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B.1 »°¶Ë´É¤Î¥â¥Ç¥ë

B.1.1 ÆÃÀ­¶ÊÀþ¤ÎÆÃħ

¡Ö¥ª¡¼¥Ç¥£¥ªÍÑ¿¿¶õ´É¥Þ¥Ë¥å¥¢¥ë¡×[1]¤Ë¤è¤ì¤Ð¡¤ »°¶Ë´É¤ÎÆÃÀ­¶ÊÀþ¤Ë¤Ï¼¡¤Î¤è¤¦¤ÊÆÃħ¤¬¤¢¤ê¤Þ¤¹¡¥
  1. ¥Ð¥¤¥¢¥¹¤¬0V¤Î¤È¤­¤è¤ê¤â¡¤ -0.5 $ \sim$ - 0.8V¤¯¤é¤¤Éé¤Î¤È¤­¤Î¤Û¤¦¤¬¡¤ ¸¶ÅÀ¤òÄ̤ë¶ÊÀþ¤Ë¶á¤¯¤Ê¤Ã¤Æ¤¤¤ë¡¥
  2. ¥«¥Ã¥È¥ª¥Õ¤Î¤È¤³¤í¤Î $ \mu$ ($ \mu_{c}^{}$)¤Ï ¥×¥ì¡¼¥ÈÅÅ°µ¤Î¤¤¤«¤ó¤Ë¤è¤é¤º°ìÄê¤Ç¤¢¤ë¡¥
  3. ¥Ð¥¤¥¢¥¹¤Î¤¦¤ó¤ÈÀõ¤¤¤È¤³¤í¤Ç¤Ï $ \mu$ ¤Ï°ìÄê¤Ç¤¢¤Ã¤Æ¡¤ ¤³¤Î¤È¤­¤Î $ \mu$ ¤ò $ \mu_{m}^{}$ ¤È¤¹¤ì¤Ð $ \mu_{m}^{}$ = 1.5$ \mu_{c}^{}$ ¤Ë¶á¤¤¡¥
  4. ¥×¥ì¡¼¥ÈÅÅ°µ¤¬°ìÄê¤Î¤È¤­¤Î gm ¤Ï¡¤ ¤Û¤Ü¥×¥ì¡¼¥ÈÅÅή Ip ¤Î0.6¾è¤ËÈæÎ㤹¤ë¡¥
  5. Ep/Eg ¤¬°ìÄê¤Ê¤é $ \mu$ ¤¬°ìÄê¤Ç¤¢¤ë¡¥
¤³¤ì¤é¤ÎÀ­¼Á¤òËþ¤¿¤¹´Ø¿ô Ip(Ep, Eg) ¤Ï¼¡¤Î¤è¤¦¤Ë¤Ê¤ê¤Þ¤¹¡¥

Ip(Ep, Eg) = G$\displaystyle \Bigl($$\displaystyle {\frac{{3-3\alpha}}{{2}}}$$\displaystyle \Bigl)^{{\frac{1}{1-\alpha}}}_{}$$\displaystyle \Bigl\{$$\displaystyle \Bigl($$\displaystyle {\frac{{1}}{{\mu_c}}}$ - $\displaystyle {\frac{{1}}{{\mu_m}}}$$\displaystyle \Bigl)$Ep$\displaystyle \Bigl\}^{{\frac{3}{2}-\frac{1}{1-\alpha}}}_{}$$\displaystyle \Bigl($Egg + $\displaystyle {\frac{{E_p}}{{\mu_c}}}$$\displaystyle \Bigl)^{{\frac{1}{1-\alpha}}}_{}$ (B.1)
¤³¤³¤Ç¡¤ Egg = Eg + 0.6 ¤Ç¡¤ $ \alpha$ ¤ÏÌó0.6¤Ç¤¹¡¥ ¾å¤Î¼°¤Ï¡¤ Egg$ \le$ 0 ¤«¤Ä Ep$ \ge$ - $ \mu_{c}^{}$Egg ¤ÎÈÏ°Ï¤Ç ¶á»÷Ū¤ËÀ®¤êΩ¤Á¤Þ¤¹¡¥

B.1.2 »°Äê¿ô

¤³¤Î¼°¤«¤é»°Äê¿ô¤òµá¤á¤Þ¤¹¡¥ Áê¸ß¥³¥ó¥À¥¯¥¿¥ó¥¹ gm ¤Ï¡¤
gm = $\displaystyle {\frac{{\partial I_p}}{{\partial E_g}}}$  
  = $\displaystyle {\frac{{1}}{{1-\alpha}}}$G$\displaystyle \Bigl($$\displaystyle {\frac{{3-3\alpha}}{{2}}}$$\displaystyle \Bigr)^{{\frac{1}{1-\alpha}}}_{}$$\displaystyle \Bigl\{$$\displaystyle \Bigl($$\displaystyle {\frac{{1}}{{\mu_c}}}$ - $\displaystyle {\frac{{1}}{{\mu_m}}}$$\displaystyle \Bigr)$Ep$\displaystyle \Bigr\}^{{\frac{3}{2}-\frac{1}{1-\alpha}}}_{}$$\displaystyle \Bigl($Egg + $\displaystyle {\frac{{E_p}}{{\mu_c}}}$$\displaystyle \Bigr)^{{\frac{1}{1-\alpha}-1}}_{}$ (B.2)
  = $\displaystyle {\frac{{I_p}}{{1-\alpha}}}$ . $\displaystyle {\frac{{1}}{{E_{gg} + \frac{E_p}{\mu_c}}}}$ (B.3)

ÆâÉôÄñ¹³ rp ¤òľÀܵá¤á¤ë¤Î¤ÏÆñ¤·¤¤¤Î¤Ç¡¤ rp ¤ÎµÕ¿ô¤òµá¤á¤Þ¤¹¡¥
$\displaystyle {\frac{{1}}{{r_p}}}$ = $\displaystyle {\frac{{\partial I_p}}{{\partial E_p}}}$  
  = G$\displaystyle \Bigl($$\displaystyle {\frac{{3-3\alpha}}{{2}}}$$\displaystyle \Bigr)^{{\frac{1}{1-\alpha}}}_{}$$\displaystyle \Bigl($$\displaystyle {\frac{{1}}{{\mu_c}}}$ - $\displaystyle {\frac{{1}}{{\mu_m}}}$$\displaystyle \Bigr)^{{\frac{3}{2}-\frac{1}{1-\alpha}}}_{}$$\displaystyle \Bigl\{$$\displaystyle \Bigl($$\displaystyle {\frac{{3}}{{2}}}$ - $\displaystyle {\frac{{1}}{{1-\alpha}}}$$\displaystyle \Bigr)$Ep$\scriptstyle {\frac{{3}}{{2}}}$-$\scriptstyle {\frac{{1}}{{1-\alpha}}}$-1$\displaystyle \Bigl($Egg + $\displaystyle {\frac{{E_p}}{{\mu_c}}}$$\displaystyle \Bigr)^{{\frac{1}{1-\alpha}}}_{}$  
      + Ep$\scriptstyle {\frac{{3}}{{2}}}$-$\scriptstyle {\frac{{1}}{{1-\alpha}}}$$\displaystyle {\frac{{1}}{{1-\alpha}}}$ . $\displaystyle {\frac{{1}}{{\mu_c}}}$$\displaystyle \Bigl($Egg + $\displaystyle {\frac{{E_p}}{{\mu_c}}}$$\displaystyle \Bigr)^{{\frac{1}{1-\alpha}-1}}_{}$$\displaystyle \Bigr\}$  
  = G$\displaystyle \Bigl($$\displaystyle {\frac{{3-3\alpha}}{{2}}}$$\displaystyle \Bigr)^{{\frac{1}{1-\alpha}}}_{}$$\displaystyle \Bigl($$\displaystyle {\frac{{1}}{{\mu_c}}}$ - $\displaystyle {\frac{{1}}{{\mu_m}}}$$\displaystyle \Bigr)^{{\frac{3}{2}-\frac{1}{1-\alpha}}}_{}$Ep$\scriptstyle {\frac{{3}}{{2}}}$-$\scriptstyle {\frac{{1}}{{1-\alpha}}}$$\displaystyle \Bigl($Egg + $\displaystyle {\frac{{E_p}}{{\mu_c}}}$$\displaystyle \Bigr)^{{\frac{1}{1-\alpha}}}_{}$  
      x $\displaystyle \Bigl\{$$\displaystyle {\frac{{1-3\alpha}}{{2(1-\alpha)}}}$ . $\displaystyle {\frac{{1}}{{E_p}}}$ + $\displaystyle {\frac{{1}}{{1-\alpha}}}$ . $\displaystyle {\frac{{1}}{{\mu_c}}}$ . $\displaystyle {\frac{{1}}{{E_{gg} + \frac{E_p}{\mu_c}}}}$$\displaystyle \Bigr\}$  
  = $\displaystyle {\frac{{I_p}}{{1-\alpha}}}$$\displaystyle \Bigl($$\displaystyle {\frac{{1-3\alpha}}{{2}}}$ . $\displaystyle {\frac{{1}}{{E_p}}}$ + $\displaystyle {\frac{{1}}{{\mu_c}}}$ . $\displaystyle {\frac{{1}}{{E_{gg} + \frac{E_p}{\mu_c}}}}$$\displaystyle \Bigr)$ (B.4)

ºÇ¸å¤ËÁýÉýΨ $ \mu$ ¤Ï¡¤gm ¤È rp ¤ÎÀѤǵá¤á¤Þ¤¹¡¥
$\displaystyle \mu$ = gmrp = $\displaystyle {\frac{{1}}{{E_{gg} + \frac{E_p}{\mu_c}}}}$ . $\displaystyle {\frac{{1}}{{\frac{1-3\alpha}{2} \cdot \frac{1}{E_p} +
\frac{1}{\mu_c} \cdot \frac{1}{E_{gg}+\frac{E_p}{\mu_c}}}}}$  
  = $\displaystyle {\frac{{1}}{{\big(\frac{E_{gg}}{E_p}+\frac{1}{\mu_c}\big)\frac{1-3\alpha}{2}
+ \frac{1}{\mu_c}}}}$ = $\displaystyle {\frac{{1}}{{\displaystyle \frac{3-3\alpha}{2} \cdot \frac{1}{\mu_c}
+ \frac{1-3\alpha}{2} \cdot \frac{E_{gg}}{E_p}}}}$ (B.5)

¤³¤³¤Ç¡¤Á°½Ò¤·¤¿»°¶Ë´É¤ÎÆÃÀ­¶ÊÀþ¤ÎÆÃħ¤¬Ëþ¤¿¤µ¤ì¤Æ¤¤¤ë¤«¡¤Ä´¤Ù¤Æ¤ß¤Þ¤¹¡¥ ¤Þ¤º¡¤1¤Ç¤¹¤¬¡¤ ¼°(B.1)¤è¤ê¡¤ ¥×¥ì¡¼¥ÈÅÅή Ip ¤Ï Eg = - 0.6 ¤Î¤È¤­¤Ë Ep ¤Î1.5¾è¤ËÈæÎ㤷¤Þ¤¹¡¥

2¤Ë´Ø¤·¤Æ¤Ç¤¹¤¬¡¤ ¥«¥Ã¥È¥ª¥Õ¤Î¤È¤³¤í¤Ç¤Ï¡¤ ¼°(B.1)¤è¤ê Egg + Ep/$ \mu_{c}^{}$ = 0 ¤Ç¤¹¤«¤é¡¤ $ \mu$ ¤Ï $ \mu_{c}^{}$ ¤È¤Ê¤ê¤Þ¤¹¡¥

3¤Ë¤Ä¤¤¤Æ¤Ï¡¤ ¼°(B.5)¤Î Egg ¤Ë0¤òÂåÆþ¤¹¤ë¤È¡¤¤³¤ì¤¬ $ \mu_{m}^{}$ ¤È¤Ê¤ê¡¤

$\displaystyle \mu_{m}^{}$ = $\displaystyle {\frac{{2}}{{3 - 3\alpha}}}$$\displaystyle \mu_{c}^{}$ $\displaystyle \approx$ 1.67$\displaystyle \mu_{c}^{}$ (B.6)
¤È¤Ê¤ê¤Þ¤¹¡¥

4¤Î´Ø·¸¤¬À®Î©¤¹¤ë¤«¤É¤¦¤«¤òÄ´¤Ù¤Þ¤¹¡¥ ¼°(B.1), (B.2)¤ò Egg + Ep/$ \mu_{c}^{}$ ¤Ë¤Ä¤¤¤Æ²ò¤­¤Þ¤¹¡¥ ¼°(B.1)¤è¤ê¡¤

Egg + $\displaystyle {\frac{{E_p}}{{\mu_c}}}$ = $\displaystyle {\frac{{I_p^{1-\alpha}}}{{\displaystyle
G^{1-\alpha}\frac{3-3\al...
...mu_c}-\frac{1}{\mu_m}\Bigr)^{\frac{1-3\alpha}{2}}
E_p^{\frac{1-3\alpha}{2}}}}}$ (B.7)
¼°(B.2)¤è¤ê¡¤

Egg + $\displaystyle {\frac{{E_p}}{{\mu_c}}}$ = $\displaystyle {\frac{{\{(1-\alpha) g_m\}^{\frac{1-\alpha}{\alpha}}}}{{\displays...
...1}{\mu_m}\Bigr)^{\frac{1-3\alpha}{2\alpha}}
E_p^{\frac{1-3\alpha}{2\alpha}}}}}$ (B.8)
¼°(B.7)¤È¼°(B.8)¤Î±¦ÊÕ¤¬Åù¤·¤¤¤È¤ª¤­¡¤ gm ¤Ë¤Ä¤¤¤Æ²ò¤¯¤È¡¤
{(1 - $\displaystyle \alpha$)gm}$\scriptstyle {\frac{{1-\alpha}}{{\alpha}}}$ = $\displaystyle {\frac{{\displaystyle
G^{\frac{1-\alpha}{\alpha}}
\Bigl(\frac{3-3...
...\mu_c}-\frac{1}{\mu_m}\Bigr)^{\frac{1-3\alpha}{2}}
E_p^{\frac{1-3\alpha}{2}}}}}$Ip1-$\scriptstyle \alpha$  
  = G$\scriptstyle {\frac{{(1-\alpha)^2}}{{\alpha}}}$$\displaystyle \Bigl($$\displaystyle {\frac{{3-3\alpha}}{{2}}}$$\displaystyle \Bigr)^{{\frac{1-\alpha}{\alpha}}}_{}$$\displaystyle \Bigl($$\displaystyle {\frac{{1}}{{\mu_c}}}$ - $\displaystyle {\frac{{1}}{{\mu_m}}}$$\displaystyle \Bigr)^{{\frac{(1-3\alpha)(1-\alpha)}{2\alpha}}}_{}$Ep$\scriptstyle {\frac{{(1-3\alpha)(1-\alpha)}}{{2\alpha}}}$Ip1-$\scriptstyle \alpha$  
gm = $\displaystyle {\frac{{3}}{{2}}}$Ip$\scriptstyle \alpha$G1-$\scriptstyle \alpha$Ep$\scriptstyle {\frac{{1}}{{2}}}$-$\scriptstyle {\frac{{3}}{{2}}}$$\scriptstyle \alpha$$\displaystyle \Bigl($$\displaystyle {\frac{{1}}{{\mu_c}}}$ - $\displaystyle {\frac{{1}}{{\mu_m}}}$$\displaystyle \Bigr)^{{\frac{1}{2}-\frac{3}{2}\alpha}}_{}$ (B.9)

¼°(B.9)¤Ï¡¤[1, p. 124]¤Ëµ­ºÜ¤µ¤ì¤Æ¤¤¤ë¼°¤Ç¤¹B.1¡¥

5¤Ï¡¤¼°(B.5)¤è¤êÌÀ¤é¤«¤Ç¤¹¡¥

B.1.3 »°¶Ë´É¤Î¥°¥ê¥Ã¥ÉÅÅή¥â¥Ç¥ë

B.1.3.1 ¥°¥ê¥Ã¥É¤¬Àµ¤Î¾ì¹ç¤Î¥«¥½¡¼¥ÉÅÅή

¤³¤ì¤Þ¤Ç¤Ï Egg$ \le$ 0 ¤Î¾ì¹ç¤Ë¤Ä¤¤¤Æ¹Í¤¨¤Æ¤­¤Þ¤·¤¿¤¬¡¤ ¤³¤³¤Ç¡¤Egg > 0 ¤Î¾ì¹ç¤ò¹Í¤¨¤Þ¤¹¡¥ Egg > 0 ¤Î¾ì¹ç¡¤¥¤¥ó¥¼¥ë¸ú²ÌB.2¤ò¹Í¤¨¤Ê¤¯¤Æ¤â¤è¤¤¤Î¤Ç¡¤$ \mu$ ¤Ï $ \mu_{m}^{}$ ¤Ç°ìÄê¤È²¾Äꤷ¤Þ¤¹¡¥

»°¶Ë´É¤Î¥«¥½¡¼¥É¤«¤éή¤ì¤ëÅÅή¤Ï¡¤ ¥°¥ê¥Ã¥É¤Î°ÌÃ֤˥ץ졼¥È¤¬¤¢¤ëÆó¶Ë´É(Åù²ÁÆó¶Ë´É)¤ò¹Í¤¨¡¤ ¤½¤Î¥×¥ì¡¼¥ÈÅÅ°µ(Í­¸úÅÅ°µ)¤ò

Est = Egg + $\displaystyle {\frac{{E_p}}{{\mu_m}}}$ (B.10)
¤È¤·¤Æ¹Í¤¨¤Þ¤¹¡¥ ¥°¥ê¥Ã¥ÉÅÅ°µ¤¬Àµ¤ÎÎΰè¤Ç¤Ï¥¤¥ó¥¼¥ë¸ú²Ì¤ò¹Í¤¨¤ëɬÍפ¬¤Ê¤¤¤Î¤Ç¡¤ Åù²ÁÆó¶Ë´É¤Î¥×¥ì¡¼¥ÈÅÅή(¥«¥½¡¼¥ÉÅÅή)¤Ï¡¤¥×¥ì¡¼¥ÈÅÅ°µ¤Î1.5¾è¤ËÈæÎ㤷¤Þ¤¹¡¥ ¤·¤¿¤¬¤Ã¤Æ¡¤¥«¥½¡¼¥ÉÅÅή¤Ï¡¤

Ik = G'Est1.5 = G'$\displaystyle \Bigl($Egg + $\displaystyle {\frac{{E_p}}{{\mu_m}}}$$\displaystyle \Bigr)^{{1.5}}_{}$ (B.11)
¤Èɽ¤»¤Þ¤¹¡¥ ¤³¤³¤Ç¡¤G' ¤ÏÅù²ÁÆó¶Ë´É¤Î¥Ñ¡¼¥Ó¥¢¥ó¥¹¤Ç¤¹¡¥

G' ¤òµá¤á¤Þ¤¹¡¥ Egg = 0 ¤Î¤È¤­¤Î Ip ¤Ï¡¤¼°(B.1)¤è¤ê¡¤

Ip = G$\displaystyle \Bigl($$\displaystyle {\frac{{3-3\alpha}}{{2}}}$$\displaystyle \Bigr)^{{\frac{1}{1-\alpha}}}_{}$$\displaystyle \Bigl($$\displaystyle {\frac{{1}}{{\mu_c}}}$ - $\displaystyle {\frac{{1}}{{\mu_m}}}$$\displaystyle \Bigr)^{{\frac{3}{2}-\frac{1}{1-\alpha}}}_{}$$\displaystyle \Bigl($$\displaystyle {\frac{{1}}{{\mu_c}}}$$\displaystyle \Bigr)^{{\frac{1}{1-\alpha}}}_{}$Ep3/2

¤Ç¡¤ Egg = 0 ¤Î¤È¤­¤Î Ik ¤Ï¡¤¼°(B.11)¤è¤ê

Ik = G'$\displaystyle \Bigl($$\displaystyle {\frac{{E_p}}{{\mu_m}}}$$\displaystyle \Bigr)^{{1.5}}_{}$

¤Ç¡¤Î¾¼Ô¤¬°ìÃפ¹¤ë¤Î¤Ç¡¤

G' = G$\displaystyle \Bigl($$\displaystyle {\frac{{3-3\alpha}}{{2}}}$$\displaystyle \Bigr)^{{\frac{1}{1-\alpha}}}_{}$$\displaystyle \Bigl($$\displaystyle {\frac{{1}}{{\mu_c}}}$ - $\displaystyle {\frac{{1}}{{\mu_m}}}$$\displaystyle \Bigr)^{{\frac{3}{2}-\frac{1}{1-\alpha}}}_{}$$\displaystyle \Bigl($$\displaystyle {\frac{{1}}{{\mu_c}}}$$\displaystyle \Bigr)^{{\frac{1}{1-\alpha}}}_{}$$\displaystyle \mu_{m}^{{3/2}}$

¼°(B.6)¤òÍѤ¤¤Æ¡¤
G' = G$\displaystyle \mu_{m}^{{-\frac{1}{1-\alpha}}}$$\displaystyle \Bigl($$\displaystyle {\frac{{1}}{{\mu_c}}}$ - $\displaystyle {\frac{{1}}{{\mu_m}}}$$\displaystyle \Bigr)^{{\frac{3}{2}-\frac{1}{1-\alpha}}}_{}$$\displaystyle \mu_{m}^{{3/2}}$  
  = G$\displaystyle \Bigl\{$$\displaystyle \mu_{m}^{}$$\displaystyle \Bigl($$\displaystyle {\frac{{1}}{{\mu_c}}}$ - $\displaystyle {\frac{{1}}{{\mu_m}}}$$\displaystyle \Bigr)$$\displaystyle \Bigr\}^{{\frac{3}{2}-\frac{1}{1-\alpha}}}_{}$ = G$\displaystyle \Bigl($$\displaystyle {\frac{{\mu_m}}{{\mu_c}}}$ -1$\displaystyle \Bigr)^{{\frac{3}{2}-\frac{1}{1-\alpha}}}_{}$  
  = G$\displaystyle \Bigl($$\displaystyle {\frac{{3\alpha-1}}{{3-3\alpha}}}$$\displaystyle \Bigr)^{{\frac{3}{2}-\frac{1}{1-\alpha}}}_{}$ (B.12)

¤È¤Ê¤ê¤Þ¤¹¡¥

¥°¥ê¥Ã¥ÉÅÅ°µ¤òÊѤ¨¤¿¾ì¹ç¤Î¡¤¥×¥ì¡¼¥ÈÅÅ°µ¤È¥«¥½¡¼¥ÉÅÅή¤Î´Ø·¸¤ò¥°¥é¥Õ¤Ëɽ¤¹¤È¡¤ ¿ÞB.1¤Î¤è¤¦¤Ë¤Ê¤ê¤Þ¤¹¡¥

¿Þ B.1: Åù²ÁÆó¶Ë´É¤Î¥«¥½¡¼¥ÉÅÅή
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¥°¥ê¥Ã¥ÉÅÅ°µ¤¬ 0V ¤Î¤È¤­¤Ï¡¤¥×¥ì¡¼¥ÈÅÅ°µ¤¬ 0V ¤Î¤È¤³¤í¤«¤é ¥×¥ì¡¼¥ÈÅÅή¤¬Î®¤ì»Ï¤á¤Þ¤¹¡¥ ¥°¥ê¥Ã¥ÉÅÅ°µ¤¬ Eg (> 0)¤Î¤È¤­¤Ï¡¤ ¥×¥ì¡¼¥ÈÅÅ°µ¤¬ - $ \mu$Eg ¤Î¤È¤³¤í¤«¤é¥×¥ì¡¼¥ÈÅÅή¤¬Î®¤ì»Ï¤á¤Þ¤¹¡¥ ¤â¤Á¤í¤ó¡¤¼ÂºÝ¤Ë¤Ï¥×¥ì¡¼¥ÈÅÅ°µ¤¬Àµ¤Ç¤Ê¤±¤ì¤Ð¥×¥ì¡¼¥ÈÅÅή¤Ïή¤ì¤Ê¤¤¤Î¤Ç¡¤ ¥°¥é¥Õ¤ÎÂèÆó¾Ý¸Â¤Ë¤Ï°ÕÌ£¤¬¤¢¤ê¤Þ¤»¤ó¡¥ ¥×¥ì¡¼¥ÈÅÅ°µ¤¬¥°¥ê¥Ã¥ÉÅÅ°µ¤è¤ê½½Ê¬¤ËÂ礭¤ÊÎΰè¤Ç¤Ï¡¤ ¥«¥½¡¼¥ÉÅÅή¤È¤·¤Æ¤³¤Î¼°¤ò»È¤¤¤Þ¤¹¡¥

B.1.3.2 ¥×¥ì¡¼¥ÈÅÅή¤ÎºÇÂçÃÍ

¼¡¤Ë¡¤¥×¥ì¡¼¥ÈÅÅ°µ¤È¥«¥½¡¼¥ÉÅÅ°µ¤¬Åù¤·¤¤¾ì¹ç¡¤ ¤¹¤Ê¤ï¤ÁÆó¶Ë´ÉÀܳ¤Î¾ì¹ç¤ò¹Í¤¨¤Þ¤¹¡¥ ¤³¤Î¾ì¹ç¡¤¥°¥ê¥Ã¥ÉÅÅή¤È¥×¥ì¡¼¥ÈÅÅή¤ÎÈæ¤Ï¡¤¥×¥ì¡¼¥ÈÅÅ°µ(¥°¥ê¥Ã¥ÉÅÅ°µ)¤Ë¤«¤«¤ï¤é¤º¤Û¤Ü°ìÄê¤Ç¤¹¡¥ ¥«¥½¡¼¥ÉÅÅή¤ËÂФ¹¤ë¥°¥ê¥Ã¥ÉÅÅή¤ÎÈæ¤ò xg ¤È¤·¤Þ¤¹¡¥

xg $\displaystyle \equiv$ $\displaystyle {\frac{{I_g}}{{I_k}}}$$\displaystyle \Bigr\vert _{{E_p=E_g}}^{}$ (B.13)
¿ÞB.2¤Ë801¤Î¥×¥ì¡¼¥ÈÆÃÀ­¿Þ¤ò¼¨¤·¤Þ¤¹¤¬¡¤ Ep < Eg ¤Î¾ì¹ç¤Ï¡¤Ep = Eg ¤Î¥«¡¼¥Ö¤òĶ¤¨¤¿¥×¥ì¡¼¥ÈÅÅή¤¬Î®¤ì¤ë¤³¤È¤Ï¤¢¤ê¤Þ¤»¤ó¡¥

801_plate.png

¿Þ B.2: 801¤Î¥×¥ì¡¼¥ÈÆÃÀ­¿Þ
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¤Þ¤¿ Ep = Eg ¤Î¥«¡¼¥Ö¤Ï¥×¥ì¡¼¥ÈÅÅ°µ¤Î1.5¾è¤ËÈæÎ㤷¤Æ¤¤¤Þ¤¹¡¥ ¤³¤ì¤é¤«¤é¡¤¥×¥ì¡¼¥ÈÅÅ°µ¤òÍ¿¤¨¤¿»þ¤Ëή¤ì¤¦¤ëºÇÂç¤Î¥×¥ì¡¼¥ÈÅÅή Ip lim ¤ò¼¡¤Î¼°¤Çɽ¤¹¤³¤È¤¬¤Ç¤­¤Þ¤¹¡¥

Ip lim = (1 - xg)GlimEp1.5 (B.14)
¤³¤³¤Ç¡¤Glim ¤Ï¥×¥ì¡¼¥ÈÅÅή¤òÀ©¸Â¤¹¤ë°ì¼ï¤Î¥Ñ¡¼¥Ó¥¢¥ó¥¹¤È¹Í¤¨¤é¤ì¤Þ¤¹¡¥

¤³¤Î xg ¤ª¤è¤Ó Glim ¤Ï¡¤ Ep* = Eg* ¤Î¥×¥ì¡¼¥ÈÅÅή Ip* ¤ª¤è¤Ó ¥°¥ê¥Ã¥ÉÅÅή Ig* ¤Î¥Ç¡¼¥¿¤¬¤¢¤ì¤Ð¤½¤ì¤òÍѤ¤¤Æ¡¤

xg = $\displaystyle {\frac{{I_g^*}}{{I_p^*+I_g^*}}}$ (B.15)
Glim = $\displaystyle {\frac{{I_p^*+I_g^*}}{{E_p^{*1.5}}}}$ (B.16)

¤Çµá¤á¤Þ¤¹¡¥ ¥°¥ê¥Ã¥ÉÅÅή¤Î¥Ç¡¼¥¿¤¬¤Ê¤¤¾ì¹ç¤Îµá¤áÊý¤Ï¸å½Ò¤·¤Þ¤¹¡¥

B.1.3.3 ¥°¥ê¥Ã¥ÉÅÅή¤È¥×¥ì¡¼¥ÈÅÅ°µ¤Î´Ø·¸

Ep$ \ge$Eg ¤Î¤È¤­¡¤¥«¥½¡¼¥É¤«¤éÊü½Ð¤µ¤ì¤¿ÅŻҤϥ°¥ê¥Ã¥É¤ª¤è¤Ó¥×¥ì¡¼¥È¤Ë¤è¤Ã¤Æ ºî¤é¤ì¤ëÅų¦¤Ë¤è¤Ã¤Æ²Ã®¤µ¤ì¡¤°ìÉô¤Ï¥°¥ê¥Ã¥É¤Ëή¤ì¹þ¤ß¡¤»Ä¤ê¤Ï¤µ¤é¤Ë²Ã®¤µ¤ì¤Æ¥×¥ì¡¼¥È¤Ëή¤ì¤Þ¤¹¡¥ ¥×¥ì¡¼¥ÈÅÅ°µ¤¬¹â¤¯¤Ê¤ì¤Ð¤Ê¤ë¤Û¤É¡¤¥°¥ê¥Ã¥É¤Ëή¤ì¹þ¤àÅÅή¤Ï¾¯¤Ê¤¯¤Ê¤ê¤Þ¤¹¡¥

Ep < Eg ¤Î¤È¤­¡¤¥°¥ê¥Ã¥É¤òÄ̤ê²á¤®¤¿ÅŻҤϡ¤¥°¥ê¥Ã¥É-¥×¥ì¡¼¥È´Ö¤ÎÅų¦¤Ë¤è¤Ã¤Æ¸ºÂ®¤µ¤»¤é¤ì¡¤°ìÉô¤Ï¥×¥ì¡¼¥È¤ËÅþ㤷¤Þ¤¹¤¬¡¤¥°¥ê¥Ã¥É¤ËÌá¤Ã¤Æ¤¯¤ëÅŻҤ⤢¤ê¤Þ¤¹¡¥ ¤·¤¿¤¬¤Ã¤Æ¡¤¥×¥ì¡¼¥ÈÅÅ°µ¤¬Ä㤯¤Ê¤ì¤Ð¤Ê¤ë¤Û¤É¡¤¥°¥ê¥Ã¥ÉÅÅή¤¬Áý¤¨¤Þ¤¹¡¥

¤³¤Î¤è¤¦¤¹¤òɽ¤¹¤Î¤¬´Ø¿ô fg(Ep) ¤Ç¡¤ Ep = Eg ¤Î¤È¤­¤Î¥°¥ê¥Ã¥ÉÅÅή¤ò´ð½à¤È¤·¤Æ¡¤ ¤µ¤Þ¤¶¤Þ¤Ê¥×¥ì¡¼¥ÈÅÅ°µ¤ËÂФ¹¤ë¥°¥ê¥Ã¥ÉÅÅή¤ÎÁêÂÐŪ¤ÊÂ礭¤µ¤òɽ¤·¤Æ¤¤¤Þ¤¹(¿ÞB.3)¡¥

fg(Ep) = 1.2$\displaystyle {\frac{{E_g}}{{E_p+E_g}}}$ + 0.4 (B.17)
¿Þ B.3: ¥×¥ì¡¼¥ÈÅÅ°µ¤ËÂФ¹¤ë¥°¥ê¥Ã¥ÉÅÅή¤ÎÊѲ½
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¤³¤Î´Ø¿ô¤Ï¡¤Ep = 0 ¤Î¤È¤­¡¤1.6 ¤È¤Ê¤ê¡¤ Ep $ \gg$ Eg ¤Î¤È¤­¡¤0.4 ¤È¤Ê¤ê¤Þ¤¹¡¥ ¤³¤Î´Ø¿ô¤òÍѤ¤¤Æ¡¤¥°¥ê¥Ã¥ÉÅÅή¤Ï¼¡¤Î¤è¤¦¤Ëɽ¤»¤Þ¤¹¡¥

Ig = xgGlimEg1.5fg(Ep) (B.18)

¤³¤³¤Ç¡¤¥°¥ê¥Ã¥ÉÅÅή¤Î¥Ç¡¼¥¿¤¬¤Ê¤¤¾ì¹ç¤Î¥°¥ê¥Ã¥ÉÅÅή¤Î¿äÄêÊýË¡¤ò½Ò¤Ù¤Þ¤¹¡¥ ¥×¥ì¡¼¥ÈÅÅ°µ¤¬¥°¥ê¥Ã¥ÉÅÅ°µ¤è¤ê¹â¤¤¾ì¹ç¡¤ ¥«¥½¡¼¥ÉÅÅή¤Ï¿ÞB.4¤Î Ik ¤Î¥«¡¼¥Ö¤Î¤è¤¦¤Ë¤Ê¤ê¤Þ¤¹(¼°(B.11))¡¥

¿Þ B.4: ¥«¥½¡¼¥ÉÅÅή¤È¥°¥ê¥Ã¥ÉÅÅή
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¥×¥ì¡¼¥ÈÅÅ°µ¤¬0¤È¤Ê¤Ã¤¿¾ì¹ç¡¤ ¥«¥½¡¼¥ÉÅÅή¤Ï¥°¥ê¥Ã¥ÉÅÅή¤ÈÅù¤·¤¯¡¤Ik ¤Î¥«¡¼¥Ö¤Èy¼´¤Î¸òÅÀ Ik0 ¤è¤ê¤âÄ㤯¤Ê¤ê¤Þ¤¹¡¥ ¤³¤³¤Ç¡¤·Ð¸³Åª¤Ë¡¤

Ig0 = 0.8Ik0 (B.19)
¤È¤·¤Þ¤¹¡¥ ¤·¤¿¤¬¤Ã¤Æ¡¤

Ig1 = $\displaystyle {\frac{{I_{g0}}}{{1.6}}}$ = 0.5Ik0

¤È¤Ê¤ê¤Þ¤¹¡¥

¼°(B.11)¤ò»È¤Ã¤Æ Ik0, Ik1, Ig1 ¤òµá¤á¤ë¤È¡¤

Ik0 = G'Eg1.5  
Ik1 = G'$\displaystyle \Bigl($Eg + $\displaystyle {\frac{{E_g}}{{\mu}}}$$\displaystyle \Bigr)^{{1.5}}_{}$ = G'$\displaystyle \Bigl($1 + $\displaystyle {\frac{{1}}{{\mu}}}$$\displaystyle \Bigr)^{{1.5}}_{}$Eg1.5  
Ig1 = 0.5Ik0 = 0.5G'Eg1.5  

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xg = $\displaystyle {\frac{{I_{g1}}}{{I_{k1}}}}$ = $\displaystyle {\frac{{0.5 G' E_g^{1.5}}}{{G' (1 + \frac{1}{\mu})^{1.5} E_g^{1.5}}}}$ = $\displaystyle {\frac{{0.5}}{{(1 + \frac{1}{\mu})^{1.5}}}}$ (B.20)
Glim = $\displaystyle {\frac{{I_{k1}}}{{E_g^{1.5}}}}$ = $\displaystyle {\frac{{G' (1 + \frac{1}{\mu})^{1.5} E_g^{1.5}}}{{E_g^{1.5}}}}$ = G'$\displaystyle \Bigl($1 + $\displaystyle {\frac{{1}}{{\mu}}}$$\displaystyle \Bigr)^{{1.5}}_{}$ (B.21)

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B.1.3.4 ¥×¥ì¡¼¥ÈÅÅή

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Ip = min(Ik - Ig, Ip lim) (B.22)
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\begin{figure}\input{figs/ig_5}
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B.1.4 ¤Þ¤È¤á

¤³¤ì¤Þ¤Ç Egg ¤Ï Eg ¤è¤ê¤âÌó 0.6V ¹â¤¤¤È¤·¤Æ¤¤¤Þ¤·¤¿¤¬¡¤ ¤³¤ÎÃͤ⿿¶õ´É¤Ë¤è¤ê°Û¤Ê¤ë¤Î¤Ç¡¤¤³¤ì¤ò Ego ¤È¤·¤Þ¤¹¡¥

Egg = Eg + Ego (B.23)
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a = $\displaystyle {\frac{{1}}{{1-\alpha}}}$ (B.24)
b = $\displaystyle {\frac{{3}}{{2}}}$ - a = $\displaystyle {\frac{{3}}{{2}}}$ - $\displaystyle {\frac{{1}}{{1-\alpha}}}$ (B.25)
c = 3$\displaystyle \alpha$ - 1 (B.26)

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$\displaystyle \Bigl($$\displaystyle {\frac{{3-3\alpha}}{{2}}}$$\displaystyle \Bigl)^{{\frac{1}{1-\alpha}}}_{}$ = $\displaystyle \Bigl($$\displaystyle {\frac{{3}}{{2a}}}$$\displaystyle \Bigr)^{a}_{}$  
$\displaystyle \Bigl\{$$\displaystyle \Bigl($$\displaystyle {\frac{{1}}{{\mu_c}}}$ - $\displaystyle {\frac{{1}}{{\mu_m}}}$$\displaystyle \Bigl)$Ep$\displaystyle \Bigl\}^{{\frac{3}{2}-\frac{1}{1-\alpha}}}_{}$ = $\displaystyle \Bigl\{$$\displaystyle \Bigl($$\displaystyle {\frac{{1}}{{\mu_c}}}$ - $\displaystyle {\frac{{3-3\alpha}}{{2\mu_c}}}$$\displaystyle \Bigr)$Ep$\displaystyle \Bigr\}^{b}_{}$ = $\displaystyle \Bigl\{$$\displaystyle \Bigl($1 - $\displaystyle {\frac{{3}}{{2a}}}$$\displaystyle \Bigr)$$\displaystyle {\frac{{E_p}}{{\mu_c}}}$$\displaystyle \Bigr\}^{b}_{}$  
  = $\displaystyle \Bigl($$\displaystyle {\frac{{3\alpha - 1}}{{2}}}$ . $\displaystyle {\frac{{E_p}}{{\mu_c}}}$$\displaystyle \Bigr)^{b}_{}$ = $\displaystyle \Bigl($$\displaystyle {\frac{{c}}{{2}}}$ . $\displaystyle {\frac{{E_p}}{{\mu_c}}}$$\displaystyle \Bigr)^{b}_{}$  

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Ip = G$\displaystyle \Bigl($$\displaystyle {\frac{{3}}{{2a}}}$$\displaystyle \Bigl)^{a}_{}$$\displaystyle \Bigl($$\displaystyle {\frac{{c}}{{2}}}$ . $\displaystyle {\frac{{E_p}}{{\mu_c}}}$$\displaystyle \Bigr)^{b}_{}$$\displaystyle \Bigl($Egg + $\displaystyle {\frac{{E_p}}{{\mu_c}}}$$\displaystyle \Bigl)^{a}_{}$

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G' = G$\displaystyle \Bigl($$\displaystyle {\frac{{ac}}{{3}}}$$\displaystyle \Bigr)^{b}_{}$ (B.27)

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Ik = $\displaystyle \left\{\vphantom{ \begin{array}{ll}
G \bigl(\frac{3}{2a}\bigl)^a ...
...rac{E_p}{\mu_m}\bigl)^{1.5}, & \mbox{$E_{gg} > 0$\ ¤Î¤È¤­} \end{array} }\right.$$\displaystyle \begin{array}{ll}
G \bigl(\frac{3}{2a}\bigl)^a \bigl(\frac{c}{2} ...
...{gg} + \frac{E_p}{\mu_m}\bigl)^{1.5}, & \mbox{$E_{gg} > 0$\ ¤Î¤È¤­} \end{array}$ (B.28)
Ig = $\displaystyle \left\{\vphantom{ \begin{array}{ll}
0, & \mbox{$E_g \le 0$\ ¤Î¤È¤...
...frac{E_g}{E_p+E_g} + 0.4\bigr), & \mbox{$E_g < 0$\ ¤Î¤È¤­} \end{array} }\right.$$\displaystyle \begin{array}{ll}
0, & \mbox{$E_g \le 0$\ ¤Î¤È¤­} \\
x_g G_{\lim...
...igl(1.2 \frac{E_g}{E_p+E_g} + 0.4\bigr), & \mbox{$E_g < 0$\ ¤Î¤È¤­} \end{array}$ (B.29)
Ip lim = (1 - xg)GlimEp1.5 (B.30)
Ip = min(Ik - Ig, Ip lim) (B.31)


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