Electrical Behavior of Vertical Pt/Au Schottky Diodes on GaN Homoepitaxy

Schottky barrier diodes on GaN on GaN substrates are fabricated for the purpose of material and technology characterization. The epitaxial layers are grown by MOCVD. I–V measurements as a function of the temperature in the range 80–480 K show ideality factor (n) and barrier height (ϕB) variations not following a thermionic (TE) model. Consequently, barrier height fluctuations are considered. In the temperature range 280–480 K, an average barrier height of 1.31 eV with a relatively large standard deviation (σ) of 0.15 eV is extracted using this model. The n(T) variation is also analyzed in order to extract the field sensibility of 1) the mean barrier height variation (ρ2 = −0.1) and 2) the barrier height standard deviation (ρ3 = −15 mV). The corrected Richardson plot using ϕB and σ values is linear and gives a Richardson constant of 31.5 A cm−2 K−2 close to the theoretical value of 26.4 A cm−2 K−2. For a deeper understanding of ϕB fluctuation origins, micro‐Raman mapping of the epitaxial layers and deep‐level transient spectroscopy (DLTS) are used. μ‐RS mappings show compressive strain for diodes having suffered electrical breakdown. DLTS analysis shows the presence of nine levels whose signatures are extracted and nature discussed.

Schottky barrier diodes on GaN on GaN substrates are fabricated for the purpose of material and technology characterization. The epitaxial layers are grown by MOCVD. I-V measurements as a function of the temperature in the range 80-480 K show ideality factor (n) and barrier height (ϕ B ) variations not following a thermionic (TE) model. Consequently, barrier height fluctuations are considered. In the temperature range 280-480 K, an average barrier height of 1.31 eV with a relatively large standard deviation (σ) of 0.15 eV is extracted using this model. The n(T ) variation is also analyzed in order to extract the field sensibility of 1) the mean barrier height variation (ρ 2 = À0.1) and 2) the barrier height standard deviation (ρ 3 = À15 mV). The corrected Richardson plot using ϕ B and σ values is linear and gives a Richardson constant of 31.5 A cm À2 K À2 close to the theoretical value of 26.4 A cm À2 K À2 . For a deeper understanding of ϕ B fluctuation origins, micro-Raman mapping of the epitaxial layers and deep-level transient spectroscopy (DLTS) are used. μ-RS mappings show compressive strain for diodes having suffered electrical breakdown. DLTS analysis shows the presence of nine levels whose signatures are extracted and nature discussed.
defects, we used Raman spectroscopy mapping (RS mapping) experiments for doping and strain homogeneity assessment, and deep-level transient spectroscopy (DLTS) for electrically active defect study.

Device Realization
The epitaxial layers were grown by MOCVD in a Close Coupled Showerhead system at T = 1020°C on a freestanding GaN substrate provided by Saint-Gobain Lumilog. The structure (Figure 1) consists of a 5 μm-thick silicon-doped film with an average doping level N d ÀN a extracted from CV measurement of 8.7 Â 10 15 cm À3 grown on top of a 0.1 μm n þ GaN buffer layer doped at 4 Â 10 18 cm À3 (not represented in Figure 1). Mesa structures, 2 μm deep, were fabricated by Cl 2 ICP-RIE etching for lateral insulation. A fluorine implant using 30, 60, and 100 keV implantation energies was used as an edge termination to reduce the electric field crowding at the Schottky contact edge. The front Schottky contact is composed of Pt/Au which overlaps the fluorine implanted regions to reduce the peak electric fields. For electric-field equipotential spreading, field plates are formed on top of a SiN x /SiO 2 insulator stack. The backside Ohmic contact is made of a Ti/Al/Ni/Au stack.

Electrical Characterization
I-V measurements have been performed in nitrogen cooled cryostat in the temperature range 77-480 K. A standard semiconductor parameter analyzer Keithley 4200 was used for the I-V characteristics measurements. The reverse characteristics were measured only to ensure that leakage current was not exceeding 1 μA at À10 V bias for the viability of DLTS measurements. The DLTS measurement was performed using a Fourier transform system from Phys Tech (HERA-DLTS system) in the temperature range 77-450 K. At each temperature the capacitance transient is analyzed using 23 different correlation function to calculate the Fourier coefficient. Using different time windows for the analysis (5 was chosen in this study), this gives up to 125 DLTS spectra in one temperature ramp and potentially as much point in the Arrhenius plot for each peak in the spectra. In order to investigate not only the top but also a fraction of the thick, low-doped n-GaN layer, a large reverse pulse V R = À20 V was used. Nevertheless, according to the nominal doping level, this corresponds approximatively to a 1.5 μm wide space charge region so 30% of the drift layer thickness. The filling pulse bias and the pulse duration were kept constant at 0 V and 1 ms, respectively.

RS Mapping
Micro-RS (μ-RS) measurements were carried out at room temperature using a confocal spectrometer (Renishaw Invia model) in back scattering geometry with a Â100 objective and a 2400 L mm À1 diffraction grating. Consequently, the spectral and spatial resolutions were around 0.1 cm À1 and 1 μm, respectively. The excitation wavelength is 532 nm. 10% of the laser 10 mW initial power is used in order to prevent any sample laser beam heating during spectral measurement. All spectra are calibrated using the 520.5 cm À1 line of a Si reference sample. 2D Raman cartographies of 320 Â 320 μm size with a step size of 5 μm have been performed on some diodes. From these measurements, series of Raman spectra have been obtained and fitted using a mixed Gaussian-Lorentzian function with the Wire 5 Renishaw software. From these fitting results, we extracted 2D E h 2 and A 1 (LO) peak position maps.

Barrier Height Analysis
Semi-log I-V characteristics as function of the temperature in the range 80-480 K are shown in Figure 2 for a 230 Â 230 μm 2 diameter diode. The exponential behavior over almost eight orders of magnitude for temperature above 240 K seems in good agreement with the thermionic emission theory which gives the following expression for the current across a uniform metal semiconductor interface where Figure 1. Schematic cross section of the vertical Schottky diodes processed on a n-GaN epitaxied on a n þ GaN substrate.
www.advancedsciencenews.com www.pss-a.com is the saturation current. A is the effective diode area, A * is the theoretical effective Richardson constant for n-type GaN (26.4 A cm À2 K À2 calculated using an electron effective mass value m * = 0.22 m 0 [10] ), R s is the series resistance of the neutral region of the semiconductor bulk inducing the voltage drop IRs, and ϕ b ðTÞ is the zero bias barrier height at a given temperature and n is the ideality factor. Nevertheless, some deviation from this ideal model can be observed below 240 K with the apparition of two regime of conduction. For a finer analysis of I(V ) curves, ϕ B and n have been extracted from the intercept and slope of the best linear fit of the linear part of forward I-V characteristics as given by Equation (1). The results are plotted in Figure 2b.
For both n and ϕ B , the large temperature dependence of both parameters has to be associated with a current transport mechanism that deviates from ideal thermionic emission theory. This is particularly true for temperature below 250 K as emphasized by the straights lines slopes rupture between regions (1) and (2) in Figure 2b. For instance, defect-assisted tunneling effect might explain this strong deviation at low temperature: the electrons pass through the Schottky barrier via the defect levels close to the conduction band. Even if it would be possible to fit the low temperature I-V curves with a parallel diode model, this would not explain the large variation observed for n and ϕ B with temperature. Furthermore, as shown by Tung, [9] this simple model does not consider the pinch-off effect in the case of small defective areas. Another approach proposed by Werner and Gutler [11] is to describe the inhomogeneity of the Schottky barrier height by a Gaussian distribution. The origin of this inhomogeneity could arise from a variety of defects: surface defects due to surface treatment, grain boundaries in the metal, melting of different metal phase at the interface, extended defects causing local barrier lowering, punctual electrical active defects causing defectassisted tunneling (seen as barrier lowering in the model), and surrounding defects due to guard ring fluorine implantation or to mesa etching process. All of these possible microscopic mechanisms for barrier height variation can be contained in two macroscopic parameters: the mean value ϕ B of the barrier and its standard deviation σ. The distribution is then given by By integrating and normalizing this distribution, we obtain the variation of the barrier height with temperature where ϕ B is the apparent barrier height measured from the forward bias I-V characteristics and σ is the zero bias standard deviation of the distribution. The variation of ideality factor n with temperature, predicting an n value larger than 1, is given by where ρ 2 and ρ 3 represent the electric field sensitivity of the mean barrier height and its standard deviation, respectively. They quantify the change in the barrier height distribution induced by the voltage, as follows ϕ B and 1 n À 1 variation as a function of reciprocal temperature are represented in Figure 3a. According to the strong change in n and ϕ B variation with temperature around 250 K outlined in Figure 2b, we used two distinct linear fits in temperature ranges (1) and (2) for the extraction of ϕ B and σ according to Equation (5) and of ρ 2 and ρ 3 according to Equation (6). The same procedure with different temperature ranges distinction was previously used in different studies. [1,4,7,8] All the extracted parameters are listed in Table 1.  (2)).
www.advancedsciencenews.com www.pss-a.com Figure 3b, known as Richardson plot, is classically used to extract barrier height and Richardson's coefficient according to the following expression This equation represents the conventional activation energy ln I 0 T 2 versus 1/T plot which should ideally be linear and gives A Ã and SBH through calculation of the intercept and slope. Again, the plot in Figure 3b shows significant deviation from the ideal thermionic model, in particular for temperature below 250 K. By replacing ϕ B by its expression from Equation (4) we obtain a modified activation energy expression According to this modified equation, a ln I 0 versus 1/T plot is obtained and is linear (see Figure 3c) with still a distinction between the two temperature ranges (1) and (2). A Ã and ϕ B extracted from this corrected Richardson's plot are also listed in Table 1.
The value of 1.31 eV for ϕ B together with the relatively large standard deviation of 150 meV extracted at high temperature (280-480 K) is in good agreement with reported values in the literature, also using Werner's analysis. [1,7] The good agreement between ϕ B values obtained from Equation (4) and (9), 1.31 and 1.33 eV, respectively, shows the coherence and the accuracy of the barrier height inhomogeneity model to describe our Schottky diode behavior in the temperature range (2). This is also confirmed by the extracted Richardson's constant value of 31.5 A cm À2 K À2 which is close to the theoretical value of 26.4 A cm À2 K À2 . For the lower temperature range (1), both the small discrepancy between the extracted value of ϕ B (0.81 and 0.94 eV, respectively, from Equation (4) and (9) and the deviation of the extracted Richardson's constant (36.4 A cm À2 K À2 ) from the theoretical value are significant indications that the TE model including barrier height inhomogeneities is not sufficient to describe the I-V characteristics. As proposed by different authors, [1,3,5] TFE current should be considered. This TFE contribution was not evidenced in the reverse characteristics which were limited to -10 V bias. Indeed at this level of reverse voltage, the field-effect Schottky barrier lowering (SBL current) is mainly observed. Further investigation at higher biases would be needed to analyze the contribution of TFE current and Fowler Nordheim current. The strong value of ρ 2 coefficient (0.31) signifies a strong dependence of the barrier height mean value with electric field. This might be an indication of a Poole-Frenkel contribution to the current at low temperature. For a deeper insight in the possible origins of these barrier height inhomogeneities, RS and DLTS measurements were performed.

Strain and Doping Homogeneity
In order to investigate possible strain and doping variations in the epitaxial layers as possible origins for the barrier height inhomogeneity, RS mapping was used. Two Raman modes, one planar E h 2 and one axial A 1 ðLOÞ, are visible in backscattering Figure 3. a) Barrier height (red spots) and 1 n À 1 (green spots) variation with reciprocal temperature. Blue and red strait lines are, respectively, linear fits to the data in temperature ranges (1) and (2) as defined in Figure 2b. b) and c) Richardson's plots and corrected Richardson's plot respectively. In figure c), the same division in two different temperature ranges is used as for figure a).  www.advancedsciencenews.com www.pss-a.com geometry for GaN. As reported earlier, both are strain and stress sensitive but the A 1 (LO) peak position is less dependent on the strain than the E h 2 position. [12,13] Only A 1 ðLOÞ is sensitive to n-doping concentration but at relatively high level (above 5 Â 10 16 cm À3 ). [14][15][16] The sensitivity to strain and stress manifests essentially as peak position variation, while A 1 ðLOÞ sensitivity to doping manifests by peak position variation toward higher values, intensity reducing, and peak broadening as the A 1 (LO) evolves to a plasmon coupled mode. Mapping has been performed in the surrounding of square diodes (150 Â 150 μm) after I-V test in reverse bias conditions. Breakdown voltage characterizations have been realized before the Raman characterizations with Raman mappings performed both on virgin diodes and on broken diodes. The mapping of E h 2 and A 1 ðLOÞ peak positions for the two types of diodes are shown in Figure 4.
Both peaks are shifted toward higher Raman shift positions by a mean value of 0.4 and 0.7 cm À1 , respectively, for E h 2 and A 1 ðLOÞ. This suggests the presence of a compressive stress for broken diodes. No inhomogeneities in these shifts are observed in the mapped area (160 μm band around the diode metallization). A participation of free carrier concentration variations in the A 1 (LO) peak position cannot be excluded which would explain the larger shift of this mode in comparison to E h 2 . We can then conclude that compressive stress is observed around broken diodes. Nevertheless, we cannot conclude whether this stress for the broken diodes was present before breakdown due to the presence of extended defects or if it was created during breakdown and, consequently, we cannot conclude if this stress participates to barrier height inhomogeneity measured in pristine diodes. In order to have a deeper insight in the possible causes of barrier height www.advancedsciencenews.com www.pss-a.com inhomogeneities, DLTS measurements were performed for analysis of electrically active defects within the drift layer.

Electrically Active Defects Study by DLTS
DLTS spectra for five different transient time windows of analysis (T w ) are represented in Figure 5a in the case of the sine Fourier coefficient b 1 . These five spectra are part of the total 115 spectra that are obtained in one temperature ramp measurement (5 T w and 23 Fourier coefficient). As can be observed, the spectra are dominated by a main peak that can be deconvoluted in three components attributed to levels called E 5 , E 6 , and E 7 in the following. Looking closer to the baselines of the spectra, one small peak appears around 160 K for T w = 0.02 s (see inset in Figure 5a) while for T w = 10 s a broad peak can be seen between 320 and 360 K (surrounded by an oval in Figure 5a). For some other Fourier coefficients, three additional peaks appear at the low temperature side of the main peak. In this way, the analysis of the total 115 spectra reveals the presence of nine different peaks. The corresponding Arrhenius plot deduced from all the Fourier coefficient analysis is displayed alongside in Figure 5b. Data scattering for levels E 1 to E 4 in the Arrhenius plot is due to weak intensity of these peaks in comparison to the main one. Data are also scattered in the case of E 8 and E 9 levels, but this appears less clearly in the Arrhenius plot due to 1/T scaling.
The signatures for the traps (activation energy and capture cross section) were extracted from the Arrhenius plot together with their concentration extracted from the DLTS peak amplitude. These values are reported in Table 2 together with tentative trap nature attribution from literature.
Among the nine electron traps signature extracted here, we can distinguish three different origins for the defects: 1) intrinsic defects (vacancy, antisite, and interstitial) most probably introduced during material growth (levels E 1 , potentially E 2 and E 8 , E 9 ); 2) impurity-related defects (C or H for levels E 5 and E 6 , Fe for level E 7 ); technology and more precisely RIE-related defect of unknown nature (levels E 3 , E 4 , and potentially E 2 ). The principal peak corresponds in part to level labeled E 7 with an activation energy of 0.55 eV. This level is most probably due to Fe contamination during the MOCVD growth process. Indeed, The spectrum for T w = 0.02 s is displayed in the inset revealing the presence of a small peak denoted E 1 . The purple oval around the baseline of T w = 10 s peak underlines the presence of a broad peak with weak intensity. b) Corresponding Arrhenius plot deduced from the Fourier analysis of the transients at different T w and for Fourier coefficient. Nine different traps signature are obtained. Possibly V N related [23] V Ga V N [24] E 2 0.30 6.1 Â 10 À15 4.3 Â 10 13 V Ga [25] or RIE-induced surface damage [26] E 3 0.32 3.4 Â 10 À16 5.9 Â 10 13 RIE-induced surface damage [26] E 4 0.34 1.4 Â 10 À16 4.6 Â 10 13 RIE-induced surface damage [23,27] E 5 0.47 2.5 Â 10 À17 1.3 Â 10 15 C or H related [28] E 6 0.51 3.5 Â 10 À17 1.0 Â 10 15 C or H related [28,29] or RIE-induced surface damage [26] E 7 0.55 3.7 Â 10 À17 1.1 Â 10 15 Fe related [18][19][20][21][22] [32,33] www.advancedsciencenews.com www.pss-a.com two recent studies showed linear correlation between trap density with activation energy E c À0.58 eV [17] and E c À0.57 eV [18] measured by DLTS and Fe concentration measured by SIMS. This confirms both previous experimental measurements indicating sensibility of E c À0.57 eV level to Fe concentration [19] and theoretical calculations predicting a level at E c À0.5 eV for Fe Ga [20] and E c À0.55 eV for Fe Ga -V N complex. [21] Moreover, this level has also been recently measured with an activation energy of 0.54 eV, in heavily Fe-doped GaN, by an acoustic technique (measurement of thermally activated conduction). [22] Concerning defects E 2 to E 4 , further studies on diodes without mesa etching will allow more accurate attribution to RIE etching.

Conclusion
The analysis of vertical GaN on GaN Schottky diodes by I-V-T measurements has shown inhomogeneity in the barrier height. Using the model developed by Werner et al., [9] we have extracted the relevant parameters (mean barrier height, standard deviation of barrier height, and filed sensitivity of these previous parameters named ρ 2 and ρ 3 ). The obtained values are coherent with previous results obtained for lateral devices. [1][2][3][4][5][6][7][8] The microscopic analysis of the origin of these barrier height inhomogeneities is still an open question. In this work, we used RS and DLTS to try to identify the origin.
Raman imaging has shown compressive strain for diodes which suffered electrical breakdown. Nevertheless, to correlate this strain to barrier height inhomogeneities, further studies would be needed. In particular, μRS mapping has to be performed on pristine diode area before metallization in order to determine if compressive stress potentially due to extended defects is present before electrical breakdown.
The DLTS analysis revealed the presence of punctual defects which may have appeared during epitaxy like Fe contamination at a level of 10 15 cm À3 (E 7 level at E c -0.55 eV) and some defects most probably due to the mesa RIE etching. These last defects despite their low concentration in the 10 13 cm À3 may have an important impact depending on their charge state on the diode conductivity as they are not dispersed in the drift layer but surrounding the diode. Further studies for different diodes area (i.e., different perimeter to surface ratio) could confirm this hypothesis (more important effect expected for small diodes with greater impact of periphery).