- Email: [email protected]
Capacitance-voltage measurements on metal-SiO2-boron-doped homoepitaxial diamond
D|AMOND AND
R TI@ LAT RIAL$ Diamond and Related Materials O ( 1997 ) 852 855
ELSEVIER
Capacitance-voltage measurements on metal-SiO2-boron-doped homoepitaxial diamond T. Inushima a.,, T. Nakama a, T. Shiraishi a, M. Mitsuhashi b T. Watanabe b a Department ~/'Communications Enghteerhzg, Tokai University, 1117 Kitakaname. Hiratsuka, Kanagawa 259-12, Japan b Kanagawa buhtstrkd Technology Research b~stitute, 705-1 Simoimaizumi, Ebina, Kanagawa 243-04, Japan
Abstract
A metal-SiO_,-boron-doped homoepitaxial diamond MIS structure was fabricated on (100) substrates of type lb synthetic diamond. Capacitance-voltage characteristics were measured tbr various boron concentrations and it was concluded that when the impurity concentration increased, an impurity band was formed 0.35 eV above the valence band which was composed of the excited state of the boron impurity and its phonon sideband. When the impurity concentration increased, the capacitance of the MIS structure decreased and the equilibrium density of holes in the films also decreased. With this impurity band the film works as a metal electrode. © 1997 Elsevier Science S.A.
Keywords." Homoepitaxy; Impurities; Electrical properties: Band structure
I. Introduction For the device application of diamond, a metal-insulator-semiconductor (MIS) structure is fundamental and is a powerful tool for understanding the impurity type and carrier number in semiconducting diamond. As for the impurities in diamond, boron is known to be the only one that works as a p,type dopant. There are two conduction mechanisms reported for p-type diamond: one is the band conduction of the carriers excited from the boron impurity [1]. The reported activation energy determined from the slope of the temperature dependence of the carrier number is 0.35-0.38 eV [2]. The other mechanism is impurity conduction, which is established by the overlap of the wavefunction of impurities [31. The mechanism of impurity conduction has been investigated since the 1960s, especially in Ge and Si, and it is now well established that the conduction mechanism changes from band conduction to impurity conduction when the dopant concentration increases and temperature is low [4]. Because of the shallow impurity level of Si and Ge, it is not clear whether the impurity band is isolated from the conduction (valence) band or merges with it. In diamond, on the other hand, * Corresponding author. 0925-9635/97/$17.00 © 1997 Elsevier Science S.A. All rights reserved. PII S0925-9635 ( 96)00723-6
the acceptor level is so deep (0.37 eV ) that the impurity conduction is discussed in terms of hopping conduction [3], and in heavily boron-doped samples of 2× 102°/cm3, it is considered that a metal insulator transition is realized [5,6]. In this report, we present the existence of tin impurity band formed in boron-doped homo-epitaxial diamond films detected by means of infrared spectroscopy. When the impurity band is formed in the midgap of the diamond, the C-V characteristics of the MIS structure are modified by the presence of the band, the experimental data for which are presented and the influence of the impurity band is discussed.
2. Experiments The diamond films were grown by a hot-filamentassisted chemical vapor deposition method using H2, CH4 and B203 diluted with C2HsOH and keeping the reaction pressure at 25Torr. The substrates were synthesized Ib diamonds with a size of 1.5 x 2 mm 2 and deposition was performed on chemically polished (100) surfaces. The impurity concentration was changed by varying the flow rate of B203 diluted with C2H5OH. Hence in this report the films denoted 10, 100, 1000,
"~ bm~hima ct al.
Diamomt . . d Rcl~m',l .llalcr'(,ds 6
5000, l0 0i~0 and 30 ~00 ppm are ~.he nominal B/C ratios in ',he reaction ~,..,:~,'~The ac~.n,~ percen~ee~ oF boro~ i~1 the films ~as not determined. The deposithm time was 3 h and lhe deposited ~hickness 4.5 ~m~. A trial to de,ermine the boron c~mcm~ra~ion in the fihns uqno the infrared absorption oi the one-phomm band was not ~,llccCssfld dltc to the strong correlation bctx~ccn tb.c oncphonon band and the excited state of the boron impurity. The deposited fihn was investigated by RHEED measurements and homoepitaxial growth was confirmed by observitag the (100t streak pattern of the film. To obtain the absorption coefficients of the deposited films, the transmitted intensity of the fihns was normalized to that of the substrate with no lilm on it, where no reflection correction was made. To investigate the accumulation and depletion characteristics of impurity-doped homoepitaxial diamond, capacitance-voltage (C-V) measurements on a metal-insulator-semiconductor (MIS) structure were carried OUt. The gate-insulator SiO 2 was deposited using an :..f. magnetron sputtering system, where synthesized SlOe was used as a target, and Ar containing 28% 02 as sputtering gas. The deposited SiO, thickness was 180 nm. Evaporated ah:minum was used as the gateelectrode with a size of 0.5 mm diameter, The measurement frequency was l kHz and the an-plitude was 0.05 V.
3. Results and discussion 3.1.
Ai~.vm?~tio, s p e c t r a
Fig. 1 shows the absorption spect,'a of homoepitaxi'd diamonds with different impurity concentrations. When the boron concentration is low, three shar? peaks are observed at 0.30, 0.35 and 0.51 eV. The peak at 0.51 eV is the optical phonon sideband associated with the peak at 0.35 eV, which is due to the transition of the hole 41100
• It
I
~4~-"-'-"
3000
I
'
I
30000 ppm
19971 ~V52 S'55
S:3
trapped at lhe boron mmurit:., to the second excited sta~e el" the accepmr [7]. The hall:width of ~he absorption a~ (},3S eV, which is reported to be se=lsitive to crys,alb inhy [8], is l0 meV and this value is similar to those of naturM [7] and plasma enhanced CVD diamond [9]. When the impurity concentration exceeds l0 000 ppm ti~c absorpt~ot~ spectrum changes drastically and the absorption commencing at the Raman phonon energy 10.I65 eV) extending to the lower energy side becomes observable having the den:,ity of state of the optical phonon. The peak at 0.16 eV is the maximum of the density of state of the TO phonon branch. At the same time the absorption coefficient around 0.35 eV increases drastically, governing the absorption from the infrared to visnble region. The absorption consis,.~ of two peaks. which are the excited ~tates of the boron impurity at 0.35eV al:d its optical phonon sideband at 0.51 eV. which indicates that there is a strong electron-phonon interaction in this film. From 1000 to 5000ppm. there is an increase of absorption in the enerov=, reeion,_ above 0.35 eV, which is thought to be due to continuur~, absc, rption resulting from photo-ionization of acceptors commencing at 0.365 eV [7, 10]. The drastic change of the absorption spectrum between 5000 and 10 000 ppm is difficult to explain by continuum absorption. There is a strong electron-phonon interaction in the l e(100ppm spectrum, hence the absorption change is understood to be due to the change of optical transition, that is fi'om direct transition between intra-impurity states to indirect transition between the ground state of the impurity and its excited states with momentum k. In lhis case the momentunl selection rule is released by the strong electron phonon interaction and lhe absorption spectrum is expressed by a Lorentz oscillator model. The absorption coefficient in this model is expressed by the dielectric functions q and e , , which are given by the resonance energy COo, broadening factor F and carrier number N in the form of plasma frequency ~o~ = N e 2 / e d n h . In diamond, nth is the effective mass of the conduction hole and e~ is the bulk dielectric constant. Then the absorption coefficient ~ is given by e~ and ea as
/ \/,00o0 m
.,~ ,,= 2000
where .~ !000
ppm
0.5
i
1.5
i0 ppm"
2
2.5
Photon energy eeVl Fig. 1. Absorption spectra of diamond films with various boron concentrations.
(,,g -,,?) el = ! + (,J~,
,
,
(O~o - co2 )2 + F-"to-
and e 2 =co~,
/"O)
)2 In order to reproduce (c,J~ -c,? + F2o~2 the absorption spectrum of the 10 000 ppm film given in Fig. 2, we used the standard parameters of diamond: ,
854
T. bmshima et al. ; Diamoml and Rehucd Materials 6 (1997) 852 +855
3t~0
251RI ":-
40110
2(RR) ,~
1500
a
30oo|L r \
-
20o0
I
3000
-~
me,is,,r ,J
- 2000
,.=
Z = ,-
20oo
[_
¢ 10OO
,°°i 0
0 0
0.5
I i.5 Photon energy levi
2
-.-~
'~
°
,o®
.~ <
I~ ]
o
-
1000
calculated "La
2.5
Fig. 2. Theoretical fitting of the absorption spectrum of the 10 000 ppm boron-doped diamond film.
mh=O.75mo, ¢r=5.7, and from the peak position of the absorption, COo=0.35 eV. F is obtained from F = h/r and z is the lifetime of carriers obtained from the conductivity. The solid line in Fig. 2 is obtained from N= 10t9/cm 3 and F=0.75 eV (a resistivity of 0.3 f~ cm), which are reasonable numbers for the 10 000 ppm film. The solid line given by Eq. (1) has some difficulty in reproducing absorption coefficients in the energy region below 0.35 eV. This discrepancy is reduced by introducing Fano interference, which occurs between the firstorder transition with conserved momentum and the second-order transition assisted by phonon momentum k [11]. When we set the so-called Fano asymmetry factor q=0.3, the index of the strength of the configuration interaction V= 0.1 eV and the shift of the resonance energy F = - 0 . 1 eV, the absorption spectrum fits well with the dashed line shown in Fig. 2. The result that the absorption spectrum is expressed by a Lorentzian function indicates that the impurity band is formed 0.35 eV above the valence band. Hence two bands exist in heavily doped homoepitaxial diamond, When the impurity concentration increases from 10 000 to 30 000 ppm, the absorption coefficient increases about 500 cm-~ over the whole energy region keeping the Lorentzian shape. This is due to free carrier absorption. The absorption spectrum of the 30 000 ppm film, which is shown in Fig. 3, can be reproduced by adding a Drude term which is obtained directly from Eq, (1) by equating the term COo=0. For the fitting procedure, we used the same Lorentzian term given in Fig. 2 for simplicity, and for the Drude term N = 1 × 10Xg/cm3 and F=2.2 eV are used. In this model the free carriers in the 30 000 ppm film exist in the impurity band and there is a gap of 0.35 eV between the valence and impurity bands. 3.2. C- V measurements
The MIS structure used in this experiment is shown in Fig. 4. Typical C - V data for the 100, 1000, and l0 000 ppm films are shown in Fig. 5 The fiat-band
0
0.5
1 1.5 Photon energy (eV)
,.'~
2.5
Fig. 3. Theoretical fitting of the absorption spectrum of the 30 003 ppm boron-doped diamond film.
: :.:.:.:.:.:
: : : :,:,:.:.:.:.:
p-:l-ype Diamond: ::
:::.:
Type
:.: : : : : : : : :
____] v
:.:
zl;Su~: :
::.:
I b Diamcnd Substrate : 0.Smm
(a)
(b)
(c)
Fig, 4. (a) Schematic drawing of the diamond MIS structure used in this experiment. (b) The equivalent circuit for the MIS structure when the doping concentration is low. (c) The equivalent circuit for the MIS structure when the doping concentration is high.
3
I 0 I~
~ 2 10 t l
-
,~
100 ppm
" o
=
~.
j
0 -15
1000 ppm
-10
-5
R
10000 ppm
0
~
5
10
15
Bias voltage (V) Fig. 5. MIS capacitance-voltage curves for the 100, 1000 and 10 000 ppm fihns.
voltage of our MIS structure is 3.2 V [12]. When the impurity concentration is 100 ppm, the C-Vcurve shows good accumulation in a negative-bias condition, as is expected for a p-type semiconductor. When the MIS structure is biased into depletion, the C-V curve shows no indication of minority-carrier electron accumulation at the diamond-SiO2 interface. This feature was also
7~ bmshima c{ al.... Diamomt am/ Related Materials 6 ~ 1997) ,~52 855
reported by Geis et al. [12]. In an accumulation condition (negativeUy biased) the obtained capacitance is 29 pF, which is 80% of the ideal capacitance t36 pg t. When the impurity concentration is 1000 ppm. we can see accumulation in negative-bias condition, but the obtained capacitance is 6 pF. which is only n6% of the ideal value. When the concentration is t0 000 ppm, the MIS structure shows a small capacitance (< 1 pF) with a weak bias-voltage dependence. This is due to the metallic condition of the deposited film. In this case the diamond MIS structure is regarded to have a series connection of two capacitors, where the deposited diamond film functions as a metal electrode, and the diamond substrate and the SiO2 film function as insulators. A schematic drawing of this structure is given in Fig. 41c) and the expected capacitance is 0.9 pF. The theoretical curves obtained by Sze (Ref. [13], chapt. 7, Eqs. (20)~ (25) and (49)) are given in Fig. 6. For the fitting procedure, we used npo=O (npo=equilibrium density of electrons), T= 300 K, and =5 V. In this case Ppo (equilibrium density of holes) is the only fitting parameter, and for c t n , and for the the 100 ppm film, Ppo = 2.5 x 10 ~5/,__3 1000 ppm film pp0=2.4x 1 0 t 4 / c m 3. The result that the Pp0 of the 1000 ppm film is one-tenth of that of the 100 ppm film is in good agreement with the fact that the 1000 ppm film shows a smaller capacitance than the 100 ppm film in a negative-biased condition. When the boron concentration increases in the diamond film, the density of the impurity is not uniformly distributed in the film and is higher than the average density in some
5 I() ::~ Z-, 4 10 's :"- 3 102a ID
g
g
il
|
|
P
o 1000 ppm [] 100 ppm - - - 1000 ppm (theoretic) 100 ppm (theoretic)
P p
-
?
? •~ 2 I0 '3 4
rO I 1023 ,,.,,-
0
g io ~ o.,..2,ooo2 ,:,.~ o ~ -10
-5
~ ~ 0
~
5
_..~
~-
l0
15
Bias voltage (V) Fig. 6. Calculated data fitted to experimental data for 100 :and 1000 ppm films by assuming l,'Fu= 5 V.
855
parts of the film. ~n this case the wavel\mctions of the excited state of the impurity begin to overlap to form an impurity band ha the forbidden band gap of diamond. Therefore~ the expected capacitance is the parallel connection of two capacitors, which are given in Figs. 4tbl and ~c). Hence, when the impurity concentration increases, the proportion of the capacitance given in Fig. 4(b) decreases and the proportion of the capacitance given in Fig. 4(c) increases. As a result, when the impurity concentration increases, the obtained capacitance decreases, and the nominal Ppo becomes small, and finally we see the metallic condition of the deposited diamond.
4. Conclusion Optical investigations performed on boron-doped homoepitaxial diamonds reveal the presence of an impurity band which was formed 0.35 eV above the ground state of the boron impurity. This band was composed of the excited state of the impurity and its phonon sideband. Capacitance-voltage characteristics of the metal-SiOz-boron-doped homoepitaxial diamond MIS structure were measured for various boron concentrations and it was shown that when the impurity concentration increased, this impurity band functioned as a metallic electrode in the diamond.
References [ ! ] A.W.S. Williams, E.C. Lightowlers and A.T. Collins, J. Phys. C. 3 (197{) ) ! 727. [2] A.I-. Collins and A.W.S. Williams, J. Phr.s.C. 4 ( 1971 ) 1789. [3] B, Massarani, J.C. Bourgom and R.M. Chrenko. Phvx. Rev. B. 17 (1978) 1758. [4] H. Fritzsche and M. Cuevas, Phys. Rev., 119 (1960) 1238. [5] H. Shiomi, Y. Nishibashi and N. Fujimori, Jpn. J. Appl. Phys., 30 (1991) 1363. [6] M. Werner et al., AppI. Phys. Lett,. 04 (1994) 595. [7] S,D. Smith and W. Taylor, Proc. Phys. Sot., 79 (1962) 1142. [8] P.T. Wedepohl, Proc. Phys. Sot'., 70 (1956) 177. [9] A. Ogasawara, T. Inushima, T. Shiraisi, S. Ohoya S. Karasawa and T. Shiomi, this volume. [10] G. Janssen, W.J.P. Van Enckevort, W. Voilenberg and L.J. Giliing, Diamond Relat. Mater.. 1 (1992) 789. [11] U. Fano, Phys. Rev.. 124 (1961) 1866. [12] M.W. Geis, J.A. Gregory and B.B. Pate, IEEE Trans. Electron Devices, ED-38 ( 1991 ) 619. [13] M. Sze, Physics of Semiconductor Devices, 2nd edn., Wiley, New York, 1981. chapt. 7.
R TI@ LAT RIAL$ Diamond and Related Materials O ( 1997 ) 852 855
ELSEVIER
Capacitance-voltage measurements on metal-SiO2-boron-doped homoepitaxial diamond T. Inushima a.,, T. Nakama a, T. Shiraishi a, M. Mitsuhashi b T. Watanabe b a Department ~/'Communications Enghteerhzg, Tokai University, 1117 Kitakaname. Hiratsuka, Kanagawa 259-12, Japan b Kanagawa buhtstrkd Technology Research b~stitute, 705-1 Simoimaizumi, Ebina, Kanagawa 243-04, Japan
Abstract
A metal-SiO_,-boron-doped homoepitaxial diamond MIS structure was fabricated on (100) substrates of type lb synthetic diamond. Capacitance-voltage characteristics were measured tbr various boron concentrations and it was concluded that when the impurity concentration increased, an impurity band was formed 0.35 eV above the valence band which was composed of the excited state of the boron impurity and its phonon sideband. When the impurity concentration increased, the capacitance of the MIS structure decreased and the equilibrium density of holes in the films also decreased. With this impurity band the film works as a metal electrode. © 1997 Elsevier Science S.A.
Keywords." Homoepitaxy; Impurities; Electrical properties: Band structure
I. Introduction For the device application of diamond, a metal-insulator-semiconductor (MIS) structure is fundamental and is a powerful tool for understanding the impurity type and carrier number in semiconducting diamond. As for the impurities in diamond, boron is known to be the only one that works as a p,type dopant. There are two conduction mechanisms reported for p-type diamond: one is the band conduction of the carriers excited from the boron impurity [1]. The reported activation energy determined from the slope of the temperature dependence of the carrier number is 0.35-0.38 eV [2]. The other mechanism is impurity conduction, which is established by the overlap of the wavefunction of impurities [31. The mechanism of impurity conduction has been investigated since the 1960s, especially in Ge and Si, and it is now well established that the conduction mechanism changes from band conduction to impurity conduction when the dopant concentration increases and temperature is low [4]. Because of the shallow impurity level of Si and Ge, it is not clear whether the impurity band is isolated from the conduction (valence) band or merges with it. In diamond, on the other hand, * Corresponding author. 0925-9635/97/$17.00 © 1997 Elsevier Science S.A. All rights reserved. PII S0925-9635 ( 96)00723-6
the acceptor level is so deep (0.37 eV ) that the impurity conduction is discussed in terms of hopping conduction [3], and in heavily boron-doped samples of 2× 102°/cm3, it is considered that a metal insulator transition is realized [5,6]. In this report, we present the existence of tin impurity band formed in boron-doped homo-epitaxial diamond films detected by means of infrared spectroscopy. When the impurity band is formed in the midgap of the diamond, the C-V characteristics of the MIS structure are modified by the presence of the band, the experimental data for which are presented and the influence of the impurity band is discussed.
2. Experiments The diamond films were grown by a hot-filamentassisted chemical vapor deposition method using H2, CH4 and B203 diluted with C2HsOH and keeping the reaction pressure at 25Torr. The substrates were synthesized Ib diamonds with a size of 1.5 x 2 mm 2 and deposition was performed on chemically polished (100) surfaces. The impurity concentration was changed by varying the flow rate of B203 diluted with C2H5OH. Hence in this report the films denoted 10, 100, 1000,
"~ bm~hima ct al.
Diamomt . . d Rcl~m',l .llalcr'(,ds 6
5000, l0 0i~0 and 30 ~00 ppm are ~.he nominal B/C ratios in ',he reaction ~,..,:~,'~The ac~.n,~ percen~ee~ oF boro~ i~1 the films ~as not determined. The deposithm time was 3 h and lhe deposited ~hickness 4.5 ~m~. A trial to de,ermine the boron c~mcm~ra~ion in the fihns uqno the infrared absorption oi the one-phomm band was not ~,llccCssfld dltc to the strong correlation bctx~ccn tb.c oncphonon band and the excited state of the boron impurity. The deposited fihn was investigated by RHEED measurements and homoepitaxial growth was confirmed by observitag the (100t streak pattern of the film. To obtain the absorption coefficients of the deposited films, the transmitted intensity of the fihns was normalized to that of the substrate with no lilm on it, where no reflection correction was made. To investigate the accumulation and depletion characteristics of impurity-doped homoepitaxial diamond, capacitance-voltage (C-V) measurements on a metal-insulator-semiconductor (MIS) structure were carried OUt. The gate-insulator SiO 2 was deposited using an :..f. magnetron sputtering system, where synthesized SlOe was used as a target, and Ar containing 28% 02 as sputtering gas. The deposited SiO, thickness was 180 nm. Evaporated ah:minum was used as the gateelectrode with a size of 0.5 mm diameter, The measurement frequency was l kHz and the an-plitude was 0.05 V.
3. Results and discussion 3.1.
Ai~.vm?~tio, s p e c t r a
Fig. 1 shows the absorption spect,'a of homoepitaxi'd diamonds with different impurity concentrations. When the boron concentration is low, three shar? peaks are observed at 0.30, 0.35 and 0.51 eV. The peak at 0.51 eV is the optical phonon sideband associated with the peak at 0.35 eV, which is due to the transition of the hole 41100
• It
I
~4~-"-'-"
3000
I
'
I
30000 ppm
19971 ~V52 S'55
S:3
trapped at lhe boron mmurit:., to the second excited sta~e el" the accepmr [7]. The hall:width of ~he absorption a~ (},3S eV, which is reported to be se=lsitive to crys,alb inhy [8], is l0 meV and this value is similar to those of naturM [7] and plasma enhanced CVD diamond [9]. When the impurity concentration exceeds l0 000 ppm ti~c absorpt~ot~ spectrum changes drastically and the absorption commencing at the Raman phonon energy 10.I65 eV) extending to the lower energy side becomes observable having the den:,ity of state of the optical phonon. The peak at 0.16 eV is the maximum of the density of state of the TO phonon branch. At the same time the absorption coefficient around 0.35 eV increases drastically, governing the absorption from the infrared to visnble region. The absorption consis,.~ of two peaks. which are the excited ~tates of the boron impurity at 0.35eV al:d its optical phonon sideband at 0.51 eV. which indicates that there is a strong electron-phonon interaction in this film. From 1000 to 5000ppm. there is an increase of absorption in the enerov=, reeion,_ above 0.35 eV, which is thought to be due to continuur~, absc, rption resulting from photo-ionization of acceptors commencing at 0.365 eV [7, 10]. The drastic change of the absorption spectrum between 5000 and 10 000 ppm is difficult to explain by continuum absorption. There is a strong electron-phonon interaction in the l e(100ppm spectrum, hence the absorption change is understood to be due to the change of optical transition, that is fi'om direct transition between intra-impurity states to indirect transition between the ground state of the impurity and its excited states with momentum k. In lhis case the momentunl selection rule is released by the strong electron phonon interaction and lhe absorption spectrum is expressed by a Lorentz oscillator model. The absorption coefficient in this model is expressed by the dielectric functions q and e , , which are given by the resonance energy COo, broadening factor F and carrier number N in the form of plasma frequency ~o~ = N e 2 / e d n h . In diamond, nth is the effective mass of the conduction hole and e~ is the bulk dielectric constant. Then the absorption coefficient ~ is given by e~ and ea as
/ \/,00o0 m
.,~ ,,= 2000
where .~ !000
ppm
0.5
i
1.5
i0 ppm"
2
2.5
Photon energy eeVl Fig. 1. Absorption spectra of diamond films with various boron concentrations.
(,,g -,,?) el = ! + (,J~,
,
,
(O~o - co2 )2 + F-"to-
and e 2 =co~,
/"O)
)2 In order to reproduce (c,J~ -c,? + F2o~2 the absorption spectrum of the 10 000 ppm film given in Fig. 2, we used the standard parameters of diamond: ,
854
T. bmshima et al. ; Diamoml and Rehucd Materials 6 (1997) 852 +855
3t~0
251RI ":-
40110
2(RR) ,~
1500
a
30oo|L r \
-
20o0
I
3000
-~
me,is,,r ,J
- 2000
,.=
Z = ,-
20oo
[_
¢ 10OO
,°°i 0
0 0
0.5
I i.5 Photon energy levi
2
-.-~
'~
°
,o®
.~ <
I~ ]
o
-
1000
calculated "La
2.5
Fig. 2. Theoretical fitting of the absorption spectrum of the 10 000 ppm boron-doped diamond film.
mh=O.75mo, ¢r=5.7, and from the peak position of the absorption, COo=0.35 eV. F is obtained from F = h/r and z is the lifetime of carriers obtained from the conductivity. The solid line in Fig. 2 is obtained from N= 10t9/cm 3 and F=0.75 eV (a resistivity of 0.3 f~ cm), which are reasonable numbers for the 10 000 ppm film. The solid line given by Eq. (1) has some difficulty in reproducing absorption coefficients in the energy region below 0.35 eV. This discrepancy is reduced by introducing Fano interference, which occurs between the firstorder transition with conserved momentum and the second-order transition assisted by phonon momentum k [11]. When we set the so-called Fano asymmetry factor q=0.3, the index of the strength of the configuration interaction V= 0.1 eV and the shift of the resonance energy F = - 0 . 1 eV, the absorption spectrum fits well with the dashed line shown in Fig. 2. The result that the absorption spectrum is expressed by a Lorentzian function indicates that the impurity band is formed 0.35 eV above the valence band. Hence two bands exist in heavily doped homoepitaxial diamond, When the impurity concentration increases from 10 000 to 30 000 ppm, the absorption coefficient increases about 500 cm-~ over the whole energy region keeping the Lorentzian shape. This is due to free carrier absorption. The absorption spectrum of the 30 000 ppm film, which is shown in Fig. 3, can be reproduced by adding a Drude term which is obtained directly from Eq, (1) by equating the term COo=0. For the fitting procedure, we used the same Lorentzian term given in Fig. 2 for simplicity, and for the Drude term N = 1 × 10Xg/cm3 and F=2.2 eV are used. In this model the free carriers in the 30 000 ppm film exist in the impurity band and there is a gap of 0.35 eV between the valence and impurity bands. 3.2. C- V measurements
The MIS structure used in this experiment is shown in Fig. 4. Typical C - V data for the 100, 1000, and l0 000 ppm films are shown in Fig. 5 The fiat-band
0
0.5
1 1.5 Photon energy (eV)
,.'~
2.5
Fig. 3. Theoretical fitting of the absorption spectrum of the 30 003 ppm boron-doped diamond film.
: :.:.:.:.:.:
: : : :,:,:.:.:.:.:
p-:l-ype Diamond: ::
:::.:
Type
:.: : : : : : : : :
____] v
:.:
zl;Su~: :
::.:
I b Diamcnd Substrate : 0.Smm
(a)
(b)
(c)
Fig, 4. (a) Schematic drawing of the diamond MIS structure used in this experiment. (b) The equivalent circuit for the MIS structure when the doping concentration is low. (c) The equivalent circuit for the MIS structure when the doping concentration is high.
3
I 0 I~
~ 2 10 t l
-
,~
100 ppm
" o
=
~.
j
0 -15
1000 ppm
-10
-5
R
10000 ppm
0
~
5
10
15
Bias voltage (V) Fig. 5. MIS capacitance-voltage curves for the 100, 1000 and 10 000 ppm fihns.
voltage of our MIS structure is 3.2 V [12]. When the impurity concentration is 100 ppm, the C-Vcurve shows good accumulation in a negative-bias condition, as is expected for a p-type semiconductor. When the MIS structure is biased into depletion, the C-V curve shows no indication of minority-carrier electron accumulation at the diamond-SiO2 interface. This feature was also
7~ bmshima c{ al.... Diamomt am/ Related Materials 6 ~ 1997) ,~52 855
reported by Geis et al. [12]. In an accumulation condition (negativeUy biased) the obtained capacitance is 29 pF, which is 80% of the ideal capacitance t36 pg t. When the impurity concentration is 1000 ppm. we can see accumulation in negative-bias condition, but the obtained capacitance is 6 pF. which is only n6% of the ideal value. When the concentration is t0 000 ppm, the MIS structure shows a small capacitance (< 1 pF) with a weak bias-voltage dependence. This is due to the metallic condition of the deposited film. In this case the diamond MIS structure is regarded to have a series connection of two capacitors, where the deposited diamond film functions as a metal electrode, and the diamond substrate and the SiO2 film function as insulators. A schematic drawing of this structure is given in Fig. 41c) and the expected capacitance is 0.9 pF. The theoretical curves obtained by Sze (Ref. [13], chapt. 7, Eqs. (20)~ (25) and (49)) are given in Fig. 6. For the fitting procedure, we used npo=O (npo=equilibrium density of electrons), T= 300 K, and =5 V. In this case Ppo (equilibrium density of holes) is the only fitting parameter, and for c t n , and for the the 100 ppm film, Ppo = 2.5 x 10 ~5/,__3 1000 ppm film pp0=2.4x 1 0 t 4 / c m 3. The result that the Pp0 of the 1000 ppm film is one-tenth of that of the 100 ppm film is in good agreement with the fact that the 1000 ppm film shows a smaller capacitance than the 100 ppm film in a negative-biased condition. When the boron concentration increases in the diamond film, the density of the impurity is not uniformly distributed in the film and is higher than the average density in some
5 I() ::~ Z-, 4 10 's :"- 3 102a ID
g
g
il
|
|
P
o 1000 ppm [] 100 ppm - - - 1000 ppm (theoretic) 100 ppm (theoretic)
P p
-
?
? •~ 2 I0 '3 4
rO I 1023 ,,.,,-
0
g io ~ o.,..2,ooo2 ,:,.~ o ~ -10
-5
~ ~ 0
~
5
_..~
~-
l0
15
Bias voltage (V) Fig. 6. Calculated data fitted to experimental data for 100 :and 1000 ppm films by assuming l,'Fu= 5 V.
855
parts of the film. ~n this case the wavel\mctions of the excited state of the impurity begin to overlap to form an impurity band ha the forbidden band gap of diamond. Therefore~ the expected capacitance is the parallel connection of two capacitors, which are given in Figs. 4tbl and ~c). Hence, when the impurity concentration increases, the proportion of the capacitance given in Fig. 4(b) decreases and the proportion of the capacitance given in Fig. 4(c) increases. As a result, when the impurity concentration increases, the obtained capacitance decreases, and the nominal Ppo becomes small, and finally we see the metallic condition of the deposited diamond.
4. Conclusion Optical investigations performed on boron-doped homoepitaxial diamonds reveal the presence of an impurity band which was formed 0.35 eV above the ground state of the boron impurity. This band was composed of the excited state of the impurity and its phonon sideband. Capacitance-voltage characteristics of the metal-SiOz-boron-doped homoepitaxial diamond MIS structure were measured for various boron concentrations and it was shown that when the impurity concentration increased, this impurity band functioned as a metallic electrode in the diamond.
References [ ! ] A.W.S. Williams, E.C. Lightowlers and A.T. Collins, J. Phys. C. 3 (197{) ) ! 727. [2] A.I-. Collins and A.W.S. Williams, J. Phr.s.C. 4 ( 1971 ) 1789. [3] B, Massarani, J.C. Bourgom and R.M. Chrenko. Phvx. Rev. B. 17 (1978) 1758. [4] H. Fritzsche and M. Cuevas, Phys. Rev., 119 (1960) 1238. [5] H. Shiomi, Y. Nishibashi and N. Fujimori, Jpn. J. Appl. Phys., 30 (1991) 1363. [6] M. Werner et al., AppI. Phys. Lett,. 04 (1994) 595. [7] S,D. Smith and W. Taylor, Proc. Phys. Sot., 79 (1962) 1142. [8] P.T. Wedepohl, Proc. Phys. Sot'., 70 (1956) 177. [9] A. Ogasawara, T. Inushima, T. Shiraisi, S. Ohoya S. Karasawa and T. Shiomi, this volume. [10] G. Janssen, W.J.P. Van Enckevort, W. Voilenberg and L.J. Giliing, Diamond Relat. Mater.. 1 (1992) 789. [11] U. Fano, Phys. Rev.. 124 (1961) 1866. [12] M.W. Geis, J.A. Gregory and B.B. Pate, IEEE Trans. Electron Devices, ED-38 ( 1991 ) 619. [13] M. Sze, Physics of Semiconductor Devices, 2nd edn., Wiley, New York, 1981. chapt. 7.