Modeling analysis of AlN and AlGaN HVPE

A. S. Segal*, D. S. Bazarevskiy, M. V. Bogdanov, and E. V. Yakovlev

STR-Group – Soft-Impact Ltd., P.O. Box 89, 194156 St. Petersburg, Russia

PACS 81.05.Ea, 81.15.Aa, 81.15.Kk, 82.33.Ya

* Corresponding author: e-mail alex.segal@str-soft.com, Phone: +7 812 554 4570, Fax: +7 812 326 6194, Web: www.str-soft.com

1 Introduction Aluminum nitride (AlN) is currently considered as a promising substrate material for the pro-duction of group-III-nitride-based UV optoelectronic de-vices and high-power high-frequency electronic devices. To date, the AlN substrates are largely produced by physi-cal vapor transport (PVT) growth of bulk crystals followed by post-growth processing of the crystals. This technology allows manufacturing 2-inch diameter high-quality AlN substrates (Refs. [1, 2]). However, despite the remarkable resent progress, the PVT technology is still poorly control-lable and rather expensive. As a result, alternative ap-proaches to the production of the AlN substrates have lately attracted much interest. Among such approaches, AlN Hydride Vapor Phase Epitaxy (HVPE) is now considered as most prospective technology (Refs. [3-5]). This technology can provide the growth of 3 inch diameter thick single-crystal AlN epilayers on sapphire or silicon-carbide substrates. The crystallo-graphic quality of the obtained AlN templates is generally lower than that of the bulk AlN substrates but it proves suf-ficient for many device applications. Correspondingly, AlN templates are currently considered as inexpensive alterna-tive to the low-accessible and expensive bulk semi-insulating substrates in high-power high-frequency elec-tronics. Besides, compatibility of AlN HVPE with the con-

ventional technology of GaN HVPE allows directly manu-facturing templates with AlGaN epitaxial layer (Ref. [6, 7]). Despite the considerable practical interest, the tech-nologies of AlN and AlGaN HVPE are still little studied. This concerns, first of all, theoretical analysis that is largely restricted by thermodynamic calculations (see Refs. [8, 9]). To find the optimal growth conditions and to de-velop the optimal equipment design, comprehensive mod-eling of these technologies is strongly desired. In this paper, we present a novel model of AlN and AlGaN HVPE. The model provides complete description of heat transfer, multi-component species diffusion, gas flow dynamics, and surface chemical reactions on both the AlN/AlGaN crystal surfaces and Al/Ga metal source sur-faces. The surface kinetics is described within the quasi-thermodynamic approach that was earlier successfully applied to study GaN HVPE (Ref. [10]). The model is im-plemented within new editions of professional software packages HEpiGaNSTM and CVDSimTM (see http://www.str-soft.com), validated using literature ex-perimental data, and then applied to modeling analysis of the technologies. The major focus is made on the content of group-III mono- and trichlorides in the vapor, rate-limiting species, and relative incorporation of Al and Ga into the alloy.

Comprehensive model of AlN and AlGaN HVPE is devel-

oped. The model combines detailed description of the trans-

port processes and quasi-thermodynamic model of surface ki-

netics at the Al/Ga metal surfaces and AlN/AlGaN crystal

surfaces. It is shown with the model that HCl dominantly

converts into trichloride AlCl3 in the Al source but into

monochloride GaCl in the Ga source. Then, AlN grows from

AlCl3 under essentially non-equilibrium conditions while

GaN – from GaCl under near-equilibrium conditions. The re-

vealed differences between the AlN and GaN growth features

explain many experimentally observed phenomena, including

a sharp saturated behavior of the AlN growth rate in variation

of the precursors flow rates and a strong effect of carrier H2

on the AlGaN composition. Generally, the model predicts a

high sensitivity of the AlGaN composition to variation of the

species flow rates due to their effect on the Ga incorporation.

2 Model description Complete description of heat transfer, multi-component species diffusion, and gas flow dynamics is provided by solving the full set of conven-tional heat conduction, radiation transfer, diffusion, and Navier-Stokes equations. Specific feature of the model is provided by the quasi-thermodynamic description of sur-face chemical reactions on the Al/Ga metal surfaces and AlN/AlGaN crystal surfaces. As it was shown in [10], at the operating temperature of 800-900 oC, HCl dominantly converts into GaCl on the Ga surface, following reaction HCl + Ga(l) -> GaCl + (1/2)H2

(R1) As for the Al source, we do not assume a-priori that HCl reacts with the Al surface to produce either mono- or tri-chloride but allow the two corresponding reactions to go in parallel HCl + Al(s) -> AlCl + (1/2)H2

(R2) 3HCl + Al(s) -> AlCl3 + (3/2)H2

(R3) Quasi-thermodynamic description of surface kinetics with reaction (R1) is presented in detail in [10], surface kinetics with reactions (R2) and (R3) is described quite similarly. Group-III chlorides generated in reaction (R1)-(R3) are transported to the substrate and interact there with NH3 to produce GaN and AlN constituents of the AlGaN alloy GaCl + NH3 -> GaN(s) + HCl + H2

(R4) AlCl + NH3 -> AlN(s) + HCl + H2

(R5) AlCl3 + NH3 -> AlN(s) + 3HCl (R6) Within the quasi-thermodynamic model, the interface species fluxes at the crystal surface are described by the extended Hertz-Knudsen equations )( e

i

w

iiiiPPJ −= βα (1)

where

iα are the sticking probabilities, ( ) 2/1

2 RTii

πμβ = are the Hertz-Knudsen factors,

iμ are the molar masses,

R is the gas constant, T is the temperature, w

iP are the

partial pressures at the interface, e

iP are the quasi-

equilibrium pressures, and subscript i stands for the spe-cies involved in surface reactions (R4)-(R6), i.e. i = GaCl, AlCl, AlCl3, NH3, HCl, and H2. The quasi-equilibrium species pressures satisfy the mass-action law equations corresponding to reactions (R4)-(R6) and accounting for activities of GaN and AlN in the alloy e

H

e

HClGaNR

e

NH

e

GaClPPxKPP

243)1( γ−= (2)

e

H

e

HClAlNR

e

NH

e

AlClPPxKPP

253γ= (3)

3

633)( e

HClAlNR

e

NH

e

AlClPxKPP γ= (4)

Here, RjK is the equilibrium constants of the correspond-ing reactions ( 64 ÷=j ), which are routinely calculated using thermodynamic properties of the species involved, x

is the AlN molar fraction in the alloy, and kγ are the ac-

tivities (k = AlN and GaN). Eqs. (1)-(4) are supplemented by the conventional stoichiometric relations between the interface species fluxes (Ref. [10]) and expressions for the activities following the regular solution approximation (Ref. [11]). Let us make some remarks on the problem statement. 1. Surface kinetic limitations in GaN HVPE are known to begin at the growth temperature of 900-950 oC and lower [12]. Similar literature data for AlN HVPE are rather limited and contradictory (see, for example, Refs. [4, 13]). So, the transition temperature between the transport-limited and kinetically limited growth conditions varies in the range of 950-1100 oC and higher, though all the papers note a minor decrease of the growth rate due to the surface kinetic limitations (normally, less than an order of magni-tude in a wide temperature range). Simultaneously, there is a trend to perform the growth under the transport-limited conditions via raising the growth temperature (in Ref. [5], for example, the growth temperature is higher than 1200 oC). In this situation, we neglect the kinetic limitations at the AlGaN crystal surfaces and assume all the species sticking probabilities, except for N2, to be unity. 2. Generally, if AlCl3 and NH3 meet each other at an insufficiently high temperature, adducts of the AlCl3-nNH3 type may appear as a result of gas-phase reactions to pro-duce small suspended particles. In elaborated processes, however, effects of gas-phase chemistry are minimized and normally do not manifest themselves (see Refs. [3-7]), for which reason they are not considered in our model. 3. Literature data on the NH3 decomposition on the AlN and GaN surfaces are also rather limited and contra-dictory. Earlier, we showed that the best agreement of the computed and experimental data in modeling of GaN HVPE is achieved under the assumption of negligible NH3 decomposition (Ref. [10]). Test computations have shown that this assumption can be extended to the AlN surfaces. Within the quasi-thermodynamic model, this corresponds to a near-zero N2 sticking probability, in which case N2 does not participate in the surface chemistry but serves as an inert carrier gas. Note that assumptions 1 and 2 correlate with thermo-dynamic analysis of Refs. [8, 9] while approximation 3 is somewhat different, as a universal 5%-decomposition of NH3 is assumed there. 3 Results and discussions The developed model was validated using the literature experimental data on the AlN growth rate and AlGaN composition. Some results of this validation are presented in Fig. 1. Figure 1 (left) shows the computed AlN growth rate vs. NH3 flow rate in comparison with the data of Ref. [13] (here, the growth temperature is 1200 oC, the total pressure is 10 hPa, the AlCl3 flow rate is 1.33 sccm, and the carrier N2 and H2 flow rates are 100 sccm each). The computed dependence is presented by two lines corresponding to the AlN growth rate at the substrate center (solid line) and to

that averaged over the substrate surface (dash line). The two lines are seen to restrict an area that contains the ex-perimental points. The difference between the two lines is attributed to some center-to-edge increase of the AlN growth rate due to thinning of the diffusion boundary layer near the edge. Anyway, both the computed and experimen-tal data exhibit a sharp common boundary between the lin-ear and saturated regions. Note that use of pure N2 carrier gas results in a uniform 25% decrease of the AlN growth rate due to lower reactive species diffusion coefficients in N2 as compared to H2, which corresponds to experimental data of [13]. Figure 1 (right) displays the computed dependencies of the AlN molar fraction in AlGaN on the Al content in group-III vapor for pure carrier N2 (solid line) and in small addition of H2 (dash line) in comparison with the data of Ref. [7] (here, the growth temperature is 1100 oC, the Ga and Al source temperatures are 850 oC and 550 oC, respec-tively, the total pressure is atmospheric, the group-III par-tial pressure is 3x10-4 atm, and the NH3 partial pressure is 0.015 atm). Good agreement of the computed and experi-mental data is observed for the two carrier gases, regard-less of the linear or sharp superlinear behavior of the de-pendencies. The developed model allows making clear treatments to the observed behavior of the crystal growth rate and al-loy composition. The treatments are based on two facts. 1. Unlike the Ga source, HCl dominantly converts into aluminum trichloride in the Al source. Fig. 2 shows com-puted 2D distributions of the AlCl (left) and AlCl3 (right) in the system for AlGaN HVPE described in [7]. It is seen that AlCl3 dominants over AlCl by factor of ~20 at the Al source temperature of 550 oC. At a lower temperature, this factor sharply increases, so that AlN dominantly grows fol-lowing reaction (R6). 2. Unlike GaN, AlN grows under the essentially non-equilibrium conditions. Within the quasi-thermodynamic model, this corresponds to the fact that due to the particular thermodynamic properties of the species involved in reac-tion (R6), equilibrium constants

6RK is negligibly small.

In this case, Eq. (4) can be approximately written as 0~

33

e

NH

e

AlClPP , so that either AlCl or NH3 quasi-

equilibrium pressure is close to zero. Which of the two species is close to zero depends on their inlet concentra-tions. To illustrate this fact, let us make a simple estimation of the interface species fluxes in AlN HVPE with the model of diffusion boundary layer. Within this model,

δμ /))(/(~ wi

giiii PPRTDJ − , where

iD are the diffusion

coefficients, giP are the inlet partial pressures, and δ is

the characteristic diffusion boundary layer thickness. For the unity sticking probabilities, the pressures w

iP and e

iP

are close to each other (Ref. [10]). Then, accounting also for the domination of AlCl3 over AlCl, the condition of the stoichiometric Al and N incorporation into the crystal can be approximately written as

)(~)(33333333

eNH

gNHNHNH

eAlCl

gAlClAlClAlCl PPDPPD −− µµ

The latter relationship shows that if

gNHNHNH

gAlClAlClAlCl PDPD

333333µµ > (deficient NH3) then

it is e

NHP

3 that is close to zero while e

AlClP

3 is spontane-

ously adjusted to provide the stoihiometric incorporation of Al and N into the crystal. In this case,

δμ RTPDJJgNHNHNHNHAlCl /~~

33333, i.e. the species in-

terface fluxes and, hence, the crystal growth rate linearly depend on the NH3 partial pressure but independent of the AlCl3 and other species partial pressures. If the opposite inequality is correct (deficient AlCl3), the situation is the contrary and AlCl3 and NH3 exchange their roles. This consideration clearly explains the observed behavior of the AlN growth rate in variation of the NH3 flow rate (Fig. 1, left), where the linear region corresponds to the deficient NH3 while the saturated region – to the deficient AlCl3. It is essential, however, that such behavior is not char-acteristic for GaN HVPE. Particular thermodynamic prop-erties of the species involved in reaction (R4) result in a non-small value of the equilibrium constant

4RK . As a re-

sult, both quasi-equilibrium pressures e

GaClP and e

NHP

3 are

far from zero but close to the corresponding inlet partial

0 1 2 3 40

50

100

Comp. center

Comp. average

Exp.Gro

wth

ra

te, µ

m/h

r

NH3 flow rate, sccm

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

No H2, comp.

No H2, exp.

10% H2, comp.

10% H2, exp.

Al fr

action in A

lGaN

Al fraction in group-III vapor

Figure 1 Left – computed AlN growth rate at the substrate center (solid line) and averaged over the substrate surface (dash line) vs.

NH3 flow rate in comparison with data of Ref. [13]. Right – computed AlN molar fraction in AlGaN vs. Al content in group-III vapor

for pure carrier N2 (solid line) and in 10% addition of H2 (dash line) in comparison with data of Ref. [7].

pressures gGaClP and g

NHP3

, which means that GaN grows under near-equilibrium conditions. In this case, the GaN growth rate exhibits no sharp saturated behavior but de-pends simultaneously on the GaCl and NH3 flow rates, as it was shown theoretically and experimentally in [10]. The revealed differences in the AlN and GaN growth features give a simple treatment to the observed strong ef-fect of carrier H2 on the Al incorporation into the alloy (Fig. 1, right). In the absence of H2, the AlN molar fraction in the alloy is determined by the interface AlCl3 flux that linearly depends on its partial pressure, as AlCl3 is defi-cient here. Small addition of H2 sharply slows down reac-tion (R4) providing incorporation of Ga into the alloy but affects in no way reaction (R6) that is responsible for the Al incorporation. This treatment is quite similar to that given in [7], however, our modeling analysis allows mak-ing some extended conclusions. According to the above consideration, the AlN growth linearly depends on the deficient precursor, normally AlCl3, but rather insensitive to all the other species. On the con-trary, GaCl growth is sensitive not only to H2 but to all the species involved in reaction (R4). Correspondingly, Al-GaN composition can be controlled by variation of the flow rates of these species. A higher Al content in the alloy is achieved by a lower NH3 flow rate or by supply of addi-tional HCl directly to the growth chamber. Generally, the model predicts a high sensitivity of the AlGaN composi-tion to variation of the species flow rates due to their effect on the Ga incorporation into the alloy while the Al incor-poration remains quite stable. 4 Conclusions Comprehensive model of AlN and AlGaN HVPE is developed, implemented numerically, validated using literature experimental data, and applied to modeling analysis of the technologies. It is revealed with the model that, first, HCl dominantly converts into trichlo-ride AlCl3 in the Al source but into monochloride GaCl in the Ga source and, second, AlN grows from AlCl3 under essentially non-equilibrium conditions while GaN – from GaCl under near-equilibrium conditions. These differences explain many experimentally observed features of the

technologies and predict some new features, which are generally caused by a high sensitivity of the Ga incorpora-tion into the alloy to variation of the species flow rates vs. high stability of the AlN incorporation that is sensitive only to the rate-limiting species, normally AlCl3.

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Ga

Al

NH3

AlGaN

Ga

Al

NH3

AlGaN

Figure 2 Distribution of the AlCl (left) and AlCl3 (right) molar fractions in the system for AlGaN HVPE presented in Ref. [7].