TUNNEL DIODLARDA TUNNEL TOKINING ANALITIK IFODASINI HOSIL QILISH

O‘ktamova Muniraxon  Abduqaxxarov Diyorbek Shokirjon o‘g‘li,  Sobirov Abdunabi Bahromjon o‘g‘li

Arxiv / №9 · 2026 / Maqola

TUNNEL DIODLARDA TUNNEL TOKINING ANALITIK IFODASINI HOSIL QILISH

Annotatsiya

O'ZBEKCHA

Ushbu ishda tunnel diodlarda kuzatiladigan tunnel tokning fizik tabiati va uning mate-matik ifodasi Esaki nazariyasi asosida tadqiq qilindi. Tunnel tok zichligining integral formulasi energetik sathlar zichligi va Fermi-Dirak taqsimot funksiyalarini hisobga olgan holda tahlil etildi hamda analitik soddalashtirish amalga oshirildi. Natijada tunnel tokning kuchlanishga bog‘liqligini ifodalovchi soda-lashtirilgan matematik model hosil qilindi. Olingan natijalar tunnel diodlarning volt-amper xarakteristika-sini nazariy jihatdan tavsiflash va manfiy differensial qarshilik hodisasini izohlashda muhim ahamiyatga ega.

Kalit so'zlar: tunnel diod, Esaki nazariyasi, manfiy differensial qarshilik, Fermi-Dirak taqsimoti, holatlar zichligi, kvant tunnellanish, tunnel o‘tish, analitik model, p–n o‘tish, tunnellanish ehtimoli.

РУССКИЙ

В работе исследована физическая природа туннельного тока в туннельных ди-одах и получено его математическое выражение на основе теории Эсаки. Проанализирована инте-гральная формула плотности туннельного тока с учетом плотности энергетических состояний и функции распределения Ферми-Дирака, после чего выполнено ее аналитическое упрощение. В ре-зультате получена упрощенная математическая модель зависимости туннельного тока от напря-жения. Полученные результаты имеют значение для теоретического описания вольт-амперной характеристики туннельных диодов и объяснения области отрицательного дифференциального сопротивления.

Ключевые слова: туннельный диод, теория Эсаки, отрицательное дифференциальное сопро-тивление, распределение Ферми-Дирака, плотность состояний, квантовое туннелирование, тун-нельный переход, аналитическая модель, p–n-переход, вероятность туннелирования.

ENGLISH

This work investigates the physical nature of tunnel current in tunnel diodes and derives its mathematical expression based on Esaki theory. The integral expression for tunnel current density is analyzed by taking into account the density of energy states and the Fermi-Dirac distribution function, followed by an analytical simplification. As a result, a simplified mathematical model describing the dependence of tunnel current on voltage is obtained. The results are important for the theoretical description of the current–voltage characteristics of tunnel diodes and for explaining the negative differential resistance region.

Keywords: tunnel diode, Esaki theory, negative differential resistance, Fermi–Dirac distribution, density of states, quantum tunneling, tunnel transition, analytical model, p–n junction, tunneling probability.

Maqola · PDF

PDF yuklab olish Yangi oynada ochish

Foydalanilgan adabiyotlar

Esaki L. New Phenomenon in Narrow p-n Junctions. Physical Review. 1958 vol. 109, р. 602–603.
Esaki L., Miyahara Y. A New Device Using the Tunneling Process in Narrow p-n Junctions // IRE Trans-actions on Electron Devices. 1960, vol. 7, № 2, p. 110–111.
Kane E.O. Theory of Tunneling in Semiconductors. Journal of Applied Physics. 1961, vol. 32, № 1, p. 83–91.
Sze S.M., Ng K.K. Physics of Semiconductor Devices. Wiley-Interscience. 2006, vol. 3, №1, p. 513–565.
Hall R.N. Observation of Tunneling in p-n Junctions // Physical Review Letters. 1959, vol. 3, №17, p. 366–368.
Karlovsky J. The curvature of the I-V characteristic of a tunnel diode // Solid-State Electronics. 1962, vol. 5, № 5, p. 353–355.
Sah C.T. Electronic Processes and Excess Currents in Gold-Doped Tunnel Diodes // Physical Review. 1961, vol. 123, № 5, p. 1593–1598.
Chynoweth A.G., Feldmann W.L., Logan R.A. Excess Tunnel Current in Silicon p-n Junctions // Physical Review. 1961, vol. 121, № 3, p. 684–694.
Minton R.M., Gmelin R. The Gallium Arsenide Tunnel Diode. RCA Review. 1961, vol. 22, №3, p. 409–415
Meyer J.J., Wheeler G.J. Analysis and design of tunnel diode oscillators // IEEE Transactions on Microwave Theory and Techniques. 1963, vol. 11, № 6, p. 537–543.

← Songa qaytish

[1] Esaki L. New Phenomenon in Narrow p-n Junctions. Physical Review. 1958 vol. 109, р. 602–603.

[2] Esaki L., Miyahara Y. A New Device Using the Tunneling Process in Narrow p-n Junctions // IRE Trans-actions on Electron Devices. 1960, vol. 7, № 2, p. 110–111.

[3] Kane E.O. Theory of Tunneling in Semiconductors. Journal of Applied Physics. 1961, vol. 32, № 1, p. 83–91.

[4] Sze S.M., Ng K.K. Physics of Semiconductor Devices. Wiley-Interscience. 2006, vol. 3, №1, p. 513–565.

[5] Hall R.N. Observation of Tunneling in p-n Junctions // Physical Review Letters. 1959, vol. 3, №17, p. 366–368.

[6] Karlovsky J. The curvature of the I-V characteristic of a tunnel diode // Solid-State Electronics. 1962, vol. 5, № 5, p. 353–355.

[7] Sah C.T. Electronic Processes and Excess Currents in Gold-Doped Tunnel Diodes // Physical Review. 1961, vol. 123, № 5, p. 1593–1598.

[8] Chynoweth A.G., Feldmann W.L., Logan R.A. Excess Tunnel Current in Silicon p-n Junctions // Physical Review. 1961, vol. 121, № 3, p. 684–694.

[9] Minton R.M., Gmelin R. The Gallium Arsenide Tunnel Diode. RCA Review. 1961, vol. 22, №3, p. 409–415

[10] Meyer J.J., Wheeler G.J. Analysis and design of tunnel diode oscillators // IEEE Transactions on Microwave Theory and Techniques. 1963, vol. 11, № 6, p. 537–543.