Conduction Mechanisms in Au/0.8 nm–GaN/n–GaAs Schottky Contacts in a Wide Temperature Range

Au/0.8 nm–GaN/n–GaAs Schottky diodes were manufactured and electrically characterized over a wide temperature range. As a result, the reverse current Iinv increments from 1 × 10−7 A at 80 K to about 1 × 10−5 A at 420 K. The ideality factor n shows low values, decreasing from 2 at 80 K to 1.01 at 420 K. The barrier height qϕb grows abnormally from 0.46 eV at 80 K to 0.83 eV at 420 K. The tunnel mechanism TFE effect is the responsible for the qϕb behavior. The series resistance Rs is very low, decreasing from 13.80 Ω at 80 K to 4.26 Ω at 420 K. These good results are due to the good quality of the interface treated by the nitridation process. However, the disadvantage of the nitridation treatment is the fact that the GaN thin layer causes an inhomogeneous barrier height.


Introduction
Metal-semiconductor (MS) contacts are very important in microelectronics [1][2][3][4]. They are used in optoelectronic devices, bipolar integrated circuits, high-temperature, and highfrequency applications [5,6]. The thermionic emission (TE) theory is the principal theory used to determine the parameters of the Schottky contact.
This deviation of the thermionic emission theory is corrected by introducing other mechanisms, operating at the Schottky barrier such as the thermionic field emission TFE and the emission field FE currents [5,11].
Therefore, the interface quality has an essential impact on device behavior and performance. In this context, surface passivation is the best method of controlling the defective states [27,30,31,[35][36][37][38][39]., Many studies on the nitridation of the GaAs surface have been carried out [27,30,37,38,[40][41][42][43] to improve the behavior and the electrical properties of the Schottky contacts (e.g., the ideality factor, barrier height, saturation current, series resistance and reverse current. Moreover, the nitride layers have good stability against the formation of amorphous surface oxides, high electronegativity, and thermal stability [27,44]. In this work, we measure the electrical characteristics of Au/0.8 nm-GaN/n-GaAs Schottky contacts fabricated by using a glow-discharge plasma source (GDS) for nitridation. Moreover, we analyze the current transport mechanisms, and several electrical parameters are characterized in a wide range of temperatures (80-420 K).

The Experiment
The Schottky contacts were elaborated using commercially available Si-doped n-GaAs (100) substrates, of a thickness of 400 µm and an electron concentration N d = 4.9 × 10 15 cm −3 . The samples were cleaned chemically using H 2 SO 4 , deionized water, cold and hot methanol sequentially and dried with N 2 . Then, the surfaces were bombarded with Ar+ ions of about 1 keV (a sample current equal to 5 µA cm −2 during 1 h) in UHV conditions [30,40]. After surface cleaning, the substrates were heated at 500 • C and nitrided using a glow discharge nitrogen plasma source, running at 5 W for 30 min in a UHV chamber (Institut Pascal, Clermont-Ferrand, France). This nitridation process led to the growth of a 0.8 nm-thick layer of undoped GaN. Following the nitridation step, the samples were annealed at 620 • C for 1 h to crystallize the GaN layer [39,45,46].
A XPS system characterized by a dual anode Al-Mg X-ray source (Institut Pascal, Clermont-Ferrand, France) and hemispherical electron energy analyzer (Institut Pascal, Clermont-Ferrand, France) were used for the in situ measurement of the chemical composition and crystal structure. The GaN thickness was calculated by comparing the experimental spectra data to the theoretical XPS peak intensities and positions [38]. The Au dots were deposited with area of 4.41 × 10 −3 cm 2 and thickened to 100 nm. A Bruker Dimension Icon atomic force microscope (AFM, Bruker, Cádiz, Spain) equipped with ScanAsyst and Nanoscope software 9.7 (ScanAsyst, Cádiz, Spain) was used to investigate the film surface roughness. Using the PeakForce tapping mode, AFM topography measurements were taken in the air. To accomplish this, a silicon tip on a nitride cantilever (ScanAsyst Air model, Cádiz, Spain), with a 0.4 N m −1 spring constant and a nominal tip radius of 2 nm were used to examine regions of 1 × 1 µm 2 with a resolution of 256 × 256 pixels. The current-voltage measurements were investigated under different temperatures (80-420 K), by a current source Keithely 220 (Laboratory of Physics of Materials and Nanomaterials Applied to the Environment, Gabès, Tunisia). stand out in the Figure 1a. This value of roughness (0.3 nm) is less than half the nomin GaN layer thickness (0.8 nm).

The Results
The roughness difference is better shown in Figure 1c where the frontier between th Au electrode and the GaN surface is shown as a rendered illuminated 3D AFM imag and the different topographies of Au and GaN are clearly shown. To bring out this d ference in roughness more clearly, the height distribution histograms shown in Figure 1 were obtained from the topography images. GaN exhibits a narrow peak, showing that comparison to Au, which has a larger peak, the surface layer is more homogeneous. T clarify the difference between the peaks, they have been fitted to a single Gaussian d tribution with a peak centered at 2.15, and 21.3 nm, and a full width at half maximu (FWHM) of 1.3 and 9.5 nm for GaN and Au, respectively. The roughness difference is better shown in Figure 1c where the frontier between the Au electrode and the GaN surface is shown as a rendered illuminated 3D AFM image, and the different topographies of Au and GaN are clearly shown. To bring out this difference in roughness more clearly, the height distribution histograms shown in Figure 1d were obtained from the topography images. GaN exhibits a narrow peak, showing that in comparison to Au, which has a larger peak, the surface layer is more homogeneous. To clarify the difference between the peaks, they have been fitted to a single Gaussian distribution with a peak centered at 2.15, and 21.3 nm, and a full width at half maximum (FWHM) of 1.3 and 9.5 nm for GaN and Au, respectively.
Surface roughness induces a non-uniformity of thickness, a distribution of interfacial charges, and a local variation of the Fermi level. These phenomena yield to the inhomogeneity of the Schottky barrier height and affect the transport mechanism [47]. Figure 2 depicts the I-V characteristics of the Au/0.8 nm-GaN/n-GaAs structure, at temperatures ranging from 80 to 420 K.
The values of the reverse current I Rev at −1 V and the threshold voltage V Th were extracted and illustrated in Figure 3. With increasing temperature, I Rev increased exponentially from 1 × 10 −7 A at 80 K to 1 × 10 −5 A at 420 K, and V Th decreased from 0.65 V at 80 K to 0.2 V at 420 K. The values of the reverse current IRev at −1 V and the threshold voltage VTh were extracted and illustrated in Figure 3. With increasing temperature, IRev increased exponentially from 1 × 10 −7 A at 80 K to 1 × 10 −5 A at 420 K, and VTh decreased from 0.65 V at 80 K to 0.2 V at 420 K.  The expression of the current for non-ideal Schottky diodes is [48]: where, is the saturation current; is the series resistance; ɸ is the bar height; n is the ideality factor; k is the Boltzmann constant; A is the effective diode a and * is the effective Richardson constant equal to 8.16 Acm K for GaAs. The expression of the current for non-ideal Schottky diodes is [48]: and where, I s is the saturation current; R s is the series resistance; qφ b is the barrier height; n is the ideality factor; k is the Boltzmann constant; A is the effective diode area, and A * is the effective Richardson constant equal to 8.16 Acm −2 K 2 for GaAs.
At the low bias voltage V, the current I is low, therefore the term IR s is low compared to V, and (Equation (1)) becomes and The n and I s values are calculated from the slope and y-intercept of ln(I)-V, respectively. The φ b value is determined as follows: The R s values are extracted using the Cheung and Cheung method [48] which is based on The extracted values of n and qφ b are plotted in Figure 4. The extracted values of n and ɸ are plotted in Figure 4. As can be seen from Figure 4, with the rising temperature, n dropped from 2 for 80 K to 1.1 for 420 K. The decrease was very slow from 250 K to 450 K, which is in accordance with the literature [5][6][7]11,26]. The low values of n may have been due to the effect of the nitridation process, which improves the quality of the interface. As the temperature rose, ɸ rose abnormally from 0.46 eV for 80 K to 0.83 eV for 420 K. These results were similar to several studies [7,12,20,[49][50][51]. For Schottky contacts, the ɸ value should decrease as the temperature rises, due to the bandgap's temperature variation [1,2,7,48,50,[52][53][54]. The ɸ behavior may be explained by tunnel effect mechanisms, such as thermionic field emission (TFE) [5,11].
The tunneling current can be expressed following [1,12,55,56] as  As can be seen from Figure 4, with the rising temperature, n dropped from 2 for 80 K to 1.1 for 420 K. The decrease was very slow from 250 K to 450 K, which is in accordance with the literature [5][6][7]11,26]. The low values of n may have been due to the effect of the nitridation process, which improves the quality of the interface. As the temperature rose, qφ b rose abnormally from 0.46 eV for 80 K to 0.83 eV for 420 K. These results were similar to several studies [7,12,20,[49][50][51]. For Schottky contacts, the qφ b value should decrease as the temperature rises, due to the bandgap's temperature variation [1,2,7,48,50,[52][53][54]. The qφ b behavior may be explained by tunnel effect mechanisms, such as thermionic field emission (TFE) [5,11].
The tunneling current can be expressed following [1,12,55,56] as where E 00 is the characteristic tunneling energy; h is the Planck constant; m * e is the effective mass of electron; and ε s is the dielectric constant of GaAs. Figure 5 shows the variation of (E 0 = nkT/q) versus kT/q. From Figure 5, E0 is about kT/q, which confirms that the TFE mechanism is domi-164 nant [26], not the theoretical mechanism TE of the Schottky contacts. This explains the 165 abnormal behavior of the barrier height and the deviation of the ideality factor from 166 unity. This may have been due to the interface states, which behaved as recombination-167 generation centers that affected the conduction mechanism [57]. 168 To further study the abnormal behavior of the barrier height, the Richardson char-169 acteristic ln(I / ) versus q/kT is presented in Figure 6 using the equation From Figure 5, E 0 is about kT/q, which confirms that the TFE mechanism is dominant [26], not the theoretical mechanism TE of the Schottky contacts. This explains the abnormal behavior of the barrier height and the deviation of the ideality factor from unity. This may have been due to the interface states, which behaved as recombination-generation centers that affected the conduction mechanism [57].
To further study the abnormal behavior of the barrier height, the Richardson characteristic ln(I s /T 2 ) versus q/kT is presented in Figure 6 using the equation Materials 2021, 14, x FOR PEER REVIEW 7 of 13 162 Figure 5. Variation of E0 (nkT/q) versus kT/q. 163 From Figure 5, E0 is about kT/q, which confirms that the TFE mechanism is domi-164 nant [26], not the theoretical mechanism TE of the Schottky contacts. This explains the 165 abnormal behavior of the barrier height and the deviation of the ideality factor from 166 unity. This may have been due to the interface states, which behaved as recombination-167 generation centers that affected the conduction mechanism [57]. 168 To further study the abnormal behavior of the barrier height, the Richardson char-169 acteristic ln(I / ) versus q/kT is presented in Figure 6 using the equation  Figure 6 gives two linear regions which are due to the inhomogeneity of the barrier height [12]. qφ b and A * values are 1.02 eV and 4.15 × 10 3 Acm −2 K −2 respectively in region 1 and equal to 0.19 eV and 3.6 × 10 21 Acm −2 K −2 respectively in region 2. These values of A * are significantly far from the theoretical value 8.16 Acm −2 K −2 for n-GaAs [52]. Figure 7 presents the variation of φ b versus n.
Materials 2021, 14, x FOR PEER REVIEW 8 of ues of * are significantly far from the theoretical value 8.16 Acm K for n-GaA [52]. Figure 7 presents the variation of ɸ versus n. The structure has two linear characteristics due to barrier height inhomogenei [58,59]. By extrapolation, the estimated values of ɸ for n = 1 are 0.87 eV for region and 0.84 eV for region 2. These values are closer than those extracted from the Richar son characteristics.
The authors of this work [5] previously performed simulations of Au/n-GaA Schottky at temperatures ranging from 80 to 400 K, with and without a thin GaN (1 nm interfacial layer. They found that Au/n-GaAs shows a homogeneous barrier height whi Au/1 nm-GaN/n-GaAs structure shows an inhomogeneous one. Therefore, the exper mental results shown here--the inhomogeneity of the barrier height shown in the Ric ardson characteristics and in the plot of ɸ versus n--are most likely because of th 0.8 nm GaN layer. Figure 8 illustrates G(I) plots of the Cheung and Cheung method temperatures 80-420 K. The structure has two linear characteristics due to barrier height inhomogeneity [58,59]. By extrapolation, the estimated values of qφ b for n = 1 are 0.87 eV for region 1, and 0.84 eV for region 2. These values are closer than those extracted from the Richardson characteristics.
The authors of this work [5] previously performed simulations of Au/n-GaAs Schottky at temperatures ranging from 80 to 400 K, with and without a thin GaN (1 nm) interfacial layer. They found that Au/n-GaAs shows a homogeneous barrier height while Au/1 nm-GaN/n-GaAs structure shows an inhomogeneous one. Therefore, the experimental results shown here--the inhomogeneity of the barrier height shown in the Richardson characteristics and in the plot of qφ b versus n--are most likely because of the 0.8 nm GaN layer. Figure 8 illustrates G(I) plots of the Cheung and Cheung method at temperatures 80-420 K. ues of * are significantly far from the theoretical value 8.16 Acm K for n-GaAs [52]. Figure 7 presents the variation of ɸ versus n. The structure has two linear characteristics due to barrier height inhomogeneity [58,59]. By extrapolation, the estimated values of ɸ for n = 1 are 0.87 eV for region 1, and 0.84 eV for region 2. These values are closer than those extracted from the Richardson characteristics.
The authors of this work [5] previously performed simulations of Au/n-GaAs Schottky at temperatures ranging from 80 to 400 K, with and without a thin GaN (1 nm) interfacial layer. They found that Au/n-GaAs shows a homogeneous barrier height while Au/1 nm-GaN/n-GaAs structure shows an inhomogeneous one. Therefore, the experimental results shown here--the inhomogeneity of the barrier height shown in the Richardson characteristics and in the plot of ɸ versus n--are most likely because of the 0.8 nm GaN layer. Figure 8 illustrates G(I) plots of the Cheung and Cheung method at temperatures 80-420 K. Rs and n were extracted by the Cheung and Cheung method for each temperature and presented in Figures 9 and 10, respectively. As can be seen, the structure gives the low resistance series Rs, which decre 13.80 Ω at 80 K to 4.26 Ω at 420 K, showing the good quality of the interface im nitridation and annealing [28].
The n values were very high at low temperatures compared to those extr the first method. This discrepancy occurred because the n values obtained b method were extracted from the low bias voltage range, where the series re very low. On the other hand, the n values extracted using the Cheung an method were extracted from all bias voltage ranges, where the series resistan bias voltages affects the calculation of the ideality factor.
Finally, the growth of a 0.8 nm of GaN layer on n-GaAs surfaces with an process led to improved electrical parameters of the Schottky contacts, such as resistance and the ideality factor. However, it can cause the inhomogeneity of height at the structure. As can be seen, the structure gives the low resistance series Rs, which decr 13.80 Ω at 80 K to 4.26 Ω at 420 K, showing the good quality of the interface im nitridation and annealing [28].
The n values were very high at low temperatures compared to those extr the first method. This discrepancy occurred because the n values obtained method were extracted from the low bias voltage range, where the series r very low. On the other hand, the n values extracted using the Cheung an method were extracted from all bias voltage ranges, where the series resista bias voltages affects the calculation of the ideality factor.
Finally, the growth of a 0.8 nm of GaN layer on n-GaAs surfaces with an process led to improved electrical parameters of the Schottky contacts, such a resistance and the ideality factor. However, it can cause the inhomogeneity of height at the structure.

Conclusion
Au/0.8 nm-GaN/n-GaAs structures were fabricated using a glow discha source (GDS), and their current-voltage characteristics were investigated fo temperatures. The samples showed good electrical parameters where n decrea As can be seen, the structure gives the low resistance series R s , which decreased from 13.80 Ω at 80 K to 4.26 Ω at 420 K, showing the good quality of the interface improved by nitridation and annealing [28].
The n values were very high at low temperatures compared to those extracted from the first method. This discrepancy occurred because the n values obtained by the first method were extracted from the low bias voltage range, where the series resistance is very low. On the other hand, the n values extracted using the Cheung and Cheung method were extracted from all bias voltage ranges, where the series resistance in high bias voltages affects the calculation of the ideality factor.
Finally, the growth of a 0.8 nm of GaN layer on n-GaAs surfaces with an annealing process led to improved electrical parameters of the Schottky contacts, such as the series resistance and the ideality factor. However, it can cause the inhomogeneity of the barrier height at the structure.

Conclusions
Au/0.8 nm-GaN/n-GaAs structures were fabricated using a glow discharge plasma source (GDS), and their current-voltage characteristics were investigated for different temperatures. The samples showed good electrical parameters where n decreased from 2 for 80 K to 1.01 for 420 K. The barrier height qφ b grew abnormally from 0.46 eV at 80 K to 0.83 eV at 420 K, due to the tunnel mechanism TFE effect. In addition, the samples showed low R s which dropped from 13.80 Ω at 80 K to 4.26 Ω at 420 K. Finally, the results strongly suggested that the GaN thin layer caused an inhomogeneous barrier height, which was also in agreement with our previous simulations [5].

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.