Prediction of performance degradation and lifetime for semiconductor
devices using Markov chain model
K. Momoda(aK. Endo(aY. Midoh(bK. Miura(bK. Nakamae(aa) Grad. Sch. Information Science and Technology, Osaka Univ.
b) Secretariat, NANO Testing Symposium

Abstract: We study on a method to predict performance degradation and lifetime of semiconductor devices under theassumption that the device characteristics can be monitored periodically. By using the Markov chain model,
degradation and lifetime of the MOSFET are predicted based on measured values of gate leakage current. MOSFET degradation states are classified into discrete states or classes according to its gate leakage current. Statetransition probabilities are obtained from measured gate leakage current data. In our study, gate leakage current
data are obtained by simulation based on the percolation model instead of actual device measurement. Experiments to predict degradation and lifetime of MOSFETs are carried out. In the experiments, gate leakage current
data obtained by simulating 1000 devices are used. The experimental results show that device monitoring canenable us to elongate lifetime of system.
Keywords: Time-to-failure modeling, Time-to-failure statistics, Markov chain model, degradation prediction, lifetime prediction, gate leakage current

1. Introduction

2. Research method

The lifetime of semiconductor devices are estimated usually by using a Weibull distribution
model. For example, in JEDEC standard [1], x%
lifetime is defined as 0.1%, which is the time atwhich the cumulative failure rate reaches to 0.1%.
That is, there is one failure device among 1000 devices. Thus the life time of devices are estimatedstatistically. If the characteristics of devise underoperation is monitored and the lifetime is estimatedfrom the monitored data, the deteriorated device
can be replaced by a new one so that the lifetimeof system is elongated. And there is the advantagethat the stock quantities of maintenance parts (devices) can be reduced.

2.1 Gate leakage current simulation
2.1.1 An overview

The leakage current characteristics is obtainedby simulation that uses the percolation model[4],[5].
In this model, the gate oxide is represented bycubic lattice. Let us suppose a 3-dimensionalmesh graph whose node is located at the centerof each cube and is connected by edges with six
adjacent nodes. Let the coordinate of the meshnode be (x, y, z) where x = 0, · · · , Nx − 1, y =0, · · · , Ny − 1, and z = 0, · · · , Nz − 1. The MOSFET surface is on y-z plane and the x-axis is perpendicular to the surface. This 3D mesh graph isimplemented as a 3D array on the simulation proThe degradation estimation for Infrastructuregram.
system has been reported [2], [3]. However, as far
as we know, there is no report regard to the elec3. Some examples of NANOTS
tronic system that is composed of semiconductor
proceeding format
devices.
In this section, some examples of NANOTS proIn this paper we try to predict the degradation or
ceeding format are shown. This section is indepenthe lifetime of devices from the periodically monident of the other part of this manuscript.
tored data by using Markov chain method. We asFigure 1 shows an example of figure. Table 1
sume that the device characteristics can be monishows an example of table. Figures and tables must
tored periodically. The leakage current in the gate
be referred in the main text.
oxide of MOSFET is used as device characteristics.
Here is an example of equation:
Contact author E-mail: miura@ist.osaka-u.ac.jp

1F (ω) = √2π∫ ∞∞f (t)ej2πωt dt.

(1)

devices under the assumption that the device characteristics can be monitored periodically. By using
the Markov chain model, degradation and lifetimeof the MOSFET are predicted based on measured
values of gate leakage current. MOSFET degra-4
10
dation states are classified into discrete states orclasses according to its gate leakage current. Statetransition probabilities are obtained from measured-6gate leakage current data. In our study, gate leakage
10current data where obtained by simulation basedon the percolation model instead of actual device
measurement. Experiments to predict degradation-8and lifetime of MOSFETs were carried out. In the10012101010experiments, gate leakage current data obtained byFrequency f [Hz]simulating 1000 devices were used. The experiFig. 1 An example of figure. Figures must be referred in the mental results show that device monitoring can enmain text.
able us to elongate lifetime of system.
-2Signal
Signal + Noise

Power spectral density P [W/Hz]

10

Table 1 An example of table. Tables must be referred in themain text.

ClasstRET [sec]tSF T [sec]∆t [sec]

C53000C43000C33000C23000C13000

3215
3329
3621
4027
4672

3650
4027
4555
5643
6863

435
698
934
1616
2191

The following show an example of itemization.
• item 1,• item 2,◦ sub-item 2(a),◦ sub-item 2(b), and• item 3.

Acknowledgement
We used IEICE and IEEE papers as reference toprepare this paper sample. The authors would liketo thank those concerned.

References[1] JESD47.01, “Stress-test-driven qualification of integratedcircuits,” JEDEC Solid State Technology Association,2011.
[2] H. Korving, and J. van Noortwijk, “Bayesian updating ofa prediction model for sewer degradation,” Urban Water
Journal, vol.5, no.1, pp.51–57, 2008.
[3] K. Kobayashi, K. Kaito, and N. Lethanth, “A Bayesianestimation method to improve deterioration prediction forinfrastructure system with Markov chain model,” International Journal of Architecture, Engineering and Construction, vol.1, no.1, pp.1–13, 2012.
[4] J. Stathis, “Percolation models for gate oxide breakdown,”
Journal of Applied Physics, vol.86, no.10, pp.5757–5766,
1999.

The following show an example of enumeration[5] S.Y. Kim, G. Panagopoulos, C.H. Ho, M. Katoozi,(numbered list).
E. Cannon, and K. Roy, “A compact SPICE model forstatistical post-breakdown gate current increase due to
1. item 1,
2. item 2,(a) sub-item 2(a),(b) sub-item 2(b), and
3. item 3.

4. Conclusions
We have studied on a method to predict performance degradation and lifetime of semiconductor

TDDB,” IEEE International Reliability Physics Symposium (IRPS), pp.2A–2, 2013.

Appendix A
If you want to write some non-essential thingsof your research such as proofs of theorems, write
them in appendix sections.