Schottky Diodes (M-S Contacts)

Schottky Diodes (M-S Contacts) Three MITs of the Day Band diagrams for ohmic and rectifying Schottky contacts Similarity to and difference from bipolar junctions on electrostatic and IV characteristics. Surface Fermi level pinning Reading assignment: Sections 2.4 of Taur & Ning Chapter 2 1

E 0 E FM x=0 x=w Φ M Φ B Φ S χ E 0 E FM Band Diagrams (1) n-type Si, Φ M >Φ S, Rectifying (2) n-type Si, Φ M <Φ S, Ohmic x=0 Φ M Φ S χ E 0 qv bi E Fn E V E 0 E Fn E V Ideal MS contacts: Intimate contacts (no hole or bubble) No intermixing/diffusion No surface charge/traps If we keep on increasing the p doping of a p + -n diode, the p side will go through Mott transition around 10 21 cm -3 and can be regarded as a M-S contact Work function of metal: energy necessary for electrons to be free electrons in vacuum. Metals can be viewed with negative or negligible bandgap (many silicides are metals electrically) Chapter 2 2

Steady-state IV of a Schottky diode N-type semiconductors Φ M > Φ S : retifying qv bi = Φ M - Φ S = Φ B -(E C -E F ) FB Φ M < Φ S : Ohmic P-type semiconductors E 0 E FM Φ M < Φ S : retifying Φ M > Φ S : Ohmic (1) n-type Si, Φ M >Φ S, Rectifying x=0 I M S I S M x=w Φ M Φ B Φ S χ E 0 q(v bi -V A ) E Fn E V What is different from the bipolar diodes? IV are dominated by carriers having enough kinetic energy to ballistically pass the potential barrier (thermionic emission) I M S remains almost constant for changing V A, since the metal electrons look at the same barrier I s M will change exponentially with V A (with η=1) since the semiconductor electrons look at a barrier height lowered by V A Chapter 2 3

Electrostatics in Schottky Contacts Retifying Schottky contact Ohmic Schottky contact I=I M S +I S M I=I M S +I S M constant I M S vanishing I S M constant I M S exponential I S M large I S M V A large I M S V A Electrostatic analysis is expected to be identical to bipolar diodes: the charge in the depletion region will support (V bi -V A ) by Poisson Eq. qn ρ = 0 W D qn D F = ε ε si 0 2ε siε 0 = qn D 0 elsewhere ( W x) x W ( V V ) bi A 0 1/ 2 x W The currents are dominated by carriers having enough kinetic energy to overcome the potential barrier (thermionic emission, with correction later) The minority diffusion/recombination exists, but usually not important due to the lower barrier height. Chapter 2 4

Thermionic Emission Over the Potential Barrier K. E. or n( v for I * ) S M R x = = 1 2 sure AR * 2 mnvx v x 4πkTm 3 h = qa * m = R m T * n 0 2 e v v min *2 n n( v min e φ / kt B ( V ) q V ( E x n( v ) dv e bi 2q = * mn F E x qv ) v / kt ( V V ) )/ kt dv e n A R 120 2 cm K A C x x A = bi x m 2 * n v A 2 x / 2 1/ 2 Richarson s constant in vacuum tube theory!! kt M S φ / kt ( qv kt ) A / e 1 Chapter 2 5 I I I S = = I = I M S AR S M = AR * + T I 2 * A S M e ( V T 2 B e = φ / kt = B 0) No N D dependence except from Φ B Have different temperature dependence from bipolar diodes No recombination, high-level injection, ideality factor close to 1 for all forwardbias regions Generally called thermionic emission current through this derivation I S

Barrier Lowering in Schottky Contacts The reverse current never saturates to I M S though as predicted in the ideal IV, since Φ B needs to be corrected in the reverse bias due to tunneling and image charge in the metal. barrier lowering due to tunneling: also called thermionic field emission 2/3 Δφ = αf barrier lowering due to image charge: also called image lowering Δ ϕ = qf /4πε siε 0 The tunneling current through the thin Schottky barrier is actually VERY important, since many M-S contacts contain A LOT of surface traps that pin the Fermi level at the mid-gap, which results in retifying contacts regardless (we need Ohmic contacts for transistors though). The key is to dope the semiconductor heavily so that the barrier is thin, thin enough that tunneling can dominate to give Ohmic contacts. Chapter 2 6 E FM E T Effective Φ B due to barrier lowering Φ B I V A surface fermi-level pinning E C E F E V

Image Force Lowering 2 q 16πε x 0 Δ φ = B qf φ = φ Δφ /4πε ε B B0 B Chapter 2 7 si 0

Band Diagram in Surface Fermi Level Pinning E 0 Independent of Φ M and Φ S, whenever Fermi level is pinned at the midgap, then E C E i E F E V there is always a halfbandgap barrier for the majority carrier. From the Poisson equation, a discontinuous potential requires a 2D charge dipole, which is the case here. The 2D charge dipole is formed by the interface trap charge and the image charge in the metal.. Chapter 2 8

Surface Fermi Level Pinning Chapter 2 9

Schottky Diodes vs. Bipolar Diodes The small-signal behavior of Schottky diodes is similar to the bipolar diode case (required by electrostatics) The transient response of the Schottky diodes is much faster than the bipolar diode case, since the minority carrier does not participate in (they surely exist, but usually very small) and there is no hold time for diode to go from ON to OFF. The bipolar current (diffusion) and the Schottky current (thermionic emission with correction) can actually be unified in one expression, but the algebra is too complex, and the interested reader should visit S. M. Sze s Physics of Semiconductor Devices (Wiley 1981), presented under the thermionic diffusion theory. Chapter 2 10

Schottky Barrier Heights for Electrons and Holes Metal Mg Ti Cr Ni W Mo Pd Au Pt φ Bn (V) 0.4 0.5 0.61 0.61 0.67 0.68 0.77 0.8 0.9 φ Bp (V) 0.6 0.5 0.51 0.42 0.3 Ψ M (V) 3.7 4.3 4.5 4.7 4.6 4.6 5.1 5.1 5.7 Silicide HfSi MoSi 2 ZrSi 2 TiSi 2 CoSi 2 WSi 2 NiSi Pd 2 Si PtSi φ Bn (V) 0.45 0.55 0.55 0.61 0.65 0.67 0.67 0.75 0.87 φ Bp (V) 0.65 0.55 0.55 0.49 0.45 0.45 0.43 0.35 0.23 Silicide is often more stable than metal on Si due to the gradual transition layer (in terms of adhesion and interface states). Silicidation together with maintaining a high surface doping concentration is still a critical CMOS technology. Typical value of contact resistance in deep submicron CMOS technology is around 10-7 Ωcm 2. For a (0.1μm) 2 contact, this is already too large, and innovation is necessary in the next ten years. Chapter 2 11

Semiconductor Heterojunction Classification According to the values of χ and Egap, there are three types of semiconductor heterojunctions: Type I, II and III. Narrow/wide bandgap, popular in electronic devices Discontinous bandgap, popular in photovoltaic Broken bandgap, special use in superlattices Chapter 2 12

Semiconductor Heterojunction Diodes For abrupt interface, ΔE C = (χ 1 χ 2 ) and ΔE V = (χ 1 χ 2 ) + E gap1 E gap2 are material constant Chapter 2 13

Common Pseudomorphic Heterojunctions Assume the lattice mismatch and residual stress are negligible, and the lattice interface at the heterojunction is ideal. This is not a good approximation for the SiGe/Si system, but acceptable for AlGaAs/GaAs system when the Al alloy composition is less than 25%. Both SiGe/Si and AlGaAs/GaAs systems are Type I For the Al 1-x Ga x As/GaAs system, χ GaAs =4.2eV, E gapgaas = 1.44eV, AlGaAs has a larger bandgap with ΔE C = 0.15x ev and ΔE V = 0.58x ev. For the Si/Si 1-x Ge x system, χ Si =4.1eV, E gapsi = 1.1eV, ΔE C = 0.05x ev and ΔE V = 0.47x ev. Remember that bandgap can be measured accurately, while affinity cannot. Therefore, the bandgap difference in the heterojunction can usually be accurately given, while the ΔE C and ΔE V is less accurate. Chapter 2 14

Quantum Well Heterojunctions E 0 is continuous unless there are charge dipole at the interface Al 0.2 Ga 0.8 As N A = 10 18 cm -3 2μm Al 0.2 Ga 0.8 As undoped 0.5μm GaAs undoped 0.5μm Al 0.2 Ga 0.8 As undoped 0.5μm Al 0.2 Ga 0.8 As N D = 10 18 cm -3 2μm E 0 ΔE C ΔE C and ΔE V are material constant ΔE V E C E F E i E V Chapter 2 15

Three MITs of the Day Diode Applications Relations of semiconductor bandgap and optical properties Photosensitive regions of diodes: optical generation that can produce currents Avalanche operations for photo-amplification Chapter 2 16

Electrical: Main applications of diodes Current rectifier: using the asymmetrical forward and reverse biases for ac-to-dc conversion or charge pumps Voltage clamp: in forward bias, regulate voltage drop across the diode to be V th ; in reverse bias (either high avalanche V BR or low Zener V BR ), regulate voltage drop to be V BR. Varactor (variable capacitor): using the reverse-bias nonlinear junction capacitance Optoelectronic: LED (spontaneous emission) and laser (stimulated emission) Photodiode and (photovoltaic) solar cell Chapter 2 17

light Optoelectronic Diodes optical fiber (glass fiber with cylindrical index gradients) light LED or laser heavily forward bias to create population inversion ultraviolet GaN λ = 1.3μm for minimal dispersion λ = 1.55μm for minimal loss for E gap between 0.95 and 0.8eV human sensitivity to visible light GaP AlAs AlGaAs GaAsP infrared GaAs 0.4 0.7 0.85 1.1 Si Photodiode often in avalanche breakdown to improve the signalto-noise ratio λ (μm) λ( μm) = E 1.24 ( ev ) photon Chapter 2 18

Electrical Properties of Photovoltaic Diodes p i n L p W Ln light E C E V Crude approximation: if the e-h pair is generated within L n, W and L p close to the junction (long-base case, of course), then they can be separated by the junction field to cause net current. ( ) n + L p W G L I I + I = I qa L + = dark illumi dark What can cause net current? Net charge has to arrive at contact with some velocity The electron-hole pair has to be generated in places where there is a separation F. Or they can diffuse into places where there is separation F before a recombination event. Chapter 2 19

Design Considerations of Photovoltaic (PV) Cells To enlarge W, an intrinsic layer can be added, but this lowers F max. To maximize L n and L p, the lifetime has to be large. When L n +L p >> W, I L will be less sensitive to the applied bias. I light absorbing coefficient α (cm -1 ) p n ~1/α for ideal absorption V A zero-current bias operating point for photovoltatic cells log(α) surface absorption I L /I max sample becomes transparent zero-bias current Chapter 2 20 λ λ

Three Basic Types of Photo Diodes Photodetectors: Preferably operating in the avalanche region (sometime called avalanche diodes) to improve sensitivity, since one photon can generate multiple electron/hole pairs from multiplication. Solar cells: Most sunlight is visible to infrared (before the ozone layer is gone) Si and GaAs can be used, but how to grow on a large area?? (thin-film) Satellite applications (cost and integration not a problem): GaAs or other direct bandgap materials (about 25-35% efficiency) Commercial applications: a-si and c-si (about 10-15% efficiency) LEDs (light-emitting diodes): Large direct bandgap material is needed for visible light (1.77eV < E gap < 3.10eV) for (0.4μm < λ < 0.7μm). Need to have both electrons and holes at the same location with small τ. New directions: GaN and organic LED. Chapter 2 21