Polarization-induced electrical conductivity in ultra-wide band gap AlGaN alloys

There is substantial interest in exploring the ultra-wide band gap (UWBG) AlGaN alloys, i.e., Al compositions greater than 50%, for high voltage diodes¹ and transistors^2–4 for power electronics applications. Ultra-wide band gap semiconductors are characterized by their large band gap energy (E_g) > 4.5 eV, which is advantageous for high voltage devices because the breakdown voltage is expected to increase as E_g⁵ and the specific on-resistance is expected to decrease as E_g^7.5.⁵ Another potential advantage of UWBG AlGaN for high voltage transistors is that the electron affinity decreases with increasing E_g, which leads to larger Schottky barriers (ϕ_b) that favor normally off operation for field effect transistors (FETs).^6,7

High electrical resistivity and poor ohmic contacts are major impediments to realizing power devices based UWBG AlGaN alloys. The alloy region of interest for electronics is 70% Al composition and higher because alloy scattering fundamentally limits the electron mobility (μ) to less than 150 cm²/V s for Al compositions between 30% and 70%.⁷ However, conventional alloyed contacts to n-type AlGaN exhibit a severe increase in contact resistivity for Al composition greater than 70%.⁸ Recently, near-ideal ohmic contacts have been demonstrated for heavily Si-doped UWBG AlGaN by grading the Al composition down to GaN, upon which ohmic contacts are readily achieved.⁹ The challenge of poor electrical conductivity remains, though, because the n-type Si doping efficacy drops precipitously for Al compositions above 80% due to either increasing Si activation energy,^10–13 increasing compensation due to defects,¹⁴ or both. Decreasing doping efficacy for Al compositions greater than 80% also makes electrical resistivity hard to control for a given Al composition by forcing a trade-off between free electron concentration (n) and μ. For example, the electrical resistivity of AlN:Si decreases with increasing free electron concentration because μ is degraded by increased scattering with non-ionized Si dopants.^15,16

Polarization-induced doping provides a pathway to overcome these impurity doping challenges for UWBG AlGaN. Strong spontaneous and piezoelectric polarization charge forms at AlGaN surfaces and heterointerfaces along the basal plane due to the discontinuity in Al composition and the resulting lattice strain.¹⁷ When a heterointerface is near the surface, such as in an AlGaN/GaN high electron mobility transistor (HEMT), a two-dimensional electron gas (2DEG) accumulates in the channel at the heterointerface to screen the dipole charge.¹⁸ This 2DEG forms in the absence of impurity dopants and is likely sourced from dangling bonds at the surface.¹⁸ This polarization-induced doping can be generalized to the case of a continuously graded AlGaN epilayer,^19–21 where a slab of polarization charge (ρ_π) forms with a spatial distribution given by

where P is the polarization vector accounting for spontaneous and piezoelectric components. Equation (1) implies that one can increase ρ_π and hence n either by increasing the degree of Al composition grading, i.e., ΔP, over a given distance or by decreasing the distance over which one grades a given range in Al composition. This approach to producing unintentionally doped (UID), highly conductive epilayers has been successfully used to form n-type AlGaN for Al compositions less than 30% for polarization-doped FETs (PolFETs),²¹ to increase the p-type conductivity in UWBG AlGaN quantum well ultraviolet light emitting diodes (UV LEDs),²² and to form both n-type and p-type layers in UID quasi-one-dimensional nanowire UV LEDs.²³ 

In this paper, we demonstrate polarization-induced doping in UID, graded AlGaN epilayers for Al composition varying between 80% and 100%. Electron mobility and n were measured from a combination of contactless sheet resistance (R_sh) and capacitance-voltage (C–V) profiling of Schottky diodes. Uniform n = 4.8 × 10¹⁷cm⁻³ was measured for epilayers with Al composition that was linearly graded from 80%–100%. The average mobility (⁠$μ¯$⁠) in the graded AlGaN epilayers was determined for different ranges of Al composition and exceeded previous reports for AlGaN:Si epilayers with uniform Al composition. A resistivity of 0.04 Ω cm was achieved for the AlGaN epilayer with Al composition graded from 80%–100% due to its simultaneously high n and high $μ¯$⁠. In addition, a large ϕ_b = 3.4 eV was measured for Ni Schottky on the AlN surface.

All group-III nitride epilayers were grown by metal-organic vapor phase epitaxy (MOVPE) in a Veeco D-125 system at 75 Torr and a pyrometer temperature of 1060 °C using conventional precursors, including trimethylgallium (TMGa), trimethylaluminum (TMAl), and ammonia. All AlGaN epilayers were grown with a V/III ratio of 1800 and a group-III molar flux of 35 micromoles/min. Separate calibration layers were used to determine the Al composition and growth rate by X-ray diffraction and in-situ reflectance respectively. The composition of the calibration layers agreed within 3 at. % with the Al/group-III ratio in the gas phase. Initially, a 2.3 μm-thick AlN epilayer was grown on (0001) c-plane sapphire substrates mis-oriented 0.2° toward the m-plane to serve as templates for subsequent growth of AlGaN test structures. First, a control sample consisting of a 0.7 μm-thick UID Al_0.86Ga_0.14N epilayer was grown on an AlN template to confirm the electrically insulating character of the high Al composition AlGaN epilayers in this study. Next, two samples were grown to demonstrate polarization-induced doping. Both samples consisted of a 0.75 μm-thick UID Al_0.8Ga_0.2N buffer followed by a 0.2 μm-thick epilayer over which the Al composition was increased linearly. During the grade, both the TMAl and TMGa source flows were adjusted to maintain a constant Group-III molar flux, ensuring a constant growth rate regardless of Al composition. For sample A, the Al composition graded was from 80% to 100% (AlN) and the compositional grade in sample B was from 80% to 90%.

Contactless R_sh measurement confirmed strong electrical conductivity in the UID graded samples and the absence of electrical conductivity in the UID Al_0.86Ga_0.14N control sample. Taken together, these findings establish that polarization-induced doping is the source for free electrons in the graded epilayers. Sheet resistances of 2500 and 20 000 Ω/□ were measured for the 80%–100% and 80%–90% samples, respectively, while R_sh for the Al_0.86Ga_0.14N control sample exceeded the 100 000 Ω/□ limit of the instrument. The 8× difference in R_sh values between the graded samples suggests that $μ¯$ is much higher for the 80%–100% sample. From Eq. (1), one expects that ρ_π for the 80%–100% should be approximately twice that for the 80%–90% sample (assuming that P is approximately linear in Al content over these alloy ranges), which implies that a large increase in $μ$ from 90% to 100% Al composition accounts for the remaining difference in R_sh. Such a trend is expected due to rapid decrease in alloy scattering for Al compositions approaching the AlN binary.⁷ 

Schottky diodes were fabricated for C-V profiling to measure ρ_π, and these data were compared with R_sh to calculate $μ¯$⁠, where it was assumed that ρ_π = n. The Schottky barrier height was also measured from C-V. Ni Schottky contacts with 300 × 300 μm² area were deposited on the AlN or Al_0.9Ga_0.1N surface using electron beam evaporation. A Ti/Al/Mo/Au stack was evaporated on the surface to attempt to form an ohmic contact, but the contact resistance remained high despite subsequent annealing. The large area, quasi-ohmic contact still enabled C-V measurement of the diodes by using a low frequency (5 kHz) ac signal to obviate series resistance effects, as confirmed by a phase angle that remained between −87° and −90° for all bias values. The average mobility was calculated from n and R_sh because reliable Hall effect measurements were not possible due to the poor ohmic contacts.

Figure 1 shows the C-V curves for the graded AlGaN Schottky diodes. The parabolic variation in the C-V curves corresponds to the graded AlGaN regions, and the abrupt drop in capacitance corresponds to depletion into the underlying UID Al_0.8Ga_0.2N template. Figure 2 shows a plot of A²/C², where A is the diode area, for the parabolic region of the C-V data from the AlGaN epilayer graded over 80%–100% Al composition. A value of ϕ_b = 3.4 eV for the Ni-AlN interface was determined from the x-intercept of the least-squares linear fit to the data. This is substantially larger than ϕ_b = 1.11 eV for the Ni-GaN interface,²⁴ which suggests that UWBG AlGaN transistors employing Ni-based gate contacts could realize a positive threshold voltage shift greater than 2 V relative to GaN transistors. This would be a significant advantage for realizing enhancement-mode operation.

Figure 1 also shows the space-charge profile of ρ_π calculated from the C-V data for both graded samples. The 80%–100% sample shows a uniform n = 4.8 × 10¹⁷cm⁻² throughout the graded region, and the abrupt drop in ρ_π at 200 nm depth from the AlN surface confirms the thickness of the graded layer. The polarization-induced doping was confirmed to be constant throughout the entire graded AlGaN region from these data because the 0 V depletion depth (x_d) calculated from

gives 81.6 nm, which agrees well with the experimental value of 80.4 nm. If ρ_π decreased (increased) significantly toward the AlN surface, the experimental x_d value would be much greater (lower) than 81 nm. The C-V data for the 80%–90% graded samples showed similar behavior except that n = 2.2 × 10¹⁷cm⁻², which is about half of that for the 80%–100% sample, as expected from Eq. (1). The drop in capacitance occurs at a smaller reverse bias for the epilayer graded from 80%–90% Al composition because there is less polarization charge to deplete.

The average mobility for both graded layers was then calculated from R_sh and n. It is important to consider the role of surface depletion when calculating $μ¯$ from R_sh and n due to the thinness of the graded layers, however, there is little data regarding the surface potential (ϕ_surf) of AlN. Electrochemical C-V measurements of AlN/GaN:Si heterostructures grown by molecular beam epitaxy (MBE) determined ϕ_surf = 1.9 eV for AlN layers of 1–4 nm thickness grown lattice-matched to GaN.²⁵ It is not clear, though, how strongly ϕ_surf varies based on growth method (MBE vs. MOVPE) and strain state (GaN vs. AlN template). Therefore, ϕ_surf was taken to be 1 eV for AlN and Al_0.9Ga_0.1N in accordance with the density functional theory calculations of ϕ_surf corresponding to a specific surface oxide stoichiometry and reconstruction that results in a surface electronic structure giving rise to donor-like surface-states that are able to provide the free electrons in UID graded AlGaN layers.²⁶ A surface depletion depth (W_surf) of 43 nm and 61 nm was calculated for the 80%–100% and 90%–100% samples, respectively, from Eq. (2) by replacing ϕ_b with ϕ_surf. Then, $μ¯$ was calculated as

where z_eff is the physical graded AlGaN thickness of 200 nm less W_surf. For the 80%–100% sample, surface depletion leaves a conductive region between 43 and 200 nm below the surface, corresponding to an AlGaN composition range of 80%–96%, for which $μ¯80% – 96%$ = 332 cm²/V s. Similarly, the 80%–90% sample has a conductive region between 65 and 200 nm below the surface, for which $μ¯80% – 87%$ = 105 cm²/V s. The average mobility for an 88%–96% AlGaN linearly graded layer can be calculated from an average of $μ¯80% – 96%$ and $μ¯80% – 87%$ weighted by their relative thicknesses to give $μ¯88% – 96%$= 509 cm²/V s.

Figure 3 plots resistivity versus Al content for several previous reports of AlGaN:Si^{10,14,16,27–30} to compare with data from the 80%–100% UID graded AlGaN sample. The advantage of polarization-induced doping for AlGaN is substantially lower resistivity than has been achieved for Si-doped AlGaN for uniform Al compositions greater than ∼85% due to comparable μ and significantly higher n for UID graded epilayers. Polarization-induced doping of UWBG AlGaN overcomes the n-μ trade-off of Al(Ga)N:Si¹⁵ by simultaneously benefiting μ by eliminating impurity scattering by intentional dopants and benefiting n by overcoming the deep dopant and/or dopant compensation problem(s). Average mobility values reported here for UID graded AlGaN epilayers grown on sapphire are comparable to the best results for AlGaN:Si and AlN:Si grown on single crystal AlN substrates^14,16 or sapphire.³⁰ For example, μ for AlGaN:Si at compositions lower than 95% are routinely below 70 cm²/V s,^14,30 compared to $μ¯80% – 96%$= 332 cm²/V s. Likewise, $μ¯88% – 96%$ = 509 cm²/V s is comparable to the best μ value reported for homoepitaxially grown AlN:Si of 426 cm²/V s.¹⁶ Improved μ for UID graded AlGaN over heavily doped Al(Ga)N:Si can be attributed to the reduced importance of alloy scattering relative to scattering by non-ionized impurities and scattering by threading dislocations as the Al composition approaches 100%.^15,16 Polarization-induced doping in graded UID AlGaN strongly mitigates both impurity and dislocation scattering because it does not rely on dopants to generate free carriers, yet it still produces sufficiently large n to effectively screen dislocation-related line charges.¹⁶ 

Improvement in μ in graded AlGaN is advantageous, but it is strong enhancement of n that contributes most significantly to reduction in resistivity. The free carrier concentration of AlGaN:Si with uniform Al decreases by three orders of magnitude, from >10¹⁸cm⁻³ to <10¹⁵cm⁻³,^12,25 when the Al composition is increased from 80% to 100%, either because Si becomes a deep dopant,^12,31 compensating acceptor formation increases,¹⁴ or both. Conversely, polarization-induced doping does not require thermal ionization of impurities to generate free carriers. It is also possible that compensating acceptor incorporation is suppressed for UID polarization-induced doping of graded AlGaN compared to AlGaN:Si. Heavy doping with shallow impurity donors can induce facile deep acceptor formation in UWBG semiconductors during growth, leading to substantial dopant compensation.³² On the other hand, the lack of significant impurity donor dopants in UID graded AlGaN could suppress deep acceptor formation relative to heavily doped AlGaN and result in polarization-induced n that is not strongly compensated.

In summary, UID AlGaN epilayers with Al composition graded over 80%–90% or 80%–100% were grown by MOVPE on sapphire and characterized using contactless R_sh and C-V measurements. The low 0.04 Ω cm resistivity of the UID AlGaN epilayer graded over 80%–100% Al composition was attributed to polarization-induced doping. Average electron mobility was calculated for several ranges of Al composition grading from C-V and R_sh data. It was shown that the UID graded AlGaN epilayers have $μ¯$ comparable to the highest reported μ values for AlGaN:Si and AlN:Si grown on AlN, likely due to reduced impurity scattering. The primary advantage of UID graded AlGaN is achieving n that is much greater than has been reported for AlGaN:Si or AlN:Si. A free carrier concentration of 4.8 × 10¹⁷cm⁻³ was observed for Al composition graded from 80% to 100%. The Schottky barrier of the Ni-AlN was measured to be 3.4 eV for the Ni-AlN interface, which is much larger than ϕ_β for Ni-GaN. The combination of low resistivity, large ϕ_b, and ultra-wide band gap energy makes UID graded AlGaN attractive as a building block for high voltage power electronics devices such as Schottky diodes or PolFETs.

This work was supported by the Laboratory Directed Research and Development program at Sandia National Laboratories. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under Contract No. DE-AC04-94AL85000.