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Mục tiêu của đề tài Hiện tượng vận chuyển điện tử trong các cấu trúc nano bán dẫn dựa trên vật liệu phân cực AlGaN/GaN và Penta-Graphene nanoribbon là nghiên cứu các hiện tượng vận chuyển điện tử trong các cấu trúc nano bán dẫn dựa trên các vật liệu AlGaN/GaN và penta-graphene nanoribbon.
BỘ GIÁO DỤC VÀ ĐÀO TẠO VIỆN HÀN LÂM KHOA HỌC VÀ CÔNG NGHỆ VIỆT NAM HỌC VIỆN KHOA HỌC VÀ CÔNG NGHỆ - PHẠM THỊ BÍCH THẢO HIỆN TƯỢNG VẬN CHUYỂN ĐIỆN TỬ TRONG CÁC CẤU TRÚC NANO BÁN DẪN DỰA TRÊN VẬT LIỆU PHÂN CỰC AlGaN/GaN VÀ PENTA-GRAPHENE NANORIBBON LUẬN ÁN TIẾN SỸ VẬT LÝ HÀ NỘI – 2020 VIỆN HÀN LÂM KHOA HỌC VÀ CÔNG NGHỆ VIỆT NAM HỌC VIỆN KHOA HỌC VÀ CƠNG NGHỆ …… ….***………… PHẠM THỊ BÍCH THẢO HIỆN TƯỢNG VẬN CHUYỂN ĐIỆN TỬ TRONG CÁC CẤU TRÚC NANO BÁN DẪN DỰA TRÊN VẬT LIỆU PHÂN CỰC AlGaN/GaN VÀ PENTA-GRAPHENE NANORIBBON LUẬN ÁN TIẾN SỸ VẬT LÝ Chuyên ngành: Vật lý lý thuyết Vật lý toán Mã số: 44 01 03 Người hướng dẫn khoa học: PGS.TS Nguyễn Thành Tiên GS.TS Đoàn Nhật Quang Hà Nội – 2020 ▲❮■ ❈❷▼ ❒◆ ✣➸ ❤♦➔♥ t❤➔♥❤ ❧✉➟♥ →♥ ♥➔②✱ tỉ✐ ✤➣ ♥❤➟♥ ✤÷đ❝ r➜t ♥❤✐➲✉ sü ❣✐ó♣ ✤ï✱ ộ trủ qỵ ổ ỗ ữớ t rữợ t tổ ❣û✐ ❧í✐ tr✐ ➙♥ s➙✉ s➢❝ ♥❤➜t ✤➳♥ ●❙✳❚❙✳ ✣♦➔♥ ◆❤➟t ◗✉❛♥❣ ✈➔ P●❙✳❚❙✳ ◆❣✉②➵♥ ❚❤➔♥❤ ❚✐➯♥✳ ❚r♦♥❣ s✉èt q✉→ tr tỹ sỹ ữợ t t➻♥❤ tr♦♥❣ ❝æ♥❣ t→❝ ❝❤✉②➯♥ ♠æ♥✱ ❝→❝ ❚❤➛② ❝á♥ ❧➔ ỳ ữớ t ú tổ ỵ tự ữủ trỏ ự ữợ q õ ỵ tự õ ụ ữ tỹ t ỳ ữợ ự ❤é trđ ❝ỉ♥❣ t→❝ ❣✐↔♥❣ ❞↕② tr♦♥❣ ♥❤➔ tr÷í♥❣✳ ❳✐♥ ✤÷đ❝ ❣û✐ ❧í✐ ❝↔♠ ì♥ ✤➳♥ P●❙✳❚❙✳ ▲➯ ❚✉➜♥✱ P●❙✳❚❙✳ ✣✐♥❤ ◆❤÷ ❚❤↔♦ ✈➔ ❝→❝ ❜↕♥ ❤å❝ ✈✐➯♥ ❝❛♦ ❤å❝ ❝ị♥❣ ♥❤â♠ ♥❣❤✐➯♥ ❝ù✉ t↕✐ tr÷í♥❣ ✣↕✐ ❤å❝ ❈➛♥ ❚❤ì ✤➣ ❝ị♥❣ ❝ë♥❣ t→❝ tr♦♥❣ ❝→❝ ❝ỉ♥❣ tr➻♥❤ ♥❣❤✐➯♥ ❝ù✉ ❦❤♦❛ ❤å❝ t❤í✐ ❣✐❛♥ q✉❛✳ ❚ỉ✐ ❝ơ♥❣ ①✐♥ ❣û✐ ❧í✐ ỡ qỵ ổ ổ t t t ỵ ❈ỉ♥❣ ♥❣❤➺ ❱✐➺t ◆❛♠ ✤➣ tr✉②➲♥ t❤ư ❦✐➳♥ t❤ù❝ ✈➔ ❤é trđ ❝ỉ♥❣ t→❝ ❤å❝ ✈ư ❝❤♦ tỉ✐ tr♦♥❣ s✉èt t❤í✐ ❣✐❛♥ t❤ü❝ ❤✐➺♥ ✤➲ t➔✐✳ ❳✐♥ ❝❤➙♥ t❤➔♥❤ ❝↔♠ ỡ qỵ ổ ổ t t ❚ü ♥❤✐➯♥ ✈➔ ❝→❝ ♣❤á♥❣ ❜❛♥ ❝❤ù❝ ♥➠♥❣ tr÷í♥❣ ✣↕✐ ❤å❝ ❈➛♥ ❚❤ì ✤➣ t↕♦ ♠å✐ ✤✐➲✉ ❦✐➺♥ ✤➸ tỉ✐ ❤♦➔♥ t❤➔♥❤ ✈✐➺❝ ❤å❝ t➟♣ ✈➔ ♥❣❤✐➯♥ ❝ù✉ tr♦♥❣ ❝→❝ ♥➠♠ q✉❛✳ ❈✉è✐ ❝ị♥❣✱ ①✐♥ ❣û✐ ❧í✐ tr✐ ➙♥ ✤➳♥ ❜↕♥ ❜➧ ✈➔ ♥❣÷í✐ t❤➙♥✱ ♥❤ú♥❣ ♥❣÷í✐ ❧✉ỉ♥ ❤é trđ ✈➔ ✤ë♥❣ ✈✐➯♥ tỉ✐ ✈÷đt q✉❛ ♥❤ú♥❣ ❦❤â ❦❤➠♥ ✤➸ ❤♦➔♥ t❤➔♥❤ ❧✉➟♥ →♥ ♥➔②✳ ❍➔ ◆ë✐✱ ♥❣➔② ✶✵ t❤→♥❣ ✶✷ ♥➠♠ ✷✵✷✵ P❤↕♠ ❚❤à ❇➼❝❤ ❚❤↔♦ ▲❮■ ❈❆▼ ✣❖❆◆ ❚ỉ✐ ①✐♥ ❝❛♠ ✤♦❛♥ ❝ỉ♥❣ tr➻♥❤ ♥➔② ✤÷đ❝ tỉ✐ t❤ü❝ ữợ sỹ ữợ t P●❙✳❚❙✳ ◆❣✉②➵♥ ❚❤➔♥❤ ❚✐➯♥ ✈➔ ❝→❝ ♥ë✐ ❞✉♥❣ ❧✐➯♥ q✉❛♥ ❝❤÷❛ ✤÷đ❝ ❝ỉ♥❣ ❜è tr♦♥❣ ❜➜t ❦ý ❧✉➟♥ →♥ ♥➔♦✳ ❈ư t❤➸✱ ❝❤÷ì♥❣ ✶ ❧➔ ♣❤➛♥ ❧÷đ❝ ❦❤↔♦ t➔✐ ❧✐➺✉ ✈➟t ❧✐➺✉ ♣❤➙♥ ❝ü❝ ✈➔ ↔♥❤ ❤÷ð♥❣ ❝õ❛ ✤✐➺♥ t➼❝❤ ♣❤➙♥ ❝ü❝ ❧➯♥ ❤✐➺♥ t÷đ♥❣ ✈➟♥ ❝❤✉②➸♥ ✤✐➺♥ tû✳ ❈❤÷ì♥❣ ✷ ✈➔ ✸ ❧➔ ❦➳t q✉↔ ♥❣❤✐➯♥ ❝ù✉ ✈➲ ❤✐➺♥ t÷đ♥❣ ❣✐❛♠ ❝➛♠ ❧÷đ♥❣ tû ✈➔ ✈➟♥ ❝❤✉②➸♥ ✤✐➺♥ tû tr♦♥❣ ❝➜✉ tró❝ t❤➜♣ ❝❤✐➲✉ ✤÷đ❝ tỉ✐ t❤ü❝ ❤✐➺♥ ❝ị♥❣ t ữợ t P ❚❤➔♥❤ ❚✐➯♥ ✈➔ ❝ë♥❣ sü P●❙✳❚❙✳ ✣✐♥❤ ◆❤÷ ❚❤↔♦✳ ❈✉è✐ ❝ị♥❣✱ ❝→❝ ❦➳t q✉↔ ✈➲ ♥❣❤✐➯♥ ❝ù✉ ❤✐➺♥ t÷đ♥❣ ✈➟♥ ❝❤✉②➸♥ ✤✐➺♥ tû tr♦♥❣ ♣❡♥t❛✲❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥ t❤✉➛♥ ✈➔ ♣❤❛ t↕♣ ỵ tt t ữủ tổ tỹ ❤✐➺♥ ❝ị♥❣ P●❙✳❚❙✳ ◆❣✉②➵♥ ❚❤➔♥❤ ❚✐➯♥✱ ❚❤❙✳ ❱ã ❚r✉♥❣ P❤ó❝ ✈➔ ●❙✳ ❘❛❥❡❡✈ ❆❤✉❥❛✱ ✤↕✐ ❤å❝ ❯♣♣s❛❧❛✱ ❚❤ö② ✣✐➸♥✳ ❍➔ ◆ë✐✱ ♥❣➔② ✶✵ t❤→♥❣ ✶✷ ♥➠♠ ✷✵✷✵ P❤↕♠ ❚❤à ❇➼❝❤ ❚❤↔♦ ✐ ▼ö❝ ❧ö❝ ❉❛♥❤ ♠ö❝ ❝→❝ ❝❤ú ✈✐➳t t➢t ❉❛♥❤ s→❝❤ ❤➻♥❤ ✈➩ ❉❛♥❤ s→❝❤ ❜↔♥❣ P❤➛♥ ♠ð ✤➛✉ ❈❤÷ì♥❣ ✶ ❚ê♥❣ q✉❛♥ ✈➲ ✈➟t ❧✐➺✉ ♥❣❤✐➯♥ ❝ù✉ ✶✳✶ ✐✐✐ ✐✈ ✐① ✶ ✶✺ ❈➜✉ tró❝ ❞à ❝❤➜t ❆❧●❛◆✴●❛◆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✶✳✶✳✶ ❈➜✉ tró❝ ❞à ❝❤➜t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✶✳✶✳✷ ❈➜✉ tró❝ ❞à ❝❤➜t ♣❤➙♥ ❝ü❝ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✶✳✶✳✸ ❷♥❤ ❤÷ð♥❣ ❝õ❛ ✤✐➺♥ t➼❝❤ ♣❤➙♥ ❝ü❝ ❧➯♥ ❤✐➺♥ t÷đ♥❣ ✈➟♥ ❝❤✉②➸♥ ✤✐➺♥ tû tr♦♥❣ ❝➜✉ tró❝ ❞à ❝❤➜t ♣❤➙♥ ❝ü❝ ❆❧●❛◆✴●❛◆ ✶✾ ✶✳✷ ✶✳✸ ❱➟t ❧✐➺✉ ❣r❛♣❤❡♥❡ ✈➔ ♣❡♥t❛✲❣r❛♣❤❡♥❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✶✳✷✳✶ ❱➟t ❧✐➺✉ ❣r❛♣❤❡♥❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✶✳✷✳✷ ❱➟t ❧✐➺✉ ❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✶✳✷✳✸ ❱➟t ❧✐➺✉ ♣❡♥t❛✲❣r❛♣❤❡♥❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✶✳✷✳✹ ❱➟t ❧✐➺✉ ♣❡♥t❛✲❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ❚r❛♥s✐st♦r ✤ë ❧✐♥❤ ✤ë♥❣ ✤✐➺♥ tû ❝❛♦ ❞ü❛ tr➯♥ ❆❧●❛◆✴●❛◆ ✈➔ tr❛♥s✐st♦r ❤✐➺✉ ù♥❣ tr÷í♥❣ ❞ü❛ tr➯♥ ❣r❛♣❤❡♥❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✐✐ ❈❤÷ì♥❣ ✷ P❤➙♥ ❜è ✤✐➺♥ tû tr♦♥❣ ❝➜✉ tró❝ ❞à ❝❤➜t ♣❤➙♥ ❝ü❝ ❆❧●❛◆✴●❛◆ ✸✽ ✷✳✶ ❍➔♠ sâ♥❣ ❜✐➳♥ ♣❤➙♥ ❝❤♦ ❝➜✉ tró❝ ❞à ❝❤➜t ✤ì♥ r➔♦ ❤ú✉ ❤↕♥ ✳ ✳ ✳ ✳ ✸✾ ✷✳✷ ❈→❝ t❤➳ ❣✐❛♠ ❣✐ú ✤✐➺♥ tû tr♦♥❣ ❝➜✉ tró❝ ❞à ❝❤➜t ♣❤➙♥ ❝ü❝ ♣❤❛ t↕♣ ✤✐➲✉ ❜✐➳♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ữủ ự ợ ởt tr tr♦♥❣ ✈ò♥❣ ❝♦♥ t❤➜♣ ♥❤➜t ✳ ✹✻ ✷✳✹ ❑➳t q✉↔ t➼♥❤ sè ✈➔ t❤↔♦ ❧✉➟♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ❈❤÷ì♥❣ ✸ ❍✐➺♥ t÷đ♥❣ ✈➟♥ ❝❤✉②➸♥ ✤✐➺♥ tû tr♦♥❣ ❝➜✉ tró❝ ❞à ❝❤➜t ♣❤➙♥ ❝ü❝ ❆❧●❛◆✴●❛◆ ✺✻ ✸✳✶ ❑➳t q✉↔ ❣✐↔✐ t➼❝❤ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✸✳✷ ❑➳t q✉↔ t➼♥❤ sè ✈➔ t❤↔♦ ❧✉➟♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✸✳✷✳✶ ✣ë ❧✐♥❤ ✤ë♥❣ ❣➙② ❜ð✐ t→♥ ①↕ ❜➜t tr➟t tü ❤ñ♣ ❦✐♠ ✈➔ t→♥ ①↕ ♥❤→♠ ❦➳t ❤ñ♣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✸✳✷✳✷ ❙♦ s→♥❤ ✈ỵ✐ ❞ú ❧✐➺✉ t❤ü❝ ♥❣❤✐➺♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ❈❤÷ì♥❣ ✹ ❍✐➺♥ t÷đ♥❣ ✈➟♥ ❝❤✉②➸♥ ✤✐➺♥ tû tr♦♥❣ ♣❡♥t❛✲❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥ ❞↕♥❣ ❜✐➯♥ r➠♥❣ ❝÷❛ ♣❤❛ t↕♣ ✼✹ ✹✳✶ ✣➦❝ t➼♥❤ ❝➜✉ tró❝ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✹✳✷ ✣➦❝ t➼♥❤ ✈➟♥ ❝❤✉②➸♥ ✤✐➺♥ tû ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ P❤➛♥ ❦➳t ❧✉➟♥ ❉❛♥❤ s→❝❤ ❝æ♥❣ ❜è ❝õ❛ t→❝ ❣✐↔ ❚➔✐ ❧✐➺✉ t❤❛♠ ❦❤↔♦ ✾✵ ✾✸ ✾✺ iii Danh mục từ viết tắt Tên Viết tắt Khí điện tử hai chiều (two-dimensional electron gas) 2DEG Armchair penta-graphene nanoribbon AAPGNR Hàm tự tương quan (Autocorrelation function) ACF Mất trật tự hợp kim (Alloy disorder) AD Armchair graphene nanoribbon AGNR Nhám rào (Barrier roughness) BR Nhám kết hợp (Combined roughness) CR Lý thuyết phiếm hàm mật độ (Density functional theory) DFT Mật độ trạng thái (Density of state) DOS Transistor hiệu ứng trường (Field effect transistor) FET Transistor hiệu ứng trường graphene (Graphene field effect transistor) Graphene nanoribbon Transistor độ linh động điện tử cao (High electron mobility transistor) Transistor hiệu ứng trường cấu trúc dị chất (Heterojunction field effect transistor) GFET GNR HEMT HFET Cấu trúc dị chất (Heterostructure) HS Điốt phát quang (Light Emitting Diode) LED Mật độ trạng thái riêng (Partial density of state) PDOS Penta-graphene PG Penta-graphene nanoribbon PGNR Nhám phân cực (Polarization roughness) PR Giếng lượng tử (Quantum well) QW Sawtooth penta-graphene nanoribbon SSPGNR Zigzag-armchair penta-graphene nanoribbon ZAPGNR Zigzag graphene nanoribbon ZGNR Zigzag penta-graphene nanoribbon ZZPGNR ✐✈ ❉❛♥❤ s→❝❤ ❤➻♥❤ ✈➩ ✶✳✶ ❙ü s➢♣ ①➳♣ ♥❣✉②➯♥ tû tr➯♥ ♠➦t ●❛ ✈➔ ◆ ❝õ❛ t✐♥❤ t❤➸ ụ t ữợ ỹ tỹ t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✶✳✷ ●✐↔♥ ỗ ũ sỹ t tỷ ❝❤✐➲✉ t↕✐ ❜➲ ♠➦t ❆❧●❛◆✴●❛◆ ❬✶✶❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✶✳✸ ❙ü t❤❛② ✤ê✐ ♠➟t ✤ë ❦❤➼ ✤✐➺♥ tû ❤❛✐ ❝❤✐➲✉ t❤❡♦ t❤➔♥❤ ♣❤➛♥ ❆❧ ✈➔ ❜➲ ❞➔② ❆❧●❛◆ ❬✶✶❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✶✳✹ ▼ët sè ❝➜✉ tró❝ ❝õ❛ ❝❛r❜♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✶✳✺ ❙ü ❤➻♥❤ t❤➔♥❤ ❝→❝ ❝➜✉ tró❝ ❝❛r❜♦♥ tø ❣r❛♣❤✐t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✶✳✻ ❈➜✉ tró❝ ❣r❛♣❤❡♥❡ ✈➔ ❤❛✐ ❞↕♥❣ ❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥✿ ③✐❣③❛❣ ✈➔ ❛r♠❝❤❛✐r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✶✳✼ ❛✮ ❱à tr➼ ♣❤❛ t↕♣ ❇ tr♦♥❣ ❆●◆❘✱ ❜✮ P❤❛ t↕♣ ◆ tr♦♥❣ ❆●◆❘✱ ❝✮ P❤❛ t↕♣ ❇✲◆ tr♦♥❣ ❆●◆❘✱ ❞✮ ▼æ ❤➻♥❤ t❤✐➳t ❜à ❝õ❛ ❆●◆❘ ♣❤❛ t ỗ t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✶✳✽ ❛✮ ❈➜✉ tró❝ ✈ò♥❣ ❝õ❛ ❆●◆❘ t❤✉➛♥ ✈➔ ❆●◆❘ ♣❤❛ t↕♣ ❇ ð ❝→❝ ✈à tr➼ ❦❤→❝ ♥❤❛✉✱ ❜✮ P❤ê ■✲❱ ❝õ❛ ❆●◆❘ t❤✉➛♥ ✈➔ ❆●◆❘ ♣❤❛ t↕♣ ❇ ð ✈à tr➼ P✹ ✈➔ P✻ t÷ì♥❣ ù♥❣ tr♦♥❣ ❤➻♥❤ ✶✳✼ ❬✽✻❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✶✳✾ ❛✮ ❈➜✉ tró❝ ✈ị♥❣ ❝õ❛ ❆●◆❘ t❤✉➛♥ ✈➔ ❆●◆❘ ♣❤❛ t↕♣ ❇✲◆ ❦➳t ❤ñ♣ ð ❝→❝ ✈à tr➼ ❦❤→❝ ♥❤❛✉✱ ❜✮ P❤ê ■✲❱ ❝õ❛ ❆●◆❘ t❤✉➛♥ ✈➔ ❆●◆❘ ♣❤❛ t↕♣ ❇✲◆ ð ✈à tr➼ P✶ ❬✽✻❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ỡ ỗ trú tỷ ✽✲❩●◆❘ ✈➔ ✹ ✈à tr➼ t↕♣ t❤❛② t❤➳ ❦❤→❝ ♥❤❛✉✱ ❜✮ ▼ỉ ❤➻♥❤ t❤✐➳t ❜à ❝õ❛ ✽✲❩●◆❘ ✤÷đ❝ tỉ✐ ❤â❛ ❜✐➯♥ ❤②❞r♦ ❬✽✼❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✶✳✶✶ ❈➜✉ tró❝ ✈ị♥❣ ❝õ❛ ❩●◆❘ ♣❤❛ t↕♣ ❇ ð ✹ ✈à tr➼ ❦❤→❝ ♥❤❛✉ ✭❛✱ ❜✱ ❝✱ ❞✮ ✈➔ ❩●◆❘ t❤✉➛♥ ✭❡✮ ❬✽✼❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✶✳✶✷ ❈➜✉ tró❝ ✈ị♥❣ ❝õ❛ ❩●◆❘ ♣❤❛ t↕♣ ◆ ð ✹ ✈à tr➼ ❦❤→❝ ♥❤❛✉ ✭❛✱ ❜✱ ❝✱ ❞✮ ✈➔ ❩●◆❘ t❤✉➛♥ ✭❡✮ ❬✽✼❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✶✳✶✸ ❈➜✉ tró❝ ♣❡♥t❛✲❣r❛♣❤❡♥❡ ❬✸✾❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✶✳✶✹ ❈→❝ ❝➜✉ tró❝ ♣❡♥t❛✲❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥ ❬✺✸❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ỡ ỗ ũ t❤➔♥❤ t↕✐ t✐➳♣ ❣✐→♣ ❝❤♦ ♠ët ❍❊▼❚✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✶✳✶✻ ▼æ ❤➻♥❤ ❍❊▼❚ ●❛◆✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✶✳✶✼ ▼æ ❤➻♥❤ tr❛♥s✐st♦r ❤✐➺✉ ù♥❣ tr÷í♥❣ ❞ü❛ tr➯♥ ❣r❛♣❤❡♥❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✷✳✶ ▼æ ❤➻♥❤ ♣❤❛ t↕♣ ✤✐➲✉ ❜✐➳♥ tr♦♥❣ ❝➜✉ tró❝ ❞à ❝❤➜t ♣❤➙♥ ❝ü❝ ❆❧✲ ●❛◆✴●❛◆✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✷✳✷ ❍➔♠ sâ♥❣ ✭❛✮ ✈➔ ❝→❝ t❤➳ ❣✐❛♠ ❝➛♠ ✭❜✮ tr♦♥❣ ❝➜✉ tró❝ ❞à ❝❤➜t ♣❤➙♥ ❝ü❝ ❆❧●❛◆✴●❛◆ ợ t ns = ì 1012 ✱ ♠➟t ✤ë ❞♦♥♦r N■ = × 1018 ❝♠−3 tữợ ố t L = 150 ❆✱ ❦❤♦↔♥❣ ❝→❝❤ tø ✷❉❊● ✤➳♥ t↕♣ Ls = 70 ✝ ❆ ❦❤✐ ♠➟t ✤ë ✤✐➺♥ t➼❝❤ ♣❤➙♥ ❝ü❝ ❧➛♥ ữủt /e = ì 1012 1013 ì 1013 ữủ ỵ tữỡ ự ❛✱ ❜ ✈➔ ❝✳ ✣÷í♥❣ ❧✐➲♥ ♥➨t ✈➔ ✤ùt ♥➨t ù♥❣ ✈ỵ✐ ♠ỉ ❤➻♥❤ r➔♦ ❤ú✉ ❤↕♥ ✈➔ ♠ỉ ❤➻♥❤ r➔♦ ✈æ ❤↕♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✷✳✸ ❍➔♠ sâ♥❣ tr♦♥❣ trú t ỹ ợ ữủ ❆❧ tr♦♥❣ ❤ñ♣ ❦✐♠ x = 0.3✱ ♠➟t ✤ë ❞♦♥♦r N■ = × 1018 ❝♠−3 ✱ ♠➟t ✤ë ✤✐➺♥ t ỹ /e = 1013 tữợ ♣❤➙♥ ❜è t↕♣ L❞ = 150 ✝ ❆ ✈➔ ❦❤♦↔♥❣ ❝→❝❤ tø ✷❉❊● ✤➳♥ t↕♣ Ls = 70 ✝ ❆ ❦❤✐ ♠➟t ✤ë ✷❉❊● ❧➛♥ ❧÷đt ❧➔ ns = 1012 ì 1012 1013 ữủ ỵ ❤✐➺✉ t÷ì♥❣ ù♥❣ ❛✱ ❜ ✈➔ ❝✳ ✣÷í♥❣ ❧✐➲♥ ♥➨t ✈➔ ✤ùt ♥➨t ù♥❣ ✈ỵ✐ ♠ỉ ❤➻♥❤ r➔♦ ❤ú✉ ❤↕♥ ✈➔ ♠æ ❤➻♥❤ r➔♦ ✈æ ❤↕♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✈✐ ✷✳✹ ❍➻♥❤ ✭❛✮✱ ❤➔♠ sâ♥❣ tr♦♥❣ ❝➜✉ tró❝ t ỹ ợ ữủ tr ❤ñ♣ ❦✐♠ x = 0.3✱ ♠➟t ✤ë ✷❉❊● ns = ì 1012 tữợ ố t L❞ = 150 ✝ ❆✱ ❦❤♦↔♥❣ ❝→❝❤ tø ✷❉❊● ✤➳♥ t↕♣ Ls = 70 ✝ ❆ ❦❤✐ ♠➟t ✤ë ❞♦♥♦r ữủt N = 1018 ì 1018 1019 ữủ ỵ tữỡ ự ❜ ✈➔ ❝✳ ❍➻♥❤ ✭❜✮✱ ❤➔♠ sâ♥❣ tr♦♥❣ ❝➜✉ tró❝ t ỹ ợ ữủ tr ❤ñ♣ ❦✐♠ x = 0.3✱ ♠➟t ✤ë ✷❉❊● ns = 1013 tữợ ố t L = 150 ✝ ❆✱ ♠➟t ✤ë ❞♦♥♦r N■ = × 1018 ❝♠−3 ❦❤✐ ❦❤♦↔♥❣ ❝→❝❤ tø ✷❉❊● ✤➳♥ t↕♣ ❧➛♥ ❧÷đt ❧➔ Ls ❂ ✵ ✝ ❆✱ ✼✵ ✝ ❆ ữủ ỵ tữỡ ự ❜ ✈➔ ❝✳ ✣÷í♥❣ ❧✐➲♥ ♥➨t ✈➔ ✤ùt ♥➨t ù♥❣ ✈ỵ✐ ♠ỉ ❤➻♥❤ r➔♦ ❤ú✉ ❤↕♥ ✈➔ ♠ỉ ❤➻♥❤ r➔♦ ✈æ ❤↕♥✳ ✳ ✳ ✺✹ ✸✳✶ ✣ë ❧✐♥❤ ✤ë♥❣ ❦❤✐ ①➨t t→♥ ①↕ ❜➜t tr➟t tü ❤ñ♣ ❦✐♠ ✭❆❉✮✱ t→♥ ①↕ ♥❤→♠ ❦➳t ❤ñ♣ ✭❈❘✮ ✈➔ tê♥❣ ❝→❝ t→♥ ①↕ ✭❚♦t✮ t❤❡♦ ♠➟t ✤ë ✤✐➺♥ t➼❝❤ ♣❤➙♥ ❝ü❝ σ/e tr♦♥❣ ❝➜✉ tró❝ ❞à ❝❤➜t ♣❤➙♥ ❝ü❝ ♣❤❛ t↕♣ ✤✐➲✉ ❜✐➳♥ ❆❧●❛◆✴●❛◆ ❦❤✐ ❜✐➯♥ ✤ë ♥❤→♠ ∆ = ✝ ❆ ✈➔ ✤ë ❞➔✐ t÷ì♥❣ q✉❛♥ Λ = 70 ✝ ❆✳ ỗ t ọ t ổ t sõ ❝➜✉ tró❝ ❞à ❝❤➜t ♣❤➙♥ ❝ü❝ ❆❧●❛◆✴●❛◆ ❦❤✐ ♠➟t ✤ë ✷❉❊● ns = 5×1012 ❝♠−2 ✱ ♠➟t ✤ë ❞♦♥♦r N■ = ì 1018 tữợ ố t↕♣ L❞ = 150 ✝ ❆ ✈➔ ❦❤♦↔♥❣ ❝→❝❤ tø t↕♣ ✤➳♥ ✷❉❊● Ls = 70 ✝ ❆❀ ❛✱ ❜✱ ❝ ù♥❣ ✈ỵ✐ ❣✐→ trà ♠➟t ✤ë ✤✐➺♥ t➼❝❤ ♣❤➙♥ ❝ü❝ σ/e ❂ × 1012 ✱ 1013 ✱ × 1013 ❝♠−2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✸✳✷ ✣ë ❧✐♥❤ ✤ë♥❣ ❦❤✐ ①➨t t→♥ ①↕ ❜➜t tr➟t tü ❤ñ♣ ❦✐♠ ✭❆❉✮✱ t→♥ ①↕ ♥❤→♠ ❦➳t ❤ñ♣ ✭❈❘✮ ✈➔ tê♥❣ ❝→❝ t→♥ ①↕ ✭❚♦t✮ t❤❡♦ ♠➟t ✤ë ❞♦♥♦r N■ tr♦♥❣ ❝➜✉ tró❝ ❞à ❝❤➜t ♣❤➙♥ ❝ü❝ ♣❤❛ t↕♣ ✤✐➲✉ ❜✐➳♥ ❆❧●❛◆✴●❛◆ ✈ỵ✐ ❤➔♠ ❧÷đ♥❣ ❆❧ x = 0.3✱ ♠➟t ✤ë ✷❉❊● ns = ì 1012 tữợ ố t L❞ = 150 ✝ ❆ ✈➔ ❦❤♦↔♥❣ ❝→❝❤ tø t↕♣ ✤➳♥ ✷❉❊● Ls = 70 ✝ ❆ ❦❤✐ ❜✐➯♥ ✤ë ♥❤→♠ ∆ = ✝ ❆ ✈➔ ✤ë ❞➔✐ t÷ì♥❣ q = 70 ỗ t ọ t❤❡♦ ♠ỉ t↔ ❤➔♠ sâ♥❣ ❝õ❛ ❝➜✉ tró❝ ❞à ❝❤➜t ♣❤➙♥ ❝ü❝ ❆❧●❛◆✴●❛◆ ❦❤✐ ♠➟t ✤ë ✷❉❊● ns = ì 1012 tữợ ố t L = 150 ✝ ❆ ✈➔ ❦❤♦↔♥❣ ❝→❝❤ tø t↕♣ ✤➳♥ ✷❉❊● Ls = 70 ✝ ❆❀ ❛✱ ❜✱ ❝ ù♥❣ ợ t r N = 1018 ì 1018 ✱ 1019 ❝♠−3 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✾✺ ❚➔✐ ❧✐➺✉ t❤❛♠ ❦❤↔♦ ❬✶❪ ❏✳ ❇❛r❞❡❡♥✱ ❲✳ ❍✳ ❇r❛tt❛✐♥✱ ❚❤❡ tr❛♥s✐st♦r✱ ❛ s❡♠✐✲❝♦♥❞✉❝t♦r tr✐♦❞❡✱ P❤②s✳ ❘❡✈✳ ✱ ✶✾✹✽✱ ✼✹ ✭✷✮✱ ✷✸✵✲✷✸✶✳ ❬✷❪ ❚✳ ▲✐✱ ▼✳ ▼❛str♦✱ ❆✳ ❉❛❞❣❛r✱ ■■■✕❱ ❝♦♠♣♦✉♥❞ s❡♠✐❝♦♥❞✉❝t♦rs✿ ✐♥t❡❣r❛t✐♦♥ ✇✐t❤ s✐❧✐❝♦♥✲❜❛s❡❞ ♠✐❝r♦❡❧❡❝tr♦♥✐❝s✱ ❈❘❈ ♣r❡ss✱ ✷✵✶✵✱ ◆❡✇ ❨♦r❦✳ ❬✸❪ ❍✳▼✳ ▼❛❝❦s❡②✱ ❋✳ ❍✳ ❉♦❡r❜❡❝❦✱ ●❛❆s ❋❊❚s ❤❛✈✐♥❣ ❤✐❣❤ ♦✉t♣✉t ♣♦✇❡r ♣❡r ✉♥✐t ❣❛t❡ ✇✐❞t❤✱ ■❊❊❊ ❊❧❡❝tr♦♥ ❉❡✈✐❝❡ ▲❡tt✳✱ ✶✾✽✶✱ ✷ ✭✻✮✱ ✶✹✼✲✶✹✽✳ ❬✹❪ ◆✳ ▲✉✱ ■✳ ❋❡r❣✉s♦♥✱ ■■■✲♥✐tr✐❞❡s ❢♦r ❡♥❡r❣② ♣r♦❞✉❝t✐♦♥✿ ♣❤♦t♦✈♦❧t❛✐❝ ❛♥❞ t❤❡r✲ ♠♦❡❧❡❝tr✐❝ ❛♣♣❧✐❝❛t✐♦♥s✱ ❙❡♠✐❝♦♥❞✳ ❙❝✐✳ ❚❡❝❤♥♦❧✳✱ ✷✵✶✸✱ ✷✽ ✭✼✮✱ ✵✼✹✵✷✸ ✭✶✲✶✶✮✳ ❬✺❪ ❨✳ ❍✉❛♥❣✱ ●r♦✇t❤ ❛♥❞ ❝❤❛r❛❝t❡r✐③❛t✐♦♥ ♦❢ ■♥x ●❛1−x ◆ ❛❧❧♦②s ❜② ♠❡t❛❧♦r❣❛♥✐❝ ❝❤❡♠✐❝❛❧ ✈❛♣♦r ❞❡♣♦s✐t✐♦♥ ❢♦r s♦❧❛r ❝❡❧❧ ❛♣♣❧✐❝❛t✐♦♥s✱ ❏✳ P❤♦t♦♥✐❝s ❊♥❡r❣②✱ ✷✵✶✷✱ ✷ ✭✶✮✱ ✵✷✽✺✵✶ ✭✶✲✶✵✮✳ ❬✻❪ ❨✳ ▲✐✱ ❙✳ ❨♦✉✱ ▼✳ ❩❤✉✱ ❡t ❛❧✳✱ ❉❡❢❡❝t✲r❡❞✉❝❡❞ ❣r❡❡♥ ●❛■♥◆✴●❛◆ ❧✐❣❤t✲ ❡♠✐tt✐♥❣ ❞✐♦❞❡ ♦♥ ♥❛♥♦♣❛tt❡r♥❡❞ s❛♣♣❤✐r❡✱ ❆♣♣❧✳ P❤②s✳ ▲❡tt✳✱ ✷✵✶✶✱ ✾✽ ✭✶✺✮✱ ✶✺✶✶✵✷ ✭✶✲✸✮✳ ❬✼❪ ■✳ ❑✉♠❡✱ ❍✳ ❚❛❦❡❞❛✱ ❚✳ ◆❛❣✉♠♦✱ ❡t ❛❧✳✱ ❯✳❙✳ P❛t❡♥t ◆♦✳ ✾✱ ✷✸✶✱ ✶✵✺✱ P❛t❡♥t ❛♥❞ ❚r❛❞❡♠❛r❦ ❖❢❢✐❝❡✱ ✷✵✶✻✱ ❲❛s❤✐♥❣t♦♥✱ ❉❈✿ ❯✳❙✳ ❬✽❪ ●✳ ❈✳ ❇❛s❛♥t❛ ❘♦✉❧✱ ❙✳ ▼✉❦✉♥❞❛♥✱ ❙✳ ❇✳ ❑r✉♣❛♥✐❞❤✐✱ ❍❡t❡r♦str✉❝t✉r❡s ♦❢ ■■■✲◆✐tr✐❞❡ ❙❡♠✐❝♦♥❞✉❝t♦rs ❢♦r ❖♣t✐❝❛❧ ❛♥❞ ❊❧❡❝tr♦♥✐❝ ❆♣♣❧✐❝❛t✐♦♥s✱ ❊♣✐t❛①②✱ ✷✵✶✽✱ ✶✼✶✲✶✾✸✳ ❬✾❪ ◆✳ ▼❛❡❞❛✱ ❚✳ ❙❛✐t♦❤✱ ❑✳ ❚s✉❜❛❦✐✱ ❡t ❛❧✳✱ ❊♥❤❛♥❝❡❞ ❡❧❡❝tr♦♥ ♠♦❜✐❧✐t② ✐♥ ❆❧✲ ●❛◆✴■♥●❛◆✴❆❧●❛◆ ❞♦✉❜❧❡✲❤❡t❡r♦str✉❝t✉r❡s ❜② ♣✐❡③♦❡❧❡❝tr✐❝ ❡❢❢❡❝t✱ ❏♣♥✳ ❏✳ ❆♣♣❧✳ P❤②s✳✱ ✶✾✾✾✱ ✸✽ ✭✼❇✮✱ ▲✼✾✾✲▲✽✵✶✳ ✾✻ ❬✶✵❪ ❊✳ P✳ P♦❦❛t✐❧♦✈✱ ❉✳ ▲✳ ◆✐❦❛✱ ❆✳ ❆✳ ❇❛❧❛♥❞✐♥✱ ❇✉✐❧t ✐♥ ❢✐❡❧❞ ❡❢❢❡❝t ♦♥ t❤❡ ❡❧❡❝tr♦♥ ♠♦❜✐❧✐t② ✐♥ ❆❧◆✴●❛◆✴❆❧◆ q✉❛♥t✉♠ ✇❡❧❧s✱ ❆♣♣❧✳ P❤②s✳ ▲❡tt✳✱ ✷✵✵✻✱ ✽✾ ✭✶✶✮✱ ✶✶✸✺✵✽ ✭✶✲✸✮✳ ❬✶✶❪ ❉✳ ❏❡♥❛✱ P♦❧❛r✐③❛t✐♦♥ ❊❢❢❡❝ts ✐♥ ❙❡♠✐❝♦♥❞✉❝t♦rs✿ ❋r♦♠ ❆❜ ■♥✐t✐♦ ❚❤❡♦r② t♦ ❉❡✈✐❝❡ ❆♣♣❧✐❝❛t✐♦♥s✱ ❙♣r✐♥❣❡r✱ ✷✵✵✽✱ ◆❡✇ ❨♦r❦✳ ❬✶✷❪ P✳ ❉❛s✱ ❚✳ ❘✳ ▲❡♥❦❛✱ ❙✳ ❙✳ ▼❛❤❛t♦✱ ❡t ❛❧✳✱ P♦❧❛r✐③❛t✐♦♥ ❊❢❢❡❝ts ✐♥ ❆❧✲ ●❛◆✴●❛◆ ❍❊▼❚s✳ ❍❛♥❞❜♦♦❦ ❢♦r ■■■✲❱ ❍✐❣❤ ❊❧❡❝tr♦♥ ▼♦❜✐❧✐t② ❚r❛♥s✐st♦r ❚❡❝❤♥♦❧♦❣✐❡s✱ ❈❘❈ Pr❡ss✱ ✷✵✶✾✱ ❯♥✐t❡❞ ❙t❛t❡s✳ ❬✶✸❪ ❖✳ ❆♠❜❛❝❤❡r✱ ❏✳ ❙♠❛rt✱ ❏✳ ❘✳ ❙❤❡❛❧②✱ ❡t ❛❧✳✱ ❚✇♦✲❞✐♠❡♥s✐♦♥❛❧ ❡❧❡❝tr♦♥ ❣❛s❡s ✐♥❞✉❝❡❞ ❜② s♣♦♥t❛♥❡♦✉s ❛♥❞ ♣✐❡③♦❡❧❡❝tr✐❝ ♣♦❧❛r✐③❛t✐♦♥ ❝❤❛r❣❡s ✐♥ ◆✲❛♥❞ ●❛✲ ❢❛❝❡ ❆❧●❛◆✴●❛◆ ❤❡t❡r♦str✉❝t✉r❡s✱ ❏✳ ❆♣♣❧✳ P❤②s✳✱ ✶✾✾✾✱ ✽✺ ✭✻✮✱ ✸✷✷✷✲✸✷✸✸✳ ❬✶✹❪ ❙✳ ❍❡✐❦♠❛♥✱ ❙✳ ❑❡❧❧❡r✱ ❨✳ ❲✉✱ ❡t ❛❧✳✱ P♦❧❛r✐③❛t✐♦♥ ❡❢❢❡❝ts ✐♥ ❆❧●❛◆✴●❛◆ ❛♥❞ ●❛◆✴❆❧●❛◆✴●❛◆ ❤❡t❡r♦str✉❝t✉r❡s✱ ❏✳ ❆♣♣❧✳ P❤②s✳✱ ✷✵✵✸✱ ✾✸ ✭✶✷✮✱ ✶✵✶✶✹✲ ✶✵✶✶✽✳ ❬✶✺❪ ❘✳ ❙✐♥❣❤✱ ▼✳ ❆✳ ❑❤❛♥✱ P✳ ❙❤❛r♠❛✱ ❡t ❛❧✳✱ ❚✇♦✲❞✐♠❡♥s✐♦♥❛❧ ❡❧❡❝tr♦♥ ❣❛s❡s ✐♥ ▼❣❩♥❖✴❩♥❖ ❛♥❞ ❩♥❖✴▼❣❩♥❖✴❩♥❖ ❤❡t❡r♦str✉❝t✉r❡s ❣r♦✇♥ ❜② ❞✉❛❧ ✐♦♥ ❜❡❛♠ s♣✉tt❡r✐♥❣✱ ❏✳ P❤②s✳ ❉✿ ❆♣♣❧✐❡❞ P❤②s✐❝s✱ ✷✵✶✽✱ ✺✶ ✭✶✸✮✱ ✶✸▲❚✵✷ ✭✶✲✶✷✮✳ ❬✶✻❪ ❆✳ ❘❛❦♦s❦✐✱ ❙✳ ❉✐❡③✱ ❍✳ ▲✐✱ ❡t ❛❧✳✱ ❊❧❡❝tr♦♥ tr❛♥s♣♦rt ✐♥ ◆✲♣♦❧❛r ●❛◆✲❜❛s❡❞ ❤❡t❡r♦str✉❝t✉r❡s✱ ❆♣♣❧✳ P❤②s✳ ▲❡tt✳✱ ✷✵✶✾✱ ✶✶✹ ✭✶✻✮✱ ✶✻✷✶✵✷ ✭✶✲✺✮✳ ❬✶✼❪ ▼✳ ❍✳ ●❛③③❛❤✱ ❇✳ ❈❤♦✉❝❤❡♥✱ ❆✳ ❋❛r❣✐✱ ❡t ❛❧✳✱ ❊❧❡❝tr♦✲t❤❡r♠❛❧ ♠♦❞❡❧✐♥❣ ❢♦r ■♥x ●❛1−x ◆✴●❛◆ ❜❛s❡❞ q✉❛♥t✉♠ ✇❡❧❧ ❤❡t❡r♦str✉❝t✉r❡s✱ ▼❛t❡r✳ ❙❝✐✳ ❙❡♠✐✲ ❝♦♥❞✳ Pr♦❝❡ss✳✱ ✷✵✶✾✱ ✾✸✱ ✷✸✶✲✷✸✼✳ ❬✶✽❪ ▼✳ ❋❡♥❡❜❡r❣✱ ❑✳ ❚❤♦♥❦❡✱ ❚✳ ❲✉♥❞❡r❡r✱ ❡t ❛❧✳✱ P✐❡③♦❡❧❡❝tr✐❝ ♣♦❧❛r✐③❛t✐♦♥ ♦❢ s❡♠✐♣♦❧❛r ❛♥❞ ♣♦❧❛r ●❛■♥◆ q✉❛♥t✉♠ ✇❡❧❧s ❣r♦✇♥ ♦♥ str❛✐♥❡❞ ●❛◆ t❡♠♣❧❛t❡s✱ ❏✳ ❆♣♣❧✳ P❤②s✳✱ ✷✵✶✵✱ ✶✵✼✱ ✶✵✸✺✶✼ ✭✶✲✻✮✳ ❬✶✾❪ ❉✳ ◆✳ ◗✉❛♥❣✱ ◆✳ ❍✳ ❚✉♥❣✱ ◆✳ ❚✳ ❚✐❡♥✱ ❊❧❡❝tr♦♥ s❝❛tt❡r✐♥❣ ❢r♦♠ ♣♦❧❛r✐③❛t✐♦♥ ❝❤❛r❣❡s ❜♦✉♥❞ ♦♥ ❛ r♦✉❣❤ ✐♥t❡r❢❛❝❡ ♦❢ ♣♦❧❛r ❤❡t❡r♦str✉❝t✉r❡s✱ ❏✳ ❆♣♣❧✳ P❤②s✳✱ ✷✵✶✶✱ ✶✵✾ ✭✶✶✮✱ ✶✶✸✼✶✶ ✭✶✲✽✮✳ ✾✼ ❬✷✵❪ ❈✳ ❉✉✱ ❲✳ ❍✉✱ ❩✳ ▲✳ ❲❛♥❣✱ ❘❡❝❡♥t Pr♦❣r❡ss ♦♥ P✐❡③♦tr♦♥✐❝ ❛♥❞ P✐❡③♦✲ P❤♦t♦tr♦♥✐❝ ❊❢❢❡❝ts ✐♥ ■■■✲●r♦✉♣ ◆✐tr✐❞❡ ❉❡✈✐❝❡s ❛♥❞ ❆♣♣❧✐❝❛t✐♦♥s✱ ❆❞✈✳ ❊♥❣✳ ▼❛t❡r✳✱ ✷✵✶✽✱ ✷✵ ✭✺✮✱ ✶✼✵✵✼✻✵ ✭✶✲✷✶✮✳ ❬✷✶❪ ❏✳ ❲✉✱ ❲❤❡♥ ❣r♦✉♣✲■■■ ♥✐tr✐❞❡s ❣♦ ✐♥❢r❛r❡❞✿ ◆❡✇ ♣r♦♣❡rt✐❡s ❛♥❞ ♣❡rs♣❡❝t✐✈❡s✱ ❏✳ ❆♣♣❧✳ P❤②s✳✱ ✷✵✵✾✱ ✶✵✻ ✭✶✮✱ ✵✶✶✶✵✶ ✭✶✲✷✽✮✳ ❬✷✷❪ ▼✳ ❊✐③❡♥❜❡r❣✱ ❏✳ ▼✳ ❇❧❛❦❡❧②✱ ❈❛r❜♦♥ ♠♦♥♦❧❛②❡r ♣❤❛s❡ ❝♦♥❞❡♥s❛t✐♦♥ ♦♥ ◆✐ ✭✶✶✶✮✱ ❙✉r❢❛❝❡ ❙❝✐❡♥❝❡✱ ✶✾✼✾✱ ✽✷ ✭✶✮✱ ✷✷✽✲✷✸✻✳ ❬✷✸❪ ❍✳ ❲✳ ❑r♦t♦✱ ❏✳ ❘✳ ❍❡❛t❤✱ ❙✳ ❈✳ ❖✬❇r✐❡♥✱ ❡t ❛❧✳✱ ❈✻✵✿ ❇✉❝❦♠✐♥st❡r❢✉❧❧❡r❡♥❡✱ ◆❛t✉r❡✱ ✶✾✽✺✱ ✸✶✽ ✭✻✵✹✷✮✱ ✶✻✷✲✶✻✸✳ ❬✷✹❪ ❙✳ ■✐❥✐♠❛✱ ❍❡❧✐❝❛❧ ♠✐❝r♦t✉❜✉❧❡s ♦❢ ❣r❛♣❤✐t✐❝ ❝❛r❜♦♥✱ ◆❛t✉r❡✱ ✶✾✾✶✱ ✸✺✹ ✭✻✸✹✽✮✱ ✺✻✲✺✽✳ ❬✷✺❪ ❑✳ ❙✳ ◆♦✈♦s❡❧♦✈✱ ❆✳ ❑✳ ●❡✐♠✱ ❙✳ ▼♦r♦③♦✈✱ ❡t ❛❧✳✱ ❚✇♦✲❞✐♠❡♥s✐♦♥❛❧ ❣❛s ♦❢ ♠❛ss❧❡ss ❉✐r❛❝ ❢❡r♠✐♦♥s ✐♥ ❣r❛♣❤❡♥❡✱ ◆❛t✉r❡✱ ✷✵✵✺✱ ✹✸✽ ✭✼✵✻✺✮✱ ✶✾✼✲✷✵✵✳ ❬✷✻❪ ❍✳ ❏✐❛♥❣✱ ❈❤❡♠✐❝❛❧ ♣r❡♣❛r❛t✐♦♥ ♦❢ ❣r❛♣❤❡♥❡✲❜❛s❡❞ ♥❛♥♦♠❛t❡r✐❛❧s ❛♥❞ t❤❡✐r ❛♣♣❧✐❝❛t✐♦♥s ✐♥ ❝❤❡♠✐❝❛❧ ❛♥❞ ❜✐♦❧♦❣✐❝❛❧ s❡♥s♦rs✱ ❙♠❛❧❧✱ ✷✵✶✶✱ ✼ ✭✶✼✮✱ ✷✹✶✸✲ ✷✹✷✼✳ ❬✷✼❪ ❆✳ ❇♦st✇✐❝❦✱ ❏✳ ▼❝❈❤❡s♥❡②✱ ❚✳ ❖❤t❛✱ ❡t ❛❧✳✱ ❊①♣❡r✐♠❡♥t❛❧ st✉❞✐❡s ♦❢ t❤❡ ❡❧❡❝tr♦♥✐❝ str✉❝t✉r❡ ♦❢ ❣r❛♣❤❡♥❡✱ Pr♦❣✳ ❙✉r❢✳ ❙❝✐✳✱ ✷✵✵✾✱ ✽✹ ✭✶✶✲✶✷✮✱ ✸✽✵✲✹✶✸✳ ❬✷✽❪ ▼✳ ❇❛t③✐❧❧✱ ❚❤❡ s✉r❢❛❝❡ s❝✐❡♥❝❡ ♦❢ ❣r❛♣❤❡♥❡✿ ▼❡t❛❧ ✐♥t❡r❢❛❝❡s✱ ❈❱❉ s②♥t❤❡✲ s✐s✱ ♥❛♥♦r✐❜❜♦♥s✱ ❝❤❡♠✐❝❛❧ ♠♦❞✐❢✐❝❛t✐♦♥s✱ ❛♥❞ ❞❡❢❡❝ts✱ ❙✉r❢✳ ❙❝✐✳ ❘❡♣✳✱ ✷✵✶✷✱ ✻✼ ✭✸✲✹✮✱ ✽✸✲✶✶✺✳ ❬✷✾❪ ❆✳ ❈✳ ◆❡t♦✱ ❋✳ ●✉✐♥❡❛✱ ◆✳ ▼✳ P❡r❡s✱ ❡t ❛❧✳✱ ❚❤❡ ❡❧❡❝tr♦♥✐❝ ♣r♦♣❡rt✐❡s ♦❢ ❣r❛♣❤❡♥❡✱ ❘❡✈✳ ▼♦❞✳ P❤②s✳✱ ✷✵✵✾✱ ✽✶ ✭✶✮✱ ✶✵✾✲✶✻✷✳ ❬✸✵❪ ❋✳ ▼♦❧✐t♦r✱ ❏✳ ●☎ ✉tt✐♥❣❡r✱ ❈✳ ❙t❛♠♣❢❡r✱ ❡t ❛❧✳✱ ❊❧❡❝tr♦♥✐❝ ♣r♦♣❡rt✐❡s ♦❢ ❣r❛♣❤❡♥❡ ♥❛♥♦str✉❝t✉r❡s✱ ❏✳ P❤②s✳ ❈♦♥❞❡♥s✳ ▼❛tt❡r✳✱ ✷✵✶✶✱ ✷✸ ✭✷✹✮✱ ✷✹✸✷✵✶ ✭✶✲✶✺✮✳ ❬✸✶❪ ❈✳ ◆✳ ❘✳ ❘❛♦✱ ❍✳ ❘✳ ▼❛tt❡✱ ❑✳ ❙✳ ❙✉❜r❛❤♠❛♥②❛♠✱ ❡t ❛❧✳✱ ❯♥✉s✉❛❧ ♠❛❣♥❡t✐❝ ♣r♦♣❡rt✐❡s ♦❢ ❣r❛♣❤❡♥❡ ❛♥❞ r❡❧❛t❡❞ ♠❛t❡r✐❛❧s✱ ❈❤❡♠✳ ❙❝✐✳✱ ✷✵✶✷✱ ✸ ✭✶✮✱ ✹✺✲✺✷✳ ❬✸✷❪ ▼✳ ❉r❛❣♦♠❛♥✱ ❉✳ ❉r❛❣♦♠❛♥✱ ●r❛♣❤❡♥❡✲❜❛s❡❞ q✉❛♥t✉♠ ❡❧❡❝tr♦♥✐❝s✱ Pr♦❣✳ ◗✉❛♥t✉♠✳ ❊❧❡❝tr♦♥✳✱ ✷✵✵✾✱ ✸✸ ✭✻✮✱ ✶✻✺✲✷✶✹✳ ✾✽ ❬✸✸❪ ❈✳ ❳✳ ●✉♦✱ ●✳ ❍✳ ●✉❛✐✱ ❈✳ ▼✳ ▲✐✱ ●r❛♣❤❡♥❡ ❜❛s❡❞ ♠❛t❡r✐❛❧s✿ ❡♥❤❛♥❝✐♥❣ s♦❧❛r ❡♥❡r❣② ❤❛r✈❡st✐♥❣✱ ❆❞✈✳ ❊♥❡r❣② ▼❛t❡r✳✱ ✷✵✶✶✱ ✶ ✭✸✮✱ ✹✹✽✲✹✺✷✳ ❬✸✹❪ ❨✳ ❙✉♥✱ ◗✳ ❲✉✱ ●✳ ❙❤✐✱ ●r❛♣❤❡♥❡ ❜❛s❡❞ ♥❡✇ ❡♥❡r❣② ♠❛t❡r✐❛❧s✱ ❊♥❡r❣② ❊♥✲ ✈✐r♦♥✳ ❙❝✐✳✱ ✷✵✶✶✱ ✹ ✭✹✮✱ ✶✶✶✸✲✶✶✸✷✳ ❬✸✺❪ ▼✳ ❳✉✱ ❚✳ ▲✐❛♥❣✱ ▼✳ ❙❤✐✱ ❡t ❛❧✳✱ ●r❛♣❤❡♥❡✲❧✐❦❡ t✇♦✲❞✐♠❡♥s✐♦♥❛❧ ♠❛t❡r✐❛❧s✱ ❈❤❡♠✳ ❘❡✈✳✱ ✷✵✶✸✱ ✶✶✸ ✭✺✮✱ ✸✼✻✻✲✸✼✾✽✳ ❬✸✻❪ ❈✳ ❚❛♥✱ ❳✳ ❈❛♦✱ ❳✳ ❏✳ ❲✉✱ ❡t ❛❧✳✱ ❘❡❝❡♥t ❛❞✈❛♥❝❡s ✐♥ ✉❧tr❛t❤✐♥ t✇♦✲ ❞✐♠❡♥s✐♦♥❛❧ ♥❛♥♦♠❛t❡r✐❛❧s✱ ❈❤❡♠✳ ❘❡✈✳✱ ✷✵✶✼✱ ✶✶✼ ✭✾✮✱ ✻✷✷✺✲✻✸✸✶✳ ❬✸✼❪ ❆✳ ❨❛♥❣✱ ❉✳ ❲❛♥❣✱ ❳✳ ❲❛♥❣✱ ❡t ❛❧✳✱ ❘❡❝❡♥t ❛❞✈❛♥❝❡s ✐♥ ♣❤♦s♣❤♦r❡♥❡ ❛s ❛ s❡♥s✐♥❣ ♠❛t❡r✐❛❧✱ ◆❛♥♦ ❚♦❞❛②✱ ✷✵✶✽✱ ✷✵✱ ✶✸✲✸✷✳ ❬✸✽❪ ❈✳ ❍✉❛♥❣✱ ❨✳ ▲✐✱ ◆✳ ❲❛♥❣✱ ❡t ❛❧✳✱ Pr♦❣r❡ss ✐♥ r❡s❡❛r❝❤ ✐♥t♦ ✷❉ ❣r❛♣❤❞✐②♥❡✲ ❜❛s❡❞ ♠❛t❡r✐❛❧s✱ ❈❤❡♠✳ ❘❡✈✳✱ ✷✵✶✽✱ ✶✶✽ ✭✶✻✮✱ ✼✼✹✹✲✼✽✵✸✳ ❬✸✾❪ ❩✳ ❙❤✉♥❤♦♥❣✱ ❩✳ ❏✐❛♥✱ ❲✳ ◗✐❛♥✱ ❡t ❛❧✳✱ P❡♥t❛✲❣r❛♣❤❡♥❡✿ ❆ ♥❡✇ ❝❛r❜♦♥ ❛❧✲ ❧♦tr♦♣❡ ◆❛♥♦s②st❡♠s✱ ✷✵✶✺✱ ✼ ✭✷✮✱ ✶✾✶✲✷✵✼✳ ❬✹✵❪ ❨✳ ❍✳ ▲✐✱ P✳ ❋✳ ❨✉❛♥✱ ❩✳ ◗✳ ❋❛♥✱ ❡t ❛❧✳✱ ❊❧❡❝tr♦♥✐❝ ♣r♦♣❡rt✐❡s ❛♥❞ ❝❛rr✐❡r ♠♦✲ ❜✐❧✐t② ❢♦r ♣❡♥t❛✲❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥s ✇✐t❤ ♥♦♥♠❡t❛❧❧✐❝✲❛t♦♠✲t❡r♠✐♥❛t✐♦♥s✱ ❖r❣✳ ❊❧❡❝tr♦♥✳✱ ✷✵✶✽✱ ✺✾✱ ✸✵✻✲✸✶✸✳ ❬✹✶❪ ●✳ ❇❡r❞✐②♦r♦✈✱ ●✳ ❉✐①✐t✱ ▼✳ ▼❛❞❥❡t✱ ❇❛♥❞ ❣❛♣ ❡♥❣✐♥❡❡r✐♥❣ ✐♥ ♣❡♥t❛✲ ❣r❛♣❤❡♥❡ ❜② s✉❜st✐t✉t✐♦♥❛❧ ❞♦♣✐♥❣✿ ❢✐rst✲♣r✐♥❝✐♣❧❡s ❝❛❧❝✉❧❛t✐♦♥s✱ ❏✳ P❤②s✳ ❈♦♥✲ ❞❡♥s✳ ▼❛tt❡r✳✱ ✷✵✶✻✱ ✷✽ ✭✹✼✮✱ ✹✼✺✵✵✶ ✭✶✲✶✵✮✳ ❬✹✷❪ ❏✳ ❏✳ ◗✉✐❥❛♥♦✲❇r✐♦♥❡s✱ ❍✳ ◆✳ ❋❡r♥❛♥❞❡③✲❊s❝❛♠✐❧❧❛✱ ❆✳ ❚❧❛❤✉✐❝❡✲❋❧♦r❡s✱ ❉♦♣❡❞ ♣❡♥t❛✲❣r❛♣❤❡♥❡ ❛♥❞ ❤②❞r♦❣❡♥❛t✐♦♥ ♦❢ ✐ts r❡❧❛t❡❞ str✉❝t✉r❡s✿ ❛ str✉❝✲ t✉r❛❧ ❛♥❞ ❡❧❡❝tr♦♥✐❝ ❉❋❚✲❉ st✉❞②✱ P❤②s✳ ❈❤❡♠✳ ❈❤❡♠✳ P❤②s✳✱ ✷✵✶✻✱ ✶✽ ✭✷✸✮✱ ✶✺✺✵✺✲✶✺✺✵✾✳ ❬✹✸❪ ❏✳ ■✳ ●✳ ❊♥r✐q✉❡③✱ ❈✳ ❱✳ ❆❧ ❘❡②✱ ❍②❞r♦❣❡♥ ❛❞s♦r♣t✐♦♥ ♦♥ ♣r✐st✐♥❡✱ ❞❡❢❡❝t❡❞✱ ❛♥❞ ✸❞✲❜❧♦❝❦ tr❛♥s✐t✐♦♥ ♠❡t❛❧✲❞♦♣❡❞ ♣❡♥t❛✲❣r❛♣❤❡♥❡✱ ■♥t✳ ❏✳ ❍②❞r♦❣✳ ❊♥❡r❣②✱ ✷✵✶✻✱ ✹✶ ✭✷✽✮✱ ✶✷✶✺✼✲✶✷✶✻✻✳ ❬✹✹❪ ❈✳ P✳ ❩❤❛♥❣✱ ❇✳ ▲✐✱ ❩✳ ●✳ ❙❤❛♦✱ ❋✐rst✲♣r✐♥❝✐♣❧❡ ✐♥✈❡st✐❣❛t✐♦♥ ♦❢ ❈❖ ❛♥❞ ❈❖2 ❛❞s♦r♣t✐♦♥ ♦♥ ❋❡✲❞♦♣❡❞ ♣❡♥t❛✲❣r❛♣❤❡♥❡✱ ❆♣♣❧✳ ❙✉r❢✳ ❙❝✐✳✱ ✷✵✶✾✱ ✹✻✾✱ ✻✹✶✲✻✹✻✳ ✾✾ ❬✹✺❪ ❉✳ ▲✐✱ ❲✳ ▲✐✱ ❏✳ ❩❤❛♥❣✱ ❈❛t❛❧②t✐❝ ❈❖ ♦①✐❞❛t✐♦♥ ❜② ❋❡ ❞♦♣❡❞ ♣❡♥t❛✲❣r❛♣❤❡♥❡✿ ❆ ❞❡♥s✐t② ❢✉♥❝t✐♦♥❛❧ st✉❞②✱ ▼♦❧✳ ❈❛t❛❧✳✱ ✷✵✶✾✱ ✹✼✵✱ ✹✽✲✺✺✳ ❬✹✻❪ ▼✳ ◗✳ ❈❤❡♥❣✱ ◗✳ ❈❤❡♥✱ ❑✳ ❨❛♥❣✱ P❡♥t❛✲●r❛♣❤❡♥❡ ❛s ❛ P♦t❡♥t✐❛❧ ●❛s ❙❡♥s♦r ❢♦r ◆❖x ❉❡t❡❝t✐♦♥✱ ◆❛♥♦s❝❛❧❡ ❘❡s✳ ▲❡tt✳✱ ✷✵✶✾✱ ✶✹ ✭✶✮✱ ✸✵✻ ✭✶✲✽✮✳ ❬✹✼❪ ▼✳ ▲✉✐s✐❡r✱ ❆✳ ❙③❛❜♦✱ ❈✳ ❙t✐❡❣❡r✱ ❡t ❛❧✳✱ ❋✐rst✲♣r✐♥❝✐♣❧❡s s✐♠✉❧❛t✐♦♥s ♦❢ ✷✲❉ s❡♠✐❝♦♥❞✉❝t♦r ❞❡✈✐❝❡s✿ ▼♦❜✐❧✐t②✱ ■❱ ❝❤❛r❛❝t❡r✐st✐❝s✱ ❛♥❞ ❝♦♥t❛❝t r❡s✐st❛♥❝❡✱ ■♥t❡r♥❛t✐♦♥❛❧ ❊❧❡❝tr♦♥ ❉❡✈✐❝❡s ▼❡❡t✐♥❣ ✭■❊❉▼✮✱ ✷✵✶✻✱ ✺✲✹✳ ❬✹✽❪ ▲✳ ❍✉✱ ❆✳ ▼❛♥❞❡❧✐s✱ ❳✳ ▲❛♥✱ ❡t ❛❧✳✱ ■♠❜❛❧❛♥❝❡❞ ❝❤❛r❣❡ ❝❛rr✐❡r ♠♦❜✐❧✐t② ❛♥❞ ❙❝❤♦tt❦② ❥✉♥❝t✐♦♥ ✐♥❞✉❝❡❞ ❛♥♦♠❛❧♦✉s ❝✉rr❡♥t✲✈♦❧t❛❣❡ ❝❤❛r❛❝t❡r✐st✐❝s ♦❢ ❡①✲ ❝✐t♦♥✐❝ P❜❙ ❝♦❧❧♦✐❞❛❧ q✉❛♥t✉♠ ❞♦t s♦❧❛r ❝❡❧❧s✱ ❙♦❧✳ ❊♥❡r❣② ▼❛t❡r✳ ❙♦❧✳✱ ✷✵✶✻✱ ✶✺✺✱ ✶✺✺✲✶✻✺✳ ❬✹✾❪ ▼✳ ❆③✐③✐✱ ❈✳ ❆③✐③✐✱ ❊❢❢❡❝t ♦❢ ▼♦❜✐❧✐t② ♦♥ ✭■❱✮ ❈❤❛r❛❝t❡r✐st✐❝s ♦❢ ●❛❛s ▼❊❙✲ ❋❊❚✱ ■♥t✳ ❏✳ ❊❧❡❝tr✳ ❈♦♠♣✉t✳ ❊♥❣✳✱ ✷✵✶✼✱ ✼ ✭✶✮✱ ✶✻✾✲✶✼✺✳ ❬✺✵❪ P✳ ❏❛♥❣✐❞✱ ❉✳ P❛t❤❛♥✱ ❆✳ ❑♦tt❛♥t❤❛r❛②✐❧✱ ●r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥ tr❛♥s✐st♦rs ✇✐t❤ ❤✐❣❤ ■❖◆✴■❖❋❋ r❛t✐♦ ❛♥❞ ♠♦❜✐❧✐t②✱ ❈❛r❜♦♥✱ ✷✵✶✽✱ ✶✸✷✱ ✻✺✲✼✵✳ ❬✺✶❪ ❆✳ P❛♥❞②❛✱ P✳ ❑✳ ❏❤❛✱ ❊❧❡❝tr♦♥✐❝ ❚r❛♥s♣♦rt ❈❤❛r❛❝t❡r✐st✐❝s ♦❢ ❛ ●r❛♣❤❡♥❡ ◆❛♥♦r✐❜❜♦♥ ❇❛s❡❞ ♣✕♥ ❉❡✈✐❝❡✱ ❏✳ ❊❧❡❝tr♦♥✳ ▼❛t❡r✳✱ ✷✵✶✾✱ ✹✽ ✭✾✮✱ ✺✼✵✷✲✺✼✵✾✳ ❬✺✷❪ ❉✳ ❙✐♥❣❤✱ ❱✳ ❙❤✉❦❧❛✱ P✳ ❑✳ P❛♥❞❛✱ ❡t ❛❧✳✱ ❈❛r❜♦♥✲♣❤♦s♣❤✐❞❡ ♠♦♥♦❧❛②❡r ✇✐t❤ ❤✐❣❤ ❝❛rr✐❡r ♠♦❜✐❧✐t② ❛♥❞ ♣❡r❝❡♣t✐❜❧❡ ■✕❱ r❡s♣♦♥s❡ ❢♦r s✉♣❡r✐♦r ❣❛s s❡♥s✐♥❣✱ ◆❡✇ ❏✳ ❈❤❡♠✳✱ ✷✵✷✵✱ ✹✹ ✭✾✮✱ ✸✼✼✼✲✸✼✽✺✳ ❬✺✸❪ P✳ ❋✳ ❨✉❛♥✱ ❩✳ ❍✳ ❩❤❛♥❣✱ ❩✳ ◗✳ ❋❛♥✱ ▼✳ ◗✐✉✱ ❊❧❡❝tr♦♥✐❝ str✉❝t✉r❡ ❛♥❞ ♠❛❣✲ ♥❡t✐❝ ♣r♦♣❡rt✐❡s ♦❢ ♣❡♥t❛✲❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥s✱ P❤②s✳ ❈❤❡♠✳ ❈❤❡♠✳ P❤②s✳✱ ✷✵✶✼✱ ✾ ✭✶✹✮✱ ✾✺✷✽✲✾✺✸✻✳ ❬✺✹❪ ❱✳ ❱✳ ❖♥✱ ▲✳ ◆✳ ❚❤❛♥❤✱ ◆✳ ❚✳ ❚✐❡♥✱ ❚❤❡ ❡❧❡❝tr♦♥✐❝ ♣r♦♣❡rt✐❡s ❛♥❞ ❡❧❡❝tr♦♥ tr❛♥s♣♦rt ♦❢ s❛✇t♦♦t❤ ♣❡♥t❛✲❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥ ✉♥❞❡r ✉♥✐❛①✐❛❧ str❛✐♥✿ ❛❜✲ ✐♥✐t✐♦ st✉❞②✱ P❤✐❧♦s✳ ▼❛❣✳✱ ✷✵✷✵✱ ✶✲✶✺✳ ❬✺✺❪ ❉✳ ◆✳ ◗✉❛♥❣✱ ❱✳ ◆✳ ❚✉♦❝✱ ◆✳ ❍✳ ❚✉♥❣✱ ❡t ❛❧✳✱ ❘♦✉❣❤♥❡ss✲✐♥❞✉❝❡❞ ♠❡❝❤❛♥✐s♠s ❢♦r ❡❧❡❝tr♦♥ s❝❛tt❡r✐♥❣ ✐♥ ✇✉rt③✐t❡ ❣r♦✉♣✲■■■✲♥✐tr✐❞❡ ❤❡t❡r♦str✉❝t✉r❡s✱ P❤②s✳ ❘❡✈✳ ❇✱ ✷✵✵✺✱ ✼✷ ✭✷✹✮✱ ✷✹✺✸✵✸ ✭✶✲✶✸✮✳ ✶✵✵ ❬✺✻❪ ❋✳ ❇❡r♥❛r❞✐♥✐✱ ❱✳ ❋✐♦r❡♥t✐♥✐✱ ❉✳ ❱❛♥❞❡r❜✐❧t✱ ❖❢❢s❡ts ❛♥❞ ♣♦❧❛r✐③❛t✐♦♥ ❛t str❛✐♥❡❞ ❆❧◆✴●❛◆ ♣♦❧❛r ✐♥t❡r❢❛❝❡s✱ ▼❘❙ ❖♥❧✐♥❡ Pr♦❝❡❡❞✐♥❣s ▲✐❜r❛r② ❆r❝❤✐✈❡✱ ✶✾✾✻✱ ✹✹✾✱ ✾✷✸✲✾✷✽✳ ❬✺✼❪ ❖✳ ❆♠❜❛❝❤❡r✱ ●r♦✇t❤ ❛♥❞ ❛♣♣❧✐❝❛t✐♦♥s ♦❢ ❣r♦✉♣ ■■■✲♥✐tr✐❞❡s✱ ❏✳ P❤②s✳ ❉✱ ✶✾✾✽✱ ✸✶✱ ✷✻✺✸✲✷✼✶✵✳ ❬✺✽❪ ❙✳ ❉❛tt❛✱ ❚✳ ❆s❤❧❡②✱ ❏✳ ❇r❛s❦✱ ❡t ❛❧✳✱ ✽✺♥♠ ❣❛t❡ ❧❡♥❣t❤ ❡♥❤❛♥❝❡♠❡♥t ❛♥❞ ❞❡♣❧❡t✐♦♥ ♠♦❞❡ ■♥❙❜ q✉❛♥t✉♠ ✇❡❧❧ tr❛♥s✐st♦rs ❢♦r ✉❧tr❛ ❤✐❣❤ s♣❡❡❞ ❛♥❞ ✈❡r② ❧♦✇ ♣♦✇❡r ❞✐❣✐t❛❧ ❧♦❣✐❝ ❛♣♣❧✐❝❛t✐♦♥s✱ ■♥ ■❊❊❊ ■♥t❡r♥❛t✐♦♥❛❧ ❊❧❡❝tr♦♥ ❉❡✈✐❝❡s ▼❡❡t✐♥❣✱ ✷✵✵✺✱ ✼✻✸✲✼✻✻✳ ❬✺✾❪ ❏✳ ❍❛ss✱ ❲✳ ❉❡ ❍❡❡r✱ ❊✳ ❈♦♥r❛❞✱ ❚❤❡ ❣r♦✇t❤ ❛♥❞ ♠♦r♣❤♦❧♦❣② ♦❢ ❡♣✐t❛①✐❛❧ ♠✉❧t✐❧❛②❡r ❣r❛♣❤❡♥❡✱ ❏✳ P❤②s✳ ❈♦♥❞❡♥s✳ ▼❛tt❡r✳✱ ✷✵✵✽✱ ✷✵ ✭✸✷✮✱ ✸✷✸✷✵✷ ✭✶✲ ✷✼✮✳ ❬✻✵❪ ▼✳ ❉✳ ❙t♦❧❧❡r✱ ❙✳ P❛r❦✱ ❨✳ ❩❤✉✱ ❡t ❛❧✳✱ ●r❛♣❤❡♥❡✲❇❛s❡❞ ❯❧tr❛❝❛♣❛❝✐t♦rs✱ ◆❛♥♦ ▲❡tt✳✱ ✷✵✵✽✱ ✽ ✭✶✵✮✱ ✸✹✾✽✕✸✺✵✷✳ ❬✻✶❪ ❊✳ ❨♦♦✱ ❏✳ ❑✐♠✱ ❊✳ ❍♦s♦♥♦✱ ❡t ❛❧✳✱ ▲❛r❣❡ ❘❡✈❡rs✐❜❧❡ ▲✐ ❙t♦r❛❣❡ ♦❢ ●r❛♣❤❡♥❡ ◆❛♥♦s❤❡❡t ❋❛♠✐❧✐❡s ❢♦r ❯s❡ ✐♥ ❘❡❝❤❛r❣❡❛❜❧❡ ▲✐t❤✐✉♠ ■♦♥ ❇❛tt❡r✐❡s✱ ◆❛♥♦ ▲❡tt✳✱ ✷✵✵✽✱ ✽ ✭✽✮✱ ✷✷✼✼✕✷✷✽✷✳ ❬✻✷❪ ❳✳ ❏✐❛♥❣✱ ❏✳ ◆✐s❛r✱ ❇✳ P❛t❤❛❦✱ ❡t ❛❧✳✱ ●r❛♣❤❡♥❡ ♦①✐❞❡ ❛s ❛ ❝❤❡♠✐❝❛❧❧② t✉♥❛❜❧❡ ✷✲❉ ♠❛t❡r✐❛❧ ❢♦r ✈✐s✐❜❧❡✲❧✐❣❤t ♣❤♦t♦❝❛t❛❧②st ❛♣♣❧✐❝❛t✐♦♥s✱ ❏✳ ❈❛t❛❧✳✱ ✷✵✶✸✱ ✷✾✾✱ ✷✵✹✕✷✵✾✳ ❬✻✸❪ ❈✳ ❙♦❧❞❛♥♦✱ ❆✳ ▼❛❤♠♦♦❞✱ ❊✳ ❉✉❥❛r❞✐♥✱ Pr♦❞✉❝t✐♦♥✱ ♣r♦♣❡rt✐❡s ❛♥❞ ♣♦t❡♥t✐❛❧ ♦❢ ❣r❛♣❤❡♥❡✱ ❈❛r❜♦♥✱ ✷✵✶✵✱ ✹✽ ✭✽✮✱ ✷✶✷✼✕✷✶✺✵✳ ❬✻✹❪ ❨✳ ▼✳ ▲✐♥✱ ❈✳ ❉✐♠✐tr❛❦♦♣♦✉❧♦s✱ ❑✳ ❆✳ ❏❡♥❦✐♥s✱ ❡t ❛❧✳✱ ✶✵✵✲●❍③ tr❛♥s✐st♦rs ❢r♦♠ ✇❛❢❡r✲s❝❛❧❡ ❡♣✐t❛①✐❛❧ ❣r❛♣❤❡♥❡✱ ❙❝✐❡♥❝❡✱ ✷✵✶✵✱ ✸✷✼ ✭✺✾✻✻✮✱ ✻✻✷✳ ❬✻✺❪ ❏✳ ❩❤❡♥❣✱ ▲✳ ❲❛♥❣✱ ❘✳ ◗✉❤❡✱ ❡t ❛❧✳✱ ❙✉❜✲✶✵ ♥♠ ❣❛t❡ ❧❡♥❣t❤ ❣r❛♣❤❡♥❡ tr❛♥✲ s✐st♦rs✿ ♦♣❡r❛t✐♥❣ ❛t t❡r❛❤❡rt③ ❢r❡q✉❡♥❝✐❡s ✇✐t❤ ❝✉rr❡♥t s❛t✉r❛t✐♦♥✱ ❙❝✐✳ ❘❡♣✳✱ ✷✵✶✸✱ ✸✱ ✶✸✶✹ ✭✶✲✾✮✳ ❬✻✻❪ ❑✳ ❙✳ ❑✐♠✱ ❨✳ ❩❤❛♦✱ ❍✳ ❏❛♥❣✱ ❡t ❛❧✳✱ ▲❛r❣❡✲s❝❛❧❡ ♣❛tt❡r♥ ❣r♦✇t❤ ♦❢ ❣r❛♣❤❡♥❡ ❢✐❧♠s ❢♦r str❡t❝❤❛❜❧❡ tr❛♥s♣❛r❡♥t ❡❧❡❝tr♦❞❡s✱ ◆❛t✉r❡✱ ✷✵✵✾✱ ✹✺✼✭✼✷✸✵✮✱ ✼✵✻✲ ✼✶✵✳ ✶✵✶ ❬✻✼❪ ❳✳ ▲✐✱ ◗✳ ❩❤❛♥❣✱ ❳✳ ❈❤❡♥✱ ❡t ❛❧✳✱ ●✐❛♥t r❡❢r❛❝t✐✈❡✲✐♥❞❡① ♠♦❞✉❧❛t✐♦♥ ❜② t✇♦✲ ♣❤♦t♦♥ r❡❞✉❝t✐♦♥ ♦❢ ❢❧✉♦r❡s❝❡♥t ❣r❛♣❤❡♥❡ ♦①✐❞❡s ❢♦r ♠✉❧t✐♠♦❞❡ ♦♣t✐❝❛❧ r❡❝♦r❞✲ ✐♥❣✱ ❙❝✐✳ ❘❡♣✳✱ ✷✵✶✸✱ ✸✱ ✷✽✶✾ ✭✶✲✹✮✳ ❬✻✽❪ ❆✳ ❆✳ ❇❛❧❛♥❞✐♥✱ ❙✳ ●❤♦s❤✱ ❲✳ ❇❛♦✱ ❡t ❛❧✳✱ ❙✉♣❡r✐♦r t❤❡r♠❛❧ ❝♦♥❞✉❝t✐✈✐t② ♦❢ s✐♥❣❧❡✲❧❛②❡r ❣r❛♣❤❡♥❡✱ ◆❛♥♦ ▲❡tt✳✱ ✷✵✵✽✱ ✽ ✭✸✮✱ ✾✵✷✲✾✵✼✳ ❬✻✾❪ ❈✳ ▲❡❡✱ ❳✳ ❲❡✐✱ ❏✳ ❲✳ ❑②s❛r✱ ❡t ❛❧✳✱ ▼❡❛s✉r❡♠❡♥t ♦❢ t❤❡ ❡❧❛st✐❝ ♣r♦♣❡rt✐❡s ❛♥❞ ✐♥tr✐♥s✐❝ str❡♥❣t❤ ♦❢ ♠♦♥♦❧❛②❡r ❣r❛♣❤❡♥❡✱ ❙❝✐❡♥❝❡✱ ✷✵✵✽✱ ✸✷✶ ✭✺✽✽✼✮✱ ✸✽✺✲✸✽✽✳ ❬✼✵❪ ❨✳ ❩❤✉✱ ❙✳ ▼✉r❛❧✐✱ ❲✳ ❈❛✐✱ ❡t ❛❧✳✱ ●r❛♣❤❡♥❡ ❛♥❞ ❣r❛♣❤❡♥❡ ♦①✐❞❡✿ s②♥t❤❡s✐s✱ ♣r♦♣❡rt✐❡s✱ ❛♥❞ ❛♣♣❧✐❝❛t✐♦♥s✱ ❆❞✈✳ ▼❛t❡r✳✱ ✷✵✶✵✱ ✷✷ ✭✸✺✮✱ ✸✾✵✻✲✸✾✷✹✳ ❬✼✶❪ ❋✳ ❖✉❨❛♥❣✱ ❇✳ ❍✉❛♥❣✱ ❩✳ ▲✐✱ ❡t ❛❧✳✱ ❈❤❡♠✐❝❛❧ ❢✉♥❝t✐♦♥❛❧✐③❛t✐♦♥ ♦❢ ❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥s ❜② ❝❛r❜♦①②❧ ❣r♦✉♣s ♦♥ ❙t♦♥❡✲❲❛❧❡s ❞❡❢❡❝ts✱ ❏✳ P❤②s✳ ❈❤❡♠✳ ❈✱ ✷✵✵✽✱ ✶✶✷ ✭✸✶✮✱ ✶✷✵✵✸✲✶✷✵✵✼✳ ❬✼✷❪ ❆✳ ❈r❡st✐✱ ●✳ ●r♦ss♦✱ ●✳ P✳ P❛rr❛✈✐❝✐♥✐✱ ◆✉♠❡r✐❝❛❧ st✉❞② ♦❢ ❡❧❡❝tr♦♥✐❝ tr❛♥s✲ ♣♦rt ✐♥ ❣❛t❡❞ ❣r❛♣❤❡♥❡ r✐❜❜♦♥s✱ P❤②s✳ ❘❡✈✳ ❇✱ ✷✵✵✼✱ ✼✻ ✭✷✵✮✱ ✷✵✺✹✸✸ ✭✶✲✽✮✳ ❬✼✸❪ ❙✳ ▼✳ ❈❤♦✐✱ ❙✳ ❍✳ ❏❤✐✱ ❙❡❧❢✲❛ss❡♠❜❧❡❞ ♠❡t❛❧ ❛t♦♠ ❝❤❛✐♥s ♦♥ ❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥s✳✱ P❤②s✳ ❘❡✈✳ ▲❡tt✳✱ ✷✵✵✽✱ ✶✵✶ ✭✷✻✮✱ ✷✻✻✶✵✺ ✭✶✲✹✮✳ ❬✼✹❪ ❋✳ ❈✳ ❙♦❞✐✱ ●✳ ❈s❛♥②✐✱ ❙✳ P✐s❝❛♥❡❝✱ ❡t ❛❧✳✱ ❊❞❣❡✲❢✉♥❝t✐♦♥❛❧✐③❡❞ ❛♥❞ s✉❜st✐t✉✲ t✐♦♥❛❧❧② ❞♦♣❡❞ ❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥s✿ ❊❧❡❝tr♦♥✐❝ ❛♥❞ s♣✐♥ ♣r♦♣❡rt✐❡s✱ P❤②s✳ ❘❡✈✳ ❇✱ ✷✵✵✽✱ ✼✼ ✭✶✻✮✱ ✶✻✺✹✷✼ ✭✶✲✶✸✮✳ ❬✼✺❪ ▲✳ P✐s❛♥✐✱ ❏✳ ❈❤❛♥✱ ❇✳ ▼♦♥t❛♥❛r✐✱ ❡t ❛❧✳✱ ❊❧❡❝tr♦♥✐❝ str✉❝t✉r❡ ❛♥❞ ♠❛❣♥❡t✐❝ ♣r♦♣❡rt✐❡s ♦❢ ❣r❛♣❤✐t✐❝ r✐❜❜♦♥s✱ P❤②s✳ ❘❡✈✳ ❇✱ ✷✵✵✼✱ ✼✺ ✭✻✮✱ ✵✻✹✹✶✽ ✭✶✲✾✮✳ ❬✼✻❪ ◆✳ ❚✳ ❚✐❡♥✱ ❱✳ ❚✳ P❤✉❝✱ ❘✳ ❆❤✉❥❛✱ ❚✉♥✐♥❣ ❡❧❡❝tr♦♥✐❝ tr❛♥s♣♦rt ♣r♦♣❡rt✐❡s ♦❢ ③✐❣③❛❣ ❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥s ✇✐t❤ s✐❧✐❝♦♥ ❞♦♣✐♥❣ ❛♥❞ ♣❤♦s♣❤♦r✉s ♣❛ss✐✈❛t✐♦♥✱ ❆■P ❆❞✈❛♥❝❡s✱ ✷✵✶✽✱ ✽ ✭✽✮✱ ✵✽✺✶✷✸ ✭✶✲✶✷✮✳ ❬✼✼❪ ●✳ ❇❡r❞✐②♦r♦✈✱ ❍✳ ❇❛❤❧♦✉❧✐✱ ❋✳ P❡❡t❡rs✱ ❊❢❢❡❝t ♦❢ s✉❜st✐t✉t✐♦♥❛❧ ✐♠♣✉r✐t✐❡s ♦♥ t❤❡ ❡❧❡❝tr♦♥✐❝ tr❛♥s♣♦rt ♣r♦♣❡rt✐❡s ♦❢ ❣r❛♣❤❡♥❡✱ P❤②s✐❝❛ ❊ ▲♦✇ ❉✐♠❡♥s✳ ❙②st✳ ◆❛♥♦str✉❝t✳✱ ✷✵✶✻✱ ✽✹✱ ✷✷✕✷✻✳ ❬✼✽❪ ❚✳❈✳ ▲✐✱ ❙✳ P✳ ▲✉✱ ◗✉❛♥t✉♠ ❝♦♥❞✉❝t❛♥❝❡ ♦❢ ❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥s ✇✐t❤ ❡❞❣❡ ❞❡❢❡❝ts✱ P❤②s✳ ❘❡✈✳ ❇✱ ✷✵✵✽✱ ✼✼ ✭✽✮✱ ✵✽✺✹✵✽ ✭✶✲✽✮✳ ✶✵✷ ❬✼✾❪ ❨✳ ◆✐✐♠✐✱ ❚✳ ▼❛ts✉✐✱ ❍✳ ❑❛♠❜❛r❛✱ ❡t ❛❧✳✱ ❙❝❛♥♥✐♥❣ t✉♥♥❡❧✐♥❣ ♠✐❝r♦s❝♦♣② ❛♥❞ s♣❡❝tr♦s❝♦♣② ♦❢ t❤❡ ❡❧❡❝tr♦♥✐❝ ❧♦❝❛❧ ❞❡♥s✐t② ♦❢ st❛t❡s ♦❢ ❣r❛♣❤✐t❡ s✉r❢❛❝❡s ♥❡❛r ♠♦♥♦❛t♦♠✐❝ st❡♣ ❡❞❣❡s✱ P❤②s✳ ❘❡✈✳ ❇✱ ✷✵✵✻✱ ✼✸ ✭✽✮✱ ✵✽✺✹✷✶ ✭✶✲✽✮✳ ❬✽✵❪ ❨✳ ❑♦❜❛②❛s❤✐✱ ❑✳ ■✳ ❋✉❦✉✐✱ ❚✳ ❊♥♦❦✐✱ ❡t ❛❧✳✱ ❊❞❣❡ st❛t❡ ♦♥ ❤②❞r♦❣❡♥✲ t❡r♠✐♥❛t❡❞ ❣r❛♣❤✐t❡ ❡❞❣❡s ✐♥✈❡st✐❣❛t❡❞ ❜② s❝❛♥♥✐♥❣ t✉♥♥❡❧✐♥❣ ♠✐❝r♦s❝♦♣②✱ P❤②s✳ ❘❡✈✳ ❇✱ ✷✵✵✻✱ ✼✸ ✭✶✷✮✱ ✶✷✺✹✶✺ ✭✶✲✽✮✳ ❬✽✶❪ ❩✳ ❑❛♥✱ ❈✳ ◆❡❧s♦♥✱ ▼✳ ❑❤❛t✉♥✱ ◗✉❛♥t✉♠ ❝♦♥❞✉❝t❛♥❝❡ ♦❢ ③✐❣③❛❣ ❣r❛♣❤❡♥❡ ♦①✐❞❡ ♥❛♥♦r✐❜❜♦♥s✱ ❏✳ ❆♣♣❧✳ P❤②s✱ ✷✵✶✹✱ ✶✶✺✭✶✺✮✱ ✶✺✸✼✵✹ ✭✶✲✼✮✳ ❬✽✷❪ ❊✳ ❏✳ ❑❛♥✱ ❩✳ ▲✐✱ ❏✳ ❨❛♥❣✱ ❡t ❛❧✳✱ ❍❛❧❢✲♠❡t❛❧❧✐❝✐t② ✐♥ ❡❞❣❡✲♠♦❞✐❢✐❡❞ ③✐❣③❛❣ ❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥s✱ ❏✳ ❆♠✳ ❈❤❡♠✳ ❙♦❝✳✱ ✷✵✵✽✱ ✶✸✵ ✭✶✸✮✱ ✹✷✷✹✲✹✷✷✺✳ ❬✽✸❪ ❙✳ ❉✉tt❛✱ ❆✳ ❑✳ ▼❛♥♥❛✱ ❙✳ ❑✳ P❛t✐✱ ■♥tr✐♥s✐❝ ❤❛❧❢✲♠❡t❛❧❧✐❝✐t② ✐♥ ♠♦❞✐❢✐❡❞ ❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥s✱ P❤②s✳ ❘❡✈✳ ▲❡tt✳✱ ✷✵✵✾✱ ✶✵✷ ✭✾✮✱ ✵✾✻✻✵✶ ✭✶✲✹✮✳ ❬✽✹❪ ▲✳ ❙✳ P❛♥❝❤❛❦❛r❧❛✱ ❑✳ ❙✳ ❙✉❜r❛❤♠❛♥②❛♠✱ ❙✳ ❑✳ ❙❛❤❛✱ ❡t ❛❧✳✱ ❙②♥t❤❡s✐s✱ str✉❝✲ t✉r❡✱ ❛♥❞ ♣r♦♣❡rt✐❡s ♦❢ ❜♦r♦♥✲❛♥❞ ♥✐tr♦❣❡♥✲❞♦♣❡❞ ❣r❛♣❤❡♥❡✱ ❆❞✈✳ ▼❛t❡r✳✱ ✷✵✵✾✱ ✷✶ ✭✹✻✮✱ ✹✼✷✻✲✹✼✸✵✳ ❬✽✺❪ ❇✳ ❍✉❛♥❣✱ ❋✳ ▲✐✉✱ ◗✳ ❨❛♥✱ ❡t ❛❧✳✱ ▼❛❦✐♥❣ ❛ ❢✐❡❧❞ ❡❢❢❡❝t tr❛♥s✐st♦r ♦♥ ❛ s✐♥❣❧❡ ❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥ ❜② s❡❧❡❝t✐✈❡ ❞♦♣✐♥❣✱ ❆♣♣❧✳ P❤②s✳ ▲❡tt✳✱ ✷✵✵✼✱ ✾✶ ✭✷✺✮✱ ✷✺✸✶✷✷ ✭✶✲✸✮✳ ❬✽✻❪ ❏✳ ▲✐✉✱ ❩✳ ❍✳ ❩❤❛♥❣✱ ❳✳ ◗✳ ❉❡♥❣✱ ❡t ❛❧✳✱ ❊❧❡❝tr♦♥✐❝ str✉❝t✉r❡s ❛♥❞ tr❛♥s✲ ♣♦rt ♣r♦♣❡rt✐❡s ♦❢ ❛r♠❝❤❛✐r ❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥s ❜② ♦r❞❡r❡❞ ❞♦♣✐♥❣✱ ❖r❣✳ ❊❧❡❝tr♦♥✳✱ ✷✵✶✺✱ ✶✽✱ ✶✸✺✲✶✹✷✳ ❬✽✼❪ ❙✳ ❙✳ ❈❤❛✉❤❛♥✱ P✳ ❙r✐✈❛st❛✈❛✱ ❆✳ ❑✳ ❙❤r✐✈❛st❛✈❛✱ ❊❧❡❝tr♦♥✐❝ ❛♥❞ tr❛♥s♣♦rt ♣r♦♣❡rt✐❡s ♦❢ ❜♦r♦♥ ❛♥❞ ♥✐tr♦❣❡♥ ❞♦♣❡❞ ❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥s✿ ❛♥ ❛❜ ✐♥✐t✐♦ ❛♣♣r♦❛❝❤✱ ❆♣♣❧✳ ◆❛♥♦s❝✐✳✱ ✷✵✶✹✱ ✹ ✭✹✮✱ ✹✻✶✲✹✻✼✳ ❬✽✽❪ ❋✳ ❱✳ ❑✉s♠❛rts❡✈✱ ❲✳ ▼✳ ❲✉✱ ▼✳ P✳ P✐❡r♣♦✐♥t✱ ❡t ❛❧✳✱ ❆♣♣❧✐❝❛t✐♦♥ ♦❢ ❣r❛♣❤❡♥❡ ✇✐t❤✐♥ ♦♣t♦❡❧❡❝tr♦♥✐❝ ❞❡✈✐❝❡s ❛♥❞ tr❛♥s✐st♦rs✱ ■♥ ❆♣♣❧✐❡❞ ❙♣❡❝✲ tr♦s❝♦♣② ❛♥❞ t❤❡ ❙❝✐❡♥❝❡ ♦❢ ◆❛♥♦♠❛t❡r✐❛❧s✱ ❙♣r✐♥❣❡r✱ ❙✐♥❣❛♣♦r❡✱ ✷✵✶✺✱ ✶✾✶✲ ✷✷✶✳ ✶✵✸ ❬✽✾❪ ❖✳ ❍♦❞✱ ❱✳ ❇❛r♦♥❡✱ ●✳ ❊✳ ❙❝✉s❡r✐❛✱ ❍❛❧❢✲♠❡t❛❧❧✐❝ ❣r❛♣❤❡♥❡ ♥❛♥♦❞♦ts✿ ❆ ❝♦♠♣r❡❤❡♥s✐✈❡ ❢✐rst✲♣r✐♥❝✐♣❧❡s t❤❡♦r❡t✐❝❛❧ st✉❞②✱ P❤②s✳ ❘❡✈✳ ❇✱ ✷✵✵✽✱ ✼✼ ✭✸✮✱ ✵✸✺✹✶✶ ✭✶✲✻✮✳ ❬✾✵❪ ◆✳ ❑✳ ❏❛✐s✇❛❧✱ P✳ ❙r✐✈❛st❛✈❛✱ ❙tr✉❝t✉r❛❧ st❛❜✐❧✐t② ❛♥❞ ❡❧❡❝tr♦♥✐❝ ♣r♦♣❡rt✐❡s ♦❢ ◆✐✲❞♦♣❡❞ ❛r♠❝❤❛✐r ❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥s✱ ❙♦❧✐❞ ❙t❛t❡ ❈♦♠♠✉♥✳✱ ✷✵✶✶✱ ✶✺✶ ✭✷✵✮✱ ✶✹✾✵✲✶✹✾✺✳ ❬✾✶❪ ◆✳ ❑✳ ❏❛✐s✇❛❧✱ P✳ ❙r✐✈❛st❛✈❛✱ ❋✐rst ♣r✐♥❝✐♣❧❡s ❝❛❧❝✉❧❛t✐♦♥s ♦❢ ❝♦❜❛❧t ❞♦♣❡❞ ③✐❣③❛❣ ❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥s✳ ❙♦❧✐❞ st❛t❡ ❝♦♠♠✉♥✐❝❛t✐♦♥s✱ ❙♦❧✐❞ ❙t❛t❡ ❈♦♠✲ ♠✉♥✳✱ ✷✵✶✷✱ ✶✺✷ ✭✶✺✮✱ ✶✹✽✾✲✶✹✾✷✳ ❬✾✷❪ ❨✳ ▲✐✉✱ ❩✳ ❈❤❡♥✱ ❙✳ ❍✉✱ ❡t ❛❧✳✱ ❚❤❡ ✐♥❢❧✉❡♥❝❡ ♦❢ s✐❧✐❝♦♥ ❛t♦♠ ❞♦♣✐♥❣ ♣❤❛✲ ❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥s ♦♥ t❤❡ ❡❧❡❝tr♦♥✐❝ ❛♥❞ ♠❛❣♥❡t✐❝ ♣r♦♣❡rt✐❡s✱ ▼❛t❡r✳ ❙❝✐✳ ❊♥❣✳ ❇✱ ✷✵✶✼✱ ✷✷✵✱ ✸✵✲✸✻✳ ❬✾✸❪ ❈✳ ❍❡✱ ❳✳ ❋✳ ❲❛♥❣✱ ❲✳ ❳✳ ❩❤❛♥❣✱ ❈♦✉♣❧✐♥❣ ❡❢❢❡❝ts ♦❢ t❤❡ ❡❧❡❝tr✐❝ ❢✐❡❧❞ ❛♥❞ ❜❡♥❞✐♥❣ ♦♥ t❤❡ ❡❧❡❝tr♦♥✐❝ ❛♥❞ ♠❛❣♥❡t✐❝ ♣r♦♣❡rt✐❡s ♦❢ ♣❡♥t❛✲❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥s✱ P❤②s✳ ❈❤❡♠✳ ❈❤❡♠✳ P❤②s✳✱ ✷✵✶✼✱ ✶✾✱ ✶✽✹✷✻✲✶✽✹✸✸✳ ❬✾✹❪ ▼✳ ❆❧✐♠✱ ▼✳ ❆❧✐✱ ❆✳ ❘❡③❛③❛❞❡❤✱ ❡t ❛❧✳✱ ❚❤❡r♠❛❧ r❡s♣♦♥s❡ ❢♦r ✐♥t❡r♠♦❞✉❧❛t✐♦♥ ❞✐st♦rt✐♦♥ ❝♦♠♣♦♥❡♥ts ♦❢ ●❛◆ ❍❊▼❚ ❢♦r ❧♦✇ ❛♥❞ ❤✐❣❤ ❢r❡q✉❡♥❝② ❛♣♣❧✐❝❛✲ t✐♦♥s✱ ▼✐❝r♦❡❧❡❝tr♦♥✳ ❊♥❣✳✱ ✷✵✶✾✱ ✷✵✾✱ ✺✸✲✺✾✳ ❬✾✺❪ ❆✳ ▼♦❥❛❜✱ ❩✳ ❍❡♠♠❛t✱ ❍✳ ❘✐❛③♠♦♥t❛③❡r✱ ❡t ❛❧✳✱ ■♥tr♦❞✉❝✐♥❣ ♦♣t✐❝❛❧ ❝❛s❝♦❞❡ ●❛◆ ❍❊▼❚✱ ■❊❊❊ ❚r❛♥s✳ ❊❧❡❝tr♦♥ ❉❡✈✐❝❡s✱ ✷✵✶✼✱ ✻✹ ✭✸✮✱ ✼✾✻✲✽✵✹✳ ❬✾✻❪ ❈✳ ▲❡❡✱ ❲✳ ▲✐♥✱ ❨✳ ▲❡❡✱ ❡t ❛❧✳✱ ❈❤❛r❛❝t❡r✐③❛t✐♦♥s ♦❢ ❡♥❤❛♥❝❡♠❡♥t✲♠♦❞❡ ❞♦✉✲ ❜❧❡ ❤❡t❡r♦str✉❝t✉r❡ ●❛◆ ❍❊▼❚s ✇✐t❤ ❣❛t❡ ❢✐❡❧❞ ♣❧❛t❡s✱ ■❊❊❊ ❚r❛♥s✳ ❊❧❡❝tr♦♥ ❉❡✈✐❝❡s✱ ✷✵✶✽✱ ✻✺ ✭✷✮✱ ✹✽✽✲✹✾✷✳ ❬✾✼❪ ❩✳ ▲✐✱ ❈✳ ▲✐✱ ❉✳ P❡♥❣✱ ❡t ❛❧✳✱ ●r♦✇t❤ ♦❢ q✉❛t❡r♥❛r② ■♥❆❧●❛◆ ❜❛rr✐❡r ✇✐t❤ ✉❧tr❛t❤✐♥ t❤✐❝❦♥❡ss ❢♦r ❍❊▼❚ ❛♣♣❧✐❝❛t✐♦♥✱ ❙✉♣❡r❧❛tt✐❝❡✳ ▼✐❝r♦st✳✱ ✷✵✶✽✱ ✶✶✽✱ ✷✶✸✲✷✷✵✳ ❬✾✽❪ ❙✳ ❋❛r❛♠❡❤r✱ ❑✳ ❑❛❧♥❛✱ P✳ ■❣✐❝✱ ❉r✐❢t✲❞✐❢❢✉s✐♦♥ ❛♥❞ ❤②❞r♦❞②♥❛♠✐❝ ♠♦❞❡❧✐♥❣ ♦❢ ❝✉rr❡♥t ❝♦❧❧❛♣s❡ ✐♥ ●❛◆ ❍❊▼❚s ❢♦r ❘❋ ♣♦✇❡r ❛♣♣❧✐❝❛t✐♦♥✱ ❙❡♠✐❝♦♥❞✳ ❙❝✐✳ ❚❡❝❤♥♦❧✳✱ ✷✵✶✹✱ ✷✾ ✭✷✮✱ ✵✷✺✵✵✼✲✵✷✺✵✶✼✳ ✶✵✹ ❬✾✾❪ ❙✳ ❘❛③❛✈✐✱ ❙✳ P♦✉r✱ P✳ ◆❛❥❛r✐✱ ◆❡✇ ●❛◆ ❜❛s❡❞ ❍❊▼❚ ✇✐t❤ ❙✐✸◆✹ ♦r ✉♥✲ ❞♦♣❡❞ r❡❣✐♦♥ ✐♥ t❤❡ ❜❛rr✐❡r ❢♦r ❤✐❣❤ ♣♦✇❡r ❛♣♣❧✐❝❛t✐♦♥s✱ ❙✉♣❡r❧❛tt✐❝❡✳ ▼✐✲ ❝r♦st✳✱ ✷✵✶✽✱ ✶✶✽✱ ✷✷✶✲✷✷✾✳ ❬✶✵✵❪ ❍✳ ❩❤❛♥❣✱ P✳ ▼❛✱ ❨✳ ▲✉✱ ❡t ❛❧✳✱ ❊①tr❛❝t✐♦♥ ♠❡t❤♦❞ ❢♦r ♣❛r❛s✐t✐❝ ❝❛♣❛❝✐t❛♥❝❡s ❛♥❞ ✐♥❞✉❝t❛♥❝❡s ♦❢ ❍❊▼❚ ♠♦❞❡❧s✱ ❙♦❧✐❞ ❙t❛t❡ ❊❧❡❝tr♦♥✐❝s✱ ✷✵✶✼✱ ✶✷✾✱ ✶✵✽✲ ✶✶✸✳ ❬✶✵✶❪ ▲✳ ❨❡♥✲❑✉✱ ◆✳ ❙❤✉✐❝❤✐✱ ▲✳ ❍s✐❛♦✲❈❤✐❡❤✱ ❡t ❛❧✳✱ ❆❧●❛◆✴●❛◆ ❍❊▼❚s ✇✐t❤ ❞❛♠❛❣❡✲❢r❡❡ ♥❡✉tr❛❧ ❜❡❛♠ ❡t❝❤❡❞ ❣❛t❡ r❡❝❡ss ❢♦r ❤✐❣❤ ♣❡r❢♦r♠❛♥❝❡ ♠✐❧❧✐♠❡t❡r ✇❛✈❡ ❛♣♣❧✐❝❛t✐♦♥s✱ ■❊❊❊ ❊❧❡❝tr♦♥ ❉❡✈✐❝❡ ▲❡tt✳✱ ✷✵✶✻✱ ✸✼ ✭✶✶✮✱ ✶✸✾✺✲✶✸✾✽✳ ❬✶✵✷❪ ❍✳ ▲❡❡✱ ▼✳ ❇❛❡✱ ❙✳ ❏♦✱ ❡t ❛❧✳✱ ❆❧●❛◆✴●❛◆ ❤✐❣❤ ❡❧❡❝tr♦♥ ♠♦❜✐❧✐t② tr❛♥s✐st♦r ❜❛s❡❞ ❜✐♦s❡♥s♦r ❢♦r t❤❡ ❞❡t❡❝t✐♦♥ ♦❢ ❈✲r❡❛❝t✐✈❡ ♣r♦t❡✐♥✱ ❙❡♥s♦rs✱ ✷✵✶✺✱ ✶✺ ✭✽✮✱ ✶✽✹✶✻✲✶✽✹✷✻✳ ❬✶✵✸❪ ❆✳ ❋❧❡t❝❤❡r✱ ❉✳ ◆✐r♠❛❧✱ ❘❡✈✐❡✇ ❛ s✉r✈❡② ♦❢ ●❛❧❧✐✉♠ ◆✐tr✐❞❡ ❍❊▼❚ ❢♦r ❘❋ ❛♥❞ ❤✐❣❤ ♣♦✇❡r ❛♣♣❧✐❝❛t✐♦♥s✱ ❙✉♣❡r❧❛tt✐❝❡✳ ▼✐❝r♦st✳✱ ✷✵✶✼✱ ✶✵✾✱ ✺✶✾✲✺✸✼✳ ❬✶✵✹❪ ❳✳ ❩❤❡♥❣✱ ❙✳ ❋❡♥❣✱ ❨✳ ❩❤❛♥❣✱ ❡t ❛❧✳✱ ❊✈❛❧✉❛t✐♦♥ ♦❢ t❤❡ ❙❝❤♦tt❦② ❝♦♥t❛❝t ❞❡❣r❛❞❛t✐♦♥ ♦♥ t❤❡ t❡♠♣❡r❛t✉r❡ tr❛♥s✐❡♥t ♠❡❛s✉r❡♠❡♥ts ✐♥ ●❛◆ ❍❊▼❚s✱ ■❊❊❊ ❚r❛♥s✳ ❊❧❡❝tr♦♥ ❉❡✈✐❝❡s✱ ✷✵✶✽✱ ✻✺ ✭✺✮✱ ✶✼✸✹✲✶✼✸✽✳ ❬✶✵✺❪ ❇✳ ❯❜♦❝❤✐✱ ❙✳ ❋❛r❛♠❡❤r✱ ❑✳ ❆❤♠❡❞✱ ❡t ❛❧✳✱ ■♥❞✉❝❡❞ tr❛♣♣✐♥❣ ✐♥ s❝❛❧❡❞ ●❛◆ ❍❊▼❚s✱ ▼✐❝r♦❡❧❡❝tr♦♥ ❘❡❧✐❛❜✳✱ ✷✵✶✼✱ ✼✶✱ ✸✺✲✹✵✳ ❬✶✵✻❪ ❆✳ ❆③❛r✐❢❛r✱ ◆✳ ❉♦♥♠❡③❡r✱ ▼✉❧t✐s❝❛❧❡ ❛♥❛❧②t✐❝❛❧ ❝♦rr❡❝t✐♦♥ t❡❝❤♥✐q✉❡ ❢♦r t✇♦✲❞✐♠❡♥s✐♦♥❛❧ t❤❡r♠❛❧ ♠♦❞❡❧s ♦❢ ❆❧●❛◆✴●❛◆ ❍❊▼❚s✱ ▼✐❝r♦❡❧❡❝tr♦♥ ❘❡✲ ❧✐❛❜✳✱ ✷✵✶✼✱ ✼✹✱ ✽✷✲✽✼✳ ❬✶✵✼❪ ❘✳ ▼❡♥♦③③✐✱ ●✳ ▼❡♠❜r❡♥♦✱ ❇✳ ◆❡♥❡r✱ ❡t ❛❧✳✱ ❚❡♠♣❡r❛t✉r❡✲❞❡♣❡♥❞❡♥t ❝❤❛r✲ ❛❝t❡r✐③❛t✐♦♥ ♦❢ ❆❧●❛◆✴●❛◆ ❍❊▼❚s✿ t❤❡r♠❛❧ ❛♥❞ s♦✉r❝❡✴❞r❛✐♥ r❡s✐st❛♥❝❡s✱ ■❊❊❊ ❚r❛♥s✳ ❉❡✈✐❝❡ ▼❛t❡r✳ ❘❡❧✐❛❜✳✱ ✷✵✵✽✱ ✽ ✭✷✮✱ ✷✺✺✲✷✻✹✳ ❬✶✵✽❪ ❙✳ ●❤♦s❤✱ ❆✳ ❉❛s❣✉♣t❛✱ ❙✳ ❑❤❛♥❞❡❧✇❛❧✱ ❡t ❛❧✳✱ ❙✉r❢❛❝❡ ♣♦t❡♥t✐❛❧✲❜❛s❡❞ ❝♦♠✲ ♣❛❝t ♠♦❞❡❧✐♥❣ ♦❢ ❣❛t❡ ❝✉rr❡♥t ✐♥ ❆❧●❛◆✴●❛◆ ❍❊▼❚s✱ ■❊❊❊ ❚r❛♥s✳ ❊❧❡❝✲ tr♦♥ ❉❡✈✐❝❡s✱ ✷✵✶✺✱ ✻✷ ✭✷✮✱ ✹✹✸✲✹✹✽✳ ❬✶✵✾❪ ❚✳ ❨❛♦✱ ❙✳ ❑✳ ❍♦♥❣✱ ❖①✐❞❡ ❛♥❞ ♥✐tr✐❞❡ s❡♠✐❝♦♥❞✉❝t♦rs✿ Pr♦❝❡ss✐♥❣✱ ♣r♦♣✲ ❡rt✐❡s✱ ❛♥❞ ❛♣♣❧✐❝❛t✐♦♥s✱ ❙♣r✐♥❣❡r ❙❝✐❡♥❝❡ ❛♥❞ ❇✉s✐♥❡ss ▼❡❞✐❛✱ ✷✵✵✾✱ ❇❡r❧✐♥✳ ✶✵✺ ❬✶✶✵❪ ❚✳ ❆♥❞♦✱ ❆✳ ❇✳ ❋♦✇❧❡r✱ ❋✳ ❙t❡r♥✱ ❊❧❡❝tr♦♥✐❝ ♣r♦♣❡rt✐❡s ♦❢ t✇♦✲❞✐♠❡♥s✐♦♥❛❧ s②st❡♠s✱ ❘❡✈✳ ▼♦❞✳ P❤②s✳✱ ✶✾✽✷✱ ✺✹ ✭✷✮✱ ✹✹✻✲✺✶✸✳ ❬✶✶✶❪ ●✳ ❇❛st❛r❞✱ ❲❛✈❡ ▼❡❝❤❛♥✐❝s ❆♣♣❧✐❡❞ t♦ ❙❡♠✐❝♦♥❞✉❝t♦r ❍❡t❡r♦✲str✉❝t✉r❡s✱ ▲❡s ❊❞✐t✐♦♥s ❞❡ P❤②s✐q✉❡✱ ✶✾✽✽✱ P❛r✐s✳ ❬✶✶✷❪ ❚✳ ❆♥❞♦✱ ❙❡❧❢✲❝♦♥s✐st❡♥t r❡s✉❧ts ❢♦r ❛ ●❛❆s✴❆❧x ●❛1−x ❆s ❤❡t❡r♦❥✉♥❝t✐♦♥✳ ■✳ s✉❜❜❛♥❞ str✉❝t✉r❡ ❛♥❞ ❧✐❣❤t✲s❝❛tt❡r✐♥❣ s♣❡❝tr❛✱ ❏✳ P❤②s✳ ❙♦❝✳ ❏♣♥✳✱ ✶✾✽✷✱ ✺✶ ✭✶✷✮✱ ✸✽✾✸✲✸✽✾✾✳ ❬✶✶✸❪ ❨✳ ❖❦✉②❛♠❛✱ ◆✳ ❚♦❦✉❞❛✱ ❊❧❡❝tr♦♥✲♣❤♦♥♦♥ ✐♥t❡r❛❝t✐♦♥s ✐♥ ♠♦❞✉❧❛t✐♦♥✲ ❞♦♣❡❞ ❆❧x ●❛1−x ❆s✴●❛❆s ❤❡t❡r♦❥✉♥❝t✐♦♥s✱ P❤②s✳ ❘❡✈✳ ❇✱ ✶✾✽✾✱ ✹✵ ✭✶✹✮✱ ✾✼✹✹✲ ✾✼✺✵✳ ❬✶✶✹❪ ❘✳ ❊♥❞❡r❧❡✐♥✱ ◆✳ ❏✳ ❍♦r✐♥❣✱ ❋✉♥❞❛♠❡♥t❛❧s ♦❢ s❡♠✐❝♦♥❞✉❝t♦r ♣❤②s✐❝s ❛♥❞ ❞❡✈✐❝❡s✱ ❲♦r❧❞ ❙❝✐❡♥t✐❢✐❝✱ ✶✾✾✼✱ ❙✐♥❣❛♣♦r❡✳ ❬✶✶✺❪ ❙✳ ❆r✉❧❦✉♠❛r❛♥✱ ❚✳ ❊❣❛✇❛✱ ❍✳ ■s❤✐❦❛✇❛✱ ❡t ❛❧✳✱ ❈❤❛r❛❝t❡r✐③❛t✐♦♥ ♦❢ ❞✐❢❢❡r❡♥t✲❆❧✲❝♦♥t❡♥t ❆❧x ●❛1−x ◆✴●❛◆ ❤❡t❡r♦str✉❝t✉r❡s ❛♥❞ ❤✐❣❤✲❡❧❡❝tr♦♥✲ ♠♦❜✐❧✐t② tr❛♥s✐st♦rs ♦♥ s❛♣♣❤✐r❡✱ ❏✳ ❱❛❝✳ ❙❝✐✳ ❚❡❝❤♥♦❧✳✱ ✷✵✵✸✱ ✷✶ ✭✷✮✱ ✽✽✽✲✽✾✹✳ ❬✶✶✻❪ ❉✳ ◆✳ ◗✉❛♥❣✱ ▲✳ ❚✉❛♥✱ ◆✳ ❚✳ ❚✐❡♥✱ ❊❧❡❝tr♦♥ ♠♦❜✐❧✐t② ✐♥ ●❛✉ss✐❛♥ ❤❡❛✈✐❧② ❞♦♣❡❞ ❩♥❖ s✉r❢❛❝❡ q✉❛♥t✉♠ ✇❡❧❧s✱ P❤②s✳ ❘❡✈✳ ❇✱ ✷✵✵✽✱ ✼✼ ✭✶✷✮✱ ✶✷✺✸✷✻ ✭✶✲ ✶✵✮✳ ❬✶✶✼❪ ❱✳ ▼✳ P♦❧②❛❦♦✈✱ ❱✳ ❈✐♠❛❧❧❛✱ ❱✳ ▲❡❜❡❞❡✈✱ ❡t ❛❧✳✱ ■♠♣❛❝t ♦❢ ❆❧ ❝♦♥t❡♥t ♦♥ tr❛♥s♣♦rt ♣r♦♣❡rt✐❡s ♦❢ t✇♦✲❞✐♠❡♥s✐♦♥❛❧ ❡❧❡❝tr♦♥ ❣❛s ✐♥ ●❛◆✴❆❧x ●❛1−x ◆✴●❛◆ ❤❡t❡r♦str✉❝t✉r❡s✱ ❆♣♣❧✳ P❤②s✳ ▲❡tt✳✱ ✷✵✶✵✱ ✾✼ ✭✶✹✮✱ ✶✹✷✶✶✷ ✭✶✲✸✮✳ ❬✶✶✽❪ ◆✳ ❚✳ ❚✐❡♥✱ ❉✳ ◆✳ ❚❤❛♦✱ P✳ ❚✳ ❇✳ ❚❤❛♦✱ ❉✳ ◆✳ ◗✉❛♥❣✱ ❊❧❡❝tr♦♥ ❞✐str✐❜✉✲ t✐♦♥ ✐♥ ♣♦❧❛r ❤❡t❡r♦❥✉♥❝t✐♦♥s ✇✐t❤✐♥ ❛ r❡❛❧✐st✐❝ ♠♦❞❡❧✱ P❤②s✐❝❛ ❇ ❈♦♥❞❡♥s✳ ▼❛tt❡r✱ ✷✵✶✺✱ ✹✼✾✱ ✻✷✲✻✻✳ ❬✶✶✾❪ ▼✳ ▼✐②♦s❤✐✱ ❚✳ ❊❣❛✇❛✱ ❍✳ ■s❤✐❦❛✇❛✱ ❙tr✉❝t✉r❛❧ ❝❤❛r❛❝t❡r✐③❛t✐♦♥ ♦❢ str❛✐♥❡❞ ❆❧●❛◆ ❧❛②❡rs ✐♥ ❞✐❢❢❡r❡♥t ❆❧ ❝♦♥t❡♥t ❆❧●❛◆✴●❛◆ ❤❡t❡r♦str✉❝t✉r❡s ❛♥❞ ✐ts ❡❢❢❡❝t ♦♥ t✇♦✲❞✐♠❡♥s✐♦♥❛❧ ❡❧❡❝tr♦♥ tr❛♥s♣♦rt ♣r♦♣❡rt✐❡s✱ ❏✳ ❱❛❝✳ ❙❝✐✳ ❚❡❝❤♥♦❧✳✱ ✷✵✵✺✱ ✷✸ ✭✹✮✱ ✶✺✷✼✲✶✺✸✶✳ ✶✵✻ ❬✶✷✵❪ ▼✳ ◆✳ ●✉r✉s✐♥❣❤❡✱ ❙✳ ❑✳ ❉❛✈✐❞ss♦♥✱ ❚✳ ●✳ ❆♥❞❡rss♦♥✱ ❚✇♦ ❞✐♠❡♥s✐♦♥❛❧ ❡❧❡❝tr♦♥ ♠♦❜✐❧✐t② ❧✐♠✐t❛t✐♦♥ ♠❡❝❤❛♥✐s♠s ✐♥ ❆❧x ●❛1−x ◆✴●❛◆ ❤❡t❡r♦str✉❝✲ t✉r❡s✱ P❤②s✳ ❘❡✈✳ ❇✱ ✷✵✵✺✱ ✼✷ ✭✹✮✱ ✵✹✺✸✶✻ ✭✶✲✶✶✮✳ ❬✶✷✶❪ ❏✳ ❆♥t♦s③❡✇s❦✐✱ ▼✳ ●r❛❝❡②✱ ❏✳ ❉❡❧❧✱ ❡t ❛❧✳✱ ❙❝❛tt❡r✐♥❣ ♠❡❝❤❛♥✐s♠s ❧✐♠✐t✲ ✐♥❣ t✇♦✲❞✐♠❡♥s✐♦♥❛❧ ❡❧❡❝tr♦♥ ❣❛s ♠♦❜✐❧✐t② ✐♥ ❆❧0.25 ●❛0.75 ◆✴●❛◆ ♠♦❞✉❧❛t✐♦♥ ❞♦♣❡❞ ❢✐❡❧❞ ❡❢❢❡❝t tr❛♥s✐st♦r s✱ ❏✳ ❆♣♣❧✳ P❤②s✳✱ ✷✵✵✵✱ ✽✼ ✭✽✮✱ ✸✾✵✵✲✸✾✵✹✳ ❬✶✷✷❪ ❙✳ ●☎♦❦❞❡♥✱ ▼♦❜✐❧✐t② ♦❢ t✇♦✲❞✐♠❡♥s✐♦♥❛❧ ❡❧❡❝tr♦♥s ✐♥ ❛♥ ❆❧●❛◆✴●❛◆ ♠♦❞✉❧❛t✐♦♥✲❞♦♣❡❞ ❤❡t❡r♦str✉❝t✉r❡✱ P❤②s✳ ❙t❛t✳ ❙♦❧✳ ❆✱ ✷✵✵✸✱ ✷✵✵ ✭✷✮✱ ✸✻✾✲ ✸✼✼✳ ❬✶✷✸❪ ❉✳ ❩❛♥❛t♦✱ ❙✳ ●♦❦❞❡♥✱ ◆✳ ❇❛❧❦❛♥✱ ❡t ❛❧✳✱ ❚❤❡ ❡❢❢❡❝t ♦❢ ✐♥t❡r❢❛❝❡✲r♦✉❣❤♥❡ss ❛♥❞ ❞✐s❧♦❝❛t✐♦♥ s❝❛tt❡r✐♥❣ ♦♥ ❧♦✇ t❡♠♣❡r❛t✉r❡ ♠♦❜✐❧✐t② ♦❢ ✷❉ ❡❧❡❝tr♦♥ ❣❛s ✐♥ ●❛◆✴❆❧●❛◆✱ ❙❡♠✐❝♦♥❞✳ ❙❝✐✳ ❚❡❝❤♥♦❧✳✱ ✷✵✵✹✱ ✶✾ ✭✸✮✱ ✹✷✼✲✹✸✷✳ ❬✶✷✹❪ ❋✳ ❋✳ ❋❛♥❣✱ ❲✳ ❊✳ ❍♦✇❛r❞✱ ◆❡❣❛t✐✈❡ ❢✐❡❧❞✲❡❢❢❡❝t ♠♦❜✐❧✐t② ♦♥ ✭✶✵✵✮ ❙✐ s✉r✲ ❢❛❝❡s✱ P❤②s✳ ❘❡✈✳ ▲❡tt✳✱ ✶✾✻✻✱ ✶✻ ✭✶✽✮✱ ✼✾✼✲✼✾✾✳ ❬✶✷✺❪ ❙✳ ❑❡❧❧❡r✱ ●✳ P❛r✐s❤✱ P✳ ❚✳ ❋✐♥✐✱ ❡t ❛❧✳✱ ▼❡t❛❧♦r❣❛♥✐❝ ❝❤❡♠✐❝❛❧ ✈❛♣♦r ❞❡♣♦✲ s✐t✐♦♥ ♦❢ ❤✐❣❤ ♠♦❜✐❧✐t② ❆❧●❛◆✴●❛◆ ❤❡t❡r♦str✉❝t✉r❡s✱ ❏✳ ❆♣♣❧✳ P❤②s✳✱ ✶✾✾✾✱ ✽✻✱ ✺✽✺✵✲✺✽✺✼✳ ❬✶✷✻❪ ❑✳ ❑☎♦❤❧❡r✱ ❙✳ ▼☎ ✉❧❧❡r✱ P✳ ❲❛❧t❡r❡✐t✱ ❡t ❛❧✳✱ ❊❧❡❝tr✐❝❛❧ ♣r♦♣❡rt✐❡s ♦❢ ❆❧①●❛✶✲ ①◆✴●❛◆ ❤❡t❡r♦str✉❝t✉r❡s ✇✐t❤ ❧♦✇ ❆❧ ❝♦♥t❡♥t✱ ❏✳ ❆♣♣❧✳ P❤②s✳✱ ✷✵✶✶✱ ✶✵✾✱ ✵✺✸✼✵✺ ✭✶✲✺✮✳ ❬✶✷✼❪ ❉✳ ❏❡♥❛✱ ❆✳ ❈✳ ●♦ss❛r❞✱ ❯✳ ❑✳ ▼✐s❤r❛✱ ❉✐s❧♦❝❛t✐♦♥ s❝❛tt❡r✐♥❣ ✐♥ ❛ t✇♦✲ ❞✐♠❡♥s✐♦♥❛❧ ❡❧❡❝tr♦♥ ❣❛s✱ ❆♣♣❧✳ P❤②s✳ ▲❡tt✳✱ ✷✵✵✵✱ ✼✻ ✭✶✸✮✱ ✶✼✵✼✲✶✼✵✾✳ ❬✶✷✽❪ ▲✳ ❍s✉✱ ❲✳ ❲❛❧✉❦✐❡✇✐❝③✱ ❊❧❡❝tr♦♥ ♠♦❜✐❧✐t② ✐♥ ❆❧x ●❛1−x ◆✴●❛◆ ❤❡t✲ ❡r♦str✉❝t✉r❡s✱ P❤②s✳ ❘❡✈✳ ❇✱ ✶✾✾✼✱ ✺✻ ✭✸✮✱ ✶✺✷✵✲✶✺✷✽✳ ❬✶✷✾❪ ▲✳ ❍s✉✱ ❲✳ ❲❛❧✉❦✐❡✇✐❝③✱ ❊❢❢❡❝t ♦❢ ♣♦❧❛r✐③❛t✐♦♥ ❢✐❡❧❞s ♦♥ tr❛♥s♣♦rt ♣r♦♣❡rt✐❡s ✐♥ ❆❧●❛◆✴●❛◆ ❤❡t❡r♦str✉❝t✉r❡s✱ ❏✳ ❆♣♣❧✳ P❤②s✳✱ ✷✵✵✶✱ ✽✾ ✭✸✮✱ ✶✼✽✸✲✶✼✽✾✳ ❬✶✸✵❪ ▼✳ ◆✳ ●✉r✉s✐♥❣❤❡✱ ❚✳ ●✳ ❆♥❞❡rss♦♥✱ ▼♦❜✐❧✐t② ✐♥ ❡♣✐t❛①✐❛❧ ●❛◆✿ ▲✐♠✐t❛t✐♦♥s ♦❢ ❢r❡❡✲❡❧❡❝tr♦♥ ❝♦♥❝❡♥tr❛t✐♦♥ ❞✉❡ t♦ ❞✐s❧♦❝❛t✐♦♥s ❛♥❞ ❝♦♠♣❡♥s❛t✐♦♥✱ P❤②s✳ ❘❡✈✳ ❇✱ ✷✵✵✸✱ ✻✼ ✭✷✸✮✱ ✷✸✺✷✵✽ ✭✶✲✼✮✳ ✶✵✼ ❬✶✸✶❪ ❆✳ ●♦❧❞✱ ❲✳ ●☎ ♦t③❡✱ ❚❤❡ ❝♦♥❞✉❝t✐✈✐t② ♦❢ str♦♥❣❧② ❞✐s♦r❞❡r❡❞ t✇♦✲ ❞✐♠❡♥s✐♦♥❛❧ s②st❡♠s✱ ❏✳ P❤②s✳ ❈✱ ✶✾✽✶✱ ✶✹✱ ✹✵✹✾✲✹✵✻✻✳ ❬✶✸✷❪ ❆✳ ●♦❧❞✱ ❲✳ ●☎ ♦t③❡✱ ▲♦❝❛❧✐③❛t✐♦♥ ❛♥❞ s❝r❡❡♥✐♥❣ ❛♥♦♠❛❧✐❡s ✐♥ t✇♦✲ ❞✐♠❡♥s✐♦♥❛❧ s②st❡♠s✱ P❤②s✳ ❘❡✈✳ ❇✱ ✶✾✽✻✱ ✸✸✱ ✷✹✾✺✲✷✺✶✶✳ ❬✶✸✸❪ ❋✳ ❙t❡r♥✱ ❲✳ ❊✳ ❍♦✇❛r❞✱ Pr♦♣❡rt✐❡s ♦❢ s❡♠✐❝♦♥❞✉❝t♦r s✉r❢❛❝❡ ✐♥✈❡rs✐♦♥ ❧❛②❡rs ✐♥ t❤❡ ❡❧❡❝tr✐❝ q✉❛♥t✉♠ ❧✐♠✐t✱ P❤②s✳ ❘❡✈✳✱ ✶✾✻✼✱ ✶✻✸✱ ✽✶✻✲✽✸✺✳ ❬✶✸✹❪ ❆✳ ●♦❧❞✱ ❊❧❡❝tr♦♥✐❝ tr❛♥s♣♦rt ♣r♦♣❡rt✐❡s ♦❢ ❛ t✇♦✲❞✐♠❡♥s✐♦♥❛❧ ❡❧❡❝tr♦♥ ❣❛s ✐♥ ❛ s✐❧✐❝♦♥ q✉❛♥t✉♠✲✇❡❧❧ str✉❝t✉r❡ ❛t ❧♦✇ t❡♠♣❡r❛t✉r❡✱ P❤②s✳ ❘❡✈✳ ❇✱ ✶✾✽✼✱ ✸✺✱ ✼✷✸✲✼✸✸✳ ❬✶✸✺❪ ▼✳ ❖✳ ▼❛♥❛sr❡❤✱ ■♥tr♦❞✉❝t✐♦♥ t♦ ♥❛♥♦♠❛t❡r✐❛❧s ❛♥❞ ❞❡✈✐❝❡s✱ ◆❏✿ ❲✐❧❡②✱ ✷✵✶✷✱ ❯♥✐t❡❞ ❙t❛t❡s ♦❢ ❆♠❡r✐❝❛✳ ❬✶✸✻❪ ❘✳ ❉✐♥❣❧❡✱ ❍✳ ▲✳ ❙t☎♦r♠❡r✱ ❆✳ ❈✳ ●♦ss❛r❞✱ ❡t ❛❧✳✱ ❊❧❡❝tr♦♥ ♠♦❜✐❧✐t✐❡s ✐♥ ♠♦❞✉❧❛t✐♦♥✲❞♦♣❡❞ s❡♠✐❝♦♥❞✉❝t♦r ❤❡t❡r♦❥✉♥❝t✐♦♥ s✉♣❡r❧❛tt✐❝❡s✱ ❆♣♣❧✳ P❤②s✳ ▲❡tt✳✱ ✶✾✼✽✱ ✸✸ ✭✼✮✱ ✻✻✺✲✻✻✼✳ ❬✶✸✼❪ ◆✳ ▼❛❡❞❛✱ ❚✳ ◆✐s❤✐❞❛✱ ◆✳ ❑♦❜❛②❛s❤✐✱ ❡t ❛❧✳✱ ❚✇♦ ✲ ❞✐♠❡♥s✐♦♥❛❧ ❡❧❡❝tr♦♥✲❣❛s ❞❡♥s✐t② ✐♥ Alx Ga1−x N/GaN ❤❡t❡r♦str✉❝t✉r❡ ❢✐❡❧❞ ✲ ❡❢❢❡❝t tr❛♥s✐st♦rs✱ ❆♣♣❧✳ P❤②s✳ ▲❡tt✳✱ ✶✾✾✽✱ ✼✸ ✭✶✸✮✱ ✶✽✺✻✲✶✽✺✽✳ ❬✶✸✽❪ ❚✳ ❍✳ ❨✉✱ ❑✳ ❋✳ ❇r❡♥♥❛♥✱ ❚❤❡♦r❡t✐❝❛❧ st✉❞② ♦❢ t❤❡ t✇♦✲❞✐♠❡♥s✐♦♥❛❧ ❡❧❡❝tr♦♥ ♠♦❜✐❧✐t② ✐♥ str❛✐♥❡❞ ■■■✲♥✐tr✐❞❡ ❤❡t❡r♦str✉❝t✉r❡s✱ ❏✳ ❆♣♣❧✳ P❤②s✳✱ ✷✵✵✶✱ ✽✾✱ ✸✽✷✼✲✸✽✸✹✳ ❬✶✸✾❪ ❉✳ ❏❡♥❛✱ ❙✳ ❍❡✐❦♠❛♥✱ ❏✳ ❙✳ ❙♣❡❝❦✱ ❡t ❛❧✳✱ ▼❛❣♥❡t♦tr❛♥s♣♦rt ♣r♦♣❡rt✐❡s ♦❢ ❛ ♣♦❧❛r✐③❛t✐♦♥✲❞♦♣❡❞ t❤r❡❡✲❞✐♠❡♥s✐♦♥❛❧ ❡❧❡❝tr♦♥ s❧❛❜ ✐♥ ❣r❛❞❡❞ ❆❧●❛◆✱ P❤②s✳ ❘❡✈✳ ❇✱ ✷✵✵✸✱ ✻✼✱ ✶✺✸✸✵✻ ✭✶✲✹✮✳ ❬✶✹✵❪ ❚✳ ❆♥❞♦✱ ❙❝r❡❡♥✐♥❣ ❡❢❢❡❝t ❛♥❞ q✉❛♥t✉♠ tr❛♥s♣♦rt ✐♥ ❛ s✐❧✐❝♦♥ ✐♥✈❡rs✐♦♥ ❧❛②❡r ✐♥ str♦♥❣ ♠❛❣♥❡t✐❝ ❢✐❡❧❞s✱ ❏✳ P❤②s✳ ❙♦❝✳ ❏♣♥✳✱ ✶✾✼✼✱ ✹✸✱ ✶✻✶✻✲✶✻✷✻✳ ❬✶✹✶❪ ❨✳ ▼❛ts✉♠♦t♦✱ ❨✳ ❯❡♠✉r❛✱ ❙❝❛tt❡r✐♥❣ ♠❡❝❤❛♥✐s♠ ❛♥❞ ❧♦✇ t❡♠♣❡r❛t✉r❡ ♠♦❜✐❧✐t② ♦❢ ▼❖❙ ✐♥✈❡rs✐♦♥ ❧❛②❡rs✱ ❏♣♥✳ ❏✳ ❆♣♣❧✳ P❤②s✳✱ ✶✾✼✹✱ ✶✸ ✭❙✷✮✱ ✸✻✼✲ ✸✼✵✳ ✶✵✽ ❬✶✹✷❪ ❋✳ ❇❡r♥❛r❞✐♥✐✱ ❱✳ ❋✐♦r❡♥t✐♥✐✱ ❉✳ ❱❛♥❞❡r❜✐❧t✱ ❙♣♦♥t❛♥❡♦✉s ♣♦❧❛r✐③❛t✐♦♥ ❛♥❞ ♣✐❡③♦❡❧❡❝tr✐❝ ❝♦♥st❛♥ts ♦❢ ■■■✲❱ ♥✐tr✐❞❡s✱ P❤②s✳ ❘❡✈✳ ❇✱ ✶✾✾✼✱ ✺✻✱ ❘✶✵✵✷✹✲ ❘✶✵✵✷✼✳ ❬✶✹✸❪ ■✳ P✳ ❙♠♦r❝❤❦♦✈❛✱ ❈✳ ❘✳ ❊❧s❛ss✱ ❏✳ P✳ ■❜❜❡ts♦♥✱ ❡t ❛❧✳✱ P♦❧❛r✐③❛t✐♦♥✲✐♥❞✉❝❡❞ ❝❤❛r❣❡ ❛♥❞ ❡❧❡❝tr♦♥ ♠♦❜✐❧✐t② ✐♥ ❆❧●❛◆✴●❛◆ ❤❡t❡r♦str✉❝t✉r❡s ❣r♦✇♥ ❜② ♣❧❛s♠❛✲❛ss✐st❡❞ ♠♦❧❡❝✉❧❛r✲❜❡❛♠ ❡♣✐t❛①②✱ ❏✳ ❆♣♣❧✳ P❤②s✳✱ ✶✾✾✾✱ ✽✻✱ ✹✺✷✵✲✹✺✷✻✳ ❬✶✹✹❪ ■✳ P✳ ❙♠♦r❝❤❦♦✈❛✱ ▲✳ ❈❤❡♥✱ ❚✳ ▼❛t❡s✱ ❡t ❛❧✳✱ ❆❧◆✴●❛◆ ❛♥❞ ✭❆❧✱ ●❛✮ ◆✴❆❧◆✴●❛◆ t✇♦✲❞✐♠❡♥s✐♦♥❛❧ ❡❧❡❝tr♦♥ ❣❛s str✉❝t✉r❡s ❣r♦✇♥ ❜② ♣❧❛s♠❛✲ ❛ss✐st❡❞ ♠♦❧❡❝✉❧❛r✲❜❡❛♠ ❡♣✐t❛①②✱ ❏✳ ❆♣♣❧✳ P❤②s✳✱ ✷✵✵✶✱ ✾✵ ✭✶✵✮✱ ✺✶✾✻✲✺✷✵✶✳ ❬✶✹✺❪ ❘✳ ▲❛♥❞❛✉❡r✱ ❙♣❛t✐❛❧ ✈❛r✐❛t✐♦♥ ♦❢ ❝✉rr❡♥ts ❛♥❞ ❢✐❡❧❞s ❞✉❡ t♦ ❧♦❝❛❧✐③❡❞ s❝❛t✲ t❡r❡rs ✐♥ ♠❡t❛❧❧✐❝ ❝♦♥❞✉❝t✐♦♥✱ ■❇▼ ❏✳ ❘❡s✳ ❉❡✈✳✱ ✶✾✺✼✱ ✶ ✭✸✮✱ ✷✷✸✲✷✸✶✳ ❬✶✹✻❪ ❨✳ ❍✳ ▲✐✱ P✳ ❋✳ ❨✉❛♥✱ ❩✳ ◗✳ ❋❛♥✱ ❡t ❛❧✳✱ ❊❧❡❝tr♦♥✐❝ ♣r♦♣❡rt✐❡s ❛♥❞ ❝❛rr✐❡r ♠♦✲ ❜✐❧✐t② ❢♦r ♣❡♥t❛✲❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥s ✇✐t❤ ♥♦♥♠❡t❛❧❧✐❝✲❛t♦♠✲t❡r♠✐♥❛t✐♦♥s✱ ❖r❣✳ ❊❧❡❝tr♦♥✳✱ ✷✵✶✽✱ ✺✾✱ ✸✵✻✲✸✶✸✳ ❬✶✹✼❪ ❙✳ ❉❛tt❛✱ ❊❧❡❝tr♦♥✐❝ ❚r❛♥s♣♦rt ✐♥ ▼❡s♦s❝♦♣✐❝ ❙②st❡♠s✱ ❈❛♠❜r✐❞❣❡ ✉♥✐✈❡r✲ s✐t② ♣r❡ss✱ ✶✾✾✼✱ ❯♥✐t❡❞ ❑✐♥❣❞♦♠✳ ❬✶✹✽❪ ❳✳ ❍❛♥✱ ❏✳ ❨❛♥❣✱ P✳ ❨✉❛♥✱ ❡t ❛❧✳✱ ❙♣✐♥✲❞❡♣❡♥❞❡♥t tr❛♥s♣♦rt ✐♥ ❛ ♠✉❧t✐❢✉♥❝✲ t✐♦♥❛❧ s♣✐♥tr♦♥✐❝ ❞❡✈✐❝❡ ✇✐t❤ ❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥ ❡❧❡❝tr♦❞❡s✱ ❏✳ ❈♦♠♣✉t✳ ❊❧❡❝tr♦♥✳✱ ✷✵✶✽✱ ✶✼ ✭✷✮✱ ✻✵✹✲✻✶✷✳ ❬✶✹✾❪ ❉✳ ❲❛♥❣✱ ❩✳ ❩❤❛♥❣✱ ❩✳ ❩❤✉✱ ❇✳ ▲✐❛♥❣✱ ▼❛❣♥❡t✐❝ str✉❝t✉r❡ ❛♥❞ ♠❛❣♥❡t✐❝ tr❛♥s♣♦rt ♣r♦♣❡rt✐❡s ♦❢ ❣r❛♣❤❡♥❡ ♥❛♥♦r✐❜❜♦♥s ✇✐t❤ s❛✇t♦♦t❤ ③✐❣③❛❣ ❡❞❣❡s✱ ❙❝✐✳ ❘❡♣✳✱ ✷✵✶✹✱ ✹✱ ✼✺✽✼ ✭✶✲✼✮✳ ❬✶✺✵❪ ▲✳ ❳✐❡✱ ❙✳ ❩✳ ❈❤❡♥✱ ❲✳ ❳✳ ❩❤♦✉✱ ❑✳ ◗✳ ❈❤❡♥✱ ▲❛r❣❡ r❡❝t✐❢②✐♥❣ r❛t✐♦ ✐♥ ❛ ♥✐tr♦❣❡♥✲❞♦♣❡❞ ❛r♠❝❤❛✐r ❣r❛♣❤❡♥❡ ❞❡✈✐❝❡ ♠♦❞✉❧❛t❡❞ ❜② t❤❡ ❣❛t❡ ✈♦❧t❛❣❡✱ ❖r❣✳ ❊❧❡❝tr♦♥✳✱ ✷✵✶✼✱ ✹✻✱ ✶✺✵✕✶✺✼✳ ❬✶✺✶❪ ❆✳ ❑✈❛s❤♥✐♥✱ ❉✳ ❑✈❛s❤♥✐♥✱ ❖✳ ❑✈❛s❤♥✐♥❛✱ ▲✳ ❈❤❡r♥♦③❛t♦♥s❦✐✐✱ ❚r❛♥s♣♦rt ✐♥✈❡st✐❣❛t✐♦♥ ♦❢ ❜r❛♥❝❤❡❞ ❣r❛♣❤❡♥❡ ♥❛♥♦❢❧❛❦❡s✱ ◆❛♥♦t❡❝❤♥♦❧♦❣②✱ ✷✵✶✺✱ ✷✻ ✭✸✽✮✱ ✸✽✺✼✵✺ ✭✶✲✻✮✳ ✶✵✾ ❬✶✺✷❪ ▲✳ ■❡♠♠♦✱ ❆✳ ❉✐ ❇❛rt♦❧♦♠❡♦✱ ❋✳ ●✐✉❜✐❧❡♦✱ ❡t ❛❧✳✱ ●r❛♣❤❡♥❡ ❡♥❤❛♥❝❡❞ ❢✐❡❧❞ ❡♠✐ss✐♦♥ ❢r♦♠ ■♥P ♥❛♥♦❝r②st❛❧s✱ ◆❛♥♦t❡❝❤♥♦❧♦❣②✱ ✷✵✶✼✱ ✷✽ ✭✹✾✮✱ ✹✾✺✼✵✺ ✭✶✲ ✶✵✮✳ ... HỌC VÀ CÔNG NGHỆ VIỆT NAM HỌC VIỆN KHOA HỌC VÀ CÔNG NGHỆ …… ….***………… PHẠM THỊ BÍCH THẢO HIỆN TƯỢNG VẬN CHUYỂN ĐIỆN TỬ TRONG CÁC CẤU TRÚC NANO BÁN DẪN DỰA TRÊN VẬT LIỆU PHÂN CỰC AlGaN/GaN VÀ PENTA-GRAPHENE. .. VẬT LIỆU PHÂN CỰC AlGaN/GaN VÀ PENTA-GRAPHENE NANORIBBON LUẬN ÁN TIẾN SỸ VẬT LÝ Chuyên ngành: Vật lý lý thuyết Vật lý toán Mã số: 44 01 03 Người hướng dẫn khoa học: PGS.TS Nguyễn Thành Tiên GS.TS... Nhám phân cực (Polarization roughness) PR Giếng lượng tử (Quantum well) QW Sawtooth penta-graphene nanoribbon SSPGNR Zigzag-armchair penta-graphene nanoribbon ZAPGNR Zigzag graphene nanoribbon