A Study of Trap Profiles in Thin Silicon Dioxide Films at Dielectric Breakdown using Percolation Model
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Mat. Res. Soc. Symp. Proc. Vol. 592 © 2000 Materials Research Society
-6.OV to the p-well while satisfying the forward bias condtion between p-well and n-substrate. The stress was interrupted periodically every 100 seconds to monitor the charge centroid and the threshold voltage shift. Such a short time interval, which is much smaller than time-to-breakdown, enables accurate evaluation of the critical charge centroid and the threshold voltage shifts just before breakdown. Charge centroid Charge centroid Zc is defined as
Z p(Z)dZ
p(Z )dZ
where Z and T are the distance from the Si/SiO2 interface and the oxide thickness, respectively. p(Z) denotes the charge density. In this study, we evaluated Zc using DiMaria's method [5] in which the centroid of the stress induced oxide charge are deduced from the gate voltage shifts needed to maintain a constant FN current through the MOS structure for positive and negative biases, AV+ and AV. Charge centroid Zc can then be obtained by zý =
l 1+ I
TY.l/ ]AV+ I
The gate bias to evaluate AV+ and AV was taken high enough for accurate calculation of Zc [6]. Before evaluating Z,, SHE injection under the oxide field of EMi= 2.0 MV/cm was carried out to fill the generated traps with electrons. This process is necessary for the following two reasons. First, filling process cancels out the positive charge trapped in the oxide film, and we can hence detect the charge centroid only for trapped electrons. Second, the filling procedure under the same E511 makes it possible to compare the amount of trapped electrons between various stress conditions with different oxide fields. This is because the fraction p of oxide traps occupied by trapped electrons is strongly dependent on the oxide field [7]. The actual trap density D(Z) can be expressed as eD(Z) = p(Z)/p
7 6 S5-
,
Fig. 1. Critical charge centroid Z ,, measured for various
03 SHE AXFN
gate voltages V , and injection methods. All data is the
4
averaged values for given stress conditions, which only has
To-=7.nm
2 to 6%error. Z, denotes the distance from Si/SiO
interface. Oxide thickness is 7.0 nm. All N
2
A
A
critical charge centroid is dependent on stress condition,
1
-6
isnot identi-
cal to Tx/2 and deviated toward Si/SiO 2 interface. Note that which indicates that electron trap profiles are also dependent on it.
7
8
VLate [V]
9
10
332
We confirmed that the filling process with such a low electric field has little effect on the oxide degradation. The critical charge centroid just before breakdown, Z , for various stress conditions are shown in Fig. 1. Measured Zc cr,are less than the half of the oxide thickness indicating the non-unifrormity of trapped electron distributions. Moreover, they are dependent on stress conditions. Threshold voltage shift Threshold voltage shift
AJth
was evaluated by measuring/d I-Vgat characteristics. Elec-
tron filling was, of course, carried out before the measurements. Using charge density function, and hence trap density function, AV, h is written in the form
(T. - Z)p
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