Electroluminescence is a light emanation phenomenon caused by the electric current passing through a stuff. In semiconducting materials, negatrons can be accelerated by a strong electric field. Electrons and holes will be excited and separated by the energetic negatrons. When negatrons and holes recombine in the stuff, the energy of the aroused negatrons will be released in the signifier of photons45.

When Ni and ZnO are brought together, a Schottky barrier is formed. As can be seen in Figure 4-1, when a metal with work map q?m is in contact with a semiconducting material with work map q?s ( ?m & A ; gt ; ?s ) , charge will reassign until the Fermi degrees align at equilibrium. The electrostatic potency of the semiconducting material is raised comparative to that of the metal. A depletion part W is formed near the junction. In the depletion part, the positive charge due to unsalaried donor ions matches the negative charge on the metal. The equilibrium contact possible V0 will forestall negatron diffusion into the metal from the semiconducting material. The possible barrier height ?B for negatron injection into the semiconducting material from the metal peers to ?m – ? , where q? is the negatron affinity. and are the Fermi degree energy of the metal and the semiconducting material. and are the conductivity set and cornice set energy of the semiconductor75.

Figure 4-1. A Schottky barrier formed by reaching an n-type semiconducting material with

a metal ( a ) set diagrams of the metal and semiconducting material before

contacting ; ( B ) set diagram for the junction at equilibrium.

When a Schottky barrier is under forward or contrary prejudice, the contact potency will alter ( Figure 4-2 ) . When a forward-bias is applied to the Schottky barrier, the contact potency is reduced to V0 – V. Electrons in the semiconducting material conductivity set can spread across the depletion part into the metal. Contrarily, the barrier tallness will increase by a contrary prejudice, which makes negatron flow from semiconducting material to metal negligible75.

Figure 4-2. Forward and change by reversal prejudice on a Schottky barrier:

( a ) forward prejudice ; ( B ) contrary prejudice.

The conveyance of negatrons in a Schottky rectifying tube consists of three constituents: thermionic emanation, field emanation and thermionic-field emission76. Figure 4-3 shows the qualitative current flow in a Schottky rectifying tube under prejudice.

Figure 4-3. Energy-band diagram screening currents flow in a Schottky rectifying tube

under prejudice: ( a ) forward prejudice ; ( B ) contrary prejudice. TE = thermionic emanation.

FE = field emanation. TFE = thermionic-field emanation

Electrons transported by these three mechanisms together contribute to the current flow in the Schottky rectifying tube.

## 4.1 Thermionic Emission Theory

Thermionic emanation is charge bearers flow over a potential-energy barrier caused by the temperature. In ordinary status, free negatrons in the metal can non go forth the metallic surface. They are attracted by a strong force called surface barrier energy ( EB ) . When the temperature increases, some of the negatrons inside the metal would obtain sufficient kinetic energy to get the better of the surface barrier. The energy that needed for the emanation of negatrons to take topographic point is the work map ( W ) , that is

. ( 4.1 )

In the equation, EF is the Fermi degree of energy of the metal. The relation between the figure of negatrons emitted by a unit country of the metallic surface and the temperature of the emitting stuffs is derived by Richardson and Dushman on the footing of Fermi-Dirac Statistics as in the equation below:

, ( 4.2 )

where J is the thermionic emanation current denseness, is the emanation invariable, T is the temperature, W is the work map of metal, K is the Boltzman invariable, vitamin E is the electron charge, m is the negatron mass, and H is the Plank ‘s invariable. The emanation invariable is the same for all the metals but the work map varies from metal to metal77.

For a Schottky barrier formed in a metal-semiconductor junction, thermionic emanation theory is applied as good. The theory assumes that the energetic bearers, which have the energy larger than that at the interface of the junction, will traverse the barrier and contribute to the current flow76.

When a forward prejudice is applied to the Schottky barrier, the contact potency between the metal and the semiconducting material is decreased. As can be seen in Figure 4-1-1, nomadic negatrons will flux from semiconducting material to the metal, which result in the great addition in the cross barrier current. At the same clip, a changeless cross barrier electron flow from metal to semiconducting material occurs since the possible barrier tallness ( ?B ) is non affected by the applied prejudice, but the resulting current is comparatively little in the instance of forward bias76.

Figure 4-1-1. Thermionic emanation in a Schottky barrier that is frontward biased.

When the Schottky barrier is rearward biased, the cross barrier current attributed to electron flow from semiconducting material to metal will diminish a batch, whereas the metal to semiconducting material negatron flow become seeable as the impregnation current76. Figure 4-1-2 shows the thermionic emanation in a contrary biased Schottky barrier.

Figure 4-1-2. Thermionic emanation in a Schottky barrier that is reverse biased.

The cross barrier current denseness from semiconducting material to metal ( ) is restricted by the concentration of negatrons with kinetic energy ( E ) sufficient to excel the barrier in the way ( x ) of conveyance:

, ( 4.3 )

where is the minimal energy needed for negatrons to shoot into the metal because of thermionic emanation, is the bearer speed in the way of conveyance. The negatron denseness between and is given by:

, ( 4.4 )

where

( 4.5 )

is the denseness of provinces and is the effectual negatron mass ;

( 4.6 )

is the Fermi-Dirac distribution map and. Assuming all the energy of negatrons in the conductivity set is kinetic energy, so:

, ( 4.7 )

, ( 4.8 )

. ( 4.9 )

The negatron denseness is given by:

, ( 4.10 )

The above equation describes the figure of negatrons per unit volume that have speeds between and distributed over all waies. By deciding the speed into its constituents along the axes with the x-axis analogue to the conveyance way, we have:

, ( 4.11 )

, ( 4.12 )

. ( 4.13 )

The speed is the minimal speed required in the ten way to overcome the barrier, which is given by:

. ( 4.14 )

Using

, ( 4.15 )

we have:

, ( 4.16 )

and is the effectual Richardson ‘s invariable. Since there is no net current flow at equilibrium, the cross barrier current denseness from semiconducting material to metal ( ) should be precisely opposite to the when V=0, which is:

. ( 4.17 )

Therefore, the entire current denseness equation of the thermionic emanation ( ) for a metal-semiconductor junction is:

. ( 4.18 )

It can besides be written as:

, ( 4.19 )

where is the barrier height dependent thermionic emanation component76. In Equation 4.19, the exponential term describes the negatron flux from semiconducting material to metal and the -1 term describes the negatron flux from metal to semiconducting material.