Supplementary Online Material for:
“Maximizing Cubic Phase Gallium Nitride Surface Coverage
on Nano-patterned Silicon (100)”
R. Liu and C. Bayram1
Department of Electrical and Computer Engineering, University of Illinois at UrbanaChampaign, Illinois, 61801, USA
Micro and Nanotechnology Laboratory, University of Illinois at Urbana-Champaign,
Illinois, 61801, USA
This pdf file includes:
- Supplementary Geometrical Model Based on Crystallography
- Figure S1
- Figure S2
- Uniformity Study of the Cathodoluminescence and Electron Backscatter Diffraction
Measurements
- Figure S3
- Figure S4
1
Innovative COmpound semiconductoR (ICOR) Laboratory; Email: [email protected];
Webpage: icorlab.ece.illinois.edu; Phone: +1 (217) 300-0978; Fax: +1 (217) 244-6375
Supplementary Online Material
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Supplementary Geometrical Model Based on Crystallography
Figure S1 shows the model sketch of GaN in a U-groove. The V- shaped red dashed lines refer to
the phase boundaries where hexagonal-to-cubic phase transitions occurs1, and the top (red) dashed
line indicates the c-GaN top surface. Under the selective growth conditions1, 2, GaN nucleates on
the Si(111) facets only and these h-GaN growth fronts meet at a 109.48° angle in the middle of the
groove. After the middle of the growth fronts meet (point A in both figures), GaN grown on top
will phase transition to cubic phase. Under these experimental / crystallographic observations, the
geometrical modelling is carried out as follows:
In the following derivation 𝑥𝑖 and 𝑦𝑖 are various dimensions as shown in the Fig. S1 and Fig. S2,
ℎ𝑐 is the critical GaN deposition thickness (defined as the GaN deposition height above Si(100)
that maximizes cubic phase GaN coverage on the U-groove surface), 𝑡𝑑 is the etch depth, 𝑝 is the
opening width, and 𝛼 is the oxide sidewall angle.
Figure S2 shows the zoomed in region indicated by the dotted square in Fig. S1. Points A, B, C in
both figures (Fig. S1 and S2) correspond to the same exact locations. The crystallographic angles
(54.74° between the (100) and (111) Si surfaces) are shown accordingly.
From Fig. S2, we see that:
𝒕𝒂𝒏𝟑𝟓. 𝟑° =
𝒚𝟐
𝒙𝟑
𝒕𝒅
𝟐𝒙𝟏
𝒑
𝒙𝟏 + 𝒙𝟑 =
𝟐
𝒕𝒅
𝒚𝟑 = 𝒚𝟐 +
𝟐
𝒕𝒂𝒏𝟓𝟒. 𝟕° =
(S1)
(S2)
(S3)
(S4)
Rearranging (S1), (S2), and (S3), we get:
𝒚𝟐 = 𝒙𝟑 𝒕𝒂𝒏𝟑𝟓. 𝟑°
(S5)
𝒕𝒅
𝟐𝒕𝒂𝒏𝟓𝟒. 𝟕°
(S6)
𝒙𝟏 =
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𝒑
− 𝒙𝟏
𝟐
(S7)
𝒑
𝒑
𝒕𝒅
− 𝒙𝟏 = −
𝟐
𝟐 𝟐𝒕𝒂𝒏𝟓𝟒. 𝟕°
(S8)
𝒙𝟑 =
Substituting (S6) into (S7):
𝒙𝟑 =
Then using (S8) in (S5):
𝒑
𝒕
𝒅
𝒚𝟐 = 𝒙𝟑 𝒕𝒂𝒏𝟑𝟓. 𝟑° =(𝟐 − 𝟐𝒕𝒂𝒏𝟓𝟒.𝟕°
) 𝒕𝒂𝒏𝟑𝟓. 𝟑°
(S9)
From Figure S1,
𝒙𝟒 = 𝒑 + 𝟐 𝒉𝑪 𝒕𝒂𝒏 𝜶
(S10)
𝒚𝟏 + 𝒚𝟑 = 𝒉𝑪 + 𝒕𝒅
(S11)
𝒕𝒂𝒏𝟑𝟓. 𝟑° =
𝒙𝟒
𝟐𝒚𝟏
(S12)
Rearranging (S12) using (S10), and (S11) using (S4):
𝒚𝟏 =
𝒙𝟒
𝒑 + 𝟐 𝒉𝑪 𝒕𝒂𝒏 𝜶
=
𝟐𝒕𝒂𝒏𝟑𝟓. 𝟑°
𝟐𝒕𝒂𝒏𝟑𝟓. 𝟑°
𝒉 = 𝒚 𝟏 + 𝒚 𝟑 − 𝒕𝒅 = 𝒚 𝟏 + 𝒚 𝟐 −
𝒕𝒅
𝟐
(S13)
(S14)
Substituting (S13) and (S9) in (S14), we get:
𝒉𝑪 =
𝒑 + 𝟐 𝒉𝑪 𝒕𝒂𝒏 𝜶
𝒑
𝒕𝒅
𝒕𝒅
+( −
) 𝒕𝒂𝒏𝟑𝟓. 𝟑° −
𝟐𝒕𝒂𝒏𝟑𝟓. 𝟑°
𝟐 𝟐𝒕𝒂𝒏𝟓𝟒. 𝟕°
𝟐
(S15)
Solving for ℎ𝑐
𝒉𝑪 = (𝟏 −
𝒕𝒂𝒏𝜶
𝒕𝒂𝒏 𝟑𝟓. 𝟑°
−𝟏
)
Supplementary Online Material
𝒑
𝒕𝒅
𝒑
𝒕𝒅
[( −
) 𝒕𝒂𝒏 𝟑𝟓. 𝟑° +
− ]
𝟐 𝟐𝒕𝒂𝒏 𝟓𝟒. 𝟕°
𝟐𝒕𝒂𝒏𝟑𝟓. 𝟑° 𝟐
(S16)
3
Simplify and plugging in values for the tangents, we have the relationship between critical
thickness and the patterning parameters:
𝒉𝑪 =
[𝟏. 𝟎𝟔𝒑 − 𝟎. 𝟕𝟓𝒕𝒅 ]
𝒕𝒂𝒏 𝜶
(𝟏 − 𝟎. 𝟕𝟏 )
(S17)
If 𝛼 is negligible ( ≈ 0°), the relationship simplifies to:
𝒉𝑪 = [𝟏. 𝟎𝟔𝒑 − 𝟎. 𝟕𝟓𝒕𝒅 ]
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(S18)
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Figure S1. GaN deposition in U-groove model (under selective growth conditions1, 2) is shown
with dimensions labelled. The red dashed triangle indicates the central region where GaN has
phase transitioned from hexagonal to cubic.
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Figure S2. Zoomed-in schematic of the boxed region indicated with continuous black box in Fig.
S1. Points labeled as A, B, C in Fig. S2 corresponds to the same points A, B, C in Fig. S1.
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Uniformity Study of the Cathodoluminescence and Electron
Backscatter Diffraction Measurements
To study the uniformity, large area (<1000 µm2) cathodoluminescence (CL) mapping on GaN with
various fill factors are carried out. Figure S3 shows the mapping of four representative grooves
with ff’s of (from top to bottom): 30%, 70%, 95%, and 120% at 5.7 K. In Fig. S3a, plain-view
SEM images of the grooves are shown, with high magnification insets showing individual groove.
Strips of c-GaN with various widths can be seen sandwiched between h-GaN strips. As the ff
increases from 30%, the c-GaN strips become more dominant, and completely covers the surface
when ff reaches 95%, similar to Fig. 1b in the manuscript. Once the ff becomes greater than 120%,
the h-GaN strips reappear at random places, sandwiching the c-GaN strips. The corresponding CL
mapping of the grooves in Fig. S3a at 355 nm, 390nm, and 425 nm are shown in Fig. S3b, c, d,
respectively. It is observed that as the ff increases, h-GaN exciton emission (355 nm) disappears,
and the DAP2 of c-GaN emission (425 nm) increases. The 390 nm emission corresponds to both
the DAP1 of c-GaN and the LO-phonon of the DAP1 of h-GaN, and therefore cannot be used to
accurately delineate the distribution of the two phases of GaN. The exciton emission of c-GaN
(378 nm) cannot be imaged easily, unfortunately, due to its relatively weak intensity compare to
other emissions. The zero phonon line of DAP1 of h-GaN also coincides with it, further undermines
the wavelength’s ability to distinguish the two phases of GaN.
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Figure S3. CL mapping of the (top to bottom) ff = 30%, 70%, 95%, 120%. (a) plain-view SEM
images with a high magnification SEM image. Monochromatic CL mapping at (b) 355 nm, (c) 390
nm, (d) 425 nm of the corresponding periods in (a) are shown.
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Figure S4. Multi-period EBSD overlay on SEM images of (a) ff = 40%, (b) ff = 65% (c) ff = 95%
periods using a beam current of 2 nA and acceleration voltage of 15 kV. Data is taken at RT.
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REFERENCES
1
C. Bayram, J. Ott, K.-T. Shiu, C.-W. Cheng, Y. Zhu, J. Kim, M. Razeghi, and D.K. Sadana,
Adv. Func. Mater. 24 (28) 4491(2014).
2
C. Bayram, C.-W. Cheng, D.K. Sadana, and K.-T. Shiu, U.S. Patent 9,059,075 (issued June 16,
2015).
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