Understanding the photoluminescence over 13-decade lifetime distribution in a-Si:H

Journal of Non-Crystalline Solids 352 (2006) 1138–1143 www.elsevier.com/locate/jnoncrysol

Section 9. Photoluminescence and recombination; Photoconductivity and photo carrier transport

Understanding the photoluminescence over 13-decade lifetime distribution in a-Si:H Takeshi Aoki

*

Department of Electronics and Computer Engineering and Joint Research Center for High-technology, Tokyo Polytechnic University (formerly Tokyo Institute of Polytechnics), Atsugi 243-0297, Japan Available online 29 March 2006

Abstract Wideband quadrature frequency resolved spectroscopy (QFRS) expanded from 2 ns to 160 s revealed that the triple-peaked lifetime distribution observed in the photoluminescence (PL) of a-Si:H consists of the well-known double-peak structure and a newly identified third component. By the exploring dependence of the lifetime distribution on the generation rate G, temperature T, PL emission energy EPL, PL excitation energy EX and external magnetic field, the former is assigned to excitonic recombination and the latter to distant-pair (DP) or nongeminate recombination. The DP component gives the same sublinear G and T dependence as light-induced electron spin resonance (LESR) results. The present paper also shows that the residual PL decay in a-Si:H persists for more than 104 s, which corresponds the DP component and agrees with the LESR results. The residual PL decay reveals that the DP recombination kinetics is monomolecular at low T and low G.  2006 Elsevier B.V. All rights reserved. PACS: 78.55.Ap; 71.35.Gg Keywords: Silicon; Luminescence

1. Introduction Although photoluminescence (PL) spectroscopy in aSi:H was nearly established in the 1970s and early 1980s [1,2], considerable debates over its exact mechanisms still continue. It has been generally agreed that in undoped a-Si:H at a low temperature T, photoexcited electrons and holes thermalize in extended and band-tail states by the hopping process and intrinsic PL arises from radiative tunneling (RT) transitions between electrons and holes localized in the respective tail states [1,2]. The PL lifetime is governed by the RT lifetime via:   2R s ¼ s0 exp ; ð1Þ a

*

Tel.: +81 46 242 9556; fax: +81 46 242 9566. E-mail address: [email protected]

0022-3093/$ - see front matter  2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2005.11.118

where R is the electron–hole (e–h) separation. The prefactor s0 is the dipole transition time usually assumed to be 108 s and a, the electron localization radius typically 1 nm. However, whether the recombination is geminate or nongeminate is still a controversial issue. This may be partly due to the rather featureless distribution of PL lifetime as well as the luminescence spectrum induced by the disorder in amorphous semiconductors; actually, excitonic absorption has not been observed in a-Si:H unlike crystalline semiconductors. Thus measuring the precise lifetime is important for studying the PL mechanisms. Quadrature frequency resolved spectroscopy (QFRS) is effective in analyzing the lifetime distribution at sufficiently low generation rates of photoexcited carriers G [3]. Bort et al. [4] used the QFRS technique to observe the G-independent lifetime distribution of a-Si:H at low T below a generation rate G of 1019 cm3 s1, and argued for the geminate recombination model, in which the steady-state carrier concentration n should vary with G

T. Aoki / Journal of Non-Crystalline Solids 352 (2006) 1138–1143

ton energies ranging from 0.9 to 1.7 eV. An optical system of f/1.0–2.0 optics was carefully designed to optimize the detection of PL signals by the PMT. QFRS spectra in the shorter lifetime range from 2 ns to 6 ls was measured by the dual-phase double lock-in (DPDL) QFRS technique [18]. The longer PL lifetime range from 1.6 ls to 160 s was measured using a digital lock-in amplifier with a low frequency limit of 1 mHz in the internal reference mode [15]. In order to measure lifetimes greater than or equal to 30 s in this mode, a time constant of 3 ks was chosen for the lock-in amplifier and thus it took 6 h to obtain one data point. The QFRS spectra for dispersed PL were measured by placing a 10 cm-f/3.0 monochromator with a resolution of 30 meV in the optical path between the sample and PMT. The spectrally-integrated PL intensity I(t) was measured by turning off 2.33 eV laser light by an electro-mechanic shutter with a speed of 30 ms after irradiation for a sufficiently long time for I(t) to reach its steady state value. The subsequent or residual PL decay of I(t) was lock-in detected at a chopping frequency of 190 Hz using a programmable current amplifier. All experimental procedures were performed electronically, including shuttering the laser beam, changing the time constant from 10 ms to 30 s interlocked with the sensitivity setting of the lock-in amplifier over 7 orders of dynamic range, and acquiring data on a computer [17]. Consequently, we could analyze the PL recombination processes of a-Si:H over 13 decades with ultrahigh sensitivity. 3. Results Fig. 1 shows QFRS spectra of a-Si:H from 2 ns to 160 s excited at the PL excitation energy EX of 2.33 eV for various generation rates G. We can see the long- and short-lived

G -3 -1 [cm s ] 22 5.0x10

S

a-Si:H

T

Ex =2.33[eV] T =3.7[K]

2.0x1022 21

QFRS Signal [a.u.]

linearly, with the average lifetime s being constant under the condition G 6 1019 cm3 s1. By contrast, the lightinduced electron spin resonance (LESR) intensity, known to be identical with n, depends on G sublinearly [4–7]. The distant-pair (DP) or nongeminate model based on Eq. (1) predicts the sublinear G-dependence of the LESR intensity, while it fails to explain the G-independence of s at G 6 1019 cm3 s1 [8]. Meanwhile, a double-peaked lifetime distribution of PL consisting of short-lived (ls) and long-lived (ms) components was observed by QFRS under the geminate condition. It is difficult to identify the two lifetime components on the basis of the RT model [9,10]. Stachowitz et al. [11] proposed exciton involvement in the double peak phenomena, attributing the short- and long-lived components to singlet and triplet excitons, respectively. We observed double-peak lifetime behavior not only in a-Ge:H but also chalcogenide amorphous semiconductors (e.g., g-As2S3 and a-Se), which supports the exciton model [12,13]. Selftrapped-exciton (STE) was assumed to be responsible for the short-lived lifetime (ls) being much longer than singlet exciton lifetime normally (ns) [14]. By developing the wideband QFRS technique, which allows analysis of lifetimes over almost 11 decades from 2 ns to 160 s, it was also discovered that the lifetime distribution is triple-peaked, accompanied with the third lifetime peak in a long lifetime range of 0.1–160 s in PL of a-Si:H and a-Ge:H under the geminate condition; the third component exhibited characteristic features of DP recombination [15]. Thus, we claimed that geminate and nongeminate (DP) recombination coexist in PL of a-Si:H and a-Ge:H at low T and low G. Moreover, a similar phenomenon was observed in chalcogenide amorphous semiconductors, indicating that the triple-peak QFRS spectrum, i.e., the coexistence of geminate and nongeminate recombination, is universal among amorphous semiconductors [16]. In addition, PL recombination for lifetimes greater than 160 s was investigated by observing residual PL decay after cessation of PL excitation at low G [17]. In addition to presenting new results, the present paper reviews previously published results, demonstrating exciton involvement in the double-peak lifetime distribution and DP recombination in the third component of PL of undoped a-Si:H. We also discuss the residual PL decay persisting for more than 104 s, showing the kinetics of DP recombination and steady-state photocarrier concentration, consistent with the LESR results.

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5.0x10

21

1.9x10

20

4.1x10

20

1.2x10

19

D

4.1x10

18

1.3x10

17

2.8x10

2. Experimental

16

6.5x10

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1.3x10

Two films of undoped a-Si:H were deposited on roughened Al substrates, one having a thickness of 1.1 lm and defect density of 2.0 · 1016 cm3, and the other, 9.3 lm and 1.4 · 1016 cm3, respectively. Spectrally-integrated PL signals excited at the photoexcitation energies EX of 1.46, 1.58, 1.81, 1.94 and 2.33 eV laser light were detected by a Hamamatsu infrared photomultiplier (PMT) at pho-

15

2.5x10

10

-8

-6

-4

-2

10 10 10 10 PL Lifetime [s]

0

2

10

Fig. 1. QFRS spectra from 2 ns to 160 s for a-Si:H at 3.7 K and EX = 2.33 eV with various G from 2.5 · 1015 to 5.0 · 1022 cm3 s1. Two data at G of 1022 cm3 s1 were taken by laser light condensed through a lens.

T. Aoki / Journal of Non-Crystalline Solids 352 (2006) 1138–1143

components fixed at sT  4 ms and at sS  3 ls, respectively, even though G changes from 2.5 · 1015 to 4.1 · 1020 cm3 s1; this is the well-known double-peak lifetime distribution observed under the so-called geminate condition G 6 1019 cm3 s1 [9,10]. By extending the longer lifetime limit of the QFRS technique, however, a third peak higher than the other two peaks is observed at sD  20 s for G  2.5 · 1015 cm3 s1 (Fig. 1). As G increases, sD continuously shifts to shorter lifetimes and the peak merges with the sT-component at G  1.3 · 1018 cm3 s1. Upon increasing G further to 1.2 · 1020 cm3 s1, the sT-component begins to shift to shorter lifetimes and merges with the short-lived sS-component. The QFRS spectrum finally becomes single-peaked at G  5.0 · 1022 cm3 s1. The two data at G of 1022 cm3 s1 were taken by laser light condensed through a lens. QFRS spectra for various monochromatized PL energies EPL are shown in Fig. 2, where PL was excited at 3.7 K, EX = 2.33 eV and G  2.3 · 1017 cm3 s1. In contrast to Fig. 1, both sS and sT shorten as EPL increases, but the third lifetime peak sD remains unchanged. Moreover, the figure indicates that the PL spectrum of each component lies at different EPL levels, in the order sS, sT, sD of decreasing EPL. PL spectra of QFRS signals of the three components were taken for the sample with a thickness of 9.3 lm at G  2.8 · 1017 cm3 s1 and T  3.7 K, at fixed frequencies of 39 kHz, 58 Hz and 1.1 Hz, corresponding to sS  4.1 ls, sT  2.7 ms and sD  0.14 s, respectively; the three spectra obtained are in the same range (see Fig. 3). The thick film causes little interference, and thus, yields more precise spectra compared with that reported previously [19]. When EX is lowered, the quantum efficiency (QE) gD proportional to the area of the third component is reduced,

τS

Resolution

0.8

τD

0.6

τT τ S

0.4 0.2 0.0

1

1.2

E

0

(a) a-Si:H

τD

15 -3 -1 G~ ~ 2.0x10 [cm s ]

T =3.7[K] Ex [eV]

10

τD

τT

τS

2.33 1.94 1.81 1.58

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(b)

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10

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-8

0.95 0.90 -6

1.8

-3 -1

1.46

-8

1.4 1.6 [eV]

PL

accompanied by a shortening of sD (Fig. 4(a)). PL excitation (PLE) spectra for the three peaks are expressed in Fig. 4(b) by dividing QE by the excitation power. The PLE spectrum of the sD component declines faster into the band-gap than the sS- and sT-components. Fig. 5 shows QFRS spectra of a-Si:H excited at 2.33 eV with G  1.0 · 1017 cm3 s1 for various temperatures T [15,19]. As T is raised from 3.7 K, the sT-component shifts to shorter lifetimes and disappears at T  85 K. The third peak at sD, on the other hand, persists up to 133 K with a continuous shift of sD to shorter lifetimes. The sS-component fades out already at T  30 K and, concomitantly, another shoulder emerges at sG  0.1 ms between sS and sT, growing into a hump at higher T. Thus, a new double-peak structure with maximums at sD and sG is established in QFRS spectra for a-Si:H at 100 K. Fig. 6 shows steady-state carrier concentration nD = gDGsD with the QE gD of the sD-component derived by deconvoluting the data of Fig. 1 and the LESR spin density as functions of G for a-Si:H [4,6,7]; the QFRS results agree with the sublinear G-dependence of n / G0.2 [15]. The

G =2.3x10 [cm s ] τT E x=2.33[eV] T =3.7[K]

1.45 1.40 1.35 1.30 1.25 1.20 1.15 1.10 1.05 1.00

10

T =3.7[K]

Fig. 3. QFRS PL spectra of a-Si:H with thickness 9.3 lm fixed at lifetime peaks sS  4.1 ls, sT  2.7 ms and sD  0.14 s at 3.7 K and EX = 2.33 eV with G = 2.8 · 1017 cm3 s1. All the peaks of the spectra are normalized to unity; the peaks for sS and sD are 30% and 80% of that for sT, respectively.

QFRS Signal [a.u.]

QFRS Signal [a.u.]

E PL [eV] 1.60 1.55 1.50

E x =2.33[eV] 17 -3 -1 G =2.8x10 [cm s ]

a-Si:H

1.0

Normalized PL Intensity [a.u.]

17

a-Si:H

Normalized QFRS Signal [a.u.]

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1.4

1.6

1.8 2 Ex [eV]

2.2

2.4

2

Fig. 2. QFRS spectra of the monochromatized PL for EPL from 0.90 to 1.60 eV under the geminate condition G = 2.3 · 1017 cm3 s1 for a-Si:H at 3.7 K and EX = 2.33 eV.

Fig. 4. (a) QFRS spectra of a-Si:H excited at various PL excitation energy EX with G  2.0 · 1015 cm3 s1 at 3.7 K. (b) PL excitation spectra (PLE) for three QFRS components sS (dashed, ,), sT (dotted, d) and sD (solid, s); each component deconvoluted and normalized by PL excitation intensity. Lines are guides for eye.

T. Aoki / Journal of Non-Crystalline Solids 352 (2006) 1138–1143

steady-state carrier concentrations nS = gSGsS and nT = gTGsT with the QEs gS and gT of the respective component

τD

a-Si:H Ex=2.33[eV] 17 G~ ~ 1.0x10 -3 -1 [cm s ]

τS

QFRS Signal [a.u.]

T [K]

4. Discussion

20

The lifetime distribution of undoped a-Si:H is triplepeaked at low temperatures under the geminate condition, its third component having a lifetime sD of 0.1–160 s. The third peak sD continues to decrease with increasing G even under the so-called geminate condition G 6 1019 cm3 s1 (Fig. 1), whereas the lifetimes sT and sS remain constant. The continuous shortening of sD with increasing G is a distinctive feature of DP recombination based on the RT model and the plots of sD vs. G correspond well to the curve calculated from the balance equation using Eq. (1) [19–21]. At sufficiently low G, the three peaks are well separated in lifetimes, suggesting that recombination events for sS, sT and sD occur via three independent channels. However, when the sD-component begins to merge with the sT-component as G approaches 1018 cm3 s1 (Fig. 1), the two recombination events at sT and sD no longer occur independently. Indeed, a further increase in G shifts the combined component of sT and sD to shorter lifetimes and merges it with the sS-component at around G  1022 cm3 s1, leading to a single-peak structure. In the QFRS spectra of dispersed PL, the two lifetime peaks sS and sT shorten with increasing EPL, whereas sD remains constant (Fig. 2). The plots of recombination rates 3 1 s1 S and sT against EPL are almost proportional to EPL [14]. These results support exciton involvement in the sS- and sT-components since the excitonic recombination rates should obey the E3PL law [22]. By contrast, DP recombination is responsible for the sD-component since Eq. (1) underlying DP recombination is independent of EPL. The PL spectrum of the QFRS signal of the sS-component is similar to that of sT and shifted to higher EPL by 40 meV despite its smaller magnitude (Fig. 3). As EX increases, the QFRS spectra for the sS- and sT-components do not change but the sD-component increases (Fig. 4 (a)). These suggest that both the sS- and sT-components originate from similar recombination processes, namely excitonic recombination with an exchange energy of 40 meV between singlet- and triplet-spins. The increase of the sDcomponent is due to thermalization or diffusion of DPs excited at the higher EX in extended or band-tail states [15]. PL peak energy for the sD-component is lower still (Fig. 3). In addition, the PLE spectrum of the sD-component declines faster into the band-gap than those of the sS- and sT-components (Fig. 4(b)). These findings suggest that the sD-component has the largest Stokes shift, resulting from the recombination of DPs deeply trapped in tail states.

40 50

τT

τG

60 70 85 100 133 -10

x2 -8

10

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0

10

2

Carrier Concentration n [cm-3]

Fig. 5. QFRS spectra of a-Si:H at EX = 2.33 eV with G  1.0 · 1017 cm3 s1 for various temperature T.

1018

a-Si:H

G 0.2

1016

nD

1014

nS

nT

12

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T =3.7 [K] E x=2.33 [eV]

LESR [4] [6] [7]

1010 10 8

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QFRS nD + nT nS

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18

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10 10 10 10 10 Generation Rate G [cm-3s-1]

22

Fig. 6. Steady-state carrier concentrations nS (d), nT (+) and nD (s) for three QFRS components sS, sT and sD, respectively, vs. generation rate G at 3.7 K with ET = 2.33 eV; two data nS (·) were taken by condensed light. LESR spin densities vs. G for a-Si:H; the plots (j) from Ref. [4], (h) from [6], (n) from [7]. Dashed line indicates the sublinear G-dependence of nD / G0.2.

5

PL intensity I (t ) [a.u.]

obtained by deconvoluting the QFRS spectra (Fig. 1) are also plotted as functions of G. Fig. 7 demonstrates that the residual PL of I(t) persists for a very long time after cessation of the PL excitation of 2.33 eV at G  2.0 · 1016 cm3 s1 under the geminate condition for two temperatures: T  3.7 and 100 K. The PL decay for 100 K ceases at around 1.5 · 103 s, while that for 3.7 K persists over 2.0 · 104 s.

3.7 10 30

10

1141

10

a-Si:H

4

10

Ex =2.33[eV] G =2.0x10 16 [cm -3 s -1 ]

3

10

3.7[K]

2

10

100[K]

1

10

0

10

0

5×102 1×103 1.5×103 2×103 Time t [sec]

Fig. 7. PL decay for a-Si:H with G = 2.0 · 1016 cm3 s1 at 3.7 and 100 K with EX = 2.33 eV.

T. Aoki / Journal of Non-Crystalline Solids 352 (2006) 1138–1143

The disappearance of the sS-component at a lower T of 30 K and that of the sD-component at 85 K (Fig. 5) are explained by attributing the sS- and sD-components to singlet and triplet excitons, respectively, since the binding energy of a singlet exciton is smaller than that of a triplet exciton by the exchange energy of 40 meV. Moreover, the T at which the sT-component disappears (85 K) corresponds to the T for the onset of instability of self-trapped holes, to which electrons are bound individually, forming STEs [23]. By contrast, the sD-component is selectively enhanced by elevating T, accompanied with the shortening of sD due to nonradiative competing recombination. At elevated T, thermal energy prevents photogenerated e–h pairs from forming excitons. However, another shoulder followed by a peak appears at sG  105–104 s between sS and sT (Fig. 5). Moreover, sG remains constant as G increases up to 1020 cm3 s1, whereas sD continues to decrease [15,19]. These observations suggest that at 100 K, geminate pairs are not formed as excitons, but rather, non-excitonic geminate pairs continue to be generated. Using the classical Onsager model, we showed the occurrence of geminate recombination even above 100 K at above-gap excitation [19]. Presumably, the spin effect on geminate pairs fades out at 100 K, but the Coulombic effect persists even above 100 K. The steady-state carrier concentration nT of the sT-component increases almost in proportion to the generation rate G under the geminate condition G 6 1019 cm3 s1, since sT and gT remain nearly constant with G (Fig. 6). As G exceeds 1019 cm3 s1, the nT is absorbed into the sublinear curve of nD / G0.2 with nT  nD  1017 cm3. At around G  1019 cm3 s1, the two components are observed to merge (Fig. 1). This implies that the recombination of triplet exciton starts to compete with that of DP’s at around the steady-state carrier concentration of 1017 cm3. Similarly, an extrapolation of the plot of nS vs. G, which deviates from a straight line at G of 1022 cm3 s1 presumably due to the irradiation condensed by a lens, intersects at the sublinear curve at around nS  nD  1018 cm3 (G  1023–1024 cm3 s1); such a coalescence of all the components is also seen in Fig. 1 at G  5.0 · 1022. At each point of coalescence, the average inter-pair dis1=3 tance between triplet excitons  0:5nT works out to be 17 3 10 nm when nT  nD  10 cm and that between the singlet excitons 5 nm obtained by nS  nT  1018 cm3. The spatial wavefunction of a singlet exciton is symmetric due to the anti-parallel spins, while that of a triplet exciton having parallel spins is antisymmetric. The exciton radius is, on average, smaller in the case of the symmetric spatial function than in the case of the antisymmetric function [24]. Thus, the triplet exciton which possesses a larger radius is absorbed into DPs at a lower concentration (nT) compared with the singlet exciton (nS). If a singlet exciton radius aex is close to the inter-pair distance 0:5nS1=3  5 nm, the exciton binding energy e2/2jaex works out to be 5 meV with a dielectric constant j of 12, which

explains the disappearance of the sS component at the low T of 30 K. Localization of STEs is probably responsible for the larger exchange energy of 40 meV than the binding energy [24]. On the other hand, Lips et al. [25] measured the e–h distance of a triplet exciton as 0.9 nm at G  1022 cm3 s1. The cause for this discrepancy remains unclear. A magnetic field of up to 0.9 T had little influence on the sS-component, but enhanced the sT-component and reduced the sD-component [19]. According to Robins and Kastner [26], the effects of magnetic field on sS and sT-component are also explainable in terms of excitonic recombination. The sS-component, assigned to the singlet exciton, is unaffected by an applied magnetic field due to total spin S = 0. Zeeman splitting induced on a triplet exciton with S = 1 will change the coupling between triplet and singlet states, leading to the enhancement of the sT-component [26]. The reduction in the sD-component by the magnetic field is explained by the paramagnetism of DP’s [19]. Unlike the QFRS, the residual PL decay I(t) obeys recombination kinetics over the full range from an initial carrier concentration to zero. We have measured I(t) for various G values and integrated from cessation of the illumination to 1 to determine the steady-state photocarrier concentration. Although this needs one fitting parameter, the integral of I(t) with respect to G agrees well with nD as well as LESR densities obtained by others [17]. Furthermore, the integrated I(t) plots against T match the LESR data as well as nD (Fig. 8) [27,28]. The PL decays at 3.7 K and 100 K last more than 2 · 104 and 1.5 · 103 s, respectively, whereas the lifetimes sD obtained by QFRS at the same T and G correspond to 8 and 0.2 s, respectively. This is because the QFRS measures an effective lifetime at a quasi-steady-state photocarrier concentration, while the residual PL decay reflects the recombination kinetics. In fact, the log–log plots of I(t) fits the derivative of a stretched exponential function well, for various T and G, indicating that the recombination kinetics of the DP is monomolecular, in particular, at low T and low G [17]. The monomolecular kinetics arises from the immobility of trapped carriers localized in tail

10 17

Carrier Con. n [cm-3]

1142

a-Si:H 10 16 10 15 10 14

QFRS [Ref.14] PL Decay + LESR [a.u.] [27] LESR [a.u.] [28]

0

20 40 60 80 100 120 140 160 Temperature T [K]

Fig. 8. Plots of steady-state carrier concentrations n; the plots (n) estimated from PL decay, ( ) from QFRS [14] and the LESR intensities in arbitrary units as functions of T for a-Si:H; (+) from Ref. [27], (j) from [28].



T. Aoki / Journal of Non-Crystalline Solids 352 (2006) 1138–1143

states, into which photocarriers are thermalized immediately after photoexcitation. 5. Conclusion Wideband QFRS revealed the triple-peak lifetime distribution in PL of a-Si:H at low temperature T and low generation rate G. The dependence of the three components on G, T, PL emission energy, PL excitation energy, and magnetic field are explained by attributing the well-known double-peak components to excitonic recombination, and the newly discovered third component to DP recombination. At high T and low G, non-excitonic geminate recombination coexists with nongeminate (DP) recombination. Steady-state carrier concentrations obtained from the DP component agree with the G- and T-dependences of LESR density. The residual PL decay is identified with the third component of QFRS spectra originating in DP recombination and shows that recombination kinetics of DP’s is monomolecular at low T and low G. Acknowledgements The author wishes to acknowledge that the present study was conducted in cooperation with K. Ikeda, D. Saito, T. Shimizu, S. Komedoori, and S. Kobayashi of Tokyo Polytechnic University, and A. Ganjoo and K. Shimakawa of Gifu University. The author thanks the Japan Private School Promotion Foundation for their financial support. This work was also partially supported by a Grant-inAid for Scientific Research (C) from the Ministry of Education, Culture, Sports, Science and Technology of Japan. References [1] R.A. Street, Adv. Phys 30 (1981) 593. [2] R.A. Street, Hydrogenated Amorphous Silicon, Cambridge University Press, 1991, p. 276.

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