2012 pn 1 2 Appendix 2.1 1 5000 km( 8 20 ) ( ) 5800K 5800K ( 1 AM0) 1 AM1.5 Spectrum Energy Density (kw/m 2 μm) AM0 2 5800K Black body 1 AM1.5 0 0.5 1 1.5 2 2.5 Wavelength (μm) 1 ( ) AM(air mass) 5800K π r2 2hc 2 1 L 2 λ 5 exp(hc/λk BT ) 1 λ r L [1]
1 (air mass, AM) AM1 AM AM 1.5 AM0 AM1.5 832W/m 2 1.3 10 11 W 151(km) 2 ( 2.6 ) 100% 100% 6.2 2.2 2 SO 2 4 Cu Cu 2+ Zn 2e e SO 4 2 SO 4 2 load diaphragm Zn 2+ SO 4 2 e 2 2e ( ) Zn Zn 2+ +2e ( ) Cu 2 ++2e Cu 1mol 2eN A (N A ) m A A+m B B m C C+m D D (1) A Ze mol ZeN A = ZF( ) A (1mol ) μ A = G A + RT log[a] (2) G A A 1mol [A] A ( ( ) ) (2) 2 R ln[a] (1) ( ) m A μ A + m B μ B = m C μ C + m D μ D m A G A + m BG B m CG C m DG D = RT ln [A]mA [B] mb [C] mc [D] md (3) load V ZFV = m C G C + m D G D m A G A m B G [B] B RT ln [A]mA mb (4) [C] mc [D] md 3 pn pn
3.1 pn p n pn p n Appendix1 n p S p n p n ( ) U U TS 2 Appendix ( 3) (n i ) pn V bi n p ev bi (A.3) n n n N D p (A.4) n p n 2 i /N A N 2 N 1,2 W = N C N1 N C N2 dn 1 = dn 2 N N 1,2 d(ln W ) ln(n 2 /N 1 )dn 1 ( ) n p (dn 1 = 1 N 1 = n n N 2 = n p d(u TS)/dn n =0 ev bi = k B T ln n n k B T ln N DN A n p n 2 = E g k B T ln N cn v (5) i N D N A (n n N D p p N A ) (4) ( ) p n 3(c) w p w n E(x) ɛɛ 0 E(x) =N A (2x + w p )+N D w n (x<0), N A w p + N D (w n 2x) (x 0) (6) (ɛ ) V bi V bi = wn w p ( E(x))dx = e ɛɛ 0 (N D + N A )w n w p = e ɛɛ 0 (N D + N A ) N D N A w 2 n w n N D = w p N A. (7) (5) (7) p N A n N pn D w p w n + + + + + + + + + + + + + + V (a) E V x (b) NAwp NDw n E c 0 V V bi ev bi p n E E F v (c) 3(a) pn (b) E(x) x (c) pn 2 Zn Zn 2+ Cu Cu 2+
SO 2 4 x ( )yz x μ e (x)( ) μ h (x)( ) n(x) =N c exp[ (E c (x) μ e (x))/k B T ], p(x) =N v exp[ (μ h (x) E v (x))/k B T ], (8a) i.e., μ e (x) =E c (x)+k B T ln n(x) N c, μ h (x) =E v (x) k B T ln p(x) N v. p, n n p p n (8b) D e d 2 n p dx 2 = n p n p0 d 2 p n G(x), D h τ e dx 2 = p n p n0 G(x). (9) τ h G(x) G(x) =0 n p0 p n0 D e,h τ e,h (e) (h) ( ) L e = D e τ e, L h = D h τ h (10) x >w n p n x< w p n p (9) n p n p0 (x ) p n p n0 (x ) ( ) ( x + wp n p (x) =δn 0 exp + n p0, p n (x) =δp 0 exp x w ) n + p n0 (11) L e L h δn 0 δp 0 (8b) (11) n p0 p n0 [ x + wp μ e (x) =E c + k B T +ln δn ] [ 0 x wn, μ h (x) =E v k B T +ln δp ] 0 L e N c L h N v x ± E (p),(n) F V (E (p) F E(n) F = ev ) 4 (12) p n 10 8 j e ev h 10 6 0 ev 0 log p, logn 0 x JJ / 0 10 4 p p n n 10 2 10 0 (a) n p p n 0 10 20 ev / k B T (b) 4 (a) pn V ( ) (b) Shockley ( (15)) J 0 (15) (15)
pn (11) 4 μ e (x) δn 0 + n p0 = n( w p )=n p0 exp ev k B T, δp 0 + p n0 = p(w n )=p n0 exp ev k B T (13) (9) x = w p j e = ed e dn p dx = ed eδn 0 wp [ De j = e n p0 + D ][ h p n0 exp ev ] L e L h k B T 1 L e = ed [ e n p0 exp ev ] L e k B T 1 en 2 i [ De L e N A + D h L h N D ][ exp ev ] k B T 1 (14) (15) (15) pn Shockley pn ( ) 4(b) Shockley 3.2 pn pn (9) G(x) x ( G) n p (x) p n (x) x n p n n0 + Gτ e x p n p n0 + Gτ h ( ( ) ev n p (x) =n p0 + Gτ e + [n p0 exp k B T ( ( ev p n (x) =p n0 + Gτ h + [p n0 exp k B T ) ] 1 Gτ e ) ] Gτ h ) 1 V =0 5(a) ( ) x + wp exp, (16a) L e ( exp x w ) n (16b) L h (15) j 0 [ j = j 0 exp ev ] k B T 1 eg(l e + L h ), (17) j sc G(τ e + τ h ) 5(b) p p J n n ln p, ln n p n V m V oc V G e n p0 n p G h p n0 x J m J sc (a) 5 (a) G pn V =0 (b) pn IV (b)
J SC J ( ) V OC 5(b) J V W = JV pn J J SC V V OC W J SC V OC W J V J max V max FF J maxv max J SC V OC 1 (18) ( filling factor) IV FF J SC V OC FF (17) J SC = eg(l e + L h ), V OC = k BT e [ ] eg(τe + τ h ) ln +1 j 0 (3) V OC (4) (4) ΔG pn (19) V OC p n0 + Gτ h n n 4(a) V OC V bi (5) T 0 ΔG E g ( e V g ) *1 ( ) pn ( ) (19) 4 pn pn 4.1 Shockley-Queisser (a) T s T c n p V J T s T c + (b) + V 6(a) pn (b) pn s R L J [2] T s 5800K T c 300K (T s T c )/T s 95% pn ( ) E g = hν g hν hν g ev = hν g *1 T 0 (5)
(2.1 ) T s hν hν g Q(ν g,t s )= 2π c 2 ν g [ exp hν ] 1 1 ν 2 dν = 2π(k BT s ) 3 x 2 k B T s h 3 c 2 x g e x 1 dx (x gk B T s hν g ) (20) Q s 6(a) pn T s A hν g AQ(ν g,t s ) P s AP s P s P s = 2πh e 2 0 [ exp hν ] 1 k B T 1 ν 2 dν = 2π(k BT s ) 4 x 2 dx (k BT s ) 5 h 3 c 2 0 e x 1 =2π5 15h 3 c 2. (21) η(x g )= hν gq P s = x g x g x 3 [ dx x 3 ] 1 dx e x 1 0 e x (22) 1 T s =6000K E g =1.1eV 43% pn Shockley-Queisser 3.2 pn [2] 6(b) θ θ =0 ω s T c T c (T c ) T c ν >ν g (20) Q(ν g,t c ) Q c Q c t c F c0 = t c Q c np V F c (V )=F c0 np n 2 i = F c0 exp ev k B T c (23) (23) pn (23) F c0 R(V ) (17) j 0 (15) [ De j 0 = e n p0 + D ] [ h Le p n0 = e n p0 + L ] h p n0. L e L h τ e τ h 1 n p0 ( ) τ e L e 2 j 0 = e [F c0 + R(0)] (24) R(V ) V R(V )=R(0) exp(ev/k B T c ) T c 4π ω s θ =0 T s F s = t s Q s T c j SC = e(f s F c0 ) (25) (19) V OC =(k B T c /e)ln(j SC /j 0 + 1) (26)
I-V [ j = j 0 exp ev ] [ 1 j SC = j 0 exp ev exp ev ] OC k B T c k B T c k B T c (27) 4 0= d( jv ) dv = j V dj [ dv = j 0 exp V OC exp V V exp V ], V c V c V c V c ( V c k ) BT c e z OC V OC /V c z m V max /V c (V max V ) z OC = z m +ln(1+z m ) (28) Q s Q c V OC V c ln(q s /Q c ) (20) T s T c ln Q c = V g /V c +orderof lnt c T c 0 V OC V g (25) (28) (17) I-V pn 7 E g t s 1 1 Shockley-Queisser (SQ ) Si 28% GaAs 30% GaAs 24% Si 22% (%) 30 20 10 Si GaAs 0 1 2 3 E g (ev) 7 (25) (28) t c = t s =1 η E g T c 300K 4.2 SQ ( ) 4.2.1 (19) J OC SQ E r N r A: E c E r B: E r E c C: E r E v D: E c E r 4 U A = c n nn r (1 f(e r )), U B = e n N r f(e r ), U C = c p N r f(e r ), U D = e p pn r (1 f(e r ))
c n e n ( ) U = U A U B = U C U D = ( σ e [n + N c exp σ h σ e v h v e N r (pn ni 2 ) Ec Er k BT )] + σ h [ p + N v exp ( Er Ev k BT )] (29) ( [3] p.68 73) σ e,h v e,h pn ( ) x = x s (n ) D h d(p n p n0 ) dx = S h (p n p n0 ) (x = x s ) (30) S h 3.2 G(x) x Appendix2 G(x) pn GaAs 8(a) E g 8(b) Al x Ga 1 x As-GaAs η coll η coll = e ( ) η coll 8(b) ( ) η coll Al x Ga 1 x As Al x 0.8 E g 2.09eV Γ E g (Γ) =2.56eV X Al Ga As 0.8 0.2 GaAs p ++ 100 80 with window (a) GaAs n coll (%) 60 40 20 without window GaAs homo junction 0 0.4 0.5 0.6 0.7 0.8 0.9 (b) Wavelength ( m) 8 (a) (Al 0.8Ga 0.2As ) GaAs (b)gaas ( ) ( )
100 80 η coll (%) 60 40 20 0 E i = 440kV/m E i = 0 Wavelength (μm) 0.4 0.6 0.8 1 9 Si (33) 2 x j =0.5μm S e =1km/s GaAs AlAs 0.5% hν < E (Γ) g E i α G(x) =αf exp( αx) p D e d 2 Δn p dx 2 + μ e E i dδn p dx Δn p τ e + Fαexp( αx) = 0 (31) Δn p n p n p0 μ e 2 x = x j : dδn p D e dx Δn pe i = S e Δn p, (32a) x =0: Δn p = 0 (32b) j (e) SC = [ eαf α 2 +2E e α L 2 (E e + α)exp( αx j )+f exp( αx j ) (S e/d e + E e )cosh(fx j )+f sinh(fx j ) e (S e /D e + E e ) sinh(fx j )+f cosh(fx j ) f exp(e e x j )(S e /D e +2E e + α) ] (S e /D e + E e ) sinh(fx j )+f cosh(fx j ) (33) E e μ ne i 2D e, f 2 E 2 e + 1 L 2 e (34) 9 η coll ( ) 4.2.2 V OC 4.1 E g /e SQ V OC FF V max
10 Si New South Waels PVCDROM I-V 7.2 4.2.3 ( 10 ) E g SQ Si 100μm 1 E g E g 4.3 4.3.1 Shockley-Queisser (1) (2) T s (3)pn (3) pn *2 pn junctions tunnel Sunlight Prism E g1 E g2 E gn Sunlight p n EgN p n E g1 11 E g pn 2 *2 (7.1 )
(1) (2) 4π *3 11 *4 pn 100% 300K (28) hν=1ev η=90% 2eV 95% (2.1 ) 94% 4.1 (28) pn pn 2 11 pn ( ) E gn >E gn 1 > >E g1 pn E gj pn I-V [4] AM1.5 87% 4.3.2 ( ) 3 a( )-SiC/μ( )-Si III-V IV [5] Solar Junction National Renewable Energy Laboratory (NREL) 43.5% (AM1.5 400 ) ( 12 web ) - 2010 InGaAs-GaAs-InGaP3 36.9% [6] 100 p n t p n t p n GaInP 2 GaAs Ge coll (%) 80 60 40 20 0 GaInP 2 GaAs Ge 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Wavelength ( m) 12 100% GaInP 2 Solar Junction Inc. web http://www.sj-solar.com/ 5 (NTT) NTT (30 ) *3 *4 2π
5.1 1980 Si Si (Appendix2) (19) G j SC τ e,h Si Si Si (1) (2) (3) (2) (1) (3) (2) 5.2 InP InP InP pn InP 16%(AM1.5) [7] 7 (a) 1MeV (γ ) Si Si GaAs InP deep level trangent spectroscopy (DLTS) 7(b) *5 [8] H4 H4 H5 InP (29) H4( ) ( 1 ) ev InP NASA *5 DLTS pn [9]
0 Normalized Maximum Power P / P (a) 1 0.9 0.8 0.7 0.6 dark GaAs 2 illum (10mW/cm ) 2 illum (70mW/cm ) 2 forward (5mA/cm ) 0.5 10 14 10 15 10 16 1MeV electron fluence (cm 2) Si InP DLTS signal (b) H4 (0.37eV) 14 1 10 cm 0min 2 Injection 249mA/cm at 190K 2min 5min H5 (0.52eV) 100 200 300 T (K) 7 (a)si GaAs InP 1MeV ( ) (AM1.5) InP (b)inp pn DLTS H4 H5 [7, 8] NASA National Renewable Energy Laboratory (NREL) H4 P (V + + P ) (P i ) P In P [10] P P + V p + In 5.3 In P In 4.3.2 ( ) InGaAs 3 36.9% Si III-V In Ga Si III-V III-V
Si III-V GaAs Si 4% Si III-V 2 (001) III V TEM Si GaAs Si GaAs 20% Si 6 6.1 1950 1974 2003 [11] ( ) 21 2000 40 Germany 30 (feed-in 20 tariff, FIT) Spain 10 Solar Power Electricity FIT Price 2007 6 0 2004 2006 2008 2010 2012 2008 Year 2600MW 2009 500MW 2009 3 69MW Euro cent /kwh
FIT ( ) Q CdTe 6.2 8 5 (5/8) 6MW 2MW MW 1. 2. ( ) 3. 4. 5. 6. 7. ( ) 8. 6.3 6.3.1 CuInSe 2 (CIS) CuIn 1 x Ga x Se 2 (CIGS) Roll-to-Roll 30 In 6000 (kw) 4000 2012.5.8 2000 5.3 0 10 20 ( ) (a) (b) 8 web http://www.tepco.co.jp/csr/renewable/megasolar/index-j.html
Roll-to-Roll Si InP Staebler-Wronski 6.3.2 CIS CIGS In Ga Cu 2 ZnSnS 4 Si Si Si Si CVD Si Si ( ) 100μm 100μm Si (001) 6.3.3 kwh ( ) 1000 7 3 [12] 2 ( )
E C.B. E g (1) (2) (3) (4) (5) (6) V.B. (a) t <0 t =0 t < 1ps 1ps 1ns t > 10 s (b) 9 (a) (1) (2) (3) ( ) (4) (5) (6) (b) (a)-(3) 7.1 7.1.1 ( 9) 1ps ( 9(a)(2)) ( 9(a)(3)-(5)) 9(b) 7.1.2 T H μ c μ v Δμ H Δμ H = μ c μ v (35) j use /e = f s N(E g,, 0,T s ) f c N(E g,,δμ H,T H )+(f c f s )N(E g,, 0,T c ), (36)
100 Efficiency (%) 80 60 40 20 direct, Δμ H <0 direct, Δμ H =0 diffuse, Δμ H =0 diffuse, Δμ H <0 0 1 2 3 Band gap (ev) 10 (40) [13] E use j use = f s d dt E(E g,, 0,T s ) f c d dt E(E g,,δμ H,T H )+(f c f s ) d dt E(E g,, 0,T c ) (37) N(E 1,E 2,μ,T) E(E 1,E 2,μ,T) 2π E2 E 2 de h 3 c 2 exp[(e μ)/k B T ] 1, 2π h 3 c 2 E 1 E2 E 1 E 3 de exp[(e μ)/k B T ] 1 (38a) (38b) f s f c 4.1 (36),(37) 3 T c T c T c 1 ΔS =(ΔE Δμ H )/T H T c Δμ = ΔE TΔS = Δμ H (T/T H )+ΔE(1 T/T H ) (39) P use = j use Δμ/e =(j use /e)[δμ H (T/T H )+ΔE(1 T/T H )] (40) 10 E g =0 85% 7.2 7.2.1 ( )
(a) 3 2 13 1 23 12 E i (ev) 1.2 1 0.8 0.6 0.4 (b) 0.35 0.62 0.8 1 1.2 1.4 1.6 1.8 2 2.2 E c (ev) 0.47 0.50 0.53 0.56 0.59 11 (a) (b) E c E i [12] 0.44 0.41 0.38 0.35 9(a)(5) 9(b) 11(a) 3 E 31 E 21 E 32 2 2 1 SQ 4.3.1 (1) 2 pn ( ) 11(b) 7.2.2 1 3 [14] pn V OC GaAs InAs InAs GaAs 7% In (001) 4 ( 12(a),(b)) GaAs InAs InAs ( 12(c)) 1 InAs GaAs
(a) (b) (c) 12 GaAs InAs (a) AFM (b) TEM 1 InAs (c) GaAs InAs InAs ( ) *6 7.2.3 (multiexciton) ( ) InP PbSe [16] pn h 7.2.4 p n Wien *6 3 ( 2011.10.17 p.45) [15]
pn [17] SF [1] M. P. Thekaekara, R. Kruger, and C. H. Duncan, Appl. Optics 8, 1713 (1969). [2] W. Shockley and H. J. Queisser, J. Appl. Phys. 32, 510 (1961). [3] P. Würfel, Physics of Solar Cells (Willey, 2005). [4]A.S.BrownandM.A.Green,PhysicaE14, 96 (2002). [5]M.A.Greenet al., Prog. in Photovoltaics 20, 12 (2012). [6] T. Agui et al., Renewable Energy, Proceedings, Yokohama 2010; O-Pv-5-4. [7] A. Yamamoto, M. Yamaguchi and C. Uemura, Appl. Phys. Lett. 44, 611 (1983). [8] K. Ando and M. Yamaguchi, Appl. Phys. Lett. 47, 485 (1985). [9], ( 1983). [10] R. W. Jansen, Phys. Rev. B 41, 7666 (1990). [11] ( ) ( 2011) [12] M. A. Green, Third Generation Photovoltaics (Springer, 2006). [13] R. T. Ross and A. J. Nozik, J. Appl. Phys. 53, 3813 (1982). [14] A. J. Nozik, Physica E 14, 115 (2002). [15] D. Guimard et al., Appl. Phys. Lett. 96, 203507 (1-3) (2010). [16] R.J. Ellingson, O.I. Micic, J. Blackburn, P. Yu, G. Rumbles, A.J. Nozik, Nano Lett. 5, 865 (2005). [17] M. De Zoysa, T. Asano, K. Mochizuki, A. Oskooi, T. Inoue, and S. Noda, Nature Photonics 6, 535(2012). Appendix1 1 0.1 ev ( ) ( ) n p D g e f h g e (E)dE = D e (E)f(E)dE, g h (E)dE = D h (E)[1 f(e)]de D h (E)f h (E)dE (A.1a) (A.1b) m e m h D e (E) = 2m 3 e 2m 3 E h Ec π 2 3 ( ), D h (E) = Ev π 2 3 E ( ) (A.2)
E c E v n n = E c g e (E)dE = 2m 3 e π 2 3 E c ( ) E Ec de m 3/2 ( ) 1+exp(E E F )/k B T 2 e k B T EF E c exp 2π k B T p E F E c E v E F m e m h ( np = N c N v exp E ) ( ( g m ) n 2 e,h k B T 3/2 ) i N c,v 2, E g E c E v (A.4) k B T 2π N c N v n i n = p E F E F = E c + E v 2 + k BT 2 ln N v = E c + E v + 3k BT ln m h N c 2 4 m e E F N D n D n + n D = N D F = U TS n D N D W S = k B ln W F = E Dn D k BT ln [ 2 n D N D! n D!(N D n D)! E D 2 nd ln N! N ln N N E F = F n D = E D k B T ln [ 2(ND n D ) n D ]. (A.3) (A.5) ] [, n D = N D 1+ 1 ( )] 1 2 exp ED E F (A.6) k B T 1/2 N A p A n D (A.3) T 0 E F E D (A.3) n p n p n p p n p Appendix2 2 1 E h g h h direct h g q E g ( ) (k) E g k k hν E g ( ) (a) k (b) k (p + ea)2 H = + V (r) p2 + V (r)+ A p 2m 0 2m 0 2m 0 = H 0 + H (A.7) H = A p/2m 0 k k k c k v k c H k v = e 2m 0 k c A p k v = ea 2m 0 k c p A k v. (A.8)
p A p A W vc = 2π k c H k v 2 δ(e ck E vk + ω) (A.9) δ(e kc E kv ω)dk =2π (2m r) 3/2 ω Eg α( ω) ( h ) E g direct indirect h ( 1 m r α( ω) ω E g 1 m + 1 v m c ) (A.10) (A.11) α( ω) ( ω E g ) 2 (A.12)