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Programming window degradation in flotox EEPROM cells
Microelectronic Engineering 15 (1991) 621-624 Elsevier
PROGRAMMING
WINDOW
DEGRADATION
621
IN F L O T O X E E P R O M
CELLS
C. Papadas a, G. Ghibaudo a, G. Pananakakis a, C. Riva b and P. Ghezzi b
aLPCS/ENSERG, URA CNRS 840, BP 257, 38016 Grenoble, FRANCE. bSGS-THOMSON Microelectrouics, Via C. Olivetti, 2, 20041 Agrate Brianza, ITALY.
Abstract A theoretical model explaining the programming window degradation as a function of the number of Write/Erase cycles in FLOTOX EEPROM cells is proposed. The collapsing of the programming window is quantitatively related to the oxide charge build-up in the FLOTOX tunnel region as the cycling number increases. The simplicity of the model permits a direct application at CAD level to be expected.
1. INTRODUCTION Much works in the literature deal with the programming window degradation in FLOTOX EEPROM structures, but up to now there is no simple formulation of the physical processes responsible for the window closing as the number of Write/Erase cycles increases [1-3]. This is generally attributed to the oxide charge build-up in the injection region as the cycling goes on, but no analytic expression exists. In this paper, a simple model which correlates quantitatively the window degradation in FLOTOX EEPROM cells and the build-up of oxide charge in the tunnel oxide region during the cycling is presented. In the following, the term write (erase) operation stands for storage of negative (positive) charge in the floating gate.
2. M O D E L
The capacitive equivalent circuit of a FLOTOX EEPROM cell is represented in Fig. 1 (a). In Fig 1 (b) is shown the equivalent circuit of the floating gate to drain tunnel capacitor with bulk oxide charge Qox whose centroid is located at a distance Xb from the silicon-dioxide interface. Q1 and Q2 are the charges at the floating gate plate of the capacitor Cfx and at the drain plate of the capacitor Cxd, respectively. Cpp, Cb and Cfd denote the coupling, the floating gate to substrate and tunnel oxide capacitances, respectively. Based on this equivalent circuit, and, from charge conservation and potential continuity equations, it is straight forward to show that the floating gate voltage Vfg can be expressed in terms of drain voltage Vd, control gate voltage Vcg, floating gate charge Qfg and oxide charge Qox as follows 0167-9317/91/$3.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved.
622
C. Papadas et aL / Programming window degradation
v ¢cj
Vfg
V
t,.
/
_
Fig. 1 : (a) Capacitive equivalent circuit of a FLOTOX EEPROM cell, (b) capacitive equivalent circuit of the floating gate to drain electrode capacitor accounting for the presence of build-up oxide charge.
C;fx
_
/
Cic >
Qox
Cxd
-I(a)
°,
Vd
Vd (b)
Vfg= Ag Vcg-k-Ad VdW ~
AdaeoxXb Qox
(1), where a is the tunnel injection area, Cox the dielectric constant of SiO2, Ct is the total capacitance (=Cpp+Cb+Cfd), A n is the control gate coupling ratio (=Cpp/Ct) and Ad is the drain coupIing ratio (=Cfd]Ct). . . . . . . . For a constant programming voltage pulse (without rising eage) ana assuming ~na~ Qox remains nearly constant during one W / E cycle, Rel. 1 enables the total floating gate charge swept in one W / E period to be evaluated as :
w/e
qfg = * ~
a e
Jr
w/e
w/e
(Emln-E~ax)
(2),
w/e
where E=ax,=in is the maximum/minimum electric field during the W / E operation. The positive (negative) sign stands for the write (erase) operation. W/ e • . , . It ]s clear from (2) that the floating gate charge shift, AQfg , due to an incremental oxide charge build-up, AQox, depends essentially on the shift of the max/rain electric field at each injection electrode. Following Bhattacharyya's calculations [2], while assuming a F - N injection current law, it can be shown that, for typical EEPROM cell parameters, any shift in the maximum field, AE=ax, due to oxide charge build-up, does not influence the value of the minimum electric field at the end of the programming pulse for both write and erase operations. This feature is supported by the observation that only the maximum injection current of the EEPROM cell is affected by charge trapping after cycling, while the current at the end of the pulse remains almost unchanged as evidenced in Fig. 2. 10 2 W/E
E
cy¢l
e
num
be rl
=
Ag=O
Fig. 2 : Experimental transient variations of the tunnel injection current I (normalized to Cpp) demonstrating the influence of W / E cycling on the maximum current• The dashed line shows the shape taken for the dynamic stress applied to tunnel oxide capacitors.
75,
101
>
o 0. U
--
1o s
lO °
lo
-1
i o
.5
i
,,
I
1 time
,
,
,
,
I
1 .s (ms)
i
B
t
C. Papadas et al. / Programming window degradation
623
Therefore, the shift of the floating gate charge principally arises from the maximum electric field change : = • a Cox AEmax / Ad (3). w]e From the Gauss law at the drain or floating gate electrodes (Fig. 1 (b)), AEmax can be expressed as: w,e 1 a~I/2 AE~ax : - a Cox" 0Qox AQox (4). According to Fig. 1 (b), Ql=---Cfd/Cxd.Qox+Cfd(Vfg-Vd) and QI+Q2=--Qox, the shifts of the high and low state threshold voltages of the EEPROM structure, AVthh and AVlth, can finally be related to the oxide charge shift using (3) and (4) as : h A Q ~ -- I i - - ( 1 - - A d ) X b 1 AQ°x (5.a), AVth:-Cpp . tfd ~ Ad Cpp e
AVlth= g = tfdb (1--Ad)A QC:p where tfd is the thickness of the tunnel oxide layer. Hence, the programming window degradation is given by : h 1 Aqox (6). AWp= AVthV t h = A d Cpp
2. RESULTS AND DISCUSSION The single--poly FLOTOX EEPROM cells investigated have been fabricated by SGS-Thomson Microelectronics in the context of the "Advanced PROM Building Blocks" ESPRIT project, tfd is about 8.5 nm, Ag is ranging between 0.7 and 0.8 and CppiS in the range 30 to 50 fF. The EEPROM structures were stressed up to 108---107 write/erase cycles with programming voltage pulses of amplitude 14 V, rise and hold times of 1 ms. During the write (erase) operation the programmation pulse was applied to the control gate (source and drain) of the structure, while the other terminals of the device were grounded. The programming window degradation was monitored by measuring the high and low threshold voltages versus the number of W/E cycles. As threshold voltage of the cell is defined the Vcg for which the Id=10 #A when Vds=l V. Fig. 3 shows typical endurance characteristics of the cells for various gate coupling ratios. After 107 W/E cycles, AWp is about 60 % for the devices with Ag=0.75. According to Rels. 7 and 8, the oxide charge build-up Qox and the corresponding centroid Xb of the tunnel oxide can therefore be evaluated as a function of the number of W/E cycles or more physically as a function of the total injected charge Qinj forced to pass through the tunnel oxide area. Qinj is calculated from the Vth h and Vth 1 data by summing all the charges which transfer from the drain to the floating gate and vice versa as the number of W/E cycles increases. The outputs of this treatment are shown in Fig. 4 (solid lines). At the early stage of stress, positive charge build-up seems to occur, while at high injection levels negative charge trapping prevails. The corresponding centroid lies around the middle of the oxide layer, as expected in such alternative stress condition. The programming window opening (collapsing) can be interpreted by positive (negative) bulk oxide charge build-up (Fig. 3).
624
C. Papadas et aL / Programming window degradation
o.s
o
•...-
.......
::::~::-
:..~
~t
( ms
) -
U
3
O.6
2
0 w
1
X
o.7
0
,,
o.~
:> o
x
-1
EEPROM
-;z
•
lO °
I
,
I
,
lO 2 n u m b l r
I
,
I
l O Jq~ of
W/l~
i
I
lO 6 cycl
e~
Fig. 3 : Typical endurance characteristics V t h v e r s u s number of W/E cycles as obtained on FLOTOX EEPROM cells with different coupling ratios.
i
I
lO -~
,
Ag--O.
I
i
I
7~,
,
I
lO-2 Qlnj(
f
I
lO ° C/cm2
10
2
)
Fig. 4 : Qox and xb]tfd variations with Qinj as obtained from EEPROM endurance data (solid lines) and dynamically stressed tunnel oxide capacitors with two pulse durations At = 0.2 and 0.3 ms (dashed lines).
In order to confirm the previous analysis, dynamic stressing experiments have been conducted on tunnel oxide capacitors on n+ substrate for simulating the degradation during W / E operations. Tunnel capacitors with similar oxide characteristics have been stressed with alternative constant voltage pulses. The pulse amplitude has been chosen in order to have an injection current density close to the maximum actual value for the EEPROM cell i.e. 20-30 mA/cm2 (dashed line in Fig. 2). The oxide charge Qox and the corresponding centroid xb/tfd have been evaluated as a function of stress from AVfn ÷, AVfn- data using classical formulas [4]. The centroid has been found to lie around the middle of the tunnel oxide as in the case of EEPROM's. As can be seen from Fig.4, the variations of Qox with the injection dose obtained on the capacitors are in very good agreement with the oxide charge build-up deduced from the EEPROM analysis. This emphasizes the consistency of our model and puts forwards the necessity to optimize the tunnel oxide quality for improving the EEPROM reliability.
4. CONCLUSION A model explaining the programming window degradation and the high and low state threshold voltage shifts as a function of W / E cycle number in FLOTOX EEPROM's has been presented. Analytical relations which correlate the programming window collapse and the oxide charge build-up in the tunnel area have been derived. 1. 2. 3. 4.
B. A. A. D.
Euzent et al, Proc. 19th Annu. Reliability Phys. Syrup., p. 11 (1981) Bhattacharyya, Solid State Electron., 27, 899 (1984) Kolodny et al, IEEE Trans. Electron Devices, ED-33, 835 (1986) J. DiMaria, J. Appl. Phys., 47, 4073 (1976).
PROGRAMMING
WINDOW
DEGRADATION
621
IN F L O T O X E E P R O M
CELLS
C. Papadas a, G. Ghibaudo a, G. Pananakakis a, C. Riva b and P. Ghezzi b
aLPCS/ENSERG, URA CNRS 840, BP 257, 38016 Grenoble, FRANCE. bSGS-THOMSON Microelectrouics, Via C. Olivetti, 2, 20041 Agrate Brianza, ITALY.
Abstract A theoretical model explaining the programming window degradation as a function of the number of Write/Erase cycles in FLOTOX EEPROM cells is proposed. The collapsing of the programming window is quantitatively related to the oxide charge build-up in the FLOTOX tunnel region as the cycling number increases. The simplicity of the model permits a direct application at CAD level to be expected.
1. INTRODUCTION Much works in the literature deal with the programming window degradation in FLOTOX EEPROM structures, but up to now there is no simple formulation of the physical processes responsible for the window closing as the number of Write/Erase cycles increases [1-3]. This is generally attributed to the oxide charge build-up in the injection region as the cycling goes on, but no analytic expression exists. In this paper, a simple model which correlates quantitatively the window degradation in FLOTOX EEPROM cells and the build-up of oxide charge in the tunnel oxide region during the cycling is presented. In the following, the term write (erase) operation stands for storage of negative (positive) charge in the floating gate.
2. M O D E L
The capacitive equivalent circuit of a FLOTOX EEPROM cell is represented in Fig. 1 (a). In Fig 1 (b) is shown the equivalent circuit of the floating gate to drain tunnel capacitor with bulk oxide charge Qox whose centroid is located at a distance Xb from the silicon-dioxide interface. Q1 and Q2 are the charges at the floating gate plate of the capacitor Cfx and at the drain plate of the capacitor Cxd, respectively. Cpp, Cb and Cfd denote the coupling, the floating gate to substrate and tunnel oxide capacitances, respectively. Based on this equivalent circuit, and, from charge conservation and potential continuity equations, it is straight forward to show that the floating gate voltage Vfg can be expressed in terms of drain voltage Vd, control gate voltage Vcg, floating gate charge Qfg and oxide charge Qox as follows 0167-9317/91/$3.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved.
622
C. Papadas et aL / Programming window degradation
v ¢cj
Vfg
V
t,.
/
_
Fig. 1 : (a) Capacitive equivalent circuit of a FLOTOX EEPROM cell, (b) capacitive equivalent circuit of the floating gate to drain electrode capacitor accounting for the presence of build-up oxide charge.
C;fx
_
/
Cic >
Qox
Cxd
-I(a)
°,
Vd
Vd (b)
Vfg= Ag Vcg-k-Ad VdW ~
AdaeoxXb Qox
(1), where a is the tunnel injection area, Cox the dielectric constant of SiO2, Ct is the total capacitance (=Cpp+Cb+Cfd), A n is the control gate coupling ratio (=Cpp/Ct) and Ad is the drain coupIing ratio (=Cfd]Ct). . . . . . . . For a constant programming voltage pulse (without rising eage) ana assuming ~na~ Qox remains nearly constant during one W / E cycle, Rel. 1 enables the total floating gate charge swept in one W / E period to be evaluated as :
w/e
qfg = * ~
a e
Jr
w/e
w/e
(Emln-E~ax)
(2),
w/e
where E=ax,=in is the maximum/minimum electric field during the W / E operation. The positive (negative) sign stands for the write (erase) operation. W/ e • . , . It ]s clear from (2) that the floating gate charge shift, AQfg , due to an incremental oxide charge build-up, AQox, depends essentially on the shift of the max/rain electric field at each injection electrode. Following Bhattacharyya's calculations [2], while assuming a F - N injection current law, it can be shown that, for typical EEPROM cell parameters, any shift in the maximum field, AE=ax, due to oxide charge build-up, does not influence the value of the minimum electric field at the end of the programming pulse for both write and erase operations. This feature is supported by the observation that only the maximum injection current of the EEPROM cell is affected by charge trapping after cycling, while the current at the end of the pulse remains almost unchanged as evidenced in Fig. 2. 10 2 W/E
E
cy¢l
e
num
be rl
=
Ag=O
Fig. 2 : Experimental transient variations of the tunnel injection current I (normalized to Cpp) demonstrating the influence of W / E cycling on the maximum current• The dashed line shows the shape taken for the dynamic stress applied to tunnel oxide capacitors.
75,
101
>
o 0. U
--
1o s
lO °
lo
-1
i o
.5
i
,,
I
1 time
,
,
,
,
I
1 .s (ms)
i
B
t
C. Papadas et al. / Programming window degradation
623
Therefore, the shift of the floating gate charge principally arises from the maximum electric field change : = • a Cox AEmax / Ad (3). w]e From the Gauss law at the drain or floating gate electrodes (Fig. 1 (b)), AEmax can be expressed as: w,e 1 a~I/2 AE~ax : - a Cox" 0Qox AQox (4). According to Fig. 1 (b), Ql=---Cfd/Cxd.Qox+Cfd(Vfg-Vd) and QI+Q2=--Qox, the shifts of the high and low state threshold voltages of the EEPROM structure, AVthh and AVlth, can finally be related to the oxide charge shift using (3) and (4) as : h A Q ~ -- I i - - ( 1 - - A d ) X b 1 AQ°x (5.a), AVth:-Cpp . tfd ~ Ad Cpp e
AVlth= g = tfdb (1--Ad)A QC:p where tfd is the thickness of the tunnel oxide layer. Hence, the programming window degradation is given by : h 1 Aqox (6). AWp= AVthV t h = A d Cpp
2. RESULTS AND DISCUSSION The single--poly FLOTOX EEPROM cells investigated have been fabricated by SGS-Thomson Microelectronics in the context of the "Advanced PROM Building Blocks" ESPRIT project, tfd is about 8.5 nm, Ag is ranging between 0.7 and 0.8 and CppiS in the range 30 to 50 fF. The EEPROM structures were stressed up to 108---107 write/erase cycles with programming voltage pulses of amplitude 14 V, rise and hold times of 1 ms. During the write (erase) operation the programmation pulse was applied to the control gate (source and drain) of the structure, while the other terminals of the device were grounded. The programming window degradation was monitored by measuring the high and low threshold voltages versus the number of W/E cycles. As threshold voltage of the cell is defined the Vcg for which the Id=10 #A when Vds=l V. Fig. 3 shows typical endurance characteristics of the cells for various gate coupling ratios. After 107 W/E cycles, AWp is about 60 % for the devices with Ag=0.75. According to Rels. 7 and 8, the oxide charge build-up Qox and the corresponding centroid Xb of the tunnel oxide can therefore be evaluated as a function of the number of W/E cycles or more physically as a function of the total injected charge Qinj forced to pass through the tunnel oxide area. Qinj is calculated from the Vth h and Vth 1 data by summing all the charges which transfer from the drain to the floating gate and vice versa as the number of W/E cycles increases. The outputs of this treatment are shown in Fig. 4 (solid lines). At the early stage of stress, positive charge build-up seems to occur, while at high injection levels negative charge trapping prevails. The corresponding centroid lies around the middle of the oxide layer, as expected in such alternative stress condition. The programming window opening (collapsing) can be interpreted by positive (negative) bulk oxide charge build-up (Fig. 3).
624
C. Papadas et aL / Programming window degradation
o.s
o
•...-
.......
::::~::-
:..~
~t
( ms
) -
U
3
O.6
2
0 w
1
X
o.7
0
,,
o.~
:> o
x
-1
EEPROM
-;z
•
lO °
I
,
I
,
lO 2 n u m b l r
I
,
I
l O Jq~ of
W/l~
i
I
lO 6 cycl
e~
Fig. 3 : Typical endurance characteristics V t h v e r s u s number of W/E cycles as obtained on FLOTOX EEPROM cells with different coupling ratios.
i
I
lO -~
,
Ag--O.
I
i
I
7~,
,
I
lO-2 Qlnj(
f
I
lO ° C/cm2
10
2
)
Fig. 4 : Qox and xb]tfd variations with Qinj as obtained from EEPROM endurance data (solid lines) and dynamically stressed tunnel oxide capacitors with two pulse durations At = 0.2 and 0.3 ms (dashed lines).
In order to confirm the previous analysis, dynamic stressing experiments have been conducted on tunnel oxide capacitors on n+ substrate for simulating the degradation during W / E operations. Tunnel capacitors with similar oxide characteristics have been stressed with alternative constant voltage pulses. The pulse amplitude has been chosen in order to have an injection current density close to the maximum actual value for the EEPROM cell i.e. 20-30 mA/cm2 (dashed line in Fig. 2). The oxide charge Qox and the corresponding centroid xb/tfd have been evaluated as a function of stress from AVfn ÷, AVfn- data using classical formulas [4]. The centroid has been found to lie around the middle of the tunnel oxide as in the case of EEPROM's. As can be seen from Fig.4, the variations of Qox with the injection dose obtained on the capacitors are in very good agreement with the oxide charge build-up deduced from the EEPROM analysis. This emphasizes the consistency of our model and puts forwards the necessity to optimize the tunnel oxide quality for improving the EEPROM reliability.
4. CONCLUSION A model explaining the programming window degradation and the high and low state threshold voltage shifts as a function of W / E cycle number in FLOTOX EEPROM's has been presented. Analytical relations which correlate the programming window collapse and the oxide charge build-up in the tunnel area have been derived. 1. 2. 3. 4.
B. A. A. D.
Euzent et al, Proc. 19th Annu. Reliability Phys. Syrup., p. 11 (1981) Bhattacharyya, Solid State Electron., 27, 899 (1984) Kolodny et al, IEEE Trans. Electron Devices, ED-33, 835 (1986) J. DiMaria, J. Appl. Phys., 47, 4073 (1976).