Exploring the influence of silicon doping on bulk GaN thermal conductivity

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The wide-bandgap semiconductor material gallium nitride (GaN) has great electrical and optical characteristics, making it useful in a variety of electronic and optoelectronic devices. And yet, when contrasted with other semiconductors, its intrinsic thermal conductivity is noticeably lower. The thermal conductivity of bulk gallium nitride (GaN) can be significantly influenced by the introduction of silicon doping. Based on a paper published in 2017 by the American Institute of Physics¹ (API), this article will describe the effects of silicon doping on the thermal conductivity of bulk GaN at elevated temperatures proving the theoretical treatment with experimental evidence.

The objective of the research

In a prior study, the researchers observed a negative correlation between the thermal conductivity of bulk GaN at ambient temperature and above, as determined using the 3ω technique, and the level of Si doping. Furthermore, the researchers observed a gradual decrease in the slope of the temperature dependence of the thermal conductivity as the Si doping increased. It was observed that the thermal conductivity of the highest doped sample exceeded that of the lower doped samples at temperatures exceeding 350 K.

In the next work¹, a modified Callaway model, adopted for n-type GaN at high temperatures, was developed to explain such behavior.

The role of thermal conductivity

Group-III nitrides, including high-electron-mobility transistors (HEMTs), Schottky barrier diodes (SBDs), light-emitting diodes (LEDs), and laser diodes (LDs), have demonstrated their potential as fundamental components in power electronics systems and solid-state lighting technology in recent years. The effectiveness of heat removal from the active section of the device is crucial for the performance and reliability of these devices, particularly when operating at high temperatures and output powers.

The thermal conductivity of group-III nitride materials has been the subject of intensive investigation in previous studies. However, the experimental data published in these studies exhibit significant variation. This variation can be attributed to disparities in the quality of the samples analyzed and the specific difficulties encountered in the measuring techniques employed.

Various GaN substrates are required for different device applications, including undoped, n-type doped, or semi-insulating substrates. Therefore, to effectively manage thermal conditions, it is imperative to possess a precise understanding of the impact of doping on the thermal conductivity of GaN. The comprehensive investigation into the role of Si doping in GaN is paramount, as Si serves as the primary dopant for attaining n-type conductivity.

The measurement process

The examined samples were obtained by cutting bulk-like GaN produced using high-voltage photoelectrochemical (HVPE) techniques along the [0001] GaN crystallographic direction on sapphire substrates. GaN layers typically have a thickness of approximately 1 mm. The samples utilized in thermal conductivity studies have lateral diameters ranging from 5×5 mm² to 10×10 mm². Silane (SiH4) was injected into the reactor with nitrogen (N2) carrier flow to accomplish silicon doping.

The thermal conductivity was determined using the utilization of the 3ω method, which involves the photo-lithographic deposition of a thin metal wire containing four contact pads into the surface of the sample, following a standardized design. The wire acts as both a heating device and a sensing mechanism. The samples were mounted on a temperature-controlled plate to conduct measurements within a temperature range of 295-470 K. To ensure the accuracy of temperature measurements, an extra thermocouple was affixed to the upper portion of the plate, close to the sample.

The 3ω technique involves the application of an alternating current with an angular frequency of ω along a wire, followed by the measurement of the voltage drop at 3ω as a function of ω. The wire undergoes Joule heating, generating a heat flux with a power oscillation frequency of 2ω. This heat flux is then dissipated into the sample located beneath. The resistance of the metal wire is influenced by the heat waves emitted by the sample, which is attributed to the non-zero temperature coefficient of resistivity. Consequently, the voltage drop across the wire exhibits the presence of a third harmonic component. The expression for the amplitude of the component V3ω is as follows:

Where αT is the temperature coefficient of resistivity, ΔT is the temperature oscillations, and V_1ω is the amplitude of the voltage drop at fundamental frequency ω. The power normalized temperature variation can be approximated by:

In this context, P represents the power exerted on the wire, l denotes the wire’s length, k signifies the heat conductivity, and C represents a constant that is unaffected by both the frequency and the wire’s length. The thermal conductivity can be determined by analyzing the slope of the V3ω versus ln(ω) dependency, as ΔT/P is directly proportional to V3ω. It should be noted that the linearity of the observed dependence across the whole frequency range (50-4000 Hz) at various temperatures, as depicted in Figure 1, serves as experimental evidence that the boundary conditions are satisfied in the experiments.

Experimental results

The introduction of impurity atoms into the crystal lattice of GaN through silicon doping results in a modification of its lattice structure. The presence of these impurities disturbs the normal configuration of atoms, resulting in alterations to the dispersion relations of phonons and the scattering of phonons. The presence of impurities leads to the scattering of phonons, resulting in a decrease in the mean free path of phonons and thus reducing the thermal conductivity.

The measurement of all GaN samples was conducted under identical conditions. The undoped sample has a thermal conductivity of k = 245±5 W/m·K at ambient temperature (T = 295 K). This value aligns with the statistics for GaN grown in free-standing HVPE. As the concentration of Si increased, the thermal conductivity steadily declined. The sample with the highest doping had a thermal conductivity of k = 210±6 W/m·K.

The observed behavior can be deemed rational and can be readily elucidated by an augmented involvement of phonon-point-defect scattering. The thermal conductivity of all samples exhibited a decrease as the temperature increased at elevated temperatures (T > 295 K), as depicted in Figure 2. Nevertheless, there was variation in the rate of decline, namely the slope of the temperature dependence of k, across different concentrations of Si.

The temperature dependence of thermal conductivity was modeled using the modified Callaway model. However, instead of using multiple scattering rate coefficients, just the changeable factors for longitudinal and transverse phonons, known as Grüneisen parameters, were utilized.

Figure 3 illustrates the relationship between thermal conductivity and Si doping at various temperatures. The incorporation of FE (Phonon-free-electron) scattering into the model is crucial for a comprehensive elucidation of the experimental data within the temperature range of 300-350K. However, beyond a temperature of 350 K, the influence of FE-scattering appears to diminish, as evidenced by the proximity of the two simulated curves.

At elevated temperatures, it is anticipated that the thermal conductivity will remain unaffected by the concentration of silicon up to [Si] ~ 1·10¹⁸ cm^-3. However, at room temperature, the thermal conductivity is only reliant on the concentration of silicon up to [Si] ~ 5·10¹⁶ cm^-3. The observed pattern of the thermal conductivity at room temperature, as depicted in Figure 3, aligns with previously documented data for thin Si-doped GaN layers located on sapphire. Nevertheless, the observed values in this study exhibited a notable increase, mostly attributed to the superior structural defect density of the bulk GaN in comparison to the thin heteroepitaxial GaN layers.

Further understanding of the primary scattering phenomena occurring at temperatures higher than room temperature can be acquired by employing a straightforward power law model to analyze the temperature-dependent thermal conductivity. The following mathematical expression can represent this model:

The thermal conductivity at room temperature, denoted as k₀, is equal to To = 295 K. The utilization of this empirical fit holds potential value in the realms of thermal management and device design since it enables the prediction of thermal conductivity characteristics across varying temperatures and doping levels.

Figure 4 illustrates an instance of such a match for all measured samples. Figure 5 illustrates the relationship between the slope, denoted as α, and the concentration of Si. The experimental results indicate a gradual drop in slope as the doping level increases, starting from α = 1.3 for the undoped sample and reaching α = 0.55 for the maximum doped sample. The observed slope for the undoped sample aligns with previously documented values for GaN produced in high-grade HVPE, specifically 1.439 and 1.22.

References

¹ P. P. Paskov, M. Slomski, J. H. Leach, J. F. Muth, and T. Paskova, “Effect of Si doping on the thermal conductivity of bulk GaN at elevated temperatures – theory and experiment” – AIP Advances 7, 095302 (2017)

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