Systemic Errors in the MOS Conductance Technique Supported by the - PowerPoint PPT Presentation

Systemic Errors in the MOS Conductance Technique Supported by the II-VI Foundation Cooperative Research Initiative S. Swandono, D. T. Morisette, and J. A. Cooper School of Electrical and Computer Engineering and Birck Nanotechnology Center Purdue University, West Lafayette, IN

Physics of the MOS Conductance Technique G P (ω) C OX C D C P (ω)

Lehovic Distributed-State Model (interface state time constant) (uniform distribution of states in energy) G P ( ω ) C OX C D C P (ω) K. Lehovic, Appl. Phys. Lett., 8 , 48 (1966).

Non-Uniform Fixed Charge Q F Gate Randomly Distributed Fixed SiO 2 Charges Q F Depletion Electric Layer Field Lines Neutral Region E. H. Nicollian and A. Goetzberger, Bell Syst. Tech. J., 46, 1055 (1967).

Nicollian & Goetzberger Model (interface state time constant) (Distribution of states in energy) (sum over all “patches” under gate) (normalized surface potential) (probability density function for the variation of surface potential across the interface) G P ( ω ) C OX C D C P (ω) E. H. Nicollian and A. Goetzberger, Bell Syst. Tech. J., 46, 1055 (1967).

Earliest Data on σ N ( E ) in Silicon (1970) Exponential decrease of Interface State σ N toward the band edge. Capture Cross Section σ N ? Surface Potential u S W. Fahrner and A. Goetzberger, Appl. Phys. Lett. , 17 , 16 (1970).

Measured Capture Cross Sections in 4H-SiC 1 2 1e-14 This Work 1 2 3 σ N ( E ) (cm 2 ) 1e-16 M. Das, Ph.D. Thesis, Purdue Univ., Dec. 1999. ? 3 1e-18 1e-20 0 0.1 0.2 0.3 0.4 0.5 E C - E (eV)

Assumptions of the Nicollian–Goetzberger Model 1. Analysis limited to biases in depletion (linear u S - V G relationship). (This allows the Gaussian probability distribution for fixed charge to be translated into a Gaussian probability distribution of surface potential u S .) 2. Interface-state parameters ( D IT , σ N ) vary slowly with energy. ( D IT can be taken outside the integral over surface potential.)

Procedure to Quantify Errors 1. Use an exact calculation that eliminates assumptions made by Nicollian & Goetzberger. 2. Assume a Gaussian distribution of fixed charge P ( Q F ), and use the exact u s - V g relationship to calculate the probability distribution of surface potential P ( u S ). 3. Choose specific values for D IT , σ N , and σ Q , and generate a G P / ω vs. ω curve. 4. Regard the G P / ω vs. ω curve as experimental data. 5. Use the original Nicollian-Goetzberger model to extract the apparent interface trap density D IT , standard deviation of surface potential σ US , and capture cross section σ N .

Assumptions of the Nicollian–Goetzberger Model 1. Analysis limited to biases in depletion (linear u S - V G relationship). 2. Interface-state parameters ( D IT , σ N ) vary slowly with energy.

The u S - V G Relationship Depletion Accumulation 20 10 Surface Potential u s E C -E F = 0.2 eV 0 -10 E C -E F = 0.5 eV 4H-SiC -20 T OX = 40 nm E C -E F = 0.8 eV -30 N D = 2e16 cm -3 -40 -50 -60 -70 -3 -2 -1 0 1 2 V G - V FB (V)

Effect of Non-Uniform Fixed Charge Q F

Mapping P ( Q F ) to P ( u s ) at E C -E F = 0.8 eV 20 10 Surface Potential u S 0 -10 -20 E C -E F =0.8 eV Gaussian Q F -30 T OX = 40 nm -40 σ Q = 2e11 cm -2 -50 -60 -70 -3 -2 -1 0 1 2 V G - V FB (V)

Mapping P ( Q F ) to P ( u s ) at E C -E F = 0.5 eV 20 10 Surface Potential u S 0 -10 E C -E F =0.5 eV -20 Gaussian Q F -30 T OX = 40 nm σ Q = 2e11 cm -2 -40 -50 -60 -70 -3 -2 -1 0 1 2 V G - V FB (V)

Mapping P ( Q F ) to P ( u s ) at E C -E F = 0.2 eV 20 10 Surface Potential u S E C -E F =0.2 eV 0 -10 Gaussian Q F T OX = 40 nm -20 σ Q = 2e11 cm -2 -30 -40 -50 -60 -70 -3 -2 -1 0 1 2 V G - V FB (V)

Effect of Bias Point (Fermi Level) 2.5 T OX = 40 nm D IT =8.48e10 eV -1 cm -2 2 σ Q = 2e11 cm -2 G P / ω (nF cm -2 ) E C -E F = 0.2 eV 1.5 E C -E F = 0.5 eV 1 0.5 E C -E F = 0.8 eV 0 1.E-08 1.E-04 1.E+00 1.E+04 1.E+08 1.E+12 ωτ

Effect of Oxide Thickness

Mapping P ( Q F ) to P ( u s ) at T OX = 10 nm 20 10 Surface Potential u S 0 E C -E F = 0.5 eV -10 Gaussian Q F -20 σ Q = 2e11 cm -2 -30 E C -E F = 0.5 eV -40 -50 -60 -70 -3 -2 -1 0 1 2 V G -V FB (V)

Mapping P ( Q F ) to P ( u s ) at T OX = 40 nm 20 10 Surface Potential u S 0 -10 Gaussian Q F E C -E F = 0.5 eV σ Q = 2e11 cm -2 -20 E C -E F = 0.5 eV -30 -40 -50 -60 -70 -3 -2 -1 0 1 2 V G -V FB (V) 19

Mapping P ( Q F ) to P ( u s ) at T OX = 150 nm 20 0 E C -E F = 0.5 eV Surface Potential u S -20 Gaussian Q F σ Q = 2e11 cm -2 -40 E C -E F = 0.5 eV -60 -80 -100 -120 -140 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 V G -V FB (V)

Effect of Oxide Thickness 3.0 σ Q = 2e11 cm -2 D IT = 8.48e10 eV -1 cm -2 2.5 E C -E F = 0.5 eV 10nm G P / ω (nF cm -2 ) 2.0 1.5 40nm 1.0 150nm 0.5 0.0 1.E-03 1.E+00 1.E+03 1.E+06 1.E+09 1.E+12 ω (rad s -1 )

Assumptions of the Nicollian–Goetzberger Model 1. Analysis limited to biases in depletion (linear u S - V G relationship). 2. Interface-state parameters ( D IT , σ N ) vary slowly with energy.

Measured D IT ( E ) in 4H -SiC

Question: How much error is introduced by an exponentially increasing D IT ? To find out, choose a bias point in the linear region of the u S – V G relationship, ( E F deep in the bandgap, far from the CB). Here the only distortion is due to the exponential D IT .

Choose a bias point with E F far from the CB Depletion Accumulation 20 E C 10 Surface Potential u s 0 -10 4H-SiC -20 T OX = 40 nm -30 N D = 2e16 cm -3 E C -E F =1.3 eV -40 -50 E i -60 -70 -3 -2 -1 0 1 2 V G - V FB (V)

Exponential Model for D IT ( E ) 1E+13 1E+12 1E+11 α = 0.2 D IT ( cm -2 eV -1 ) E C -E = 1.3 eV 1E+10 D IT0 = 1.09e8 eV -1 cm -2 1E+09 Uniform 1E+08 α = 0 1E+07 1E+06 1E+05 0 0.5 1 1.5 2 E C - E (eV )

Impact of Exponential D IT ( E ) 1.2E-2 T OX = 40 nm Exponential D IT 1.0E-2 E C -E F = 1.3 eV σ Q = 2e11 cm -2 G P / ω (nF cm -2 ) 8.0E-3 6.0E-3 4.0E-3 2.0E-3 Uniform D IT 0.0E+0 1.E-16 1.E-12 1.E-08 1.E-04 1.E+00 1.E+04 ω (rad s -1 )

Combined Effects • Non-linear u S – V G relationship • Exponential D IT ( E ) • σ N assumed constant (uniform with respect to energy)

T OX = 10 nm, ( E C - E F ) = 0.5 eV 3.5 σ Q = 2e11 cm -2 3.0 α = 0.2 2.5 G P / ω (nF cm -2 ) 2.0 1.5 Exact Fit using Calculation 1.0 Nicollian- Goetzberger 0.5 model 0.0 1.E-03 1.E+00 1.E+03 1.E+06 1.E+09 1.E+12 ω (rad s -1 )

Total Error in D IT ( E ) at T OX = 10 nm 1.E+12 E C – E F = 0.5 eV σ Q = 2e11 cm -2 α = 0.2 D IT (cm- 2 eV -1 ) 1.E+11 Apparent Real 1.E+10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 E C -E (eV )

Total Error in σ N ( E ) at T OX = 10 nm 1.E-14 E C – E F = 0.5 eV σ Q = 2e11 cm -2 α = 0.2 1.E-15 σ N (cm 2 ) 1.E-16 Apparent 1.E-17 Real 1.E-18 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 E C -E (eV )

T OX = 40 nm, ( E C - E F ) = 0.5 eV 14 E C – E F = 0.5 eV 12 σ Q = 2e11 cm -2 α = 0.2 G P / ω (nF cm -2 ) 10 8 6 Exact Fit using 4 Calculation Nicollian- Goetzberger 2 model 0 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10 1.E+12 ω (rad s -1 )

Total Error in D IT ( E ) at T OX = 40 nm 1.E+12 E C – E F = 0.5 eV σ Q = 2e11 cm -2 α = 0.2 D IT (cm -2 eV -1 ) 1.E+11 Apparent Real 1.E+10 0 0.2 0.4 0.6 0.8 E C -E (eV )

Total Error in σ N ( E ) at T OX = 40 nm E C – E F = 0.5 eV 1.E-08 σ Q = 2e11 cm -2 α = 0.2 1.E-10 ϒ = 0.749 σ N (cm 2 ) 1.E-12 Apparent 1.E-14 Real 1.E-16 1.E-18 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 E C -E (eV )

T OX = 150 nm, ( E C - E F ) = 0.5 eV 3.5 E C – E F = 0.5 eV 3.0 σ Q = 2e11 cm -2 α = 0.2 G P / ω (nF cm -2 ) 2.5 Exact 2.0 Calculation 1.5 Fit using 1.0 Nicollian- Goetzberger 0.5 model 0.0 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10 1.E+12 ω (rad s -1 )

Total Error in D IT ( E ) at T OX = 150 nm 1.E+12 Apparent D IT (cm -2 eV -1 ) Real 1.E+11 E C – E F = 0.5 eV σ Q = 2e11 cm -2 α = 0.2 1.E+10 0 0.2 0.4 0.6 0.8 E C -E (eV )

Total Error in σ N ( E ) at T OX = 150 nm 1.E-08 E C – E F = 0.5 eV σ Q = 2e11 cm -2 α = 0.2 γ = 0.921 1.E-10 σ N (cm 2 ) 1.E-12 Apparent 1.E-14 Real 1.E-16 1.E-18 0 0.2 0.4 0.6 0.8 E C -E (eV )

D IT ( E ) Exponential D IT (E) near CB. σ US ( E ) σ US decreasing toward CB. Exponential σ N (E) toward CB. σ N ( E ) W. Fahrner and A. Goetzberger, Appl. Phys. Lett. , 17 , 16 (1970). Surface Potential u S

Apparent σ US vs. Energy Exponential D IT T OX = 40 nm, σ Q = 2x10 11 cm -2 Apparent σ US Tox = constant σ Q = constant σ US ratio ≈ σ Q ratio σ US ratio < Tox ratio T OX = 10 nm, σ Q = 2x10 11 cm -2 T OX = 40 nm, σ Q = 5x10 10 cm -2 E C – E (eV)

Conclusions • A rapidly increasing D IT ( E ) and a non -linear u S - V G relationship cause errors in the MOS conductance technique. • Data extraction is more accurate with thinner oxides. • The apparent energy dependence of σ N is an artifact caused by an increasing D IT ( E ) and a non -linear u S - V G relationship. • We are creating calibration curves to estimate the actual interface state parameters from the apparent parameters measured on real devices.

Thank you! Supported by the II-VI Foundation Cooperative Research Initiative