly dependent on the programming voltage as suggested by eqn (1). Both the linear (R2) and exponential (R3) programming waveforms exhibit a much reduced peak current which occurs after a delay of about 1 ms. This delay can be reduced by increasing the ramp rates of R2 and R3, but this would be at the expense of a larger peak tunneling current. With the trapezoidal programming waveform (R4), both of the above problems are avoided as it creates a constant current and field in the tunnel oxide. The threshold voltage response curves reveal that a trapezoidal programming waveform achieves the desired V,w most rapidly, whereas, the other waveforms show an asymptotic approach toward the desired threshold value. Figure 3 shows the deviation in tunneling current and threshold voltage from their nominal values when the initial trapezoidal voltage V,(O) and trapezoidal ramp rate R, vary by + 10%. As expected from eqns (3) (4) and (7), the final to R, + 10% have values of V,, corresponding

YEE KWOK

roughly the same 10% variation, whereas with V,(O) + lo%, the final V,, deviates by as much as about 15%. This is explained by the tunneling current characteristics which show that the initial current increases by about 5 times for a + 10% change in V,(O) because of the FN relationship [eqn (l)]. The tunneling current rapidly decays to the nominal constant current values. For the purpose of comparison, the initial tunneling curent for the square programming waveform (Rl) in Fig. 2(b) is two or more orders of magnitude larger because V,(O) for RI in Fig. 2(b) is larger than V,(O) + 10% in Fig. 3(b). If V,(O) - 10% is taken as the nominal value so that the range of error is from 0% to -2O%, the initial current surge for the trapezoidal waveform can be avoided. In practice, all pulse waveforms have finite rise and fall times. The results of Fig. 4 show the tunneling current response to trapezoidal programming waveforms with finite rise and fall times, where this time has been approximated by simple ramps. Relatively large rise and fall times of - 100 1s have only a marginal effect on the shape of constant tunneling current density (J,,, = 0.03 A/cm*) but can be more pronounced at higher tunneling current density (J,,, = 0.15 A/cm’).

20 z

15

g? 10 5 0.16 T 2 V

0.10

3 5 0.05 r 4

E 3

2 0

r -2 -4 0.4

0.6

0.8

Time (msec) Fig. 3. (a) The effect of variation in the initial write voltage write programming

waveform

and (b) on the tunneling

V,(O) and ramp rate (R,) of the trapezoidal current density and (c) the threshold voltage.

Trapezoidal

programming

waveform

for EEPROM

-

20 J tun -0.15

7

15

9

10

A/cm2

rising

and

falling

5 0.20 0.15

; 2

0.10 3 5 0.05 <

@I

0.00

ktz

2.0

1.5

1.0

0.5

Time (msec) Fig. 4. (a) Write programming pulses with 0.1 ms rise and fall time for a target tunneling current J,,, = 0.03 and 0.15 A/cm2 and (b) its effect on the shape of the tunneling current density.

20 9 V >"

E

15 10 5

_

0.15

"E $ 0.10 V g 0.05 5 4 2 ZO ca >

2 -4 -6

0.0

0.5

1.0

1.5 Time

2.0

2.5

3.0

= A

3.5

(msec)

Fig. 5. (a) The four programming waveforms Rl-R4 same as in Fig. 2(a) during the erase operation, (b) tunneling current density response and (c) threshold voltage response.

SIK ON KONG and CHEEYEE KWOK

1098

0.20 G E 0.15 2 - 0.10 I $ 0.05 4 E

2

s-Q,

0 -2 -4

0.6 0.4 Time (msec)

0.8

Fig. 6. Changes in the (a) tunneling current density response and (b) threshold voltage response as a result of k 10% change in the initial value V,(O) of the trapezoidal erasure pulse applied to the drain.

Figure 5 shows the erasure tunneling current and threshold voltage responses to the same four programming waveforms used in the write operation.

Current peaks are prominent in all four waveforms and are similar in shape to the measured tunneling currents in Bez’s experiment[3]. The constant voltage erase pulse (Rl) produces a large peak current density (99 A/cm’) which can be attributed in part to the magnitude of the constant voltage and the erase coupling ratio. The trapezoidal programming voltage (R4) produces a current peak about five times its nominal “constant” current level. The occurrence of this peak is attributed to the collapse of the deep depletion region when sufficient numbers of holes are generated by the band-to-band tunneling and impact ionization processes[3,8]. This results in pinning down of the silicon surface potential, and hence, a greater proportion of the voltage difference between the floating gate and the drain appears across the tunnel oxide. In the case of the linear and exponential

ramp programming waveforms (R2 and R3), the peak tunneling current occurs when the voltage is sufficiently high to cause the collapse of the deep depletion. With the same set of programming waveforms as in the write operation, the AV, in Fig. 5(c) are in general greater than the corresponding AV,, in Fig. 2(c). Furthermore, the AV,, of different waveforms are not necessarily consistent. These results occur because k, is greater than k,. The erase threshold voltage response in Fig. 5(c) shows that the trapezoidal waveform produces the fastest response to the final threshold voltage. Fig. 6 shows the variations in the tunnel current density (.I,,,) and the threshold voltage (V,,) as a result of a f 10% variation of the initial drain voltage [Vd(0)] of a trapezoidal waveform. The nominal curve, V,(O) + O%, represents “constant current conditions” as described by eqns (9)-(11). Since the same trapezoidal ramp rate (R,) is maintained for different curves, the peak tunneling current remains

0.06

c 2E 0.06

Constant

current

ramping

< -

0.04 z 720.02

~“.“‘...“,‘.“.“‘.“.“‘,“““‘.““.I.’.

0.00 0

0.2

0.4 0.6 Time (msec)

0.8

1.0

Fig. 7. Suppression of the peak erasure tunnel current by increasing the doping in the drain.

Trapezoidal programming waveform for EEPROM

s

20

-

15

$

10

s

5

1099

Q 0.15 % 0.10 Y go.05 a 3 4

t

lkl

& 2 B 0 sf -2 “E $ g G z 2

0.5 0.4 0.3 0.2 0.1 4

b

El

_*! ;

1;

0.0

0.5

1.0 1.5 2.0 Time (msec)

2.5

3.0

3.5

V, = 14[1 -exp(-r/0.0001)]; E2-V,, Fig. 8. (a) Exponential programming waveforms: El-V,, V,, = 14[1 - exp( - r/0.0007)]; E&-V , Vd = 8.955 + 5.045[ I V,, = 14[1 -exp(-t/0.0004)]; E3-V,, exp( -t/O.OOCt4)], (b) the current density response and (c) the threshold vo Itage response during the write operation, (d) the current density response and (e) the threshold voltage response during the erase operation.

at about 2.5 times the constant current level, except when k’,(O) values are sufficiently large to rapidly initiate deep depletion collapse behavior. The shifts in time of the different current peaks from the peak of V,(O) + 10% imply a reduction of effective tunneling time, which results in a reduction of the erase threshold voltage change as seen in Fig. 6(b). Figure 7 shows the suppression of the peak tunneling current with increased n-dopant concentration (IV,,,). This results in a reasonably constant tunneling current[3]. This is because for higher N,,, , more holes need to be produced by impact ionization to collapse the deep depletion layer. Therefore, the rate of increase of the tunnel voltage due to the collapse of the deep depletion layer slows down[6], the rate of increase of J,,, reduces and the peak height is reduced.

Finally as a comparison to the trapezoidal waveform, Fig. 8 shows the tunneling current and responses to exponential threshold voltages waveforms of time constants 0.1 ms (El), 0.4 ms (E2), and 0.7ms (E3), for both the write and erase operations. It can be seen that the smaller the time constant, the larger the current peak, and therefore the faster the programming time. E4 is an exponential waveform with a dc. voltage superimposed on it. While it shows improvements in the programming time and/or peak current density when compared with El-E3, it is not trapezoidal waveform.

as well

optimized

as the

CONCLUSION

Simulations of the tunneling current and threshold voltage response to four different programming

SIK ON KONG and CHEE YEE KWOK

1100

waveforms have been presented. A new programming waveform: trapezoidal waveform is shown to produced constant tunneling current and field across the tunnel oxide during the write operation. The programming time is optimized since the delay between the programming waveform and the initial tunneling current is minimal Similar conditions can be achieved in the erase operation at high n + dopant concentration beneath the tunnel oxide. It is expected that such controlled “stress” on the tunnel oxide should improve the long term reliability of FLOTOX EEPROM devices.

Acknowledgements-Thanks are to be given to Dr Mark Gross for reading the manuscript and giving useful comments and to Dr Henry Chen for setting up and maintaining the computer system that this work is generated on.

REFERENCES 1. B. Euzent, N. Boruta, J. Lee and C. Jeng, IEEE/Proc. IRPS, p. 11 (1981). 2. C. Papadas, G. Ghibando, G. Pananakakis, C. Riwa and P. Ghezzi, IEEE Electron Device Letl. EDL-13, 89 (1992). 3. R. Bez, D. Cantarelli and P. Cappelletti, IEEE Trans. Elecfron Devices ED-37, 1081 (1990). 4. G. Yaron, S. J. Prasad, M. S. Ebel and M. B. K. Leong, J. Solid Sf. Circuits X-17, 833 (1982). 5. C. Wu and C. Chen, So/id-St. Electron. 35, 705 (1992). 6. S. 0. Kong and C. Y. Kwok, to be published. 7. P. I. Suciu, B. P. Cox, D. D. Rinerson and S. F. Cagnina, IDEM, p. 837 (1982). 8. A. Bhaltacharyya, Solid-St. Electron. 27, 899 (1984). 9. A. Kolodny, S. T. K. Nich, B. Citan and J. Shappir, IEEE Trans. Electron Devices ED-33, 835 (1986). 10. R. Bez, D. Cantarelli, P. Capelletti and F. Maggioni. J. Physique C4, 677-681 (1988). 11. M. S. Liang, C. Chang, Y. T. Yeow and C. Hu, IEEE Elecfron Device Letf. EDL-4, 350 (1983).

APPENDIX Basic Simulation Symbols A tun A PP A cll A, A,, x L”” x wn Xw X fox N ,“” N& ; k k, V,, (0) V,, (0) V..

Parameters

Names tunnel area poly-poly overlap area channel area control gatedrain overlap area control gate-source overlap area tunnel oxide thickness gate oxide thickness Inter-poly oxide thickness field oxide thickness tunnel area N-doping density channel area P-doping density Fowler-Nordheim constant (pre-exponential) Fowler-Hordheim constant (exponential) write operation coupling constant erase operation coupling constant threshold voltage before write operation threshold voltage before erase operation neutral cell threshold voltaae

Values 0.64 pm2 20.0 grn” 1.5 pm(L) x 2.5 pm(W) 4.36 pm2 1.25 pm2 8nm 40 nm 25 nm 0.7 pm 5 x 10’s crne3 1 x 10’6cm-) 3.69 x lo-’ AV-’ 223 MV cm-’ 0.709 0.832 -3.ov 3.0 v ov