9群（電子材料・デバイス） 3編（半導体） 章 応用編

1 9 3 2 . 9 - 3 . 2 . 2012 1/(36).. 9 3 2 . 9 - 3 - 2 . 2-1 Si [2010 6 ]. Si 14 . 15 N . 30 cm SEG 11 N . SOG 7 N .. pn Si . SOI Silicon-On-Insulator LSI .. Si SiO2 MOSFET . Si . Si SiO2 Si . SOI .. Si(111) . 7 7 .. 2-1-1 Si . 111. Si 4 4 4 Oh Fd 3m . 7. - ( ) . T 1), 2) . mm a = + 10-5(T-273)+ 10-9(T-273)2 (300 K<T<1100 K). = 10-6 K-1 (T = ). = g cm-3 @ 298 K. Tm = 1687 K . = ( + 10-3T + 10-6 T 2)-1 W/cm-1K-1 . D = 636 K GPa c11 = c12 = c44 = -1. cm . (TL)O( )=520 TO(X)= LO,LA(X)= TA(X)= TO( )= LO( )= LA( )= TA( )= TO(L)= LO(L)= LA(L)= TA(L)= 103m/s 298K. //[001] //[110] //[110] //[001] // [11 0] 2012 2/(36).. 9 3 2 . //[111] [111] {111} {110} . cm2/Vs @300 K <1015 cm-3 . = 1350 ( ) = 370. 2-1-2 Si . Si 2 1 3) . 2 . Brillouin 0,0, 0 [ ,0, 0 a ] 6.

2 25 v 1 . 1 .. 2 25 v 2 c 4.. eV Si .. 5 L3 .. L1 .. X1. eV . 0 L3'. X4. -5. L1. X1. L2'. -10.. L X U, K .. k 2 1 Si . m0 1), 2) . E gind T - 10-4T2/(T+636) eV . E gdir T - 10-4T2/(T+125) eV .. (SO) 0 = eV . mt = m0, ml = m0.. mhh = m0 mlh= m0. SO ( ) mSO = eV . u = d = 5a 15c = b = d = 25 v = a 14 3 1. (B) 10 cm s- . 6 -1. 30 cm Auger (Cn+Cp) 10 s .. 2012 3/(36).. 9 3 2 . 2-1-3 Si . Si 2 2 1 ( 25 v 15c ) eV . < E < Eg . O(10- ) esu Im{ } . 3 12.. Re{ } . 3. 8 8.. 6 6. k n 4 4. 2 2. 0 0. 0 2 4 6 8 10. eV . 2 2 Si n k 1),2) . 2 2 4. @300 K n= + ( ) ( ) + . -1 1. (TPA) GW cm- m, 100 K. 18 18 2 1. (FCA) >5 m = ( 10 n + 10 p) ( m) cm- .. 1) T he Landolt-B rnstein Database Group III Condensed Matter, III/41a1a, b Semiconductors- Group IV. Elements, IV-IV and III-V Compounds Part a, b.

3 URL: 2) URL: . 3) J. R. Chelikowsky and M. L. Cohen, Phys. Rev. B, , , 1976. 2012 4/(36).. 9 3 2 . 9 - 3 - 2 . 2-2 Ge, SiGe [2010 6 ]. Ge 14 . Si . Ge Ge Ge Si .. n = 4 . Si1-xGex ( 0 x 1) SixGe1-x Ge Si .. Si1-xGex Si Ge .. Ge Si 4 % . Si Si1-xGex Si(Ge) Ge . Si1-xGex y . z {z>y} {z<y} .. Si1-xGex HBT .. 2-2-1 SixGe1-x . SixGe1-x ( 0 x 1) C, Si Oh Fd 3m . 7. x . Si1-xGex x . 1), 2) . x = L .. a = + + nm @ 300 K. = ( + ) 10-6 K-1 ( 0 x ) @ 300 K. = ( + x) 10-6 (K-1 ( x ) @ 300 K. = + - g cm-3 @ 300 K.. T( )=1139 - 738x +263x2 T( )= 1139 - 80x - 395x2 @ 300 K.. + W/cm-1K-1 ( x ) @ 300 K. (Ge) = W/cm-1K-1 . D= 640-266x K .. GPa c11 = c12 = c44 = @300 K. -1. cm . (LT)O( ) 520 - (Si-Si); 410 (Si-Ge); 288+ (Ge-Ge). x Ge L cm-1 . TO(L) = LO(L) = LA(L) = TA(L) = = 3900 = 1900 cm2/Vs @300 K.

4 2012 5/(36).. 9 3 2 . Si Si1-xGex >105 K. 2-2-2 Ge SiGe . Ge L k 1,1,1 2 a 8 . Si1-xGex 0 x Si x Ge . Egind Ge x 2 3 . Si Ge 0 x 1 Si . Si(001) 1-x x . 2 4 4 2 . 4 2. 2 3 .. 2. (eV). L. 2 . hh- 4 u zz xx . E cave 3. 1. 1) + eV. 3) u zz xx . 3. 4. , x . 2 3 Si1-xGex 2 4 Si1-xGex . 1), 3).. Si 1) + 90 meV .. 1), 2), 3).. eV [Ge]. -4 2. Egind (T) = - 10 T / (T + 210). dir -5 2. Eg (T) = - 10 T / (T + 398). [ Si1-xGex] @300 K. 2. Egind (x) = - + ( 0 x ). Eg (x) = - ( x ). ind [Si(001) Si1-xGex]. 2 3). Egind (x) = - + . ( L 6c ) mt = m0, ml= m0 ( x ). ( 1c ) mt = m0, ml = m0 ( 0 x ). [Ge] mhh = m0 [Ge] mlh= m0. SO mSO = ( - ) m0.. 0 ( 7v 6v )= . eV . 14 3 -1. (B) [Ge] 10 cm s .. 2012 6/(36).. 9 3 2 . 2-2-3 Ge, SiGe . Ge Si Eg . Ge L . eV @300 K Egdir ( 1).

5 1,2).. 2. n = + x + @ 300 K. = + x @ 300 K. 1/GWcm m, 100 K.. 1) URL: {/Ge/, /Si/} . 2) The Landolt-B rnstein Database Group III Condensed Matter, Numerical Data and Functional Relationships in Science and Technology III/34C3, Optical properties. Part 3; III/41a1a, b Semiconductors- Group IV. Elements, IV-IV and III-V Compounds Part a, b;. URL: . 3) C. G. Van de Walle and R. M. Martin, Phys. Rev., , , 1986. 2012 7/(36).. 9 3 2 . 9 - 3 - 2 . 2-3 C( ). [2010 6 ]. 2-3-1 . eV Si .. Si GaAs n . p .. (B) (P) pn . D+ + e- D0 + ED . D+ e- D0 ED . n . ND NA . n n N A . C e x p ED / k BT . N (3 1). ND N A n 2.. N C 2M C 2 mde *. k BT / h 2 . 3. 2 (3 2). 10. 18. T [K]. 800 700 600 500 400 300. kB T 18. ND = 5x10 cm -3. 17. 10. NC h weak mde* 10. 16 compensation Electron concentration, n [cm ].

6 -3. MC . 15. 10 c = NA/ND. mde* = (ml* mt* mt* ) 1/3 MC = 6 =0. * *. ml = m0 mt = m0 10. 14. strong -5. 1x10. B P compensation -4. 13 1x10. 10.. -3. (3 1) (3 2) 10. 12 1x10. eV 11. 10. 2 5 c = NA/ND . 10. 10. ED = eV ND = 5 1018 cm-3 1000/T [1/K]. (3 1) . 2 5 P . c . c 1 10-4 . 2012 8/(36).. 9 3 2 . c = 1 10-5 . 1010 1014 cm-3 c 1 10-4 c = 0 . P B .. 2-3-2 pn . n p pn . n NDn p NAp 1 1018 cm-3 . 12 6 1018cm-3 c = 1 % 1 pn . 2 6(a). n p 2 6(b) 1 .. xSn xSp 2 6(b) 1 2 . 6(c) n p X = 200 nm . n0 = 1011 cm-3 p0 = 5 1014 cm-3 .. Position, x (nm). 1 % . -200 -150 -100 -50 0 50 100 150 200. Space-charge density (cm ).. -3. Space-charge density (cm ). -3. 18. a 300 K 18.. 17 17. n-side p-side .. 17. n0 p0 . 17. 18. 18. dN A(x)/dx 1016 cm-3 . dN D(x)/dx b 2 6(c) n0/2 p0/2.

7 - +. 11 14. 5x10 5x10. Electron density in n-side (cm ). n p . Hole density in p-side (cm ). -3. -3. 11. c n p p0 14. 4x10 4x10. 3x10. 11. n0 3x10. 14. p0/2. 11 14. 2x10 2x10. n0/2. 11 14. 1x10 1x10.. 0. -200 -150 -100 -50 0. 0. 50 100 150 200. Position, x (nm). 2 6 (a) (b) 1 . (c) . 2012 9/(36).. 9 3 2 . 9 - 3 - 2 . 2-4 GaAs [2010 6 ]. GaAs 13 15 1 1 . GaAs . FET Field Effect Transistor HEMT High Electron Mobility Transistor HBT . Heterobipolar Transistor . MMIC Monolithic Microwave Integrated Circuits InGaAs . GaAs . GaAs .. 2-4-1 GaAs 1). GaAs Zinc Blende Structure . 300 K a = 187 k bar a 4 .946 . b 4 .628 c 5 .493 ,at 209 k bar, 28 NaCl . T . ( 10 2 T 10 5 T 2 ) ( 10-6 /K) 120 K T 350 K. ( 10 3 T 2 .82 10 6 T 2 ) ( 10-6 /K) 200 K T 1000 K.

8 5 . 3176 g/cm3 at K. Tm 1513 K . 1 2 .27 K cm / W . D 360 K > 140 K. D 340 K at 0 K. c11 11 . 9 1011 dyne / cm2 . c12 5 . 38 1011 dyne / cm2 . c44 5 . 95 1011 dyne / cm2 . cm-1 . LO ( ) 285 .0 LO ( X) 240 .7 LO ( L) 238 .3 . TO ( ) 267 .3 TO ( X) 252 .0 TO ( L) 261 .3 . LA ( X ) 226 . 7 LA ( L) 208 .7 . TA ( X ) 78 . 7 TA ( L ) 62 . 0. m/s at 300 K. [1 0 0 ] 4 .731 10 3 3 .345 10 3. [1 1 0 ] 5 .235 10 [ 0 0 1 ] . 3. 3 .345 10 3. [1 1 0 ] 2 .476 10 3. [1 1 1 ] 5 .397 10 . 3. 2 .796 10 3. 2012 10/(36).. 9 3 2 . 2-4-2 GaAs 1). GaAs 2 7 .. k (0,0,0 ) . 2 L.. [ k ( / a , / a , / a ) ] 3 X.. [ k (2 / a , 0 , 0 ) ] . E g . L E L (T ) E X (T ).. E g (300K)= eV , E g (77K)= eV , E g ( ) = eV 2 7 GaAs . E g (T ) 1 .519 5 .408 10 4 T 2 /(T 204 ) eV.

9 E L (T ) 10 5 T 2 /(T 204 ) eV . E X (T ) 0 .462 8 .05 10 5 T 2 /(T 204 ) eV . 0 .067 m 0. 0 .51m 0 . 0 .082 m 0 .. a ( 1c ) a ( 15 v ) 13 .5 . b 2 . 0 d 5 . 4 eV . 2-4-3 GaAs 2). GaAs n k R . 2 8 . eV 2 . 7 L -line . eV eV. X -line 2 8 GaAs . K -line eV n k . R 10.. cm-1 .. 1) O. Madelung, W. von der Osten, U. R ssler, Landolt-B rnstein, Numerical data and functional relationships in science and technology, new series group 3 volume 22 a, Intrinsic properties of group IV elements and III-V, II-VI and I-VII compounds semiconductors crystal and solid state physics, Springer, p. 136-139 and p. 346-349, 1989.. 2) ( ), , , p. 327, 406. 1994. 2012 11/(36).. 9 3 2 . 9 - 3 - 2 . 2-5 AlGaAs [2010 6 ]. AlGaAs 13 15 GaAs AlAs . Al GaAs . Al AlGaAs GaAs AlGaAs GaAs.

10 InGaAs . 1968 . n AlGaAs p AlGaAs GaAs . GaAs . AlGaAs . AlGaAs GaAs AlAs . AlGaAs . Al . nm GaAs AlGaAs . 2-5-1 AlGaAs . AlGaAs Ga Al GaAs AlAs . AlGaAs Misibility Gap x = 0 1 . AlxGa1-xAs AlGaAs . 5 meV Ga Al 13 .. Al x 1 . a 5 .6533 0 .0078 x at 300 K. 6 .4 1 .2 x 10-6 /K . 5 .36 1 .6 x g/cm3 . T m 1511 58 x 560 x 2 K . T m 1511 1082 x 580 x 2 K . c 0 . 08 0 .03 x cal / g K . 1 2 . 27 20 . 83 x 30 x 2 K cm / W . D 370 54 x 22 x 2 K at 300 K. c11 11 . 88 0 . 14 x 1011 dyne / cm2 . c12 5 . 38 0 . 32 x 1011 dyne / cm2 . c44 5 . 94 0 . 05 1011 dyne / cm2 . GaAs-type AlAs-type . Al . GaAs type LO 292 .2 52 .8 x 14 .4 x 2 T O 268 .3 5 .2 x 9 .3 x 2 cm-1 . AlAs type LO 359 .7 70 .8 x 26 .8 x 2 T O 359 .7 4 .4 x 2 .4 x 2 cm-1 . 2012 12/(36).