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Anomalous mobility enhancement in Si doping superlattices
Solid State Communications, Printed in Great Britain.
Vol. 58, No. 11, pp. 819-822,
1986.
ANOMALOUS MOBILITY ENHANCEMENT
0038-1098/86 $3.00 + .OO Pergamon Journals Ltd.
IN Si DOPING SUPERLATTICES
Kiyokazu Nakagawa and Yasuhiro Shiraki Central Research Laboratory,
Hitachi Ltd., Kokubunji,
Tokyo 185, Japan
(Received 4 February 1986 by H. Kamimura) Enhanced Hall mobility has been measured in Si doping superlattices with pipi or nini doping profiles grown by molecular beam epitaxy. Although the carrier concentration is large, in the range of 10’s cmm3, the mobility of holes in the pipi doping superlattice has the temperature dependence such as that expressed in the T -23 law which is characteristic of high purity bulk crystals. The hole mobility is about twice that of high purity crystals, rising up to 40,000 cm2/V.s at about 30K. In the case that p-type impurity concentration is comparable to n-type impurity concentration, no mobility enhancement is observed and the mobility is anomalously depressed. The mechanisms for drastical change in the mobility of doping superlattices have not yet been clarified.
RECENTLY THERE HAVE BEEN many reports on artificial semiconductor superlattices. These superlattices are composed of periodic crystalline layers which have different compositions (compositional superlattices) [ 1, 21 or which are doped differently (doping superlattices) [3,4] . In such a compositional superlattice as GaAs-AlGaAs, electrons released from donors are accumulated in the GaAs regions and form a two dimensional electron gas (ZDEG) system. It is wellknown that 2DEG possesses high mobility especially in the case of modulation doped GaAs-AlGaAs superlattices where donors are selectively doped in AlGaAs layers. This mobility enhancement is mainly due to the fact that conduction electrons accumulated in GaAs layers are spatially separated from their parent donor impurities in AlGaAs layers which act as scatterers. In doping superlattices, on the other hand, neither theoretical predictions nor experimental results on mobility enhancement have been reported so far. In doping superlattices, which are sometimes called nipi, pipi or nini structures, mobile electrons and holes exist in the same spatial regions of their parent donor and acceptor impurities. As a result, mobility enhancement similar to that of modulation doping in compositional superlattices is not generally expected. Recently, we have observed, for the first time, that the mobility enhancement is achieved even in the doping superlattice [5]. This anomalous mobility enhancement was found in silicon doping superlattices with properly designed doping profiles and the hole mobility exceeded that of undoped, high purity, bulk Si crystals. In this paper, we report the electrical properties of various kinds of doping superlattices in more detail. Silicon doping superlattices studied here were 819
prepared by using the molecular beam epitaxy (MBE) technique. The substrates used here were n and p-type (100) silicon wafers with S-10cm. MBE growth was performed in a commerical MBE machine whose base pressure was about 2 x 10-r’ torr. Doping was carried out using conventional Knudsen cells. Antimony and gallium were used as n and p-type dopants, respectively. The substrate temperature during growth was 74O’C and the growth rate was about 3A/s. The period of superlattices, that is, the thickness of a pair of n and p-layers, was changed from 200 to 650A, and the doping profile was changed from nipi, where the impurity concentration of n and p-layers is comparable, to nini or pipi structures where the n or p-layers are much more heavily doped than the other layers. Typical examples of these doping superlattices which show electrical properties very different from those of bulk crystals are listed in Table 1 In order to evaluate electrical properties of p or n-layers of superlattices, selective electrodes were made by ion implantation with 100 keVB’ ions at a dose of 3 x 10” cm -2 for p-layer contact or with 180 keVP+ ions at a dose of 3 x IO” cmm2 for n-layer contact. Post annealing was done in flowing nitrogen gas at 550°C for 8 h to activate implanted impurities. A six-electrode structure for electrical measurements was made by reactive ion etching. Hall mobilities of Si doping superlattices at room temperature and 77K are shown as a function of carrier concentration in Fig. 1. The solid and dot-dashed lines represent mobility vs carrier concentration in bulk crystals at room temperature [6]. It is very striking in this figure that two samples, 110 and 111 show much higher mobility than bulk silicon. On the other hand, the other samples, 112 and 122, have lower mobility.
820
210”
ANOMALOUS MOBILITY ENHANCEMENT Si Doping Superlattice
IN Si DOPING SUPERLATTICES
1 ’ ’ 1”“”” ’ “7 0,
0.0 R T. . 77K
h
\
Vol. 58, No. 11
0,
Si : Doping
o\
O\
Superlattice
%
_
a, ok?
511 %
(p)
\0
l-0 %lO
CARRER
CObiGZbTRATON
Moreover, it was observed that the mobility of the former two samples becomes higher at 77K, but the latter two samples show lower mobility at 77K than at room temperature. The mobility of these samples is plotted as a function of temperature in Fig. 2. The temperature dependence of conductivity, mobility and carrier concentration of sample 111 where impurity concentration in the n and p-layers are 1 x 1016 and 1 x 1018 cmm3 respectively, is shown in Fig. 3. As can be seen in the figure, the hole mobility of sample 111 monotonically increases as the temperature is decreased and rises up to 40,000 cm2/V.s at about 30 K. The carrier concentration of this sample remains on the order of 10” cme3 down to lOOK, but rapidly decreases below this temperature. It should be pointed out that although the carrier concentration is very high above IOOK, the mobility changes in a manner of T-2.2 which is characteristic of high purity bulk crystals [7] . The T- 2.2 dependence of bulk silicon is explained in
Sample
#Ill #112 #122
e
’
10’
I
10’
I111111 m2 TEMPERATUREC
I,,,,,
1 103
K )
Fig. 2. Hall mobility of holes and electrons in Si doping superlattices as a function of absolute temperature. terms of acoustic phonon scattering of holes in crystals where the impurity scattering can be neglected. In sample 110, where the impurity concentration in the n-layers is 5 x IOr cme3 and the p-layers are undoped, electron mobility enhancement is observed. However, as can be seen in Fig. 2, the enhancement is not so significant compared with sample 111 and the mobility does not strongly depend on temperature. The mobility of samples 112 and 122, on the other hand, decreases as the temperature is decreased. Sample 122 in particular shows a drastic drop around 100 K. The multilayer structure of the samples examined here is not very widely used one for electrical measurements, and in addition the electrodes are specially prepared with the aid of ion implantation. For this reason, the question of whether or not the mobility enhancement observed here is an apparent phenomenon
ofSi doping superlattices
Sub.
Non-doped
No. of
Cond.
d(a)
d(a)
Layers
Type
- 1 x lOi8 -
_ 300 _
300 540
20 20 20
P
-5
300
-
15
P
Sub. Temp.
n-type
(“C)
n(cme3)
d(A)
p(cmC3)
P(100) P(100)
740 740 740
-5 x 1o16 -1 x lOI -5x 10”
300 300 60
n(lO0)
740
-1
300
No. #IlO
%, \
lcrn-21
Fig. 1. Hall mobility of holes and electrons in Si doping superlattices at room temperature and 77 K as a function of sheet carrier concentration. Hole and electron concentrations per cubic centimeter are also given by lower two scales, where the thickness of conductive layers of samples is assumed to be the projected range plus standard deviation. Solid and dot-dashed lines represent mobility in bulk crystals at room temperature.
Table 1. List
--\
(n)
P(100)
x lOI
p-type
x 1or7
n n
ANOMALOUS MOBILITY ENHANCEMENT
Vol. 58, No. 11
l--
102'
821
IN Si DOPING SUPERLATTICES I
I
Superlattice
1020 F
E ” a 6 1019 5 E e 5 1
5 B K 10'8 3
'OlO
50
100
A 5cIO
TEMPERATURE (K)
Fig. 4. Hall mobility of holes in sample 122 as a function of absolute temperature. Hall mobility of bulk crystals [S] are also shown. I I
TEMP&RE(
JO’7
2
10: K)
Fig. 3. Hole Hall mobility, carrier concentration, and conductivity of sample 111 as a function of absolute temperature. The line (-+ -) indicates the mobility of the bulk Si where the carrier concentration is less than 1 x 10” cmm3. resulting form the multilayer structure of the samples should be examined before going into a detailed discussion about the mechanism of the mobility enhancement. Although electrodes are selective for p or n-layers, one cannot completely eliminate the possibility that electrodes are not perfect and that both electrons and holes accidentally contribute to the electrical conduction in doping superlattices. If both holes and electrons exist in the sample, the flow in the opposite directions between current electrodes and are deflected to the same Hall electrode due to Lorentz force in Hall measurements. Since the Hall voltage is determined by superposition of hole and electron components, they cancel each other in this case. Therefore, the mobility calculated from this Hall voltage becomes somewhat smaller than mobilities of electrons and holes in the sample, and as a result mobility enhancement apparently does not occurs in doping superlattices. It is, therefore logical to assume that the observed enhancement is an inherent nature of the doping superlattices grown here. The temperature dependence of the mobility, T-‘.’ > of sample 111, which shows anomalous mobility enhancement, suggests that a mechanism similar to that in high purity bulk silicon determines the electrical
conduction of the doping superlattice. In ordinary doping superlattices with nipi structures, the carriers are confined in the potential wells and size quantization may occur. However, carriers are in the wells where their parent impurities are doped, and as a result the mobility is strongly affected by scattering due to these impurities. It is, therefore, hardly expected that the mobility is enhanced due to the dimensionality like compositional superlattices. In sample 111, where the impurity concentration of the n-type region is much lower than that of the p-layers, the n-layers are thought not to practically have impurity scattering centers for holes. So, if holes of p-layers happen to flow into these n-type doping regions, a similar situation to the modulation in compositional superlattices appears and mobility enhancement can be expected. Since the period of superlattice of sample 111 is much shorter than the screening length, it is deduced that the built-in potential is too small to confine the holes to the acceptor doped regions. Therefore, some of the holes in heavily doped layers can overflow into the lightly doped regions. These holes spread widely in crystals and the size quantization may be lifted. In this situation, both low mobility holes confined in the wells and overflowing high mobility holes contribute to the electrical ccnduction. According to the two-carrier conduction theory, the apparent mobility as well as conductivity is normally determined by the carrier having the higher mobility, if the concentrations of the higher and lower mobility carriers are comparable. As pointed out above, holes which overflow into the n-layers are not quantized anymore and their mobility may be determined by the same scattering
822
ANOMALOUS MOBILITY ENHANCEMENT
mechanism as that in bulk crystals with the same impurity concentration as the n-layers of the doping superlattices. The mobility of a bulk crystal in the same doping level as the n-layer of sample 111 is high and almost the same as that of high purity crystals [8]. Consequently, the mobility of the doping superlattice may be determined by holes with high mobility overflowing into lightly doped regions. The temperature dependence of the mobility of the bulk silicon in the same doping level is, moreover, known to be very similar to that of high purity silicon above IOOK. This may be a reasonable explanation why the doping superlattice shows temperature dependence of mobility similar to that of high purity bulk crystals. The main features of the doping superlattice with enhanced mobility are roughly understood in terms of a mechanism similar to modulation doping. However, the results described below still remain to be explained. (1) The hole mobility of the sample with a pipi structure, sample 111, is about twice as large as that of high purity bulk crystals above lOOK. This high mobility has not been observed in any Si samples. (2) The only difference between samples 110 and 111 is that the doping level of the n-layers in sample 110 is higher than that in the p-layers (i.e. nini structure) while the p-layer doping level is high in sample 111. Consequently, similar anomalous enhancement in electron mobility is expected for sample 110. In fact, this sample has larger mobility than that of bulk crystals. However, the mobility enhancement is not very large compared with superlattices with pipi structures and the temperature dependence is quite different from that of high purity bulk crystals in contrast with sample 111. (3) In sample 112, which has an nini structure but different thicknesses of doped (60 A) and undoped (540A) regions, the mobility is smaller than that of bulk crystals. From the point of view of carrier overflow into lightly doped regions, this sample should show more significant mobility enhancement, but in fact this does not occur. (4) The doping concentration of the p-layers of sample 122 is slightly larger than that of the n-layers. In these doping profiles, carriers are thought to be largely affected by doped impurities, as they are in heavily doped bulk crystals. As shown in Fig. 4, however, the hole mobility is much more depressed than that of bulk crystals in the same doping levels. These results cannot be explained by the simple two-carrier conduction mechanism discussed above. A possible explanation is that the periodicity of doping superlattices modifies band structures and then the effective mass of carriers is lightened [9]. Another possibility is the contribution of light-mass holes to the electrical conduction due to the strain generated by impurity doping. It is known that the sticking probability
IN Si DOPING SUPERLATTICES
Vol. 58, No. 11
of neutral Ga and Sb beams on Si surfaces is very small and in the range of 0.01, which is evaluated from the carrier concentration in doped epitaxial films. Although irradiated impurity atoms are mainly desorbed from the surface, there are some atoms included but unactivated in epitaxial layers. These unactivated atoms possibly induce strain field around doped regions and the lightmass hole branch of the valence band may be raised above the heavy hole branch. If so, light-mass holes will dominate the electrical conduction, achieving enhanced mobility in superlattices. However, as yet no comprehensive theoretical examinations of these models have been completed. In summary, enhanced Hall mobility has been measured in Si doping-superlattices with pipi or nini doping profiles grown by molecular beam epitaxy. Hole mobility of a doping superlattice where the impurity concentration of p-layers is much higher than that of n-layers exceeded the mobility of high purity bulk crystals with no impurity scattering, whilst the carrier concentration of the doping superlattice was in the range of IOr cme3. Above 100 K, the temperature dependence of the doping superlattice mobility approximately followed the T-*.* law which is characteristic of high purity bulk crystals. On the other hand, in doping superlattices where impurity profiles are similar to conventional pnpn structures, the mobility was found to be anomalously depressed in contrast to pipi or nini structures. In order to fully understand doping superlattices, more detailed studies are necessary. Acknowledgements - The authors wish to thank Dr. Y. Murayama, Dr. Y. Katayama, Dr. E. Yamada and Dr. A. Ishizaka for helpful discussions. This work was performed under the management of the Research and Development Association for Future Electron Devices as a part of the Research and Development Project of Basic Technology for Future Industries sponsored by Agency of Industrial Science and Technology, MITI, REFERENCES 1.
2. 3. 4. 5.
6. 7. 8. 9.
L.L. Chang, L. Esaki, W.E. Howard & R. Ludeke, J. Vat. Sci. Technol. 10,ll (1973). R. Dingle, H.L. Stoermer, A.C. Gossard & W. Wiegmann,AppZ. Phys. Lett. 33,665 (1978). G.H. Doehler, Phys. Status Solidi (b) 53, 79 (1972). K. Ploog, A. Fischer & H. Kuenzel,J. Electrochem. Sot. 128,400 (1981). K. Nakagawa & Y. Shin&i, 2nd Int. Symp. on Modulated Semiconductor Structures, Kyoto, (1985). J.C. Irvin, Bell System Tech. J. 41,387 (1962). G. Ottaviani, L. Reggiani, C. Canali, F. Nava & A.A. Quaranta, Phys. Rev. B12,3315 (1975). F.J. Morin & J.P. Maita. Phvs. Rev. 96.28 (1954). J.A. Moriarty & S. K&hnamurty, J. ‘A&. Phis. 54,1892 (1983).
Vol. 58, No. 11, pp. 819-822,
1986.
ANOMALOUS MOBILITY ENHANCEMENT
0038-1098/86 $3.00 + .OO Pergamon Journals Ltd.
IN Si DOPING SUPERLATTICES
Kiyokazu Nakagawa and Yasuhiro Shiraki Central Research Laboratory,
Hitachi Ltd., Kokubunji,
Tokyo 185, Japan
(Received 4 February 1986 by H. Kamimura) Enhanced Hall mobility has been measured in Si doping superlattices with pipi or nini doping profiles grown by molecular beam epitaxy. Although the carrier concentration is large, in the range of 10’s cmm3, the mobility of holes in the pipi doping superlattice has the temperature dependence such as that expressed in the T -23 law which is characteristic of high purity bulk crystals. The hole mobility is about twice that of high purity crystals, rising up to 40,000 cm2/V.s at about 30K. In the case that p-type impurity concentration is comparable to n-type impurity concentration, no mobility enhancement is observed and the mobility is anomalously depressed. The mechanisms for drastical change in the mobility of doping superlattices have not yet been clarified.
RECENTLY THERE HAVE BEEN many reports on artificial semiconductor superlattices. These superlattices are composed of periodic crystalline layers which have different compositions (compositional superlattices) [ 1, 21 or which are doped differently (doping superlattices) [3,4] . In such a compositional superlattice as GaAs-AlGaAs, electrons released from donors are accumulated in the GaAs regions and form a two dimensional electron gas (ZDEG) system. It is wellknown that 2DEG possesses high mobility especially in the case of modulation doped GaAs-AlGaAs superlattices where donors are selectively doped in AlGaAs layers. This mobility enhancement is mainly due to the fact that conduction electrons accumulated in GaAs layers are spatially separated from their parent donor impurities in AlGaAs layers which act as scatterers. In doping superlattices, on the other hand, neither theoretical predictions nor experimental results on mobility enhancement have been reported so far. In doping superlattices, which are sometimes called nipi, pipi or nini structures, mobile electrons and holes exist in the same spatial regions of their parent donor and acceptor impurities. As a result, mobility enhancement similar to that of modulation doping in compositional superlattices is not generally expected. Recently, we have observed, for the first time, that the mobility enhancement is achieved even in the doping superlattice [5]. This anomalous mobility enhancement was found in silicon doping superlattices with properly designed doping profiles and the hole mobility exceeded that of undoped, high purity, bulk Si crystals. In this paper, we report the electrical properties of various kinds of doping superlattices in more detail. Silicon doping superlattices studied here were 819
prepared by using the molecular beam epitaxy (MBE) technique. The substrates used here were n and p-type (100) silicon wafers with S-10cm. MBE growth was performed in a commerical MBE machine whose base pressure was about 2 x 10-r’ torr. Doping was carried out using conventional Knudsen cells. Antimony and gallium were used as n and p-type dopants, respectively. The substrate temperature during growth was 74O’C and the growth rate was about 3A/s. The period of superlattices, that is, the thickness of a pair of n and p-layers, was changed from 200 to 650A, and the doping profile was changed from nipi, where the impurity concentration of n and p-layers is comparable, to nini or pipi structures where the n or p-layers are much more heavily doped than the other layers. Typical examples of these doping superlattices which show electrical properties very different from those of bulk crystals are listed in Table 1 In order to evaluate electrical properties of p or n-layers of superlattices, selective electrodes were made by ion implantation with 100 keVB’ ions at a dose of 3 x 10” cm -2 for p-layer contact or with 180 keVP+ ions at a dose of 3 x IO” cmm2 for n-layer contact. Post annealing was done in flowing nitrogen gas at 550°C for 8 h to activate implanted impurities. A six-electrode structure for electrical measurements was made by reactive ion etching. Hall mobilities of Si doping superlattices at room temperature and 77K are shown as a function of carrier concentration in Fig. 1. The solid and dot-dashed lines represent mobility vs carrier concentration in bulk crystals at room temperature [6]. It is very striking in this figure that two samples, 110 and 111 show much higher mobility than bulk silicon. On the other hand, the other samples, 112 and 122, have lower mobility.
820
210”
ANOMALOUS MOBILITY ENHANCEMENT Si Doping Superlattice
IN Si DOPING SUPERLATTICES
1 ’ ’ 1”“”” ’ “7 0,
0.0 R T. . 77K
h
\
Vol. 58, No. 11
0,
Si : Doping
o\
O\
Superlattice
%
_
a, ok?
511 %
(p)
\0
l-0 %lO
CARRER
CObiGZbTRATON
Moreover, it was observed that the mobility of the former two samples becomes higher at 77K, but the latter two samples show lower mobility at 77K than at room temperature. The mobility of these samples is plotted as a function of temperature in Fig. 2. The temperature dependence of conductivity, mobility and carrier concentration of sample 111 where impurity concentration in the n and p-layers are 1 x 1016 and 1 x 1018 cmm3 respectively, is shown in Fig. 3. As can be seen in the figure, the hole mobility of sample 111 monotonically increases as the temperature is decreased and rises up to 40,000 cm2/V.s at about 30 K. The carrier concentration of this sample remains on the order of 10” cme3 down to lOOK, but rapidly decreases below this temperature. It should be pointed out that although the carrier concentration is very high above IOOK, the mobility changes in a manner of T-2.2 which is characteristic of high purity bulk crystals [7] . The T- 2.2 dependence of bulk silicon is explained in
Sample
#Ill #112 #122
e
’
10’
I
10’
I111111 m2 TEMPERATUREC
I,,,,,
1 103
K )
Fig. 2. Hall mobility of holes and electrons in Si doping superlattices as a function of absolute temperature. terms of acoustic phonon scattering of holes in crystals where the impurity scattering can be neglected. In sample 110, where the impurity concentration in the n-layers is 5 x IOr cme3 and the p-layers are undoped, electron mobility enhancement is observed. However, as can be seen in Fig. 2, the enhancement is not so significant compared with sample 111 and the mobility does not strongly depend on temperature. The mobility of samples 112 and 122, on the other hand, decreases as the temperature is decreased. Sample 122 in particular shows a drastic drop around 100 K. The multilayer structure of the samples examined here is not very widely used one for electrical measurements, and in addition the electrodes are specially prepared with the aid of ion implantation. For this reason, the question of whether or not the mobility enhancement observed here is an apparent phenomenon
ofSi doping superlattices
Sub.
Non-doped
No. of
Cond.
d(a)
d(a)
Layers
Type
- 1 x lOi8 -
_ 300 _
300 540
20 20 20
P
-5
300
-
15
P
Sub. Temp.
n-type
(“C)
n(cme3)
d(A)
p(cmC3)
P(100) P(100)
740 740 740
-5 x 1o16 -1 x lOI -5x 10”
300 300 60
n(lO0)
740
-1
300
No. #IlO
%, \
lcrn-21
Fig. 1. Hall mobility of holes and electrons in Si doping superlattices at room temperature and 77 K as a function of sheet carrier concentration. Hole and electron concentrations per cubic centimeter are also given by lower two scales, where the thickness of conductive layers of samples is assumed to be the projected range plus standard deviation. Solid and dot-dashed lines represent mobility in bulk crystals at room temperature.
Table 1. List
--\
(n)
P(100)
x lOI
p-type
x 1or7
n n
ANOMALOUS MOBILITY ENHANCEMENT
Vol. 58, No. 11
l--
102'
821
IN Si DOPING SUPERLATTICES I
I
Superlattice
1020 F
E ” a 6 1019 5 E e 5 1
5 B K 10'8 3
'OlO
50
100
A 5cIO
TEMPERATURE (K)
Fig. 4. Hall mobility of holes in sample 122 as a function of absolute temperature. Hall mobility of bulk crystals [S] are also shown. I I
TEMP&RE(
JO’7
2
10: K)
Fig. 3. Hole Hall mobility, carrier concentration, and conductivity of sample 111 as a function of absolute temperature. The line (-+ -) indicates the mobility of the bulk Si where the carrier concentration is less than 1 x 10” cmm3. resulting form the multilayer structure of the samples should be examined before going into a detailed discussion about the mechanism of the mobility enhancement. Although electrodes are selective for p or n-layers, one cannot completely eliminate the possibility that electrodes are not perfect and that both electrons and holes accidentally contribute to the electrical conduction in doping superlattices. If both holes and electrons exist in the sample, the flow in the opposite directions between current electrodes and are deflected to the same Hall electrode due to Lorentz force in Hall measurements. Since the Hall voltage is determined by superposition of hole and electron components, they cancel each other in this case. Therefore, the mobility calculated from this Hall voltage becomes somewhat smaller than mobilities of electrons and holes in the sample, and as a result mobility enhancement apparently does not occurs in doping superlattices. It is, therefore logical to assume that the observed enhancement is an inherent nature of the doping superlattices grown here. The temperature dependence of the mobility, T-‘.’ > of sample 111, which shows anomalous mobility enhancement, suggests that a mechanism similar to that in high purity bulk silicon determines the electrical
conduction of the doping superlattice. In ordinary doping superlattices with nipi structures, the carriers are confined in the potential wells and size quantization may occur. However, carriers are in the wells where their parent impurities are doped, and as a result the mobility is strongly affected by scattering due to these impurities. It is, therefore, hardly expected that the mobility is enhanced due to the dimensionality like compositional superlattices. In sample 111, where the impurity concentration of the n-type region is much lower than that of the p-layers, the n-layers are thought not to practically have impurity scattering centers for holes. So, if holes of p-layers happen to flow into these n-type doping regions, a similar situation to the modulation in compositional superlattices appears and mobility enhancement can be expected. Since the period of superlattice of sample 111 is much shorter than the screening length, it is deduced that the built-in potential is too small to confine the holes to the acceptor doped regions. Therefore, some of the holes in heavily doped layers can overflow into the lightly doped regions. These holes spread widely in crystals and the size quantization may be lifted. In this situation, both low mobility holes confined in the wells and overflowing high mobility holes contribute to the electrical ccnduction. According to the two-carrier conduction theory, the apparent mobility as well as conductivity is normally determined by the carrier having the higher mobility, if the concentrations of the higher and lower mobility carriers are comparable. As pointed out above, holes which overflow into the n-layers are not quantized anymore and their mobility may be determined by the same scattering
822
ANOMALOUS MOBILITY ENHANCEMENT
mechanism as that in bulk crystals with the same impurity concentration as the n-layers of the doping superlattices. The mobility of a bulk crystal in the same doping level as the n-layer of sample 111 is high and almost the same as that of high purity crystals [8]. Consequently, the mobility of the doping superlattice may be determined by holes with high mobility overflowing into lightly doped regions. The temperature dependence of the mobility of the bulk silicon in the same doping level is, moreover, known to be very similar to that of high purity silicon above IOOK. This may be a reasonable explanation why the doping superlattice shows temperature dependence of mobility similar to that of high purity bulk crystals. The main features of the doping superlattice with enhanced mobility are roughly understood in terms of a mechanism similar to modulation doping. However, the results described below still remain to be explained. (1) The hole mobility of the sample with a pipi structure, sample 111, is about twice as large as that of high purity bulk crystals above lOOK. This high mobility has not been observed in any Si samples. (2) The only difference between samples 110 and 111 is that the doping level of the n-layers in sample 110 is higher than that in the p-layers (i.e. nini structure) while the p-layer doping level is high in sample 111. Consequently, similar anomalous enhancement in electron mobility is expected for sample 110. In fact, this sample has larger mobility than that of bulk crystals. However, the mobility enhancement is not very large compared with superlattices with pipi structures and the temperature dependence is quite different from that of high purity bulk crystals in contrast with sample 111. (3) In sample 112, which has an nini structure but different thicknesses of doped (60 A) and undoped (540A) regions, the mobility is smaller than that of bulk crystals. From the point of view of carrier overflow into lightly doped regions, this sample should show more significant mobility enhancement, but in fact this does not occur. (4) The doping concentration of the p-layers of sample 122 is slightly larger than that of the n-layers. In these doping profiles, carriers are thought to be largely affected by doped impurities, as they are in heavily doped bulk crystals. As shown in Fig. 4, however, the hole mobility is much more depressed than that of bulk crystals in the same doping levels. These results cannot be explained by the simple two-carrier conduction mechanism discussed above. A possible explanation is that the periodicity of doping superlattices modifies band structures and then the effective mass of carriers is lightened [9]. Another possibility is the contribution of light-mass holes to the electrical conduction due to the strain generated by impurity doping. It is known that the sticking probability
IN Si DOPING SUPERLATTICES
Vol. 58, No. 11
of neutral Ga and Sb beams on Si surfaces is very small and in the range of 0.01, which is evaluated from the carrier concentration in doped epitaxial films. Although irradiated impurity atoms are mainly desorbed from the surface, there are some atoms included but unactivated in epitaxial layers. These unactivated atoms possibly induce strain field around doped regions and the lightmass hole branch of the valence band may be raised above the heavy hole branch. If so, light-mass holes will dominate the electrical conduction, achieving enhanced mobility in superlattices. However, as yet no comprehensive theoretical examinations of these models have been completed. In summary, enhanced Hall mobility has been measured in Si doping-superlattices with pipi or nini doping profiles grown by molecular beam epitaxy. Hole mobility of a doping superlattice where the impurity concentration of p-layers is much higher than that of n-layers exceeded the mobility of high purity bulk crystals with no impurity scattering, whilst the carrier concentration of the doping superlattice was in the range of IOr cme3. Above 100 K, the temperature dependence of the doping superlattice mobility approximately followed the T-*.* law which is characteristic of high purity bulk crystals. On the other hand, in doping superlattices where impurity profiles are similar to conventional pnpn structures, the mobility was found to be anomalously depressed in contrast to pipi or nini structures. In order to fully understand doping superlattices, more detailed studies are necessary. Acknowledgements - The authors wish to thank Dr. Y. Murayama, Dr. Y. Katayama, Dr. E. Yamada and Dr. A. Ishizaka for helpful discussions. This work was performed under the management of the Research and Development Association for Future Electron Devices as a part of the Research and Development Project of Basic Technology for Future Industries sponsored by Agency of Industrial Science and Technology, MITI, REFERENCES 1.
2. 3. 4. 5.
6. 7. 8. 9.
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