Como calcular barrera Schottky semiconductor metal-Si

Calcula barrera Schottky phi_B = phi_M - chi_S junction metal-semiconductor Si GaAs GaN. Diodos Schottky MOSFET solar photovoltaic RF. Walter Schottky Alemania 1886-1976 + Mott 1938. CIEMAT + UPC + Indra electronics.

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Como calcular la barrera Schottky (phi_B) propiedad fundamental junction metal-semiconductor electronica semiconductores: phi_B(n-type) = phi_M - chi_S n-type; phi_B(p-type) = E_g - phi_B(n) p-type. phi_M work function metal eV (Al 4.28; Cu 4.65; Au 5.1; Pt 5.65); chi_S electrón affinity (Si 4.05; GaAs 4.07; GaN 4.1; SiC 3.7); E_g bandgap (Si 1.12; GaAs 1.42; GaN 3.4; SiC 3.26).

Modelo Mott-Schottky 1938: phi_B = phi_M - chi_S ideal + Bardeen 1947 Fermi pinning real ~ 2/3*E_g.

Densidad corriente saturación Richardson: J_s = A**T^2*exp(-phi_B/kT) + A** = 1.2e6 A/m^2/K^2 Si + Bethe 1942.

I-V Schottky diodo: I = I_s*(exp(qV/(nkT))-1) + n ideality 1.05-1.5.

Tipos contacto: ohmic phi_B1 eV power rectifier.

Numeros relacionados: V_bi built-in; W depletion width; Richardson A; image force lowering; tunneling TFE.

Aplicaciones: Schottky diodes 1N5817 power; SiC 600V 1200V; GaN HEMT power; MOSFET source/drain; solar cells photovoltaic; PtSi infrared detectors; RF mixers HF VHF UHF. Historia: Walter Hermann Schottky (Zurich 1886 - Pretzfeld 1976) Wurzburg + Berlin Siemens + Rostock 1927-1958; 1938 Phys Z 41:570 'Halbleitertheorie der Sperrschicht' classico Schottky barrier + 1914 shot noise + 1916 photodetector + 1923 Schottky barrier diode + Schottky diode eponym + Werner Schottky Institute TU Munich.

Nevill Mott (UK 1905-1996) Cambridge Cavendish 1954-1971; 1938 Proc Cam Phil Soc 34:568 classico Mott-Schottky + 1949 Mott transition + Premio Nobel Física 1977 con Anderson Van Vleck.

John Bardeen (1908-1991) Bell Labs + UIUC; 1947 Phys Rev 71:717 classico Fermi pinning + 1947 transistor + 1957 BCS + Doppio Premio Nobel 1956 + 1972 only 2 Nobel Physics.

Hans Bethe (1906-2005) Cornell; 1942 MIT Radiation Lab + Manhattan + Premio Nobel 1967.

Simon Sze (Taiwan-USA 1936-2023) Bell Labs; 1969 'Physics of Semiconductor Devices' 1st + 3rd 2007 Wiley 832 pages classico. Legado: Sze-Ng 2007 + Yu-Cardona 2010 + Streetman-Banerjee 2014 + Pierret 1996 + Tu-Mayer-Feldman 2003 + Tung 2014.

España investigación: CSIC IMB-CNM Barcelona 11000 + Si Schottky; CSIC ICN2 Bellaterra 280; CIEMAT 1300; BSC Barcelona 1100; INTA Madrid 1500; Tecnalia 1500; BIST Barcelona 200; ICFO Castelldefels 400; IFAE Barcelona 200.

Universidades: UPC Barcelona 30000; UPM 38000; UCM 80000; UAM 30000; UC3M 22000; UAB 35000; UB 60000; Sevilla 65000; Granada 60000; UPV/EHU 47000.

Industria semiconductor: X-Fab Spain 200; Indra 56000; GMV 3300; Sener 2400.

Solar PV: Iberdrola 39000; Acciona Energía 11000; Endesa 9700; EDP Renovaveis 4000.

RF defensa: Indra 56000 radar Schottky; GMV 3300; Sener 2400; Hisdesat 200.

EV automotive Schottky: SEAT Martorell 14000; Renault España 6500; Mercedes Vitoria 5500; Iberdrola 39000 EV charging.

Formula Schottky

n-type: phi_B(n) = phi_M - chi_S; p-type: phi_B(p) = E_g - phi_B(n); J_s = A**T^2*exp(-phi_B/kT).

Valores tipicos: Au-nSi 1.05 eV; Al-nSi 0.23 eV ohmic; Pt-nGaAs 1.58 eV; Au-pSi 0.07 eV; Al-nGaN 0.18 eV.

Historia y contexto

Walter Schottky (1886-1976) Wurzburg + Berlin Siemens + Rostock 1927-1958; 1938 Phys Z 41:570 classico Schottky barrier + Schottky diode eponym.

Nevill Mott (1905-1996) Cambridge Cavendish; 1938 Mott-Schottky theory + Premio Nobel 1977.

John Bardeen (1908-1991) UIUC; 1947 Fermi pinning + transistor + BCS + Doppio Premio Nobel 1956 + 1972.

Hans Bethe (1906-2005) Cornell; 1942 thermionic emission + Premio Nobel 1967.

Simon Sze (1936-2023) Bell Labs; 1969 Wiley classico textbook. Legado: Sze-Ng 2007 + Yu-Cardona 2010 + Streetman-Banerjee 2014 + Tung 2014.

España investigación: CSIC IMB-CNM 11000; CSIC ICN2 280; CIEMAT 1300; BSC 1100; INTA 1500; Tecnalia 1500; BIST 200; ICFO 400; IFAE 200.

Universidades: UPC 30000; UPM 38000; UCM 80000; UAM 30000; UC3M 22000; UAB 35000; Sevilla 65000.

Semiconductor: X-Fab Spain 200; Indra 56000; GMV 3300.

Solar PV: Iberdrola 39000; Acciona Energía 11000; Endesa 9700.

RF defensa: Indra 56000; GMV 3300; Sener 2400.

EV automotive: SEAT 14000; Renault 6500; Iberdrola 39000.

Tabla Schottky

  • phi_B(n) = phi_M - chi_S
  • phi_B(p) = E_g - phi_B(n)
  • J_s = A**T^2*exp(-phi_B/kT)
  • Au-nSi: 1.05 eV
  • Al-nSi: 0.23 eV ohmic
  • Bardeen pinning: 2/3*E_g

5 ejemplos numericos

  1. Au-nSi: 1.05 eV high rectifier.
  2. Al-nSi ohmic: 0.23 eV.
  3. Pt-nGaAs: 1.58 eV.
  4. Au-pSi: 0.07 eV ohmic p-type.
  5. Al-nGaN power HEMT: 0.18 eV.

Limitaciones

Mott-Schottky ideal + Bardeen pinning + Image force + Tunneling TFE + Surface states + Temperature.

Errores comunes

  • n-type vs p-type signo.
  • Mott-Schottky vs Bardeen.
  • Ohmic vs Schottky.
  • Richardson constant.
  • Image force lowering.

Aplicaciones

  1. SiC Schottky power: Indra electronics + automotive SEAT.
  2. MOSFET source/drain: X-Fab Spain.
  3. Solar PV: Iberdrola + Acciona Energía.
  4. RF mixers: Indra + GMV radar.
  5. GaN HEMT:.
  6. Infrared: classical PtSi.
  7. Solar HJT: Iberdrola HJT.
  8. EV battery: Iberdrola charging.
  9. Mott-Schottky capacitance: doping concentration.
  10. QD contacts: classical.

Actualizado a julio de 2026

Preguntas frecuentes

Que es la barrera Schottky phi_B?

Barrera Schottky phi_B = phi_M - chi_S (n-type) y phi_B(p) = E_g - phi_B(n) (p-type) mide altura barrera energetica para electrones o holes en junction metal-semiconductor. Determina comportamiento rectifying (phi_B>0.5 eV diodo Schottky) o ohmico (phi_B<0.1 eV MOSFET source/drain). Walter Schottky Alemania 1886-1976 + 1938 Phys Z 41:570 classico + Mott 1938.

Modelo Mott-Schottky vs Bardeen Fermi pinning?

Mott-Schottky 1938 ideal: phi_B = phi_M - chi_S depende work function metal. Bardeen 1947 Phys Rev 71:717: surface states density pin Fermi level a phi_B real ~ 2/3*E_g + independiente phi_M. Si Ge GaAs Bardeen pinning. Cowley-Sze 1965 partial + Tung 2014.

Que es Richardson thermionic emission?

Richardson thermionic emission J_s = A**T^2*exp(-phi_B/kT) corriente saturacion Schottky + A** = 1.2e6 A/m^2/K^2 Si + 8.16e6 GaAs. Hans Bethe 1942 MIT Radiation Lab + Premio Nobel Física 1967 stellar nucleosynthesis.

Diferencia Schottky vs ohmic contact?

Ohmic phi_B0.5 eV rectifying + I = I_s*(exp(qV/(nkT))-1) + diodos signal RF + SiC power Wolfspeed STMicroelectronics world-leading + classical Sze 2007 832 pages.

Tipos diodos Schottky industriales?

Diodos Schottky: 1N5817 1N5819 power Si low Vf 0.3V; SiC 600V 1200V power Wolfspeed + STMicroelectronics + Vishay world-leading EV inverter; GaN HEMT power switching; PtSi infrared 1-5 um military; small signal RF mixer.

Que es image force lowering?

Image force lowering Delta_phi = sqrt(qE/(4*pi*epsilon_s)) reducción efectiva barrera Schottky 0.05-0.1 eV en diodos reales + applied field E + classical Sze 2007 832 pages + correccion importante para device modeling preciso.

Aplicaciones industriales Schottky?

Aplicaciones: SiC Schottky power Indra electronics + automotive SEAT Renault EV; MOSFET X-Fab Spain; solar PV Iberdrola + Acciona Energía HJT; RF mixers Indra + GMV radar; GaN HEMT classical; infrared PtSi; solar HJT; EV battery SiC; Mott-Schottky capacitance doping; QD contacts BIST.

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