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For the nano-LED device, the emission of light can be explained by the electroluminescence mechanism from a metal-semiconductor-metal junction formed by Ni and ZnO. The electroluminescence requires injection of electrons and holes into the semiconductor. The source of the carrier transport in metal-semiconductor junctions needs to be investigated. In this chapter, the three main components of electron transport in Schottky diodes will be presented.
Electroluminescence is a light emission phenomenon caused by the electric current passing through a material. In semiconductors, electrons can be accelerated by a strong electric field. Electrons and holes will be excited and separated by the energetic electrons. When electrons and holes recombine in the material, the energy of the excited electrons will be released in the form 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 function qΦm is in contact with a semiconductor with work function qΦs (Φm > Φs), charge will transfer until the Fermi levels align at equilibrium. The electrostatic potential of the semiconductor is raised relative to that of the metal. A depletion region W is formed near the junction. In the depletion region, the positive charge due to uncompensated donor ions matches the negative charge on the metal. The equilibrium contact potential V0 will prevent electron diffusion into the metal from the semiconductor. The potential barrier height ΦB for electron injection into the semiconductor from the metal equals to Φm - χ, where qχ is the electron affinity. and are the Fermi level energy of the metal and the semiconductor. and are the conduction band and valance band energy of the semiconductor75.
Figure 4-1. A Schottky barrier formed by contacting an n-type semiconductor with
a metal (a) band diagrams of the metal and semiconductor before
contacting; (b) band diagram for the junction at equilibrium.
When a Schottky barrier is under forward or reverse bias, the contact potential will change (Figure 4-2). When a forward-bias is applied to the Schottky barrier, the contact potential is reduced to V0 - V. Electrons in the semiconductor conduction band can diffuse across the depletion region into the metal. Contrarily, the barrier height will increase by a reverse bias, which makes electron flow from semiconductor to metal negligible75.
Figure 4-2. Forward and reverse bias on a Schottky barrier:
(a) forward bias; (b) reverse bias.
The transport of electrons in a Schottky diode consists of three components: thermionic emission, field emission and thermionic-field emission76. Figure 4-3 shows the qualitative current flow in a Schottky diode under bias.
Figure 4-3. Energy-band diagram showing currents flow in a Schottky diode
under bias: (a) forward bias; (b) reverse bias. TE = thermionic emission.
FE = field emission. TFE = thermionic-field emission
Electrons transported by these three mechanisms together contribute to the current flow in the Schottky diode.
4.1 Thermionic Emission Theory
Thermionic emission is charge carriers flow over a potential-energy barrier caused by the temperature. In ordinary condition, free electrons in the metal cannot leave the metallic surface. They are attracted by a strong force called surface barrier energy (EB). When the temperature increases, some of the electrons inside the metal would obtain sufficient kinetic energy to overcome the surface barrier. The energy that needed for the emission of electrons to take place is the work function (W), that is
In the equation, EF is the Fermi level of energy of the metal. The relation between the number of electrons emitted by a unit area of the metallic surface and the temperature of the emitting materials is derived by Richardson and Dushman on the basis of Fermi-Dirac Statistics as in the equation below:
where J is the thermionic emission current density, is the emission constant, T is the temperature, W is the work function of metal, k is the Boltzman constant, e is the electron charge, m is the electron mass, and h is the Plank's constant. The emission constant is the same for all the metals but the work function varies from metal to metal77.
For a Schottky barrier formed in a metal-semiconductor junction, thermionic emission theory is applied as well. The theory assumes that the energetic carriers, which have the energy larger than that at the interface of the junction, will cross the barrier and contribute to the current flow76.
When a forward bias is applied to the Schottky barrier, the contact potential between the metal and the semiconductor is decreased. As can be seen in Figure 4-1-1, mobile electrons will flow from semiconductor to the metal, which result in the great increase in the cross barrier current. At the same time, a constant cross barrier electron flow from metal to semiconductor occurs since the potential barrier height (ΦB) is not affected by the applied bias, but the resulting current is relatively small in the case of forward bias76.
Figure 4-1-1. Thermionic emission in a Schottky barrier that is forward biased.
When the Schottky barrier is reverse biased, the cross barrier current attributed to electron flow from semiconductor to metal will decrease a lot, whereas the metal to semiconductor electron flow become visible as the saturation current76. Figure 4-1-2 shows the thermionic emission in a reverse biased Schottky barrier.
Riverse bias TE.png
Figure 4-1-2. Thermionic emission in a Schottky barrier that is reverse biased.
The cross barrier current density from semiconductor to metal () is restricted by the concentration of electrons with kinetic energy (E) sufficient to surpass the barrier in the direction (x) of transport:
where is the minimum energy required for thermionic emission into the metal, is the carrier velocity in the direction of transport. The electron density between and is given by:
is the density of states and is the effective electron mass;
is the Fermi-Dirac distribution function and . Assuming all the energy of electrons in the conduction band is kinetic energy, then:
The electron density is given by:
The above equation describes the number of electrons per unit volume that have velocities between and distributed over all directions. By resolving the velocity into its components along the axes with the x-axis parallel to the transport direction, we have:
The velocity is the minimum velocity required in the x direction to surmount the barrier, which is given by:
and is the effective Richardson's constant. Since there is no net current flow at equilibrium, the cross barrier current density from semiconductor to metal () should be exactly opposite to the when V=0, which is:
Therefore, the total current density equation of the thermionic emission () for a metal-semiconductor junction is:
It can also be written as:
where is the barrier height dependent thermionic emission component76. In Equation 4.19, the exponential term describes the electron flux from semiconductor to metal and the -1 term describes the electron flux from metal to semiconductor.