Epitaxial defects influence the Quantum efficiency of an LED device.  During deposition of an epitaxial structure on a substrate, various non-radioactive defects appear because of lattice mismatch and thermal expansion mismatch between the substrate and the epitaxial structure.  Defects, such as dislocation, may have a density raging from 109 cm−2 to 1011 cm−2.  As a result, spontaneous polarization and piezoelectric effect may generate a significantly built-in electric field, which reduces luminous efficiency of the LED.  LED device temperature increases as injected current increases, such that the LED device wavelength may drift and the luminous efficiency may be reduced, i.e. Droop phenomenon. 
A conventional epitaxial structure is formed on a substrate by thin film depositions.  FIG.  1 is a schematic diagram of a conventional LED device.  Conventional LED device 100 includes epitaxial layers 114 formed on a buffer layer 104 over a flat substrate 102.  The epitaxial layers 114 include an n-type semiconductor 106, an active layer 108 for light emission, and a p-type semiconductor 110.  The buffer layer 104 is added between the substrate 102 and the epitaxial layers 114 to help reduce epitaxial layers 114 defect density.  However, the conventional epitaxial structure often has a high a leakage current and a low production yield. 
FIG.  2 is a schematic diagram of a conventional LED device on a patterned sapphire substrate (PSS).  As illustrated in FIG.  2, a conventional LED device 200 includes epitaxial layers 214 formed on patterned sapphire substrate 202.  A buffer layer 204 covers bumps 212 of PSS 202.  Epitaxial layers 214 are formed over buffer layer 204.  Again, the buffer layer 204 is added to reduce defect density of the epitaxial layers 214. 
Various developments have been made toward reducing epitaxial defect density.  Dong-Sing Wuu, in US Patent Publication No.  2010/0184279A1, entitled “Method of Making an Epitaxial Structure Having Low Defect Density”, filed on Jan. 15, 2010, discloses an epitaxial structure with relatively low defect density.  Wuu discloses that a first epitaxial layer is laterally formed on a substrate, and then the first epitaxial layer is etched to form some pits or recesses on the surface of the first epitaxial layer.  Wuu further discloses that a defect-termination layer is deposited on the first epitaxial layer and a portion of the defect-termination layer is removed by a chemical mechanical polishing process to form a plurality of defect-termination blocks that fill the recesses on the surface of the first epitaxial layer.  The defect-termination blocks have polished surfaces that are substantially flush with surface of the first epitaxial layer.  However, it is very difficult to accurately control the cleanness of the etching treatment and the shape of the pits or recesses.  This method may have a high risk for increasing defect density. 
Lin, in US Patent Publication No.  2009/0256159A1, entitled “GAN Semiconductor Device”, filed on Mar. 27, 2009, discloses a buffer layer on a flat substrate.  Lin also discloses an amorphous metal-rich nitride thin film covering a partial upper surface of the flat substrate.  Because the metal-rich nitride is amorphous, the epitaxial growth direction of the buffer layer grows upwards in the beginning and then turns laterally.  The probability of the epitaxial defects extending to the semiconductor stack layer is reduced and the reliability of the GaN semiconductor device is improved.  Although Lin's method may reduce defect density, the method does not improve light emission. 
Hsu, in US Patent Publication No.  2008067916A1, entitled “light Emitting Device Having a Patterned Substrate and the Method Thereof”, filed on Jul. 30, 2007, discloses an epitaxial structure grown on a patterned sapphire substrate (PSS) to reduce defect density.  However, Hsu's method improves light emission only slightly. 
There still remains a need for developing methods for reducing defect density and improving light emission for LED devices.