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Atomic layer epitaxy of aluminum nitride: Unraveling the connection between hydrogen plasma and carbon contamination Steven C. Erwin, and John L. Lyons ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b04104 • Publication Date (Web): 23 May 2018 Downloaded from http://pubs.acs.org on May 23, 2018

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is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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ACS Applied Materials & Interfaces

Atomi layer epitaxy of aluminum nitride: Unraveling the onne tion between hydrogen plasma and arbon ontamination ∗

Steven C. Erwin

∗

and John L. Lyons

Center for Computational Materials S ien e, Naval Resear h Laboratory, Washington, DC 20375

E-mail: steve.erwinnrl.navy.mil; john.lyonsnrl.navy.mil

Abstra t

Atomisti ontrol over the growth of semi ondu tor thin lms, su h as aluminum nitride, is a long-sought goal in materials physi s. One promising approa h is plasmaassisted atomi layer epitaxy, in whi h separate rea tant pre ursors are employed to grow the ation and anion layers in alternating deposition steps. The use of a plasma during the growthmost often a hydrogen plasmais now routine and generally onsidered riti al, but the pre ise role of the plasma is not well understood. We propose a theoreti al atomisti model and elu idate its onsequen es using analyti al rate equations, density-fun tional theory, and kineti Monte Carlo statisti al simulations. We show that using a plasma has two important onsequen es, one bene ial and one detrimental. The plasma produ es atomi hydrogen in the gas phase, whi h is important for removing methyl radi als left over from the aluminum pre ursor mole ules. But atomi hydrogen also leads to atomi arbon on the surfa e and, moreover, opens a hannel for trapping these arbon atoms as impurities in the subsurfa e region, where they remain as unwanted ontaminants. Understanding this dual role leads us to propose 1

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a solution for the arbon ontamination problem whi h leaves the main benet of the plasma largely unae ted. KEYWORDS: atomi layer epitaxy (ALE), nitride lm growth, arbon ontamination, hydrogen plasma, kineti Monte Carlo (kMC)

Introdu tion

Atomi layer epitaxy is a promising te hnique for growing thin rystalline semi ondu tor lms at relatively modest temperatures and with layer-by-layer ontrol. Su h ontrol is possible be ause the growth of ea h atomi layer is self-limitingthat is, it automati ally stops when the layer is omplete. This property makes atomi layer epitaxy espe ially well suited for growing ompound semi ondu tors su h as aluminum nitride in a polar dire tion be ause separate, independent deposition steps are used for the aluminum layer and the nitrogen layer. The two growth steps generally rely on mole ular pre ursors for the two omponents: in the ase of AlN epitaxy the Al sour e is typi ally trimethylaluminum (TMA), Al (CH ) , and the N sour e is often ammonia, NH , but many other pre ursors are also possible. One drawba k to using ammonia is that ra king it requires high temperatures and spe ial

atalysts. An alternative approa h is to use a hydrogen plasma, whi h liberates nitrogen atoms from NH even below 600 C. Indeed, plasma-assisted atomi layer epitaxy has qui kly be ome established as an attra tive te hnique for growing epitaxial lms of AlN, as well as other nitrides, at modest temperatures with nearly atomisti ontrol. Despite this promise, a full understanding of how the hydrogen plasma ae ts atomi layer epitaxial growth is not yet in hand. Plasmas produ e ions, neutral atoms, ele trons, and photons, but the role of these spe ies in the growth remains un lear. In this paper we

larify this situation and arguefrom the results of density-fun tional theory al ulations, kineti Monte Carlo (kMC) simulations, and an analyti al model for rate equationsthat using a hydrogen plasma has two previously unre ognized onsequen es, one of whi h is 2 ACS Paragon Plus Environment 112

2

3

13

◦

3

3 6

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bene ial and the other detrimental. The bene ial onsequen e is that atomi hydrogen, whi h is produ ed in the plasma through the disso iation of H2 , is riti al for removing methyl radi als, CH3 , from the AlN surfa e, whi h are left over after the TMA pre ursor de omposes. These groups are strongly bound to the surfa e, but an be easily removed if they ombine with hydrogen atoms in the gas phase to form methane mole ules, CH4 , whi h are very weakly bound and readily desorbed with the available thermal energy. The detrimental onsequen e arises from an alternative rea tion pathway taken when a surfa e methyl group and gas-phase hydrogen atom ombine. In this alternative pathway, hydrogen abstra tion instead

removes

a hydrogen atom to form CH2 .

This abstra tion

rea tion an o

ur repeatedly until just a arbon atom is left on the surfa e. This adsorbate

an then undergo a trapping rea tion to form a subsurfa e arbon impurity

su ient atomi hydrogen is present

but only when

. Therefore, atomi hydrogen plays an unexpe ted and

dual role in the growth of AlN: it removes methyl groups, whi h would otherwise blo k subsequent layers from growing, but it also reates trapped arbon impurities, whi h are detrimental for most intended appli ations.

3,1416

In this work we demonstrate theoreti ally the dual role of the hydrogen plasma, onrm that its predi ted onsequen es are onsistent with existing experimental results, and propose a simple solution that nearly eliminates the detrimental onsequen es while retaining the benets.

Overview and preliminaries The deposition me hanisms and energeti s for various pre ursors on gallium nitride have been investigated previously in great detail.

17,18

Here we limit the s ope of our investigation to one

parti ular stage of AlN epitaxy, beginning immediately after a omplete Al monolayer has been formed from TMA pre ursors. We assume an atomi ally at surfa e of AlN(0001) in the

3



(a)

H adsorption H abstraction

gas:

desorption

surf:

CH4

H + CH3

H2 + CH2

(b)

H ads

H abs

CH3

H + CH2

H2 + CH

(c)

H ads

H abs

CH2

H + CH

H2 + C

Page 4 of 28

(d)

H ads

CH

H + C

(e) impurity trapping

C C*

Figure 1: Overview of the hemi al rea tions onsidered at the Al-terminated (0001) surfa e of aluminum nitride after the growth of an aluminum layer from the trimethylaluminum (TMA) pre ursor, Al(CH3 )3 . Complete de omposition of the TMA mole ules leaves the surfa e overed by strongly bound CH3 methyl radi als whi h, if not removed, prevent the growth of the subsequent nitrogen layer. (a-d) Atomi hydrogen, reated in the gas phase by the hydrogen plasma, an ombine with CH3 to trigger a sequen e of hydrogen adsorption and hydrogen abstra tion rea tions. This sequen e leads to a ompetition between two terminal pro esses: (a) desorption of CH4 , and (e) in orporation of atomi C as a trapped subsurfa e impurity. The ve panels illustrate the sequen e of rea tions, as des ribed in the text. usual Al-polar orientation, so that ea h Al atom in the top layer has three ba k-bonds to N atoms in the se ond layer. The TMA mole ule onsists of three methyl groups surrounding an Al atom at the enter. To remove these methyl groups from TMA in the gas phase requires signi ant energy: 3.4, 1.5, and 2.8 eV for removing the rst, se ond, and third group, respe tively; similar behavior has been observed in studies of trimethylgallium (TMG). 19 Hen e, TMA in the gas phase is thermodynami ally very stable at the temperatures used in atomi layer epitaxy, typi ally 200 to 600 ◦ C. This stability is lost, however, when TMA adsorbs on the partially ompleted aluminum layer of AlN. We used density-fun tional theory (DFT, see Methods for te hni al details) to study the energeti s of TMA adsorbed at an aluminum-va an y site of AlN(0001), be ause this situation plausibly des ribes how the aluminum atom is delivered to the lo ation it eventually o

upies in the ompleted layer. We nd that TMA de omposes upon adsorption. The disso iation is energeti ally downhill with an energy gain of 6 eV and no a tivation barrier; this de omposition was also predi ted for TMG on the surfa e of gallium arsenide. 20 The aluminum atom lls in the va an y, as intended. But the three methyl groups whi h are released an form strong ovalent bonds to three neighboring surfa e aluminum atoms, if they are present. The energy required to desorb one of these bound methyl groups is 2.8 4


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eV a

ording to DFT, far more than is available thermally. Thus it is evident that growing the aluminum layer using TMA omes at a steep pri ea omplete layer of methyl radi als strongly bound to the surfa e. In a tual pra ti e, these methyl groups are somehow removed and ontinued growth is indeed possible. How this may happen is the subje t of the remainder of this paper. We rst

onsider several very simple removal me hanisms that do involve a hydrogen plasma, and on lude that none of them are plausible. (1) Using the DFT a tivation energy of 2.8 eV and a standard attempt frequen y of 10 s , the Arrhenius desorption rate of CH at 500 C is on e every 50 hours. This (2) rea tion is energeti ally uphill by 3.0 eV and hen e will rarely o

ur at normal growth temperatures. (3) This rea tion is energeti ally downhill by 1.0 eV with no a tivation barrier. But free methyl radi als in the gas phase are unlikely to exist, be ause they would ombine to make ethane. (4) This rea tion is energeti ally downhill by 1.6 eV with no a tivation barrier. However, the H disso iation energy is 4.5 eV and so, in the absen e of a plasma, almost no free hydrogen atoms are expe ted at normal growth temperatures. not

Dire t desorption of a methyl radi al.

13

−1

◦

3

Asso iative desorption of two methyl groups as an ethane mole ule, C2 H6 .

Rea tion of an adsorbed methyl with a gas-phase methyl to form ethane, whi h then

desorbs.

Rea tion of an adsorbed methyl with a gas-phase hydrogen atom to form methane,

whi h then desorbs.

2

Me hanism and analyti al model We turn now to our proposed me hanism. As before, we assume that the surfa e of AlN is

overed by a omplete monolayer of CH mole ules adsorbed at aluminum sites. We further assume that the plasma reates a partial pressure p of atomi hydrogen in equilibrium with 3

H

5



Page 6 of 28

the larger nominal pressure p . Under typi al plasma onditions we expe t that p /p is of order 0.1 or less. We now investigate how the monolayer of CH evolves in time as a fun tion of temperature T and pressure p . Figure 1 illustrates all the surfa e hemi al rea tions that we onsider. (a) Atomi hydrogen in the gas phase an adsorb on CH and onvert it to CH , whi h is weakly bound and easily desorbed thermally. But an alternative rea tion is equally likely: hydrogen abstra tion leading to CH , whi h is strongly bound to the surfa e, plus H whi h returns to the gas phase. (b) These strongly bound CH mole ules an then similarly ombine with atomi hydrogen via adsorption or abstra tion to reate CH or CH+H , respe tively. ( ) These CH mole ules are also strongly bound and an then undergo two similar rea tions to

reate CH or adsorbed atomi C. (d) Adsorbed C an be onverted to CH via adsorption. (e) Alternatively, adsorbed C an undergo a surfa e rea tion to be ome a trapped impurity atom, denoted C , in the subsurfa e region. A

ording to our DFT al ulations, all of the hydrogen adsorption and abstra tion rea tions are energeti ally downhill with no a tivation barrier. Hen e, the rate of ea h rea tion is proportional to the arrival rate (the ux) f of atomi hydrogen at the rea tant site. We assume that atoms arriving within an area A given by the AlN(0001) unit ell rea t with the adsorbed hydro arbon mole ule. The kineti theory of gases then gives H2

H

H2

3

H

3

4

2

2

2

3

2

2

∗

(1)

p f = pH A/ 2πmH kB T .

The remaining two rea tions in Figure 1the desorption of CH and the trapping of atomi arbon as a subsurfa e impurityare thermally a tivated. For the CH desorption the DFT a tivation barrier is very small, less than 0.1 eV, and so we assume that CH immediately desorbs after it forms. For the trapping of atomi arbon the a tivation barrier is a mu h more ompli ated issue to whi h we will return at length. For now the rate of this rea tion will simply be designated as f . 4

4

4

∗

6


Page 7 of 28

100

Coverage (monolayers)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


CH3 CH2 10- 1

CH C

10- 2 0

20

40

60

80

100

120

140

Time (seconds)

Figure 2: Time evolution of adsorbed hydro arbon populations of CH , CH , CH, and atomi C, a

ording to the analyti al rate-equation model without impurity trapping and the kineti Monte Carlo simulation des ribed below (symbols). Here, the arbon impurity trapping pro ess in Figure 1(e) was deliberately omitted in order to rst illustrate the behavior of a simpler system of inter onversion rea tions, CH ↔ CH ↔ CH ↔ CH ↔ C, having only one exit hannelnamely, the immediate desorption of CH mole ules reated when gasphase atomi H ombines with surfa e CH . The temperature was 500 C and the pressure of the atomi hydrogen gas was 10 mTorr. 3

4

3

2

2

4

◦

3

−4

7



Page 8 of 28

We now develop two analyti al models for the time evolution of the populations Θ (t) of the various hydro arbons CH (n = 4, 3, 2, 1, 0) on the AlN surfa e. The rst model for simpli ity omits the arbon trapping rea tion; the se ond model in ludes it. n

n

Model without impurity trapping

The rst model onsists of a set of oupled rst-order dierential equations for the populations Θ (t) of CH . For example, the overage of CH varies a

ording to 2

n

n

(2)

d 1 1 Θ2 (t) = f Θ3 (t) − f Θ2 (t) + f Θ1 (t) dt 2 2

with similar equations for the other hydro arbon spe ies. In matrix form these equations are:      Θ  4     Θ3         d    = f Θ 2  dt        Θ1      Θ0

1 2

0

0

0

0 −1

1 2

0

0

1 2

0

−1

1

0

0

1 2

0

0

1 2

0

0

0

−1

1 2

−1

Θ   4    Θ3       Θ  .   2      Θ1    Θ0

(3)

By diagonalizing this system and applying the initial ondition Θ (0) = 1, the exa t solutions for Θ (t) are readily obtained. They are plotted in Figure 2 as solid urves for a typi al experimental growth temperature of 500 C and atomi hydrogen pressure of 0.1 mTorr. This pressure orresponds to plausible values for the base hydrogen pressure, p = 1 mTorr, and plasma disso iation fra tion, 10%. These analyti solutions provide a useful referen e for understanding the results of the more ompli ated approa hes used later in this work. After 50-60 se onds of transient behavior, the overage of all four hydro arbons CH de rease exponentially with the same time onstant t . This time onstant is given by the smallest eigenvalue of the above matrix 3

n

◦

H2

n

0

8


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as t0 = αf −1 = α

p

(4)

2πmH kB T /pH A

where α = 2/(2 − 2 + √2) ≈ 13.1. In this rst model, the only exit hannel available to hydro arbons is as CH . Equation 4 shows that the rate of hydro arbon removal is proportional to rate of atomi hydrogen arrival, but is slowed down by one order of magnitude by the hain of inter onversion rea tions, CH ↔ CH ↔ CH ↔ CH ↔ C. Nevertheless, the population of all hydro arbons eventually goes to zero. This is not the behavior observed in experiments, whi h generally show residual

arbon on the order of several per ent even after long times. The se ond model, des ribed next, orre ts this de ien y. p

4

4

3

2

Model with impurity trapping

The se ond model in ludes the impurity trapping pro ess shown in Figure 1(e), but is otherwise identi al to the rst model. The one rea tion that leads to the trapped impurity population Θ o

urs at the rate f , and so the set of oupled equations now be omes: ∗ 0

∗

   Θ4      Θ    3         Θ   d  2  = f   dt  Θ1         Θ    0     Θ∗0

1 2

0

0

0

0

0 −1

1 2

0

0

0

1 2

0

0

−1

1

0

0

0

1 2

0

0

1 2

0

0

0

1 2

0

0

0

0

−1

−1 − f ∗ /f 0 f ∗ /f

0

   Θ4     Θ    3      Θ2   .    Θ1       Θ    0   Θ∗0

(5)

These equations an again be solved analyti ally for any value of f /f . For illustration we

onsider three values: 0.1, 1, and the limit f /f → ∞. Figure 3 shows the time evolution of all ve hydro arbon populations when f /f = 0.1. Just as in the rst model, the populations of the adsorbed hydro arbons on the surfa e de rease exponentially. But the population of ∗

∗

∗

9



trapped subsurfa e arbon impurities C∗ in reases with time and rea hes a onstant value of approximately 7% at long times. This value is already lose to the trapped arbon on entrations observed experimentally 4 at the high end of standard growth temperatures (roughly 500 ◦ C), suggesting the model an apture the essential behavior at those temperatures. 100

Coverage (monolayers)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 28

CH3

f*/f CH2 10- 1

f*/f = 1

CH

f*/f = 0.1 C C* 10- 2 0

20

40

60

80

100

120

140

Time (seconds)

Figure 3: Time evolution of hydro arbon populations with the arbon impurity trapping pro ess in luded. The trapped arbon impurity on entration depends on the ratio of the trapping rate f ∗ to the arrival rate f of atomi hydrogen. The ase illustrated here (heavy bla k urve) is for f ∗ /f = 0.1, whi h leads to a nal arbon impurity on entration [C∗ ℄ = f ∗ /(4f ∗ +f ) ≈ 7%. Also shown are the trapped arbon on entrations for two other ratios, f ∗ /f = 1 and f ∗ /f → ∞ (thin bla k urves), whi h lead to nal arbon on entrations of 1/5 and 1/4, respe tively (for larity, the on omitant hanges in hydro arbon populations are not shown). Temperature and atomi hydrogen pressure are the same as in Figure 2. For larger impurity trapping rates, the asymptoti nal overage of trapped arbon in reases (thin bla k urves in Figure 3). This in rease is highly non-linear in the ratio of trapping to adsorption rates: for f ∗ /f = 1, Θ∗0 has the limit 1/5, while for f ∗ /f → ∞, Θ∗0

has the limit 1/4. These high arbon on entrations are quite lose to the values obtained experimentally 4 at lower growth temperatures (roughly 200 ◦ C), suggesting the model is

apable of apturing this behavior as well. 10


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Finally, we derive a result that will be useful later in this paper by solving Eq. 5 under steady-state onditions orresponding to the limit of long time. This yields a simple expression for the nal on entration of trapped arbon as a fun tion of f and f ∗ : [C∗ ] = lim Θ∗0 (t) = t→∞

f∗ . 4f ∗ + f

(6)

It is trivial to onrm that Eq. 6 yields the limiting trapped arbon on entrations dis ussed above for dierent ratios f ∗ /f . So far this model treats arbon impurity trapping as a simple rea tion with a single rea tion rate f ∗ . The reality is more ompli ated, for two reasons. First, the impurity trapping rea tion has an a tivation barrier and is therefore strongly temperature dependent. Se ond, the value of this barrier depends sensitively on the lo al overage of adsorbed atomi hydrogen, whi h in turns depends on temperature and pressure. The onsequen es of both ee ts an be studied within our analyti al model by making these two modi ations. But we turn rst to the impurity trapping rea tion itself and then later return to the predi tions of the modied model.

Carbon impurity trapping Consider again the overview of hydro arbon rea tions sket hed in Figure 1. To investigate the arbon impurity trapping rea tion in Figure 1(e) it is important to determine rst the adsorption geometry at the most favorable adsorption site, s, for ea h hydro arbon. We used DFT to nd the lowest energy adsorption geometry CHn (s) of ea h spe ies. The results, shown in Figure 4, are CH3 (Al), CH2 (bridge), CH1 (H3 ), C(T4 ), where H3 and T4 are standard labels for the two dierent three-fold oordinated surfa e sites. Ea h hydrogen adsorption rea tion hanges a given hydro arbon spe ies and its adsorption geometry a

ording to CHn (s)+H→CHn+1 (s). Likewise, ea h hydrogen abstra tion

rea tion hanges a given hydro arbon spe ies and its adsorption geometry a

ording to 11



C Al

Figure 4: Side and top views of hydro arbons CHn adsorbed on aluminum nitride. The sequen e from left to right illustrates the redu tion of a methyl group (by su

essive hydrogen abstra tions) to a arbon atom, leading ultimately to a trapped arbon impurity in the subsurfa e region. Red atoms are arbon, white are hydrogen, green are aluminum, blue are nitrogen. The lowest energy adsorption site for ea h spe ies is shown. For larity, the lo al relaxations of the substrate indu ed by the adsorbates are not shown here.

12


Page 12 of 28

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CHn (s)+H→CHn−1 (s)+H2 .

A

ording to our DFT al ulations ea h of these rea tions is

energeti ally downhill with no a tivation barrier and hen e ea h of these rea tions o

urs as the same rate, proportional to the arrival rate

f

of atomi hydrogen.

The rea tion that traps atomi arbon is very dierent.

Two low-energy metastable

ongurations of a single arbon atom are shown at the far right of Figure 4. (1) A surfa e adsorbate C(T4 ) lo ated dire tly above a subsurfa e nitrogen atom and ovalently bonded to the three neighboring aluminum atoms. (2) A subsurfa e substitutional impurity CN for whi h the nitrogen atom has moved to the surfa e as an adsorbate N(T4 ). The lowest energy pathway onne ting these two ongurations is the on erted ex hange me hanism

21,22

in whi h the arbon and nitrogen atom tra e a roughly ir ular

path around their ommon enter (Figure 5). This rea tion is energeti ally downhill with an a tivation barrier whose value, a

ording to DFT, strongly depends on the nature of the three nearest-neighbor surfa e aluminum atoms. If these aluminum atoms are bare then the barrier is very high, 3.5 eV, and so the rea tion shuts down.

But if hydrogen atoms are

adsorbed on them then the barrier is far smaller, 0.8 eV, and this rea tion be omes very fast. The reason for the redu ed barrier is simple: when Al-H bonds form they redu e the strength of the Al-C and Al-N ba k-bonds that determine the a tivation barrier.

Predi ted on entration of arbon impurities Carbon ontamination at low temperatures We now investigate the predi tions of the analyti al model for the on entration of trapped

arbon impurities. At low and moderate temperatures, atomi hydrogen readily adsorbs at any aluminum site not already o

upied by a hydro arbon. We assume, for the moment, that these hydrogens atoms do not desorb. Therefore the relevant barrier for arbon trapping is

13



Page 14 of 28

C N N C Figure 5: Rea tion pathway for trapping an adsorbed arbon atom (upper left) as a arbon impurity in the subsurfa e region (lower right). In this on erted ex hange rea tion, the

arbon and nitrogen atoms tra e an approximately ir ular pathway around their ommon

enter.

The a tivation barrier for this rea tion is 0.8 eV if hydrogen atoms are adsorbed

on the three neighboring surfa e aluminum atoms, and 3.5 eV if they are absent.

Lo al

relaxations of the surrounding atoms are shown for the s enario with adsorbed hydrogen but the hydrogen atoms themselves are omitted here for larity.

∆ = 0.8

eV and the arbon trapping rate is

f ∗ = ν0 exp(−∆/kB T ),

where we take the attempt frequen y to be Hen e the trapping rate rate

f

f∗

ν0 = 1012

−1

s

(7)

, a reasonable approximate value.

23

is strongly temperature dependent while the hydrogen arrival

is only weakly dependent; see Figure 6(a).

∗ Using the expression for the nal on entration [C ℄ of trapped arbon (Eq. 6) we an now ∗ obtain an expli it predi tion for the temperature dependen e of [C ℄; see Figure 6(b). The qualitative behavior is easily understood: at very low temperatures the on erted ex hange rea tion shuts down and therefore no arbon is trapped, while at higher temperatures this rea tion be omes mu h faster than the hydrogen arrival rate and therefore the trapped

arbon on entration approa hes its limiting value 1/4.

14


Page 15 of 28

Rate (Hz)

104

(a)

f

100

1

f*

0 1 0

025 Coverage (monolayers)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


5

200 15 ◦ Tature ( C)

100

25

3

25

3

(b)

02 015 01

[C*]

0 5 0 5

1

15

2 ◦

Temperature ( C) Figure 6: (a) Temperature dependen e of the arrival rate f of atomi hydrogen at pressure 0.1 ∗ mTorr (red) and of the trapping rate f of arbon impurities (blue). The trapping pro ess is thermally a tivated with an a tivation barrier

∆ = 0.8

eV obtained from DFT al ulations.

(b) The resulting temperature dependen e of the trapped arbon impurity on entration, ∗ ∗ ∗ [C ℄ = f /(4f + f ).

15



Page 16 of 28

Atomi hydrogen overage To make this model more realisti we address now the overage of atomi hydrogen on the available aluminum sites. In the spirit of the model we do not attempt a omplete des ription, but instead try to apture the main features and espe ially the temperature dependen e. Atomi hydrogen an desorb from aluminum sites by several possible me hanisms. Here we onsider only two be ause this su es to illustrate the onsequen es for arbon trapping. The rst route is a simple hydrogen abstra tion rea tion: a surfa e-bound hydrogen atom

an ombine with a gas-phase hydrogen atom and then desorb as H2 . This rea tion is the predominant one at low and moderate temperatures. The rate of this abstra tion rea tion is equal to the arrival rate adsorption rate

f

of gas-phase atomi hydrogen. In steady state onditions, the

Rads = (1−ΘH )f

and the desorption rate

the steady-state overage of atomi hydrogen is

Rdes = ΘH f

ΘH = 0.5

are equal, whi h implies

at low to moderate temperatures;

see Figure 7(a). At higher temperatures hydrogen atoms an diuse on the surfa e, ombine to form H2 , and then desorb.

∆ = 2.1

This asso iative desorption rea tion has a DFT a tivation barrier

eV and so be omes important at the higher end of typi al growth temperatures,

500 to 600

◦

C. Hen e it strongly ae ts the steady state overage of atomi hydrogen at

these temperatures. By adding the rates of the two desorption me hanisms we obtain an expression for the hydrogen overage that exhibits this strong dependen e on temperature:

ΘH (T ) =

f 1 . 2 f + νo exp(−∆/kB T )

(8)

Finally, we onsider the quantum nature of the hydrogen adsorbate. Rather than developing an original model for this ee t, we use a theoreti al result derived by other authors for the temperature-dependent sti king oe ient

S(T )

of atomi hydrogen atoms on a metal,

whi h a

ounts for energy lost to ele tron-hole pairs.

24

By appropriately modifying Eq. 8

we then obtain our nal result for the steady state overage of atomi hydrogen, shown in

16


Page 17 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 7(a).

Carbon ontamination at high temperatures We return now to predi ting the on entration of arbon impurities in AlN over the full range of relevant temperatures. Two simple modi ations to Eq. (6) are required be ause all of the rea tions involve atomi hydrogen. First, the arbon trapping rea tion requires three neighboring hydrogen atoms to be simultaneously present. As a result, the average rate of this rea tion s ales with Θ3H (T ) and so we make the repla ement f ∗ → f ∗ Θ3H (T ).

Se ond, the adsorption of atomi hydrogen varies with temperature a

ording to its sti king

oe ient and so we make the repla ement f → f S(T ).

By re-evaluating Eq. (6) with these hanges, we obtain our nal result for the on entra-

tion of arbon impurities over the full range of temperatures; see Figure 7(b). The behavior at low temperatures is un hanged from earlier: the arbon trapping rea tion turns on around 100 ◦ C and allows the maximum possible arbon on entration, 25%, for temperatures above that point. But at still higher temperatures, around 500 ◦ C, atomi hydrogen starts to be driven o the aluminum sites and so the trapping rea tion begins to shut down again. The qualitative behavior in Figure 7(b) is already strongly reminis ent of the experimental ndings reported in Ref. 4: the measured on entration of arbon in AlN grown using TMA pre ursor mole ules went from a maximum of 30% at 200 ◦ C to 5% at 500 ◦ C and nally to 1% at 550 ◦ C. In the nal part of this paper we set aside the rate-equation model and arry out expli it atomisti simultations using the kMC method. These serve two purposes: to validate the predi tions of the analyti al model and to set the stage for subsequent, more omplex investigations beyond the s ope of rate equations.

17


#! # S #! # #! # ! " E$%&gy (m%'(

gen

c

H

Page 18 of 28

(a)

0

100

200

300

400

[H]

6

◦

Temperature ( C)

erage (monolayers)

(b)

[C*]

Carbon

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

rage (monolayers)


4 ◦

Temperature ( C)

Figure 7: (a) Theoreti al temperature dependen e of the overage of atomi hydrogen adsorbed at available aluminum sites at pressure 0.1 mTorr. The strong suppression at high temperatures arises from two ee ts: (1) the onset of thermally a tivated asso iative desorption of H2 mole ules, for whi h the a tivation barrier is 2.1 eV; (2) the redu tion of the hydrogen sti king oe ient due to in reased elasti s attering. Inset shows the theoreti al sti king oe ient S used for atomi hydrogen, as al ulated in Ref. 24. (b) Predi ted temperature dependen e of the on entration of arbon impurities trapped in the AlN substrate after growth has ompleted, taking into a

ount both the intrinsi temperature dependen e of the trapping pro ess (whi h leads to the in rease around 100 ◦ C) and the average hydrogen

overage of the neighboring aluminum sites (whi h leads to the de rease around 500 ◦ C).

18


9 87

Carbon

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


erage (monolayers)

Page 19 of 28

*,/* *,.) :nal

*,.* 100 s

*,-) 20 s Exp

*,-* *,*) *,**

200

300

)**

400

+**

◦

Temperature ( C)

Figure 8: Predi ted temperature and time dependen e of the on entration of arbon impurities trapped in AlN for atomi hydrogen pressure 0.1 mTorr, as obtained from kMC simulations (solid ir les). Snapshots are shown at three plasma exposure times: 20 s, 100 s, and the nal limiting values. Experimental values from Ref. 4 (diamonds) are shown for

omparison. Curves are guides to the eye.

19



Page 20 of 28

Kineti Monte Carlo simulations We arried out atomisti simulations of hydro arbon inter onversion and arbon trapping on aluminum nitride using the kMC method 25 as implemented in

kmos. 26

The surfa e was

represented by a periodi super ell with dimensions 300×300 relative to the AlN(0001) primitive ell. All hydro arbons were allowed to diuse to their preferred adsorption site unless

this move was blo ked by other adsorbates. The rates of all rea tions were the same as in previous se tions. To onrm that this atomisti approa h gives results onsistent with the analyti rateequation approa h, we rst simulated the system without impurity trapping des ribed earlier. The results for Θn (t) at every kMC time step ti are plotted in Figure 2. The agreement with the analyti al results is ex ellent. This onsisten y gives onden e in both approa hes and, moreover, onrms that our kMC super ell is su iently large to give onverged results with no need for nite-size orre tions. We next turn to atomisti simulations of the full system. These simulations in luded the impurity trapping rea tion and the dependen e of its rate on the o

upation of nearby aluminum sites by atomi hydrogen, as well as expli it hydrogen adsorption, sti king probability, and asso iative desorption on aluminum sites. We took snapshots of the trapped

arbon impurity on entration at three dierent plasma exposure times: 20 s, 100 s, and the nal limiting values. Our kMC simulation results are shown in Figure 8 along with experimentally observed trapped arbon on entrations from Ref. 4. The qualitative features of the kMC simulations broadly reprodu e those of both the rate-equation model and the experiment: 4 high arbon

on entrations around 25% at lower temperatures and mu h smaller on entrations of order 1% at higher temperatures. The temperature range over whi h this redu tion o

urs is roughly 200 ◦ C, in reasonable agreement with the experimental range of about 300 ◦ C. The redu tion with temperature is somewhat slower ompared to the rate-equation result in Figure 8, a onsequen e of treating the hydrogen o

upation atomisti ally, but the qualitative 20


Page 21 of 28

n coverage (monolayers)

QRWV

(a)

QRWQ QRUV QRUQ

[C*]

kj

ig QRQV f

QRQQ QRQQ1

1 QRQU0 QRUQ0 XYZ[\c ]^_`Zgen a`bdde`b (mTorr)

10

(seconds)

14

tP Mt

12 10 8

K

6

ML

4

con

s ON t

y

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


K J

t0

2 0

;

Page 1

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