chap3

Device Electronics for Integrated Circuits, 3/E by Richard S. Muller and Theodore I. KaminsCopyright © 2003 John Wiley & Sons. Inc. All rights reserved.

These excess carriers can be created by

Optical excitation

Photoluminescence

Electron bombardment

Cathodoluminescence

Electroluminescence due to current-a forward biased ‘pn’ junction


OPTICAL ABSORPTION

* Good technique for measurement of band gap of a material

•Two possible cases arise when light of some particular wave length is shone on a sample.

hν ≥ Eg hν < Eg

Will be abosrbed in SC

Will be transmitted through SC.


Photon of energy Eg

a c

b

Eg

Ec

Ev

OPTICAL ABSORPTION ( Contd.)


If a beam of photons with h > Eg falls on a semiconductor, then a predictable amount of absorption is going to occur.

Ratio of transmitted light to incident light will depend on

1. Photon wavelength

2. Thickness of sample



Figure 4—4Band gaps of some common semiconductors relative to the optical spectrum.


Figure 4—6Excitation and band-to-band recombination leading to photoluminescence.



E = hC / λ

= 1.24 / λ


Steady state ( Contd.)

Thus the excess carrier densities for electrons and holes under steady illumination will be given as :

δn = gop n

δp = gop p


Quasi Fermi levels

* Quasi Fermi levels are indicators of relative occupancy of bands, under conditions, when excess carriers are present

* There are separate Quasi Fermi levels for electrons and holes represented by Fn and Fp respectively.


Quasi Fermi levels ( Contd.)

The positions of Quasi Fermi levels relative to the position of intrinsic Fermi level are given by following two equations :

n = ni e (Fn – E

i) / kT

p = ni e (Ei – F

p) / kT


In summary When excess carriers are present, the deviations of Fn and Fp from Ef indicate how far the electron and hole populations are from the equilibrium values no and po.

The separation of Quasi Fermi levels Fn – Fp is a direct measure of the deviation from equilibrium

( At equilibrium Fn = Fp = Ef).

Quasi Fermi levels ( Contd.)


Problem : Suppose that in a sample 1013 EHP / cm3 are created optically every microsecond in a silicon sample with n0 = 1014 / cm3 and n = p = 2 micro seconds.

(a)Calculate the steady state excess electron ( or hole ) concentration.

(b)Find out the percentage change in the concentration of electrons and holes as a result of induction of these excess carriers.

(c) Find the position of Quasi Fermi levels for electrons and holes w.r.t intrinsic level. Show these levels with the help of an energy band diagram.


Figure 4—11Quasi-Fermi levels Fn and Fp for a Si sample with n0 = 1014 cm23, tp = 2 ms, and gop = 1019 EHP/cm3-s (Example 4–4).


Figure 4—12Spreading of a pulse of electrons by diffusion.

Diffusion Process


Figure 4—13An arbitrary electron concentration gradient in one dimension: (a) division of n(x) into segments of length equal to a mean free path for the electrons; (b) expanded view of two of the segments centered at x0.


Figure 4—14Drift and diffusion directions for electrons and holes in a carrier gradient and an electric field. Particle flow directions are indicated by dashed arrows, and the resulting currents are indicated by solid arrows.


Figure 4—15Energy band diagram of a semiconductor in an electric field %(x).


Figure 3.2 (p. 142)(a) Allowed electronic-energy states g(E) for an ideal metal. The states indicated by cross-hatching are occupied. Note the Fermi level Ef1 immersed in the continuum of allowed states. (b) Allowed electronic-energy states g(E) for a semiconductor. The Fermi level Ef2 is at an intermediate energy between that of the conduction-band edge and that of the valence-band edge.


Figure 3.3 (p. 142)Pertinent energy levels for the metal gold and the semiconductor silicon. Only the work function is given for the metal, whereas the semiconductor is described by the work function qΦs, the electron affinity qXs, and the band gap (Ec – Ev).


Figure 3.4 (p. 144)(a) Idealized equilibrium band diagram (energy versus distance) for a metal-semiconductor rectifying contact (Schottky barrier). The physical junction is at x = 0. (b) Charge at an idealized metal-semiconductor junction. The negative charge is approximately a delta function at the metal surface. The positive charge consists entirely of ionized donors (here assumed constant in space) in the depletion approximation. (c) Field at an idealized metal-semiconductor junction.


Figure 3.5 (p. 146)Idealized band diagrams (energy versus distance) at a metal-semiconductor junction (a) under applied forward bias (Va > 0) and (b) under applied reverse bias (Va < 0). The semiconductor is taken as the reference (voltage ground) as shown in (c). The vacuum levels for the two cases are not shown.


Many of the properties of pn junctions can be realized by forming a suitable Metal – Semiconductor contact ( Schottky Contact).

-Simple to fabricate

-Switching speed is much higher.

Metal Semiconductor junctions are also used as Ohmic contact to carry current into and out of the semiconductor device.

M S Junctions


Vacuum level EO refers to energy of free electrons . Difference between Fermi level EF and Vacuum level is called work function φ of materials.

Work function φm is an invariant property of metal. Is the minimum amount of energy required to free up electrons ( 3.66 eV for Mg and 5.15 eV for Ni. )

Some definitions

M S Junctions


Ideal MS Contacts : Assumptions

M and S are in intimate contact, on atomic scale

No oxides or charges at the interface.

M S Junctions


When negative charges are brought near the metal surface, positive (image charges) are induced in the metal.

When this image force is combined with an applied electric field, the effective work function is somewhat reduced.

This barrier lowering is called the Schottky effect.

Some facts

M S Junctions


Four different cases arise

M – n SC

Φ M > φS

M – n SC

Φ M < φS M – p SC

Φ M > φS

M – p SC

Φ M < φS

M S Junctions


The band-bending, and thus the depletion region, lies entirely within the semiconductor as the metal cannot be depleted. Also that although the currents are described as diffusion currents, the physical situation is very different to that in a semiconductor and so the usual diffusion equations (in particular the Einstein relations) cannot be used.

M S Junctions


M S JunctionsMetal - n SC ( φ m > φ SC )


M S JunctionsMetal - p SC ( φ m < φ SC )


M S JunctionsAppreciation of rectifying contacts


General condition to ensure an Ohmic Contact

Contacts must provide minimal resistance. Extremely easy flow of carriers. That is least expected from a Contact.

M S Junctions


M S Junctions


Figure 3.6 (p. 147)Plot of 1/C2 versus applied voltage for an ideal metal-semiconductor junction.


Figure 3.7 (p. 148)Schematic representation of space charge at a metal-semiconductor junction with nonuniform doping in the semiconductor.


Example: Schottky Barrier Diode (p. 149)


Example: Schottky Barrier Diode (cont., p. 150)


Figure 3.8 (p. 151)Classical energy diagram for a free electron near a plane metal surface at thermal equilibrium [E1(x)], and with an applied field –ξ [E2(x)].


Figure 3.9 (p. 154)(a) Band diagram of a rectifying metal-semiconductor junction under forward bias. The applied voltage Va displaces the Fermi levels: qVa = Efs – Efm. (b) The potential across the surface depletion layer is decreased to Φi – Va.


Figure 3.10 (p. 156)Measured values of current (plotted on a logarithmic scale) versus voltage for an aluminum-silicon Schottky barrier. Values for Is = JśA and n are obtained from an empirical fit of the data to Equation 3.3.17.


Figure 3.11 (p. 157) Electron-energy diagram for a Mott barrier (near-insulating region at the surface with a sharp transition at x = xd to a highly conducting region). The solid line indicates thermal equilibrium; the dotted line, a forward bias of Va volts with the metal held at ground potential. (b) Potential diagram for the Mott barrier.


Figure 3.12 (p. 159)Metal-semiconductor barrier with a thin space-charge region through which electrons can tunnel. (a) Tunneling from metal to semiconductor. (b) Tunneling from semiconductor to metal.


Figure 3.13a (p. 160)(a) An idealized equilibrium energy diagram for a Schottky ohmic contact between a metal and an n-type semiconductor.


Figure 3.13b (p. 160)(b) Charge at an ideal Schottky ohmic contact. A delta function of positive charge at the metal surface couples to a distributed excess-electron density n’(x) in the semiconductor.


Figure 3.13b (p. 160)(c) Field.


Figure 3.13c (p. 160)(d) Potential at an idealized Schottky ohmic contact. The Debye length LD is a characteristic measure of the extent of the charge and field.


Figure 3.14 (p. 162) Bonding diagram for a silicon crystal near its surface (straight lines indicate coupled pairs of bonding electrons). The bonds at a clean semiconductor surface are anistropic and, consequently, the allowed energy levels differ from those in the bulk.


Figure 3.15 (p. 163)Approximate distribution of Tamm-Schockley states in the diamond lattice [8]. The distribution appears to peak sharply at an energy roughly one-third of the bandgap above Ev.


Figure 3.16 (p. 164)Band structure near a metal-semiconductor contact according to the model of Cowley and Sze [9]. The model considers a thin interfacial layer of thickness that sustains a voltage Δ at equilibrium. Acceptor-type surface states distributed in energy are assumed to be described by a distribution function Ds states cm-2 eV-1.


Figure 3.17 (p. 165)Band diagram for a semiconductor surface showing a thin surface layer containing acceptor-type surface sates distributed in energy. A surface-depletion region is present because of charge in the surface states.


Figure 3.18 (p. 167)Schottky-barrier-gate, field-effect transistor. Current ID flowing from drain to source is modulated by gate voltage VG that controls the dimensions of the depletion region. This, in turn, modulates the cross-sectional conducting area for ID. The source and drain contacts are ohmic because they are made to highly doped material.


Figure 3.19 (p. 167)Special processing techniques improve the performance of Schottky diodes shown here in cross section. (a) The diffused p-type guard ring leads to a uniform electric field and eliminates breakdown at the junction edges and corners. (b) The metal field plate is an alternative means for achieving the same effect.


Figure 3.20 (p. 168)Linear plot of current versus voltage for a Schottky diode illustrating the concept of a diode “turn-on voltage.”


Figure 3.21 (p. 170) Diagrams for ideal metal-semiconductor Schottky diodes.


Figure P3.2 (p. 171)


Figure P3.2 (cont., p. 172)


Figure P3.4 (p. 172)

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