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As discussed in section 3.3, according to thermionic emission equation for Schottky diode, at forward biased, the current can be expressed as (Sze, 1981):
Valid for V >3kT/q
where is the applied voltage, q is the electronic charge, kT is the thermal energy and is the saturation current defined equation 3.22 as:
Where is the diode area, is the Schottky barrier height, is the effective Richardson constant and was calculated to be 1.19 x105AK-2m-2 by using a value of 0.11 for the effective electron mass/free electron mass ratio for CdTe. The ideality factor 'n' was defined in equation 3.24 as:
Saturation current introduced to describe the experimental semi log I-V curve data from the thermionic emission theory using ideality equation. The ideality factor n of the diode was calculated from the slope of the linear region of the semi log I-V curve. Using equation 3.23, the zero biased barrier height was determined from the saturation current that was obtained from the intercept of the extra plotted linear region with current axis at = 0.
The values for both n and are listed in Table 4.1 for junctions at various times after formation (while at room temperature) and in Table 4.2 for a sample which was subjected to a series of annealing treatments in vacuum at 150C°.
In Figure 4.1 the logarithmic dependence of Current with forward biased voltage is seen to extended over more than five order of magnitude allowing 'n' to be easily deduced from the gradient. Any interfacial oxides layer resulting from exposure of the semiconductor surface to the atmosphere between growth and metallization would have the effect of making ideality factor a voltage dependent parameter rather than a constant (Rhoderick and Williams, 1988). The linearity observed in Figure 4.1 clearly shows that any existing interfacial layer must be insignificant thickness and value for 'n' which was deduced from Figure 4.1 being close to 1 indicated the cross barrier transport process in predominantly via thermionic emission.
According to Pattabi et al. (2007) an ideality factor greater than unity is generally attributed to the presence of a bias dependent Schottky barrier height. Image forces, tunneling, generation-recombination, interface impurities and interfacial oxide layer are possible factors which could lead to a higher ideality factor. The ideality factor represents a direct measure of interface uniformity.
This trend in behavior due to annealing for sample 228F, with an initial rapid fall in the barrier height being followed by lower changes and greater stability is clearly similar to that observed for sample 228A which remained at room temperature for four weeks. It was noted above that this behavior must be due to chemical reaction or diffusion processes in the region of the M/S interface. This suggests that the processes which influence the barrier height may be due to some out-diffusion from the interior of the semiconductor to its surface. Clearly they are not dependent on the presence of the gold layer although some interaction between the Au contact and the underlying semiconductor is expected to occur (Dharmadasa et al., 1989; Van Meirhaeghe et al., 1991).
Although Au is a p-type dopant in CdTe, the data in table 4.1 and 4.2 indicates that the changes in interface characteristics are not dependent on the presence of Au during the process of annealing. An alternative explanation is that there is an outward diffusion of Cd (similarly leading to the generation of acceptor states near-surface region).This interpretation of the results is entirely agreement with the conclusion reached by Dharmadasa et al. (1994) on the effect of chemical etch treatments. Those etchants which were found to leave the surface rich in Cd tended to produce barrier heights greater than 0.9 eV while those leaving the surface deficient in Cd produced barrier heights which were ~ 0.2 eV lower, as found in the case of the annealed samples studied in this project. Thus, it is clear that interface reaction lead to a substantial change in the defect structure in the vicinity of the junction but further work will be necessary to determine the exact structure of the defects states which might be responsible for Fermi level pinning before and after the reaction and the associated reduction in barrier height.
5.2 Effect of Ion Plating Technique
Table 4.3 shows data from I-V characteristics as a function of ion etching time. A drastic change in I-V characteristics of ion-plated Au/n-CdTe Schottky barriers samples (228C, 228D, 228E) was observed. A gradual upward shift in graphical lines of I-V characteristics of these samples was observed with increasing ion etching time as shown in Figures 4.2, 4.3, and 4.4.
The effect of different ion etching time suggests that a substantial density of defects has been created below the Au contacts as a result of ion bombardment of the surface during the plating process. The presence of defects in the depletion region, acting as recombination centers, leads to an additional forward bias current component with an ideality factor of approximately 2 (Shah et al., 2003)
As can be seen from Figure 4.4, there is a linear relationship between the barrier height and ideality factor i.e. the barrier height becoming smaller as the ideality factor increases. Change in ideality factor indicates that current transport mechanisms other than thermionic emission are present. As this value of n is significantly greater than 2 (Table 4.3), as would be expected for a carrier recombination mechanism, as discussed earlier, it seems probable that carrier tunneling may also be playing a role (Popovic, 1978). It is not expected that a simple tunneling process would be operating in the case of samples with doping densities of 1015-1017 cm-3.The net doping density in CdTe was too low for tunneling (it require> 1017cm-3) (Padovani and Stratton, 1966), but it is possible for electron to tunnel via ladder of closely spaced states in depletion region to combine with holes i.e. multi step tunneling (Ercelebi et al., 1990; Ou, et al. 1984, Ay and Tolunay, 2007).
These results indicate that the possible effect of plasma-induced surface defects is that they contribute to the conductivity of the contact by acting as fast recombination centers (Ponon, 1985) along with multi step tunneling centers. This suggests that it might be a useful way of farming low resistance (ohmic) junction using a lower work function metal.
5.3 Effect of Different Doping Concentrations
The ideal I-V characteristics of a Schottky diode exhibits exponential bias dependence as described in section 3.3 can be reduced to
For v > 3kT/q
The magnitude of this saturation current is governed by the effective barrier height i.e. the difference between the conduction band minimum (CBM) at the surface of Au/n-CdTe and the Fermi level of the metal (Au).
The value of the barrier height can be calculated from the measured saturation current using equation 3.22:
Deviation from this ideal behaviour can be seen in Figures 4.6, 4.7, and 4.8.Those deviations are attributed to image force lowering (IFL), recombination phenomena due to the presence of deep traps and the existence of high electric field (Martin, 1981).Table 4.4 shows barrier height and ideality factor 'n' deduced from I-V characteristics on CdTe Schottky diodes for different doping concentration ranges 2.3-1016-1-1018 cm−3.
Figure 4.10 shows a linear relationship between and 'n' which is very similar to Fig. 4.5 i.e. for ion plated samples. It has been demonstrated theoretically and experimentally that the linear relationship between and 'n' can be attributed to the lateral inhomogeneties of the barrier height in Schottky diodes. According to Tung's model (Tung, 1992), the Schottky barrier consists of laterally inhomogeneous patches of different barrier heights. The patches with lower barrier height have larger ideality factors and vice versa. The presence of traps also modifies the slope of the forward current and at the same time the value of the ideality factor, which is higher than unity for both samples (low and high doped sample) (Koutsouras et al., 2005).
Figure 5.1: A Schematic diagram showing the reduction of M/S barrier height
due to band-gap narrowing.
With increasing dopant concentration, the width of the depletion region '' i.e. given by relation given in Eq.3.11:
at a given bias decreases leading to higher electric fields at the interface. Low barrier or effective barrier height rather than observed, for low and heavily doped sample (549E, 549F), which is the reason for the higher slop under reverse bias for doped samples. However, the enhanced recombination rate due to the presence of deep trap levels also contributes generation and recombination effect and can not be excluded.
With heavier doping, increasing number of new donor-type energy levels are created underneath the conduction band edge. Under these circumstances, the donors are so close together that the donor levels are no longer discrete and non-interacting energy levels. These are rather degenerate merging together to create an impurity bond, and causing band-gap narrowing (BGN) of the conduction band. Obviously, the BGN is the highest near M/S interface, and the lowest in the bulk. The effective M/S barrier height is thus reduced, as shown schematically in Figure 5.1 (Noor Mohammad, 2004).
The sharp tip of the conduction band edge in contact with the metal is particularly lowered, and the new barrier height becomes , where is the barrier height without BGN, and is the barrier height with BGN. However, a much more resistance arises from the CdTe/InSb junction. It has been shown that there is a potential barrier at this interface, associated with a conduction band discontinuity of ~0.31 eV (Van Welzenis and Ridley, 1984).
From a detailed analysis of I-V characteristics for gold-contacted devices with similar dimensions to those in present study, effective resistance value of ~100Ω have been deduced for the CdTe/InSb junction region (Sands and Scott, 1995). According to the thermionic emission theory, the contact resistivity at the M/S contact depends only on the effective M/S barrier height, as given by (Sze, 1981)
Where S is the contact area; q, K and T are electronic charge, Boltzman constant and temperature respectively and is the Richardson constant (with a value of ~ 1.2 -105 Am-2K-2 for CdTe). is the resistance associated with the front metal/CdTe junction. According to Yousaf et al. (2000), assuming < 10Ω then < 0.1 Ωcm2 and the corresponding upper limit for effective barrier height is 0.38 eV which is consistence with studies of Al contacts on clean vacuum cleaved surfaces of CdTe which yielded barrier heights of ~ 0.1 eV (Patterson et al., 1981).
Almost all the previous investigation emphasized tunneling as the primary mechanism for low contact resistivity in n-CdTe. The present study dose not rule out the importance of tunneling in creating low contact resistivity. However, it demonstrates that, depending on how much is lower than , thermionic emission, rather than tunneling, may indeed be the primary cause for low contact resistivity even in the tunnel contacts. If the surface treatment is very good, and the metal parameter (e.g., metal thickness, metal deposition temperature, metal work function, metal combination, etc.) are optimum, then may be significantly lower than . This, together with BGN and IFL can then play a crucial role for yielding thermionic emission based low contact resistivity.
The following conclusions can be reached from the studies on the effects of annealing time and temperature, ion plating technique and different doping concentration in range of 2.3-1016-1-1018 cm−3 on I-V characteristics of the Au/n-CdTe Schottky barrier diodes samples:
Gold contact formed to n-CdTe by vacuum evaporation yield Schottky barriers with initial barrier height in excess of 0.88-0.95 eV. This reduced to 0.66-0.68 eV in a period of time which is dependent on temperature. This reduction is found to be accompanied by a partial compensation of the sallow donors in the semiconductor region close to the contact, a process which can be attributed to a preferential out diffusion of Cd from this region to the contact surface.
It has been shown that the use of simple vapour deposition on Au on n-type CdTe epilayers gave rectifying behaviour with barrier height 0.90 eV. A drastic change in barrier height was observed by the use of ion-assisted plasma process, an ion etching time of 15-20 sec to Au contact. This reduction in barrier height is attributed to the plasma- induced surface defects that contribute to the high conductivity of the contact by acting as recombination centers along with multi step level tunneling centers.
The doping dependence of the barrier height and the ideality factor was observed by the results of I-V characteristics of Au/n-CdTe Schottky barriers for different doping concentration. The ideality factor increases with increasing carrier concentration and as a result barrier height decreases. This is due to the effect of the interfacial layer and interface states.
From Comparative study of ion plated and doped samples of Au/n-CdTe Schottky diode, a linear relationship between the effective barrier heights and ideality factors was found which shows that barrier height decreases as ideality factor increases. As a result conductivity increases. From which it can be concluded that:
When n = 1 then all transport of electron is from the top of the barrier and thermionic emission current mechanism should be dominant.
When 1< n < 2, then tunneling current mechanism is dominant.
When n = 2, then all transport is due to generation and recombination current.
When n > 4 then there is not simple tunneling but step level tunneling occurred.
Effect of doping in Au/n-CdTe Schottky diode shows that if n-CdTe is heavily doped with significant conduction band bending near M/S interface, tunneling is possible through metal/CdTe contact. The semiconductor region at the interface thus becomes very thin (i.e. BGN) allowing an unhindered flow of electrons via tunneling.
Effect of doping on I-V characteristics of Au/n-CdTe shows that barrier width (w) decreases with the increasing doping density in accordance with (Eq.3.11).
The main conclusion to be drawn from the comparative study of I-V characteristics of Au/n-CdTe Schottky barriers, formed by the ion-plating process and doping process, leads us to a much reduced contact resistance. This suggests that it might be a useful way of forming stable and low resistance (ohmic) junction. To form stable and low resistance (ohmic) junctions, a low work function metal (e.g., Al etc.) may be suitable for thin film MBE grown devices.
5.5 Recommendations for Future Work
The results obtained in determining the properties of Au/n-CdTe Schottky barriers by I-V characteristics lead to several possible future work that may be conducted:
More detailed study is necessary to determine the precise nature of the new interface of Au/n-CdTe contact and exact structure of defect states.
Many devices need low resistivity contacts without the burden of heavy doping. More detailed work is required on moderately doped semiconductors to achieve low resistive contact.
More detailed work is required to determine the properties of thermionic emission (TE) based low resistive contacts.