Model for Low-Temperature Growth of Gallium Nitride

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A Model for Low-temperature Growth of Gallium Nitride Chao Wu, Jiadong Yu, Yanxiong E, Yi Luo, Zhibiao Hao, Jian Wang, Lai Wang, Changzheng Sun, Bing Xiong, Yanjun Han, and Hongtao Li Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.6b00583 • Publication Date (Web): 16 Aug 2016 Downloaded from http://pubs.acs.org on August 16, 2016

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Crystal Growth & Design

A Model for Low-temperature Growth of Gallium Nitride Chao Wu, Jiadong Yu, Yanxiong E, Yi Luo*, Zhibiao Hao*, Jian Wang, Lai Wang, Changzheng Sun, Bing Xiong, Yanjun Han, and Hongtao Li Tsinghua National Laboratory for Information Science and Technology, Department of Electronic Engineering,Tsinghua University, Beijing 100084, China KEYWORDS:semiconductor, Gallium Nitride, low-temperature growth, growth model, surface diffusion

ABSTRACT: A low growth temperature is essential to realize low-cost and large-area GaNbased lighting and display. In this work, through detailed investigation under PAMBE, a physical model for low-temperature growth of GaN under N-rich condition is proposed based on the facts that the desorption process of Ga adatoms can be ignored and the energy for lattice incorporation of Ga adatoms comes only from active N species. A normalized diffusion length (NDL, a dimensionless parameter) is also introduced to provide further insight: the diffusion rate and diffusion time of Ga adatoms are determined by the growth temperature and N flux, respectively, meanwhile the average distance between Ga adatoms is affected by both Ga flux and N flux. Excellent agreement between theoretical predictions and experimental results validates this

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model and demonstrates the importance of NDL in optimizing the growth condition. The model and NDL could be applied in growing III-nitrides under N-rich condition by various lowtemperature growth techniques where group-III adatoms are unable to incorporate into the lattice by their own kinetic energy.

INTRODUCTION III-nitride semiconductors with tunable direct bandgaps ranging from UV to IR wavelengths have been widely applied in light-emitting diodes, laser diodes, photo-detectors and high power microwave/millimeter-wave devices, etc.1-4Usually, a high growth temperature (> 800 ℃) is required to dissociate the precursors and/or overcome the surface energy barrier of atom migration in growing III-nitrides by mostly-used metal-organic chemical vapor deposition (MOCVD) and molecular beam epitaxy (MBE) technologies.5,6 Although high growth temperature can realize high-quality crystal, it inevitably brings several drawbacks: (i) the commercially available substrates are limited to heat-resisting materials such as sapphire, SiC and Si, but excluding the commercial soda-lime glass with relatively low softening point (≈ 620 ℃) for low-cost and large-area lighting and display;7 (ii) it is difficult to grow In-rich alloys at high temperature because of low vapor pressure and dissociation temperature of InN;8 and (iii) high-temperature growth degrades the performance of Si-based CMOS devices, restricting the integration of III-nitrides with Si CMOS technology.9 Apparently, lowtemperature growth is promising to get rid of these drawbacks, especially the limitation on substrate material. To date, a considerable number of low-temperature growth techniques have been employed to grow III-nitrides, including radio-frequency reactive sputtering,10 pulsed


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sputtering deposition,7,11 pulsed laser deposition,12,13 plasma-assisted MBE (PAMBE),14,15 laser MBE,16 atomic layer deposition,17 remote plasma chemical vapor deposition,18 migration enhanced afterglow chemical vapor deposition,19and electron cyclotron resonance MOCVD,20 etc. The key measure to reduce the growth temperature is using plasma instead of thermal energy to dissociate the precursors. Some of these techniques have achieved quite good crystalline quality even under room-temperature growth.11-13 But unfortunately, the physical model for lowtemperature growth of III-nitrides is still unclear, and the kinetic model successfully applied in high-temperature growth is no longer valid in low-temperature growth, as the atom incorporation and desorption processes are completely different. In this work, through detailed investigation under PAMBE, a model for low-temperature growth of GaN under N-rich condition is proposed to reveal its physical mechanism, and a normalized diffusion length (NDL, a dimensionless parameter) is introduced for growth parameter optimization. It should be noted that Ga-rich condition is not considered in this work because Ga droplets will be formed as excessive Ga adatoms cannot be evaporated at such low temperature. The model is built based on two characteristics of low-temperature growth: (i) the desorption process of Ga adatoms (critically important in high-temperature growth) can be ignored as the thermal desorption rate becomes extremely low (substrate temperature < 620 ℃),21 and (ii) energy necessary for Ga adatoms to overcome the energy barrier of lattice incorporation comes predominantly (here in after considered as only) from active N species in nitrogen plasma, not substrate heating. The potential energy of all active N species is higher than 6.2 eV, while the threshold value of GaN formation reaction is only 1.9 eV.22,23 In the derivation of NDL, only the surface diffusion of Ga adatoms will be considered, and it is assumed that Ga and N atoms will react into GaN when and only when both of them are in the simplest repeating unit of potential


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energy surface since the minimum of surface potential energy is just situated around the middle of the unit.24A series of growth experiments are then carried out to validate the model and demonstrate the role of NDL in growth optimization.

LOW-TEMPERATURE GROWTH MODEL The second characteristic mentioned above is demonstrated by our experiments on lowtemperature migration-enhanced epitaxy (MEE) of GaN. In high-temperature growth, compared to the regular growth method that simultaneously supplies Ga and N fluxes, the MEE growth method will result in smoother surface due to longer diffusion time of Ga adatoms.25,26But in practice, under low-temperature growth of GaN, MEE just results in rougher surface than the regular method (see Figure S1 of the Supporting Information). The explanation: in lowtemperature MEE growth, energy received by Ga adatoms from substrate heating is far from enough for lattice incorporation, thus Ga adatoms will have long diffusion length and gather into many small clusters before colliding the active N species. Finally, these clusters will form islands on the surface. Based on the above discussions, a physical model is proposed for low-temperature growth of GaN, as illustrated in Figure 1: (a) the arriving Ga adatoms keep moving randomly on GaN surface as they cannot escape from the surface; (b) after a period of time, some of them will collide with arriving N species and incorporate into the lattice, some will gather into clusters, and the others will continue moving randomly and wait for active N species; (c) the arriving active N species will either incorporate into the lattice by colliding with Ga adatoms or escape from the surface in a short period of time.27 Since the diffusion length of active N species is essentially


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zero,27only the surface diffusion of Ga adatoms will be considered in the derivation of NDL as follows.

Figure 1. Schematic of low-temperature growth model of GaN. Following the Einstein equation, the surface diffusion length is given as28

exp

(1)

where is the temperature-independent diffusion coefficient, is the diffusion activation barrier height, is the Boltzmann constant, T is the temperature, and is the lifetime of diffusion event. We will discuss more on , as the values of and are independent of the growth parameters and can be found in previous literature.24,29 The GaN films grown at low temperature in this work are Ga-polar from the results of KOH etching experiments, and N-rich growth condition gives N-terminated surface, therefore the NDL derivation is based on N-terminated (0001) GaN surface. On this surface, as illustrated


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in Figure 2, the area of the smallest unit containing exactly one Ga atom (defined as a SITE) is

√

in this work, where

is the lattice constant of GaN.

Figure 2. Atomic structures (top and side view) for the N-terminated (0001) GaN surface. The large/small solid circles indicate Ga/N atoms, respectively. A N atom in the first and second layer is marked by N1L and N2L, respectively. The position with highest energy is directly on top of the surface N atoms. On the other hand, there are two minimum energy positions: hcp which has subsurface atom and fcc which has no subsurface atom. The favorable diffusion path along lowest energy path (hcpfcc hcp) is marked by yellow dashed line with arrow.24 The purple diamond box surrounded by dotted line represents a SITE which is the smallest unit in the NDL derivation. Since the lifetime of Ga adatoms is determined only by the collision with active N species, the collision rate between Ga adatoms and active N species can be described as !/ , ACS Paragon Plus Environment

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wheren is the number density of Ga adatoms on GaN surface. On the other hand, the average number of Ga adatoms in one SITE is ! , which is equal to the probability of an arriving active N species colliding with a Ga adatom. Let #$ be the number of arriving active N species in unit time per unit area, then the collision rate between Ga adatoms and active N species can be %

written as #$ ! . Thus we have & #$ ! , or '

)

(

(2)

* +

Substituting Equation (2) into Equation (1), can be expressed as

exp )

(

* +

(3)

Considering the typical growth parameters as 0.007cm s 2(,29 1.75 eV,246 800K, (

(

#$ 9 monolayer/s (ML/s) 9 × 1.14 × 10(F cm2 s 2( , 8.81 × 102(G cm , then the calculated average diffusion length of Ga adatom at 530 ℃ is 5.38 nm, which has the same order of magnitude as that at 1050 ℃ (220 nm) estimated in Ref. 27. This is because the diffusion time of Ga adatoms can be very long in low-temperature growth although the diffusion rate is extremely low. In order to further understand the influence of surface diffusion length on film quality, we define a normalized diffusion length (NDL) as HI

J'

(4)

K

(

where d is the average distance between Ga adatoms and can be estimated by L %. Let #MN be the number of arriving Ga atoms in unit time per unit area, as the desorption process is


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negligible at such low temperature, n can be written as ! #MN . Combining with Equation (2), we have )

L ) *

(5)

OP

Substituting Equation (3) and (5) into Equation (4), we finally obtain

)

HI exp )QOP Q

* +

(6)

Roles of the growth parameters can be understood from the above derivation: the diffusion rate and diffusion time of Ga adatoms are determined by the growth temperature and N flux, respectively; while the average distance between Ga adatoms is affected by both Ga flux and N flux.

EXPERIMENTAL SECTION All the GaN samples are grown on two-inch sapphire (0001) substrates by a PAMBE system (SVTA 35N). Prior to the growth of GaN film, the substrate is outgassed at 280 ℃ in a preparation chamber, then annealed at 940 ℃ for 40 min in the growth chamber. After annealing, nitridation is performed at 780 ℃ for 30 min. Then the substrate is cooled down to the growth temperature. The first 15 nm AlN is grown at 530 ℃ as buffer layer, and then 150 nm GaN is grown at various growth conditions. The growth temperature measured by thermocouple varies between 300 ℃ and 600 ℃ . The samples are grown by regular growth method that simultaneously supplies Ga and N fluxes. The equivalent Ga flux is changed from 1/24 ML/s to 3/16 ML/s by adjusting the temperature of Ga cell. N2 flow rate is adjusted to achieve different


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equivalent N flux from 1/12 ML/s to 3/2 ML/s, while the radio frequency power of N plasma source is fixed at 400 W. In addition, a bilayer MEE method with continuous Ga flux and pulsed N flux is also employed to assist the discussion. The typical growth temperature, Ga flux and N flux are 530 ℃, 1/16 ML/s and 1/4 ML/s, respectively. The growth procedures are monitored by RHEED. After growth, the surface morphologies of the as-grown GaN films are analyzed by atomic force microscopy (AFM), and the crystalline qualities are studied by Raman spectroscopy and transmission electron microscopy (TEM). The Raman spectra are recorded using Z(XX)ZS geometry, where Z is along the c-axis of GaN film. All measurements are performed at room temperature.

RESULTS AND DISCUSSION The influence of Ga fluxes is studied by varying the equivalent Ga flux from 1/24 ML/s to 3/16 ML/s. A bilayer MEE method with continuous Ga flux and pulsed N flux is also chosen as a reference, because it essentially corresponds to short distance between Ga adatoms. NDL values calculated from Equation (6) are shown in Figure 3a and 1 × 1 μm and 5 × 5 μm root mean square (RMS) roughness of GaN films are plotted in Figure 3b. The minimum RMS roughness of GaN grown with 1/16 ML/s Ga flux suggests that there is an optimal window of NDL for smooth growth. Figure 3d illustrates the reflection high energy electron diffraction (RHEED) patterns (e//) obtained at the end of GaN growth. GaN film grown with 1/16 ML/s Ga flux shows sharp streaky RHEED patterns indicating a smooth growth mode, while GaN film grown either with 3/16 ML/s Ga flux or by MEE method shows spotty patterns indicating a three-dimensional island growth mode which leads to rough surface. The appearance of three-


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dimensional islands can be attributed to the formation of Ga clusters during the growth, which is mainly due to the short distance between Ga adatoms.

Figure 3. (a) NDL values, (b) RMS roughness, (c) Raman spectra and (d) RHEED patterns (e//) of GaN films grown with different Ga fluxes and MEE method.


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From the bright-field (BF) TEM image at low magnification of the GaN film grown with 1/16 ML/s Ga flux, as shown in Figure 4a, the defects are identified as Shockley and Frank partial dislocations because the dislocations are parallel to the film/substrate interface rather than threading through the film.30 Since partial dislocations are formed at the boundaries between two stacking faults or between a stacking fault and the perfect lattice, stacking faults are considered as major defects in such kind of samples. Figure 4b depicts the high-resolution (HR) TEM image at the bottom of the GaN film. The cubic phase with ABCABC atomic arrangement, which is one of the sources of stacking faults, can be clearly observed in hexagonal GaN. Raman spectroscopy is employed to further study the defects in GaN films. Usually, compressive/tensile strain will result in blue/red shift in phonon frequencies, respectively. For GaN film on sapphire, both lattice- and thermal-mismatch cause compressive strain, whereas defects such as stacking faults and threading dislocations usually contribute to tensile strain.31 From the Raman spectra in Figure 3c, the peak at 577cm2( corresponding to sapphire substrate can be observed for all samples.31GaN films grown with 1/24, 1/20 and 1/16 ML/s Ga fluxes exhibit peaks at 563cm2( , while GaN film grown with 3/16 ML/s Ga flux or by MEE method exhibits a peak at 566 cm2( or 566.5 cm2(. These peaks correspond to the E (TO) mode of hexagonal GaN which is sensitive to the strain in the film. Since the E (TO) peak of a free standing bulk GaN film is centered at 567.6 cm2( ,32 the presence of red shifts reveals tensile strain existing in these GaN films. The peak at 563 cm2( , with red shift of 4.6 cm2(, is mainly caused by a considerable amount of stacking faults. The peaks at 566 cm2( and 566.5 cm2( are very close to 567.6 cm2( , demonstrating a dramatically reduction of stacking faults in the GaN films grown with 3/16 ML/s Ga flux or by MEE method. This can also be verified from the BFTEM image of GaN film grown by MEE method in Figure 4c, where the stacking faults are


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replaced by threading dislocations. Physically, the reason is that Ga clusters can lower the energy barrier of surface diffusion,33 resulting in more Ga adatoms incorporating into hexagonal rather than cubic GaN binding site,34which means the reduction of stacking faults.

Figure 4. (a) BF-TEM image at low magnification and (b) HR-TEM image of the GaN film grown with 1/16 ML/s Ga flux.(c) BF-TEM image at low magnification of the GaN film grown by MEE method. The GaN interlayer contains stacking faults as it is grown with 1/16 ML/s Ga flux to provide a smooth surface for subsequent growth. Next, the equivalent N flux is varied in the range of 1/12~3/2 ML/s to study the influence of N flux. The corresponding NDLs, RHEED patterns, RMS roughness and Raman spectra are shown in Figure 5. When NDL is large (27.21), the as-grown GaN film exhibits spotty RHEED patterns, rough surface and E (TO) peak at 566.5 cm2( as a result of Ga clusters formation during the growth. When NDL is small (1.51), the surface roughness of GaN film is also large, due to the relatively short diffusion length of Ga adatoms. In addition, it is apparent that all the GaN films grown with NDLs between a certain range exhibit E (TO) peak at 563 cm2( , coinciding with the results in Figure 3.


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Figure 5. (a) NDL values, (b) RHEED patterns (e//), (c) RMS roughness and (d) Raman spectra of GaN films grown with different N fluxes. Finally, the influence of growth temperature are studied by choosing substrate temperatures as 300 ℃, 480 ℃, 530 ℃ and 600 ℃, respectively. The corresponding NDLs, RHEED patterns, RMS roughness and Raman spectra are shown in Figure 6.When the growth temperature decreases to 300 ℃ , the RHEED shows typical patterns of cubic-GaN (111) surface,35 and a broad peak around 552 cm2( originating from the transverse optical (TO) mode of cubic GaN is also observed. These results indicate that the GaN film grown at 300 ℃ is mainly cubic, which means that the NDL has to be calculated by adjusting the parameters in Equation (6) to those of cubic GaN. In order to ensure the consistency in this work that hexagonal-GaN is expected and cubic-GaN is considered as defect, the NDL of 300 ℃-grown


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sample is not given in Figure 6a. From the other three samples, the same conclusion can be obtained that either large or small NDL will lead to rough surface and large NDL will result in Ga clusters.

Figure 6. (a) NDL values, (b) RHEED patterns (e//), (c) RMS roughness and (d) Raman spectra of GaN films grown at different temperatures. The variations of RMS roughness and Raman E (TO) phonon position as a function of NDL are summarized in Figure 7. Obviously, the low-temperature growth mode can be tentatively classified into three regions according to the NDL value: (i) relatively small NDL leads to rough epi-surface and high density of stacking faults, (ii) under medium NDL, the episurface becomes quite smooth whereas the density of stacking faults is still high, and (iii) when


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NDL is relatively large, an extremely low density of stacking faults can be achieved but with rough epi-surface. These three regions are marked by different colors with fuzzy boundaries. We can see that it might be too difficult to achieve very smooth epi-surface and extremely low density of stacking faults simultaneously. The specific value of NDL is a compromise between these two specs and will be experimentally determined on a case-by-case basis. It is interesting to note that, as the growth kinetics and crystal structures of III-nitrides such as AlN, InN and GaN are similar, our model and NDL expressed by Equation (6) could be applied in low-temperature growth of III-nitrides (including cubic phase) under N-rich condition, while only the specific values of parameters in Equation (6) ( and ) and the expression of need to be adjusted accordingly.

Figure 7. Variations of RMS surface roughness and Raman E (TO) phonon position as a function of NDL.

CONCLUSIONS In summary, a physical model for low-temperature growth of GaN under N-rich condition is proposed based on the facts that the desorption process of Ga adatoms can be ignored and the


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energy for lattice incorporation of Ga adatoms comes only from active N species. A dimensionless parameter NDL is also introduced to provide further insight: the diffusion rate and diffusion time of Ga adatoms are determined by the growth temperature and N flux, respectively, meanwhile the average distance between Ga adatoms is affected by both Ga flux and N flux. Excellent agreement between theoretical predictions and experimental results validates this model and demonstrates the importance of NDL in optimizing the growth condition. Our model and NDL could be applied in growing III-nitrides under N-rich condition by various lowtemperature growth techniques where group-III adatoms are unable to incorporate into the lattice by their own kinetic energy.

ASSOCIATED CONTENT Supporting Information. Illustration of four kinds of growth methods and the corresponding changes of RHEED patterns after 8 loops of growth. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]; [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Funding Sources


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National Basic Research Program of China (Grant Nos. 2013CB632804 and 2015CB351900) National Natural Science Foundation of China (Grant Nos. 61574082, 61210014, 61321004, 61307024 and 51561165012) High Technology Research and Development Program of China (Grant No. 2015AA017101) Tsinghua University Initiative Scientific Research Program (Grant Nos. 20131089364, 20161080062 and 20161080068) Open Fund of the State Key Laboratory on Integrated Optoelectronics (Grant No. IOSKL2015KF10) Notes The authors declare no competing financial interest. ACKNOWLEDGMENT The authors would like to thank Professor Chongcheng Fan for his help in manuscript preparation. This work was supported by the National Basic Research Program of China (Grant Nos. 2013CB632804 and 2015CB351900), the National Natural Science Foundation of China (Grant Nos. 61574082, 61210014, 61321004, 61307024 and 51561165012), the High Technology Research and Development Program of China (Grant No. 2015AA017101), the Tsinghua University Initiative Scientific Research Program (Grant Nos. 20131089364, 20161080062 and 20161080068), and the Open Fund of the State Key Laboratory on Integrated Optoelectronics (Grant No. IOSKL2015KF10). REFERENCES


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For Table of Contents Use Only A Model for Low-temperature Growth of Gallium Nitride Chao Wu, Jiadong Yu, Yanxiong E, Yi Luo*, Zhibiao Hao*, Jian Wang, Lai Wang, Changzheng Sun, Bing Xiong, Yanjun Han, and Hongtao Li

A model for low-temperature growth of GaN under N-rich condition is proposed to reveal its physical mechanism, while a normalized diffusion length (NDL) is introduced for growth parameter optimization. Both are validated/demonstrated by the agreement between theoretical prediction and experimental data, and could be applied in growing III-nitrides under N-rich condition by various low-temperature growth techniques.


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Model for Low-Temperature Growth of Gallium Nitride

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