SiC Electronic Structure: Density Functional Theory for Mobility Calculation

1. SiC Electronic Structure with Density Functional Theory, and Monte Carlo for Mobility CalculationPart 1S. Salemi, A. Akturk, S. Potbhare N. Goldsman

2. Outline • Structures without Si Dangling Bonds • Retrieve the band gap with the hybrid functionals • The evolution of Gap • The place of defects in the bang gap • Carbon interstitial, and pair of carbons in SiC, oxide, and interface • Oxygen vacancy in oxide • Silicon interstitial in the oxide • Silicon vacancy in SiC • The Effect of Defect Passivation: • Incorporation of N at the interface • In oxide side • In SiC Side (shekl ro nadaaram) • Carbon (interstitial, and pair of carbon) Passivation, • Total DOS • DOS of the defect • Oxygen Vacancy, • Silicon Dangling Bonds at Interface, • Silicon Vacancy in SiC Side. • The incorporation of nitrogen, and phosphorus at the interface • The formation of interface layer • The related mobility calculation

3. Motivation for Passivation • High interface trap densities at the 4H-SiC/SiO2 interface near the conduction band is the main reason of low channel mobility in 4H-SiC MOSFETs. • Experiments show the improvement of channel mobility by post-oxidation annealing process: • Hydrogen postoxidation annealing improves the channel mobility of 4H-SiC MOSFETs on the (0001)-Si face [1] • Thermally grown oxides annealed in nitric oxide (NO) ambient provides reduction of interface-trap density [2,3] • Phosphorus incorporation in the interface after postoxidation annealing in phosphoryl chloride (POCl3) improves channel mobility[4,5] • Therefore, understanding of the mechanisms underlying passivation of interface defects allows for process optimization. [1]K. Fukuda et al., Appl. Phys. Lett. 77, 866 (2000), [2]S. Dimitrijev et al., IEEE Electron Device Lett. 18, 175 (1997) [3]H.-F. Li et al., Appl. Phys. Lett. 70, 2028 (1997), [4]Dai Okamoto et al., IEEE Electron Device Letters, 31, 7, (2010) [5]Dai Okamoto et al., Appl. Phys. Lett. 96, 203508 (2010)

4. Density Functional Theory Based Simulation of Carrier Transport in Silicon Carbide-Silicon Dioxide Interfaces 3. Density of States 2. Detailed Band Structure 1. Xtal Energy Scattering 4. Averaged Dispersion Relation Scattering 6 4 7. Field/Energy Dependent Curves Drift 3 5 Drift No Scattering 2 1 Drift Momentum 6. Semiclassical Monte Carlo 5. Scattering Rates

5. The Band Gap Problem in DFT • Density functional theory is a ground state theory. • The eigenstates of Kohn-Sham equation are the eigenvalues of a fictitious single-particle equation. However, their eigenfunctions give the true electron density. • The band structure of semiconductors defined as the energies of one-particle excitations, related to the difference between total energies of states differing by one electron. • The lowest conduction-band energy is given by: • the highest valence-band energy is given by: • Therefore, the band gap is given by: • In Kohn-Sham formalism the conduction and valence energies are given as: • However, from the definition of the valence band edge: • The attempt is focused on neglecting the difference between.

6. Retrieving the Real Band Gap • Kohn-Sham band gap is: • The band gap of N particle: • By replacing by • By adding an electron to a semiconductor, the exchange-correlation potential jumps by a constant. This discontinuity gives the difference between the true band gap and the one obtained from the ground state, one-particle equation. • Solution: using hybrid functional, which is a mixture of a DFT and a Hartree-Fock calculation. The jump of the exchange correlation potential as the result of adding one electron

7. The Evolution of Band Gap (1) Starting from 4H-SiC unit cell • Hybrid functional for retrieving the real band gap: PBE0 • Software: QE CB and a-quart unit cell GAP VB Si Blue; C Yellow Density of States Band Structure to a 4H(0001)SiC/SiO2 supercell CB SiO2 Si Blue; O Red GAP H atoms 72-atom SiC VB Density of States Band Structure Si Blue; C Yellow; O Red; H Small Blue [1]Paolo Giannozzi et al., Journal of Physics: Condens. Matter 21, 395502 (2009)

8. The Evolution of Band Gap (2) • The abrupt structure without dangling bond (for reference) • Using hybrid functional to retrieve the real band gap • The evolution of band gap from SiC to the interface, and oxide by using the local density of states Local Density of States a-quartz Interface: oxygen: red, carbon: black, silicon: blue SiC

9. Defects at SiC/SiO2 at Abrupt Interface • Oxidation process as the origin of the possible defects: • The basic assumption is that three oxygen atoms arriving at the same spot on the SiC side of the interface, causes the emission of a CO molecule, leaving a VCO2 defect (two oxygen in a carbon vacancy) behind. • The CO molecules either break up later producing interstitial carbon (Ci) atoms which may cluster, or leave into the oxide where they can form carbon rich clusters. • The possible defects can be: • Interstitial oxygen at the interface: Oiif • Carbon interstitial • Carboninterstitial sharing a lattice carbon site at the interface: (C-Ci)C • Pair of carbon interstitials (Ci)2 P. Deak et al; Physica B 340–342 (2003) 1069–1073 M. Di Ventra, S.T. Pantelides, Phys. Rev. Lett. 83 (1999) 1624.

10. Defects in SiO2/ Possible Nit Traps • Slow acceptor states, which are fixed w.r.t. the CB of SiO2 are believed to make the Nit traps; their origin is in SiO2 • They are independent of substrate orientation and even the oxidation process. • Possible defects in a-quartz are: • Oxygen vacancy • Si interstitial • C interstitial • A pair of carbons J. M. Knaup,* P. Deák, and Th. Frauenheim; PHYSICAL REVIEW B 72, 115323 2005

11. The Location of defects in the Bang Gap/1 • The abrupt structure without dangling bond is kept as the reference • Hybrid functional is used to retrieve the real band gap • Carbon interstitial, and pair of carbons are placed in several forms, and positions in SiC, oxide, and interface • Oxygen vacancy is placed in oxide • Silicon interstitial in the oxide • Silicon vacancy in SiC • The place of defects are marked both in the underestimated band gap, and the real band gap retrieved by hybrid functional • The place of defects are aligned with respect to the DOS; DOS of the structures are aligned with respect to the deep, valence states, far from the gap and therefore unaffected by local changes.

12. The Location of defects in the Bang Gap/2 • In Bulk SiC, and at the interface: • The place defect peak is strongly dependent on the form, and location of defects • The peaks of occupied states related to carbon interstitial, and a pair of carbons in SiC side, and at the interface are mainly in the vicinity of valence band • The peaks of unoccupied states (if there are any) related to carbon interstitial, and a pair of carbons in SiC side, and at the interface are mainly in in the vicinity of conduction band • Silicon vacancy introduces traps near the valence band. • Silicon interstitial in oxide (near the interface) introduces traps near the conduction band. • Oxygen vacancy in the oxide (near the interface) introduces traps near the conduction band.

13. The Effect of Defect Passivation • Carbon interstitial, and pair of carbons, placed in several forms, and positions in SiC, oxide, and interface are passivated by nitrogen, and phosphorus • Carbon interstitials are either passivated by hydrogen, nitrogen, and phosphorus connected to them • In the case that passivation remove the carbons, the passivant replace the defect. • Oxygen vacancy in oxide, is passivayed by nitrogen, and phosphorus in the place of vacancy • Silicon vacancy in SiC is passivayed by nitrogen, and phosphorus in the place of vacancy • Silicon interstitial in the oxide is passivated by nitrogen

14. Nitrogen Passivation of Carbon Dangling Bonds • SiC/SiO2 structure with a carbon interstitial in is made, • N passivates the states in the bandgap. Interface states pushed away after N treatment C interstitial C interstitial passivated by N Mobility versus External Field for Abrupt Structure with C Interstitial in SiC before, and after N Passivation • Assuming a transition region thickness of 1nm and total trap density of 1013 cm-2 • Calculated mobility is 20 cm2/Vs Mobility (cm2/Vs)

15. Nitrogen Passivation of Carbon Dangling Bonds/ LDOS after Passivation • The effect of the density of states on carbon interstitial before, and after passivation (in the case that C is connected to N) is studied; • Carbon passivated after Connected to Nitrogen. LDOS of Ci after N Passivation

16. Nitrogen Passivation of C Dangling Bonds (Ci), Removing the Defect • It was also found that annealing in NO remove the carbon excess [7]. • The valence shell of nitrogen contains one electron more than the valence shell of carbon. • Replacing the carbon interstitial with nitrogen atoms is expected to lead to the removal of defect levels associated with the carbon dangling bonds. Interface states pushed away after N treatment Mobility versus External Field for Abrupt Structure with C Interstitial in SiC before, and after Replacing N C interstitial Is replaced by N Mobility (cm2/Vs) [7] Chang K-C, Porter L M, Bentley J, Lu C-Y and Cooper J Jr 2004 J. Appl. Phys. 95 8252

17. Nitrogen Passivation of Carbon Dangling Bonds/ LDOS after C Removal • The effect of the density of states on carbon interstitial before, and after passivation (in the case that C removed by N) is studied;

18. Nitrogen Passivation of Oxygen Vacancy • SiC/SiO2 structure with an oxygen vacancy in oxide is made; • The vacancy is replaced by a N atom; • N pushed the Nit away from band edge. Interface states pushed away after N treatment O vacancy passivated by N • Assuming a transition region thickness of 1nm and total trap density of 1013 cm-2 • Calculated mobility is around 20 cm2/Vs Mobility (cm2/Vs)

19. Nitrogen Passivation of O Vacancy/ LDOS • The local density of states related to oxygen vacancy on the silicon atoms at the surface of SiC before, and after N Passivation.

20. N, and P Passivation of Si Vacancy at the Interface Si Vacancy passivated by P • According to our calculation, silicon vacancy in SiC side makes trap density near the valence band • Nitrogen, and phosporus passivation remove those traps.

21. Debate over Si Dangling Bonds • Afanas’ev et al. [1] ruled out the existence of Pb centers (silicon dangling bonds) at the interface of SiC/SiO2 structures: • the interface traps at SiC/SiO2 are different from Pb centers of Si/SiO2, and • the hydrogen passivation with the same Si/SiO2 conditions is ineffective for SiC/SiO2 interface at the same co. • Afanas’ev et al. concluded that the traps at SiC/SiO2 interface are due to carbon clusters. • Fukuda, et al. [2] reported the reduction of interface trap densities (at 0.2–0.6 eV) below the conduction band for n-type 4H-SiC MOS on the (0001) Si face above 800C, and hence the improvement of channel mobility. • Reduction does not happen in 400C (as Si/SiO2) interface traps. • Conclusion: interface defects are due to both Si, and C dangling bonds. • Since they didn’t observed any C clusters, they concluded that carbon clusters are sample dependent. • Tsuchida et al. [3]claimed the ATR spectroscopy showed clear surface polarity dependencies of C–H, and Si–H stretch modes on the 6H–SiC surfaces after H2 annealing at 1000. [1]V. V. Afanas’ev, et al.; Appl. Phys. Lett. 76, 1585 .2000.. Appl. Phys. Lett. 78, 2001 [2]Fukuda, K. et al; Appl. Phys. Lett., 76, 1585, 2000 [3]H. Tsuchida, I. Kamata, and K. Izumi, “Infrared Spectroscopy of Hydrides on the 6H-SiC Surface” Appl. Phys. Lett. 70, 3072, 1997

22. Passivation of Si Dangling Bonds by H, and N Si passivated by H Si passivated by N Si-H Bond-Length=1.4A Si-N Bond Length=1.7A • H passivation does not remove all the traps near the CB because wide bandgap of SiC encompasses the energy levels of Si-H bonds; therefore, some states are still inside the gap, near the conduction band. • N passivation pushes the energy levels of interface traps away from CB edge due to strong Si-N bonds and Si-N-O bridges; • Therefore, N treatment reduces Dit in upper half of the bandgap

23. Passivation of Si Dangling Bonds by P, and As Si passivated by H Si passivated by N Si-P Bond Length=2.1A Si-As Bond Length=2.3A • Phosphorus removes the traps near CB edge, Mechanism is not clear: • Phosphorus in Si/SiO2 may relax strain in SiO2 near interface and Arsenic • Prediction for Arsenic (the third element after N and P in periodic table): Removal of Nit through Arsenic passivation Mobility (cm2/Vs)

24. Passivation of Si Dangling Bonds/ LDOS • The local density of states related to silicon dangling bonds on the silicon atoms at the surface of SiC before, and after Passivation.

25. Incorporation of Passivants at the Interface • Goal: Study the effect of N bonds at the interface • The formation of silicon oxynitride in the oxide side • Probable cause: the formation of N-Si-O bridges, called silicon oxynitride (SiON) at the interface [1] N-Si-O Bridge Band gap widens after after N treatment Si-N Bond Length=1.7A ? P-Si-O Bridge Si-P Bond Length=2.1A [1] S. Dimirrijevet al., IEEE ELECtron Dev. Lett., vol. 18, 1997,[2] H.F.Li, et al., Applied physics letters vol 70, 1997, [3]P.Jamet, et al., Appl. Phys., vol.90, 2001, [4]P.Jamet, et al., Mater. Sci. Forum, vol.389-393, 2002, [1]T. Shirasawa, et al. Phys. Rev. Lett. 98, 2007

26. Transition Layer: Silicon Oxycarbide (CSi/SiO2) • During the oxidation of the SiC surface, carbon release in the form of CO molecules; • Some of the C-O bonds remain trapped inside the interface. • The investigations on amorphous silicon oxycarbide glasses, based on XPS and Fourier transform infrared spectroscopy, show clear evidences of C-O-Si bridges. • The (Si1-xCxO2) is produced by replacing some Si atoms by C in a-quartz. • A large value for x is unfavorable because the quartz-like CO2 phases are unstable at low pressures. • The particular value x= (1/3) is very suitable. • Si1-xCxO2 can be made by the replacement of Si atoms with C atoms in the a-quartz cell Cesar R. S. da Silva, Joao F. Justo, and Ines Pereyra; App. Phys. Lett. 84, No. 24, June 2004

27. Transition Layer: Silicon Oxycarbide (OC SiC) • The formation energy resulted from ab-initial shows the dominance of OC over Oi in bulk SiC • This dominance gives a theory behind the oxidation behavior of SiC • When oxygen atoms arrive at the SiC/SiO2 interface, they substitute carbon atoms forming a thin oxygen contaminated Si-rich interface layer which has still to undergo a structural reconstruction to form SiO2. • The presence of such a layer has been observed by x-ray photoelectron spectroscopy XPS. The net chemical composition of this layer should be close to that of SiO. A.Gali, D. Heringer, P. Dea´k, Z. Hajnal, Th. Frauenheim, R. P. Devaty, and W. J. Choyke; PHYSICAL REVIEW B 66, 125208 (2002)

28. Summary • Several SiC/SiO2 structures are made to investigate the effect of different defects, and transition layer on the density of states, and mobility; • the densities of states is calculated by using DFT technique; • The effect of carbon interstitial, carbon pairs (in SiC, oxide, and at interface), oxygen vacancy in oxide, silicon interstitial in oxide, and silicon vacancy in SiC is studied. • The effect of passivation on the defects, and structures have been studied: • The effect of H, N, P passivation on the strucrures, and defects is studied; • The new structures based on N-Si-O, and P-Si-O make the band gap wider; • It seems that N, and P passivate both the traps near conduction, and valence bands. • Monte Carlo simulation is used to show the effect of interface on transition layer mobility as well as ionized impurity limited mobility; • An areal trap density of 1013 cm-2 results in extremely low mobilities ~10-40 cm2/Vs; • Passivation of the defects at the SiC/SiO2 interface by N, P and As seems to reduce Nit and give rise to larger mobilities.