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Determination of the density of states in p-doped hydrogenated amorphous silicon by means of the modulated photocurrent experiment
Journal of Non-Crystalline Solids 164-166 (1993) 423-426 North-Holland
,OURNALO~~ ~ ' ~ d ~ ~l~
Determination of the density of states in p-doped hydrogenated amorphous silicon by means of the modulated photocurrent experiment C. Longeaud a, J.P. Kleider a, D. Mencaraglia a, A. Amaral b, C.N. Carvalho b. aLaboratoire de G6nie Electrique de Paris (CNRS D0127), Ecole Sup6rieure d'Electricit6, Universit6s Paris VI et Paris XI, Plateau de Moulon, 91192 Gif sur Yvette Cedex, France bDept. Fisica, Instituto Superior T6cnico/C.F.M./U.N.L./, av. Rovisco Pais, 1000 Lisboa, Portugal The density of states (DOS) of p - d o p e d a-Si:H has been measured with the M o d u l a t e d Photocurrent (MPC) technique for various concentrations of B2H 6 and B(CH3) 3 in the gas phase during the deposition. For both types of dopant the measured DOS exhibits a large increase with the concentration of dopant. However, the E04 gap decreases when doping with B2H6 whereas it is almost unchanged when doping with B(CH3) 3. The evolution with the concentration of p dopant of the DOS measured by the MPC technique is discussed in the light of models found in the literature. 1. I N T R O D U C T I O N The density of states (DOS) in p - d o p e d a-Si:H has been poorly studied compared with the extensive studies achieved on n d o p e d a-Si:H [1]. However, some behaviours of the pd o p e d a-Si:H have already been put forward, the two major ones being: (i) the decrease of the electronic mobility and lifetime [2] and (ii) the evolution of the absorption spectra whose significant features, from which one could deduce a DOS shape, vanish as soon as the film is highly doped ([B]/[Si]> 0.5 % in the gas phase). This behaviour is accompanied by a diminution of the E04 gap in the case of B2H 6 doping [3], whereas only small changes in the E04 gap are observed for B(CH3)3 d o p e d materials [4]. Both of these features are linked ~o the evolution of the DOS with p doping. It is :he p u r p o s e of this paper to address this 9articular point.
Polytechnique (France) [6]. The B(CH3)3 doped samples were all p r e p a r e d at the Ecole Polytechnique. The films were fitted with coplanar Cr electrodes for current measurements. We present in Fig. 1 the dependence upon the B2H 6 content of dark conductivity parameters along with that of the E04 gap deduced from optical transmission measurements. The B2H 6 doped samples coming from both laboratories exhibited a reduction of the E04 gap with the increase of dopant concentration in the gas phase. On the contrary, the B(CH3) 3 d o p e d materials do not exhibit such a decrease of the (For details [4]). E04 gap see -r"-" ..... 4,~.,L~.~ ~ 10-2 " . I - < ~ ~ ~ -~ g 10_4 ..~ > 104
,,,,-
1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2
-.+
•
'. S A M P L E S ,
METHOD
AND
RESULTS
All the a-Si:H films were obtained in ' E C V D s y s t e m s b y RF glow discharge tecomposition of a mixture of silane and B2H 6 ~r B(CH3) 3. The B2H 6 d o p e d samples were ;laborated either at the Centro de Fisica ¢lolecular (Portugal) [5] or at the Ecole
"~ Ix`` " - ~ - _.v._ _ - x Uo 10-8 . , .,i,. .... . t ?,..if': . . :-,.'f.
0
1
>, ~a
2
B2H6/(B2H6+SiI__I4)(%)
Figure 1. Room temperature dark conductivity (o), E04 gap (+) and activation energy of the dark conductivity (x) versus concentration of dopant in the gas phase
0022-3093/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved.
424
C. Longeaud et al. / Density of states in p doped hydrogenated amorphous silicon
The DOS of intrinsic and p-doped samples was m e a s u r e d b y m e a n s of the M o d u l a t e d P h o t o c u r r e n t (MPC) experiment for various concentrations of boron in the gas phase. In this e x p e r i m e n t we m e a s u r e the m o d u l u s I Iacl a n d the p h a s e shift (I) of the p h o t o c u r r e n t resulting from the illumination with an alternative flux of a biased coplanar sample. The MPC experiment performed at a given temperature T and angular frequency o) can be used to probe the DOS at an energy AEm,T a w a y from the mobility edge Eme of the type of carrier which gives the p r e d o m i n a n t contribution to the m o d u l a t e d photocurrent. AEm,T is given by
AEm,T = ]Eme- Eco,T I = kBT In (v I co),
conduction band tail as d e d u c e d from Time-ofFlight (TOF) e x p e r i m e n t s p e r f o r m e d on intrinsic samples [9]. c-.... ~ 102°! .... ~ " ~ ' . . . . ' . . . . ' . . . . ' .... ' ' " ~ N, ~ 10 m N% m ._,_ ~ \ ~ N, ,.~a 10t6 "~--+,,. o "*-~"" ~>" ~"* "~ 10t4 . . . . ' . . . . . . . . . . . . . . ' . . . . ' .... ' .... ' .... 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ~ I Eme- Em.TI (eV) e
(I)
kB being the Boltzmann constant and v the at-
Figure 2. Evolution of DOS with boron concentration (o) [B/Si] = 0.33 %, (x) [B/Si] = 0.1 ppm, (+) intrinsic. Lines are guides for the eye.
tempt-to-escape frequency. The ratio N(E (0,T) -N(E0),T)/N(Eme) of the DOS at E0),T to that at Eme is then obtained from [7] N ( E m , T ) = - 2 - [ S q " ~ G sin((I))lla~ ac - e0] ,
(2)
In Fig. 3, we present the DOS d e d u c e d from Eqs. (1)-(2) for heavily B2H 6 and B(CH3) 3 doped samples ([B]/[Si] = 0.26 % and 0.33 %, respectively). .-.
where g is the free carrier mobility, ~ is the electric field, S is the c o n d u c t i o n cross s e c t i o n n a l area, G a c is the a l t e r n a t i v e component of the generation rate and q is the absolute value of the electronic charge. Since o) can be n e g l e c t e d in Eq. (2), the M P C experiment actually m e a s u r e s the lowest of
~ 1020 ~ "-" ~ ,~ 1018 "~ >,
electron or hole N(Em,T)V/p ratio, for this ratio determines the p r e d o m i n a n t type of carrier [8]. For a given temperature the frequency of the illumination is varied from 12 Hz to 39.9 kHz in 21 points so that f i + l = f i x l . 5 , a n d the temperature is varied from 420 K to 150 K in 30-K steps. To plot the DOS we have assumed
~
in the following that v=1012 s -1, N(Eme ) = 1021 cm-3eV -1 and ~t= 10 cm2V-ls -1 in Eqs. (1)(2) in order to compare the results. The DOS m e a s u r e d on intrinsic and B(CH3) 3 d o p e d a-Si:H are presented in Fig. 2 where only the points obtained at f = 3.5 k H z at different t e m p e r a t u r e s are d i s p l a y e d for reasons of clarity. As a matter of c o m p a r i s o n we have d r a w n on the figure (full line) the shape of the
,,
>.
,,~
~'~o *Oo +
:" +++% "-.'-.'t~
++"::::.
$88oo++, ~m 1016 . . . . , . . . . , . . . . , . . . . , . . . . i . . . . ~. . . . ~ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
I E ~ - E [o.TI (eV) Figure 3. DOS of heavily boron doped a-Si:H: (o) B ( C H 3 ) 3, (+) B2H 6. All the points for all temperatures and frequencies are displayed. 3. DISCUSSION With extremely low d o p i n g (0.1 p p m of B ( C H 3 ) 3 in the gas p h a s e ) , g i v i n g compensated samples, a drastic increase of the probed DOS is observed, that leads to a b u m p
425
C. Longeaud et al. / Density of states in p doped hydrogenated amorphous silicon
(=1018 cm-3eV -1) at an energy = 0.4 eV from the mobility edge. For a higher concentration of boron in the gas phase ([B]/[Si] = 0.33 %) the b u m p disappears and is replaced by an exponentially varying DOS reaching =1021 cm-3eV -1 at = 0.25 eV from the mobility edge. Note that this high value of the DOS is close to the value usually assumed for the DOS at the band edge. This is obtained because of the v and ~t values taken in Eqs. (1)-(2) to plot the DOS from the experimental data. A decrease of ~t or an increase of v by a factor of ten would lead to a DOS ten times lower (see Eq. (2)). As explained in Sec. 2, we cannot know easily whether the probed DOS has to be scaled from the conduction or the valence band edge. Therefore, two interpretations can be proposed for the observed modifications of the DOS: (i) i n d e p e n d e n t l y of the d o p a n t concentration we always probe the DOS in the u p p e r half of the gap and the disorder i n t r o d u c e d b y the d o p a n t results in a broadening of the conduction band tail that must be accompanied with a much more pronounced enlargement of the valence band tail, or (ii) the increase with the dopant concentration of the DOS in the upper half of the gap is so pronounced that, whereas for low concentrations of dopant we probe the DOS in the upper half of the gap, we probe the DOS in the l o w e r half of the gap for h i g h concentrations of dopant. In both cases, p doping results in a strong increase of the DOS in the upper half of the gap. A choice between these two interpretations can be made in the light of models for the DOS p r o p o s e d by different authors [2,10]. Street [2] suggested that an increase of the DOS in the upper half of the gap results in a Fermi level closer to the valence band edge. This was confirmed by Pierz et al [10] who d e d u c e d an approximate shape of the DOS from Photothermal Deflection Spectroscopy (PDS) or Constant Photocurrent Method (CPM) m e a s u r e m e n t s p e r f o r m e d on the same samples. A possible shape of the DOS of p-doped a-Si:H, and its evolution with dopant concentration is shown on Fig. 4, where the band tail states (full lines) are described by two exponential distributions as found from TOF measurements [9]. According to this model we can explain the results of Fig. 2 in the following way. As the
sample is lightly doped a bump appears close to the band edge (=0.4 eV) in the reconstructed DOS. But, as it can be seen on Fig. 2 (full line), the band tail seems to remain the same for both intrinsic and c o m p e n s a t e d samples. Therefore, since this band tail is the conduction band tail, as found from TOF, we are likely to probe the upper part of the DOS for both samples [11].
.... ~ ~ ~ o ~
' ......
' ' ' / o-"" ......... ( ..... [B1 "" °"°° ~i"* ~it,('''.''''° --,[/.].
/
. . . E
Ec v
Energy
Figure4. Increase of the deep states of p-doped a-Si:H with increase of the dopant concentration. On the opposite, when the sample is heavily doped, the DOS of the upper half of the gap is so huge that we are likely to probe the valence band tail. Moreover, though we expected different DOS shapes from one dopant to the other because of the different evolutions of the E04 gap [4], the two DOS plotted in Fig. 3 are quite similar. For both types of dopant the characteristic energies of the exponentially decreasing DOS are of the order of 32 meV, a value that is much lower than the values ranging from 45 meV for the best intrinsic samples to 70 meV for the highly d o p e d samples - of the Urbach tail usually reported [4,10]. However, even if we choose different values for the parameters used to reconstruct the DOS (~t and v essentially), as suggested at the beginning of this section, the valence band tail has to flatten for this band tail to reach N(Ev). Note that the slope of the valence band tail we deduced from the MPC experiment corresponds to what was already found in TOF experiments performed on intrinsic samples [9]. In the energy range probed by means of the MPC technique, it does not seem that the valence b a n d tail is m o d i f i e d b y the introduction of dopants. If such a modification
426
C. Longeaud et al. / Density of states in p doped hydrogenated amorphous silicon
occurred, as suggested by some authors [12], it should be in the 0.2 eV range of energy of the valence band tail too close to the band edge to be probed by the MPC technique, Finally, the valence band tail seems to be much steeper than what is found from the Urbach tail [10]. Actually, the Urbach tail, as m e a s u r e d from PDS, is the result of a convolution between the full states from which an electron can be extracted by the light and the empty ones that can accept this electron, Thus, its variations with hv are dominated by the highest part of the DOS, that is the upper part of the valence band tail which is not probed by the MPC experiment. Consequently, even in undoped samples, the Urbach tail essentially depends on the part of the f u l l states of the valence band tail that flattens close to the band edge. This can be easily demonstrated by means of a numerical simulation calculating the convolution product giving the absorption coefficient [13]. In the same way, since an optical transition only needs a full and an e m p t y states, an increase of the empty states in the upper half of the gap will result in an increase of the absorption coefficient and, consequently, in a decrease of the E04 gap, generally associated with a complete disparition of the Urbach tail. According to our results this is certainly what occurs in the case of heavily B2H 6 d o p e d samples. Though the probed DOS seem to be identical (see Fig. 3), the fact that such a decrease of the E04 gap is not observed in B(CH3) 3 d o p e d samples for extremely high concentrations of dopant in the gas phase ([B]/[Si] > 1 % ) is p r o b a b l y due to an incorporation of carbon into the layer resulting in a simultaneous increase of E04. 4. CONCLUSIONS The application of the MPC experiment to p - d o p e d s a m p l e s confirms the p r e v i o u s models: p doping results in a strong increase of the DOS in the upper half of the gap. Such an increase can explain the decrease of the E04 gap in B2H6 d o p e d samples. In B(CH3)3 doped samples this decrease of E04 is probably balanced by the incorporation of carbon into the layer.
Another important point is that the valence band tail slope d e d u c e d from the MPC technique is steeper than the slope deduced from the Urbach tail, and does not seem to be altered by the introduction of dopants. ACKNOWLEDGEMENTS We thank P. Roca i Cabarrocas for the deposition of the doped samples at the Ecole Polytechnique. This w o r k was partially supported by PIRSEM-CNRS, ADEME, and JNICTcontracts. REFERENCES 1. M. Stutzmann, D.K. Biegelsen and R.A. Street, Phys. Rev. B, 35 (1987) 5666. 2. R.A. Street, J. of Non Cryst. Solids, 77&78 (1985) 1. 3. Y. Hamakawa, Annual Research Report of the Semiconductor Laboratory, Osaka University (1985) 54. 4. A. Lloret, Z.Y. Wu, M.L. Th6ye, I. E1 Zawawi, J.M. Siefert and B. Equer, Appl. Phys. A, 55 (1992) 573. 5. A. Amaral, L.Rodrigues, L. Guimaraes, R. Martins, D. Mencaraglia, Z. Djebbour, J.P. Kleider and C. Longeaud, Proceedings of the 10 th European Photovoltaic Solar Energy Conference, Lisbon, Portugal, Kluwer Academic Publishers, (1991)368. 6. P. Roca i Cabarrocas, J.B. Chevrier, J. Huc, A Lloret, J.Y. Parey and J.P.M. Schmitt, J. Vac. ScienceTech. A, 9(1991) 2331. 7. R. Br6ggemann, C. Main, J. Berkin and S. Reynolds, Phil. Mag. B, 62 (1990) 29. 8. C. Longeaud and J.P. Kleider, Phys. Rev. B, 45 (1992) 11672. 9. R. Vanderhaghen, C. Longeaud, Journal of non Cryst. Solids, 114 (1989) 540. 10.K. Pierz, W. Fuhs and H. Mell, Phil. Mag B, 63 (1991) 133. 11.J.P. Kleider, C Longeaud and O. Glodt, Journal of non Cryst. Solids, 137&138 (1991) 447. 12.B. Von Roedern, L. Ley, M. Cardona and F.W. Smith, Phil. Mag. B, 40 (1979) 433. 13.If the reader is interested, we can send a copy of the software.
,OURNALO~~ ~ ' ~ d ~ ~l~
Determination of the density of states in p-doped hydrogenated amorphous silicon by means of the modulated photocurrent experiment C. Longeaud a, J.P. Kleider a, D. Mencaraglia a, A. Amaral b, C.N. Carvalho b. aLaboratoire de G6nie Electrique de Paris (CNRS D0127), Ecole Sup6rieure d'Electricit6, Universit6s Paris VI et Paris XI, Plateau de Moulon, 91192 Gif sur Yvette Cedex, France bDept. Fisica, Instituto Superior T6cnico/C.F.M./U.N.L./, av. Rovisco Pais, 1000 Lisboa, Portugal The density of states (DOS) of p - d o p e d a-Si:H has been measured with the M o d u l a t e d Photocurrent (MPC) technique for various concentrations of B2H 6 and B(CH3) 3 in the gas phase during the deposition. For both types of dopant the measured DOS exhibits a large increase with the concentration of dopant. However, the E04 gap decreases when doping with B2H6 whereas it is almost unchanged when doping with B(CH3) 3. The evolution with the concentration of p dopant of the DOS measured by the MPC technique is discussed in the light of models found in the literature. 1. I N T R O D U C T I O N The density of states (DOS) in p - d o p e d a-Si:H has been poorly studied compared with the extensive studies achieved on n d o p e d a-Si:H [1]. However, some behaviours of the pd o p e d a-Si:H have already been put forward, the two major ones being: (i) the decrease of the electronic mobility and lifetime [2] and (ii) the evolution of the absorption spectra whose significant features, from which one could deduce a DOS shape, vanish as soon as the film is highly doped ([B]/[Si]> 0.5 % in the gas phase). This behaviour is accompanied by a diminution of the E04 gap in the case of B2H 6 doping [3], whereas only small changes in the E04 gap are observed for B(CH3)3 d o p e d materials [4]. Both of these features are linked ~o the evolution of the DOS with p doping. It is :he p u r p o s e of this paper to address this 9articular point.
Polytechnique (France) [6]. The B(CH3)3 doped samples were all p r e p a r e d at the Ecole Polytechnique. The films were fitted with coplanar Cr electrodes for current measurements. We present in Fig. 1 the dependence upon the B2H 6 content of dark conductivity parameters along with that of the E04 gap deduced from optical transmission measurements. The B2H 6 doped samples coming from both laboratories exhibited a reduction of the E04 gap with the increase of dopant concentration in the gas phase. On the contrary, the B(CH3) 3 d o p e d materials do not exhibit such a decrease of the (For details [4]). E04 gap see -r"-" ..... 4,~.,L~.~ ~ 10-2 " . I - < ~ ~ ~ -~ g 10_4 ..~ > 104
,,,,-
1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2
-.+
•
'. S A M P L E S ,
METHOD
AND
RESULTS
All the a-Si:H films were obtained in ' E C V D s y s t e m s b y RF glow discharge tecomposition of a mixture of silane and B2H 6 ~r B(CH3) 3. The B2H 6 d o p e d samples were ;laborated either at the Centro de Fisica ¢lolecular (Portugal) [5] or at the Ecole
"~ Ix`` " - ~ - _.v._ _ - x Uo 10-8 . , .,i,. .... . t ?,..if': . . :-,.'f.
0
1
>, ~a
2
B2H6/(B2H6+SiI__I4)(%)
Figure 1. Room temperature dark conductivity (o), E04 gap (+) and activation energy of the dark conductivity (x) versus concentration of dopant in the gas phase
0022-3093/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved.
424
C. Longeaud et al. / Density of states in p doped hydrogenated amorphous silicon
The DOS of intrinsic and p-doped samples was m e a s u r e d b y m e a n s of the M o d u l a t e d P h o t o c u r r e n t (MPC) experiment for various concentrations of boron in the gas phase. In this e x p e r i m e n t we m e a s u r e the m o d u l u s I Iacl a n d the p h a s e shift (I) of the p h o t o c u r r e n t resulting from the illumination with an alternative flux of a biased coplanar sample. The MPC experiment performed at a given temperature T and angular frequency o) can be used to probe the DOS at an energy AEm,T a w a y from the mobility edge Eme of the type of carrier which gives the p r e d o m i n a n t contribution to the m o d u l a t e d photocurrent. AEm,T is given by
AEm,T = ]Eme- Eco,T I = kBT In (v I co),
conduction band tail as d e d u c e d from Time-ofFlight (TOF) e x p e r i m e n t s p e r f o r m e d on intrinsic samples [9]. c-.... ~ 102°! .... ~ " ~ ' . . . . ' . . . . ' . . . . ' .... ' ' " ~ N, ~ 10 m N% m ._,_ ~ \ ~ N, ,.~a 10t6 "~--+,,. o "*-~"" ~>" ~"* "~ 10t4 . . . . ' . . . . . . . . . . . . . . ' . . . . ' .... ' .... ' .... 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ~ I Eme- Em.TI (eV) e
(I)
kB being the Boltzmann constant and v the at-
Figure 2. Evolution of DOS with boron concentration (o) [B/Si] = 0.33 %, (x) [B/Si] = 0.1 ppm, (+) intrinsic. Lines are guides for the eye.
tempt-to-escape frequency. The ratio N(E (0,T) -N(E0),T)/N(Eme) of the DOS at E0),T to that at Eme is then obtained from [7] N ( E m , T ) = - 2 - [ S q " ~ G sin((I))lla~ ac - e0] ,
(2)
In Fig. 3, we present the DOS d e d u c e d from Eqs. (1)-(2) for heavily B2H 6 and B(CH3) 3 doped samples ([B]/[Si] = 0.26 % and 0.33 %, respectively). .-.
where g is the free carrier mobility, ~ is the electric field, S is the c o n d u c t i o n cross s e c t i o n n a l area, G a c is the a l t e r n a t i v e component of the generation rate and q is the absolute value of the electronic charge. Since o) can be n e g l e c t e d in Eq. (2), the M P C experiment actually m e a s u r e s the lowest of
~ 1020 ~ "-" ~ ,~ 1018 "~ >,
electron or hole N(Em,T)V/p ratio, for this ratio determines the p r e d o m i n a n t type of carrier [8]. For a given temperature the frequency of the illumination is varied from 12 Hz to 39.9 kHz in 21 points so that f i + l = f i x l . 5 , a n d the temperature is varied from 420 K to 150 K in 30-K steps. To plot the DOS we have assumed
~
in the following that v=1012 s -1, N(Eme ) = 1021 cm-3eV -1 and ~t= 10 cm2V-ls -1 in Eqs. (1)(2) in order to compare the results. The DOS m e a s u r e d on intrinsic and B(CH3) 3 d o p e d a-Si:H are presented in Fig. 2 where only the points obtained at f = 3.5 k H z at different t e m p e r a t u r e s are d i s p l a y e d for reasons of clarity. As a matter of c o m p a r i s o n we have d r a w n on the figure (full line) the shape of the
,,
>.
,,~
~'~o *Oo +
:" +++% "-.'-.'t~
++"::::.
$88oo++, ~m 1016 . . . . , . . . . , . . . . , . . . . , . . . . i . . . . ~. . . . ~ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
I E ~ - E [o.TI (eV) Figure 3. DOS of heavily boron doped a-Si:H: (o) B ( C H 3 ) 3, (+) B2H 6. All the points for all temperatures and frequencies are displayed. 3. DISCUSSION With extremely low d o p i n g (0.1 p p m of B ( C H 3 ) 3 in the gas p h a s e ) , g i v i n g compensated samples, a drastic increase of the probed DOS is observed, that leads to a b u m p
425
C. Longeaud et al. / Density of states in p doped hydrogenated amorphous silicon
(=1018 cm-3eV -1) at an energy = 0.4 eV from the mobility edge. For a higher concentration of boron in the gas phase ([B]/[Si] = 0.33 %) the b u m p disappears and is replaced by an exponentially varying DOS reaching =1021 cm-3eV -1 at = 0.25 eV from the mobility edge. Note that this high value of the DOS is close to the value usually assumed for the DOS at the band edge. This is obtained because of the v and ~t values taken in Eqs. (1)-(2) to plot the DOS from the experimental data. A decrease of ~t or an increase of v by a factor of ten would lead to a DOS ten times lower (see Eq. (2)). As explained in Sec. 2, we cannot know easily whether the probed DOS has to be scaled from the conduction or the valence band edge. Therefore, two interpretations can be proposed for the observed modifications of the DOS: (i) i n d e p e n d e n t l y of the d o p a n t concentration we always probe the DOS in the u p p e r half of the gap and the disorder i n t r o d u c e d b y the d o p a n t results in a broadening of the conduction band tail that must be accompanied with a much more pronounced enlargement of the valence band tail, or (ii) the increase with the dopant concentration of the DOS in the upper half of the gap is so pronounced that, whereas for low concentrations of dopant we probe the DOS in the upper half of the gap, we probe the DOS in the l o w e r half of the gap for h i g h concentrations of dopant. In both cases, p doping results in a strong increase of the DOS in the upper half of the gap. A choice between these two interpretations can be made in the light of models for the DOS p r o p o s e d by different authors [2,10]. Street [2] suggested that an increase of the DOS in the upper half of the gap results in a Fermi level closer to the valence band edge. This was confirmed by Pierz et al [10] who d e d u c e d an approximate shape of the DOS from Photothermal Deflection Spectroscopy (PDS) or Constant Photocurrent Method (CPM) m e a s u r e m e n t s p e r f o r m e d on the same samples. A possible shape of the DOS of p-doped a-Si:H, and its evolution with dopant concentration is shown on Fig. 4, where the band tail states (full lines) are described by two exponential distributions as found from TOF measurements [9]. According to this model we can explain the results of Fig. 2 in the following way. As the
sample is lightly doped a bump appears close to the band edge (=0.4 eV) in the reconstructed DOS. But, as it can be seen on Fig. 2 (full line), the band tail seems to remain the same for both intrinsic and c o m p e n s a t e d samples. Therefore, since this band tail is the conduction band tail, as found from TOF, we are likely to probe the upper part of the DOS for both samples [11].
.... ~ ~ ~ o ~
' ......
' ' ' / o-"" ......... ( ..... [B1 "" °"°° ~i"* ~it,('''.''''° --,[/.].
/
. . . E
Ec v
Energy
Figure4. Increase of the deep states of p-doped a-Si:H with increase of the dopant concentration. On the opposite, when the sample is heavily doped, the DOS of the upper half of the gap is so huge that we are likely to probe the valence band tail. Moreover, though we expected different DOS shapes from one dopant to the other because of the different evolutions of the E04 gap [4], the two DOS plotted in Fig. 3 are quite similar. For both types of dopant the characteristic energies of the exponentially decreasing DOS are of the order of 32 meV, a value that is much lower than the values ranging from 45 meV for the best intrinsic samples to 70 meV for the highly d o p e d samples - of the Urbach tail usually reported [4,10]. However, even if we choose different values for the parameters used to reconstruct the DOS (~t and v essentially), as suggested at the beginning of this section, the valence band tail has to flatten for this band tail to reach N(Ev). Note that the slope of the valence band tail we deduced from the MPC experiment corresponds to what was already found in TOF experiments performed on intrinsic samples [9]. In the energy range probed by means of the MPC technique, it does not seem that the valence b a n d tail is m o d i f i e d b y the introduction of dopants. If such a modification
426
C. Longeaud et al. / Density of states in p doped hydrogenated amorphous silicon
occurred, as suggested by some authors [12], it should be in the 0.2 eV range of energy of the valence band tail too close to the band edge to be probed by the MPC technique, Finally, the valence band tail seems to be much steeper than what is found from the Urbach tail [10]. Actually, the Urbach tail, as m e a s u r e d from PDS, is the result of a convolution between the full states from which an electron can be extracted by the light and the empty ones that can accept this electron, Thus, its variations with hv are dominated by the highest part of the DOS, that is the upper part of the valence band tail which is not probed by the MPC experiment. Consequently, even in undoped samples, the Urbach tail essentially depends on the part of the f u l l states of the valence band tail that flattens close to the band edge. This can be easily demonstrated by means of a numerical simulation calculating the convolution product giving the absorption coefficient [13]. In the same way, since an optical transition only needs a full and an e m p t y states, an increase of the empty states in the upper half of the gap will result in an increase of the absorption coefficient and, consequently, in a decrease of the E04 gap, generally associated with a complete disparition of the Urbach tail. According to our results this is certainly what occurs in the case of heavily B2H 6 d o p e d samples. Though the probed DOS seem to be identical (see Fig. 3), the fact that such a decrease of the E04 gap is not observed in B(CH3) 3 d o p e d samples for extremely high concentrations of dopant in the gas phase ([B]/[Si] > 1 % ) is p r o b a b l y due to an incorporation of carbon into the layer resulting in a simultaneous increase of E04. 4. CONCLUSIONS The application of the MPC experiment to p - d o p e d s a m p l e s confirms the p r e v i o u s models: p doping results in a strong increase of the DOS in the upper half of the gap. Such an increase can explain the decrease of the E04 gap in B2H6 d o p e d samples. In B(CH3)3 doped samples this decrease of E04 is probably balanced by the incorporation of carbon into the layer.
Another important point is that the valence band tail slope d e d u c e d from the MPC technique is steeper than the slope deduced from the Urbach tail, and does not seem to be altered by the introduction of dopants. ACKNOWLEDGEMENTS We thank P. Roca i Cabarrocas for the deposition of the doped samples at the Ecole Polytechnique. This w o r k was partially supported by PIRSEM-CNRS, ADEME, and JNICTcontracts. REFERENCES 1. M. Stutzmann, D.K. Biegelsen and R.A. Street, Phys. Rev. B, 35 (1987) 5666. 2. R.A. Street, J. of Non Cryst. Solids, 77&78 (1985) 1. 3. Y. Hamakawa, Annual Research Report of the Semiconductor Laboratory, Osaka University (1985) 54. 4. A. Lloret, Z.Y. Wu, M.L. Th6ye, I. E1 Zawawi, J.M. Siefert and B. Equer, Appl. Phys. A, 55 (1992) 573. 5. A. Amaral, L.Rodrigues, L. Guimaraes, R. Martins, D. Mencaraglia, Z. Djebbour, J.P. Kleider and C. Longeaud, Proceedings of the 10 th European Photovoltaic Solar Energy Conference, Lisbon, Portugal, Kluwer Academic Publishers, (1991)368. 6. P. Roca i Cabarrocas, J.B. Chevrier, J. Huc, A Lloret, J.Y. Parey and J.P.M. Schmitt, J. Vac. ScienceTech. A, 9(1991) 2331. 7. R. Br6ggemann, C. Main, J. Berkin and S. Reynolds, Phil. Mag. B, 62 (1990) 29. 8. C. Longeaud and J.P. Kleider, Phys. Rev. B, 45 (1992) 11672. 9. R. Vanderhaghen, C. Longeaud, Journal of non Cryst. Solids, 114 (1989) 540. 10.K. Pierz, W. Fuhs and H. Mell, Phil. Mag B, 63 (1991) 133. 11.J.P. Kleider, C Longeaud and O. Glodt, Journal of non Cryst. Solids, 137&138 (1991) 447. 12.B. Von Roedern, L. Ley, M. Cardona and F.W. Smith, Phil. Mag. B, 40 (1979) 433. 13.If the reader is interested, we can send a copy of the software.