Characterization and Modeling Analysis for Metal-Semiconductor-Metal GaAs Diodes with Pd/SiO2 Mixture Electrode

Characterization and modeling of metal-semiconductor-metal (MSM) GaAs diodes using to evaporate SiO2 and Pd simultaneously as a mixture electrode (called M-MSM diodes) compared with similar to evaporate Pd as the electrode (called Pd-MSM diodes) were reported. The barrier height (φ b) and the Richardson constant (A*) were carried out for the thermionic-emission process to describe well the current transport for Pd-MSM diodes in the consideration of the carrier over the metal-semiconductor barrier. In addition, in the consideration of the carrier over both the metal-semiconductor barrier and the insulator-semiconductor barrier simultaneously, thus the thermionic-emission process can be used to describe well the current transport for M-MSM diodes. Furthermore, in the higher applied voltage, the carrier recombination will be taken into discussion. Besides, a composite-current (CC) model is developed to evidence the concepts. Our calculated results are in good agreement with the experimental ones.

In addition, Chiu et al. [19][20][21][22] reported a new MSM hydrogen sensor with two multifinger Schottky contacts. Unlike conventional MS and MOS diodes, a mixture of palladium and silicon dioxide (SiO 2 ) is deposited upon the semiconductor layer. Compared to commonly used MS and MOS diodes, M-MSM diodes obtained excellent performance of high sensitivity. However, the currentvoltage (I-V) curve represents the diode current operated as sensor in N 2 . I-V curve for M-MSM diodes differ from one for MS diodes in that the former exhibit the multiple-step phenomenon, while the latter are not. The reason of causing the multiple-step phenom-enon is very interesting but there are no descriptions in Chiu et al. reported [22]. In this paper, characterization and modeling of M-MSM GaAs diodes were reported. The w b and the A* were determined by a deduced equations from the I-V curve that operated at various temperature. The carrier over both the metalsemiconductor barrier and the insulator-semiconductor barrier are considered simultaneously on the thermionic emission process that can be used to describe well the current transport for M-MSM diodes. With increasing the applied voltage, the number of minority carrier at the semiconductor surface is larger than of the majority carrier. The carrier recombination will be taken into consideration. Furthermore, a composite current (CC) model is developed to evidence the concepts. The calculated results are in good agreement with the experimental ones. Finally, conclusions were made.

Device Structure and Fabrication
The epitaxial structure was grown on a (100)-oriented GaAs substrate by LP-MOCVD. It consisted of a 0.6 mm n + -GaAs layer, and a 0.8 mm n-GaAs layer with 8610 16 cm 23 doping concentration. The process started with mesa isolation. HCl was used to remove the native oxide on the 0.8 mm n-GaAs layer after a device mesa. Two multiple-fingers Schottky electrodes forming a MSM diodes were implemented by thermally depositing a 30 nm mixture with various weight-ratios of Pd to SiO 2 . Both the finger width and the finger-to-finger spacing are 5 mm. The area of the multiple-fingers electrode was A < 8610 24 cm 2 . Another MSM diodes with a 30 nm Pd directly deposited upon the GaAs layer was also fabricated for comparison. Device measurement was carried out by a custom-made 235 ml flow-through test chamber made from stainless steel and filled with the 99.99% nitrogen gas at a flow rate of 500 sccm. Fig. 1 shows the schematic views for the finally fabricated M-MSM diodes.

Determination of Barrier Height and Richardson Constant
I-V curves of Pd-MSM diodes at various temperatures in the range of 300 K to 330 K are shown in Fig. 2. The solid symbols are the calculated results. Because the quality of the epitaxial wafer and the evaporative Pd are excellent and uniform, all curves indicate bidirectional and symmetrical. The thermionic-emission process for carrier and the image-force lowering are considered simultaneously on the current of Pd-MSM diodes (I Pd ), I Pd can be expressed as [23].
where A* = 8.9 A/k-cm 2 is the Richardson constant for GaAs and be given by and w b = 0.80 eV is the barrier height and be given by Other parameters of A < 861024 cm2, T = 300 K to 330 K, q = 1.6610219 C [23], k = 1.38610223 J/K [23], N d = 861016 cm23, e o = 8.85610214 F/cm [23], e S ' = 10.8, e S = 12.9 [23], Vn = 0.05 V, V = 0 V to 5V are the contact area, an absolute temperature, the unit electronic charge, the Boltzmann constant, the doping concentration, the permittivity of free space, the relative permittivity of GaAs near the Pd, the relative permittivity of GaAs, the Fermi potential from conduction-band edge, and an applied voltage, respectively. Following the previous article [24], the electron approaches the metal with the thermal velocity, and one might except that there is not enough time for the semiconductor to become fully polarized by the electric field, so that e S ' is less then e S . For our calculation in Fig. 2, the results are also represented with a good agreement found. This means that the I Pd together with the extracted device-parameters is very promising for well describing for Pd MSM diodes behaviors.

Experimental Performance and Modeling Deducing
Unlike the Fig. 2 represented I Pd , Fig. 3 shows I-V curves with a multiple-step phenomenon of M-MSM diodes with the mixture electrodes in the weight-ratio of SiO 2 to Pd equal to 1/3 at various temperatures in the range of 300 K to 330 K. The solid symbols are the calculated results. In order to probe into the multiple-step phenomenon in I-V curves, Fig. 4(a) where the effective oxide-contact area is A ox <5.1061024 cm2. The e i = 3.56 [23] and the d = 30 nm are the relative permittivity and the thickness of mixture, respectively. Other parameters are the same as IMS. To notice Fig. 4 (d), lnw b against V represents a straight line with the applied voltage larger then 4 V. When a larger voltage is applied (.4 V), the bands bend even more downward so that the intrinsic level Ei at the surface crosses over the Fermi level EF. At this point the number of holes (minority carriers) at the surface is larger then that of the electrons, the thermionic-emission of electrons will be recombined by holes and the current is proportional to qV/gkT. Therefore, the current component of recombination (IRB) is considered on IM. The current IRB can be expressed as [23] I RB~IRBS : e qV gkT ð6Þ where IRBS = 4.81610216 A, and g = 8.1 are the saturation current of recombination, and an ideality factor, respectively. Then, IM can be approximated by the sum of Eqs. 4, Eqs. 5, and Eqs. 6. In Fig. 3, calculated results at various temperatures are also included with a good agreement found. This means that IM together with the extracted parameters is very promising for well describing M-MSM diodes behaviors. Figure 5(a) shows I-V characteristics of M-MSM diodes with the mixture electrodes in various weight-ratios of SiO 2 to Pd. I-V characteristic of Pd-MSM diodes is also shown for comparison. I M that were marked by solid symbol together with the extracted parameters are shown in Fig. 5(b). I M together with the extracted parameters is very promising for well describing the experimental results.
On the other hand, e s ' and e i associated with the mixture in various weight-ratios of SiO 2 to Pd are the key parameters and play an important role on the performance of M-MSM diodes. For simplifying the calculation of the relative permittivity, the composition of mixture is uniform for assumption. Fig. 6 shows the schematic view of Pd/SiO 2 mixture electrode for M-MSM diodes. e s ' is proportional to the ratio of A Pd and A ox . So the effective relative permittivity of GaAs near the mixture (e 0 s,eff ) can be calculated as  Consideration of equivalent circuit, the capacitance of mixture can be expressed as  Fig. 7. e s ' and e i are also shown for comparison. Consideration of boiling point of Pd (2963uC) more then SiO 2 (2230uC), the actual weight-ratio of SiO 2 and Pd is larger than the prepared weight-ratio of SiO 2 to Pd after evaporation.

Conclusions
In summary, characterization and modeling of MSM GaAs diodes using to evaporate SiO 2 and Pd simultaneously as the mixture electrode were investigated. Effects of operating at various temperatures and a mixture with the various weight-ratios of SiO 2 to Pd on electrical performances were investigated. w b and A* were determined to the thermionic emission process to describe well the current transport for Pd-MSM diodes in the consideration of the carrier over the metal-semiconductor barrier. In addition, in the consideration of the carrier over both the metal-semiconductor barrier and the insulator-semiconductor barrier simultaneously, thermionic emission process can be used to describe well the current transport for M-MSM diodes. Furthermore, in the higher applied voltage, the number of minority carriers at the semiconductor surface is larger then of the majority carrier. The carrier recombination will be taken into discussion. Besides, I M was developed to evidence the concepts. Our calculated results are in good agreement with the experimental ones.

Author Contributions
Conceived and designed the experiments: SWT. Performed the experiments: SWT. Analyzed the data: SWT. Contributed reagents/materials/ analysis tools: SWT SWL. Wrote the paper: SWT.