Connection between dangling-bond relaxation and metastability in p-type hydrogenated amorphous silicon

Connection between dangling-bond relaxation and metastability in p-type hydrogenated amorphous silicon

JOURNAL OF NON~LL]NES ~ ELSEVIER Journal of Non-CrystallineSolids 190 (1995) 133-141 Connection between dangling-bond relaxation and metastability ...

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JOURNAL OF

NON~LL]NES ~ ELSEVIER

Journal of Non-CrystallineSolids 190 (1995) 133-141

Connection between dangling-bond relaxation and metastability in p-type hydrogenated amorphous silicon Richard S. Crandall *, Martin W. Carlen National Renewable Energy Laboratory, 1617 Cole Blvd., Golden, CO 80401, USA

Abstract

Transient capacitance experiments on p-type hydrogenated amorphous silicon (a-Si:H) that show a connection between dangling bond relaxation and metastability are described. The data suggest that neutral dangling bonds are reversibly converted into metastable positive charged dangling bonds by hole trapping. These metastable positive dangling bonds reconvert to neutral dangling bonds upon annealing at elevated temperature. The annealing kinetics for this process are the same as those observed for annealing of quenched-in conductivity changes in p-type a-Si : H.

1. Introduction

The discovery of the Staebler-Wronski effect [1] produced intense interest in metastable changes in hydrogenated amorphous silicon, a - S i : H . Light [1], charge injection [2], charge extraction [3,4] or quenching from elevated temperature [5] all produce these metastable changes. One result of these metastable changes is an increase in the density of neutral dangling bond defects, D, (a threefold-coordinated Si atom). This deep D center in the mobility gap of a-Si : H controls most of its electronic properties, making it an important factor for thin-film electronic devices such as solar cells, transistors and light emitting diodes. Dersch et al. [6] proposed that a weak S i - S i bond was broken by light, resulting in the observed increase in neutral dangling bonds, D O. This basic model is commonly referred to as the 'bond-break-

* Corresponding author. Tel: + 1-303 231 1913. Telefax: + 1303 231 1272. E-mail: [email protected].

ing model' of metastability. Adler [7], on the other hand, proposed an alternative model that did not require bond-breaking but involved defects present in a-Si:H. He postulated that charged dangling bonds, D + and D - , were present in undoped a - S i : H and they could convert to a metastable D o by trapping of photo-generated carriers as described by the following reactions: D++ e ~ D o

(la)

D - + h ~ D O.

(lb)

A necessary step in both reactions is rehybridization (e.g., sp 2 ~ sp 3) and bond angle shifts of 10 to 20 ° to stabilize the D O [7]. This results in movement of the surrounding atoms to accommodate the bond angle changes. These new D O are indistinguishable from the native D °, but they are metastable. Annealing is just the reverse reaction converting the metastable D O to charged dangling bonds. In the sense of the Adler mechanism, a native defect, the charged dangling bond, converts to a metastable configuration by charge trapping rather than forming

0022-3093/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0022-3093(95)00266-9

134

R.S. Crandall, M. W. Carlen /Journal of Non-Crystalline Solids 190 (1995) 133-141

a new metastable defect. This is different from the bond-breaking model which forms new metastable defects, D O. A signature of the Adler model of metastability [7] is charge-trapping during creation and emission of charge during annealing. Branz et al. [8] have reviewed charge trapping and metastability in the context of the Adler model. To convert to a metastable D °, the defect must surmount a barrier to reconfiguration before the trapped charge escapes. This requirement causes the low observed efficiency of metastable defect production. Both the energy released by the charge carrier upon trapping and thermal phonons may contribute the energy needed to surmount the barrier. The Adler model suggests that one-carrier injection, even in the absence of recombination, will produce the Staebler-Wronski metastability by carrier trapping. This has been confirmed by capacitance measurements on n-type Schottky barrier devices [2] and metal/insulator/a-Si:H structures [9] that all show electron-trapping-induced metastability. In addition, capacitance measurements on p - i - n and n - i - p solar cells and p / n junction devices [2,10] all show hole-trapping and electron-trapping metastability. Either forward-bias carrier injection or illumination can produce these metastable changes. Illumination produces hole and electron trapping. Both creation and annealing of the metastable defects are thermally activated with barriers for annealing ranging from 0.4 to 1.6 eV depending on the sample [11]. Recently, a slow relaxation process associated with electronic transitions from D-defects in both n-type [12] and p-type [13] a-S/: H was reported. By using junction capacitance and spin transient measurements, Cohen et al. [12] found that an electron's thermal release time, rrel, is proportional to its residence time in the defect. This electron residence time in the defect is taken to be equal to the filling pulse width, ~-p. The shape of these capacitance or spin transients are close to a power law and extend to minutes at room temperature. In addition, the decays of the trapped charge are virtually independent of temperature. Similar results were found for holes in p-type a-S/: H by Carlen et al. [13] Depending on the position of the Fermi level, EF, the D defect may be in different charge states. By capturing electrons or holes, the D defect can convert

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I , I L I Q- 100 QO 110Q+

120

Bond Angle (degrees)

Fig. 1. Transition energy level diagram for the different charge state configurationsof the dangling bond after Ref. [19]. between these different charge states. Only the D O, however, can be directly observed using electron spin resonance (ESR). Structural relaxation processes, i.e., adjustments of bond angles and positions of neighbor atoms due to capture or removal of charge on a D defect, are generally thought to happen faster than microseconds, as inferred from Stokes shift and luminescence measurements [14,15]. From the theoretical models of the threefold-coordinated amphoteric dangling bond, one might expect some bizarre behavior of the dangling bond when its charge changes. Several calculations have shown that the D defect undergoes energy level shifts of more than 0.5 eV on charge change [16-18]. The angles between Si-Si bonds correspond to 96, 105 and 115 °, respectively, for the relaxed D - , D O and D ÷ configurations, Qq [19]. Here the superscript, q, is - , 0 or + . The energy level diagram of Fig. 1 shows the dependence of transition energies on the configuration of the dangling bond [19]. The levels are those of the fully relaxed defect, corresponding to transitions without bond angle change, calculated by the procedure of Ref. [19]. For example, the ( - / 0 ) transition in Q+ lies closest to the conduction band. Branz and Schiff [19] proposed that dangling bond relaxation is the movement of the dangling bond from one of these configurations to another with the accompanying changes in bond angles. After charge capture, the bond angles quickly change to accommodate the new configuration. For example, on electron capture by the D O in the QO configuration, the resulting D - relaxes toward the Q - configuration. If the relaxation is slow, then the

R.S. Crandall, M. W. Carlen/Journal of Non-Crystalline Solids 190 (1995) 133-141

total energy of a dangling bond after a charge change does not immediately correspond to its fully relaxed value. However, the energy eigenvalues change rapidly as in crystalline material. Because of the inability of this disordered system to adjust quickly to these large configuration changes, the system slowly reaches its new equilibrium. Branz and Fedders [18,20] model this movement of atoms as a one-dimensional random walk in the configuration of atomic positions. They then reproduce with Monte Carlo simulations the general features observed by Cohen et al. [12] Their result shows a power law emission with an exponent of - 0 . 5 , close to the observed value [12] and confirms the temperature-independent proportionality between thermal release time and Zp. They refer to their picture of slow relaxation as the structural memory model. During this structural memory phase, the total energy remains roughly constant. However, the electronic energy of the dangling bond changes rapidly with its bond angles as they adjust to the new charge. The total energy remains constant because the rapid bond angle change is accommodated by an increase in strain energy in the surrounding atoms. As long as this strain energy does not dissipate, the system can walk back to its original configuration and emit the charge. Henceforth, we use the notation (Qq)* to denote a contfiguration that is undergoing relaxation and has not yet dissipated its strain energy. For example, electron capture is e + D°(Q °) ---> D (Q-)*---> D - ( Q - ) with the final step being a slow relaxation toward D - in Q-. If the strain energy does not dissipate, the defect will thermally emit its electron from either the (Q0). or ( O - ) * configuration. If the time to walk back to the (QO). configuration is shorter than the thermal emission time from the ( Q - ) * configuration, the electron emits from the shallower (QO). level. If the walking time is long, it emits from the deeper ( Q - ) * level. Experiments [12,13] indicate that thermal emission from both configurations can be observed. If the dangling bond retains its electron long enough and relaxes far enough, a final step, invoking a coordinated movement of many atoms can release the strain energy and transfer the system to a new stable or metastable state with a configuration Q [18]. Whether this new state is stable or metastable depends on the position of the Fermi level.

135

A few years ago we examined metastability in the p-layer of junction devices [4]. In light of our new data showing dangling bond relaxation in p-type a-Si:H [13], we wish to extend our earlier measurements to investigate the role relaxation plays in metastability. The experiments described in this paper suggest that dangling bond relaxation is apparently the precursor to metastability. We find that metastability results in loss of D O and for each D O that disappears a positive charge is metastably trapped. The simplest interpretation of this result is that the D O are converted into metastable D ÷. This represents a metastable configuration rather than a new defect. We will see that this is a natural consequence of relaxation.

2. Overview In this paper, we concentrate on the metastability-related aspects of hole trapping in p-type a-Si:H by studying emission transients observed in capacitance measurements on p / n junction devices. Section 4 describes experiments that establish the connection between relaxation and metastability. First we review relaxation data and then show that relaxation is present even at elevated temperature where the emission transient is dominated by annealing of the metastably trapped hole. Finally we present data indicating that a D O can be converted to a metastable D +"

3. Experimental details 3.1. Sample preparation

The a-Si:H samples are fabricated using radiofrequency glow discharge of silane and doping gases. Details of the deposition conditions are published elsewhere [21]. Trimethylboron (TMB) and phosphine, respectively, are used for the p- and n-type doping. The H content of the samples is about 10%. The films are grown on 1 × 1 in 2. 7059 glass substrates coated with SnO 2 that serves as a back contact to the p layer. To probe p-type samples we deposited the following sequence on the SnO2-coated

136

R.S. Crandall, M. W. Carlen /Journal of Non-Crystalline Solids 190 (1995) 133-141

glass; a 20 nm thick 1 vol.% (TMB/SiH 4) p+ layer; a thick lightly doped p-type layer, about 0.05 vol.% (TMB/SiH); a 40 nm thick 1 vol.% (PH3/SiH 4) doped n-type layer and a metallic contact. The thick, lightly doped p-type layer varies between 420 nm and 1.5 ~m in different samples. The dark current activation energy of the p-type layer is 0.6 eV as measured on a companion film on a glass substrate. Between the p- and n-type layers is an 8 nm i-layer. Without this layer the p / n junction is not blocking in reverse bias. Sample 20 does not contain the p÷-layer between the SnO 2 and p-layer whereas sample 90 does. The sample area is about 600 mm 2 and the area of the AI top contact is 5 mm 2. Additional details are given in Ref. [13], which describes measurements on samples 20 and 90 as well as tests to eliminate the possibility of measurement artifacts that could dominate our results.

3.2. Measurement technique

pulse allows majority carrier holes to fill previously depleted regions. The bias returns to - 2 V at the end of the voltage pulse and trapped holes are emitted.

4. Results In this section we present examples of charge transients and the method of data analysis for the devices described above. As discussed in Ref. [13], dangling bond relaxation and annealing of metastable trapped charge are often observed during the same capacitance transient. However, at low temperature and for short majority carrier pulses one observes only a pure dangling-bond relaxation. At high temperature the transient shows mainly metastability annealing. A power-law decay of the form

N(t)

= 0.5 Nrel(t//"/-rel)

(2)

c

The capacitance is measured by a standard lock-in technique using a frequency of 10 kHz and an ac test voltage of 30 mV rms. The devices are mounted in an evacuated liquid nitrogen Dewar capable of maintaining a stable temperature. Measurements are performed at different temperatures between 299 and 470 K. The trapped charge, N(t), using the depletion width approximation [3] is related to the capacitance by

gives the best description of the relaxation regime, where c is the power-law exponent, N~eI is the number of defects and 'TreI is the time for N(t) to decrease to 0.5 NreI. The value of c is about 0.5 for n-type [12] a-Si:H and about 0.3 for p-type [13] a-Si:H. This pure power-law relaxation is only observed at short 'rp. A stretched-exponential decay of the form

N(t) cx C 2 ( - 0 )

N(t)

- C2(t),

where the steady-state reference capacitance, C ( - 0 ) , is measured prior to the voltage pulse. We use this depletion width approximation and a built-in voltage of 1.1 V to calculate N(t). Prior to each series of measurements at a certain temperature, T, the device is reverse-bias annealed [3,4] in the dark at about 480 K at - 2 V for at least 2 min and then cooled to the measurement temperature at the same voltage. This is done to ensure that the starting conditions of any defects are always the same. In addition this treatment produces the maximum number of D o in the depletion width at the beginning of the experiment [22]. The experiment begins with the bias at - 2 V. The bias voltage is then pulsed to a value between 0 and - 1 V, for rp of 0.1 ms -100 s depending on the experiment. This

=Nme t exp( -- (t/rmet)

~)

(3)

gives the best description of metastability annealing. The characteristic time, rmet, for this decay exhibits an Arrhenius behavior with a characteristic energy that depends on sample type [10,11,23,24]. Fig. 2 shows transients measured at 299 K and exhibiting pure relaxation behavior. The charge emission transients measure the holes injected during the pulse and trapped on D O. Data are taken in order of increasing pulse time. At this temperature any metastable trapped holes do not anneal on the timescale of the measurements and produce only a slight decrease in the dc capacitance with each pulse. For the data in Fig. 2 this dc capacitance decrease is about 5.7% for the total pulse time of 111.1 ms. We discuss this effect in more detail below. At higher temperature the same conditions as used

137

R.S. Crandall, M.W. Carlen /Journal of Non-Crystalline Solids 190 (1995) 133-141 I

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sample 90 at 299 K. The measuring bias is - 2 V and the pulse to -0.5 V.

for the data in Fig. 2 produce a large number of metastable trapped holes that anneal on nearly the same timescale as relaxation. Fig. 3 shows capaci-

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tance transients representing annealing of metastable trapped holes as well as power-law relaxation behavior at short time. The signal amplitude for these transients is much larger than those shown in Fig. 2 because many more of the defects can be measured at this higher temperature. At 299 K, only the subset of the defects lying within about 0.5 eV of the valence band are detected using the measuring frequency of 10 kHz. The data in Fig. 3 clearly show the mixing of the two decay modes. The emission transient for the shortest pulse (0.1 ms) decays like a power law for short times and then a stretched exponential for longer times. For the longest pulse (10 s), the decay exhibits mostly a stretched exponential time dependence. However, the initial part is a fast power-law decay indicative of relaxation. The longer Tp also result in longer times for the metastable trapped holes to thermally anneal. This behavior is present at all temperatures and shown in more detail in Fig. 4 for measurements at 439 K. The solid lines through the datapoints in Fig. 3 are the result of a leastsquare-error fit using a sum of Eqs. (2) and (3) with

10 4

Time after end of pulse (s)

Fig. 3. Decay transients for sample 90 exhibiting both relaxation and metastability annealing at 364 K and the same pulse and bias conditions as in Fig. 2. The data are represented by symbols and the solid lines are the best fits to the data using a sum of Eqs. (2) and (3). The dashed and dotted lines, respectively, represent the pure power law, Eq. (2) and stretched exponential, Eq. (3) functions used to fit the 7p = 0.1 ms data. The fitting constants are in Table 1

Table 1 Fitting constants to the data in Fig. 3 "rp (S)

c

Nr¢ 1 (1017 c m - 3 )

~'met (s)

fl

Nine t (1017 c m - 3 )

0.0001 0.006 10

0.25 0.21 0.11

2.4 2 0.9

1000 1249 5400

0.9 0.7 0.9

0.12 1.6 2.7

The densities are calculated from the capacitance changes using the depletion width approximation.

R.S. Crandall, M.W. Carlen /Journal of Non-Crystalline Solids 190 (1995) 133-141

138

the fitting constants given in Table 1. The transients described by Eqs. (2) and (3) used to fit the data for ~-p= 0.1 ms are also shown in the figure. At 7p = 0.1 ms, metastability annealing contributes less than 5% to the measured emission transient. For the 6 ms pulse roughly half the observed transient corresponds to dangling bond relaxation and half to metastability annealing. For this pulse length, "/'met is five orders of magnitude longer than Tre~. However, at ~-p.= 10 s, trapped hole annealing contributes about ~ to the transient. Metastable trapped hole annealing transients depend weakly on ~-p by contrast with relaxation which shows a linear variation of "/'reI with ~'p. Fig. 4 is a semilog plot of the metastability annealing transients for a variety of rp at T = 439 K. The data show, that both ~'mct and the density of metastable trapped holes increases slowly with ~-p. Table 2 lists the parameters used in a least-square-error fit of Eq. (3) to the data. We omit these fits from Fig. 4 for clarity. Metastability annealing under all conditions gives similar results. Ref. [13] presents data for '/'met for samples 20 and 90 as a function of temperature together with data for annealing of quenched-in conductivity from Street and co-workers [23,24]. Both the D + in (Q+) D O in (Q0) charge emission observed in our experiments and annealing of quenched-in conductivity increase lie along the same In(tree t) versus 1/T line. The 'attempt-to-escape' frequency is 1 × 109 s -1 and the activation energy is 0.93 eV for both data sets. Fig. 5 shows the variations in 7r~t and Nmet versus ln(~-p) that emphasize the salient features in Fig. 4. By contrast with relaxation, s-met varies as ln(~-p). Nmet, however, increases rapidly at short rp and slowly at longer ~'p. We find similar results at other temperatures.

Table 2 Fitting constants to the data in Fig. 4

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0.0 10 -2

10 0 Pulse time

10 2

(S)

Fig. 5. Variation of ~'met and the number of metastable trapped holes, Nmet, with ~'p for the data shown in Fig. 4.

The data presented in Figs. 3 - 5 are for temperatures high enough that the metastability anneals during the time of measurement. At lower temperatures the metastability anneals so slowly that measurements of D O relaxation can be made during a time in which the change in metastable trapped holes is imperceptible. For example, complete annealing requires over 105 s at room temperature [13]. We exploit this opportunity to demonstrate that the number of D O decreases as the number of metastable trapped holes increases. The increase in the number of these metastable trapped holes can be measured by the decrease in the dc capacitance. The experiment to probe these changes in the density of D defects proceeds as follows. We apply a series of progressively longer preparatory - 0 . 5 V pulses to trap the holes in the depletion width. After the fast charge transient (due to D defect relaxation) following each preparatory pulse has died away, a short (Tp = 6 ms) probe voltage pulse produces a charge transient due to the D defects that can undergo relaxation. The amplitude of these probe transients measures the number of remaining D O. We label each curve with the sum of all the pulse times,

rs.

rp (s)

7"met (s)

#

Ninet (1017 c m - 3 )

0.006 0.011 0.1 1 10 100

2.9 3.2 4.9 6 7.8 9.1

0.7 0.73 0.8 0.83 0.77 0.69

5.5 5.9 6.8 7.2 7.3 7.6

The data in Fig. 6 show that the magnitude of the decay transient for these Zp = 6 ms probe pulses decreases as the sample spends more preparatory time at the - 0 . 5 V. Nevertheless, the shape of the probe transient does not change indicating that it can still be used as a method to count the remaining D O since the maximum of the probe transient is propor-

R.S. Crandall, M.W. Carlen /Journal of Non-Crystalline Solids 190 (1995) 133-141 :

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I

able result that the number of holes trapped during degradation equals the number of D O that are lost during degradation. For this temperature 20% of the total (1.2 X 1018 cm -3) D O are converted to D +.

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Ts=O.O061 s .~-~"100 T X ~ = 07 ~. 0 2 2

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~2 ~"

Ts=1.5 s

-\

10 [

10-2 10-1

5. Discussion

~,~,~

i

I

I

100

101

102

103

Time (s) Fig. 6. Trapped charge emission transients using a 6 ms probe pulse at 310 K for sample 90. The probe pulses are from - 2 to - 0 . 5 V. The time, Ts, used to label each curve is the total time that the bias had been at - 0 . 5 V since the beginning of the experiment.

The result that D o can trap holes and convert to positive D + in a metastable configuration has a natural explanation in terms of the Adler mechanism. Although Adler [7] proposed reactions (la) and (lb) to explain the production of metastable D °, his model implies the reactions D°+e~D

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AD*(cm -3) Fig. 7. The change in positive charged defects, labeled AD +, determined from the change in dc capacitance and the change in AD O determined from probe pulse. Measured at 310 K for sample 90 and at 327 K for sample 20.

(4a)

+

(4b)

and D°+h~D

tional to the number of D o that trap holes and relax. In fact the amplitude has decreased nearly threefold after the sample has been degraded for 1.5 s indicating that less than 30% of the original D O remain in the depletion width. During this degradation time the dc capacitance has decreased indicating an increase in positive charge in the depletion width. Fig. 7 compares the decrease in D O with the increase in trapped positive charge for different Ts for samples 90 and 20. The data show the remark-

-

might also produce metastable charge trapping. These two reactions are just the inverse to reactions (la) and (lb). Reaction 4(b) is applicable to the experiments described above where holes are trapped on D O during an injection pulse. If the barrier to conversion of the D O in configuration Q0 to D ÷ in configuration Q+ can be surmounted, a metastable D + results. If not, the hole is quickly thermally emitted. Our experiments show a significant temperatureactivated barrier for this reaction as well as the inverse reaction that anneals the metastable D ÷ back to D O. The connection between relaxation and metastability described in the above experiments now becomes clear in terms of the Adler mechanism [7] and the structural memory model for relaxation proposed by Branz and Fedders [18,20]. Relaxation is just the deepening of the transition level due to bond angle change in response to the charge trapped on the D O. However, if this change proceeds far enough, the elasticity of relaxation is lost and the system remains frozen in the configuration consistent with the charge on the D. While the defect remains in the elastic or structural memory region the system undergoes a random walk over nearly equal sized energy barriers. In this regime the walk away from the equilibrium (Q0). configuration toward the (Q +) * configuration is similar to the return walk back toward the (O0). config-

140

R.S. Crandall, M. W. Carlen /Journal of Non-Crystalline Solids 190 (1995) 133-141

experiments of Gardner and Cohen [25]. They show that raising the temperature causes the defect to move faster towards its deepest and stable configuration and lowering the temperature causes the defect to move slower toward this configuration.

iii

"6

o..

Configuration

6. Summary

Fig. 8. Sketch of potential energy versus configuration.

uration. Thus the times for the random walk in either direction are the same. If, however, during the random walk toward the (Q÷)* configuration the system reaches a configuration from which there is a high barrier for the return trip, it will remain frozen in this metastable configuration. Consequently the system can not return to the Q0 configuration until a time much longer than the time required to reach this new configuration. The dependence of ~'m~t on ~'p shown in Figs. 4 and 5 is a natural consequence of the ideas behind the structural memory model. The longer that the dangling bond remains charged, the farther it can walk away from the (Q0), configuration and the better chance it has to find a metastable configuration. This idea is sketched in Fig. 8. The domain in configuration space with roughly equal size potential barriers represents the space where the defect undergoes elastic relaxation in the ( Q q ) * configuration. As long as the system remains in this domain no metastable configurations are encountered. If, however, the system falls into potential well 1 it loses its elasticity and forms a metastable state. The D q now thermally emits from well 1 with a time, '/'met, determined by the properties of this well. '/'met is considerable longer than the time to thermally emit from the ( Q q ) * configuration. If zv is longer than '/'met for well 1, the system has a chance to escape well 1 and reach the deeper well 2, thus producing a metastable configuration with a longer 1"met. This qualitative discussion suggests why defects anneal more slowly for longer degradation time. Temperature plays a role analogous to time. The higher the temperature the faster the walk since the potential barriers can be surmounted quicker. Evidence for this can be found in the temperature jump

We measured thermally assisted charge emission rates as a function of voltage filling pulse length and temperature for p-type a-Si:H. The data show that relaxation and metastability are intimately related. In the charge emission transients one can observe both relaxation and annealing of metastability. Nevertheless, they can be easily distinguished because they decay on different timescales and each has its own unique time dependence. Near room temperature the transients show mostly relaxation and at higher temperature they show mostly metastability annealing. The following important features are observed. (1) Hole injection converts neutral dangling bonds to metastabily trapped positive charge. One neutral dangling bond converts into one positively charged dangling bond. (2) The number of D O that convert to D ÷ depends strongly on temperature and weakly (logarithmically) on the time of hole injection. (3) The characteristic time to convert the metastable D ÷ back to D O varies logarithmically with the time during which the D O convert to D ÷. The authors are indebted to Klaus Lips and Howard Branz for helpful suggestions. R.C. wishes to express his great appreciation for the time spent with Marvin Silver and experiencing his joy in life and science. His active and critical mind was an inspiration to all. This work was supported by the US Department of Energy under Contract No. DEAC02-83CH10093.

References [1] D.L. Staebler and C.R. Wronski, Appl. Phys. Lett. 31 (1977) 292. [2] R.S. Crandall, Phys. Rev. B24 (1981) 7457.

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