Hall効果測定による化合物半導体中の不純物準位の評価に関する研究
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- ゆあ つくとの
- 5 years ago
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1 4 9 M00 Hall
2 4 M00 Hall H.Matsuura, K.ishikawa, K.Morita, M.Segawa, and W.Susaki: etermination of densities and energy levels of impurities and traps in semiconductor by a new method based on Hall-effect measurements, Extended abstracts of the 0th electronic materials symposium (EMS0). pp (F5). Jun.00 H. Matsuura, K. Morita, K. ishikawa, T. Mizukoshi, M. Sagawa and W. Susaki : cceptor ensities and cceptor Levels in Undoped GaSb etermined by Free Carrier Concentration Spectroscopy, Jpn. J. ppl. Phys. to be published at February, 00.
3 Hall 4 M00
4 000 4 Hall Hall GaSbInGaSblGaSb4H-SiC Hall FCCSFree Carrier Concentration Spectroscopy GaSbInGaSblGaSb4H-SiC Hall FCCS 3 Molecular Beam EpitaxyMBE InGaSblGaSb X-Ray iffraction XR FCCS 4 GaSbInGaSblGaSb4H-SiC Hall Hall FCCS Hall 5 4H-SiC 6 GaSb InGaSb l 4H-SiC l 4H-SiC Te lgasb FCCS 4H-SiC M00
5 (). ().GaSb ()..Undoped GaSb..InGaSblGaSb.34H-SiC () () (3).4 (6) Free Carrier Concentration SpectroscopyFCCS (7). S ( T, Eref ) (7). H T, E () ( ref ) E ref.3 (5) X-Ray iffractionxr (6) 3.Bragg (6) 3.Vegard (7) 3.3 (7) 3.4Undoped InGaSbTe doped lgasb (0) Hall (3) 4.van der Pauw (5) 4. Hall (3) 4.3 (36) 4.3. (36) 4.3. (37) 4.4 (39) 4.5ifferential Hall Effect Spectroscopy(HES) (4) 4.6FCCS (44) (48) 5. (48) 5.4H-SiC (49)
6 (5) 6.undoped GaSb (5) 6.. ouble cceptor Model ( 6.. cceptor cceptor (55) 6..3 cceptor cceptor4 cceptor5 6.undopedInGaSb (57) 6.. In,Ga Undoped In0.6Ga0.84Sb, In0.8Ga0.8Sb (6) 6.. Sb/(In+Ga), 3, 5 Undoped In0.Ga0.8Sb (6) 6.34H-SiC (6) 6.3.l implanted 4H-SiC (6) 6.3. l doped 4H-SiC Wafer (68) 6.4Te doped lgasb (7) 7 (76)
7 . CPUCentral Processing Unit RM(ynamic Random ccess Memory) LSILarge Scale Integrated Circuit Si ppm Parts Per Million 00 - GasGaSbGa - SiC p n pn Hall Hall Hall Hall FCCSFree Carrier Concentration Spectroscopy GaSb 6H-SiC4H-SiC FCCS Hall
8 .GaSb pn λ E λ =.4 / E [µm] g g 5 µm COCH4 InP µm GaSb, Ins, InSb, lsb.65 µm ) GaSb GaSb p n..undoped GaSb Undoped GaSb MBEMolecular Beam Epitaxy: p ) GaSb pn Undoped GaSb Undoped GaSb Beam Equivalent Pressure, BEP..InGaSb, lgasb GaSb, InSb, lsb InGaSb, lgasb GaSb.9 m TypeIn0.Ga0.8Sb/l0.4Ga0.6Sb/GaSb Undoped In0.Ga0.8Sb lgasb n Te MBE lgasb Te Kundsen cellk- GaTe3 BEP Te Te lgasb Te Te
9 . 4H-SiC O CC CC Si MOSFETMetal Oxide Semiconductor Field Effect Transistor IGBT Insulated Gate Bipolar Transistor Si SiC(Silicon Carbide) Si. ev 00 SiC 300 Si 00 Si kv 300 Si SiC SiC SiC (C) (Si) B C C B SiC 3
10 B C C B 00 SiC 4H-SiC 4H-SiC SiC 4H-SiC 3.3 ev H-SiC 6H-SiC 4H-SiC 4H Ramsdell C [000] BCB 4 hexagonal xis [000] 4 Layers B C B C Si toms C toms Hexagonal Site Cubic Site 4H-SiC 4
11 SiC SiC pn SiC Lely SiC SiC CVChemical Vapor eposition SiC SiC T E = a 0 exp kt T Si SiC lsic Si Si Si SiC Si SiC 800 m Si SiC l SiC High Temperature cm s - Low iffusion Coefficient Si Low Temperature cm s - High iffusion Coefficient 5
12 .4 Hall p T p T ln ( p ( T )) / T p T FCCSFree Carrier Concentration Spectroscopy Gas MBE GaSb Gas MBE InGaSb n 4H-SiC l 4H-SiC l 4H-SiC Gas MBE Te lgasb 6
13 Free Carrier Concentration SpectroscopyFCCS S (, E ). T ref Hall p T n n T S ( T E ) ( T ) 3)-9) p Eref, ref exp (.) kt kt k :Boltzmann T :: E ref p T p ( T ) = f ( E ) m + i= ( T ) + n n i= k i= l i= i TEi i THi f i ( E ) TEi [ f ( E )] (.) i [ f ( E )] i n i m i k TE i l TH i E i E i E TEi E THi E n ( T ) f ( E Fremi-irac f ( E) = ) (.3) E EF + exp g kt 7
14 Fermi-irac ( E f ) + = kt E E g E f F exp (.4) g 4 (.) Fermi-irac.3.4 (.) E F g g g T, E ref S = = = = = = kt E kt T n kt E kt E F kt E E kt E F kt E E kt E F kt E E kt E F kt E E kt E T S n i i m i i i i l i i i k i i i m i i i n i ref ref TH TH ref TH TH ref TE ref TE TE ref ref exp exp exp exp exp exp, (.5) + = kt E E g kt E E F F F exp exp (.6) + = kt E E g kt E g E F F F exp exp (.7) kt E E kt i i ref exp (.8) 8
15 (.8)T T peak E i E = ref (.9) k S ( T, E ) peak ref ( ) iexp = (.0) kt peak p (.5) S T, E ref S T, E ref 6 n(t ) S j i i ref ( T, E ) = exp F( E ) ref i= kt E E kt m n Eref i + THi exp (.) i= i= kt kt j = k + l + m + n ( S T, E ref ) =05 cm -3 =0. ev =04 cm -3 p T ( ref E ) ). p(t S T, E. peak E S( T, E ref ). S ( T, E ref ) S T, E ) peak E ( ref =05 cm -3 E =0. ev =04 cm -3 i Hole Concentration [ 0 4 cm -3 ] p type Si = 0 5 cm E = 0. ev = 0 4 cm Temperature [K]. p T E F E F -E V [ev] 9
16 S(T,0)[ 0 6 cm -3 ev - ] peak Temperature [K] T, E ref ( =05 cm -3 E =0. ev =04 cm -3 ) Hole Concentration [ cm -3 ]. S p type Si = cm -3 E = 0.64 ev 0. = cm Temperature [K].3 p T E F E F -E V [ev] S(T,0)[ 0 0 cm -3 ev - ].3.. peak Temperature [K].4 S( T, E ref ) ( =6.608 cm -3 E =0.64 ev =.400 cm -3 ) 0
17 = cm -3 E =0.64 ev =.400 cm -3 ( p T ).3 p ( T ) S( T, E ref ).4 peak E S( T, E ref ).4 00 K peak E =6.708 cm -3 E =0.64 ev =9.309 cm -3
18 H (, Eref ). T S T, E ) H ( ref ( kt ) T, E ref p( T ) Eref H ( T, Eref ) exp (.).5 kt.5 πm V = h p h ( T ) = k T k T F ( T ) = ( T ) V0 (.3) E V exp (.4) kt p (.)T (.3) p T (.4) n E E H ref i= kt kt m TEi ETEi Eref + exp I i= kt kt k E E i i ref + exp I i= kt kt l THi ETHi Eref + exp I i= kt kt i i ref ( T, E ) exp I ( E ) m n i + i= i= n( T ) V0 E + exp kt THi ref V0 E exp kt EF kt i ( E ) ( E ) i ( E ) ref E kt TEi THi F (.5) I ( E) = g V0 EF E + exp kt (.6) I ( E) = g V0 E E + exp F kt (.7) m h h Plank p (.5) n( T ) (.5) S( T, E ref )
19 i Ei Eref exp (.8) kt kt (.8)T T peak H E i E = ref (.9) k ( T, E ) peak ref H T, E ref H ( ) iexp = (.0) kt j peak i i ref ( T, E ) = exp I( E ) ref i= kt m n V0 E THi + i exp i= i= kt j = k + l + m + n ( I ) E E kt i ref E E i ( T, Eref H T, E ref H ) j kt F (.) (.6) (.7) T T peak i E i H T peak i, E ref i ( ref S T, E ) =05 cm -3 E =0. ev =04 cm -3.3 ( p T ) H ( T, E ref ).5 peak E =05 cm -3 E =0. ev =04 cm -3 H ( T, Eref ) S( T, E ref ) H ( T, E ref ) H T, E ) ( ref H(T,0.6)[ 0 40 cm -6 ev -.5 ] 3 0 peak Temperature [K].5 H ( T, E ref ) ( =05 cm -3 E =0. ev =04 cm -3 ) 3
20 = cm -3 E =0.64 ev =.400 cm -3 H(T,0.6)[ 0 40 cm -6 ev -.5 ] peak Temperature [K].6 H ( T, E ref ) ( =6.608 cm -3 E =0.64 ev =.400 cm -3 ) ( ref S T, E ) >> S( T, E ref ) H ( T, Eref ) H ( T, E ref ) 4
21 .3 E ref Hall ( p T ) H T, E ) H (T,0) E ref ( ref.00 7 cm -3 E 0. ev.7 H (T,0) E ref =0 ev =0.06 ev 5 K.007 cm -3 E 0. ev.7 H (T,0) E =0 E ref ev =-0.03 ev 5 K E ref E ref ref H(T,E ref ) [ 0 38 cm -6 ev -.5 ] 3 0 p type = 0 7 cm -3 E = 0. ev E ref =0.06 peak E ref = Temperature T [K].7 E =0 E =0.06 ref ref H(T,E ref ) [ 0 38 cm -6 ev -.5 ] peak E ref =0 p type = 0 7 cm -3 E = 0.03 ev E ref = Temperature T [K].8 E =0 E =-0.03 ref ref 5
22 3 X-Ray iffractionxr X-Ray iffrationxr X 3.Bragg 3.. Bragg d sinθ = nλ (3..) λ d n X X X Cu ) θ X sin 3..Bragg 6
23 3. Vegard 3 3 L.Vegard XR Vegard - Vegard a lxga-xsb lsb GaSb Vegard 4) a = 6.36x ( x) (3..) InxGa-xSb InSb GaSb a = 6.478x ( x) (3..) Vegard 3.3 Vegard E k Γ, Χ, L g InGaSb GaSb 0.7 evinsb 0.8 ev 0.4 g ( x) = 0.7( x) + 0.8x + 0.4x( x ) E (3.3.) InxGa-xSb Γ, Χ, L 3.. Γ, Χ, E g lsb GaSb lxga-xsb lxga-xsb L Γ, Χ, L 3.. x = 0.48 Χ L x 0.48 X x 0.48 E g ( x).05( x). x X E = 6 (3.3.) g + 7
24 InxGa-xSb lxga-xsb Γ, Χ, 3.. In0.6Ga0.84SbIn0.8Ga0.8SbIn0.Ga0.8Sbl0.6Ga0.4Sb E g 3.3. L In x Ga -x Sb Energy Gap, E g [ev].5 X L 0.5 Γ GaSb InSb Mole Fraction InSb, x 3.3.InxGa-xSb Energy Gap, E g [ev].5 l x Ga -x Sb Γ L X GaSb lsb Mole Fraction lsb, x 3.3.lxGa-xSb 8
25 3.3. InxGa-xSb lxga-xsb Γ, Χ, L Γ E g X E g L E g Band Gap [ev] InxGa-xSb lxga-xsb InSb or lsb GaSb BowingParameter InSb or lsb.63.6 GaSb BowingParameter InSb or lsb GaSb BowingParameter InGaSb, lgasb E g In0.6Ga0.84Sb In0.8Ga0.8Sb In0.Ga0.8Sb l0.6ga0.4sb E [ev] g (004) a 3.4. a 9
26 3.4Undoped InGaSbTe doped lgasb MBE Undoped InGaSb Te doped lgasb XR XR Rigaku Rint Ultima + (00) Gas MBE In,Ga Undoped InGaSb µm XR Undoped InGaSb (00) InGaSb (3..) In0.6Ga0.84SbIn0.8Ga0.8Sb X-ray Intensity [a.u.] deg deg. In x Ga -x Sb (004) : In 0.6 Ga 0.84 Sb : In 0.8 Ga 0.8 Sb Gas (004) ngle θ [deg.] 3.4. Undoped InGaSb XR 3.4. Undoped InGaSb BEP Ratio Sb/(In+Ga) = 3 In0.6Ga0.84Sb In0.8Ga0.8Sb BEP [Torr] In Ga Sb
27 (00) Gas MBE Sb (In+Ga) BEP, 3, 5 Undoped InGaSb µm XR Undoped InGaSb (004) 59.8 InGaSb 6.9 (3..) In Ga0.8Sb deg. In 0. Ga 0.8 Sb (004) In 0. Ga 0.8 Sb :Sb/(In+Ga)= :Sb/(In+Ga)=3 :Sb/(In+Ga)=5 X-ray Intensity [a.u.] 0.5 Gas (004) ngle θ [deg.] Undoped InGaSb XR 3.4. Undoped InGaSb Undoped In0.Ga0.8Sb 3 5 Evaporative Temperature [] In Ga Sb Substrate Temperature [] InGaSb or lgasb m Semi-Insulating Gas (00) 3.4.4
28 Te doped lgasb (00) Gas MBE (00) Gas MBE Te Te doped lgasb Undoped lgasb µm XR lgasb (004) 60.5 lgasb 6. Te Te doped lgasb Undoped lgasb (3..) l 0.6Ga0.4Sb deg. l x Ga -x Sb (004) X-ray Intensity [a.u.] ngle θ [deg.] Gas (004) Te doped lgasb XR lgasb l0.6ga0.4sb Te dope Undope Te evaporative Temperature [] Evaporative Temperature [] Ga l Sb Substrate Temperature []
29 4 Hall Hall 879 E.H.Hall 4. p 4. p n Lorentz F q v B ( ) F = q B = qvb F B B v (4.) Lorentz Lorentz FE FE qe = V q d H = (4.) F = (4.),(4.) Hall V B F E V H = vbd (4.3) I I = qpvad (4.4) p (4.3)(4.4) V IB IB = vbd = RH (4.5) qpd d H = Hall R H = n R nq R H H R H + = p (4.6) pq (4.6) Hall n p H VH I FB a d FE B 4.Hall 3
30 (4.5) p n n B p = = (4.7) VH RHq qd I T p ( p T ), n ( n T ) Hall µ (4.7) VH d I R = = = (4.8) qpρ B ρ ρ µ H ρ T Hall µ T Hall van der Pauw van der Pauw 4
31 4.van der Pauw van der Pauw Hall 4.. van der Pauw 4 van der Pauw van der Pauw 4 ρ ) π R R R, , 4, 34 ρ = F, 43 d (4..) ln R 3, 4 ρ,43 R,43, 3, 4ρ R d F R R 3, 4 R 3,4, R 34, ρ34, R34,, R4, 3 ρ 4, 3 R4, 3, R, 43,34 3,4 van der Pauw 4..Hall 5
32 ρ, 34, ρ 3, 4 R,43, R 3, 4 πr exp ρ,34,43 d πr + exp ρ 3,4,43 d = (4..) πr,34d x + y =, ρ,43 πr x y = ρ 3,4,43 d πd x = + ) ρ ( R,43 R3, 4,43 d ( R,43 R3, 4,43 π y = ) ρ (4..3)(4..4) (4..) (4..3) (4..4) πr exp ρ = exp = cosh,34,43 ( ( x + y) ) + exp( ( x y) ) ( x y) πd = cosh ρ d πr + exp ρ.43 ( R + R ),34 ( y) exp x cosh x y = cosh 3,4,43 3,4 d (4..5) πd cosh ρ ( R ) = ( +,34 R3,4 exp R,34 R3, 4 ρ,43,43 πd ) (4..6) R R,34,34 R > R + R,34 R3,4 3,4 3,4 = R F R ln,34 3,4 ln exp R F R arccosh,34 3,4 (4..7) 6
33 R,34 (4..) ρ (4..7) F R3,4 4.. van der Pauw ρ 4.. (Source+)-(Source-) (Measure +)-(Measure-) R R V = (4..8) I V I R,43 R3, 4 R34, R 4, 3,,, R R,43 34, V = I V = I (43) () () (34) V I V I (43) () () (34) R R 3,4 4,3 V = I V = I R 4.. (4) (3) (3) (4) V I V I (4) (3) (3) (4) (4..9) 7
34 / 43 (Source -) 3 (Measure -) (Source +) 3 (Measure -) I (Source +) 4 (Measure +) (Source -) V I V 4 (Measure +) 3 / 4 I I (Source +) 3 (Source -) (Source -) 3 (Source +) (Measure+) V 4 (Measure -) (Measure+) V 4 (Measure -) 34 / (Measure+) 3 (Source +) (Measure +) 3 (Source -) V I V I (Measure -) 4 (Source -) (Measure -) 4 (Source +) 4 / 3 V V (Measure-) 3 (Measure+) (Measure-) 3 (Measure +) (Source -) 4 (Source +) (Source +) 4 (Source -) I I 4..ρ 8
35 4..3 n Hall µ H 4..3 (4.7) n B n = (4..0) R + 3,4 R4,3 qd (4.8) Hall µ H d R3,4 + R4,3 µ H = (4..) B ρ d B ρ R 3,4 R 4,3 R R 3,4 4,3 V = I V = I (4) (3) (3) (4) V I V I (4) (3) (3) (4) (4..) 4..3 V V (Measure+)-(Measure-) I I 9
36 3 / 4 (Measure +) 3 (Source -) I (Measure +) 3 (Source +) (Source +) 4 (Measure -) (Source -) I 4 (Measure -) 4 / 3 (Source +) 3 (Measure+) (Source -) 3 (Measure +) I (Measure -) 4 (Source -) (Measure -) I 4 (Source +) 3 / 4 (Measure+) 3 (Source -) (Measure +) 3 (Source +) I (Source +) I 4 (Measure -) (Source -) 4 (Measure -) 4 / 3 (Source +) 3 (Measure+) (Source -) I 3 (Measure +) I (Measure -) 4 (Source -) (Measure -) 4 (Source +) 4..3 n Hall µ H 30
37 4. Hall MMR Hall 0 m 50 µ.0 V 0. µv 00 k 00 k lgasb SiC 00 k MMR Hall Power Unit Suppling for Magnetic Coil V V Serial Comunication Magnet Field Controller and Voltage Source Meter H50 K0 Sample Magnetic Coil Suppling for Magnetic Field Measuring Instrument Controlled Computer Temperature Controller 4.. MMR Hall 4..MMR Hall Voltage Controlling and Measure Range Current Measure Range Temperature Controlling and Measure Range Magnetic Field Controlling Range 3 Measuring Range µv V µ m K K T
38 5 kgf/cm Joule-Thomson Pt MMR K-0 Hall MMR H-50 Voltage and Currnet Source Measure Unit 87S SMU38 MU Power Unit Suppling for Magnetic Coil GP-IB Comunication V V Voltage Measure Meter H50 K0 Cable Connecting Box Sample Measuring Instrument Controlled Computer V Switching System Current Measure Meter Magnet Field Controller Temperature Controller Magnetic Coil Suppling for Magnetic Field 4.. Hall 3
39 Keithley egital Multi Meter Keithley SMU 38 HI LO V SwitchingCircuit Keithley egital Multi Meter Keithley Scanner 700 Switching System HI HI LO LO HI LO HI LO 4..3 Hall Sample 33
40 Hall Windows 00 k Hall Windows Hall van der Pauw Keithley Scanner 700 Switching System Keithley Scanner 700 Switching System Keithley 70 Matrix Card 0 V 0.5µV 0.µV Keithley egital Multi Meter 000 n Keithley egital Multi Meter 00 GP-IB Windows Windows Hall Measuring Instrument ame Using Function Control and Measure Range MMR H-50 Magnet Field Controller.4 T MMR K-0 Temperature Controller 80 K 730 K Keithley egital Multi Meter 000 Voltage Measure Meter 0.µV 000 V Keithley egital Multi Meter 00 Current Measure Meter 0 p 3 Keithley SMU 38 Voltage and Current Source 0µV 000 V p Keithley Scanner 700 Switching System Hall Measuring Range Voltage Controlling and Measure Range µv 0 V Current Controlling and Measure Range n Temperature Controlling and Measure Range 80 K 730 K Magnetic Field Controlling Range.4 T Resistance Measuring Range µ Ω G Ω 34
41 Hall 00 k Undoped l0.6ga0.4sb K 0.47 GΩ GΩ Hall 0.47 GΩ 4..4 Windows Hall Undoped l 0.6 Ga 0.4 Sb Resistance [Ω] Over 00kΩ ew System can be measured in measure range 00 kω to GΩ Temperature [K] 4..5 Undoped l0.6ga0.4sb 35
42 4.3 van der Pauw Hall 4.. lgasb SiC Hall l p type 4H-SiC Wafer 400 m 4.3. CREE 4H-SiC Wafer5 mm0 mm l u Ti/l l mm mm Keithley SMU min. 3. 0min. 4. 5min. 5. 5min. 6. HF(50%)0min. 7. HF 8. 0min. 9. 5min. 0.. lu m Ti/l Ti0.m l(0.9 m). Sample Electrode
43 4.3. p-type 4H-SiC Wafer u, l ( 900), l( 700) Ti/l 4H-SiC Wafer R.T H-SiC Wafer Ti/l l 900G l SiC l 700 l 5 k u 0k G Contact u l l Ti/l nealing Temperature, Time 400, min. 900, min. 700, min. 900, min. p type 4H-SiC Wafer Temperature R.T. Current [m] 0 - :Ti/l Contact :l Contact(700 nealed) - :l Contact(900 nealed) :u Contact(400 nealed) Voltage [V]
44 3K l( 700) Ti/l 4H-SiC Wafer H-SiC Wafer Ti/l Ti/l l( 700) Hall Hall l Hall K l 0. mv Ti/l 0 l Ti/l V Hall 0. mv Hall l p type 4H-SiC Hall Ti/l 0.5 p type 4H-SiC Wafer Temperature 3 K Current [m] : Ti/l Contact : l Contact(700 nealed) Voltage [V] K 4H-SiC Wafer 3 K Voltage [mv] l (700 nealed) Ti/l K 38
45 4.4 van der Pauw * x E m * d x m = qe (4.4.) dt (4.3.) t x qe m = t * (4.4.) qe t dt qe t exp = τ (4.4.3) 0 * * m τ τ m τ v E d qτ = E (4.4.4) m v d * µ v d = µe (4.4.5) µ qτ µ = (4.4.6) * m µ i µ = µ µ i (4.4.7) 3) -.5 ( T ) 4 8π qh C.5 =.5.5 dsm ( kt ) µ l = T (4.4.8) 3E C E ds µ T 3).5 i v d 39
46 .5 ( kt ). 5 π ε µ BT (4.4.9) 64 s i T = 3 *.5 I q m I µ ( T ) (4.4.7) µ ( T ) = + = (4.4.0) µ l T µ i T T BT dµ T dt ( T ) dµ dt.5 = BT BT.5.5.5T + T dµ T = 0 T Max = dt 3 B. 5 ( T ) Max Max (4.3.) = µ T (4.3.) µ l ( T ) µ ( T ) ( µ T ) ( µ T ) i CREE l p type 4H-SiC Wafer 4.4. Hall µ T I µ T (4.4.) = 3393 µ T i ( T) µ -T.5 µ i ( T ) = (4.3.3).5 µ ( T ) T 4.4. ( µ T) T. 5 = B 0.00, B i µ i ( T ) =.5.5 (4.3.4) 3393T 0.00T i i I 40
47 4.4. µ T (4.4.9) B = = cm -3 I = 0.00 I i 0 4H-SiC Wafer Hall Mobility [cm V - sec - ] : Experimental data µ(t) : Simulated Result µ S (T) Temperature [K] 4.4. µ T 80 Hall Mobility [cm / V sec] : Experimental data µ(t.5 ) : Simulated Result µ S (T.5 )=0.00T T.5 [K.5 ] µ T T i 4
48 4.5ifferential Hall Effect Spectroscopy(HES) Hall ( p T ) p( T ) ln p T / ( ) T Hoffmann HESifferential Hall Effect Spectroscopy F ( T ) f ( E ) 4) HES kt dp T / d E E dp E EF dkt kt = + (4.5.) de E F F kt def kt ( E ) f EF kt = g + g E exp E exp E kt F E kt F (4.5.) E EF / kt dkt / def << E EF g exp dp( T ) kt kt (4.5.3) def E EF + g exp kt F kt dp T / d E EF E i i 4( kt dp( T )/ d E F ) peak E Ei + F kt peak 4 ( T ) F ln g E g p kt dp T / d E T j+ T j i kt dp ( T )/ d EF dp T kt ( j+, T j ) T j+ + T j p( T j+ ) p( T j ) = k de E ( T ) E ( T ) F F j+ F j (4.5.4) E F 4
49 E ( T T ) F j+ ( T j+ ) ( T ) j kt j+ V kt j V, = + j ln ln (4.5.5) q p T j+ q p T j 4.5. Undoped GaSb Sb/Ga 0 HES spline spline E60 mev.06 cm -3 (4.5.3) 4.5. HES HES kt dp(t)/d E F [ 0 6 cm -3 ] 0 undoped GaSb Flux ratio of Sb/Ga = 0 : Calculation using raw experimental p(t) : Calculation using spline function of p(t) : Simulated result using E, E = 60 mev =. 0 6 cm -3 peak E F [mev] 4.5. HES 43
50 4.6FCCS Undoped GaSb Sb/Ga 0 FCCS 8),9) spline ( p T ) (.) H T, E ref ) Sb/Ga 0 H ( T, 0. 0) K peak 00 K 300K shoulder K 00 K peak 4.6. peak85 K H T peak, cm -6 ev -.5 T H(T,-0.0) [ 0 36 cm -6 ev -.5 ] H(T,-0.0) [ 0 36 cm -6 ev -.5 ] peak undoped GaSb Sb/Ga = 0 shoulder shoulder Temperature [K] 4.6. H ( T, 0.0) peak Experimental data : H(T,-0.0) : Simulated result E = 9 mev = cm -3 : Simulated result E = mev = cm -3 = cm -3 undoped GaSb Sb/Ga = Temperature [K] 4.6. H( T, 0.0) 44
51 (.5) E H T, Eref E Eref H( T, Eref ) = exp I ( E ) (4.6.) kt kt (4.6.) E 9 mev.30 6 cm -3 H ( T, 0. 0) E H( T, Eref ) E Eref V0 Eref EF H T, Eref = exp I ( E) + exp (4.6.) kt kt kt kt (4.6.) peak H T, E mev cm cm -3 = 80 K 4.6. peak E E H ref ref kt kt kt ref V0 ref F T, E H T, E exp I ( E ) exp E E (4.6.3) H ( T,0. 06) 00 K peak 5 T peak H ( T peak, 0.06 ) cm -6 ev -.5 E.406 cm -3 kt 03 K 66 mev H(T,0.06) [ 0 36 cm -6 ev -.5 ] peak Temperature [K] : Experimental data : Simulated result H ( T,0.06) 45
52 peak E H T,0.06 (4.6.4) E H ( T,0.06) = exp I( E ) (4.6.4) kt kt (4.6.4) H ( T,0. 06) peak E Eref H 3( T, Eref ) H ( T, Eref ) exp I ( E ) (4.6.5) kt kt H3 ( T,0. ) 300 K T peak3 309 K H3 T peak3, cm -6 ev -.5 E 3 6 mev cm -3 peak3 E 3 3 H3 T,0. (4.6.6) 3 E3 0. H3( T,0.) = exp I( E3 ) (4.6.6) kt kt (4.6.6) H3( T,0. ) ( p T ) p n i= ( T ) = f ( E ) i i + (4.6.7) H3(T,0.) [ 0 37 cm -6 ev -.5 ] peak3 : Experimental data : Simulated result Temperature [K] H3( T,0.) 46
53 4.6.5 FCCS 350 K Hole Concentration [ 0 6 cm -3 ] 4 3 undoped GaSb Sb/Ga = 0 : Experimental data : Simulated result Temperature [K] E = mev = cm -3 E = 66 mev = cm -3 E 3 = 6 mev 3 = cm -3 = cm
54 5 CV Hall Hall 5. ( ρ x) Poisson p p x Poisson d V dx ( x) ρ( x) = (5..) ε ε 0 s V x x ε ε 0 ρ x + ( x) q( ) = ρ (5..) d 0 ( x) x = 0 V x = (5..3) dv x = d = 0, V ( x) = Vd -V (5..4) dx V V d (5..)(5..4) (5..) V ( x) q = q = + + ( ) q( ) x + ( ) ( x d ) + ( V V ) 0 ε ε 0 ε ε s s + ε ε (5..3)(5..5) d 0 d s dx + ( V V ) d q + s + ( ) ε ε 0 s d (5..5) d ε ε = + q 0 s ( V V ) d (5..6) 48
55 d Q Q = q + + ( ) d = q( ) ε 0 ε ( V V ) s d (5..7) C C = dq dv q = + ( ) ε ( V V ) 0ε s d / (5..8) (5..8) C C q = + ( ) ε 0ε s ( V V ) d = V + V (5..9) q + + d ( ) ε q( ) ε ε ε 0 s 0 S C + + d ( ) ε qs( ) ε ε ε 0 s 0 s = V + V (5..0) qs C V + V d s 5.4H-SiC CREE l 4H-SiC Wafer( 0 mm0 mm400m) 5.. Ti/l 0.5 mm 0.96 mm u l Horiba -500 CVmeter 4.3. Sample Schottky Electrode l Coating GlassPlate
56 5.. l /C V 5..3 /C V cm -3 V d = 6.8 V 4H-SiC 0 Capacitance [pf] H-SiC Wafer 93 K l Electrode Voltage [V] /C [ 0-6 pf - ] : - = cm -3 V dif = 6.8 V 4H-SiC Wafer 93 K l Electrode Voltage [V] 5..3/C V 50
57 u 5..4 /C V 5..5 /C V cm -3 V d = 5.5 V Capacitance [pf] H-SiC Wafer 93 K u Electrode Voltage [V] 5..4 /C [ 0-6 pf - ] : - = cm -3 V dif = 5.5 V 4H-SiC Wafer 93 K u Electrode Voltage [V] 5..3/C V 5
58 6 6.Undoped GaSb (00) Gas MBE Sb Ga Sb/Ga 6 80 Undoped GaSb µm 470 Ga Torr Sb Sb/Ga Torr.70-6 Torr Torr 5000 /hour 77 mm Undoped InGaSb In van der Pauw Hall p T Hall 0. m.4 T 8340 K p(t ) v ( T ) ln p T 6.. ( T ) Sb/Ga Undoped GaSb p T spline p T 6.. spline EF = kt (6..) E F 3 3 πm k v h 4-3 ( T ) = T = T cm h 0.3 mh 3 v 7) E F (6..) Sb/Ga mev mev0 887 mev Hole Concentration [ 0 6 cm -3 ] undoped GaSb : Sb/Ga = 6 : Sb/Ga = 8 : Sb/Ga = 0 : Spline function of p(t) Temperature [K] 6.. 5
59 4.6 Sb/Ga 0 Sb/Ga Undoped GaSb 9 mev 9 mev K cceptor 940 mev cceptor 6694 mev cceptor3 436 mev cceptor4 78 mev cceptor5 Sb/Ga 6 cceptor4 Sb/Ga 8 cceptorcceptor4 Sb/Ga 0 cceptor4 cceptor Sb/Ga Sb/Ga Sb/Ga 680 FCCS Fermi Level [mev] undoped GaSb : Sb/Ga = 6 : Sb/Ga = 8 : Sb/Ga = Temperature [K]
60 6..FCCS undoped GaSb Flux ratio of Sb/Ga Wafer cceptor [cm -3 ] cceptor cceptor 3 cceptor 4 cceptor 5 [mev] [cm [cm -3 [mev] [cm -3 [mev] -3 [mev] [cm -3 ] ] ] ] Hole Concentration [ 0 6 cm -3 ] undoped GaSb Experimental data : Sb/Ga = 6 : Sb/Ga = 8 : Sb/Ga = 0 Temperature [K] : Simulated result
61 6.. ouble cceptor Model PLPhoto LuminescenceHall Undoped GaSb 8) Hall GaSb Sb Ga Ga (ouble cceptor Model) ( p T ) ouble cceptor Model Undoped GaSb Sb Sb Sb GaGaSb Sb vacancy VSb 040 mev 6000 mev 8) FCCS ouble cceptor cceptor cceptor3 Sb/Ga 60 cceptor cceptor3 ouble cceptor 6.. cceptor cceptor 6.. cceptor cceptor Sb/Ga Eltoukhy 40 mev Sb/Ga 40 mev GaSb Sb vacancy VSb 9) mev 40 mev 80 mev cceptor Sb/Ga 8 Sb/Ga VSb cceptor cceptor Sb/Ga 8 Undoped GaSb Sb/Ga cceptor3 Eltoukhy 80 mev Sb/Ga Undoped GaSb Gas 9) Undoped GaSb Wafer 9 mev 9 mev 9 mev cceptor3 Sb/Ga Wafer Undoped GaSb Gas 55
62 6..4 cceptor4 cceptor5 Sb/Ga 6 78 mev Sb/Ga mev Xu undoped GaSb Ga vacancy Ga vacancyvga - 7 mev3 Ga vacancyvga 3-9 mev 0) VGa - cceptor mev VGa 3- cceptor5 59 mev VGa - VGa 3- Ga vacancy 56
63 6.Undoped InGaSb (00) Gas MBE In,Ga Undoped In0.6Ga0.84Sb, In0.8Ga0.8Sb (Sb) (In+Ga)BEP, 3, 5 Undoped In0.Ga0.8Sb m mm Undoped InGaSb In van der Pauw Hall ( p T ) Hall 0. m.4 T 8540 K mh 3. (3.3.)Vegard In In0.Ga0.8Sb ( T ) In0.6Ga0.84Sb In0.8Ga0.8Sb p 0.6Ga0.84Sb, In0.8Ga0.8Sb K ( ) T ln p T / E 0.6 ev 3.3. In g 0.6Ga0.84Sb In0.8Ga0.8Sb E g 0.57 ev 0.56 ev 350K 350K Undoped In0.8Ga0.8Sb Hole Concentration [cm -3 ] 0 7 Undoped InGaSb : In 0.6 Ga 0.84 Sb : In 0.8 Ga 0.8 Sb Temperature [K] 6.. In0.6Ga0.84Sb, In0.8Ga0.8Sb p T 57
64 p Spline T (.) H T, E ref In0.8Ga0.8Sb H ( T,0. 09) K peak 70 K peak peak K H T peak, cm -6 ev -.5 E T H T, Eref E Eref V0 Eref EF H( T, Eref ) = exp I( E ) + exp (6..) kt kt kt kt (6..) peak H T, E 87 mev cm cm -3 peak E Eref H ( T, Eref ) H ( T, Eref ) exp I( E ) (6..) kt kt 6..3 H ( T, 0) 50 K peak peak 6..3 T 5 K H ( 0) T peak, cm -6 ev -.5 E peak 87 mev H T, E ref E Eref V0 Eref EF H ( T, Eref ) = exp I( E ) + exp (6..3) kt kt kt kt H(T,0.009) [ 0 37 cm -6 ev -.5 ] undoped In 0.8 Ga 0.8 Sb Peak Experimental data :H(T,0.009) :Simulated result E = 87 mev = cm -3 = cm Temperature [K] 6.. H( T,0.09) 58
65 (6..3) peak H T, E 45 mev.806 cm cm FCCS (Sb) (In+Ga)BEP, 3, 5 Undoped In0.Ga0.8Sb H(T,0) [ 0 37 cm -6 ev -.5 ] Peak Experimental data :H(T,0) :Simulated result E = 45 mev = cm -3 =. 0 6 cm -3 undoped In 0.8 Ga 0.8 Sb Temperature [K] 6..3 H ( T,0) Undoped InGaSb Hole Concentration [cm -3 ] Experimental data :In 0.6 Ga 0.84 Sb :In 0.8 Ga 0.8 Sb Temperature [K] :Simulated results
66 6.. Undoped In0.6Ga0.84Sb, In0.8Ga0.8Sb In0.6Ga0.84Sb In0.8Ga0.8Sb cceptor -3 [cm ] cceptor E [mev] [cm ] cceptor 3 E [mev] [cm ] Hole Concentration [cm -3 ] In 0. Ga 0.8 Sb :Sb/(In+Ga)= :Sb/(In+Ga)=3 :Sb/(In+Ga)=5 :Simulated results /T [K - ] (Sb) (In+Ga)BEP, 3, 5 Undoped In0.Ga0.8Sb In0.Ga0.8Sb Sb/(In+Ga) BEP Ratio 3 5 cceptor -3 [cm ] cceptor E [mev] [cm ] cceptor 3 E [mev] [cm ]
67 K cceptor 4046 mev cceptor 8700 mev cceptor3 6.. In,Ga Undoped In0.6Ga0.84Sb, In0.8Ga0.8Sb 6.. Ga cceptor 3 Undoped In0.6Ga0.84Sb cceptor In cceptor cceptor In cceptor 3 Ga 6.. Sb/(In+Ga), 3, 5 Undoped In0.Ga0.8Sb 6.. Sb/(In+Ga) cceptor Sb/(In+Ga) cceptor 3 InGaSb Sb Sb Sb VacancyVSb cceptor In cceptor 3 Ga Ga Sb Vacancy In Sb Vacancy XR Sb/(In+Ga) X Sb Vacancy X Sb Vacancy InSb GaSb In Sb Ga Sb Ga Sb In Sb Vacancy Sb/(In+Ga) In Sb Vacancy Sb Vacancy cceptor 4045 mev In Sb Vacancy 8700 mev Ga Sb Vacancy 6
68 6.34H-SiC 6.3.l implanted 4H-SiC n-4h-sic n doped 4H-SiC 5 m,.50 5 cm -3 n 4H-SiC 0.97 MeV 7 l 30 4 cm -3 SIMS(Secondary Ion Mass Spectrometry) n 4H-SiC l m cm -3 l ) SiC r SIMS.0 m l.3 m RIE (Reactive Ion Etching) p 4H-SiC m p 4H-SiC Ti/l van der Pauw Hall ( p T ) Hall.4 T 0040 K p T l implanted 4H-SiC 443 Spline p ( T ) (.) H ( T, E ref ) H ( T,0.35) K peak 380 K peak T peak 386 K H ( T,0. 35) cm -6 ev -.5 l Concentration [cm -3 ] Eched layer p-type layer formed by l implantation epth from Surface [µm] 6.3..SIMS n 4H-SiC l 6
69 0 8 l Implanted 4H-SiC at R.T. Hole Concentraton [cm -3 ] 0 7 Experimental data nealing Temperature : 443 : Temperature [K] p T H(T,0.35) [ 0 4 cm -6 ev -.5 ] 3 l Implanted 4H-SiC at R.T. nealing Temperature 443 peak Experimental data Simulation results : f( E ) E = 89 mev = cm -3 = cm -3 : f F ( E ) E = 67 mev = cm -3 = cm Temperature [K] H( T,0.35) 63
70 E (.5) H T, Eref E Eref V0 Eref EF H( T, Eref ) = exp I ( E ) + exp (6.3.) kt kt kt kt (.7) V0 E EF I ( E) = = V 0 exp f F ( E) (6.3.) EF E kt g + exp kt (6.3.) peak H T, E 67 mev.809 cm cm -3 ( T ) p T p SIMS l 508 cm cm -3 SiC iamondga Fermi-irace )(6.3.) (.4) Fermi-irac f F E f F ( E ) E F ( = E + 4exp E kt f ) F f E E (6.3.3) f ( E ) = (6.3.4) E ex E EF Er EF + 4exp - gexp + g rexp kt kt r= kt E r g r r =, g =, E = 0 ex f ( E) = f F ( E) Fermi-irac E E ( E E ) g E exp E r r r r= kt ex =, g r = r (6.3.5) E Er g r + g r r= kt E r E r * m = 3.6 ( r ) m ε r 0 s ex (6.3.6) 64
71 ε s = r 7 E = 36 mev, E = 34 mev, E 3 = 5 mev, E4 = 8.5 mev, E5 = 5.4 mev, E6 = 3.8 mev, E7 =.8 mev mev cm cm -3 ε s 0 H( T,0. 35) p(t ) Fermi-irac Fermi-irac SIMS l 50 8 cm -3 l implanted 4H-SiC575 r = 7 E = 36 mev, E = 34 mev, E3 = 5 mev, E4 = 8.5 mev, E 5 = 5.4 mev, = 3.8 mev, E =.8 mev E FCCS l implanted 4H-SiC l l implanted 4H-SiC 85 mev89 mev 4H-SiC l PLPhoto Luminescence 559 mev 3) l 65
72 ( E ) f F ( E ) Fermi-irac f E F E f 67 mev.80 9 cm cm -3 f 89 mev cm cm -3 E 0 8 l Implanted 4H-SiC at R.T. nealing Temperature 443 Hole Concentraton [cm -3 ] Experimental data Simulation results : f( E ) E = 89 mev = cm -3 = cm -3 : f F ( E ) E = 67 mev = cm -3 = cm Temperature [K] f FCCS l implanted 4H-SiC nealing Temperature E [cm -3 ] E [mev] [cm -3 ]
73 0 8 l Implanted 4H-SiC at R.T. Hole Concentraton [cm -3 ] 0 7 Experimental data nealing Temperature : 443 : 575 Simulated results Temperature [K] f E 67
74 6.3. l doped 4H-SiC Wafer CREE l doped 4H-SiC Wafer0 mm0 mm, 400m FCCS Ti/l van der Pauw Hall p T Hall.4 T p T (.) H T, E ref H T,0.9 K Spline K peak peak T 537 K H T,0.36 peak cm -6 ev -.5 peak Fermi-irac p T Fermi-irac r = 0 E = 36 mev, E = 34 mev, E 3 = 5 mev, E 4 = 8.5 mev, E5 = 5.4 mev, E6 = 3.8 mev, E7 =.8 mev E 8 =. mev E 9 =.7 mev E 0 =.4 mev Hole Concentraton [cm -3 ] l-doped 4H-SiC Experimental ata Spline function of p(t) Temperature [K] l doped 4H-SiC Wafer p T 68
75 H(T,0.9) [ 0 40 cm -6 ev -.5 ] l-doped 4H-SiC Temperature [K] peak Experimental data Simulated results : f( E ) E = 89 mev = cm -3 = cm -3 : f F ( E ) E = 74 mev = cm -3 = cm H( T,0.9) Hole Concentraton [cm -3 ] l-doped 4H-SiC Experimental data Simulated results : f( E ) E = 89 mev = cm -3 = cm -3 : f F ( E ) E = 74 mev = cm -3 = cm Temperature [K]
76 Fermi-irac Fermi-irac l implanted 4H-SiC Fermi-irac l doped 4H-SiC Wafer l 89 mev 4H-SiC l 70 mev 3) l F ( E ) f Fermi-irac f E F E E f 74 mev.70 8 cm cm cm -3 f 89 mev cm cm cm -3 E f E Fermi-irac f F E Fermi-irac istribution Function F ( E ) Proposed istribution Function f.30 8 cm -3 f cm -3 E C-V Measurement Results cm -3 Hall Mobility from Ionized impurity cm -3 70
77 6.4Te doped lgasb (00) Gas MBE Te Te doped l0.6ga0.4sb m mm undoped InGaSb In van der Pauw Hall n T Hall.4 T 4540 K 3. (3..)Vegard Te Te doped l n T Te m e 0.6Ga0.HSb Electron Concentraton [cm -3 ] Te doped l 0.6 Ga 0.4 Sb Experimental data Evaporate Temperature : 330 : Temperature [K] 6.4. Te doped l0.6ga0.4sb n T 7
78 Te 40 H T, K peak 350 K peak Zhu Te doped lgasb Te X-center-like traps Te doped lxga-xsb x > 0. Te doped l0.5ga0.5sb Hall ( n T ) ( ln( n T )) / T 4) 0 mev Te 6.4. peak374 K H T peak, cm -6 ev -.5 F ( T E n f E f ( E ) ( f ) ) = + E ex E EF exp - gexp kt kt + r= Er E g rexp kt F (6.4.) E r r g E ex 3. (3..) Vegard 4.9 = r 7 E = 7.4 mev, E =.8 mev, E3 = 0.8 mev, E4 = 0.46 mev, E 5 = 0.9 mev, E 6 = 0.0 mev, E 7 = 0.5 mev 66 mev cm. 4 0 cm H ( T,0. 7) 6.4. Fermi-irac mev.8 0 cm. 8 0 cm 6.4. n T Fermi-irac Undoped l0.6ga0.4sb p T lgasb ( ) T ln p T / E.33 g ev 3.3. l0.6ga0.4sb.39ev 45 K400 K cm -3 E g 7
79 Te doped l0.6ga0.4sb Fermi-irac cm cm -3 Undoped l0.6ga0.4sb cm cm H(T,0.7) [ 0 4 cm -6 ev -.5 ] Te doped l 0.6 Ga 0.4 Sb Te Evaporate Temperature 40 Temperature [K] peak Experimental data Simulated results : f( E ) E = 66 mev = cm -3 = cm -3 : f F ( E ) E = 9 mev = cm -3 = cm H ( T,0.7) Electron Concentraton [cm -3 ] Te doped l 0.6 Ga 0.4 Sb Te Evaporate Temperature 40 Experimental data Simulated results : f( E ) E = 66 mev = cm -3 = cm -3 : f F ( E ) E = 9 mev = cm -3 = cm Temperature [K]
80 Te 330 Te doped l0.6ga0.4sb Te 36meV 66meV Te Hole Concentration [cm -3 ] Undoped l 0.6 Ga 0.4 Sb :Experimental data : E g =.33 [ev] Saturation Range /T [K - ] Undoped l0.6ga0.4sb p T 6.4. FCCS Te doped l Te evaporative Temperature Ga0.4Sb ensity[cm-3] onor Energy Level[meV] ensity[cm-3]
81 Electron Concentraton [cm -3 ] Te doped l 0.6 Ga 0.4 Sb Experimental data Evaporate Temperature : 330 : 40 :Simulated results Temperature [K]
82 7 Hall FCCS Gas MBE Sb Ga 680 undoped GaSb 5 undoped GaSb Sb/Ga 8 Undoped InGaSb 40meV 90meV 4045 mev In Sb Vacancy 8700 mev Ga Sb Vacancy 4H-SiC l implanted 4H-SiC l 85 mev89 mev l doped 4H-SiC Wafer l 89 mev Te doped l0.6ga0.4sb Te 36meV66meV Te 76
83 GaSb l 4H-SiC 77
84 ),,, : (H) G79. )M. Lee,. J. icholas, K. E. Singer, and B. Hamilton: J. ppl. Phys. 59 (985) )H. Matsuura, M. Yoshimoto and H. Matsunami: Jpn. J. ppl. Phys. 34 (995) L37. 4)H. Matsuura, K. Sonoi: Jpn.J.ppl.Phys. 35 (996) L555. 5)H. Matsuura: Jpn. J. ppl. Phys. 36 (997) )H. Matsuura, Y. Uchida, T. Hisamatsu and S. Matsuda: Jpn. J. ppl. Phys. 37 (998) )H. Matsuura, T. Kimoto and H. Matsunami: Jpn. J. ppl. Phys. 38 (999) )H. Matsuura, Y. Masuda, Y. Chen, and S. ishino: Jpn. J.ppl. Phys. 39 (000) )H. Matsuura, Y. Uchida,. agai, T. Hisamatsu, T. buraya and S. Matsuda: ppl. Phys. Lett. 76 (000) 09. 0) :, (989) ),, :-, )van der Pauw : Philips Res. Repts 3 (958). 3)S.M.Sze: Physics of Semiconductor evice, nd ed.,wiley,y(98) 4)H. J. Hoffmann: ppl. Phys 9 (979) )H. Matsuura, K. Morita, K. ishikawa, T. Mizukoshi, M. Sagawa and W. Susaki: Jpn. J. ppl. Phys. to be published at February, 00. 6)H. Matsuura, K. ishikawa, K. Morita, M. Segawa and W. Susaki: Extended abstracts of the 0th electronic materials symposium (EMS0). pp (F5).Jun.00. 7)C.Kittel: Introduction to Solid State Physics, 5th edition, Wiley, ew York, )K. akashima: Jpn. J. ppl. Phys. 0 (98) ). H. Eltoukhy, J. E. Greene: J. ppl. Phys. 50 (979) )H. Xu: J. ppl. Phys.: 68 (990) ) : (999). )H.Matsuura : International Conference on Silicon Carbide and Related Materials, pp.749, (00) 3) Gary L Harris : Properties Of Silicon Carbide, ISPEC. (995). 4)Yu Zhu, Yoshikazu Tekeda, and kio Sasaki: J.ppl. Phys. 64 (988)
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