Hydrogen diffusion and electronic metastability in amorphous silicon

Physica B 17(I (1991) 69-81 North-Holland

Hydrogen diffusion and electronic metastability in amorphous silicon R.A. Street Xerox Palo Alto Research Center, Palo Alto, CA 94304, USA

Hydrogen diffusion and its role in the many electronic metastability phenomena in hydrogenated amorphous silicon (a-Si:H) is reviewed. A-Si:H contains about 10 at% hydrogen, most of which is bonded to silicon. The hydrogen diffuses at relatively low temperatures by releasing hydrogen from the Si-H bonds into interstitial sites. The reactions of hydrogen with the silicon dangling bonds and the weak bonds provide a hydrogen-mediated mechanism for electron-structural interactions, which are manifested as electronic metastability. The annealing of light-induced defects, the equilibration of defects and dopants, the stretched exponential relaxation kinetics, and the atomic structure formed during growth, are all attributed to hydrogen diffusion.

1. Introduction Hydrogenated a - S i : H has a low defect density, exhibits doping and photoconductivity, and can be fabricated into useful electronic devices. In contrast, unhydrogenated a-Si has a high defect density, virtually no photoconductivity and cannot be doped. The main beneficial role of H is the termination of silicon dangling bonds for which it is ideally suited, being a small atom forming a single bond to silicon. However, the 10% concentration of hydrogen in good quality a-Si:H is far larger than is needed to passivate the defects present in a-Si. a-Si:H is an alloy of Si and H, in which the hydrogen plays an important role in determining the structure and electronic properties. The hydrogen structure is quite complex, having various bonding geometries, for example - S i - H , =Si-H 2, as well as an inhomogeneous distribution [1]. Hydrogen in a-Si:H is not very stable, even though it forms a strong bond to silicon. Heating a-Si:H above 300-400°C causes hydrogen to be released as H 2. Excess hydrogen is also absorbed by the material when the surface is exposed to atomic H. Both the hydrogenation and the evolution require the diffusion of hydrogen, which is observed at temperatures above 200°C. 0921-4526/91/$03.50

Instabilities in the electronic structure are a characteristic property of a-Si:H. The best known is the Staebler-Wronski effect, in which illumination causes the creation of dangling bond defects [2, 3]. The defects are removed by annealing at 150-200 ° , about the same temperature at which significant diffusion of hydrogen occurs. Similar reversible changes in the defect states are also induced by heat and voltage bias [4-6]. a-Si:H also exhibits irreversible changes in its electronic properties, associated with annealing over a wider temperature range. Thus, when a-Si:H is heated to high temperature to release hydrogen, there is an increase in the defect density [7], as would be anticipated if hydrogen is released from a S i - H bond. Film growth at low temperature also exhibits irreversible structural changes upon annealing, which is not associated with the evolution of hydrogen, but nevertheless has been attributed to hydrogen motion [7]. Although many different models have been proposed for the electronic instabilities, most associate the effect with the diffusion of hydrogen [6-12]. The fact that hydrogen diffusion occurs at the temperature range of the electronic instabilities, and that an electronic defect is formed when a S i - H bond is broken, both argue

© 1991 -Elsevier Science Publishers B.V. (North-Holland)

R . A . Street / Hydrogen diffilsion and ch'ctronic metastability in amorl)hous silicon

7tl

Increasing Hydrogen Diffusion

Frozen Structure

i Defect i Irreversible ', Equilibration l Structure/Compositional I Changes

i

Temperature Fig. 1. Illustration of the association o f t h c i n c r c a s i n g h y d r o gcn diffusion with the electronic equilibration and instability mechan isnls.

strongly that hydrogen diffusion causes thc instabilities, and this paper describes some of the more detailed evidence for this conclusion. Figure 1 summarizes the relation between the hydrogen diffusion and the electronic stability. The hydrogen is immobile at very low temperature, and the structure is frozen. Macroscopic hydrogen diffusion causes H ew)lution at high temperature, giving irreversible changes in the structure, composition and electronic properties. At intermediate temperatures the hydrogen diffusion over microscopic distances allows reversible defect equilibration. The study of hydrogen diffusion is therefore particularly interesting because of its relation to the electronic properties. This paper reviews the diffusion and then discusses models which relate the diffusion to the electronic metastability, through the chemical reactions between hydrogen and the silicon network. The models generally gave a good account of the measurements but there is still considerable uncertainty about the details of the hydrogen reactions.

sures the hydrogen concentration profile after some of the hydrogen is evolved by annealing. The evolution technique deduces the hydrogcn concentration from the thickness or time dependence of the hydrogen evolution rate. These measurements may not give the same diffusion coefficient. SIMS measures the interdiffusion of D and H, when the total concentration is constant, while the other two techniques measure diffusion when there is a hydrogen concentration profile. Since hydrogen has complex reactions with silicon, there is not nccessarily a simplc relation between the concentration and the chemical potential, which is the usual assumption of the analysis. However, the different techniques do give approximately the same diffusion coefficient. Figure 2 shows the temperature dependencc of the hydrogen diffusion for doped and undoped a-Si:H obtained from SIMS. The diffusion coefficient, D~j, is thermally activated, D n = DH. exp[--- ED/kT

T

].

T

(1

I

q

1l

-.. 10-15 t)

2. Hydrogen diffusion Diffusion occurs when there is a gradient in the chemical potential, and is obtained from the rate of change of a concentration profile. The various techniques used to measure the hydrogen diffusion in a-Si:H are SIMS [13], nuclear reaction profiling [14], and thermal evolution [15]. The SIMS technique usually involves the growth of films containing a thin deuterated layer, and measurement of the deuterium profile after annealing. The nuclear reaction technique mea-

lOag,lOaP

10-18

1.6

1.8

2.0

2.2

TEMPERATURE I O 0 0 / T (K) Fig. 2. The temperature dependence of the hydrogen diffusion in doped and undoped a-Si:H. The undopcd data arc those of Carlson and Magcc 1131.

R.A. Street / Hydrogen diffusion and electronic metastability in amorphous silicon

The undoped material has the lowest diffusion coefficient, having a value of 1 0 - 1 7 c m 2 s i at 250°C and an activation energy, E D, of 1.5 eV. Many measurements give similar values, provided that the deposition conditions are chosen to give good electronic quality a-Si:H [16-19]. Examples of the concentration profiles obtained by SIMS in boron doped a-Si:H are shown in fig. 3, for different anneal times at 200°C. The profiles of high quality a-Si:H samples generally give a good fit to the error function shape expected for a single diffusion coefficient. All the hydrogen appears to diffuse with the same D H, although the experiments cannot detect immobile hydrogen in concentrations less than about 20% of the total. (Note that the concentration step seen in fig. 3 is not due to non-diffusion hydrogen but arises from the different deposition conditions in the two layers which can give the same chemical potential even though the H concentrations are different [16].) The single value of D H is quite surprising in view of the inhomogeneous hydrogen distribution and suggests that most of the hydrogen is in approximately similar bonding sites. Hydrogen profiles

1021

i

2

4

71

r

i

DEUTERIUM DIFFUSION 10 .2 B2H6/SiH4

.I

E 3

IZ ILl 0 ,T u.

2

O Z

_O1×10-1~ ¢/1

0.8

m u. u.

0.6 I IO 1= ANNEAL TIME (hours)

0.1

I 100

Fig. 4. The time dependence of the diffusion coefficient for a p-type sample measured at 200°C.

in crystalline silicon generally do not fit an error function shape because there are different bonding sites and competing diffusion mechanisms [20, 21]. Despite the single value of D u obtained from the profiles, the hydrogen diffusion has the interesting property of being time dependent [16, 22]. Figure 4 shows data for boron doped a-Si:H in which D H decreases with time, following the relation D H = D,,t # ',

150°(~I 230°C 150°C H IH+D H

(2)

102 82 H6/Sill 4

where /3 is about 0.8 at 250°C. Figure 5 shows other examples of the time dependence of D u in

,,7, 10 20

E o 1019

1 0 -~4 O O

a 10 la

I 0 -~5

~

"~

1017 I

J

0.2

0.4

I

0.6

I

0.8

1.0

Depth (gin) Fig. 3. Examples of the deuterium profiles from which the diffusion coefficient is deduced. The p-type sample contains a deuterated layer, and the growth temperature of the different layers is indicated. The profiles fit well to an error function shape. The anneal times at 200°C are: A; control, B; 0.5 h, C; 9h, D; 200h.

\ ~

305°C~'~

"~

SAMPLE#

"~ 10-,6.

27 o . v

29 •

• •

CM

•

500

T(K)

600

"~

Ref. 5 550oc x 300oc. 250°C.

10 4

o°c

o

. ~ . ~ . 270oc "*,.. "~ 275°C~,~

10 5

lO ~

t (sec)

Fig. 5. Examples of the time dependence of the hydrogen diffusion coefficient in undoped a-Si:H [22].

72

R . A . Street / ttydrogen diJ]usion and electronic metastahility in amorphous silicon

undoped a-St:H, showing that it is a general effect. Doping causes an increase in the H diffusion coefficient compared to undoped a-St: H, particularly in p-type material, where the increase is about a factor 1000 at 250°C and the activation energy is reduced to about 1.3eV [16]. Compensated a-Si:H has a low D H, similar to undoped a-St:H, indicating that the doping dependence is an electronic effect rather than representing a change in film structure induced by doping. A higher diffusion coefficient is also observed in undoped a-Si:H deposited under non-optimal growth conditions [23, 24]. In this case, the increase of D H is explained by the presence of large voids or columnar growth morphology in the macroscopic film structure. Hydrogen recombines into H~ molecules which diffuse easily along the voids, whereas the voids in good quality a-Si:H are not interconnected and hydrogen diffuses as atomic H [25]. Figure 6 shows hydrogen evolution data for films deposited at low temperature [26]. There are two evolution peaks; one at 200-400°C and the other at 400-600°C. In films deposited at 250°C, only the upper peak, is present [7] indicating the degree to which the hydrogen distribution depends on deposition conditions. The temperature of the evolution peaks in fig. 6 reflects the doping dependence of the diffusion [261.

102o ~,~

1%PH 3 UD 1%BzH~//~k ... ...... ...//

1019 ...."

//.

Ts =40°C d~l!am

.-

z 101a

10~7

200

400 T(°C)

600

800

Fig. 6. The hydrogen evolution spectrum for samples grown at 40°C. The low temperature peaks are absent in material grown under optimal conditions. The doping dependence reflects the higher diffusion coefficients in doped material

[261.

Virtually sill the hydrogen in a-St: H is bonded to silicon. Some H. is trapped in voids, but its concentration is too small to affect the diffusion measurements. The H diffusion is generally presumed to occur by the release of hydrogen from the bonds into a mobile interstitial site. Silicon does not diffuse significantly at low temperatures [27], so that hydrogen diffusion cannot occur through the motion of a silicon atom to which hydrogen is attached. A possible reaction to describe diffusion is the breaking of an S i - H bond to give a silicon dangling bond and interstitial H, Si-H ~ Si-+H,

(3)

The diffusion rate can be expressed sis

l)~=D~,exp{

(Ej -E kT

)}

(4)

where E, is the energy of the mobile interstitial hydrogen, and E , , is the hydrogen chemical potential and the diffusion activation energy,

El), is E i -Era. Figure 7 illustrates the energy levels of hydrogen in silicon and a model for diffusion in aSi:H. The left side shows the energy of hydrogen in different interstitial and bonding sites. Calculations of H in crystalline silicon indicate that the lowest energy interstitial of a single H atom is the bond center site ( S i - H - S i ) with a binding energy of about l eV compared to free hydrogen in vacuum [20]. S i - H has a much higher binding energy, lying roughly 3 eV from the vacuum. There may be other bonding states of hydrogen at higher energy, for example the paired hydrogen complex proposed by Chang and Chadi [28], but probably none at lower energy than Si-H. The model for diffusion in a-Si:H on the right side of fig. 7 includes some expected effects of the disorder. It is assumed that hydrogen is bonded as S i - H , although other tightly bound states may also be present [29], and no distinction is made between isolated and clustered Sill, since the diffusion data does not distinguish the different sites. Diffusion occurs by excitation

R.A. Street

Hydrogen diffusion and electronic metastability in amorphous silicon

Energy

Energy

/

0 /

Density of States

Interstitial

J

El ~ / ~ H ~ j ~ ~Mobile H Bond-Center EBC H

/

//

EH / ' / / / /

/~-H in Weak _// Si-SiBonds

~O ~-

I1I

Bonded /

H

a-Si:H

H in Vacuum

..

73

/

EH

Si-H

_ ~ " ~ - - - ~ Si-H

Fig. 7. Illustration of the hydrogen energies in silicon. The left figure shows energy levels of interstitial and bonded H and the right figure is a simple model for a-Si:H which includes the disorder.

to the interstitial sites where hydrogen is expected to have a low migration energy, giving an effective energy of diffusion at the energy E~. The disorder of the Si-H network tends to broaden all the energy levels. The Si-H bond energy may not vary much because the hydrogen is small and bonded to only one Si atom. There is broad distribution of interstitial energies associated with distortions of the Si-Si bonds, which have substantial bond angle and bond length distributions. We expect that the hydrogen binding energy increases as the bond is distorted, and eventually the bond breaks to give a Si-H bond and a neighboring silicon dangling bond [16]. This bond breaking process is illustrated in fig. 8 and is pertinent to the discussion of defect equilibration in section 3.1. This simple diffusion model therefore comprises Si-H bonds, a distribution of interstitial sites and an energy E 1 of H migration, as shown

"Strong" @ ~ Si-Si I -- H .... Bond

BondCenter Hydrogen

Increasing Disorder

"Weak" Si-Si Bond

_~

H~

Si-H + Dangling Bond

Fig. 8. Illustration of how the disorder of a-Si : H may change the bond center hydrogen bonding site in a normal silicon to a broken bond in a weak Si-Si bond.

in fig. 7, with diffusion occurring by the reaction in eq. (3). This same model is applied to the discussion of metastability and growth processes later in the paper. The diffusion model leads to a diffusion coefficient. DH

DH0 ~

N D is the density of dangling bonds, which depends on the chemical potential approximately as

ND = NH exp{

(E"kT-EH) }.

(6)

Combining eqs. (5) and (6) leads to eq. (4) and relates together the diffusion, the defect density and the chemical potential. The analysis assumes that the hydrogen has an equilibrium distribution between its various bonding states, which usually applies to diffusion. |t follows that the defects are also in equilibrium, since they are governed by same reaction, eq. (3). Section 3.1 discusses the evidence that defect equilibrium does occur at the temperatures of the diffusion measurement. The various energies in fig. 7 can be estimated, but are not known with precision. The very low defect density in a-Si:H suggests that the chemical potential is well above E H. However, the

R . A . Street / tlydrogen di~JUsion and electronic metastahilitv in amofT~hou.~ silicon

74

experimental t e m p e r a t u r e dependence

of N D is

V,I

N* ~ 1017cm "

AE ~ 0 . 3 e V ,

(7)

as is shown in the next section. The chemical potential probably varies strongly with temperature because of the specific distribution of hydrogen bonding states. According to the model, the S i - H binding energy is,

E~-E~

(E D+AE).

dependent H diffusion in a-Si:H is also a result of the distribution of hydrogen trapping states, and one expects that an exponential distribution of traps woukt lead to the observed power h m decay [31]. However, the hydrogen diffusion is more complicated than the electronic transport. in part because it represents the motion of a large number of hydrogen atoms, near their equilibrium distribution. It is still not rcsolved whether the dispersion arises from the weak bond distribution, the distribution of interstitial energies or the distribution of S i - H bonds.

(S)

The 1.5 eV activation energy of diffusion, together with the assumption that the energy E~ is about 1 eV below the vacuum level, gives E n 2.SeV. This is reasonably consistent with the expected binding energy, given the many uncertainties in the values. The diffusion process described by eq. (3) involves a silicon dangling bond which is an electronic defect with states in the gap. Doping reduced the energy required to release the hydrogen because the defect gap state is charged. The energy reduction is E D - E v, where E D is the gap state energy and E v is the Fermi energy. Thus the reduction in D u by doping can be explained as a purely electronic effect, and any other mechanism that changes the Fermi energy, such as charge accumulation at an interface, is expected to give a similar change in the diffusion. T h e r e is a further doping dependence if the hydrogen interstitial is charged, as is indicated by m e a s u r e m e n t s of crystalline silicon [3{)]. The charge state of mobile hydrogen in a-Si: H is not easily deduced from the measurements, and its role in the doping dependence is simihirly unclear. The time dependence of the diffusion is one of the most notable distinctions between the diffusion in ordered and disordered materials. The dispersive diffusion of electrons in a m o r p h o u s semiconductors has long been recognised as a result of the distribution of trapping sites [311 . It therefore is reasonable to suppose that the time

3. The interaction of hydrogen and the electronic structure

Atomic diffusion is frequently treated as being uncoupled from the electronic state of a material because diffusion typically occurs at a much higher t e m p e r a t u r e than the electronic measurements. The low t e m p e r a t u r e diffusion of hydrogen in a-Si:H does not allow this separation of structural and electronic changes. Furthermore, hydrogen reacts with the silicon structure in a way that directly influences the electronic states. The most obvious example is the termination of a silicon dangling bond, which removes a state in the gap. However, hydrogen can also break SiSi bonds, by the mechanism in fig. 8, allowing the creation of defects. Thus the diffusion of hydrogen directly modifies the electronic structure and the effects occur at low enough temperatures to influence electronic measurements. A corollary to the observation that hydrogen motion changes the electronic structure, is that a change in the electronic structure modifies the hydrogen diffusion. The doping dependence to the diffusion is explained as an electronic effect brought about because the energy required to release hydrogen from a S i - H bond depends on the position of the Fermi energy. This can be generalized to the idea that any electronic excitation can influence the hydrogen distribution. Hydrogen motion therefore provides a mechanism for electron-structural interactions, which are discussed in the remainder of this paper. The

R.A. Street / Hydrogen diffusion and electronic metastability in amorphous silicon

hydrogen reactions explain the metastability phen o m e n a , which are reversible structural changes resulting from electronic excitation. The metastability occurs because the room temperature diffusion of hydrogen is sufficiently slow that the relaxation time is longer than normal experimental times.

3, 1. Equilibrium and metastable defect formation The hydrogen diffusion is discussed in terms of 3 reactions in which S i - H bonds break to give electronic defects and interstitial H. When the hydrogen distribution is in equilibrium as indicated by its diffusion, it follows that there is also an equilibrium defect distribution. Defect equilibration is indeed observed in the temperature range of hydrogen diffusion. The defect equilibration has a thermally activated relaxation rate which is consistent with the hydrogen diffusion rates (see section 3.2). Thus, the metastable defect properties are linked to the hydrogen diffusion. Metastable defect creation occurs following electronic excitations within the material. Prolonged illumination creates defects [2], as does charge accumulation [5], either at a dielectric or resulting from a high current. The metastable defects arc the silicon dangling bonds characterized by their electron spin resonance at g = 2.0055 [3]. Although hydrogen motion is presumed to be involved in the defect creation, no hydrogen hyperfine structure, or other direct evidence has yet been found, so that direct proof of the model is lacking. Figure 9 shows the t e m p e r a t u r e dependence of the equilibrium defect density in undoped aS i : H . The notable feature of the results is the weak t e m p e r a t u r e dependence, corresponding to an activation energy of 0.2-0.3 eV. Such a low formation energy would normally be associated with a very large defect density. As is shown shortly, the low defect energy arises from the disorder, so that the defect creation occurs at the few sites at which the energy is low, giving both a low defect density and creation energy. The relaxation kinetics of the defect equilibration

75

3x1016

1016 LU C~ I-"

3x1015

1015 1.4

1.6 1.8 2.0 2.2 TEMPERATURE 1000/3" (K-1)

2.4

Fig. 9. The temperature dependence of the equilibrium defect density of undoped a-Si : H measured by ESR. The solid line is a fit to the data using the hydrogen-mediated weak bond model, described in the text. have an activation energy of about 1.5 eV [6], again consistent with the hydrogen diffusion activation energy. The relaxation time varies with sample deposition conditions, and is also larger than for light induced defects. The defect creation process is explained by the breaking of weak Si-Si bonds to form dangling bonds, by the general reaction [32], weak bond ~ dangling b o n d s .

(9)

It seems unlikely that a broken Si-Si bond can be stable without some mechanism to the two dangling bonds apart. Recent experiments show that the diffusion rate of defects is unmeasureably small, and the separation of the defects is attributed to the motion of hydrogen. There have been several models proposed, one of which is illustrated in fig. 10 [6]. This is a scheme in which the hydrogen is released from a S i - H bond, diffuses some distance~and breaks a weak Si-Si bond forming a strong bond to one of the

R . A . Street / Hydrogen diffi~sion and electronic metastabilitv in amoq~hou.s ,~ilicon

76

Weak Bond

¢ Fig. ]0. Model of hydrogen-mediated weak bond breaking. The model corresponds to the reaction in eq. (3), assuming thai interstitial hydrogen breaks a weak Si-Si bond as in fig. 7.

silicon atoms. Two spatially separated defects are formed, which are stable until there is further hydrogen motion. This model is essentially the same as the diffusion reaction, with the added simplification that the interstitial hydrogen traps in a weak Si-Si bond by breaking the bond and forming a new S i - H bond and another dangling bond defect (see fig. 8). The defect formation energy U. is half the energy of the reaction because two dangling bonds are formed. The weak bond model also links the distribution of electronic states with the hydrogen bonding energies. The model assumes, so far without complete theoretical confirmation, that the defect formation energy is [6, 10, 32] U=E D

E,.~,.

S.2. Kinetics of metasmble defects The defect equilibration in doped and undoped a - S i : H has a relaxation time which corresponds to a change in the bonding coordination of silicon or dopant atoms within the network. The form of the relaxation is shown in fig. 11 and its t e m p e r a t u r e dependence, with an activation energy of about 1 eV is shown in fig. 12 [33, 34]. In view of the low t e m p e r a t u r e diffusion, hydrogen motion is the obvious candidate for the relaxation mechanism, although other possibilities have been considered. The relaxation data of fig. 11 are not described by a single time constant, but instead extend over more than four orders of magnitude in time [33[. Thc time dependence follows a stretched exponential relation,

(l(t)

E D is the defect gap state energy and E,h is the energy of an electron in the valence band tail. 7-

T

The model assumes that the only significant energy in the defect creation is that of the electronic state as it changes from a weak Si-Si bond into a defect. The calculations of the equilibrium defect density agree well with the data as shown by the example in fig. 9. This model may be a considerable oversimplification, but has the attractive attribute of giving a mapping between the electronic density of states and the hydrogen bonding configurations.

&nu, = l t , , e x p [ - ( t / 7 ) ~ ] .

"

!

.

1.0 ~

.

.

(ll) .

n-TYPE a-Si:H

,.4 0.6 ~ 0.4

~= 0.70 ~

0.61~'~58

~.56

~4

~45

J

0 ..................................

10

102

103

104 TIME (SEC)

105

106

107

108

Fig. I1. T i m e d e p e n d e n c e of the s t r u c t u r a l c h a n g e s a s s o c i a t e d with the defect and d o p a n t e q u i l i b r a t i o n of n-type a - S i : H . The solid lines are fits of the d a t a to s t r e t c h e d e x p o n e n t i a l d e c a y , with p a r a m e t e r /3 as shown.

77

R.A. Street / Hydrogen diffusion and electronic metastability in amorphous silicon

[

]

which occurs within an environment that is itself time dependent. If k has a time dependent form,

I

106

(13)

k ( t ) = k(,t ~ i , 105

then the integration of eq. (12) gives, n-TYPE

N ( t ) = N 0 e x p [ - ( t / r ) ~ ].

,~ 10 4

(14)

LLI

Kohlrausch used this analysis to explain his first observation of stretched exponential relaxation

I..-

Z 103

_o I..-

0.95eV /

/

[35].

p-TYPE

X

Equation (13) implies that the atomic motion which causes the structural relaxation has a power law time dependence. The t e m p e r a t u r e dependence of the p a r a m e t e r /3, measured from the relaxation data (fig. 11), is shown in fig. 13 and follows the relation,

J--I 1 0 2 LU E

10

•

•

RELAXATION DATA

©

7i ANNEALING DATA

(15)

/3 = T / T ~ , 10-1

I

2.0

2.5 3.0 TEMPERATURE 1000/T (K d)

I

3.5

Fig. 12. The temperature dependence of the relaxation time of the defect and dopant equilibration in doped a-Si:H, showing activated behaviour with energy about 1 eV. The solid lines in the data of fig. 11 are fitted to this expression, with values of /3 ranging from 0.5-0.7 as indicated. Stretched exponential relaxation describes the equilibration of many disordered materials and has been widely studied since it was first observed by Kohlrausch in 1847 [35]. It is observed below the glass transition t e m p e r a t u r e of many oxide and polymeric glasses, as well as spin glasses and other disordered systems, and is apparently a general characteristic of glassy disorder. Although the analysis of stretched exponential decay from a microscopic model is complex, the form can be derived from an assumed time dependence of the rate constant, k, in the rate equation, dN/dt

= - k(t)N.

(12)

The time dependence of k ( t ) reflects a relaxation

with T c = 600 K. Hydrogen has a diffusion coefficient, Dn, which decreases as a power law in time, and the time dependence of D H has the right form and magnitude to account for the stretched exponential relaxation. Furthermore, the experimental values o f / 3 obtained from the

I

I

I

I

I

I

a-Si:H 1.0

+

0.8

~-

0.6

0.4

0.2

I '~' 0

I 1 oo

I 200

undoped ESR

I r I 300 400 500 TEMPERATURE (K)

[ 600

700

Fig. 13. Temperature dependence of parameter /3 obtained from the stretched exponential decay, compared to the value obtained from dispersive hydrogen diffusion.

78

R . A . Street / ttydrogen di[ltcsion attd electronic metastabilitv in amorpho.,s silicon

decay of nUT agree well with the dispersion p a r a m e t e r of the hydrogen diffusion (fig. 13). Therefore, a quantitative link between the structural relaxation and the diffusion of bonded hydrogen is established. 3.3.

The hydrogen glass m o d e l

The defect equilibration is similar to the behaviour of glasses near the glass transition temperature, with a low t e m p e r a t u r e frozen state and a high t e m p e r a t u r e equilibrium. Stretched exponential relaxation is also a characteristic of glasses. These similarities lead to the proposal that the bonded hydrogen in a - S i : H can be considered to be a glass [36]. This model divides the a-Si: H network into two components: a rigid silicon network, and a network of bonded hydrogen which is mobile with glass-like properties. Whether or not the hydrogen-glass is a valid description depends in part on the definition of a glass, which is a rather loose term. The relaxation kinetics of a - S i : H are similar to the glass with an equilibration t e m p e r a t u r e equivalent to the glass transition t e m p e r a t u r e and stretched exponential relaxation. Two other connections can be made with the properties of normal glasses, through the viscosity and the specific heat. The viscosity of a normal glass is about 10 I; P at the glass transition temperature. The liquid viscosity, ri, is related to the diffusion coefficient by the Stokes-Einstein relation, riD = k T/6qra ,

(16)

where a is the hopping distance of the diffusing species. The glass transition t e m p e r a t u r e is therefore expected at a diffusion coefficient of about 10 > cme/s, for a hopping length of a few ,~. Table 1 compares the equilibration temperature measured from the conductivity experiments with the predicted value obtained by extrapolating the hydrogen diffusion coefficient data of fig. 2. The two temperatures agree quite well, and account for the doping dependence of the equilibration temperature. The glass transition is also characterized by a broad endothermic feature in the specific heat.

Table I Comparison of the m e a s u r e d and calculated equilibration temperatures for dilfercnt doping types.

Material

T, (measured) ("

7, (1). :: I() >' cm ' s ) : ( '

p-t~pc n-type undopcd

~1) 13() 2lift

lift I f~l)

7()

Figure 14 shows that a feature of this type is observed in n-type a - S i : H , [37] with a broad peak in the t e m p e r a t u r e range 120-18()°C. The t e m p e r a t u r e and its dependence on the cooling rate, identify it with thc electronic equilibration effects, and the t e m p e r a t u r e of the feature also has the same dependence on substrate tcmperature during growth as the equilibration temperature measured from the conductivity. The effect in specific heat is small, because only hydrogen atoms participate in the structural equilibration.

4. The role of hydrogen in the growth a - S i : H is usually grown from a silane plasma, which induces the growth of films by dissociating the Sill 4 into reactive gas radicals. The structure and electronic properties of the fihns depend on the plasma conditions, such as substrate temperature, power and gas composition [1]. The variations in structure of a-Si: H are usually attributed to different mixtures of silicon-containing gas radicals, such as Sill+, Sill+, etc. [371 , and

1.0

-7

0

(b)Stow ~ .

/jJ

~-1.0

(a)Foist Cooting

\ / \U

-2.0 CD

~ -3.0

510

log

r

150

200

250

TEHPERATUF~E I'CI

Fig. 14. Diflcrcnlhd scanning calorimctcrv measurements oi the heat released during cquilibral.ion of n-type a Si: H after fast and slow cooling [37].

R.A. Street / Hydrogen diffusion and electronic metastability in amorphous silicon

not much attention has been given to the role of atomic hydrogen, which is also created by the plasma. The preceding discussion of H diffusion and defect equilibration is based on the particular distribution of Si-H and weak Si-Si bond states which are defined by the atomic structure of the a-Si:H film. Recently it is suggested that the structure is itself determined by the hydrogen during growth [38]. Hydrogen diffusion occurs at normal growth temperature of a-Si:H (200-300°C). The hydrogen distribution in the film is close to equilibrium and described by a chemical potential. The interchange of hydrogen across the growing surface implies that the hydrogen chemical potentials in the plasma and the film are (at least approximately) equal. At the growing surface reactions occur between the silicon and the hydrogen that result in the formation of the film structure. We argue that the hydrogen chemical potential determines the occupancy of the various bonding configurations. When there are several alternative structural configurations for silicon and hydrogen bonds, energy minimization leads to a preferred structure which depends on the position of the hydrogen chemical potential. In this way the plasma can influence the film structure through the hydrogen chemical potential. Atomic H forms a strong bond to silicon and the optimum structure is one which minimizes the hydrogen which is not strongly bonded to silicon.Thus, ideal bonding in a-Si:H consists of Si-Si and Si-H bonds, but not dangling silicon bonds or interstitial hydrogen. The bond angle and bond length disorder cause a distribution of Si-Si (and possibly Si-H) bond strengths. This argument leads to the hydrogen density of states distribution model shown in fig. 7, with Si-H bonds lying below the hydrogen chemical potential, and the Si-Si bonds mostly unoccupied by hydrogen and above /xH. The weakest Si-Si bonds are closest to /XH, since these are most easily broken by hydrogen through a reaction of the general type, weak bond + H ~ broken bond + S i - H .

(18)

A Si-H bond which loses its hydrogen and a

79

weak bond which gains a hydrogen atom, both transform to dangling bonds. A high density of both types of states at ~H is therefore not a low energy configuration. An ideal amorphous structure, therefore, is one in which the hydrogen density of states distribution has a minimum at /xH as a consequence of the reactivity of hydrogen with the silicon network. The minimum in the density of states at /xH allows the hydrogen to determine the silicon network structure. When the growth conditions are altered, the position of/x H may change and the distribution of states is modified by reconstructing the network to give either Si-H bonds or stronger Si-Si bonds, to maintain /xH at the minimum. The different network structures which follow from a change in/x H are illustrated in fig. 15, and indicate that an increase in the energy of/x H should cause a narrower weak bond distribution. Thus, the hydrogen provides a mechanism in which the growth reactions determine the structure by inducing a minimum weak bond density at /xH. The model does not consider the specific reactions, but there is evidence that bonded hydrogen in the film is removed by reaction with hydrogen from the plasma [40]. As with the diffusion process, hydrogen

Si-Si Bonds >,

.~

== oJ rIJJ

o rn

,

g 2 g.

"13

Si-H Bonds

Density of States

Fig. 15. The hydrogen density of states distribution as in fig. 7, showing the S i - H bonds below /~n and the Si-Si bond above gH which are mostly unoccupied by hydrogen, and the m i n i m u m at the hydrogen chemical potential. The dashed line shows the modified density of states for a higher/-~H with a narrower distribution of weak bonds.

80

R.A. Street / Hydrogen diffusion and electronic metastabilio' in amorphous silicon

reactions create Si dangling bonds which may bond to each other or may acquire hydrogen. Similarly weak Si-Si bonds are broken by the hydrogen and may be reformed as different stronger bonds [41]. The growing film surface is assumed to have a high hydrogen concentration and a high disorder, both originating from the attachment of SiH~ (x = 1 - 3 ) radicals. The subsurface reactions involving hydrogen lead to a film structure which is determined by the position of /xH and the equilibrium hydrogen distribution. This growth model does not apply to low t e m p e r a t u r e growth (<200°C) because there is insufficient hydrogen diffusion. Instead defective material results from hydrogen not being properly equilibrated. The H content and the disorder are higher than for an ideal a - S i : H film. H o w e v e r , subsequent annealing of the film allows hydrogen equilibration and improves the structural order, with a corresponding reduction in the defect density [7]. At higher temperatures, the H diffusion is fast enough to allow the film structure and H content to be determined by the H chemical potential. A higher t e m p e r a t u r e reduces /xH, and therefore induces a more disordered film and a lower hydrogen concentration. O p t i m u m films are therefore grown at the lowest t e m p e r a t u r e consistent with sufficient diffusion to equilibrate the hydrogen (corresponding to the boundary between the frozen and equilibrium states in fig. 1). The model further predicts that hydrogen dilution and increased RF power raise #H and give more ordered material at deposition temperatures above about 300°C. In contrast, at deposition temperatures of 250°C or below, the increased growth rate of a high RF power reduces the time available for hydrogen equilibration and causes kinetically limited growth. An increasing hydrogen chemical potential tends to reduce the disorder of the Si-Si bonds. However, the evidence that the valence band tail slope is never less than 45-50 meV [32], indicates that there is a minimum possible weak bond disorder in a-Si:H. We propose that when /a H is too high to be consistent with the minimum disorder, a transition to growth of micro-crystalline silicon results. The model suggests that

the micro-crystalline growth is enhanced by high H dilution in the plasma, high RF power and low temperature, since all three raise the chemical potential. These are indeed the observed conditions [42], although the films revert to being a m o r p h o u s at low t e m p e r a t u r e because the H diffusion rate is too low to allow equilibration.

5. Summary Hydrogen has a profound effect on the electronic properties of a - S i : H through its diffusion at relatively low temperature. The redistribution of hydrogen during the diffusion process changes the distribution of defect and dopant states and provides a mechanism for electron structure interactions. This mechanism is proposed to explain the defect and dopant equilibration and the various defect metastability p h e n o m e n a . The characteristic stretched exponential relaxation describing the electronic equilibration can be related to the time-dependent dispersive diffusion of hydrogen. It is proposed that the diffusion of hydrogen near the growth surface is a major factor determining the structure of the a - S i : H films and the transition to microcrystallinity.

Acknowledgements Much of the research described here was performed in collaboration with J. Kakalios, M. Hack, W.B. Jackson, C.C. Tsai and K. Winer, and was supported by the Solar Energy Research Institute.

References [11 J.C. Knights, J. Non-Cryst. Solids 35 & 36 (1980) 159. [2] D.L. Staeblcr and C.R Wronski, Appl. Phys. Len. 31 (1977) 292. [3] M. Stutzmann, WB. Jackson and C.C. Tsai. Phys. Rcv. B 32 (1985) 23. [4] Z.E. Smith, S, Atjishi, I). Slobodin, V. Chu, S. Wagner, P.M. Lenahan, R.R. Arya and M.S. Bcnncll, Phys. Rcv. l_ett. 57 (1986) 2450.

R.A. Street / Hydrogen diffusion and electronic metastability in amorphous silicon [5] W.B. Jackson and M.D. Moyer, Proc. MRS Symp. 118 (1988) 231. [6] K. Winer and R.A. Street, Phys. Rev. Lett. 63 (1989) 880. [7] D.K. Biegelsen, R.A. Street, C.C. Tsai and J.C. Knights, Phys. Rev. B 2(I (1979) 4839. [8] D.E. Carlson, Appl. Phys. A 41 (1986) 305. [9] S. Zafar and E.A. Schiff Phys. Rev. B 40 (1989) 5235. [10] Z.E. Smith and S. Wagner, Phys. Rev. Lett. 59 (1987) 688. [11] M. Stutzmann, Philos. Mag. B 60 (1989) 531. [12] S.T. Pantelides, Phys. Rev. Lett. 58 (1987) 1344. [13] D.E. Carlson and C.W. Magee, Appl. Phys. Lett. 33 (1978) 81. [14] M. Reinelt, S. Kalbitzer and G. MOiler, J. Non-Cryst. Solids 59 & 60 11983) 169. [15] W. Beyer and H. Wagner, J. Appl. Phys. 53 (1982) 8745. [16] R.A. Street, C.C. Tsai, J. Kakalios and W.B. Jackson, Philos. Mag. B 56 (19871 305. [17] S.F. Chou, R. Schwarz, Y. Okada, D. Slobodin and S. Wagner, Proc. MRS Symp. 95 (1987) 165. [18] A.V. Dvurechenskii, I.A. Ryazantsev and L.S. Smirnov, Sov. Phys. Semicond. 16 (1982) 400. [19] N. Sol, D. Kaplan, D. Dieumegard and D. Dubreuil, J. Non-Cryst. Solids 35 & 36 (1980) 291. [2(I] N.M. Johnson, Phys. Rev. B 31 (1985) 5525. [21] N.M. Johnson, C. Herring and D.J. Chadi, Phys. Rev. Lett. 56 (1986) 769. [22] J. Shinar, R. Shinar, S. Mitra and J.Y. Kim, Phys. Rev. Lett. 62 (1989) 2001. [23] V. Petrova-Koch, H.P. Zeindl, J. Herion and W. Beyer, J. Non-Cryst. Solids 97 & 98 (1987) 807. [24] R.A. Street and C.C. Tsai, Philos. Mag. B 57 (1988) 663.

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[25] W. Beyer, Physica B 170 (1991) 105 (these Proceedings). [26] W. Beyer, J. Herion and H. Wagner, J. Non-Cryst. Solids 114 (1989) 217. [27] P.D. Persans and A.F. Ruppert: in Semiconductor Based Heterostructures, eds. M. Green et al. (MRS Pittsburgh, USA, 1987). [28] K. Chang and D.J. Chadi, Phys. Rev. Lett. 62 (1989) 937. [29] W.B. Jackson, Phys. Rev. B 41 (1990) 1(1257. [30] N.M. Johnson and C. Herring, Phys. Rev. B 38 (1988) 1581. J. Zhu, N.M. Johnson and C. Herring, Phys. Rev. B 41 (1990) in press. [31] H. Scher and E.W. Montroll, Phys. Rev. B 12 (1975) 2455. T. Tiedje and A. Rose, Solid State Commun. 37 (1980) 49. [32] M. Stutzmann, Philos. Mag. B 56 (1987) 63. [33] J. Kakalios, R.A. Street and W.B. Jackson, Phys. Rev. Lett. 59 (1987) 1037. [34] R.A. Street, M. Hack and W.B. Jackson, Phys. Rev. B 37 (1988) 4209. [35] R. Kohlrausch, Ann. Phys. (Leipzig) 12 (1847) 393. [36] R.A. Street, J. Kakalios, C.C. Tsai and T.M. Hayes, Phys. Rev. B 35 (1987) 1316. [37] S. Matsuo, H. Nasu, C. Akamatsu, R. Hayashi~ T. lmura and Y. Osaka, Jpn. J. Appl. Phys. 27 (1988) L132. [38] A. Gallacher and J. Scott, J. Solar Cells 21 (1987) 147. [39] R.A. Street, in press. [40] Y. Muramatsu and N. Yabumoto, Appl. Phys. Lett. 49 (1986) 1230. [41] K. Winer, Phys. Rev. B 41 (1990) 7952. [42] A. Matsuda, J. Non-Cryst. Solids 59 & 60 (1983) 767.