Chapter 3 Result and Discussion
3.3 Mechanism
In this chapter, we will discuss density of states (DOS) in the amorphous silicon and back channel effect in the a-Si TFTs.
1. Density of states (DOS) in the amorphous silicon
In a-Si film, defects are uniformly distributed over the film volume. The crystalline order is lost within a distance of the order of the lattice parameter. This results in the modification of band structure. The energy gap of a-Si is 1.5eV, compared to 1.1 eV of single crystal silicon. The lack of a long-range order also implies that some of the bonds are unsaturated, that is, dangling. In practice, a
concentration of dangling bonds in the material is not avoidable. Reconstructed bonds can form among dangling bonds. Both dangling and reconstructed bonds give rise to electronic energy levels in the energy gap, and the dangling bond states are believed to be located near mid-gap [35] (Figure 3-31). Other gap states can be introduced purely as a consequence of the random fluctuations of the crystalline potential. These states (disorder-induced localized states) are located at energies close to the conduction and valence bands, and they constitute the so-called band tails [35]
(Figure 3-31). As a results, the energy gap is occupied with a continuum of states, and is described by the DOS function N(E), which is expressed in cm-3eV-1.
The a-Si:H TFT operation theory [36] (Figure 3-32) is very different from crystal silicon MOSFET. When no voltage is applied, the energy bands are closed to the flat band condition. If a gate voltage, which is positive but less than threshold voltage, the Fermi level moves through the deep states, which are occupied. Meanwhile, some space charges locate in the tail band and the occupancy of these states is low, since they are above the Fermi level. Thus, the deep states dominate the total space charge.
The small fraction of the band tail electrons above the conduction band mobility edge makes the increasing of source-drain current. The space charges in the deep states increase in proportion to the increase in the gate voltage, but the current increases exponentially as the band bending increases. Above the threshold voltage, the space charge in the band tail states exceeds the space charge in the deep states, even though the Fermi level is still below the tail states. Now, both the total space charge and the source-drain current increase linearly with the applied gate voltage and we have a well define filed effect mobility. The mobility is thermally activated with an activation energy given by the width of the tail states, not by EC-EF.
As mentioned above, we know that the Fermi level shift with the gate voltage is strongly dependent on the density of states (DOS). At high density of states more carriers must be induced in order to fill the states from EF upward. Therefore, it is necessary to apply higher gate voltage in order to induce more carriers in the channel.
easily filled at low concentration of the induced charge and the Fermi level is easily shifted at low gate voltages. From correlation between the DOS and the gate voltage allows obtaining the shape of the density of states by studying the dependence of Ea
vs. Vg.
The information on DOS shape is important for understanding the physical mechanisms responsible for the device behaviors. The DOS shape is related to the threshold voltage, subthreshold swing, and field effect mobility of the TFTs.
2. Back channel effect in the a-Si TFTs
Figure 3-33 depicts the leakage characteristics of the TFT [37]. Here, we identify three distinguishable regions, which are characterized by ohmic conduction, front channel conduction and conduction at the back interface. The relative dominance of each mechanism is determined by bias conditions and device geometry, and is elaborated in the reference paper [37]. Here, we discuss the reverse subthreshold region (back channel region).
When we apply low positive (or negative) gate voltages, the drain-source current changes exponentially with the gate-source voltage [37]. This region is known as the subthreshold region, either for forward and reverse regimes of operation. At low positive VGS, the accumulation of electrons at the front a-Si:H / a-SiNx:H interface is responsible for subthreshold conduction, whereby the TFT’s drain-source current varies exponentially with the gate voltage. The extension of the band bending at the interface into the bulk a-Si:H layer provides a low concentration of free electrons, which in turn enables conduction by virtue of diffusion. As the gate voltage is decreased to zero and to low negative values, this accumulation of electrons at the front interface decreases only to leave behind electrons at the back a-Si:H / a-SiNx:H interface, which now become responsible for the reverse subthreshold behavior (conduction at the back interface). As the gate voltage is decreased further to high negative VGS, there is a growing accumulation of holes at the front interface. The
conduction of this front hole channel is responsible for the exponential increase in the current at high negative gate and high positive drain voltages (Figure 3-33). The current is limited by field-enhanced generation of holes at the gate-drain overlap vicinity by virtue of the Poole-Frenkel effect.
At low negative VGS, the presence of electrons at the back interface and the extended band bending in the bulk a-Si:H provides a conduction path for leakage [37].
The density of electrons at the back interface is dependent on the applied gate voltage.
An increase in the negative gate voltage decreases band bending and thus the electron density at this interface. Therefore, the charge at the back interface can be reduced to zero from its initial negative value (electrons) and can then become positive (holes) by virtue of the negative gate voltage.
Figure 3-34 shows the band diagram for an arbitrary cross section of the TFT in the middle of the channel, which illustrates the accumulation of electrons at the back interface. At low negative VGS, Gauss’ Law yields for the electric field (ESi) in the a-Si:H at the back interface
( )
Here, q denotes the elementary charge, εSi the dielectric constant of a-Si:H, the density of interface states,DSSb ψSb the band bending, and ψSb0 the no-voltage band bending at the back interface. The applied voltage Va can be written as
(3-2) Where Vi is the voltage drop over the gate insulator and
(3-3) Here, φ is the gate metal work function, M χS the electron affinity in a-Si:H, and the difference between the conduction band edge and the intrinsic Fermi-level in a-Si:H. Gauss’ Law for the electric field (E
ECFn
SS) at the front interface gives
2
(
0)
Where Ci is the gate dielectric capacitance per unit area, DSSf is the density of interface states, ψSf is the band bending at the front interface and ψSf0 is the zero-voltage band bending at the front interface. Reference paper [37], we can get the following equation At low negative VGS, the trapped carriers at the interface are much higher than those trapped in the donor-like tail states. The reduces above equation to
Above equation shows the effect of the applied voltage on the band bending at the two interfaces. Then, we substitute below equation into above equation. The voltage drop (VSi) across the a-Si:H layer is
(
Sb Sb SiThe current density Jch in the back channel due to the presence of free electrons,
is
Where nfree is the density of free electrons, μn is the effective mobility of electrons in the a-Si:H bulk, Efn is the quasi Fermi level of electrons, and x is the position. The density of free electrons can be written as
T T
Where NC is the density of free carriers at the conduction band edge and VT is the thermal voltage. Integrating Jch over the channel thickness yields the total current at the back interface (IBC), as Here, δ is the thickness of the electron accumulation layer close to the back interface. Then, calculates above equation and refers to paper [37], we can get the following equation Where, Sr denotes the reverse sub threshold slope and γn is a fitting parameter.
Comparing the slopes of the current-voltage characteristics in the reverse and forward subthreshold regimes, the density of states at the back and front interfaces can
be obtained. However, the front interface has an interface state density that is smaller by a factor of three only compared to the back interface.
T
From above equation, we also know that the density of back interface states (Dssb) is lesser, reverse subthreshold swing (Sr) is smaller.