Dislocations in GaN/Sapphire: Their Distribution and Effect on Stress and Optical Properties
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5'I ru 4-GaN GaNcubic,:aN LiGaO 2 ,
W *SiC
-2
GaP
n
GaAs 3
4
5
6
lattice constant (A) Figure 1: Bandgaps and lattice constants of GaN and related materials. depth in the GaN epilayers grown on the c-plane of sapphire [3, 4]. In an attempt to explain this observation we study the effect of threading dislocations on the stress distribution. Effect of dislocations and grain boundaries on the lifetime of minority carriers and on the performance of the GaN devices is discussed. EFFECT OF LASER BEAM WIDTH ON THE RAMAN SHIFT In a Raman experiment spectra originate from different points (x, y, z) in the volume of the structure sampled by the laser light (see Fig. 2). The stress does not vary in the x and y directions and therefore the observed Raman shift varies only with depth z [3, 4]. The effect 875 Mat. Res. Soc. Symp. Proc. Vol. 482 ©1998Materials Research Society
o
1
z (Rm) 2
3
4
ZU
SaN1.01 CZ0.5 Q/--- X
0----
oy
0
50
2
1O0 150 Z (j-m)
0
200
Figure 2: The sample and the axes of co-
Figure 3:
ordinates.
sured Raman shift AE2'eff(zo) in the 4 pm thick [3] and open circles in the 200 pim thick [4] GaN epilayers. Solid curves are the corrected values of AE~P(zo) (see text).
Square symbols are the mea-
of the depth of penetration of the beam in the x direction and that of the beam width in the y direction can be ignored. The intensity of laser light is therefore assumed to vary only in the z direction,
_zo ) 11(z,zo) = 0exp 2( B2
()
()
where center of the beam is at z 0 . 1 0 in Eq. (1) is the intensity at the center of the incident beam. 2B is the beam width at I/Io = 1/e2 and is assumed to be = 2 ym [5]. lo can be taken to be unity without loss of generality. In the geometry used in [3, 4] (see Fig. 2) E 2 Raman mode is active in GaN. The strain shifts this mode by AE2. We assume that the spectrum originating from the point z is given by a Lorenzian line with peak frequency AEP(z) and halfwidth A (A is taken to be 1.8 cm-1 [6]) and write the equation for the intensity IR(AE 2 , z, zo) of the Raman spectrum as [5], IR(AZE 2 , z, zo) =
1 ,,E2
(AE 2 -AE2(Z))
exp(2( 2)1 Z_(O) B21
(2)
The peak frequency AEP(z) of IR(AE 2, z, zo) depends on the stress at z. If the laser beam
width is assumed to be zero (which is not possible in practice) the spectrum at z = z0 is independent of the light intensity factor in Eq. (2). To account for the effect of the beam width, the spectra from all points z are superposed to obtain the intensity IR,(AE2, zo) of the spectrum which is observed in an experiment [5], IRI (AE 2, zo) =
I JR(AE 2 , z, zo)dz.
(3)
The peak position AEPeff(zO) of IRI (AE 2 , z 0 ) is the observed Raman shift. The observed shifts AEP2,,(z 0 ) in two GaN epilayers [3, 4] are shown by symbols (dashed curves are to guide the eye) in Fig. 3. We made a computer program to obtain the spectra IR(AE2, z, zo) from the observed spectrum IRl(AE2, zo). The program assumes different guess values of IR(AE2, z, zo) and integrates the right hand side of Eq. (3). This process is repeated until
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