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Spin dependent recombination at dislocations in silicon
SPIN DEPENDENT RECOMBINATION DISLOCATIONS IN SILICON
AT
D. NEUBERT,K. HOFFMANN, H. TE~CHMANN and R. !?+CHLIEF Physikalisch-Technische Bundesanstalt, Institut Berlin, Berlin, Germany Abstract-The unpaired electrons of dislocations with an edge component in Si give rise to an EPR signal. Under the resonant condition, a decrease of photoconductivity[S] is observed. We have observed the derivative of the resonant signal at a microwave frequency of 9.2GH.7 by modulating the sweeping magnetic field. The relaxation time of the spin system was studied by varying the modulation frequency. The amplitude of the resonant signal is discussed with respect to dependence of the background signal on the sweeping magnetic field. The signal consists of more than one absorption line and has been resolved into its components by computer evaluation. The energy level structure of the dislocations which produce the signal has been derived from Hall effect measurements and conventional optical methods. The influence of deformation temperature and the role of other heat treatment produced defects as a possible source of the signal are discussed. The strength of the effect is related to the strong polarization of exchange coupled paramagnetic centers. The experimental results suggest that the recombination process is of the triplet type. The anomalous phase of the resonant signal is explained by resonant emission of microwave power.
NOTATION
B
magnetic induction, T EO energy of neutral dislocation above valence band, eV width of dislocation band, eV electronic charge, 1.6 X lo-l9 C occupancy factor of a dislocation, of a dislocation site g-factors exchange integral, eV interaction constant Boltzmann constant, 1.38x 10mz3 J K-’ LD Debye length, cm m number of sites in a dislocation segment number of sites with spin up (down) in a dislocation m,.’ segment N.4 acceptor concentration, cm-’ donor concentration. cm-’ ND dislocation density, cm-’ Nd concentration of dislocation sites, cm-’ NS n electron concentration in undeformed sample, cm-’ electron concentrationin deformed sample, crnv3 nd number of sites in a dislocation n, number of occupied (unoccupied) dislocation sites n,‘. n, P polarization of dislocation sites P polarization of conduction electrons P hole concentration in undeformed sample, cm-3 hole concentration in deformed sample, cm-’ Pd R sample resistance capture cross sections, cm’ s. s, T temperature of taking a measurement, K TO temperature for which dislocation is neutral, K Td deformation temperature, K number of independent paramagnetic segments in a 4 dislocation line
I. DBLDCATIONS AS PARMlAGI%l’IC CBAMS In an elemental semiconductor, a dislocation with an edge component consists of a linear chain of atoms which do not have a 4th valence partner as in the undisturbed diamond structure. These edge atoms, also called dislocation sites, represent in fact the lattice sites of a one dimensional lattice. If the dislocation is neutral, each site is occupied by one electron, the “dangling bond” electron. As suggested by Shockley[ I]. there are three different states of a site:
tnj
fs =
+ 1 electron accepted 0 site neutral i - 1 electron given off.
In order to characterize the charge state of the dislocation line, Read121 has introduced an occupancy factor f by
where n,+, n,- and n, refer, respectively, to the number of sites with fs = + I, fs = - 1 and the total number. Only sites with f, = 0 are paramagnetic. For a charged dislocation, the sites with fi it 0 break the dislocation line into at least 2, = f. m, finite segments with an average number of at most m, sites with m, = f’.
Greek symbols mobility, m* V-’ s-’ Bohr magneton, 9.27 x lo-% J T-’ potential in band bending, V sample conductivity, a-’ cm-’ fast decay time constant due to bipolar recombination, s intermediate decay time constant, s slow decay time constant due to monopolar trap ping, s.
(2)
In a magnetic field, the magnetic moments get orientated and the resulting polarization P of a segment is given by
u,’ and m ,’ refer, respectively, to the number of
D.
1446
NEUBERT et 01.
sites with spin up, spin down in the segment. In a
magnetic field, also the magnetic moments of the conduction electrons get orientated which results in a polarization p. As remarked by Lepine[3], in a photoconductivity experiment the recombination of an electron hole pair via a paramagnetic recombination center depends on the relative spin orientation of conduction electron and recombination center. In a singlet collision (antiparallel spin orientation), the capture cross section S is given by S=So(l-pP)
(4)
and in a triplet collision (parallel spin orientation) by S=So(l+pP)
(5)
u = u. corresponds to the Rat band condition. Since the Debye length LD - ni_“’ is strongly temperature dependent, it is more informative to present space charge properties as a function of doping at constant temperature than as a function of temperature at constant doping. Hall effect measurements taken at 294 K are shown in Fig. l(a). The crystals with an electron concentration n < Ri (ni = intrinsic carrier concentration) are p-type with p = ni2/n. Evidently, by trapping of electrons at dislocation sites. n-type samples may convert to p-type samples. In p-type samples, dislocation sites may either trap holes or electrons with a corresponding decrease or increase of free holes. The coordinates may be read as energy scales and from the neutral state of a dislocation the energy of this state is determined to be E,= 0.4eV above the valence band.
where So is the spin independent part of the capture cross section. This concept of spin dependent recombination was originally[3] connected with paramagnetic surface states of silicon, but later shown by Lepine, Grazhulis and Kaplan[4] and Wosinski and Figielski[Sl to be applicable to recombination at dislocations in Si under the resonant condition of EPR. The experiments were interpreted as being consistent with a recombination via a singlet collision. In this contribution, the discussion of measurements and interpretation of the spin dependent recombination in Si (Section 4) shah be. preceeded by a discussion of the determination of the occupancy factor and energetic position of the dislocations (Section 3). 2 SAMPU PREPARATION
Dislocations were produced by uniaxial compression in a (123)direction of (lll)-orientated dislocation free crystals. The deformation temperature was either 970 or 1270K. The resulting dislocations were edge- and 60”dislocations and their density was N., = 5 x 10’cm-2 as determined by etch pit counting. For each deformed sample an “annealed” sample was prepared which was subjected to the same temperature treatment as the deformed one. The sample dimensions were 30x 4x I mm3. The contacts were lightly doped gold wires which were spot welded by a capacitor decharging. Care was taken to avoid any contamination of the samples during the different stages of preparation.
3. I The occupancy factor f As shown by Schroter[6] the dislocation sites form a one dimensional band where the Fermi level of the crystal always coincides with the occupation limit of this band. The relationship between the charge trapped at the dislocation sites and the resulting space charge and band bending has been calculated by Neubert[7] from the solution of the Poisson equation Ld($+$$)=sinhu-sinhuo
(6)
where u and u0 are crystal potentials in units of kT and
nFig. 1. Determination of the occupancy factor f by the Hall effect. (a) Carrier concentration after deformation vs concentration before deformation (n, = intrinsic carrier concentration) V = not annealed, 0 = annealed reference samples. (b) Occupancy factor f derived from (a).
The occupancy factor f (Fig. lb) is calculated by use of the neutrality condition and is of the form expected by theory (Fig. 1 in [7]). Evidently, for highly doped crystals, by eqn (2) the paramagnetic segments of a dislocation chain are rather short and have only of the order of m, = 10 sites. Close to the neutral dislocation state, m, may be 1000 or even infinite at the neutral point. For lower temperatures, the occupancy curve is shifted to higher values with a resulting shortening of the paramagnetic segments. 3.2 Photoconductivity decay times Whereas an undeformed crystal has a decay time of the order of 100~s. the photoconductivity transient times after excitation vary over more than nine orders of magnitude in a deformed sample (Fig. 2). The transient time r1 is due to bipolar recombination and is of the order of 10 ns with only a slight temperature dependence.
1447
Spin dependentrecombinationat dislocationsin silicon
to spin dependent photoconductivity? Principally, any of the three processes mentioned above involve an interaction with the paramagnetic dislocation sites and thus should be spin dependent. At present, experimental limitations in detection sensitivity seem to allow only the study of processes connected with bipolar recombination at high excitation levels.
light
1 time
-
Hg. 2. Transient pbotoconductivityof a deformed sample (except curve C). (a) Time resolution 10ms (schematicdrawing).(b) Time resolution2 ns (actual recordingwith a transientrecorder); A: laser puls, B: deformed sample, C: undeformed sample. (c) Temperaturedependence of the decay time ~3. During illumination the space charge barrier is reduced.
The transient time 72 is due to the up building of the space charge barrier and the decay of photoconductivity is logarithmically in accordance with the theory of Morrison[8]. If the final (dark equilibrium) barrier height e& is essentially reproduced, it takes still a time with characteristic time constant 73r 73-I - n exp (- erb;/kT), in order to establish complete thermal equilibrium. 73 does not exist for a neutral dislocation (T = To). At high temperatures, the number n of free electrons is equal to the intrinsic carrier concentration and In 73 varies linearly with l/T. The width of the dislocation band cannot be determined from transient times, but has been determined by Kos and Neubert[9] from spectral conductivity measurements as AE,, = 0.26 eV. In passing we note that Grazhulis, Kveder and Nukhina[lO] have also found a neutral dislocation state at E = 0.4eV. Further, they measure a microwave conductivity at 0.25 eV which we would ascribe to transitions within the band at Eo= 0.4eV of width A&,. For n-type samples, these authors determine from Hall effect measurements a second dislocation state symmetrically to E, with respect to midgap. By our experience this is a “ghost” state, which is obtained by the not admissable extrapolation of the f values obtained for highly doped n-type samples to zero doping (see Fig. lb). Such a “ghost” state is in fact not existent. Which of the transient times is expected to be related
4. SPINDepwDplT coNDucTrvlTY 4.1 Experimental setup For measuring the effect of spin dependent conductivity our experimental setup is very similar to a conventional EPR configuration (Fig. 3). The sweeping magnetic field is modulated by two modulating coils outside the cavity (modulation frequency usually 2 kHz, amplitude 0.2 x lo-‘T). The change of resistivity is measured by lock-in detection. The sample is placed in the maximum of the microwave magnetic component of the X-band microwave cavity with its contacts outside of the resonator. On the front of the cavity are some slots to illuminate the sample with a 150W incandescent lamp. The temperature of the sample can be changed from 100 to 400 K by a N2 gas flow. 4.2 The resonant signal With our experimental setup we measure du/dB as a function of magnetic field B, from which we calculate du/a dB where u is the conductivity of the sample under illumination. The magnetic field runs from B = - 1 T to + 1 T. Thus, the “resonant” signal sits on a “background” signal (Fig. 4). First we consider the resonant signal. We have investigated doping concentrations between 5 x lOI and 5 x lOI cm-’ in the temperature range 100 K < T < 400 K. Our findings are: the signal appears as well in n- as in p-type samples independent on deformation temperature. Thus in contrast to the EPR signal, also deformation at Td > 1070K gives a resonant photoconductivity signal. The signal was not found in only annealed samples which is to be expected from the Hall effect measurements (Fig. 1) which showed insignificant change of sample property under annealing. By varying the modulation frequency we had expected to find some effect of spin relaxation time. Up to a modulation frequency of 20 kHz no such effect was found, for higher frequencies the investigations are in progress. In order to improve the resolution of the asymmetric resonant signal, it was decomposed by a computer program, which finds the underlying single lines by a fitting process to the registered signal under the condition of least square errors. For our samples, 3 lines were found in all samples with the following g-factors: g, = 2.001 R2= 2.004 g3 =. 2.009. The half width of the lines was =8 x 1’ ‘4T. The amplitude of g2 was always the strongest, but the ratio of
D. NEUBERT et al.
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OSCILLOSCOPE lMICrowaVC Control
1
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Fig. 3. Experimental setup for measuringspin dependentrecombination.
n-81. defolmed No:7.8 IO”cm~’
it has been calculated by Opechowski and Bryan[l4]. The polarization PE, of a chain with m, spins and interaction constant K = JIZLT is then obtained by differentiation with respect to B as eK sinh (gmB/kT) [evzK + e2K sinh (g&/kT)]“”
pi3 =
I
see Appendix of [5]
I tanb (gpoB/kT)
m, -+a K#O. I
(7)
Fig.
4.
Spin dependentconductivity.(a) The resonant signaland its components.(b) The “background”signal.
the three amplitudes varied independently from each other for different samples. These g-values are found also, among other g-values, by Alexander, Bartelsen and Weber[ 1l] in EPR. These authors relate the g-values to dislocations in special crystallographic orientations. The resonance lines found in spin dependent conduction, however, do not seem to be sensitive to crystallographic orientations, since the form of the signal seems to be rather universal as may be seen by a comparison with the signal obtained by Figielski et ~1.[5.12,16] on samples deformed by bending. 4.3 The background signal If in fact the effect of spin dependent photoconductivity exists, it should exist at any magnetic field, not only at the resonant signal, where it is detected with special high sensitivity. First we consider the strength of the effect. We adopt the point of view of Wosinski[ 121:The spin polarization along the paramagnetic chain is strongly enhanced by a positive exchange integral I between neighbouring sites and thus is much larger than with zero interaction. As discussed by Hill[ 131,the partition function for the linear king model may be calculated exactly. For a finite chain
Before we give a numerical evaluation of this formula, we give an estimate of the magnetic field dependence of the magnetoresistance effect which cannot be excluded D priori. For our range of doping, impurity scattering can be neglected and the magnetoresistance AR/R = R(B) - R(O)/R(O) is dominated by acoustic scattering and given by[15] AR/R = -A&
0.38p2B2, /LB ~31 = o l3 fiBz= 1. I . 7
(8)
For an order of magnitude estimate we neglect the different mobilities of holes and electrons and take p = 0.1 m2 V-’ s-‘. Thus in our experimental range holds FB ~0.1 and d(Au/o)/dB = -7.6 x 10-3RT-‘. This is an order of magnitude smaller than the measured effect (Fig. 4b) and by this estimate magnetoresistance can be excluded as an explanation. A numerical evaluation of eqn (7) shows clearly (Fig. 5) that the polarization depends strongly on the number of sites m, forming the chain. Further, the number of sites for which the polarization saturates with respect to an increase of the number of sites depends strongly on the interaction constant K. For K = I, an increase of m, above 200 does not result in a further increase of polarization, for K = 5 saturation sets in if m. = 2000. At T = 100K, our experimental range corresponds to the abzissa
Spin dependent recombinationat dislocationsin silicon
0
0.01 0.02 0.03 0.04 0.05 0.06
g!oBlkTFig. 5. Polarization of dislocation segments (m, = number of sites, K = interaction constant). photoconductivity recombination increases, the decreases with increasing capture cross section, i.e. 1 dS --= SodB
1 do ---. odB
According to the experimental background curve (Fig. 4b), it holds du/dB < 0 and we obtain for the change of capture cross section with magnetic field
_w>o, SodB By eqn (4) and eqn (5), this holds for triplet recombination but not for singlet recombination. Thus, we are led to the conclusion that, in contrast to the interpretation of previous authors(3,4,5], the spin dependent recombination is of the triplet type. For a quantitative interpretation of background curves, the expression --:0:;
dP -‘a+
P dB
has to be calculated which remains still to be done. For
1449
the curve of 4b, a rough estimate shows that it might . . K-3 relate to a polartzatton such as P,,,,_~M, from the occupancy factor f one gets by eqn (2) for this sample (ND =7.8x 10’3cm-2) a value m, = 100. However, the final conclusion depends on a detailed numerical analysis. Since under the condition of EPR the polarization is decreased, the change of conductivity should be opposite to the change due to increasing magnetic field. Apparently, as seen from Fig. 4, the change of conductivity at resonance has the same sign as the change of conductivity of the background signal. Thus, the phase of the signal is anomalous. Under normal conditions, at EPR resonance there is a transition from level 1 to level 2 (Fig. 5). It has been observed[ 121that in taking the EPR signal of dislocation under illumination, the phase of the signal is anomalous, also it has been observed[16] that the Q-factor of the microwave cavity increases under EPR resonance of an illuminated deformed sample. Ah these results point to the fact that there is not a resonant absorption, but a resonant emission of microwave power. Thus, there is a transition from level 2 to level 1 under resonant condition. As an interpretation of this effect, we suggest that due to strong optical excitation the electron system is strongly heated and takes advantage of any channel to cool down. By opening the microwave channel 2-r 1, relaxation of the system to the lowest energy level 1 is enhanced. 5. slJMMARYANDcoNclAlsIoN There are no facts which suggest that the effect of spin dependent recombination is not due to dislocations. The effect is well in accordance with a Shockley-Read type dislocation model and the notion of an occupancy factor. The strength of the effect has been related in accordance with other authors to the strong polarization of exchange coupled paramagnetic dislocation sites. Whether the recombination process is in fact, in contrast to the findings of other authors, of the triplet type as deduced from our experiments, needs further confirmation. Experimentally, it should be fruitful to vary the relative power of photoexcitation and microwave power at resonance in order to get more information on the relationship between the normal and the anomalous phase of the resonant signal. Also, a detailed statistical treatment of the dynamics of the recombination process seems to be necessary for a full understanding of the effect.
CONOUCTION ELECTRONS
Ii DISLOCATION SITES <-?: B=G
TRIPLET RECUdBINATION
SINGLET RECOMBINATIOE;
B:O
2: B*O
Ev Fig. 6. Mechanismsof spin dependent recombination.
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D. NEUBEFZT et al.
Acknowledgemenl-We thank W. Moeckel for providing data on the fast recombination process and H. Kuenzel and F. Liepe for assistance in various stages of the work.
WCES I. W. Shockley, Phys. Reu. 91, 228 (1953). 2. W. T. Read, Phil, Mug. 45.775 (1954). 3. D. Lepine, Phys. Rev. E 6, 436 (1972). 4. D. Lepine, V. A. Grazhulis and D. Kaplan, Physics of Semiconducrors (Edited by F. G. Fumi), p. 1081. North-Holland, Amsterdam (1977). 5. T. Wosinski and T. Figielski. Phys. SIalus Solidi (6) 83, 93 (1977). 6. W. Schrater, Phys. Status Solidi 21.211(1%7). 7. D. Neubert. Inst. Phys. Conf. Ser. No. 23, p. 398 (1975). 8. S. R. Morrison, Phys. Rev. 101.619 (1956).
9. H.-J. Kos and D. Neubert. Phvs. Status Solidi la) 44. 259 (1977).
10. V. A. Grazhulis. V. V. Kveder and V. Yu. Nukhina, Phys. Sralus Solidi (a) 43. 407 (1977); 44. 167 (1977). II. H. Alexander, L. Bartelsen and E. Weber, Proc. 5th fnt. Summer School on Dejecrs, p. 89. PWN, Warsaw (1978). 12. T. Wosinsky, Proc. 5th Inr. Summer School on fhzfects, p. 241. PWN, Warsaw (1978). 13. T. L. Hill, Statistical Mechanics. p. 322. McGraw-Hill. New York (1956). 14. W. Opechowski and J. M. Bryan, Canad. J. Phys. 29. 236 (1951). und StromIS. W. Heywang and H. W. P&l. Banderstrktur transport, Halbleiter Elektronik Ed. 3, p. 213. Springer. Berlin (1976). 16. T. Wosinski, T. Figielski and A. Makosa, Phys. Status Solidi (a) 37. KJ7 (1976).
AT
D. NEUBERT,K. HOFFMANN, H. TE~CHMANN and R. !?+CHLIEF Physikalisch-Technische Bundesanstalt, Institut Berlin, Berlin, Germany Abstract-The unpaired electrons of dislocations with an edge component in Si give rise to an EPR signal. Under the resonant condition, a decrease of photoconductivity[S] is observed. We have observed the derivative of the resonant signal at a microwave frequency of 9.2GH.7 by modulating the sweeping magnetic field. The relaxation time of the spin system was studied by varying the modulation frequency. The amplitude of the resonant signal is discussed with respect to dependence of the background signal on the sweeping magnetic field. The signal consists of more than one absorption line and has been resolved into its components by computer evaluation. The energy level structure of the dislocations which produce the signal has been derived from Hall effect measurements and conventional optical methods. The influence of deformation temperature and the role of other heat treatment produced defects as a possible source of the signal are discussed. The strength of the effect is related to the strong polarization of exchange coupled paramagnetic centers. The experimental results suggest that the recombination process is of the triplet type. The anomalous phase of the resonant signal is explained by resonant emission of microwave power.
NOTATION
B
magnetic induction, T EO energy of neutral dislocation above valence band, eV width of dislocation band, eV electronic charge, 1.6 X lo-l9 C occupancy factor of a dislocation, of a dislocation site g-factors exchange integral, eV interaction constant Boltzmann constant, 1.38x 10mz3 J K-’ LD Debye length, cm m number of sites in a dislocation segment number of sites with spin up (down) in a dislocation m,.’ segment N.4 acceptor concentration, cm-’ donor concentration. cm-’ ND dislocation density, cm-’ Nd concentration of dislocation sites, cm-’ NS n electron concentration in undeformed sample, cm-’ electron concentrationin deformed sample, crnv3 nd number of sites in a dislocation n, number of occupied (unoccupied) dislocation sites n,‘. n, P polarization of dislocation sites P polarization of conduction electrons P hole concentration in undeformed sample, cm-3 hole concentration in deformed sample, cm-’ Pd R sample resistance capture cross sections, cm’ s. s, T temperature of taking a measurement, K TO temperature for which dislocation is neutral, K Td deformation temperature, K number of independent paramagnetic segments in a 4 dislocation line
I. DBLDCATIONS AS PARMlAGI%l’IC CBAMS In an elemental semiconductor, a dislocation with an edge component consists of a linear chain of atoms which do not have a 4th valence partner as in the undisturbed diamond structure. These edge atoms, also called dislocation sites, represent in fact the lattice sites of a one dimensional lattice. If the dislocation is neutral, each site is occupied by one electron, the “dangling bond” electron. As suggested by Shockley[ I]. there are three different states of a site:
tnj
fs =
+ 1 electron accepted 0 site neutral i - 1 electron given off.
In order to characterize the charge state of the dislocation line, Read121 has introduced an occupancy factor f by
where n,+, n,- and n, refer, respectively, to the number of sites with fs = + I, fs = - 1 and the total number. Only sites with f, = 0 are paramagnetic. For a charged dislocation, the sites with fi it 0 break the dislocation line into at least 2, = f. m, finite segments with an average number of at most m, sites with m, = f’.
Greek symbols mobility, m* V-’ s-’ Bohr magneton, 9.27 x lo-% J T-’ potential in band bending, V sample conductivity, a-’ cm-’ fast decay time constant due to bipolar recombination, s intermediate decay time constant, s slow decay time constant due to monopolar trap ping, s.
(2)
In a magnetic field, the magnetic moments get orientated and the resulting polarization P of a segment is given by
u,’ and m ,’ refer, respectively, to the number of
D.
1446
NEUBERT et 01.
sites with spin up, spin down in the segment. In a
magnetic field, also the magnetic moments of the conduction electrons get orientated which results in a polarization p. As remarked by Lepine[3], in a photoconductivity experiment the recombination of an electron hole pair via a paramagnetic recombination center depends on the relative spin orientation of conduction electron and recombination center. In a singlet collision (antiparallel spin orientation), the capture cross section S is given by S=So(l-pP)
(4)
and in a triplet collision (parallel spin orientation) by S=So(l+pP)
(5)
u = u. corresponds to the Rat band condition. Since the Debye length LD - ni_“’ is strongly temperature dependent, it is more informative to present space charge properties as a function of doping at constant temperature than as a function of temperature at constant doping. Hall effect measurements taken at 294 K are shown in Fig. l(a). The crystals with an electron concentration n < Ri (ni = intrinsic carrier concentration) are p-type with p = ni2/n. Evidently, by trapping of electrons at dislocation sites. n-type samples may convert to p-type samples. In p-type samples, dislocation sites may either trap holes or electrons with a corresponding decrease or increase of free holes. The coordinates may be read as energy scales and from the neutral state of a dislocation the energy of this state is determined to be E,= 0.4eV above the valence band.
where So is the spin independent part of the capture cross section. This concept of spin dependent recombination was originally[3] connected with paramagnetic surface states of silicon, but later shown by Lepine, Grazhulis and Kaplan[4] and Wosinski and Figielski[Sl to be applicable to recombination at dislocations in Si under the resonant condition of EPR. The experiments were interpreted as being consistent with a recombination via a singlet collision. In this contribution, the discussion of measurements and interpretation of the spin dependent recombination in Si (Section 4) shah be. preceeded by a discussion of the determination of the occupancy factor and energetic position of the dislocations (Section 3). 2 SAMPU PREPARATION
Dislocations were produced by uniaxial compression in a (123)direction of (lll)-orientated dislocation free crystals. The deformation temperature was either 970 or 1270K. The resulting dislocations were edge- and 60”dislocations and their density was N., = 5 x 10’cm-2 as determined by etch pit counting. For each deformed sample an “annealed” sample was prepared which was subjected to the same temperature treatment as the deformed one. The sample dimensions were 30x 4x I mm3. The contacts were lightly doped gold wires which were spot welded by a capacitor decharging. Care was taken to avoid any contamination of the samples during the different stages of preparation.
3. I The occupancy factor f As shown by Schroter[6] the dislocation sites form a one dimensional band where the Fermi level of the crystal always coincides with the occupation limit of this band. The relationship between the charge trapped at the dislocation sites and the resulting space charge and band bending has been calculated by Neubert[7] from the solution of the Poisson equation Ld($+$$)=sinhu-sinhuo
(6)
where u and u0 are crystal potentials in units of kT and
nFig. 1. Determination of the occupancy factor f by the Hall effect. (a) Carrier concentration after deformation vs concentration before deformation (n, = intrinsic carrier concentration) V = not annealed, 0 = annealed reference samples. (b) Occupancy factor f derived from (a).
The occupancy factor f (Fig. lb) is calculated by use of the neutrality condition and is of the form expected by theory (Fig. 1 in [7]). Evidently, for highly doped crystals, by eqn (2) the paramagnetic segments of a dislocation chain are rather short and have only of the order of m, = 10 sites. Close to the neutral dislocation state, m, may be 1000 or even infinite at the neutral point. For lower temperatures, the occupancy curve is shifted to higher values with a resulting shortening of the paramagnetic segments. 3.2 Photoconductivity decay times Whereas an undeformed crystal has a decay time of the order of 100~s. the photoconductivity transient times after excitation vary over more than nine orders of magnitude in a deformed sample (Fig. 2). The transient time r1 is due to bipolar recombination and is of the order of 10 ns with only a slight temperature dependence.
1447
Spin dependentrecombinationat dislocationsin silicon
to spin dependent photoconductivity? Principally, any of the three processes mentioned above involve an interaction with the paramagnetic dislocation sites and thus should be spin dependent. At present, experimental limitations in detection sensitivity seem to allow only the study of processes connected with bipolar recombination at high excitation levels.
light
1 time
-
Hg. 2. Transient pbotoconductivityof a deformed sample (except curve C). (a) Time resolution 10ms (schematicdrawing).(b) Time resolution2 ns (actual recordingwith a transientrecorder); A: laser puls, B: deformed sample, C: undeformed sample. (c) Temperaturedependence of the decay time ~3. During illumination the space charge barrier is reduced.
The transient time 72 is due to the up building of the space charge barrier and the decay of photoconductivity is logarithmically in accordance with the theory of Morrison[8]. If the final (dark equilibrium) barrier height e& is essentially reproduced, it takes still a time with characteristic time constant 73r 73-I - n exp (- erb;/kT), in order to establish complete thermal equilibrium. 73 does not exist for a neutral dislocation (T = To). At high temperatures, the number n of free electrons is equal to the intrinsic carrier concentration and In 73 varies linearly with l/T. The width of the dislocation band cannot be determined from transient times, but has been determined by Kos and Neubert[9] from spectral conductivity measurements as AE,, = 0.26 eV. In passing we note that Grazhulis, Kveder and Nukhina[lO] have also found a neutral dislocation state at E = 0.4eV. Further, they measure a microwave conductivity at 0.25 eV which we would ascribe to transitions within the band at Eo= 0.4eV of width A&,. For n-type samples, these authors determine from Hall effect measurements a second dislocation state symmetrically to E, with respect to midgap. By our experience this is a “ghost” state, which is obtained by the not admissable extrapolation of the f values obtained for highly doped n-type samples to zero doping (see Fig. lb). Such a “ghost” state is in fact not existent. Which of the transient times is expected to be related
4. SPINDepwDplT coNDucTrvlTY 4.1 Experimental setup For measuring the effect of spin dependent conductivity our experimental setup is very similar to a conventional EPR configuration (Fig. 3). The sweeping magnetic field is modulated by two modulating coils outside the cavity (modulation frequency usually 2 kHz, amplitude 0.2 x lo-‘T). The change of resistivity is measured by lock-in detection. The sample is placed in the maximum of the microwave magnetic component of the X-band microwave cavity with its contacts outside of the resonator. On the front of the cavity are some slots to illuminate the sample with a 150W incandescent lamp. The temperature of the sample can be changed from 100 to 400 K by a N2 gas flow. 4.2 The resonant signal With our experimental setup we measure du/dB as a function of magnetic field B, from which we calculate du/a dB where u is the conductivity of the sample under illumination. The magnetic field runs from B = - 1 T to + 1 T. Thus, the “resonant” signal sits on a “background” signal (Fig. 4). First we consider the resonant signal. We have investigated doping concentrations between 5 x lOI and 5 x lOI cm-’ in the temperature range 100 K < T < 400 K. Our findings are: the signal appears as well in n- as in p-type samples independent on deformation temperature. Thus in contrast to the EPR signal, also deformation at Td > 1070K gives a resonant photoconductivity signal. The signal was not found in only annealed samples which is to be expected from the Hall effect measurements (Fig. 1) which showed insignificant change of sample property under annealing. By varying the modulation frequency we had expected to find some effect of spin relaxation time. Up to a modulation frequency of 20 kHz no such effect was found, for higher frequencies the investigations are in progress. In order to improve the resolution of the asymmetric resonant signal, it was decomposed by a computer program, which finds the underlying single lines by a fitting process to the registered signal under the condition of least square errors. For our samples, 3 lines were found in all samples with the following g-factors: g, = 2.001 R2= 2.004 g3 =. 2.009. The half width of the lines was =8 x 1’ ‘4T. The amplitude of g2 was always the strongest, but the ratio of
D. NEUBERT et al.
1448
OSCILLOSCOPE lMICrowaVC Control
1
LO MOOULATION
COILS
Fig. 3. Experimental setup for measuringspin dependentrecombination.
n-81. defolmed No:7.8 IO”cm~’
it has been calculated by Opechowski and Bryan[l4]. The polarization PE, of a chain with m, spins and interaction constant K = JIZLT is then obtained by differentiation with respect to B as eK sinh (gmB/kT) [evzK + e2K sinh (g&/kT)]“”
pi3 =
I
see Appendix of [5]
I tanb (gpoB/kT)
m, -+a K#O. I
(7)
Fig.
4.
Spin dependentconductivity.(a) The resonant signaland its components.(b) The “background”signal.
the three amplitudes varied independently from each other for different samples. These g-values are found also, among other g-values, by Alexander, Bartelsen and Weber[ 1l] in EPR. These authors relate the g-values to dislocations in special crystallographic orientations. The resonance lines found in spin dependent conduction, however, do not seem to be sensitive to crystallographic orientations, since the form of the signal seems to be rather universal as may be seen by a comparison with the signal obtained by Figielski et ~1.[5.12,16] on samples deformed by bending. 4.3 The background signal If in fact the effect of spin dependent photoconductivity exists, it should exist at any magnetic field, not only at the resonant signal, where it is detected with special high sensitivity. First we consider the strength of the effect. We adopt the point of view of Wosinski[ 121:The spin polarization along the paramagnetic chain is strongly enhanced by a positive exchange integral I between neighbouring sites and thus is much larger than with zero interaction. As discussed by Hill[ 131,the partition function for the linear king model may be calculated exactly. For a finite chain
Before we give a numerical evaluation of this formula, we give an estimate of the magnetic field dependence of the magnetoresistance effect which cannot be excluded D priori. For our range of doping, impurity scattering can be neglected and the magnetoresistance AR/R = R(B) - R(O)/R(O) is dominated by acoustic scattering and given by[15] AR/R = -A&
0.38p2B2, /LB ~31 = o l3 fiBz= 1. I . 7
(8)
For an order of magnitude estimate we neglect the different mobilities of holes and electrons and take p = 0.1 m2 V-’ s-‘. Thus in our experimental range holds FB ~0.1 and d(Au/o)/dB = -7.6 x 10-3RT-‘. This is an order of magnitude smaller than the measured effect (Fig. 4b) and by this estimate magnetoresistance can be excluded as an explanation. A numerical evaluation of eqn (7) shows clearly (Fig. 5) that the polarization depends strongly on the number of sites m, forming the chain. Further, the number of sites for which the polarization saturates with respect to an increase of the number of sites depends strongly on the interaction constant K. For K = I, an increase of m, above 200 does not result in a further increase of polarization, for K = 5 saturation sets in if m. = 2000. At T = 100K, our experimental range corresponds to the abzissa
Spin dependent recombinationat dislocationsin silicon
0
0.01 0.02 0.03 0.04 0.05 0.06
g!oBlkTFig. 5. Polarization of dislocation segments (m, = number of sites, K = interaction constant). photoconductivity recombination increases, the decreases with increasing capture cross section, i.e. 1 dS --= SodB
1 do ---. odB
According to the experimental background curve (Fig. 4b), it holds du/dB < 0 and we obtain for the change of capture cross section with magnetic field
_w>o, SodB By eqn (4) and eqn (5), this holds for triplet recombination but not for singlet recombination. Thus, we are led to the conclusion that, in contrast to the interpretation of previous authors(3,4,5], the spin dependent recombination is of the triplet type. For a quantitative interpretation of background curves, the expression --:0:;
dP -‘a+
P dB
has to be calculated which remains still to be done. For
1449
the curve of 4b, a rough estimate shows that it might . . K-3 relate to a polartzatton such as P,,,,_~M, from the occupancy factor f one gets by eqn (2) for this sample (ND =7.8x 10’3cm-2) a value m, = 100. However, the final conclusion depends on a detailed numerical analysis. Since under the condition of EPR the polarization is decreased, the change of conductivity should be opposite to the change due to increasing magnetic field. Apparently, as seen from Fig. 4, the change of conductivity at resonance has the same sign as the change of conductivity of the background signal. Thus, the phase of the signal is anomalous. Under normal conditions, at EPR resonance there is a transition from level 1 to level 2 (Fig. 5). It has been observed[ 121that in taking the EPR signal of dislocation under illumination, the phase of the signal is anomalous, also it has been observed[16] that the Q-factor of the microwave cavity increases under EPR resonance of an illuminated deformed sample. Ah these results point to the fact that there is not a resonant absorption, but a resonant emission of microwave power. Thus, there is a transition from level 2 to level 1 under resonant condition. As an interpretation of this effect, we suggest that due to strong optical excitation the electron system is strongly heated and takes advantage of any channel to cool down. By opening the microwave channel 2-r 1, relaxation of the system to the lowest energy level 1 is enhanced. 5. slJMMARYANDcoNclAlsIoN There are no facts which suggest that the effect of spin dependent recombination is not due to dislocations. The effect is well in accordance with a Shockley-Read type dislocation model and the notion of an occupancy factor. The strength of the effect has been related in accordance with other authors to the strong polarization of exchange coupled paramagnetic dislocation sites. Whether the recombination process is in fact, in contrast to the findings of other authors, of the triplet type as deduced from our experiments, needs further confirmation. Experimentally, it should be fruitful to vary the relative power of photoexcitation and microwave power at resonance in order to get more information on the relationship between the normal and the anomalous phase of the resonant signal. Also, a detailed statistical treatment of the dynamics of the recombination process seems to be necessary for a full understanding of the effect.
CONOUCTION ELECTRONS
Ii DISLOCATION SITES <-?: B=G
TRIPLET RECUdBINATION
SINGLET RECOMBINATIOE;
B:O
2: B*O
Ev Fig. 6. Mechanismsof spin dependent recombination.
1450
D. NEUBEFZT et al.
Acknowledgemenl-We thank W. Moeckel for providing data on the fast recombination process and H. Kuenzel and F. Liepe for assistance in various stages of the work.
WCES I. W. Shockley, Phys. Reu. 91, 228 (1953). 2. W. T. Read, Phil, Mug. 45.775 (1954). 3. D. Lepine, Phys. Rev. E 6, 436 (1972). 4. D. Lepine, V. A. Grazhulis and D. Kaplan, Physics of Semiconducrors (Edited by F. G. Fumi), p. 1081. North-Holland, Amsterdam (1977). 5. T. Wosinski and T. Figielski. Phys. SIalus Solidi (6) 83, 93 (1977). 6. W. Schrater, Phys. Status Solidi 21.211(1%7). 7. D. Neubert. Inst. Phys. Conf. Ser. No. 23, p. 398 (1975). 8. S. R. Morrison, Phys. Rev. 101.619 (1956).
9. H.-J. Kos and D. Neubert. Phvs. Status Solidi la) 44. 259 (1977).
10. V. A. Grazhulis. V. V. Kveder and V. Yu. Nukhina, Phys. Sralus Solidi (a) 43. 407 (1977); 44. 167 (1977). II. H. Alexander, L. Bartelsen and E. Weber, Proc. 5th fnt. Summer School on Dejecrs, p. 89. PWN, Warsaw (1978). 12. T. Wosinsky, Proc. 5th Inr. Summer School on fhzfects, p. 241. PWN, Warsaw (1978). 13. T. L. Hill, Statistical Mechanics. p. 322. McGraw-Hill. New York (1956). 14. W. Opechowski and J. M. Bryan, Canad. J. Phys. 29. 236 (1951). und StromIS. W. Heywang and H. W. P&l. Banderstrktur transport, Halbleiter Elektronik Ed. 3, p. 213. Springer. Berlin (1976). 16. T. Wosinski, T. Figielski and A. Makosa, Phys. Status Solidi (a) 37. KJ7 (1976).