Advanced Characterization of the
Bias Temperature Instability

ausgeführt zum Zwecke der Erlangung des akademischen Grades
eines Doktors der technischen Wissenschaften

eingereicht an der Technischen Universität Wien
Fakultät für Elektrotechnik und Informationstechnik

Philipp Hehenberger

Julius Raabstraße 25/3
A-2345 Brunn am Gebirge, Österreich

Matr. Nr. 0025027
geboren am 12. Oktober 1980 in Wien, Österreich

Wien, im Dezember 2011

It is unwise
to be too sure
of one’s own wisdom.

It is healthy
to be reminded that
the strongest might weaken
and the wisest might err.

Mahatma Gandhi


To Veronika

List of Abbreviations
List of Symbols
 Physical Constants
 Chemical Symbols
1 Introduction
 1.1 Historical Background
 1.2 BTI – Causes and Impacts
 1.3 Modeling BTI with Defects
2 Measurement Methods
 2.1 Measurement-Stress-Measurement
  2.1.1 Monitoring I
D   at V
  2.1.2 Direct Monitoring of VTH
  2.1.3 Extended-Measurement-Stress-Measurement Setup
 2.2 Transfer-Characteristics
  2.2.1 Fast Pulsed ID(VG )  -characteristics
  2.2.2 Improved Method of Reisinger
 2.3 On-The-Fly (OTF)
 2.4 Charge Pumping
 2.5 On-the-Fly Fast Charge Pumping
 2.6 Capacitance Voltage Profiling
3 Previous Modeling Attempts
 3.1 Reaction Diffusion Model
  3.1.1 Stress Phase
  3.1.2 Back Diffusion of Hydrogen during Recovery
 3.2 Extensions of the Reaction-Diffusion Model
  3.2.1 Dispersive-Reaction-Rate Models
4 Two Components Contributing to Bias Temperature Instability
 4.1 Universality of BTI recovery
 4.2 Assumption of a Permanent Component
  4.2.1 Temperature and Voltage Dependence of Universal Law
  4.2.2 Measurement Delay
 4.3 ΔVTH   versus ΔV θ
 4.4 Conclusion
5 Pulsed BTI Measurements
 5.1 Pulsed ID(VG)  -Characteristics
 5.2 Further Data Extraction Options
  5.2.1 Determination of the Fitting Region
  5.2.2 Impact of the Pulse Amplitude
  5.2.3 Varying Pulse Rise/Fall Times
  5.2.4 Consequences
 5.3 Experimental Identification of Defects
 5.4 OFIT versus CP
 5.5 Analysis of the OFIT Technique
  5.5.1 Dependence on Gate Voltage Low-Level
  5.5.2 Hysteresis due to Stress
 5.6 Extrapolation of Oxide Trap Contribution
 5.7 Simulation of the Charge Pumping Current
 5.8 Results
 5.9 Conclusion
6 Short-Term NBTI
 6.1 Gate Pulse Settings
 6.2 Data Extraction
  6.2.1 Offset
  6.2.2 Initial Measurement as Reference
  6.2.3 Gate Voltage Criteria
  6.2.4 Brute-Force Truncation of the Transient
  6.2.5 Final Setting of Parameters
 6.3 Logarithmic Stress Behavior
  6.3.1 Used Samples and Stress Conditions
  6.3.2 Temperature Scaling
  6.3.3 Voltage Scaling
  6.3.4 Oxide Thickness Scaling
  6.3.5 Extracted Prefactors
 6.4 Power-Law Stress Behavior
 6.5 Relaxation Behavior
 6.6 Fast Ramp versus Fast-VTH   -Method
 6.7 Conclusions
7 Relaxation of Negative/Positive BTI
 7.1 Raw Measurement Results
 7.2 Schematic Recovery Behavior
 7.3 Extraction Routine
 7.4 Discussion of the Experimental Output
  7.4.1 Stress Time Component
  7.4.2 Oxide Electric Field Component
 7.5 Short-Term and Long-Term Relaxation
  7.5.1 Entire Relaxation
  7.5.2 Change in ΔVTH
 7.6 Emission Time Constants
 7.7 Conclusions
8 Latest Modeling Attempts - Hole Trapping
 8.1 Rate Equations
 8.2 Elastic Hole Trapping
 8.3 Coupled Double-Well Model
 8.4 Two-Stage Model
 8.5 Multi-Phonon Emission
  8.5.1 Approximation of the Vibronic Transition
  8.5.2 Radiative Multi-Phonon Emission
  8.5.3 Non-Radiative Multi-Phonon Theory
 8.6 Conclusion
9 Modeling NBTI in High-k SiGe pMOSFETs
 9.1 Inverse Modeling
 9.2 Multi-State Defect Model
  9.2.1 Distribution of Defects
  9.2.2 Reservoir of Holes - Classical vs. Quantum Mechanical Description
 9.3 Results
 9.4 Conclusions
10 Summary and Outlook
A Extracting V θ  Based on the Level 1 model
 A.1 OTF1
 A.2 OTF2
 A.3 OTF3
B Ideal MOS Capacitor
 B.1 Surface Space Charge Region of an n-Type MOS Capacitor
 B.2 Results for p-Type Semiconductors
C Diffusion-Limited Stress Phase of the Reaction-Diffusion Theory
D Multi-Phonon Emission
 D.1 Radiative Multi-Phonon Emission
 D.2 Non-Radiative Multi-Phonon Process
Own Publications
Curriculum Vitae