Matsuura Laboratory SiC SiC 13 2004 10 21 22
H-SiC ( C-SiC HOY
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n E C E D ( E F E T Matsuura Laboratory
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Osaka Electro-Communication University Unoped n 3C-SiC Electron concentration (cm -3 ) 10 17 10 16 0 5 10 1000/T (K -1 ) Matsuura Laboratory
Osaka Electro-Communication University Matsuura Laboratory ln n ( T ) 1/ T Hoffmann H ( T, E ref ) n( T ) ( kt ) 2 5 / 2 exp E ref kt
Osaka Electro-Communication University ln n ( T ) 1/ T 1 E D =124 mev N D =1x10 16 cm -3 ) 1 0 1 6 N D =1x10 16 cm -3 n ( T ) [ c m - 3 ] 1 0 1 5 1 0 1 4 E D =127 mev 1 0 1 3 E n( T ) exp D 2kT 1 0 1 2 0 5 1 0 1 5 1 0 0 0 / T [ K - 1 ] Matsuura Laboratory
E D1 =124 mev N D1 =1x10 16 cm -3. ( E D2 =64 mev N D2 =5x10 15 cm -3 ) B. (N =1x10 15 cm -3 ) n(t) [cm -3 ] 10 16 10 15 10 14 10 13 E D =54 mev N D =1.48x10 16 cm -3 E D =251 mev N D =8.9x10 15 cm -3 10 12 0 5 10 15 1000/T [K -1 ] B
Osaka Electro-Communication University n( T ) n = N C ( T ) exp E kt F n ( T ) = ND i[ 1 fd( EDi )] N i= 1 n N Di E Di N (2n+1) Matsuura Laboratory
Matsuura Laboratory Osaka Electro-Communication University Electron concentration (cm -3 ) 10 17 10 16 n 3C-SiC 0 5 10 1000/T (K -1 )
Osaka Electro-Communication University kt dn( T ) de F Hoffmann EF?? Spline
Osaka Electro-Communication University Free Carrier Concentration Spectroscopy (FCCS) n(t) H ( T, E ) ref T peaki n ( T ) ( kt ) E Di E k peak i, Eref ) 2 5 / H1( T ref 2 N kt exp Di peaki E ref kt Matsuura Laboratory
Matsuura Laboratory FCCS Windows http://www.osakac.ac.jp/labs/matsuura/
Osaka Electro-Communication University Undoped 3C-SiC (100) n Si Si 2 (CH 3 ) 6 1350 3C-SiC 32 m Si 5x5 mm 2 5 kg 1 m 85 K~500 K Matsuura Laboratory
Matsuura Laboratory Osaka Electro-Communication University Spline
Matsuura Laboratory Osaka Electro-Communication University FCCS H ( T, Eref ) n( T ) ( kt ) 2 5 / 2 exp E ref kt 51 mev 7.1x10 16 cm -3
Theoretical expression of FCCS signal is H ( T, E ref ) = i N N kt C0 kt Di N exp E exp E ref Di kt E kt E ref F I D ( E ) Di FCCS signal, in which the influence of the previously determined donor species ( E D2, N D2 ) is removed, is 2 n( T ) E N E E H 2 ref E 5 / 2 D ( kt) kt kt kt ref D2 D2 ref ( T, E ) = exp exp I ( ) D2
H2 Osaka Electro-Communication University 2 n( T ) E N E E H 2 ref E 5 / 2 ( kt) kt kt kt ref D2 D2 ref ( T, E ) exp exp I( ) D2 1 18 mev 3.8x10 16 cm -3 Matsuura Laboratory
H3 Osaka Electro-Communication University Matsuura Laboratory 114 mev 1.1x10 17 cm -3
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Matsuura Laboratory Osaka Electro-Communication University Undoped 3C-SiC FCCS 3 18 mev 51 mev 114 mev? FCCS H.Matsuura et al. Jpn. J. ppl. Phys. 39(2000)5069.
.Matsuura et al. J. ppl. Phys. 96(2004)7346. Donor Level [mev] 200 180 160 140 120 100 80 60 40 20 n 3C-SiC 3 2 1 0 10 15 10 16 10 17 Total Donor Density [cm -3 ] 10 18 E E E D3 D2 D1 180 9.8 10 5 3 = 71.8 3.38 10 = 51.9 5.97 10 N 5 3 5 3 D N N D D
Osaka Electro-Communication University n 4H-SiC H.Matsuura et al. J. ppl. Phys. 96(2004)5601. 150 n-type 4H-SiC epilayer N D [cm -3 ] Donor Level [mev] 100 50 E 5 D2 =.7 4.65 10 123 N 3 D Simulation using E D1 (N D ) = 70.9-3.38x10-5 1/3 N D E D2 (N D ) = 123.7-4.65x10-5 1/3 N D 0 10 14 10 15 10 16 10 17 10 18 Doping Donor Density [cm -3 ] E 5 D1 =.9 3.38 10 70 N 3 D
Problem in heavily doped p-type wide bandgap semiconductors The acceptor density, which is determined by the curve-fitting method using the temperature dependence of the hole concentration, is always much higher than the doping density.
Hole Concentration [cm -3 ] 10 18 10 17 10 16 10 15 10 14 10 13 10 12 10 11 Heavily l-doped 6H-SiC Heavily l-doped 6H-SiC : Experimental p(t) 2 3 4 5 6 7 8 9 10 1000/T [K -1 ] 2. C-V characteristics f 1. Hall-effect measurement Fermi-Dirac (FD) distribution function FD N ( E ) N = = 1 = E 1+ 4exp 2.5 10 4 10 mev 19 18 E kt Results determined by curve-fitting E = 180 cm cm FD F 3 3
E r 1 m 1 = 13.6 h ε m r 2 2 s * 0 [ev] p-type wide bandgap semiconductors (GaN, SiC, diamond) 1. Si 2. Semiconductor cceptor level (r=1) 1 st excited state level (r=2) SiC 146 mev 37 mev GaN 101 mev 25 mev Si B (45 mev)
E F (T) [mev] 400 300 200 100 0 Position of Fermi level in 6H-SiC : Heavily l-doped 6H-SiC : Lightly l-doped 6H-SiC E cceptor levels E F (T) E E F (T) E V 100 200 300 400 Temperature [K] Heavily doped case 1 st 2 nd
1. f FD ( E ) = 1+ g exp 2. f ( E ) = 1+ g ( T )exp 1 E E kt kt E E 2 g g (T) 1 F F
cceptor degeneracy factor In f FD ( E ) g = 4 In f ( E ) g E E E T T = g + g r ( ) ( ) 1 r exp exp ex r= kt kt 2 Degeneracy factors of excited states Excited state levels verage energy of acceptor level and excited state levels E ( ) Er E Er g r exp r= 2 = kt E ex ( T ) E + Er 1 g r exp r= 2 kt H. Matsuura New J. Phys. 4(2002)12.1.
Heavily l-doped 6H-SiC Hole Concentration [cm -3 ] 10 18 10 17 10 16 10 15 10 14 10 13 10 12 10 11 Heavily l-doped 6H-SiC : Experimental p(t) 2 3 4 5 6 7 8 9 10 1000/T [K -1 ] H ( T, E ) H(T,0.248) [x10 42 cm -6 ev -2.5 ] 4 3 2 1 p( T ) ( kt ) exp Heavily l-doped 6H-SiC Peak 0 100 200 300 400 Temperature [K] From the peak, N =2.5 10 19 cm -3 and E =180 mev for f FD ( E ) N =3.2 10 18 cm -3 and E =180 mev for f ( E ) Since the l-doping density is 4 10 18 cm -3, the influence of excited states on p(t) should be considered. ref 2 5/ 2 E kt ref
FCCS H(T,0.248) [x10 42 cm -6 ev -2.5 ] 4 3 2 1 Heavily l-doped 6H-SiC Experimental H(T,E ref ) Simulated H(T,E ref ) : f FD ( E ) : f( E ) H ( T, E ref ) = N N 1 kt V0 E exp kt N D 1 E exp kt ref E E kt ref I F ( E ) 1 0 100 200 300 400 Temperature [K] The H(T,E ref ) simulation for f( E ) is in better agreement with the experimental H(T,E ref ) than that for f FD ( E ).
Heavily doped 6H-SiC Lightly doped 6H-SiC f( E ) f FD ( E ) f( E ) f FD ( E ) N [cm -3 ] 3.2x10 18 2.5x10 19 4.1x10 15 4.9x10 15 E [mev] 180 180 212 199 Doping density [cm -3 ] 4.2x10 18 ~6x10 15 Only in heavily doped samples, f FD ( E ) cannot be used to analyze p(t). H. Matsuura J. ppl. Phys. 95(2004)4213.
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cceptor degeneracy factor In f FD ( E ) g = 4 + = = kt T E kt E E g g T g r r r ) ( exp exp 1 ) ( ex 2 Degeneracy factors of excited states In f ( E ) ( ) = = + = 2 2 ex exp 1 exp ) ( r r r r r r r kt E E g kt E E g E E T E verage energy of acceptor level and excited state levels Excited state levels
f ( E ) = 1+ g ( T 1 )exp E kt E F 4 p-type 6H-SiC 3 g (T) 2 1 Simulations : g (T) : g 0 100 200 300 400 Temperature [K] g (T) 4
Ionized cceptor Density [cm -3 ] 10 18 10 17 Heavily l-doped 6H-SiC Simulations N = 3.2x10 18 cm -3 E = 180 mev N D = 9.0x10 16 cm -3 : f FD ( E ) : f( E ) 100 200 300 400 Temperature [K]
Ionized cceptor Density [cm -3 ] Lightly l-doped 6H-SiC 10 16 10 15 10 14 Lightly l-doped 6H-SiC N - (T) simulations N = 4.1x10 15 cm -3 E = 212 mev N D = 1.0x10 14 cm -3 : f FD ( E ) : f( E ) 100 200 300 400 Temperature [K] Lightly doped
Osaka Electro-Communication University cceptor Level [mev] p 4H-SiC 500 450 400 350 300 250 200 150 100 50 l l-doped 4H-SiC epilayers 0 10 14 10 15 10 16 10 17 10 18 10 19 10 20 cceptor Density [cm -3 ]. Matsuura et al. J. ppl. Phys. 96(2004)2708.
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2 MOS d Ψ q = D 2 dx ε Poisson equation ( + ) N N + p n S ε 0 SiO 2 n + p p n + n - n + resistivity ρ = 1 qµ n n 1 σ = Matsuura Laboratory
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Osaka Electro-Communication University Electron Mobility [cm 2 V -1 s -1 ] 10 4 10 3 n-type 4H-SiC Epilayers Doping density [cm -3 ] : 8.8x10 14 : 2.2x10 15 : 2.4x10 15 : 3.5x10 16 : 6.8x10 16 : 9.4x10 17 10 2 100 1000 Temperature [K] β( N T D ) µ n( T, ND ) = µ n( 300, ND ) 300
Osaka Electro-Communication University β β(n D ) 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2 1.9 1.8 1.7 1.6 ( N ) D = 1.54 + 1. 35 1+ 1.08 N D 1.14 10 : Experimental : Simuration n-type 4H-SiC 1.5 10 14 10 15 10 16 10 17 10 18 10 19 Doping Donor Density [cm -3 ] 17 S. Kagamihara et al. J. ppl. Phys. 96(2004)5601.
Osaka Electro-Communication University Electron Mobility [cm 2 /(V-s)] 1000 800 600 400 200 300 K Our results W.J.Schaffer et al H.Matsunami et al J.Pernot et al W.Gotz et al.schoner et al C.H.Carter Jr. et al S.Nakashima et al Simulation results 0 10 14 10 15 10 16 10 17 10 18 10 19 10 20 Doping Donor Density [cm -3 ] S. Kagamihara et al. J. ppl. Phys. 96(2004)5601. µ n ( 300, N ) D = 1+ 977 N D 1.17 10 17 0.49
H. Matsuura et al. J. ppl. Phys. 96(2004)2708. p 4H-SiC µ p ( T N ) = µ ( 300, N ), p T 300 β ( N ) β 0.53 ( N ) = 2.51+ 0. 456 N 1+ 8.64 10 17 µ p ( 300, N ) = 37.6 + 0. 356 1+ 68.4 N 2.97 10 18
H. Matsuura et al. Jpn. J. ppl. Phys. 37(1998)6034. H. Matsuura et al. ppl. Phys. Lett. 79(2000)2092. H. Matsuura et al. Jpn. J. ppl. Phys. 42(2003)5187. p Si Divacancy Donor-like
Osaka Electro-Communication University p 4H-SiC 4.6 MeV 10 16 4H-SiC epilayer 2.6x10 14 cm -2 Hole Concentration [cm -3 ] 10 15 10 14 10 13 10 12 : Before irradiation : fter irradiation 1 2 3 4 5 6 7 8 1000/ T [K -1 ] Before irradiation fter irradiation E 1 [mev] 203 206 N 1 [cm -3 ] 6.2 10 15 8.2 10 14 E 2 [mev] 365 383 N 2 [cm -3 ] 4.2 10 15 3.4 10 15 N D [cm -3 ] 3.4 10 13 7.4 10 14 l H. Matsuura et al. ppl. Phys. Lett. 83(2003)4981.
Matsuura Laboratory FCCS