Statistical Models for Hot Electron Degradation in Nano-Scaled MOSFET Devices
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1 2006, 대한 산업공학회 추계학술대회 Session C3 : Statistical models Statistical Models for Hot Electron Degradation in Nano-Scaled MOSFET Devices Seong-joon Kim, Suk Joo Bae Dept. of Industrial Engineering, Hanyang University, Seoul, KOREA
2 Contents Introduction MOSFET Device Physics of Hot Electron Degradation Statistical Model Conclusion 2
3 Excited About the Future Opportunities for Reliability on Nano-Devices The Study of reliability - has play a vital role in the engineering of the products - will play an even bigger role for industries in nanofabrication in the next decade. But, current reliability theories and methods are - Only partially applicable to systems operating on a nanometer scale. In order to investigate the ultimate reliability limitations for nano-device - A full understanding of the physics and statistics of the defect generation is quite important. 3
4 In this Presentation We investigate physical models for the defects (hot carriers) generation leading to failure based on statistical properties for nano-scaled MOSFETs. 4
5 MOSFET(Metal Oxide Semiconductor Field-Effect Transistor) The MOSFET is the most common field-effect transistor In both digital and analog circuits. The MOSFET is composed of a channel of n-type or p-type semiconductor material, and accordingly it is called a NMOSFET or a PMOSFET. 5
6 MOS(Metal Oxide Semiconductor) Structure NMOSFET A layer of metal on top of a semiconductor die Gate A layer of silicon dioxide(sio 2 ) is a dielectric material. oxide Silicon(Si) Source and drain regions of Semiconductor Body region of semiconductor N+ N+ Source Drain P (Body) 6
7 MOS(Metal Oxide Semiconductor) Operation Positive Gate-Body voltage is applied source V S S G V G Gate D oxide V D drain P N+ Channel N+ N-Channel is created by gate-body voltage. and It is called Drain current. body 7
8 MOS(Metal Oxide Semiconductor) Operation No or negative voltage is applied between gate and body source V S S G V G Gate D oxide V D drain P - - N+ - Channel N+ body The channel disappears and no current can flow between the source and drain. 8
9 Trend of MOSFET Devices increasing demand for faster logic and memory devices The dimensions of the transistors have been reduced significantly. Electric Field between source and drain Length of channel(l) is short, then drain voltage has more effects on the drain current. N+ - - source Channel Channel N+ drain N+ L L L L Length of Channel 9
10 Hot carrier Interface trap generation The creation of interface trap (Defect) is mainly caused by desorption of hydrogens produced during manufacturing process Si-Si0 2 interface O H O O H O O Silicon Substrate Si Si Si Si Si Si Si Si Si Si Si Si Si Si 1. electrons or holes with high kinetic energies (hotcarrier) are attracted to the Si-SiO 2 interface - - oxide 2. These weaken the Si-H bond until it breaks. 3. As a result, the hydrogen diffuses into the oxide or Si substrate, subsequently creating interface traps. N+ source - Channel L - h N+ drain 10
11 Activation Energy Distribution of Hot-Electrons Electron need sufficient activation energies to surmount a surface energy barrier to generate interface traps activation energies are directly linked to interface trap defects. Therefore, A model for hot electron degradation is achieved via the distribution of hot-electron activation energies. Identify the energy distribution of these electrons as a function of the number of interface traps over time to evaluate reliability of MOSFET devices. 11
12 Activation Energy Distribution : Stage 1 Derivation of Activation Energy Distribution The degradation of a MOSFET device : a lifetime constant that has units of time : hot carrier activated trap density at time t : Concentration of interface traps at time t : the power of terms 12
13 Activation Energy Distribution : Stage 2 Derivation of Activation Energy Distribution A lifetime is defined as the time to reach a fixed number of interface traps. : critical energy in electronvolts for generating an interface trap : minimum energy(ev) that an electron must possess to create impact ionization : Power supply voltage this term can be obtained experimentally. ϕit β τ = C3 exp ϕ0vdd Experimentally observed lifetime. 13
14 Activation Energy Distribution : Final Derivation of Activation Energy Distribution The degradation of a MOSFET device Experimentally observed lifetime. ϕit β τ = C3 exp, ϕ0vdd The degradation of a MOSFET device can be approximated by using the following distribution on the hot-electron activation energies Popular Logistic distribution form 14
15 Bimodal Activation Energy of Hydrogens Defects do not necessarily have the same activation energy. In fact, there exist multiple paths and competing mechanisms for the release of hydrogen(h) yields inhomogeneous activation energy. Activation energy of hydrogen around 3.5eV Hydrogen desorbs into the SiO 2 below 3eV Final hydrogen state is closer to the silicon bulk 15
16 Mixed form of Activation Energies As a result, the time-dependent HCI(Hot Carrier Injection) degradation model is a mixture of activation energy distribution. Mixture of logistic distributions The degradation model of a MOSFET device 16
17 Parameter Estimation in Logistic Distribution The CDF of the random variable X having the logistic distribution for, where and are location and scale parameters. Using the method of maximum likelihood to estimate logistic distribution (degradation model) parameters. 17
18 Parameter Estimation in Logistic Distribution The log-likelihood function MLEs satisfy the following likelihood equations : 18
19 Properties of MLE The MLEs satisfy following relation L Where is the true value of and the Fisher information is given by Theorem ˆ l '(X ) n Let μ be the mle of μ, and let ζn=x n, then l''(x n ) n( ζ ˆ μ) 0 as n n 19
20 Mixture of Logistic Distributions The PDF of two points discrete mixture of logistic distribution where To solve the MLE equations, Simplex algorithm Conjugate gradient Direct algorithm Simulated annealing 20
21 Simulated Activation Energy distribution By experimentally observed data, we simulate the model with given parameter value 21
22 Bimodal Energy Distribution 22
23 Future Research Mixture Webull Model & Change point analysis % ˆ ˆ % β 1 ˆ * β % β ˆβ ˆ* β 1 * ˆβ 0.06 ˆ% ˆ η = 20, % β = 3.6 η = ˆ β = * * ˆ 40, 8 p = weibulltest 23
24 Future Research Mixture Webull Model & Change point analysis We can estimate the position of change point such that SIC(Schwarz Information Criteria) is the minimal. N=1000, p=0.3, estimated change point = 314 % ˆ ˆ η = 20, % β = 3.6 weibulltest η = ˆ β = * * ˆ 40, 8 p = 0.3 sic
25 Question And Answer 질문하세요 25
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