Power law model for positive charge build-up in silicon dioxide due to high-field stressing

Solid-Slate

Elecmmics

Vol. 36, No. 5, pp. 723-726, 1993

Printed in Great Britain. All rights reserved

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0038-l 101193 $6.00 + 0.00 c 1993 PergamonPressLtd

POWER LAW MODEL FOR POSITIVE CHARGE BUILD-UP IN SILICON DIOXIDE DUE TO HIGH-FIELD STRESSING R. M. PATRIKAR, R. LAL and J. VASI Department

of Electrical

Engineering,

Indian

Institute

of Technology,

Bombay,

Bombay

400076,

India

(Received 18 September 1992; in revised form 5 November 1992) Abstract-Positive charge growth in the oxide of a MOS capacitor due to tunnel injection during high-field stressing is found to obey a power law with respect to time. This law is valid for both constant voltage and constant current stress, though the constants of the power law are different. Monotonic increase in positive charge build-up is observed until breakdown. Thus positive charge build-up is a signature of wearout and can be used to monitor the oxide degradation.

shown that this positive charge is due to hole trap generation[lO]. In general it is assumed that the energy gained by electrons is dissipated in the oxide, creating damage. However a relation which equates all energy loss to creation of positive charge in the SiO, cannot be true, because some energy is certainly lost in creating electron traps, interface states, phonon scattering etc. Our stress studies confirm that there is, among other kinds of defect generation, net positive charge buildup until breakdown, irrespective of the stress technique. These measurements were made on many wafers from different runs and it was found that the growth of the positive charge depends upon the dielectric quality of the oxide. The monotonic growth of positive charge after each stress cycle in our experiments does suggest that if the oxide is grossdefect-free, a certain part of the energy is converted into creating positive charge. After a certain amount of energy is dissipated in the SiOz with accompanying positive charge build-up, it breaks down. At least, this seems to be the wearout mechanism which is important as far as device operation is concerned. We have done a detailed study of positive charge generation for different stress conditions. These results are presented in this paper. The samples used in this study were metal gate MOS capacitors with oxide thickness between 20 and iU nm. The substrate was 1 R cm (100) P type Si. The gate oxide was grown in Oz at 950°C followed by a 20 min anneal in nitrogen at the same temperature. Aluminum evaporation was done in an electron beam evaporation system. Square dots of 1 mm’ were formed by photolithography. The back oxide was etched and aluminum was evaporated for the back contact. Postmetallisation anneal was performed at 450°C for 20 min in nitrogen. The capacitors were stressed by two techniques: constant voltage and constant current. The configuration used to stress the device consisted of: a Keithley 220 current source for constant current stressing, a

INTRODUCTION Dielectric strength of gate oxides is an important consideration in MOS devices. Dielectric strength is usually characterised by electrical properties of a MOS capacitor at high fields. Although there is no consensus about the details of the high-field effects, such as the process operative during the final stages of breakdown, there are certain observations which are common. A well established and accepted observation is that there is positive charge build-up in the oxide after stressing[l]. Way back in 1955, Rose[Z] suggested that positive charge plays an important role in determining the high-field properties of insulators. Indeed, the main model for the dielectric breakdown of SiO, in MOS structures has for long been based on a feedback mechanism, where positive charge buildup in the oxide enhances the field at the cathode, the majority carrier injecting electrode, thereby inducing current runaway. In the early work[3], the positive charge was attributed to immobile holes produced by impact ionisation in the SiOz bulk. However, it was shown[3] that holes are not immobile and serious doubts were raised about the importance of impact ionisation. In the last 20 years, numerous models for explaining the phenomenon of positive charge generation in the oxide during high-field stressing have been proposed. The main plausible mechanisms are: trapping/ detrapping of holes occurring near the interface due to the high fields[4], hole production by impact ionisation and subsequent trapping near the Si-SO2 interface[5], hole injection from the anode[6], bond breaking and chemical effects[7], diffusion of neutral species[8], and various combinations of these effects. Surprisingly, until date none of these mechanisms has been ruled out completely. It has also been proposed that the positive charge consists of two components, hole trapping in existing hole traps and positive charge due to some unidentified defects described as Anomalous Positive Charge (APC)[9], We have 723

R. M.

124

PATRIKAR

et

al.

Keithley 619 electrometer to monitor the voltage necessary to maintain a constant current and a Keithley 617 electrometer/voltage source for constant voltage stressing. High frequency C-V (HFCV) plots were taken with a PAR 410 C-V meter and recorded on an X-Y recorder. Except for HFCVs the data acquisition and plotting was done with a HP 9826 instrument controller. In most of the experiments, the oxide was stressed for definite duration and HFCVs were taken after the stress cycle. POSITIVE

CHARGE

BUILD-UP

Positive charge build-up in the oxide was observed after all types of high-field stress in accumulation. The positive charge build-up seems to depend on the applied field and charge fluence. Another important observation is that the flatband shift as a function of time obeys a power law for both constant-voltage stressing as well as constant-current stressing. The power law parameters depend on the magnitude of the stress voltage or current. For constant voltage stressing, Fig. I shows that the plot log AVh vs log t is a straight line. Figure 2 shows that plot of log A V,,, vs log t is a straight line for constant-current stressing. We also found that using the power law gives the minimum residue and minimum standard deviation in least square fits. Other least square fits tried were the exponential, logarithmic and polynomial (up to the third order). Thus flatband shift as a function of time of stressing can be written as AVh = ath

(1)

where, AVfi is the flatband shift due to high-field stressing, t is the time of stressing and a and b are constants. We found that the constants a and b depend upon the applied field and process parameters like thickness and dielectric quality of the oxide. We found that this relation remains valid until breakdown and can be used to predict the flatband shift at any instant of time.

102

I

11

Fig. 2. AVh t on log scale for constant-current

103

Figure 3 shows the plot of flatband shift vs time for constant-voltage stressing. Initially the oxide was stressed for small intervals of time and then stressed for a long time. The constants n and b in the eqn (I) were obtained by the least-square-fitting program by taking data points only in the initial regime and the curve was plotted. Figure 3 shows that the power law fits the data well and the flatband shift after a long time also can be predicted with this law. Figure 4 shows the plot of flatband shift vs time for constant-current stressing. Initially the oxide was stressed for small intervals of time and then stressed for a long time. Fitting constants were again obtained by using data points from the early portion of the stress. Figure 4 shows that the power law fits the data for all times. Thus this law can be used to predict the positive charge build-up in the oxide as a function of time for constant-current stressing also. In this mode of stressing also the law is valid until the breakdown. In inversion, positive charge build-up is less compared to accumulation for the same stress current and

r

7500

104

Time (s) Fig. 1. AV, vs t on log scale for constant-voltage

stressing.

I

I I I,,,,

,,,I,

102 Time (s)

4000

103 -

IO2

102 I 10

Time

(s)

Fig. 3. AV, vs t for the constant-voltage

stressing.

stressing. Curve is drawn for the power law fit with data points in initial region.

Charge

725

buildup in SiO,

2000

1

2 2 iz

500

x_x-x

A

x’ 0

750

U

I 6 x 10-l

1500

Time (s)

Current

Fig. 4. AVta vs t for the constant-current stressing. Curve is drawn for the power law fit with data points in initial region.

I 1.2 x 10-O

II

(A)

Fig. 5. A V,,, vs current in inversion and in accumulation constant-current stressing: (A) stressing in inversion; stressing in accumulation.

for (B)

POSITIVE CHARGE BUILD-UP AND BREAKDOWN

time. When the capacitor is stressed at constant voltage, the applied voltage is divided between the oxide and the depletion region. Since positive charge build-up depends on the charge fluence and field, much lower flatband shifts are observed in this case compared to that in accumulation, which is as expected. Moreover, the current in the device depends on the silicon minority carrier generation lifetime which may be a function of depth and surface generation. Because of this, flatband voltage as a function of voltage applied becomes very complicated to interpret. However since there is always less current in this mode compared to accumulation, one always observes less positive charge build-up. Table 1 shows positive charge build-up in the oxide as a function of time for different voltages in accumulation and in inversion. In constant-current stress, current through the oxide is the same in inversion as in accumulation and the cathode field in the oxide is the same field. Figure 5 compares the positive charge growth for stressing in accumulation and in inversion. In this case also positive charge build-up is less in inversion. This is because silicon is the cathode in this case and the electron trapping or trapped hole recombination occurs near the Si-SiO, interface. The positive charge build-up continues to increase until breakdown in inversion also. Thus there seems to be a correlation between this charge build-up and breakdown properties. This is discussed in the next section.

Wearout type breakdown and positive charge growth seem to be related. Trap generation in the oxide seems to be a wearout mechanism[ll]. Trap generation depends mainly upon the field across the oxide and the time of stressing apart from factors such as thickness and processing history[lf]. Figure 6 shows plots of the flatband voltage shift vs charge passed through the oxide at different fields for constant voltage stressing. This figure shows that positive charge build-up also depends on the field applied and the charge passed through the oxide. Figure 7 shows the plot of the flatband voltage shift vs charge passed through the oxide for different currents. This figure shows that positive charge buildup does not depend only on the charge passed through the oxide but also on the current which in turn implies that it depends on the field applied. Thus this feature of the positive charge build-up is similar to trap generation. Thus

Table I. Flatband shift after constant voltage stress for constant charge through oxide (charge 1.25 x 10-j C/cm’) Field (MVicm) 11.0

10.5 10.0 9.5

AV,

(substrate bias) flllVI I400 275 125 100

AV,

(gate bias) tmV) 50 15 30 20

0-

0

3 x 10-S

6 x 1O-3

9 x 10-3

Charge (C/cm’) Fig. 6. A V, vs charge fluence for constant-voltage stressing: (A) for field 10 MV/cm; (B) for field 10.5 MV/cm; (C) for field 11 MV/cm.

726

R. M. PATRIKAR e/ ul.

breakdown (AVv,,,J. Thus AVb,,, shows the same trends as observed in other breakdown tests of the oxide. This discussion also shows that AVn),,m can be treated as a breakdown parameter analogous to Qbd.

CONCLGION

Positive charge build-up in the oxide is a generally observed phenomenon. We have developed a power law model for the growth of positive charge based on our experimental observations. We have also shown that positive charge build-up and wearout of the oxide 01 0

1.5 x 10-3

Charge

3 x 10-3

Sr. No.

I 2 3

Thickness of oxide (nm) 20 22.5 26

easily

Positive

charge

build-up

can

be

and can be used as a quick indicator

of oxide wearout. We have suggested a method of assessing the dielectric integrity based on this[l4].

(C/cm’)

Fig. 7. A Vn, vs charge fluence for constant current stressing: (A) for current I x IO-' A; (B) for current 5 x IO-‘A; (C) for current 1.25 x IO-“A. Table 2. Charge to breakdown

are correlated.

monitored

A~knoM,ledgrmml~The support of the Ministry of Human Resource Development under its Thrust Area Programme in Microelectronics is gratefully acknowledged.

and AV,,,m for the oxide with different thicknesses AVfi,m WI 21 IO 4

Qhd at contant field (C, cm’) 6 1.5 0.1

there is a close relation between the positive charge build-up and wearout of the oxide. The following discussion will show that the positive charge build-up as a function of thickness has the same trend as Qh,, We have found that most of the capacitors on a wafer break down when the AVm exceeds a certain limit A Vhllm. We observed that MOS capacitors with 22 nm thick oxide suffer breakdown when the flatband shift exceeds 10 V. Observations for oxides with different thicknesses are given in Table 2, which also gives the values of Q,,s for these oxides. These values are measured for constant-voltage stressing at a field of 10.5 MV/cm. This table shows that the positive charge build-up also depends upon the thickness of the oxide and the trend of the growth is again similar to that of Qbd. These observations show that thinner oxides have higher Q,,s. Also it has been observed that thinner oxides have better reliability and higher breakdown fields[l3]. Table 2 shows that thinner oxides have higher values of flatband voltage shifts at

REFERENCES

I. M. V. Fischetti, in Insulating Films On Semiconductors (Edited by J. J Simon and J. Buxo). Elsevier Science, Amsterdam (I 986). 2. A. Rose, Phys. Rec. 97, 1538 (1955); Phys. Rec. 97, 322 (1955). 3. Z. A. Weinberg, Appl. Phys. Lett. 27, 437 (1975). 4. P. Olive. B. Ricco and E. Sangiorgi, J. uppl. Phys. 54, 5267 (1983). 5. T. H. Distefano and M. Shatzkes, Appl. Phys. Left. 25, 685 (1974). 6. Z. A. Weinberg, W. C. Johnson and M. A. Lampert. J. uppl. Phys. 47, 248 (1976). 7. C. T. Sah, J. Y. C. Sun and J. J. T. Tzou, J. uppl. Phys. 54, 5864 (1983). 8. Z. A. Weinberg, D. R. Young, D. J. DiMaria and G. W. Rubflop. J. appt. Phys. 50, 5757 (1979). F. J. Feigl and R. J. Zeta, J. uppl. 9. L. P. Trombetta, Phys. 69, 2512 (1991). IO. R. M. Patrikar, R. Lal and J. Vasi. Physics qf’Semiconduttor Devices. p. 142, Supplementary Proceedings of F$h Itllernational Workshop (Edited by W. S. Khokle and S. C. Jain). Tata McGraw-Hill, Delhi, India (1989). J. Shappir and D. FrohmanI I. Y. Nissan-Cohen, Bentchkowsky, J. uppl. Phys. 60, 2024 (1986). 12. S. Holland and C. Hu, J. elecrrochem. Sot. 133, 1705 (1986). 13. Y. Hokari, T. Baba and N. Kawamura, IEEE Trans. Electron Devices ED-32, 2485 (1984). 14. R. M. Patrikar and R. Lal, Microelectron. Reliab. 32, 961 (1992).