Chapter 10. Junctions Junctions
• Surface ~ simplest one; junction between vacuum/surface • Metal/Metal qq potential is set up MM12 • Metal/Semiconductor Blocking contact ~ Schottky barrier Ohmic contact ~ low resistance • Semiconductor/Semiconductor a. Homojunction ~ both side of junctions are same b. Heterojunction ~ each side is different c. Iso-type ~ types are same to both sides < n types or p types > d. Anisotype < p + n > • M/I/M, MIS, SIS, MOS Surfaces
Termination of the periodic potential Chemisorption of oxygen on n-type → localized states at the surface Semiconductor surface
Surface state bending of band gives Ɛ
positively charged O - depletion region Ec 2 chemisorption + + separation of charge EF - d - negatively charged surface
Ev state
- • As more O2 are formed, the energy bands bend at the surface of the semiconductor because of the local field that is built up. Metal/Metal
qcp Ɛ q qB q A A contact qB potential
B B A A
• Transfer of electron until EF are same for both of metals
• A potential difference cp known as the contact potential is set up between two metals.
• If qqqqqABcpAB ,
• EF has to be same in thermal equilibrium for whole system Although an internal field exists, no potential can be measured in an external circuit connecting the two metals together. Local electric field is measured by the Kelvin Probe method – vibrating method Metal/Semiconductor – Schottky Barrier
q D qS S ≡ electron qM qM affinity S q E - S b - ++
Wd
qEE () SS cF Blocking contact
• Blocking contact if 𝑞Φ 𝑞Φ for n-type and 𝑞Φ 𝑞Φ for p-type • A flow of electrons from the semiconductor to the metal in order to equalize the Fermi energies in the two materials.
• An internal field 𝑞Φ is developed in the semiconductor.
• 𝑞Φ 𝑞 Φ Φ : diffusion potential, built-in potential
• 𝐸 𝑞Φ 𝜒 : Energy barrier Metal/Semiconductor – Schottky Barrier
• The width of the depletion region + Ionized donor density = ND E r 0 dE Nq D dx r 0 d E dx d 2 Nq D Boundary conditions 2 : Poisson's equation dx r 0 𝜕𝜙 𝐸 𝑥 𝑊 Nq 2 𝜕𝑥 0 at qW D 2 𝜙 𝜙 at 𝑥 𝑊 DD 𝜙 0 at 𝑥 0 2 r 0 Metal/Semiconductor – Schottky Barrier
• In the depletion region Wd, potential change Φ
𝑥 𝑊 ,Φ Φ / 2𝜀 𝜀 𝑞Φ 𝑞Φ 𝑊 𝑞 𝑁
→ The more donors, the smaller 𝑊 .
• If we include the effects of an applied voltage Φapp , / 2𝜀 𝜀 𝑞Φ 𝑞Φ 𝑞Φ 𝑊 The more donors or the larger 𝑞 𝑁 applied voltage can recued the contact resistance. → The larger applied voltage, the smaller 𝑊 . Metal/Semiconductor – Schottky Barrier metal semiconductor depletion region
Wd conductor dielectric nearly conductor
1 / 2𝜀 𝜀 𝑞Φ 𝑞Φ 𝐶/𝐴 𝑊 𝑞 𝑁 1 M SD 𝜀 𝜀 𝐴 slope ∝ 𝐶 𝑁 𝑑 1 2 𝑞Φ 𝑞Φapp app 𝐶/𝐴 𝜀 𝜀 𝑞 𝑁 Method to measure 𝑁 and Φ Metal/Semiconductor – Schottky Barrier
• JV characteristics of Schottky barrier (n-type semiconductor)
J qq () + DMS + qMS
V EE q Metal - Metal + cF SS
𝐽 → 𝐴𝑇 𝑒𝑥𝑝 𝑞Φ 𝜒 /𝑘𝑇 𝐽 → 𝐴𝑇 𝑒𝑥𝑝 𝑞Φ 𝜒 𝑞Φapp /𝑘𝑇 (only change by 𝑞Φapp) Metal/Semiconductor – Schottky Barrier
• 𝐽net 𝐽 → 𝐽 → 𝐴𝑇 𝑒𝑥𝑝 𝑞Φ 𝜒 /𝑘𝑇 𝑒𝑥𝑝 𝑞Φapp/𝑘𝑇 1
≡ J0 , not depend on the Φapp
• Basic equation for current in a M/S junction J
𝐽net 𝐽 𝑒𝑥𝑝 𝑞Φapp/𝑘𝑇 1
For forward bias with positive 𝑞Φapp
𝐽 𝐽 𝑒𝑥𝑝 𝑞Φapp/𝑘𝑇 forward J0
For reverse bias with negative 𝑞Φapp Φapp
𝐽reverse 𝐽 Metal – Metal + reverse forward Metal/Semiconductor – Schottky Barrier J
J0
Φapp reverse forward
• In a forward bias, contact potential is reduced from 𝑞Φ to 𝑞 Φ Φ ) → forward current (metal to semiconductor) • In a reverse bias, contact barrier increases to 𝑞 Φ Φ ) → negligible electron flow from semiconductor to metal • In both cases, metal-to-semiconductor electron flow is determined by 𝑞 Φ 𝜒 • Diode equation: 𝐼 𝐼 𝑒𝑥𝑝 𝑞Φapp/𝑘𝑇 1 Ohmic contact
qqDSM() q qM S S e- SM q
metal n-semiconductor Accumulation region (reservoir of e-) n-type: 𝑞Φ 𝑞Φ • Electrons flow without any barrier contact does not make any change in J. p-type: 𝑞Φ 𝑞Φ (opposite of Schottky barrier) Ohmic contact
• The accumulation layer in the semiconductor serves as a ready reservoir of electrons for conduction in the material available at the contact, and thus application of an electric field measures only the conductivity (R) of the semiconductor.
J
R
V p-n junction - homojunctions
𝜒 q n e- n 𝑞Φ 𝑞Φ 𝑞Φ 𝜒 𝐸 𝐸 𝐸 qp p 𝜒 𝐸 𝐸 p
h+ p-type n-type
Depeletion region
W = Wp+ Wn
Similar to two Schottky barriers
p-type n-type Wp Wn p-n junction - homojunctions
When no electric field is applied (Φapp = 0) When an electric field (Φapp) is applied
Minority carrier n qkTapp / p nep y Majority y carrier qqDapp
qapp
Majority x carrier x peqkTapp / Minority n pn carrier
Majority carriers ~ e- in n-type, h+ in p-type Minority carriers ~ h+ in n-type, e- in p-type p-n junction - homojunctions
J • 𝐽 𝐽 𝐽
app/ 𝐽 𝐽 𝑒 1 J0 𝑞𝐷 𝑛 𝑞𝐷 𝑝 𝐽 Φ 𝐿 𝐿 app p - p +
• The p-n junction shows the similar form with a Schottky barrier (Φapp dependence of J ) Note: The pre-exponential reverse saturation current (J0) has a different definition with Schottky barrier. Applications of p-n junctions
• Rectifier • Amplifier • p-n-p type transistor • Field-effect transistor • Photodetector • Phototransistor • Solar cell • Light emitting diode • Tunnel diode Applications of p-n junctions
Photodetector: operating under a reverse bias J e-h pair - light - +
+ Φapp ΔI
• Increase of current by light irradiation number of collected electrons Photoconductivity gain ≡ 1 number of absorbed photons Applications of p-n junctions Solar cell: no applied bias
e-h pair - light - +
+ Open circuit voltage
O Short circuit current
The band gap of about 1.4 eV proves to be optimal for solar energy conversion application. Applications of p-n junctions Light emitter: Forward biased p-n junction
e-h pair - - + -
LED, Laser + +
• Direct band gap materials are favored for light emitting application. • GaAsP (R), InGaN (B), GaN (B) • By coating a blue LED with phosphor materials, a portion of the blue light can be converted to red and green (or yellow) lights for white light. Semiconductor-semiconductor junctions: Heterojunctions
An isotope heterojunction between two n-type materials with the same electron density, but showing a discontinuity at the interface because of a difference in electron affinities.
Ec 12 EEEvGG21 2 1 qEEEE ()() DcFcF11 1 2 2 2 DD211122// NN D D
A positive value of Δ𝐸 or a negative value of Δ𝐸 implies a spike impeding the transport of electrons or holes, respectively. Semiconductor-semiconductor junctions: Heterojunctions
Energy band diagrams for p-n heterojunctions. The materials in (a) and (b) have the same band gaps, but in (a) the p-type material has a smaller electron affinity than the n-type material, whereas in (b) the situation is reversed. van der Waals Heterojunctions Multiple quantum well Epitaxially grown MQW Lattice mismatch (MQW)laser
2D semiconductors van der Waals heterostructure WSe2 MoS2 MoS2 WSe2
MoS2 WSe2
EF
• Stacking of 2D semiconductors for heterostructure • Less interaction between layers (almost flat band) Appl. Phys. Lett. 102, 012111 (2013) • No issue of lattice mismatch