% % In Lecture 4, we will briefly discuss the Hazen's formula F_i=(i-a)/(n-2*a+1) % as a correct way of plotting the data. The code below establishes that median rank % formula for cumulative distribution is % F_i=(i-0.3)/(n-0.6+1) with a=0.3. % % Purpose
ECE695: Reliability Physics of Nanoelectronic Devices
Final Exam: Dielectric Breakdown and Data Analysis
Muhammad Ashraful Alam
Network of Computational Nanotechnology
Discovery Park, Purdue University.
1. Answer T/F for the following questions (20x2=40 p
EE695: Reliability Physics of Nanoelectronic Devices
Homework 9: Data Analysis
Muhammad Ashraful Alam
Network of Computational Nanotechnology
Discovery Park, Purdue University.
In Lectures 31-36, we discussed the problem of data analysis relevant for reli
119
38. CHARGE GENERATION BY PARTICLES
38.1
Review/Background:
In the previous two lectures, we learned about the different sources of radiation
as well as the intensity of radiation in terms of the flux of particles. The sources of
radiation we discussed
Reliability Physics of Nanoelectronic Devices
Final Exam: Dielectric Breakdown and Data Analysis
Muhammad Ashraful Alam
Network of Computational Nanotechnology
Discovery Park, Purdue University.
1. Answer T/F for the following questions (20x2=40 points)
T
89
28. CIRCUIT IMPLICATIONS OF DIELECTRIC
BREAKDOWN
28.1
Review/Background
In the previous lectures, Time Dependent Dielectric Breakdown (TDDB) of thin
dielectrics has been shown to be an uncorrelated mechanism which results in soft
breakdown of oxides. A
127
30. BREAKDOWN IN DIELECTRICS WITH DEFECTS
30.1
Review/Background
Breakdown in dielectrics has always been an important problem with a broad
range of physical and technological implications. The physics of breakdown for thick
dielectrics is very differ
107
37. EFFECT OF RADIATION DAMAGE SOFT ERRORS
37.1
Review/Background:
This lecture will focus on radiation-induced reliability issue, which is the fourth
reliability mechanism other than NBTI, HCI, and TBBD. In the previous lecture, the
importance of rad
143
31. COLLECTING AND PLOTTING DATA
31.1
Review/Background
So far we have discussed the physics of various reliability issues of modern
transistor such as NBTI degradation, HCI, TDDB, etc. However, in practice, we need
experimental data before making any
107
29. BREAKDOWN OF THICK DIEELCTRICS PART 1
29.1
Review/Background
Most of topics we covered so far address major reliability problems of thin
oxides in logic transistors: NBTI, HCI and TDDB. Physics of thick dielectrics is
important for two reasons: Fi
Lecture 9: Reachability
Outline of Lecture
Reachability
General Transition Systems
Algorithms for Reachability
Safety through Reachability
Backward Reachability Algorithm
Reachability
Given hybrid automaton H
: set of
Invariant set: set for which
Lecture 5: Computational Tools I
1 / 20
A Computational Perspective
Qualitative properties of control systems can be quantified:
Reachability: cost/time/probability to reach a target state
Observability: energy of excited output
R
Stability: exponentia
% % % % % % %
-EE650: Reliability Physics of Nanoelectronic Devices A MATLAB CODE TO STUDY THE STATICIS OF NBTI Written by M. Alam and E. Islam (Oct. 10, 2006) -
% NoDev: Total number of Si-H bonds per transistor % m: Minimum number of broken Si-H bonds i
% % STATISTICS OF GATE DIELECTRIC BREAKDOWN (Finite Size Percolation Model) % %# % This program simulates 3D percolation model to get breakdown statistics. % Trap are generated randomly in a 3D grid till device breakdown occur. % The shorting path is assu
Lecture 2: Discrete and Continuous
Dynamics
August 24, 2016
1 / 12
Dynamics of Hybrid Systems
The state of hybrid systems:
Continuous state x X where X Rn
Discrete state q Q where Q = cfw_q1 , q2 , . . .
Dynamics of hybrid systems:
Continuous dynamics
Lecture 3: Hybrid System Models
August 29, 2016
1 / 13
Hybrid State Space
The (hybrid) state of a hybrid system consists of
Discrete state (mode) q Q = cfw_q1 , . . . , qN or cfw_q1 , q2 , . . .
Continuous state x X (e.g. Euclidean space Rn )
Hybrid st
Lecture 4: Hybrid System Solutions
1 / 12
Hybrid Time Sets
A hybrid time set is a succession of time intervals
cfw_I0 , I1 , . . . , IN
Each interval (except the last one) is of the form [i , i0 ]
Last interval IN = [N , N0 ] or IN = [N , N0 ) or IN =
AAE668 & ECE 695 Homework #1
Due 09/29
Please include the detailed steps for obtaining the solutions, including the Matlab codes if applicable.
Problem 1: Construct a hybrid system model for one practical system. You need to identify the discrete and
cont
Lecture 7: Basic Lyapunov Theory
1 / 10
Stability Notions
System x = f (x) has an equilibrium point at xe if f (xe ) = 0.
An (isolated) equilibrium point xe is called (locally)
stable (in the sense of Lyapunov) if > 0, > 0 s.t.
kx(0) xe k kx(t) xe k , t
Lecture 6: Computational Tools II
1 / 12
Motivation
LMI F (z) = F0 + z1 F1 + + zk Fk 0, Fi Sn , recast as
x T F (z)x =
X
fij (z)xi xj 0,
x1 , . . . , xn R
i,j
- Nonegativity of a quadratic multivariate polynomial
- Coefficients are affine functions of co
Lecture 8: Analysis of Hybrid Systems
Outline of Lecture
Objectives
Modeling
Analysis (Verification) : Prove that a hybrid automaton
satisfies certain properties
Synthesis (Controller design): Choose control inputs so that
the closed loop hybrid au
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