Thermal Residual Stress Modeling in AIN and GaN Multi Layer Samples
- PDF / 497,384 Bytes
- 6 Pages / 417.6 x 639 pts Page_size
- 74 Downloads / 165 Views
Cite this article as; MRS Internet J. Nitride Semicond. Res. 4S1, G3.18 (1999)
ABSTRACT Thermal residual stresses can detrimentally affect the electronic and optical properties of epitaxial films thereby shortening device lifetime. Based on our earlier work on thermal expansion of nitrides, we provide a finite element modeling analysis of the residual stress distribution of multilayered GaN and AlN on 6H-SiC. The effects of thickness and growth temperatures are considered in the analysis. INTRODUCTION Group III-nitride based semiconductors have direct band gaps that can provide blue or ultraviolet light-emitting devices and high temperature optoelectronics. Recent work [1-3] has highlighted some of the difficulties and successes with their thin film device fabrication. Processing such devices often relies on the high temperature growth of epitaxial layers on different substrates with different coefficients of thermal expansion.
Residual stresses introduced by cooling or
heating may detrimentally affect device long term performance and lifetime. The stress-strain distribution in these electronic composite structures can be calculated from the temperature dependence of their thermoelastic properties. The results provide a guide for optimizing interfacial processing. For an axially symmetric problem without a body force, the equilibrium equations of the system are: I •(rOar•) 0-00 c0-o 0 (1) r
Or EU_ + Or
r
0Z +
z
=(00 r(2)
Where the O•j are the components of the stress tensor for a coordinate system (r, 0, z). After assuming displacements U and V along the r and z directions respectively, the strain tensor is
G 3.18 Mat. Res. Soc. Symp. Proc. Vol. 537 0 1999 Materials Research Society
err
ý
au Or U
eoo =
(3)
aV -
ezz =
Oz 0U
0)V
"Oz
Or
er, --
Hooke's law is then C11
U09C2C
KILC,,
C12
C13
11
C3
er_--AT] 0 je., -aAT O
Oje
a,
0
0
0
C44
L
uAT(4)
er,
Where a1 and a. are the mean coefficients of thermal expansion along the a- and the c-axes and the C1j are the elastic constants. For a hexagonal crystal, there are five independent elastic constants. A 2-D code, PDEase2, developed by SPDE, Inc. and distributed by Macsyma, is applied to calculate the stress-strain distributions of multilayer GaN/A1N or GaN/SiC structures. This code permits calculation of the stress/strain distribution for a cylindrically symmetrical system as shown in Fig. 1,
- --- -
10mm-
GaN
---
40mm
Figure 1. Geometry of the disk-shaped sample.
where the two layers are separated by a sharp interface. The GaN layer is either on top of AIN or SiC. For simplicity, a linear elastic continuum model for anisotropic samples was utilized. The c-axis is assumed to be perpendicular to the interface. Thermoelastic property measurements for AIN and GaN have been reviewed [4] and high temperature thermal expansion was calculated semiempirically. These results, plus work on SiC thermal expansion [5], permit us to calculate the stress-strain distributions for disk-shaped samples. The mean thermal expansion between 298°K and
Data Loading...
