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Threading Dislocations and Carrier Mobility of GaN Thin Films
Marcus Woo & Prof. Han Zhang
Cornell University, Peking University
Introduction
The semiconductor GaN garners much interest because of its applications towards light emitting diodes (LEDs), laser diodes, and because of its photoluminescence ability. In addition, there is further interest in GaN because of its tendency to have high threading dislocation densities in the crystal structure because of the lattice mismatch between the thin film and the substrate. Therefore, much research has been done to study the effects of such dislocations and defects on the physical properties of GaN. Threading dislocations (linear dislocations) are comprised of edge-type and screw-type dislocations, and some studies show that these different types of dislocations affect the properties of GaN thin films differently (Du et al. 2000). Specifically, we have studied the effects of threading dislocations on carrier mobility. Using X-ray diffraction rocking curve scans of GaN, we are able to determine the relationship between dislocation density and carrier mobility.
Experimental
The samples were grown on a plane of sapphire at 1040°C, 1050°C, and 1060°C using metal-organic vapor phase epitaxy (MOVPE). The sources of Ga and N were trimethlgallium (TMGa) and NH3 and the carrier gas was hydrogen of high purity. Using the Philips X’Pert Material Research Diffractometer (MRD) with a four crystal monochromator that generates a pure Cu Ka1 line of wavelength l = 0.15406 nm, we have measured rocking curves (scans along the w-axis) of five GaN samples. We found rocking curves of five different planes for each sample (Table 1). These five planes were used to calculate the amount of screw and edge-type dislocations in the samples. The measured FWHM of each curve and of each sample is shown below (Table 2). Using standard procedures, we have obtained two measurements of the carrier mobility of the samples. We use the average values in our analysis.
| Face (hkl) |
2q |
Tile angle Y |
| (002) |
34.647124 |
0 |
| (103) |
63.5849 |
32.025 |
| (102) |
48.199755 |
43.177693 |
| (101) |
36.914387 |
61.95 |
| (201) |
70.662401 |
75.081203 |
Table 1. Positions of each measured rocking curve
|
Sample |
| Face |
1 |
2 |
3 |
4 |
5 |
| (002) |
.2385 |
.4584 |
.2181 |
.2531 |
.3501 |
| (103) |
.5144 |
.4788 |
.2532 |
.3019 |
.5520 |
| (102) |
.6104 |
.5522 |
.2633 |
.3049 |
.5876 |
| (101) |
.7472 |
.5313 |
.2229 |
.3253 |
.6650 |
| (201) |
.7963 |
.5665 |
.2479 |
.3543 |
.5878 |
Table 2. Measured FWHM of each face of each sample
Discussion
It is essential to examine the different types of threading dislocations and how each type affects the physical properties of GaN. From the FWHM of the rocking curves, we can determine dislocation density. The measured FWHM can be decomposed into two parts, one that represents the rocking curve normal to the crystal surface, and one that is parallel to the crystal surface. The FWHM that is normal to the surface represents edge dislocation, while the FWHM that is parallel to the surface represents screw dislocation. The surface normal FWHM is also called the twist component because the edge dislocation creates a slight angle in the lattice, causing a twist in the structure. The in-plane FWHM is also known as the tilt component. Knowing the FWHM of each component allows us to determine how the different types of dislocations relate to the carrier mobility of GaN. However, it is experimentally difficult to measure the FWHM of the in-plane component.
Theory and Calculations
Srikant et al. (1997) provides a method in which the in-plane FWHM can be calculated from the surface normal reflections. With this method, we first take each rocking curve of each plane and fit it to a Pseudo-Voigt function:
Where G(x) is a Gaussian distribution and L(x) is a Lorentzian distribution, and f is the fraction of Lorentzian character of the distribution. The composition of the measured FWHM as a function of the tilt angle Y, W(Y), can be expressed as:
The value n is given by:
Fitting the Pseudo-Voigt function to the curve results in a value for f, and thereby a value for n.  and  are the tilt and twist components of the measured FWHM, and can be calculated by:
The parameterm describes the level of interdependence between the tilt and twist FWHM distributions. Using the appropriate matrix techniques in the theory of rigid body rotation,  and  are given by:
Wz and Wy are the in-plane twist angle and the surface normal tilt angle, respectively. We fit the Pseudo-Voigt function to all five faces of GaN and take the average values of f. Then we fit the measured data to obtain the best value for m and Wz. Wy is already known, since it is the surface normal FWHM. Wz and Wy represent the dislocation densities of the screw and edge dislocations, respectively. To calculate an actual density, we can use the theory proposed by Ayers (1993). However, for our own purposes, an explicit calculation of the dislocation density is unnecessary.
Results and Analysis
We have calculated values for Wz and the interdependence parameter m. The results are tabulated below (Table 3). Plotting Wy and Wz versus carrier mobility, we see that the wider the rocking curve, the lower the mobility (Figure 1). Both types of threading dislocations impede the mobility, but screw dislocations have a more pronounced effect, causing mobility to decrease faster. Elsner and Jones (1997) propose that the mechanism behind decreasing mobility involves the ability of dislocations to trap certain impurities in the crystal. These trapped impurities thereby hinder charge carriers to move.
Plots of the interdependence parameter m versus carrier mobility imply that there is no relation between these two properties (Figure 2). The amount of interdependence between screw and edge dislocations does not seem to affect the carrier mobility of GaN. However, Shi et al. (2002) have performed rocking curves on similar samples and have found that there is a strong relationship between carrier mobility and the parameter m. Their study finds that higher levels of interdependence leads to increased carrier mobility. There are several reasons that can explain this discrepancy. In performing our rocking curves, we maintained the X-ray beam intensity level to be the same for all faces of the sample. However, the faces with a higher Y-angle have significantly weaker reflections. Because of the weaker intensities, background noise in the curve plays a larger role, decreasing the precision of the fits during the calculations. Another source of discrepancy may lie in our choices of faces. We used the highest peak of the j-scan to perform the rocking curve. We also restricted our j-scan to a range of 120°. We might have been more able to reproduce the results of Shi et al. had we kept the choice of face consistent or if we had chosen a face beyond our range.
We have also plotted Wy and Wz with the parameterm (Figure 3). It is apparent that there is no strong relationship between the amount of edge and screw dislocations and the level of interdependence between edge and screw dislocations.
One interesting result is that of a negative value form in sample five. As m increases, the level of interdependence between screw and edge dislocations increases. A value of m= 0 implies no relation, while a value of m= 1 implies a very strong relation. However, our calculated value form is small enough that it can be attributed to uncertainties in the calculation. As mentioned above, certain fits might not be perfect because of low intensities.
| Sample |
Carrier Mobility (cm2/V·s) |
FWHM of twist (Wy) |
FWHM of tilt (Wz) |
f |
m |
| 1 |
9.4 |
.2385 |
.843 |
.6835 |
.225 |
| 2 |
1.5 |
.4584 |
.577 |
.7084 |
.413 |
| 3 |
178.7 |
.2181 |
.215 |
.6626 |
.184 |
| 4 |
119.55 |
.2531 |
.359 |
.6766 |
.377 |
| 5 |
5.5 |
.3501 |
.554 |
.653 |
-.0240 |
Table 3. Calculated results for all five samples
Conclusion
We have found the screw and edge dislocation composition of five samples of GaN from X-ray rocking curves. We have also calculated values for the parameter m, which describes the amount of interdependence between the screw (tilt distribution) and the edge (twist distribution) dislocations. In comparing with previously measured values for carrier mobility, we have attempted to find relationships among these properties. Our measurements show that an increase in dislocations impede carrier mobility, where screw dislocations affect mobility more strongly. This agrees with other analyses and theory. But contrary to other measurements, we do not find a relationship between screw and edge interdependence and mobility. Finally, our measurements do not reflect a relationship between the amount of edge and screw dislocations and the level of interdependence.
Acknowledgments: We would like to thank J. Y. Shi, Y. Z. Wang, S. X. Wang, and H. Zhang for support and assistance. We would also like to acknowledge the National Science Foundation for support in this Research Experience for Undergraduate program.
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References
J.E. Ayers, J. Crystal Growth, 135 (1994)
J. Elsner and R. Jones, P.K. Sitch, V.D. Porezag, M. Elstner, and Th. Frauenheim, M.I. Heggie, S. Oberg, P.R. Briddon, Phys. Rev. Lett., Vol. 79, No. 19 (1997)
X. Du, Y.Z. Wang, L.L. Cheng, G.Y. Zhang, H. Zhang, Mater. Sci. and Eng. B75 (2000)
J.Y. Shi, L.P. Yu, Y.Z. Wang, G.Y. Zhang, H.Zhang, Appl. Phys. Lett. 80, 2293 (2002)
V. Srikant, J.J. Speck, D.R. Clarke, J. Appl. Phys. 82 (1997)
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