# Stress and Grain Boundary Properties of GaN Films Prepared by Pulsed Laser Deposition Technique

Authors: D. Ghosh; S. Hussain; B. Ghosh; R. Bhar; A. K. Pal
Journal: ISRN Materials Science
 (2014)

---

## Abstract

Polycrystalline gallium nitride films were successfully deposited on fused silica substrates by ablating a GaN target using pulsed Nd-YAG laser. Microstructural studies indicated an increase in the average crystallite size from ~8 nm to ~70 nm with the increase in substrate temperature from 300 K to 873 K during deposition. The films deposited here were nearly stoichiometric. XPS studies indicated two strong peaks located at ~1116.6 eV and ~395 eV for Ga2p3/2 and a N1s core-level peak, respectively. The films deposited at substrate temperature above 573 K are predominantly zinc blende in nature. PL spectra of the films deposited at higher temperatures were dominated by a strong peak at ~3.2 eV. FTIR spectra indicated a strong and broad absorption peak centered ~520 cm−1 with two shoulders at ~570 cm−1 and 584 cm−1. Characteristic Raman peak at ~531 cm−1 for the A
1(TO) mode is observed for all the films. Grain boundary trap states varied between 3.1
×
10
15 and 7
×
10
15 m−2, while barrier height at the grain boundaries varied between 12.4 meV and 37.14 meV. Stress in the films decreased with the increase in substrate temperature.


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## Body

## 1. Introduction

Gallium nitride (GaN) is a promising material for applications in optoelectronic devices, such as ultraviolet-blue-green light-emitting diodes (LEDs) and laser diodes (LDs), due to its direct wide band gap and good thermal stability. It is equally suitable for high-temperature and high-power electronic applications. Depending on the growth conditions, GaN crystallizes either in the stable hexagonal (wurtzite,α-phase) or metastable cubic (zinc-blende, β-phase) polytypes. The prevalent deposition techniques for depositing GaN thin films are mainly metal-organic chemical vapor deposition (MOCVD) and molecular beam epitaxy (MBE). Recently, amorphous and polycrystalline GaN thin films deposited using magnetron sputtering technique [1–7] and laser ablation [8–10] technique have also been reported.GaN thin films with wurtzite structure were deposited by Chen et al. [5] by using reactive DC magnetron sputtering technique. The films exhibited a polycrystalline structure with a strong (002) orientation and were utilized as active channel layer to produce top-gate n-type thin-film transistors (TFTs). Highly textured polycrystalline GaN films having an average grain size of several hundred angstroms were obtained by Christie et al. [7] using an RF plasma-assisted molecular beam epitaxy system on quartz substrates. Zou et al. [6] reported the deposition of GaN films on glass substrates by the middle frequency magnetron sputtering method. Amorphous gallium nitride (a-GaN) films with thicknesses of 5 and 300 nm were deposited by Wang et al. [8] on n-Si (100) substrates by pulsed laser deposition (PLD), and their field emission (FE) properties were reported. Hong et al. [9] reported the deposition of GaN films on Si (400) wafers by a pulsed laser deposition technique. They observed that although the film and the substrate did not have any interface epitaxy, out-of-plane texture of the film was controllable. Lopez et al. [10] reported a process to produce GaN films activated with Eu3+ ions by the pulsed laser deposition (PLD) technique. The film was found to contain submicron size crystals with hexagonal shape. Sanguino et al. [11] deposited GaN thin films on prenitridated c-plane sapphire at two substrate temperatures (600°C and 650°C) by cyclic pulsed laser deposition. Increase in the surface mobility for a better crystal growth was associated with increasing substrate temperature during deposition. Tong et al. [12] deposited GaN thin films on Si (111) substrates using PLD assisted by gas discharge. The structure, surface morphology, and optoelectronic properties of the films were found to be strongly dependent on the substrate temperature and the laser incident energy.One of the current issues in GaN research is to deposit high quality GaN polycrystalline thin films using inexpensive substrate and at a relatively lower substrate temperature. Trap states at the grain boundary region and residual stress would modulate the electron transport process in these polycrystalline films. Excepting the attempt made by Chowdhury et al. [3] on Be-doped polycrystalline GaN films, none of the above reports addressed the grain boundary phenomena associated with GaN polycrystalline films adequately. The density of trap states at the grain boundary (Q
t
~
1
×
10
15
m
-
2) and the barrier height (
E
b
~
1.6
eV
) reported by Chowdhury et al. were significantly higher than those one would expect for a good device material. However, they did not report the stress content in the films. Hence, it is apparent that the information on GaN in polycrystalline thin film form reported so far is far from being comprehensive and complete. Thus, there exists still a definite need to synthesize polycrystalline GaN films by appropriate deposition technique so that films containing lesser amount of density of trap states with associated lower barrier height and stress can be achieved. This would ensure unhindered electron transport in the device grade material thus synthesised.A successful attempt of synthesizing GaN in polycrystalline form by ablating GaN (99.995%) target under controlled deposition condition is reported here. The synthesized films were characterized by measuring optical, microstructural, photoluminescence, and compositional properties. Information related to stress and grain boundary properties has also been documented.


## 2. Experimental Details

A PLD system evacuated to a level of 10−7 Torr was used to ablate a GaN target (99.99% purity, Sigma Aldrich) by using a Nd:YAG laser (wavelength (λ) = 355 nm, pulse duration (τ) = 10 ns, frequency (f) = 10 Hz) for depositing GaN films on fused silica (quartz) and Si (100) substrates (for FTIR measurements). GaN films were deposited at four different substrate temperatures: 473 K, 673 K, 773 K, and 873 K. Time of deposition for all the films was ~9 minutes. The laser fluence was maintained at 8 J/cm2 and the laser beam was focused with an f
=
23 cm glass lens on the target at an angle of 45°, with respect to the normal. The target was rotated at 10 rpm to avoid fast drilling. The distance between the target and the substrate was maintained at ~6.5 cm.Compositional information was obtained by EDAX (Oxford Instruments’ INCA Energy 250 Microanalysis System) and Photoelectron Spectroscopy (XPS). XPS measurements were carried out using a M/s SPECS (Germany) make spectrometer.  Al-Kα linewas used as the X-ray source at 1486.74 eV. The anode was operated at a voltage of 15 kV and source power level was set to 400 W. An Ar ion source was also provided for sputter-etch cleaning of specimens. It was operated at 2 kV and 50 μA. This value varied depending on the sample. Spectra were collected using the DLSEGD-PHOIBOS-HSA3500 analyzer. The surface morphology of the films was studied by Field Emission Scanning Electron Microscope (FESEM) (Carl Zeiss SUPRA 55). X-ray diffraction (XRD) studies were carried out by using Rigaku MiniFlex XRD (0.154 nm Cu Kα line) to obtain the microstructural information. Photoluminescence (PL) measurements were recorded at 300 K by using a 300 W xenon arc lamp as the emission source. A Hamamatsu photomultiplier along with a 1/4 m monochromator was used as the detecting system. FTIR spectra were recorded in the range of 400–4000 cm−1 by using a Nicolet-380 FTIR spectrometer. Raman spectra were recorded using Renishaw inVia micro-Raman spectrometer using 514 nm Argon laser.


## 3. Results and Discussion

### 3.1. Microstructural Study

GaN films were deposited on fused silica substrates and Si (100) substrate at different substrate temperature (T
s). The FESEM pictures of four representative films deposited at 473 K, 673 K, 773 K, and 873 K are shown in Figures 1(a)–1(d), respectively. The FESEM images (Figures 1(a)–1(d)) reveal that the films are compact with well-dispersed polycrystals constituting the films. It was observed that the grain sizes (D) increased (inset of Figure 1(b)) with the increase in substrate temperatures during deposition. The grain size varied between 8 nm to 70 nm with increasing substrate temperature. It may be indicated here that the films grown here are compact and the grain size obtained for these films was significantly larger than those reported for GaN polycrystalline films prepared by sputtering technique [3]. Hong et al. [9] reported a grain size ~100–300 nm for the GaN films deposited by PLD technique on Si (400) wafers kept at 900°C. Comparing the substrate temperature during deposition, grain size obtained here compares favorably with those obtained by Hong et al. The grain size of the films reported in this communication is larger than that reported by Lopez et al. [10] for the Eu3+ doped GaN thin films grown on (0001) oriented Al2O3 substrates by the PLD growth technique.FESEM pictures for four representative GaN films deposited atT
s: (a) 473 K, (b) 673 K (inset shows the variation of grain size with substrate temperature), (c) 723 K (inset shows the corresponding XRD trace), and (d) 873 K (inset shows the corresponding grain size distribution).
(a)
(b)
(c)
(d)A representative histogram of a film deposited at 873 K is shown in the inset of Figure1(d) which shows a narrow distribution of the grain size. Gradual increase in grain size was observed for films as the substrate temperature was increased from 300 K to 623 K after which rapid grain growth was observed. XRD pattern of a representative GaN film deposited at T
s
=
773
K is shown in the inset of Figure 1(c). It may be mentioned here that the XRD patterns are dominated by sharp peaks corresponding to reflections from (101), (102), and (004) planes of GaN. The peak at ~73° became sharper for films deposited at 873 K at the expense of other peaks. This would mean that films deposited above 773 K became preferentially oriented in (004) direction.


### 3.2. XPS Studies

Figure2(a) shows the general survey XPS spectrum of a representative GaN film deposited at 873 K. The general survey scans of all the films were found to be the same. A low intense peak for C1s could be located at ~288.03 eV. This is shifted by ~3.63 eV from its standard value towards higher binding energy. The survey scan is dominated by two strong peaks at ~1117 eV (Figure 2(b)) and 1143.7 eV (Figure 2(c)) for Ga2p3/2 and Ga2p1/2 core-level spectra, respectively [13, 14]. The above intense peak ~1117 eV would correspond to Ga–N bond in GaN. There are a few lower intensity peaks for Ga3d5/2 and Ga3p1/2 at ~21 eV and 107 eV, respectively. The peak at 107 eV could be deconvoluted (inset of Figure 2(c)) in two peaks located at ~116.2 eV and 109.5 eV. The peak at ~116.2 eV could be identified as arising due to Ga3p1/2 and the peak at ~109.5 eV is due to Ga3p3/2. The peak  ~537 eV overlaps with that of O1s. Oxygen peak arises due to physisorbed oxygen at the surface. Low intensity peak of N1s around ~395 eV is also observed (Figure 2(d)). This peak is associated with the binding energies of N as Ga–N [15].XPS spectra of a representative GaN film deposited at 873 K: (a) general survey, (b) Ga2p3/2 core-level spectra, (c) Ga2p1/2 core-level spectra (inset shows the spectra for Ga3p1/2), and (d) N1s core-level spectra.
(a)
(b)
(c)
(d)


### 3.3. Photoluminescence Studies

PL spectra recorded at 80 K and at an excitation of 3.4 eV for the films deposited at 473 K and 873 K are shown in Figures3(a) and 3(b), respectively. PL spectra for films deposited at lower substrate temperatures (Figure 3(a)) contained three peaks located at ~3.2 eV, 2.91 eV, and ~2.63 eV, while films deposited above 773 K indicated a single peak at ~3.2 eV (Figure 3(b)). The peak at ~3.2 eV could be associated with near band edge luminescence, while the luminescence peaks at ~2.63 eV and 2.91 eV for films deposited at lower substrate temperatures could be identified due to transitions between deep donor and shallow acceptor pairs. The origin of the deep donor may be due to nitrogen vacancy or Ga interstitial site-related defects. The deep acceptor levels arise due to Ga vacancy (
V
Ga
) or gallium vacancy with oxygen on a nitrogen site complex.PL spectra for films deposited at (a) 473 K and (b) 873 K, (c) transmittance (T
r) spectra, and (d) plots of (α
h
ν)2  versus h
ν for a representative GaN film deposited at 873 K. Inset of (c) shows variation of band gap (
E
g
) with substrate temperature (T
s) and inset of (d) shows the plot of ln
⁡
(
α
h
ν
) versus ln
⁡
(
h
ν
-
E
g
).
(a)
(b)
(c)
(d)


### 3.4. Band Gap and Optical Constants

The absorption coefficients (α) of GaN films were determined by measuring transmittance and reflectance in these films [16, 17]. Films deposited at higher substrate temperature were more absorbing (Figure 3(c)) than those deposited at lower temperatures. This may be due to compactness of the films and lesser number of trap states at the grain boundaries. The absorption coefficient (α) may be written as a function of the incident photon energy (h
ν) as follows:
(1)
α
=
(
A
h
ν
)
{
h
ν
-
E
g
}
m
,
where A is a constant and varies for different transitions indicated by different values of m and E
g is the corresponding band gap of the material.Now, (1) may be rewritten as
(2)
ln
⁡
(
α
h
ν
)
=
ln
⁡
A
+
m
ln
⁡
(
h
ν
-
E
g
)
,
(3)
[
d
(
ln
⁡
α
h
ν
)
d
(
h
ν
)
]
=
m
h
ν
-
E
g
.Equation (3) indicates that a plot of d
[
ln
⁡
(
α
h
ν
)
]
/
d
[
h
ν
] versus h
ν will show a divergence at h
ν
=
E
g from which a rough estimate of E
g may be obtained and as such by using (2), the value of m can easily be evaluated from the slope of the plot of ln
⁡
(
α
h
ν
) versus ln
⁡
(
h
ν
-
E
g
). Figure 3(d) (inset) shows the plot of ln(α
h
ν) versus ln
⁡
(
h
ν
-
E
g
) for a representative film deposited at 873 K. The value of m was obtained from the slope ~0.51 which indicates a direct transition to be present in the film. The band gap was determined by extrapolating the linear portion of the plot of (α
h
ν)2 versus h
ν (Figure 3(d)) and was calculated to be ~3.27 eV. The band gaps obtained for films deposited at different substrate temperatures (T
s) are shown in Table 1 and the variation of E
g with T
s is shown in the inset of Figure 3(c). It could be observed that the films deposited at temperatures higher than 573 K had band gap ~3.2 eV to 3.27 eV. Films deposited at lower temperatures indicated gradual increase in band gap ~2.9 eV to 3.11 eV. It may be noted here that the fall in the transmittance versus wavelength curve (not shown here) was sharper for films deposited at higher substrate temperatures.Table 1
Different quantities related to GaN films obtained from this study.
Sample number and substrate temperature (T
s)
E
g (eV)
Grain size from SEM (nm)
Λ
d (nm)
Q
t (1015 m−2)
E
b (meV)
Stress(GPa)
GaN-1473 K
2.90
8
38.3
7
37.2
0.37
GaN-2573 K
3.11
12
35.5
6.6
33.2
0.31
GaN-3673 K
3.21
14
33.2
6.0
26.2
0.25
GaN-4773 K
3.24
35
30.4
5.2
18.1
0.17
GaN-5873 K
3.27
70
28.9
3.1
12.4
0.11The optical constants (refractive indexn and extinction coefficient k) of the polycrystalline GaN films were determined from the transmittance versus wavelength traces by using the Kramers-Kronig (KK) model [18] and the modified KK model given by Xue et al. [19]. Using the values for the real part of the refractive index (n) and the extinction coefficient (k), the real and complex part of the dielectric constant (ε
1 and ε
2, resp.) can be estimated by using the relations:
(4)
ε
1
=
n
2
(
λ
)
-
k
2
(
λ
)
,
ε
2
=
2
n
(
λ
)
k
(
λ
)
.The values ofn and k obtained as above are shown in Figures 4(a) and 4(b), respectively. The refractive indices for these GaN films were found to vary from 2.05 to 2.35 within the measured energy range. Their dielectric constant varied from 3.75 to 5.5 as shown in Figures 4(c) and 4(d).(a) Plots ofn versus λ, (b) plots of k versus λ, (c) plots of ε
1 versus λ, and (d) plots of ε
2 versus λ of a representative GaN film.
(a)
(b)
(c)
(d)


### 3.5. FTIR and Raman Studies

FTIR spectra for all the films deposited at different substrate temperatures on Si (100) were found to be dominated by a strong and broad absorption peak centered ~520 cm−1 with two shoulders at ~570 cm−1 and 584 cm−1. Figure 5(a) shows the FTIR spectra for a representative polycrystalline GaN films deposited at T
s
=
873
K. The broad peak ~520 cm−1 may be ascribed to the presence of peaks due to Ga–N stretching mode at ~570 cm−1 and E
1
(
LO
) phonon or A
1
(
LO
) phonon mode at ~584 cm−1 [20]. In addition to these peaks, presence of absorption peaks at ~990 cm−1 and 1521 cm−1 could be due to the Si–O bonds originating from the substrate (silicon).ss.(a) FTIR and (b) Raman spectra of a representative GaN film deposited at 873 K.
(a)
(b)Raman spectra for a mixed cubic and hexagonal GaN are generally governed by the relations between the phonon modes of the two modifications. The wurtzite structure of GaN arises from the zincblende structure by compressing the crystal along the (111) axis which becomes thec-axis of the hexagonal phase. Also, it may happen that changing the stacking of layers along this axis would result in a doubling of the number of atoms in a primitive unit cell. This would culminate in splitting of T
2 mode of the cubic phase into the A
1 and E
1 modes of the hexagonal phase. Since the hexagonal distortion is small, the above splitting will also be generally small.GaN films deposited at lower substrate temperatures are predominantly hexagonal in structure and cubic GaN content in the films increases as the deposition temperature is increased. Thus, one would expect relevant signatures in Raman modes in such films. Figure5(b) shows the Raman spectra of a GaN films deposited at 873 K. The Raman spectrum showed a first-order Raman active phonon mode at ~531 cm−1 for A
1
(
TO
) modes. Three broad peaks spreading over 570 cm−1 to 680 cm−1 have their centers at 571 cm−1, 616 cm−1, and 644 cm−1, corresponding to the first order high frequency E
2, overtone of E
1
(
TO
), and A
1
(
TO
) overtone modes, respectively. The strongest E
2 (high) phonon line in the spectrum reflects the characteristics of the hexagonal crystal phase of the GaN film. The Raman peak at 672 cm−1 would arise from the optical-phonon branch at the zone boundary.It is known that at high defect densities wave vector conservation in the Raman scattering process breaks down and phonons from the entire Brillouin zone can be observed in the Raman spectrum [21]. Thus, the Raman spectrum would reflect the total phonon density of states due to disorder-activated Raman scattering (DARS). The Raman peak at 672 cm−1 probably arises from the optical-phonon branch at the zone boundary. Siegle and coworkers [22] have reported second-order Raman scattering experiments on hexagonal and cubic GaN covering the acoustic and the optical overtone spectral region. The hexagonal modes lying between the first-order peaks at ~616 cm−1 and ~644 cm−1 could be attributed to the overtone processes of the highest acoustic-phonon branch either at the zone boundary (L point) or from the B mode at the Γ point.


### 3.6. Grain Boundary Studies from Below-Band-Gap Absorption Studies

GaN films deposited here could be seen to consist of aggregates of randomly distributed grains and grain boundary regions. Size of the grains increased as the substrate temperature during deposition was increased (inset of Figure1(b)). The grain boundary region would contain a large amount of defect states which become charged after trapping free carriers from the neighbouring grains. In addition to these intrinsic defect states at the grain boundary regions of the GaN films, a considerable amount of thermal stress due to the mismatch of thermal expansion coefficients of the film (
α
film
) and substrate (
α
subs
) is bound to appear in these films. This would result in fluctuating nature of the potential [23–25]. The band gap (
E
g
) would in turn also have a fluctuating nature. This would result in additional indirect optical transitions below the fundamental band gap of the material. The details of the processes have already been reported elsewhere [23–25]. Following the detailed procedure reported by Maity et al. [23], the relevant grain boundary parameters like density of trap states (Q
t) and barrier height at the grain boundary (E
b) were computed from the theoretical fit of normalized absorption coefficients α
/
α
0 below the band gap region.Figure6(a) shows representative plots of the experimental data of normalized absorption coefficients α
/
α
0 for a representative GaN film deposited at 873 K. It may be mentioned here that the contribution due to the thermal disorder at a specific temperature (at which the optical absorption has been recorded) is fixed, the ultimate shape of α
/
α
0 versus (
E
g
-
h
ν
) plot will depend on the amount of the intrinsic disorder or the density of the defect states present in the film. The grain boundary parameters (Q
t and E
b) were estimated from the best fit theoretical curve (shown in Figure 6(a)) corresponding to the experimental data of α
/
α
0 versus (
E
g
-
h
ν
), α
0 being the value of α at E
g. The values of Q
t and E
b are given in Table 1.(a) Variation ofα
/
α
0 versus (
E
g
-
h
ν
) for a representative GaN film deposited at 873 K. -▲-: theoretical best fit curves. (b) Variation of trap state density (Q
t) and barrier height (E
b) with grain size and (c) variation of stress (S) with grain size (—■—) and density of trap state (Q
t) (—▲—) at grain boundary region for GaN films deposited at 873 K.
(a)
(b)
(c)Variation ofQ
t and E
b with grain size (i.e., with substrate temperature during deposition) is depicted in Figure 6(b). It could be observed that the density of trap states (Q
t) at the grain boundaries decreased from 7
×
10
15
m
-
2 to 3.1
×
10
15
m
-
2 for films deposited at higher temperatures. These values are smaller than those reported for the rf sputtered films [3]. The barrier height at the grain boundaries (E
b) was significantly smaller compared to those reported by Chowdhury et al. [3]. As the films are high resistive, the number density of charge carriers will be small. The films would be fully depleted of charge carriers when the density of trap states at the grain boundaries is large for films deposited at lower temperatures. As the number density of trap states decreased for films deposited at higher substrate temperatures, probability of the trap states to get fully filled by the charge carriers will increase leaving behind the grains partially depleted. This has been reflected by the exponential fall in E
b with the grain size.


### 3.7. Determination of Stress

Earlier reports by various workers indicated that the material properties (e.g., stress, strain, and barrier height) are very much influenced by the presence of trap states at the grain boundaries which are, in fact, highly insulating regions. The details of the technique have already been discussed elsewhere [24]. It has been observed in the earlier section that grain boundaries in polycrystalline GaN films effectively control the electron transport as well as optical absorbance. Besides the above grain boundary effects, mechanical stress due to lattice dilation was seen to modulate the lattice ordering at the grain and grain boundary region. This would modulate the below-band-edge optical absorption processes as a whole in the form of electrostatic fluctuations of the band edge [26–28] and hence information on the stress could also be generated from the above.The disorders in the film would result in considerable amount of indirect optical transitions for photon energyh
ν
<
E
g which in turn would produce a broad absorption band tail, in contrast to the sharp absorption edge produced in a single-crystalline material. The specific shape of the absorption band tail which depends on the initial and final states of the transitions concerned will be determined by the intrinsic strain (
δ
a
/
a
)
gb. The intrinsic strain could be determined by the density of the defect states at the grain boundary region of the film since the other contributions in the total strain would remain constant for a particular substrate material at a specific temperature.Now, considering contributions from both the thermal and grain boundary effects the strain(
δ
a
/
a
) and stress (S) in the GaN films may be expressed as
(5)
(
δ
a
a
)
total
=
(
δ
a
a
)
gb
+
(
δ
a
a
)
th
,
S
total
=
S
gb
+
S
th
.Here,S
gb
,
(
δ
a
/
a
)
gb, and S
th, (
δ
a
/
a
)
th correspond to the grain boundary and thermal components of stress and strain, respectively. The thermal stress arises when the film is cooled after deposition. The stress due to grain boundaries will, in general, be proportional to the total grain boundary area which in turn would depend inversely on the average grain size [25, 28, 29]. We have considered the lattice dilation at finite temperature as due to phonon vibration and defect states in the polycrystalline GaN films [23, 25, 27].From the experimentally obtained values of residual strain(
δ
a
/
a
) obtained as above and by knowing the standard values of Young’s modulus Y (GPa) and the Poisson’s ratio (
γ
) for a given film material, the true stress (S) can be obtained from (6) as shown below:
(6)
S
=
[
Y
1
-
γ
]
(
δ
a
a
)
.Stresses in the films thus evaluated are shown in Figure6(c). It may be noted that the stress decreased from 0.38 GPa to 0.1 GPa for films deposited at higher temperature, that is, with increase in grain size (Table 1 and Figure 6(c)). This result is in commensurate with the fact that, at a reasonable deposition rate, the adatoms will have increased mobility with increased substrate temperature during deposition to facilitate grain growth. Further, with increased grain size, grain boundaries would decrease resulting in decrease in the density of trap states.


## 3.1. Microstructural Study

GaN films were deposited on fused silica substrates and Si (100) substrate at different substrate temperature (T
s). The FESEM pictures of four representative films deposited at 473 K, 673 K, 773 K, and 873 K are shown in Figures 1(a)–1(d), respectively. The FESEM images (Figures 1(a)–1(d)) reveal that the films are compact with well-dispersed polycrystals constituting the films. It was observed that the grain sizes (D) increased (inset of Figure 1(b)) with the increase in substrate temperatures during deposition. The grain size varied between 8 nm to 70 nm with increasing substrate temperature. It may be indicated here that the films grown here are compact and the grain size obtained for these films was significantly larger than those reported for GaN polycrystalline films prepared by sputtering technique [3]. Hong et al. [9] reported a grain size ~100–300 nm for the GaN films deposited by PLD technique on Si (400) wafers kept at 900°C. Comparing the substrate temperature during deposition, grain size obtained here compares favorably with those obtained by Hong et al. The grain size of the films reported in this communication is larger than that reported by Lopez et al. [10] for the Eu3+ doped GaN thin films grown on (0001) oriented Al2O3 substrates by the PLD growth technique.FESEM pictures for four representative GaN films deposited atT
s: (a) 473 K, (b) 673 K (inset shows the variation of grain size with substrate temperature), (c) 723 K (inset shows the corresponding XRD trace), and (d) 873 K (inset shows the corresponding grain size distribution).
(a)
(b)
(c)
(d)A representative histogram of a film deposited at 873 K is shown in the inset of Figure1(d) which shows a narrow distribution of the grain size. Gradual increase in grain size was observed for films as the substrate temperature was increased from 300 K to 623 K after which rapid grain growth was observed. XRD pattern of a representative GaN film deposited at T
s
=
773
K is shown in the inset of Figure 1(c). It may be mentioned here that the XRD patterns are dominated by sharp peaks corresponding to reflections from (101), (102), and (004) planes of GaN. The peak at ~73° became sharper for films deposited at 873 K at the expense of other peaks. This would mean that films deposited above 773 K became preferentially oriented in (004) direction.


## 3.2. XPS Studies

Figure2(a) shows the general survey XPS spectrum of a representative GaN film deposited at 873 K. The general survey scans of all the films were found to be the same. A low intense peak for C1s could be located at ~288.03 eV. This is shifted by ~3.63 eV from its standard value towards higher binding energy. The survey scan is dominated by two strong peaks at ~1117 eV (Figure 2(b)) and 1143.7 eV (Figure 2(c)) for Ga2p3/2 and Ga2p1/2 core-level spectra, respectively [13, 14]. The above intense peak ~1117 eV would correspond to Ga–N bond in GaN. There are a few lower intensity peaks for Ga3d5/2 and Ga3p1/2 at ~21 eV and 107 eV, respectively. The peak at 107 eV could be deconvoluted (inset of Figure 2(c)) in two peaks located at ~116.2 eV and 109.5 eV. The peak at ~116.2 eV could be identified as arising due to Ga3p1/2 and the peak at ~109.5 eV is due to Ga3p3/2. The peak  ~537 eV overlaps with that of O1s. Oxygen peak arises due to physisorbed oxygen at the surface. Low intensity peak of N1s around ~395 eV is also observed (Figure 2(d)). This peak is associated with the binding energies of N as Ga–N [15].XPS spectra of a representative GaN film deposited at 873 K: (a) general survey, (b) Ga2p3/2 core-level spectra, (c) Ga2p1/2 core-level spectra (inset shows the spectra for Ga3p1/2), and (d) N1s core-level spectra.
(a)
(b)
(c)
(d)


## 3.3. Photoluminescence Studies

PL spectra recorded at 80 K and at an excitation of 3.4 eV for the films deposited at 473 K and 873 K are shown in Figures3(a) and 3(b), respectively. PL spectra for films deposited at lower substrate temperatures (Figure 3(a)) contained three peaks located at ~3.2 eV, 2.91 eV, and ~2.63 eV, while films deposited above 773 K indicated a single peak at ~3.2 eV (Figure 3(b)). The peak at ~3.2 eV could be associated with near band edge luminescence, while the luminescence peaks at ~2.63 eV and 2.91 eV for films deposited at lower substrate temperatures could be identified due to transitions between deep donor and shallow acceptor pairs. The origin of the deep donor may be due to nitrogen vacancy or Ga interstitial site-related defects. The deep acceptor levels arise due to Ga vacancy (
V
Ga
) or gallium vacancy with oxygen on a nitrogen site complex.PL spectra for films deposited at (a) 473 K and (b) 873 K, (c) transmittance (T
r) spectra, and (d) plots of (α
h
ν)2  versus h
ν for a representative GaN film deposited at 873 K. Inset of (c) shows variation of band gap (
E
g
) with substrate temperature (T
s) and inset of (d) shows the plot of ln
⁡
(
α
h
ν
) versus ln
⁡
(
h
ν
-
E
g
).
(a)
(b)
(c)
(d)


## 3.4. Band Gap and Optical Constants

The absorption coefficients (α) of GaN films were determined by measuring transmittance and reflectance in these films [16, 17]. Films deposited at higher substrate temperature were more absorbing (Figure 3(c)) than those deposited at lower temperatures. This may be due to compactness of the films and lesser number of trap states at the grain boundaries. The absorption coefficient (α) may be written as a function of the incident photon energy (h
ν) as follows:
(1)
α
=
(
A
h
ν
)
{
h
ν
-
E
g
}
m
,
where A is a constant and varies for different transitions indicated by different values of m and E
g is the corresponding band gap of the material.Now, (1) may be rewritten as
(2)
ln
⁡
(
α
h
ν
)
=
ln
⁡
A
+
m
ln
⁡
(
h
ν
-
E
g
)
,
(3)
[
d
(
ln
⁡
α
h
ν
)
d
(
h
ν
)
]
=
m
h
ν
-
E
g
.Equation (3) indicates that a plot of d
[
ln
⁡
(
α
h
ν
)
]
/
d
[
h
ν
] versus h
ν will show a divergence at h
ν
=
E
g from which a rough estimate of E
g may be obtained and as such by using (2), the value of m can easily be evaluated from the slope of the plot of ln
⁡
(
α
h
ν
) versus ln
⁡
(
h
ν
-
E
g
). Figure 3(d) (inset) shows the plot of ln(α
h
ν) versus ln
⁡
(
h
ν
-
E
g
) for a representative film deposited at 873 K. The value of m was obtained from the slope ~0.51 which indicates a direct transition to be present in the film. The band gap was determined by extrapolating the linear portion of the plot of (α
h
ν)2 versus h
ν (Figure 3(d)) and was calculated to be ~3.27 eV. The band gaps obtained for films deposited at different substrate temperatures (T
s) are shown in Table 1 and the variation of E
g with T
s is shown in the inset of Figure 3(c). It could be observed that the films deposited at temperatures higher than 573 K had band gap ~3.2 eV to 3.27 eV. Films deposited at lower temperatures indicated gradual increase in band gap ~2.9 eV to 3.11 eV. It may be noted here that the fall in the transmittance versus wavelength curve (not shown here) was sharper for films deposited at higher substrate temperatures.Table 1
Different quantities related to GaN films obtained from this study.
Sample number and substrate temperature (T
s)
E
g (eV)
Grain size from SEM (nm)
Λ
d (nm)
Q
t (1015 m−2)
E
b (meV)
Stress(GPa)
GaN-1473 K
2.90
8
38.3
7
37.2
0.37
GaN-2573 K
3.11
12
35.5
6.6
33.2
0.31
GaN-3673 K
3.21
14
33.2
6.0
26.2
0.25
GaN-4773 K
3.24
35
30.4
5.2
18.1
0.17
GaN-5873 K
3.27
70
28.9
3.1
12.4
0.11The optical constants (refractive indexn and extinction coefficient k) of the polycrystalline GaN films were determined from the transmittance versus wavelength traces by using the Kramers-Kronig (KK) model [18] and the modified KK model given by Xue et al. [19]. Using the values for the real part of the refractive index (n) and the extinction coefficient (k), the real and complex part of the dielectric constant (ε
1 and ε
2, resp.) can be estimated by using the relations:
(4)
ε
1
=
n
2
(
λ
)
-
k
2
(
λ
)
,
ε
2
=
2
n
(
λ
)
k
(
λ
)
.The values ofn and k obtained as above are shown in Figures 4(a) and 4(b), respectively. The refractive indices for these GaN films were found to vary from 2.05 to 2.35 within the measured energy range. Their dielectric constant varied from 3.75 to 5.5 as shown in Figures 4(c) and 4(d).(a) Plots ofn versus λ, (b) plots of k versus λ, (c) plots of ε
1 versus λ, and (d) plots of ε
2 versus λ of a representative GaN film.
(a)
(b)
(c)
(d)


## 3.5. FTIR and Raman Studies

FTIR spectra for all the films deposited at different substrate temperatures on Si (100) were found to be dominated by a strong and broad absorption peak centered ~520 cm−1 with two shoulders at ~570 cm−1 and 584 cm−1. Figure 5(a) shows the FTIR spectra for a representative polycrystalline GaN films deposited at T
s
=
873
K. The broad peak ~520 cm−1 may be ascribed to the presence of peaks due to Ga–N stretching mode at ~570 cm−1 and E
1
(
LO
) phonon or A
1
(
LO
) phonon mode at ~584 cm−1 [20]. In addition to these peaks, presence of absorption peaks at ~990 cm−1 and 1521 cm−1 could be due to the Si–O bonds originating from the substrate (silicon).ss.(a) FTIR and (b) Raman spectra of a representative GaN film deposited at 873 K.
(a)
(b)Raman spectra for a mixed cubic and hexagonal GaN are generally governed by the relations between the phonon modes of the two modifications. The wurtzite structure of GaN arises from the zincblende structure by compressing the crystal along the (111) axis which becomes thec-axis of the hexagonal phase. Also, it may happen that changing the stacking of layers along this axis would result in a doubling of the number of atoms in a primitive unit cell. This would culminate in splitting of T
2 mode of the cubic phase into the A
1 and E
1 modes of the hexagonal phase. Since the hexagonal distortion is small, the above splitting will also be generally small.GaN films deposited at lower substrate temperatures are predominantly hexagonal in structure and cubic GaN content in the films increases as the deposition temperature is increased. Thus, one would expect relevant signatures in Raman modes in such films. Figure5(b) shows the Raman spectra of a GaN films deposited at 873 K. The Raman spectrum showed a first-order Raman active phonon mode at ~531 cm−1 for A
1
(
TO
) modes. Three broad peaks spreading over 570 cm−1 to 680 cm−1 have their centers at 571 cm−1, 616 cm−1, and 644 cm−1, corresponding to the first order high frequency E
2, overtone of E
1
(
TO
), and A
1
(
TO
) overtone modes, respectively. The strongest E
2 (high) phonon line in the spectrum reflects the characteristics of the hexagonal crystal phase of the GaN film. The Raman peak at 672 cm−1 would arise from the optical-phonon branch at the zone boundary.It is known that at high defect densities wave vector conservation in the Raman scattering process breaks down and phonons from the entire Brillouin zone can be observed in the Raman spectrum [21]. Thus, the Raman spectrum would reflect the total phonon density of states due to disorder-activated Raman scattering (DARS). The Raman peak at 672 cm−1 probably arises from the optical-phonon branch at the zone boundary. Siegle and coworkers [22] have reported second-order Raman scattering experiments on hexagonal and cubic GaN covering the acoustic and the optical overtone spectral region. The hexagonal modes lying between the first-order peaks at ~616 cm−1 and ~644 cm−1 could be attributed to the overtone processes of the highest acoustic-phonon branch either at the zone boundary (L point) or from the B mode at the Γ point.


## 3.6. Grain Boundary Studies from Below-Band-Gap Absorption Studies

GaN films deposited here could be seen to consist of aggregates of randomly distributed grains and grain boundary regions. Size of the grains increased as the substrate temperature during deposition was increased (inset of Figure1(b)). The grain boundary region would contain a large amount of defect states which become charged after trapping free carriers from the neighbouring grains. In addition to these intrinsic defect states at the grain boundary regions of the GaN films, a considerable amount of thermal stress due to the mismatch of thermal expansion coefficients of the film (
α
film
) and substrate (
α
subs
) is bound to appear in these films. This would result in fluctuating nature of the potential [23–25]. The band gap (
E
g
) would in turn also have a fluctuating nature. This would result in additional indirect optical transitions below the fundamental band gap of the material. The details of the processes have already been reported elsewhere [23–25]. Following the detailed procedure reported by Maity et al. [23], the relevant grain boundary parameters like density of trap states (Q
t) and barrier height at the grain boundary (E
b) were computed from the theoretical fit of normalized absorption coefficients α
/
α
0 below the band gap region.Figure6(a) shows representative plots of the experimental data of normalized absorption coefficients α
/
α
0 for a representative GaN film deposited at 873 K. It may be mentioned here that the contribution due to the thermal disorder at a specific temperature (at which the optical absorption has been recorded) is fixed, the ultimate shape of α
/
α
0 versus (
E
g
-
h
ν
) plot will depend on the amount of the intrinsic disorder or the density of the defect states present in the film. The grain boundary parameters (Q
t and E
b) were estimated from the best fit theoretical curve (shown in Figure 6(a)) corresponding to the experimental data of α
/
α
0 versus (
E
g
-
h
ν
), α
0 being the value of α at E
g. The values of Q
t and E
b are given in Table 1.(a) Variation ofα
/
α
0 versus (
E
g
-
h
ν
) for a representative GaN film deposited at 873 K. -▲-: theoretical best fit curves. (b) Variation of trap state density (Q
t) and barrier height (E
b) with grain size and (c) variation of stress (S) with grain size (—■—) and density of trap state (Q
t) (—▲—) at grain boundary region for GaN films deposited at 873 K.
(a)
(b)
(c)Variation ofQ
t and E
b with grain size (i.e., with substrate temperature during deposition) is depicted in Figure 6(b). It could be observed that the density of trap states (Q
t) at the grain boundaries decreased from 7
×
10
15
m
-
2 to 3.1
×
10
15
m
-
2 for films deposited at higher temperatures. These values are smaller than those reported for the rf sputtered films [3]. The barrier height at the grain boundaries (E
b) was significantly smaller compared to those reported by Chowdhury et al. [3]. As the films are high resistive, the number density of charge carriers will be small. The films would be fully depleted of charge carriers when the density of trap states at the grain boundaries is large for films deposited at lower temperatures. As the number density of trap states decreased for films deposited at higher substrate temperatures, probability of the trap states to get fully filled by the charge carriers will increase leaving behind the grains partially depleted. This has been reflected by the exponential fall in E
b with the grain size.


## 3.7. Determination of Stress

Earlier reports by various workers indicated that the material properties (e.g., stress, strain, and barrier height) are very much influenced by the presence of trap states at the grain boundaries which are, in fact, highly insulating regions. The details of the technique have already been discussed elsewhere [24]. It has been observed in the earlier section that grain boundaries in polycrystalline GaN films effectively control the electron transport as well as optical absorbance. Besides the above grain boundary effects, mechanical stress due to lattice dilation was seen to modulate the lattice ordering at the grain and grain boundary region. This would modulate the below-band-edge optical absorption processes as a whole in the form of electrostatic fluctuations of the band edge [26–28] and hence information on the stress could also be generated from the above.The disorders in the film would result in considerable amount of indirect optical transitions for photon energyh
ν
<
E
g which in turn would produce a broad absorption band tail, in contrast to the sharp absorption edge produced in a single-crystalline material. The specific shape of the absorption band tail which depends on the initial and final states of the transitions concerned will be determined by the intrinsic strain (
δ
a
/
a
)
gb. The intrinsic strain could be determined by the density of the defect states at the grain boundary region of the film since the other contributions in the total strain would remain constant for a particular substrate material at a specific temperature.Now, considering contributions from both the thermal and grain boundary effects the strain(
δ
a
/
a
) and stress (S) in the GaN films may be expressed as
(5)
(
δ
a
a
)
total
=
(
δ
a
a
)
gb
+
(
δ
a
a
)
th
,
S
total
=
S
gb
+
S
th
.Here,S
gb
,
(
δ
a
/
a
)
gb, and S
th, (
δ
a
/
a
)
th correspond to the grain boundary and thermal components of stress and strain, respectively. The thermal stress arises when the film is cooled after deposition. The stress due to grain boundaries will, in general, be proportional to the total grain boundary area which in turn would depend inversely on the average grain size [25, 28, 29]. We have considered the lattice dilation at finite temperature as due to phonon vibration and defect states in the polycrystalline GaN films [23, 25, 27].From the experimentally obtained values of residual strain(
δ
a
/
a
) obtained as above and by knowing the standard values of Young’s modulus Y (GPa) and the Poisson’s ratio (
γ
) for a given film material, the true stress (S) can be obtained from (6) as shown below:
(6)
S
=
[
Y
1
-
γ
]
(
δ
a
a
)
.Stresses in the films thus evaluated are shown in Figure6(c). It may be noted that the stress decreased from 0.38 GPa to 0.1 GPa for films deposited at higher temperature, that is, with increase in grain size (Table 1 and Figure 6(c)). This result is in commensurate with the fact that, at a reasonable deposition rate, the adatoms will have increased mobility with increased substrate temperature during deposition to facilitate grain growth. Further, with increased grain size, grain boundaries would decrease resulting in decrease in the density of trap states.


## 4. Conclusion

Polycrystalline films of GaN were deposited with different grain sizes by varying the substrate temperature during pulse laser deposition. Grain size varied between 8 to 70 nm as the substrate temperature during sputtering changed from 300 K to 873 K. XPS studies indicated two strong peaks located at ~1116.6 eV and ~395 eV for Ga2p3/2 and N1s core-level spectra, respectively. Photoluminescence measurement at 300 K exhibited a strong peak at ~2.91 eV followed by a low intensity peak for band edge luminescence at ~3.20 eV. The luminescence at ~2.63 eV could be identified due to transitions between deep donor and shallow acceptor pairs. FTIR spectra were dominated by a strong and broad absorption peak centered ~520 cm−1 with two shoulders at ~570 cm−1 and 584 cm−1. First-order Raman active phonon mode at ~513 cm−1 for A
1
(
TO
) modes was observed. Additionally, three broad peaks spreading over 570 cm−1 to 680 cm−1 that appeared in Raman spectra have their centers at 570 cm−1,  614 cm−1,  and 644 cm−1, corresponding to the first-order high frequency E
2, overtone of E
1
(
TO
), and A
1
(
TO
) overtone modes, respectively. Density of trap states at the grain boundary (Q
t) changed from 7
×
10
-
15
m
-
2 to 3.1
×
10
-
15
m
-
2 and the barrier height (E
b) decreased from 37.17 meV to 12.4 meV as the grain size increased with the increase in deposition temperature. The stress decreased from 0.38 GPa to 0.1 GPa for films deposited at higher temperature.



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*Source: 521701-2014-03-17.xml*