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Title: Low Frequency Modulated Optical Reflectance for the One-Dimensional Characterization of Ultra Shallow Junctions (Lage frequentie gemoduleerde optische reflectie voor de eendimensionale karakterisatie van ultra dunne juncties)
Other Titles: Low Frequency Modulated Optical Reflectance for the One-Dimensional Characterization of Ultra Shallow Junctions
Authors: Dortu, Fabian; S0035232
Issue Date: 5-May-2009
Abstract: The scaling down of the metal oxide semiconductor field-effect transisto r (MOSFET) has fostered the development of new characterization techniqu es that must be able to probe features of ever smaller dimensions. One o f the key elements is the control of the properties of the ultra-shallow junctions (USJs) encountered in the source and drain extension regions of a MOSFE T. In this thesis, we have developed the theory of photo modulated optical reflectance (PMOR) for the characterization of USJs in silicon. We have assessed the theory by comparing it with experimental measurements on Bo ron doped chemical vapour deposition box-like profiles acquired with the Carrier Illumination (CI) metrology tool. CI allows to measure the prob e laser differential reflectance as a function of the power of the pump laser, also known as a power curve. The possibilities and lim itations of PMOR and especially of PMOR on CI have been deeply assessed. The work has been divided into two main tasks, namely the direct and the inverse problem. The direct problem, i.e. the simulation of a power cur ve from a known active doping profile, has been addressed through the de velopment of a finite element code for the simulation of a semiconductor under optical injection, of suitable approximations and of compact expr essions for speed optimization as needed for solving the inverse problem . The inverse problem, i.e. the reconstruction of the active doping profile from a given power curve, has been addressed using different methods of increasing complexi ties, including direct nonlinear optimization based on iterations on the direct problem. We have shown that CI was able to reconstruct box-like doping profiles w ith junction depths in the range 15-70 nm and with active doping concent rations of up to 1e20 /cm3. The accuracy of the technique is however str ongly affected by surface recombinations, which limits its practical use in the present implementation. We believe, however, that this limitatio n could be eliminated by using an ultrafast (sub-picosecond) pumping mec hanism, and we have proposed a reconstruction method that would be suite d for the reconstruction of arbitrary monotonic non-retrograde doping pr ofiles.
Table of Contents: 1 Introduction
1.1 Motivation
1.2 Overview of USJ characterization
1.2.1 Secondary Ion Mass Spectroscopy (1D)
1.2.2 Spreading Resistance Probe (1D)
1.2.3 Micro Four Point Probe (0D/1D)
1.2.4 Scanning Spreading Resistance Microscopy (2D)
1.2.5 Electron holography (1D)
1.2.6 Junction Photo Voltage (0D)
1.2.7 Others
1.3 Optical probes for USJ characterization
1.3.1 Reflectometry and Ellipsometry
1.3.2 Photo Modulated Optical Reflectance
1.3.2.1 Generalities
1.3.2.2 CI State of the art and objective
1.4 Content

2 Experimental setup
2.1 Hardware setup
2.2 Measurement conditions

3 Optical modeling
3.1 Fourier Components (signals)
3.2 Reflectance
3.2.1 First order reflection
3.2.2 First order Maxwell wave equation
3.2.3 Transfert matrix formulation
3.2.4 Comparison
3.2.5 Lateral integration
3.3 Refractive index
3.3.1 The thermo-optic model (Jellison)
3.3.2 The electro-optic free carrier absorption model (Drude)
3.3.3 The electro-optic free carrier absorption model (Schumann)
3.3.4 The band-to-band absorption model (Smith)
3.4 Summary

4 Material modeling
4.1 Plasma
4.1.1 The drift-di�ffusion equations
4.1.2 The ambipolar diff�usion equation
4.1.3 The steady-periodic ambipolar diff�usion equations
4.1.4 Absorption and optical generation models
4.1.5 Bulk Recombination models
4.1.6 Surface Recombination models
4.1.6.1 Single trapping center
4.1.6.2 Pb center
4.1.7 Band Gap Narrowing models
4.1.8 Mobility and Diff�usivity models
4.2 Temperature
4.2.1 The heat equation
4.2.2 Heat generation model
4.2.3 Analytical solution
4.3 General solution of the Helmholtz equation
4.4 Finite element formulation
4.4.1 The Gummel map for the DD equations in Slotboom's variables
4.4.2 Resolution flow chart

5 Experiment vs. Theory
5.1 Surface charging
5.1.1 The capacitor model
5.1.2 Removal of the charging contribution
5.2 Uniform doping
5.2.1 Experimental data
5.2.2 General information about the simulation
5.2.3 MEDICI vs. FSEM
5.2.4 Analysis of the models
5.2.4.1 Bulk recombinations
5.2.4.2 Surface recombinations
5.2.4.3 Mobilities
5.2.4.4 Injection dependent BGN
5.2.4.5 High illumination power (GW/cm2)
5.2.4.6 Frequency eff�ects
5.3 Nonuniform doping
5.3.1 Experimental data
5.3.2 Preliminary analysis of the experimental data
5.3.2.1 Temperature dependence on the layer thickness
5.3.2.2 Impact of the lateral pro�le on the signal
5.3.3 General information about the simulations
5.3.4 MEDICI vs. FSEM solutions
5.3.5 General behavior of the solution
5.3.6 Analysis of the models
5.3.6.1 Injection dependent BGN
5.3.6.2 Surface Recombinations
5.3.6.3 Layer mobility
5.4 Conclusion

6 Approximated Solutions
6.1 Nonlinear currentless approximation
6.2 Flat Quasi Fermi Level (FQL) and Doping Layer Invariant Bulk Level (LIBL) approximations
6.2.1 Excess carrier concentration in the layer
6.2.2 Lateral decay length in the layer
6.2.3 Junction potential
6.2.4 Extension to arbitrary pro�files
6.2.5 LIBL approximation validity
6.2.6 FQL approximation validity
6.3 Conclusion

7 Inverse Problem
7.1 The inflection point method
7.2 The high vs low power derivative method
7.2.1 Error estimation by Monte-Carlo approach
7.3 Direct optimization
7.4 Backward deconvolution by staircase doping pro�file approximation
7.5 Conclusion

8 Conclusions

A APPENDIX
A.1 BX10 data
A.1.1 BX10 output �file description
A.1.2 Normalized R1 legacy calculation
A.1.3 Laser power uncertainty
A.2 Reference phase calculation
A.3 n,k, K1; K2
A.4 Fundamental relations at interface
A.5 First order surface di�fferential reflectance
A.6 Maxwell wave equation
A.6.1 Calculation of Aspnes semi-infi�nite integral
A.6.2 Calculation of Aspnes reflectance from the phase derivative
A.7 Reflectance functional derivative
A.7.1 First order reflection
A.7.2 First order Maxwell wave equation
A.8 Use of maxima for interference calculation
A.9 Nonlinear steady periodic approximation
A.9.0.1 The harmonic recombination terms
A.9.0.2 Jacobian
A.10 The drift-diff�usion (DD) equations
A.10.1 Expression of the currents in Slotboom's variables
A.10.2 Expression of the currents in Slotboom's variables (relative to intrinsic level)
A.10.3 Expression of the currents in drift-diffusion form
A.10.4 Fermi-Dirac statistics
A.10.5 Einstein relation in Fermi-Dirac statistics
A.10.6 The Drift-Diff�usion equation in Slotboom variables
A.10.7 The Gummel map for the drift-diff�usion equations
A.10.8 Equilibrium
A.11 Matrix expressions for the Helmoltz equation
A.12 Interface traps
A.13 Solution of 1d Poisson equation with surface charges
A.14 Fitting of substrate excess carrier concentration and excess temperature as a function of pump power
A.15 Silicon optical functions
A.16 CVD samples description
URI: 
Publication status: published
KU Leuven publication type: TH
Appears in Collections:Nuclear and Radiation Physics Section
Molecular and Cellular Medicine - miscellaneous (-)

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