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72 KKU Science Journal Volume 39 Number 1 <strong>Review</strong> Heywang (1961, 1964) ‡ªìπºŸâ∑’Ë‡ πÕ·∫∫ ®”≈Õß∑’Ë‡ªìπ∑’Ë¬Õ¡√—∫Õ¬à“ß°«â“ß¢«“ß·∫∫·√° ‡¢“ Õ∏‘∫“¬ª√“°Ø°“√≥å PTCR «à“‡°‘¥®“°°“√¡’°”·æß»—°¬å (potential barrier) À√◊Õ—Èπªî¥ (blocking layer) ∑’Ë ¢Õ∫‡°√π (grain boundary) ´÷ËßÕ¬Ÿà√–À«à“ß‡°√π (grains) ¢Õß BaTiO 3 ‡¢“‡ πÕ«à“—Èπªî¥ (blocking layer) ¥—ß°≈à“«¡’æƒµ‘°√√¡°“√√—∫Õ‘‡≈Á°µ√Õπ (electron accepting state) ¥—ßπ—Èπ¡—π®÷ß∑”Àπâ“∑’Ë‡À¡◊Õπ°—∫¥—° §Õ¬®—∫Õ‘‡≈Á°µ√Õπ®“°Õ–µÕ¡¢Õß “√‡®◊Õµ—«„Àâ (donor dope atom) ∑”„Àâ‡°‘¥—Èπ¢Õß°“√æ√àÕß Õ‘‡≈Á°µ√Õπ (electron depletion layer) ∑”„Àâ·∂∫°“√π” (conduction band) ∑’Ë¢Õ∫‡°√π‚§âß¢÷Èπ‡°‘¥‡ªìπ√Õ¬µàÕ back-to-back Schottky À√◊Õ°”·æß»—°¬å (potential barrier) ¥—ß· ¥ß„π√Ÿª∑’Ë 2 §«“¡°«â“ß¢Õß—Èπ¢Õß°“√ æ√àÕßÕ‘‡≈Á°µ√Õπ (electron depletion layer; d) À“‰¥â®“° N s d 2N d (1) ‡¡◊ËÕ N s ‡ªìπ§«“¡Àπ“·πàπ¢Õß ∂“π–µ—«√—∫ (acceptor state) ∑’Ë¢Õ∫‡°√π ·≈– N d §◊Õ §«“¡ Àπ“·πàπ¢ÕßÕ–µÕ¡¢Õß “√‡®◊Õµ—«„Àâ¬—ßº≈ (effective donor atom) ¿“¬„π‡°√π §«“¡ Ÿß¢Õß°”·æß»—°¬å (φ) À“‰¥â®“° (Cho, 2006) eN s (2) 8 0 gb N d ‡¡◊ËÕ ε 0 , ε gb §◊Õ ¿“æ¬Õ¡ (permittivity) ¢Õß ÿ≠≠“°“»·≈–¢Õ∫‡°√π µ“¡≈”¥—∫ ·≈– e §◊Õ ª√–®ÿ¢ÕßÕ‘‡≈Á°µ√Õπ ‡π◊ËÕß®“° BaTiO 3 ‡ªìπ “√ª√–°Õ∫‡ø√å‚√- Õ‘‡≈Á°∑√‘° ¥—ßπ—Èπ∑’ËÕÿ≥À¿Ÿ¡‘ Ÿß°«à“Õÿ≥À¿Ÿ¡‘§Ÿ√’®÷ß¡’ æƒµ‘°√√¡µ“¡°Æ¢Õß Curie-Weiss °≈à“«§◊Õ gb 2 C T (3) ‡¡◊ËÕ T §◊Õ Õÿ≥À¿Ÿ¡‘ C §◊Õ §à“§ß∑’Ë¢Õß Curie-Weiss ´÷Ëß¡’§à“ª√–¡“≥ ~120,000 Õß»“‡´≈‡´’¬ ·≈– θ §◊Õ Õÿ≥À¿Ÿ¡‘ Curie-Weiss (Curie-Weiss temperature) ®“° ¡°“√ (3) ·≈– ¡°“√ (2) ®–‡ÀÁπ «à“°”·æß»—°¬å¡’§à“‡æ‘Ë¡¢÷Èπ‡¡◊ËÕÕÿ≥À¿Ÿ¡‘‡æ‘Ë¡¢÷Èπ ‡π◊ËÕß®“° §«“¡πà“®–‡ªìπ∑’ËÕ‘‡≈Á°µ√Õπ®–¢â“¡°”·æß»—°¬å¢÷Èπ°—∫ §«“¡ Ÿß¢Õß°”·æß»—°¬å ·≈–Õÿ≥À¿Ÿ¡‘ ¥—ßπ—Èπ ¿“æ §«“¡µâ“π∑“π‰øøÑ“∑’Ë¢Õ∫‡°√π (ρ gb ) ¢Õß PTCR- BaTiO 3 ®÷ß·ª√µ“¡§«“¡ Ÿß¢Õß°”·æß»—°¬å·≈–Õÿ≥À¿Ÿ¡‘ µ“¡ ¡°“√ (Moulson, 2003) (4) ‡¡◊ËÕ R §◊Õ §à“§ß∑’Ë ·≈– k §◊Õ §à“§ß∑’Ë ‚∫≈´‘¡—π (Boltzmann constant) ®–‰¥â«à“ gb R exp e kT ·∑π (3) ‰ª„π (2) ·≈â«·∑π (2) ‰ª„π (4) 2 2 e N s (5) gb R exp 1 8 0 N dC T ®“° (5) ®–‡ÀÁπ«à“∑’ËÕÿ≥À¿Ÿ¡‘ Ÿß°«à“Õÿ≥À¿Ÿ¡‘ §Ÿ√’ ¿“æ§«“¡µâ“π∑“π‰øøÑ“∑’Ë¢Õ∫‡°√π‡æ‘Ë¡¢÷ÈπÕ¬à“ß ‡≈¢’È°”≈—ß (exponentially) ‚¥¬¿“æ√«¡®–‡ÀÁπ‰¥â«à“ ·∫∫®”≈Õß¢Õß Heywang Õ∏‘∫“¬ª√“°Ø°“√≥å PTCR «à“ ç∑’ËÕÿ≥À¿Ÿ¡‘ Ÿß°«à“Õÿ≥À¿Ÿ¡‘§Ÿ√’ (T C ) ¿“æ§«“¡ µâ“π∑“π‰øøÑ“¢Õß¢Õ∫‡°√π‡æ‘Ë¡¢÷ÈπÕ¬à“ß√«¥‡√Á« ‡¡◊ËÕÕÿ≥À¿Ÿ¡‘‡æ‘Ë¡¢÷Èπ ¥—ßπ—Èπ ¿“æ§«“¡µâ“π∑“π‰øøÑ“ ¢Õß«— ¥ÿ®÷ß‡æ‘Ë¡¢÷ÈπÕ¬à“ß√«¥‡√Á«‡¡◊ËÕ‡æ‘Ë¡Õÿ≥À¿Ÿ¡‘é ·∫∫®”≈Õß∑’Ë Õß´÷ËßÕ∏‘∫“¬ª√“°Ø°“√≥å PTCR ‡ªìπ·∫∫®”≈Õß¢Õß Daniels (1978, 1979) ·∫∫®”≈Õßπ’ÈÕ∏‘∫“¬ª√“°Ø°“√≥å PTCR «à“‡°‘¥®“° °“√°√–®“¬µ—«¢Õßµ”Àπ‘ (defect) „π‘Èπß“π PTCR ‡¡◊ËÕ‡®◊Õ (dope) BaTiO 3 ¥â«¬‰ÕÕÕπ®”æ«°µ—«„Àâ (donor) ‡àπ ·∑π∑’Ë Ba 2+ ‰ÕÕÕπ¥â«¬ La 3+ ‰ÕÕÕπ À√◊Õ ·∑π Ti 4+ ‰ÕÕÕπ¥â«¬ Nb 5+ ‰ÕÕÕπ Õ“®®–‡°‘¥ µ”Àπ‘µà“ßÊ ‰¥â¥—ßµàÕ‰ªπ’È
∫∑§«“¡ «“√ “√«‘∑¬“»“ µ√å ¡¢. ªï∑’Ë 39 ©∫—∫∑’Ë 1 73 N d + + Potential barrier + + + + + + + + + + + + + + + + d N S - - - Grain boundary Acceptor state Conduction band Fermi level √Ÿª∑’Ë 2 —Èπªî¥ (blocking layer) ∑’Ë¢Õ∫‡°√π (grain boundary) µ“¡·∫∫®”≈Õß¢Õß Heywang (1961, 1964) 1) µ”Àπ‘Õ‘‡≈Á°∑√Õπ‘° å (electronic defect) La 1 2 2 2 6 e 2 x x 2O3 TiO2 LaBa Ti Ti OO O2 2 2) µ”Àπ‘‰∑µ“‡π’¬¡‰ÕÕÕπ (Titanium ion defect) La O 2 3 / x 2TiO2 2LaBa 2TiTi 6OO O2 3) µ”Àπ‘àÕß«à“ß·∫‡√’¬¡ (Barium vacancy defect) La 9O // x 2O3 3TiO2 2LaBa VBa 3TiTi 1 2 x O / Daniels (1976, 1978/1979) ∫Õ°«à“¢≥–∑’Ë ‡º“ºπ÷° (sinter) „π∫√√¬“°“»·∫∫ÕÕ°´‘‡¥—π BaTiO 3 ∑’Ë‡®◊Õ¥â«¬‰ÕÕÕπµ—«„Àâ®–¡’µ”Àπ‘À≈—°‡ªìπµ”Àπ‘ Õ‘‡≈Á°∑√Õπ‘° å (electronic defect) ´÷Ëß∑”„Àâ‡°‘¥ Õ‘‡≈Á°µ√Õπ®”π«π¡“°‡ªìπæ“À–ª√–®ÿ (Hill, 1991) µàÕ¡“‡¡◊ËÕ≈¥Õÿ≥À¿Ÿ¡‘≈ß¡“µ”Àπ‘À≈—°¢Õß BaTiO 3 ∑’Ë ‡®◊Õ¥â«¬‰ÕÕÕπµ—«„Àâ®–‡ªìπàÕß«à“ß·∫‡√’¬¡ (Barium // vacancy defect; V Ba ) ·≈–µ”Àπ‘¥—ß°≈à“«®–¡’®”π«π ¡“°¢÷Èπ‡¡◊ËÕ≈¥Õÿ≥À¿Ÿ¡‘≈ß‰ª‡√◊ËÕ¬Ê µàÕ¡“àÕß«à“ß ·∫‡√’¬¡ (Barium vacancy defect) ´÷Ëß‡°‘¥∑’Ë¢Õ∫‡°√π ®–·æ√à®“°¢Õ∫‡°√π‡¢â“‰ª„π‡°√π ·µà‡π◊ËÕß®“°µ”Àπ‘ π‘¥π’È·æ√à (diffuse) ‰¥ââ“¡“°®÷ß¡—°®–‰¡à “¡“√∂·æ√à ‡¢â“‰ª„π‡°√π‰¥âÀ¡¥ à«π„À≠à®÷ß¬—ß§ß‡°“–°—πÕ¬Ÿà µ“¡¢Õ∫‡°√π Õ“®®–¡Õß—Èπ¢Õßµ”Àπ‘π‘¥π’È«à“‡ªìπ —Èπ¢Õß©π«πÀÿâ¡√Õ∫Ê ‡°√π ¥—ß√Ÿª∑’Ë 3a Daniels (1976, 1991) Õ∏‘∫“¬µàÕ‰ª«à“—Èπ¢Õß©π«ππ’È¡’ æƒµ‘°√√¡‡ªìπµ—«√—∫ (acceptor) ∑”Àπâ“∑’Ë®—∫Õ‘‡≈Á°µ√Õπ ®“°‡π◊ÈÕ “√ (bulk) ·≈–∑”„Àâ‡°‘¥°”·æß»—°¬å¢«“ß°—Èπ °“√‡§≈◊ËÕπ∑’Ë¢Õßæ“À–ª√–®ÿ¥—ß√Ÿª∑’Ë 3b
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