Thermal equilibrium processes in doped amorphous silicon

Journal of Non.Crystalline Solids 97&98 (1987) 767-774 North-HoUand,Amsterdam

767

Section 13 : Stability

Thermal Equilibrium Processes in Doped Amorphous Silicon J. Kakalios and R. A. Street Xerox Palo Alto Research Center, Palo Alto, CA 94304 Recent evidence that the electronic properties of doped hydrogenated amorphous silicon are influenced by thermal equilibrium processes are reviewed. The slow relaxation of the localized state distribution follows a stretched exponential time decay which we attribute to the dispersive diffusion of bonded hydrogen.

INTRODUCTION The thermodynamic ground state of a solid is thought to be its crystalline phase; the existence of non-equilibrium structures is therefore an important attribute of amorphous materials. Indeed, for a long time it was believed that amorphous silicon and related materials that are deposited as thin films have non-equilibrium structures that are determined solely by the deposition kinetics. 1 This view has lately been increasingly challenged, so that we now understand that thermal equilibrium controls many properties of hydrogenated amorphous silicon (a-Si:H). Early work on a-Si:H has shown that structural rearrangements of the bulk could take place. For example, damage created by particle bombardment or illumination can be reversed by annealing, indicating that thermally induced structural rearrangements do occur. 2 More recently the concept of a thermal equilibrium at the growing surface was introduced to explain the doping process in a-Si:H. 3 Evidence now suggests that equilibrium persists into the bulk of the sample down to temperatures of about 100°C, and that the changes in the bonding structure are enabled by the motion of bonded hydrogen.4-~° In this paper we will review some basic features of the thermal equilibration of the defect structure and show that the defect compensation model of doping, together with the proposal that the defect structure is in metastable thermal equilibrium can account very well for our experimental observations. We then show that studies of hydrogen motion provide key insights into the nature of metastabilities in a-Si:H. All of the measurements described here are performed on n-type doped a-Si:H although the same effects are observed in p-type doped material. The primary experiments used are the voltage-pulse charge sweep-out 11 and the d.c. dark conductivity. 12 The sweep-out technique measures the total density of occupied shallow band tail states net while the d.c. conductivity (~ is sensitive to those shallow state electrons excited above the mobility edge. The density of electrons nBT in the band tail and overlapping donor states is related to the densities of donors NooNoR and dangling bonds NOB by the charge neutrality expression naT = NDONOR - NDB (1) Changes in the density of localized states (NDoNOR , NDB) are therefore reflected in electronic properties such as nBm or 0. 0022-3093/87/$03.50 ©Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

J. Kakalios, R.A. Street / Thermal equilibrium processes

768

THERMAL EQUILIBRIUM

AND

RELAXATION

EFFECTS

The equilibrium is characterized by a thermally activated equilibration time, and an equilibrium state that is temperature dependent. 1° These properties are seen in fig. 1 which shows the time dependence of nBT for a 10 .2 PHJSiH 4 doped sample. RBT slowly decays to a new equilibrium state value n E even though the sample is both annealed and stored in the dark. The sample is first annealed at 210°C to bring it into equilibrium and then allowed to relax at a lower temperature. The time to reach equilibrium is about a year at room temperature but is of the order of a few minutes at 125°C and has an activation energy of "~" 1 eV. Similar results are found for other doping levels and for ptype samples, though for p-type doped a-Si:H the relaxation time constant is much faster, of the order of several hours at room temperature. From eq. (1) it is clear that the relaxation of nBT must result from a time dependence of the density of dangling bonds and or donors. A consequence of the activated equilibration time is that the material properties are sensitive to the rate at which the sample is cooled following a high temperature anneal. As a sample is cooled, the relaxation time will eventually become so long that equilibrium cannot be maintained and the structure is effectively frozen into a non-equilibrium state. Clearly a slow cooling rate allows the equilibrium to persist to a lower temperature. We therefore make the distinction between the two states of the material . equilibrium and frozen-in - which have very different electrical properties. The two regimes of behaviour are separated by a temperature we denote T E. These two states are seen in fig. 2 which shows Arrhenius plots of the conductivity for a 10 .5 PH3/SiH 4 doped a-Si:H sample for fast and slow cooling and after relaxation in the dark for over seven months (defined as the RESTED state). 13 Below the equilibration temperature T E of about 140°C the conductivity curves are sensitive to the prior thermal history whereas above T E the ~ curves merge and the sample is in thermal equilibrium. The conductivity curve above T E has an extrapolated activation energy of 0.4 eV and a preexponential factor a o of 200 ohm-lcm -1. From fig. 1 we note that after seven months ('~-- 1.8 x 10 7 sec) at room temperature the dark t

i

-~

'

SWEEP

OUT

12

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Fig. 1: The relaxation of the occupied band tait density nBT for n-type a-Si:H at different temperatures after annealing at 210°C.

z

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2

i

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10

102

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103 TIME

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104 105 (SEC)

J

106

i

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--

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769

J. Kakalios, R.A. Street / Thermal equilibrium processes

conductivity should be nearly fully relaxed to its steady state equilibrium value.

The

activation energy of the RESTED state curve in fig. 2 is 0.42 eV, which suggests that below T E the sample slowly relaxes to the same state which it rapidly reaches above T E. Measurements of nBT and ~r are sensitive to the difference between NDONOR and NOB and do not provide any information on whether or not both states equilibrate. We have investigated the equilibration of the donor band indirectly by using PDS, C-V and bias annealing experiments. 14'16 A depletion bias applied at elevated temperatures to a charge sweep out sample will move the Fermi level deep into the gap away from its equilibrium position. To compensate the density of localized states is altered, either by increasing NDONOR or by decreasing NDB to restore equilibrium and increase neT to its original value. When the bias is removed and the sample is cooled to room temperature an excess nBT is measured. As shown in fig. 4 for a 10 -5 PH3/SiH 4 doped sample nBT can be increased by a factor of 40 by this technique from an initial density of 1016 cm "3 to nearly 4 x 1017 cm -3 Both NDONOR and ND8 were " " 1017 cm 3 originally, so we conclude that even if the dangling bond density decreased to zero, the donor density must have increased by a factor of four. Figure 4 implies that NDONOR will increase as net increases. Photo-thermal deflection spectroscopy measurements, which are sensitive to the deep dangling bond density, are unable to detect any change in NDB with annealing and rapid quenching, to within an accuracy of better than 10%. 15 The implication is that in doped a-Si:H, equilibration results from changes in only the dopant density. i

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Fig. 2: The temperature dependence of the d.c. dark conductivity after a 180°C anneal for different cooling rates and when stored in the dark for seven months (RESTED).

1

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Fig. 3: A schematic diagram of the density of states for 10 p.p.m. PH 3 doped a-Si:H.

J. Kakalios, R.A. Street / Thermal equilibrium processes

770

A quantitative understanding of the high temperature equilibrium state and the cooling rate dependence of the conductivity data in fig. 2 is obtained from the defect compensation model of doping.3,16 In doped a-Si:H the doping process introduces ionized donor or acceptor states which reside in the band tail and oppositely charged dangling bond defects which lie deeper in the gap. A schematic diagram for the density of states of a 10-5 PH3/SiH 4 doped a-Si:H sample is shown in fig. 3. This density of states is obtained from a variety of experimental measurements as described elsewhere.16 Above the equilibration temperature the defect structure is in metastable thermal equilibrium and the defect energy is minimized when there are approximately equal densities of dangling bonds and charged dopants. The Fermi energy will then lie between the dangling bond band and the band tail states, at an energy denoted Emi n in fig. 3. Modelling calculations using the density of states in fig. 3 do indeed show that charge neutrality is obtained when the Fermi energy is 0.37 eV below the conduction band edge, consistent with the results in fig. 2. This is within the 90 meV uncertainty of Ea above T E due to the limited available data. Experiments are underway to extend the high temperature (~ data to a wider temperature range and improve the accuracy of Ea. The main property of the equilibrium state is that the Fermi energy is much less temperature dependent that in the frozen-in state. The physical reason for this can be understood in the following manner. The formation energy of a positively charged donor is Up - (Ep - El), where Up is the formation energy of a neutral donor, and Ep. Ef is the energy difference between the donor band and the Fermi energy, and represents the energy gained by moving an electron from the neutral donor to the Fermi energy. An equivalent expression applies to dangling bonds. In the absence of equilibrium effects, raising the temperature will move the Fermi energy deeper into the gap. However, this will lower the formation energy of donors (and raise that of dangling bonds) so that in equilibrium more donors are found which tends to raise Er Thus we see that the equilibrium effects offset the statistical shift and keep Ef pinned, almost independent of temperature. This analysis is confirmed by free energy minimization calculations. 15 101s 10 "S PH3'SiH 4 300K

~ 1017

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..1

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Fig. 4: Band tail density nBT at room temperature after annealing at elevated temperatures with a depletion bias and with no applied bias.

J. Kakalios, R.A. Street / Thermal equilibrium processes THE

ROLE

OF

771

HYDROGEN

As indicated by eq. (1), thermal equilibration of the electronic properties must result from rearrangements of the underlying bonding structure. We have proposed that changes in the defect structure are mediated by motion of the bonded hydrogen,5,~° although other groups have suggested that equilibration follows from rearrangements of only the silicon network.69 The evidence supporting the role of hydrogen in the equilibration is the following. Measurements of the hydrogen diffusion coefficient DR show that significant diffusion indeed occurs in the temperature range where the defect structure equilibrates. ~7 Moreover, DR is several orders of magnitude larger for p-type doped a-Si:H as compared to n-type a-Si:H, which agrees with the several orders of magnitude faster relaxation rate found in p-type films. The temperature dependent relaxation time results, in our model, from the hydrogen diffusion coefficient being thermally activated. ]

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Fig. 5: Normalized relaxation d a t a from Fig. 1 fitted to a stretched exponential time dependence.

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Fig. 7: The time dependence of the dark conductivity for n-type a-Si:H at 110°C for samples deposited at 230°C with incident rf power of 2, 15 and 25W.

772

J. Kakalios, R.A. Street / Thermal equilibrium processes

The influence of hydrogen motion is also seen in the time dependence of the decay of nBT which follows directly from the dispersive diffusion of bonded hydrogen. ~8 Figure 5 shows the normalized relaxation data of nBT in fig. 1, which is well described by a stretched exponential time dependence. AnBT/Ano

=

(nST - nE)/(n O - hE)

= exp [-(t/~')~]

(2)

An excellent fit is obtained with ,B = 0.45 at room temperature, increasing up to 0.7 at 125°C.

The relaxation time ~- defined by eq. (2) is thermally activated with an activation

energy of about 0.95 eV and a preexponential factor To = 2 X 10 "10 sec. The stretched exponential relaxation time dependence given by eq. (2) can be directly related to the hydrogen diffusion. For small departures from equilibrium the decay is given

by dAnBT/dt = -v E AnBT where u E is the equilibration rate of the defect structure.

(3) Shelsinger and Montrol119 have

shown that if ~'E has a power law time dependence, that is, u E ~ t "e, then the decay of AnBT will be given by the stretched exponential form of eq. (2), with /~ = 1 - ~x. From our assumption that the equilibration of the defect structure is mediated by the motion of hydrogen it follows that any time dependence of PE will be reflected in D R. By measuring OH at a fixed temperature for varying annealing times lz we find that D R does indeed decrease as a power law for both n-type and p-type samples. The decay parameter ~x is 0.8 at 200°C and increases to 1 at 300°C. The temperature dependence of the relaxation dispersion parameter ~ from fig. 5 and from the time dependence of D R is shown in fig. 6. Both the relaxation and the diffusion data obey a common temperature dependence of the form fl = 1 - ~x = T/T o where the data in fig. 6 is consistent with T o = 600°K. The dispersion in the hydrogen motion arises from a distribution of Si-H bonding energies; the results are consistent with an exponential distribution in energy with characteristic width kT o. The transition from a metastable thermal equilibrium to a slowly relaxing state which exhibits stretched exponential time dependence is characteristic of a glass. As we argued above, the four-fold coordinated silicon network is very rigid and is unlikely to be able to accomodate the glassy structural rearrangements. The fact that amorphous silicon can not be quenched from the melt is further evidence that the glass-like behaviour does not arise from the silicon network. As we have shown, the motion of bonded hydrogen can readily account for the temperature and time dependence of the defec~ structure. We have therefore proposed that the bonded hydrogen forms a separate glass-like sub-network within the non-equilibrium silicon network. 5 In this model tne c~.quitibration temperature T E is associated with the glass transition temperature. A consequence of this "hydrogen glass" model is that only those states influenced by the motion of hydrogen will be in thermal equilibrium. For example, measurements of the hole drift mobility in p-type and undoped a-Si:H have shown no change in the valence b,~nd tail slope with annealing and quenching. 2° This is consistent with the notion that the bPnd t~,il states arise from [he

J. ttakalios, i~.A. Street / Thermal equilibrium processes

773

intrinsic disorder of the silicon network and not from the Si.H bonds. DISCUSSION If hydrogen does indeed alter the defect structure as it diffuses, then the density of localized states in undoped a-Si:H should also be in metastable thermal equilibrium. Since the Fermi energy is pinned in the middle of the gap in undoped a-Si:H, the conductivity will not be as sensitive to changes in the defect density. Several groups have reported reversible changes in the properties of undoped a-Si:H using techniques sensitive to the dangling bond density.6,8-9 The hydrogen diffusion coefficient is much lower in undoped aSi:H than in doped films, so the relaxation time constants will be many orders of magnitude slower and indeed this is shown by experiments.9 The equilibration of a-Ge:H and amorphous alloys have so far not been investigated. In particular, amorphous alloys have defect densities that are typically several orders of magnitude higher than in pure a-Si:H and so it would be interesting to determine whether or not these excess defects are in thermal equilibrium. In the Introduction we noted that previously a-Si:H was viewed as a non-equilibrium material whose properties were determined solely by the deposition process. This was based on the observation that the a-Si:H film's properties are influenced by varying the deposition conditions such as the growth rate. Recently, Tsai and co-workers have shown that there are two regimes of glow discharge deposition of a-Si:H. 21 At one extreme is chemical vapor deposition (CVD) where the growth rate is limited by a surface reaction and the other extreme is physical vapor deposition (PVD) where the growing surface takes up the impinging atoms where they strike. As shown in fig. 7, the detailed behavior of the equilibration depends on the deposition conditions under which the sample is grown, although qualitatively all a-Si:H films show similar behavior. By increasing the incident power during deposition and increasing the growth rate, we can span the two regimes of glow discharge deposition; from CVD for the 2W sample to PVD conditions for the sample grown with high rf power and argon dilution. As the rf power is increased and the samples in fig. 7 are grown further out of equilibrium, the relaxation of the defect structure becomes progressively slower.22 Further work is necessary to determine whether this is due to the micro-structure of the hydrogen itself, or to an increase in the intrinsic silicon disorder. The quantitative relation between the time and temperature dependence of the hydrogen motion and the electronic equilibrium data strongly suggests that hydrogen motion is the underlying cause of the equilibration process. More generally, the hydrogenglass model may be responsible for other metastable effects in a-Si:H, such as the light induced degradation of transport properties, also known as the Staebler.Wronski effect. The insertion of hydrogen into weak Si-Si bonds has been proposed by Stutzmann and co. workers as a mechanism for dangling bond creation in the Staebler-Wronski effect. 23 We have recently shown that the annealing of excess dangling bonds created by extended illumination also follows a stretched exponential time dependence. The triangle data points in fig. 6 are fl values obtained by fitting the time decay of photo-induced dangling bonds in

J. Kakalios, R.A. Street / Thermal equilibrium processes

774

undoped a-Si:H, measured by electron spin resonance, to eq. (2) at various temperatures.24 The good agreement of the temperature dependent dispersion parameter for these measurements as well as the observation that the creation of near interface defects by biasing a-Si:H/a-SiN x transistor structures, and the decay of persistent photoconductivity in doping modulated a-Si:H also obey a stretched exponential time dependence, suggests that the same mechanism of structural relaxation via hydrogen diffusion underlies the metastabilities in a-Si:H. Further work is needed to verify if this is indeed the case.

ACKNOWLEDGEMENTS This research was performed in collaboration with W. B. Jackson, C. C. Tsai, T. M. Hayes, M. Hack and R. Thompson and is supported by the Solar Energy Research Institute.

REFERENCES 1.

H. Fritzsche, Fundamental Physics of Amorphous Semiconductors, ed. by F. Yonezawa (Springer-Verlag, Berlin), 1 (1981).

2.

H. Schade and J. I. Pankove, J. Phys. Colloq. Orsay, Fr. 42, C4-327 (1981).

3.

R. A. Street, Phys. Rev. Lett. 49, 1187 (1982).

4. Z E. Smith and S. Wagner, Phys. Rev. B 32, 5510 (1985). 5. R. A. Street, J. Kakalios and T. M. Hayes, Phys. Rev. B34, 3030 (1986). 6. Z E. Smith, S. Aljisha, D. Slobodin, V. Chu, S. Wagnmer, P. M. Lenahan, R. R. Arya and M. S. Bennett, Phys. Rev. Lett. 57, 2450 (1986). 7. Y. Bar-Yam, D. Adler and J. D. Joannopoulos, Phys. Rev. Lett. 57, 467 (1986). 8. G. Muller, S. Kalbitzer and H. Mannsperger, Appl. Phys. A 39, 243 (1986). 9. T. J. McMahon and R. Tsu, to be published. 10. R. A. Street, J. Kakalios, C. C. Tsai and T. M. Hayes, Phys. Rev. B 35, 1316 (1987). 11. R. A. Street and J. Zesch, Phil. Mag. B 50, L19 (1984). 12. J. Kakalios and R. A. Street, Phys. Rev. B 34, 6014 (1986). 13. J. Kakalios and R. A. Street, Proc. Int. Conf. on the Stability of Amorphous Silicon (in press). 14. R. A. Street and J. Kakalios, Phil. Mag. B 54, L21 (1986). 15. R. A. Street, M. Hack and W. B. Jackson, to be published. 16. R. A. Street, J. Non-Cryst. Solids 77 & 78, 1 (1985). 17. R. A. Street, C. C. Tsai, J. Kakalios and W. B. Jackson, Phil. Mag. B (in press). 18. J. Kakalios, R. A. Street and W. B. Jackson, Phys. Rev. Lett. (in press). 19. M. F. Shlesinger and E. W. Montroll, Proc. Natl. Acad. Sci. U.S.A. 81, 1280 (1984). 20. R. A. Street and J. Kakalio$, Phys. Rev. Lett. 58, 2504 (1987). 21. C. C. Tsai, J. C. Knights, G. Chang and B. Wacker, J. Appl. Phys. 59, 2998 (1986). 22. J. Kakalios, R. A. Street, C. C. Tsai and R. Weisfield, MRS Proc. 95 (in press). 23. M. Stutzmann, W. B. Jackson and C. C. Tsai, Phys. Rev. B 32, 23 (1985). 24. W. B. JacPson and J. Kakalios, to be published.