3. Metal-Semiconductor Contacts3.1 Introduction Metal-semiconductor contacts have been known to have rectifying properties since 1874. The earliest radio receivers used a metal point contact to a galena (PbS) crystal, while in the valve era, power supplier commonly used “metal” (actually metal-metal oxide) rectifiers. The theory of metal-semiconductor contacts is attributed to Schottky (1938). Today, specially manufactured Schottky diodes are often used in rectification since they have a smaller forward voltage drop than P-N junction rectifiers.

There is also the problem of making metallic contacts to semiconductors, where a rectifying action is not wanted. The Schottky theory also permits the identification of the conditions necessary for the preparation fo ohmic (as opposed to rectifying) metal contacts on semiconductors.3.2 The metal-semiconductor junctionThe basic requirement for a metal-semiconductor is the same as for a P-N junction: the Fermi levels must line up. However, the problem now is in establishing reference levels with respect to which these levels are measured. The reference level is the “vacuum” level. For a metal, the energy required to remove an electron into the “vacuum” is given by the work function m:

E E qvac F m (m in volts)

EF (semiconductor)(n-type shown)

EF (metal)

Evac

Ec

Ev

qm

qs

qVn

electrons

The equivalent measure for the semiconductor is the electron affinity s . Since a semiconductor will always have some electrons in the conduction band, a “photoelectric effect” experiment will measure the difference between EC , not EF , and the vacuum level.The true work function for a semiconductor is:

s = χs +Vn (qVn = EC – EF)

Exactly as in the case of the PN junction, diffusion currents flow across the junction (to equalise the Fermi levels).

Although the situation is superficially similar to that of the p-n junction, there are several important differences. 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.

The metal-N type semiconductor junction is particularly important because both diffusion currents are with electrons - no holes are involved. Such a junction is therefore unipolar. This results in a faster device, not only because electrons are normally more mobile than holes, but also because minority carrier recombination does not

EF

W

Vbi=m – sVb=m - s

= m-s+Vn

occur. In a metal-P type semiconductor junction, the forward current is carried entirely by holes injected from the semiconductor into the metal. Although the resulting devices are also very fast because hole lifetime in the metal is negligible, they are not truly unipolar devices since recombination still occurs.

Experiment shows that Vbi (and Vb) are largely independent of the nature of the metal and hence of m. This is because the interaction takes place with surface states in the semiconductor, and not with the bulk metal.

Depletion layer width and junction capacitance can be obtained in a similar way as for the p-n junction, using Vbi or, under bias, VD=Vbi - VA. Similar arguments also show qualitatively that such a junction is rectifying.

3.3 Junction currents

Considering a metal-N type semiconductor junction, a forward bias consists of making the metal positive and the semiconductor negative, which lowers the barrier. This increases the electron current injected from the semiconductor into the metal without much affecting the reverse “uphill” current from the metal. Reverse bias raises the barrier and decreases the injected electron current. Again, an exponential dependence on diffusion potential (VD = Vbi - VA) is obtained.

Discussion of the current through the junction is however very different from the bipolar junction. The main contribution to the current through the junction is caused by electrons thermally overcoming or tunnelling through the barrier Vb . Thermionic

emission is the most important contribution to the device current under moderate electric fields. The electron energy distribuition is quasi-exponential, so even a small reduction in barrier height by means of a forward bias can increase this current significantly.

The height of the potential barrier is given by:

and, if positive, results in the behaviour noted above.

If zero or negative, the junction is not rectifying and is referred to as an ohmic contact (discussed later).

3.4 The Schottky effect

thermionic emission

field-induced emissionqVb

EC

The barrier in the metal-semiconductor junction is further reduced when the diode is forward biased by the Schottky effect.

This lowering can be evaluated using the “image charge” method (see Blakemore pp 192-193, or Sze pp 250-251).

xq

q

ms

s

4

4

E

E

The effect is actually stronger in a metal-vacuum surface rather than a metal-semiconductor junction (because of the high s) and results in field emission (the cold-cathode effect). Even in semiconductors, however, a useful reduction of 1-2V can occur.

3.5 Thermionic emission theoryThermionic emission across a metal-semiconductor junction is similar to thermionic emission from a metal into the vacuum, except

x

-qEx

PE of ejected electron

resultant PE curve

xm

q

that the appropriate electron density functions and electric field values are used. The vacuum case is covered in Blakemore pp. 188-191. The case for a Schottky junction is considered here.

The current density across such a barrier is given by the number of electrons with energies sufficient to overcome the barrier.

where vx is the velocity of the electrons in the direction of the junction, and

dn N E F E dE ( ) ( )

N(E) being the density of states and F(E) the Fermi-Dirac distribution function.

Using the usual approximations for F(E) and N(E):

and if we further assume that all the energy of the conduction-band electrons is keinetic (free-electron approximation)

qV b

E n(E)

EFEC

qVbi

qVn

E E m vC 12

2*

where v is the total electron velocity (v2=vx2+ vy

2+vz2)

Substituting,

dnm

he e dE

mh

e e v dv

E EkT

E EkT

m vkT

qVkT

C C F

n

4 2

2 4

3 2

32

3

2 2

2

* /

* *

Using the standard transformation 4v2dv=dvx dvydvz,, and letting vox be the velocity corresponding to just overcoming the barrier,

J qmh

e v e dv v e dv v e dv

qm kh

T e e

s m

qVkT

x

m vkT

xv y

m vkT

y z

m vkT

z

qVkT

m vkT

n x

ox

y z

n ox

2

4

3

2 2 2

2

32 2

2 2 2

2

* * * *

* *

since the integrals in vy and vz vanish.Recall that

B bi n oxV V m v 12

2*

and that once bias is applied, Vbi has to be replaced by Vbi - VA, so:

J A T e e

Aqm kh

s m

qkT

qVkT

B A

*

**

2

2

3

4

which has the required exponential dependence on VA.

The total current is:

where Jm->s is the reverse current flow that is largely unaffected by the applied potential. Since J(VA=0)=0, it follows that:

so:

We therefore have a law similar to that for the junction diode:

J J e

J A T e

S

qVkT

S

qkT

A

BN

1

2**

where the factors A** and BN differ from the A* and B to take into account the factors such as the Schottky effect.The advantage of Schottky diodes over p-n junction diodes in circuit applications stem from their higher speed (no minority carriers) and lower forward voltage drop (small barrier height). On the other hand they suffer from low reverse breakdown voltages and greater temperature sensitivity of leakage currents.3.6 Ohmic contacts The realization that a metal-semiconductor contact may rectifying makes the matter of passing a current from a metal wire into a semiconductor chip a complicated matter. Of course, the equations:

implies that the barrier disappears if m < s for an n-type semiconductor for example. Such a contact is characterized by an accumulation (rather than depletion) region which is essentially an ohmic conductor.`

Although this is a general mechanism, metals with suitable work functions are neither easy to find nor necessarily convenient to use. However, given that a Schottky diode has a smaller forward voltage than a p-n junction, the existence of a Schottky diode in series with a p-n junction diode can be neglected. In addition, the properties of the Schottky contact can be degraded (as a diode) to ensure a more ohmic-like behaviour.

As the doping level is increased, the depletion region becomes narrower. This results in a large tunnelling current (equivalent to Zener breakdown in a p-n junction). Metal-semiconductor contacts that are not required to be rectifying are therefore made to very heavily doped regions, so that the breakdown voltage of the contact is small enough to be ignored in comparison with the voltage across the device itself. Note that this happens naturally with alloyed junctions, but has to be specially made with diffusion processes.

3.7 Thermoelectric coolers

Although current can flow freely across an ohmic contact, there is still a small energy difference between the electron levels on the two sides of the junction. Typically, this energy is given off – or absorbed – from the bulk material as heat.

Consideration of the energy diagram for a metal – n-type contact above, electrons must gain energy as they travel from the metal into the semiconductor, so heat is absorbed and the junction cools. Conversely, when electrons travel from the semiconductor to the metal they lose energy and the junction warms up. Recall that conventional current flow is opposite to the electron flow.

This of course happens at any junction between materials with different work functions (it is the thermoelectric, or Peltier, effect) but is particular useful in semiconductors not only because the energy differences are larger but also because semiconductors come

increasing doping levels

I

V

in two types and the energy differences can be arranged to add, rather than subtract as they do in metal-metal junctions.

The energy carried by one electron across a junction is the sum of the change in potential energy and the thermal kinetic energy of the electron, which for an n-type semiconductor is:

Hence the Peltier Coefficient between a metal and a semiconductor is: