Quantifying the Effects of Disorder on Mobility of Nitride Semiconductors

Measuring the degree of disorder within crystalline samples began in the early 1930s with Bragg and Williams, who developed the order parameter S—which ranges from 0 (disordered) to 1 (ordered)—to quantify the degree of disorder in binary metal alloys. Recently, we have extended their x-ray diffraction based methodology to measure S from Raman spectra, reflection high-energy electron diffraction patterns (RHEED) and electron microscopy images. Quantifying the degree of disorder in samples allows for relationships to be uncovered between the order parameter and property of materials. In fact, for system-level properties that are dominated by pair-wise interactions, it can be shown using cluster expansion theory in combination with spin modeling that these properties have a linear dependence on S². Recently, we have experimentally verified this relationship holds for band gaps of semiconductors ranging from 2D to heterovalent ternary materials. Here, we demonstrate that the mobility of electrons in nitride semiconductors also exhibits a linear relationship with S².<br/><br/>Samples of undoped GaN, Mg-doped InN and Zn-doped InN were grown by plasma-assisted molecular beam epitaxy, and their degree of ordering was measured using both RHEED patterns and SEM images. For GaN, samples were grown in compositions ranging from Ga-rich to N-rich; all of these samples were determined to be n-type from Hall effect measurements. The electron mobility of the samples was observed to increase linearly with decreasing value of S. The largest range of order parameters and mobilities was obtained for nominally stoichiometric samples, where mobilities varied linearly from 138 cm²/(Vs) to 5 cm²/(Vs) for S² values between 0.113 and 0.332, respectively. For Mg-doped InN, samples were grown with Mg concentrations ranging from 1×10¹⁶ to 1×10²⁰cm^-3 and all samples were confirmed to be n-type by variable magnetic field Hall effect measurements. Similar to undoped GaN, these samples all exhibited a linear increase in the electron mobility with decreasing S of the sample. The largest range of order parameters was obtained for doping concentrations on the order of 1×10¹⁷ cm^-3, where measured electron mobilities ranged from 295 cm²/(Vs) to 16 cm²/(Vs) for S² values between 0.064 and 0.221, respectively. For Zn-doped InN, samples were grown with Zn concentrations ranging from 1×10¹⁵ to 1×10¹⁶cm^-3 and all samples were determined to be n-type. Like the GaN and Mg-doped InN samples, the Zn-doped InN samples all showed an increase in electron mobility with decreasing S value. The largest range of order parameters was obtained for doping concentrations on the order of 1×10¹⁵ cm^-3, where measured electron mobilities varied linearly between 700 cm²/(Vs) and 48 cm²/(Vs) for S² values between 0.008 and 0.202, respectively.<br/><br/>These experimentally-verified linear relationships between disorder and electron mobilities for each material, as well as the trends observed among these materials, can be physically understood through the lens of structural motifs (nearest neighbor bonding environments of the atoms in the lattice) and the dependence of the different motif types on the degree of disorder within the lattice. Importantly, these results present a possible pathway to increase the mobility of nitride semiconductors through the control of the degree of disorder in the materials, and present a framework for investigating similar relationships between disorder and mobility in other semiconductor systems.<br/><br/>This work was supported in part by the National Science Foundation under Grant DMR-2003581, and the MacDiarmid Institute for Advanced Materials (New Zealand).