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New results in transport phenomena in uncompensated n-type InSb with extremely low carrier density
Phys~a lI7B & ll8B (1983) 235-237 North-HollandPubhslungCompany
235
HEW RESULTS IN TRANSPORT PHENOMENA IN UNCOMPENSATED n-TYPE InSb WITH EXTREMELY LOW CARRIER DENSITY A. KADRI, R.L. AULOMBARD,
C. BOUSQUET,
A. RAYMOND,
J. L. ROBERT
Centre d'Etudes d'Electronlque des Solides , assocle au C.N.R.S. ( L.A. n ° 21) U.S.T.L. Place Eugene Batalllon, 34060 MONTPELLIER C~dex (France) S. POROWSKI, High Pressure Research Center,
L. KONCZEWICZ
Pollsh Academy of Sclences,
WARSAW (Poland)
We report new experimental results of low temperature (4.2 K - 95 K) transport phenomena in uncompensated n-type InSb sample, where very low free carrier concentratlons are obtained using the properties of a metastable impurity state. By varying free electron density in the same sample, from ]0 II cm -3 to 1014 cm -3 the metal-non metal transition is observed. The evidence of an activation energy of the hydrogenlc level corresponding to the effective Rydberg is given. Above 40 K the role of a donor-llke impurity level is shown.
I.
INTRODUCTION
A great interest has been devoted to the studies of low free carrier density n-type InSb, and different methods have been used to obtain such samples using either growing techniques (purification, compensation ...) or external perturbations (magnetic field, compression...). Recently, some workers (l) performing experiments on n-type InSb at 77 K have shown the possibility to obtain low electron concentrations and hlgh mobIiIties by freezing electrons on a metastable state (connected with X minimum) using hlgh pressure techniques and an appropriate temperature treatment. In the present work, we use this method to induce large changes of the free carrier density on a very low compensated n-type InSb sample on which transport experiments have been performed in the temperature range from 4.2 K to 95 K. By uslng this previous method on a very pure sample, we have obtained very interesting new results, which lead to a new progress in the study of transport phenomena in n-type InSb.
hydrostatlc pressure is removed. If temperature is then raised to 100 - ||0 K, a reexcltation of carriers is observed, giving different "states" for the same sample characterized by different free carrier density. Our experiments were performed on a very weakly compensated sample of n-type InSb with an initi~ free carrier density of 7.5 lO 13 cm -3 at low temperature and a compensation ratio of about 5%. The sample was put in a Cu-Be bomb, where hydrostatic pressure up to 15 Kbars were given by a gas compressor using He as transmitting medium. The sample under high hydrostatic pressure was cooled to 80 K. Then the temperature was slowly decreased to 4.2 K, while the pressure was gradually removed, taking care not to freeze the helium gas. Hall measurements were performed in the 100 5000 Gauss magnetic field range, to be sure that the formula n - |/ RHe holds i.e at the Hall coefficient saturation (r = |) which appears before the beginning of the magnetic freeze-out regime. -
2.2
Experimental results
2. EXPERIMENTS 2.1
Experimental procedure
The basls of the prevlous mentlonned method is the use of the properties of a metastable impurity state, which is associated with the X minimum and whose existence in n-type InSb has been shown in several transport experlments (l,2,3). If hydrostatic pressure above |3 Kbars is applied at a temperature higher than |40 K, electrons of the conduction band are trapped on thls level in such a way that the decrease of the temperature below 100 K will prevent ~ny reexcitatlon of the carriers, even when the
0 378--4363/83/0000-0000/$03.00 © 1983 North-Holland
In fig. I, the free electron concentration versus temperature is shown for five different "states" of the same sample. As it can be seen the free carrier density decreases strongly when the temperature is lowered from 95 K to 40 K, then it reaches a plateau in the 40 K - 15 K range, followed by a small drop down to the lowest available temperature 4.2 K. In fig. 1(a) a very low carrier density never reached in n-type Ingb has been obtained without ~ny external stress or compensation. For this low~st concentration, below 30 K, we could not measure the Hall coefficient. On the contrary, the resistivity (fig. 2(a) ) has been measured down to 4.2 K.
A Kadn et al / N e w results zn transport phenomena
236
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.
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.""
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,,
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I0 000 Fig.
]
005 Electron perature,
010
015
concentrations
versus
tem-
Points are experimental, solid lines are calculated with N A = 6. |012 cm -3
This can be due to the existence of a hopping process. 3.
1/T I,,K
020
ANALYSIS OF THE EXPERIMENTAL RESULTS
In fig. l-f we have plotted the temperature dependence of the intrinsic carrier concentr~ion. It clearly appearsthat in the 4.2 K - 95 K range no contribution to the conduction can be expected from these carriers. A detailed analysis has been done on the basis of the neutrality equation, taking into account the contribution of three levels : a hydrogenic one which is active at low temperature, a deep level, active above 40 K, and one or several acceptor levels always ionized. - In a first step, we don't take into account any level broadnlng or band tailing effect. The best fit to the data is obtained at low temperatures if the acceptor density N. is equal to • . A 6.1012 cm -3. Thls result is In good agreement wlth the one obtained from the analysis of the magnetic freeze out experiments done on the same sample. Moreover the high experimental moblllties we have measured, are in agreement with the theoretical predictions of LitwinStaszewska et al (]) for low compensated samples. - In a second step, we consider a broadnlng of the hydrogenic level and a band tailing of the r conduction band assuming in both cases a gausslan llke distribution function with a respectively 7 and y' half width. In this caae
Fig. 2
Variations of experimental resistivity with temperature
too, calculations show that the compensation remains low. In the case of low free carrier density (fig. l-b, l-c), the values of y and 7' we have obtained must be lower than 0.5 meV with N A = 6.1012 cm -3. This seams reasonnable since both the effect of disorder and electron interaction for our high pure sample must be low, with increasing free electron concentrations (flg. l-d, l-e) the best fitting are obtained assuming higher values of 7 and y' up to 2 meV. As a result, In the low temperature range (4.2 K - ]5 K), we have shown the existence of an activation energy of 0.6 meV for the case of fig. |-b. Thls value is close to the theoretical lonisatlon energy of the hydrogenlc level (effective Rydberg) which is about 0.63 meV in n-type InSb (4). From fig. ]-b to flg. I-c, it can be seen a decrease of the activation energy wlth increasing free carrier density. In the case of flg. ]-d no activation energy appears. This result shows a metal-non metal transition due to the changes of the free carrier denslty without applying any stress. In the high temperature range (40 K - 95 K), the conductivity is controlled by the donor like impurity level, characterized by a density of states of 3.10 13 em -3 and an activation energy of 55 meV. Though we are not aware of any transport experiment which has detected such a level, experlmental evidences from pbotoeonduetivity and photoelectromagnetlc measurements have indicated a deep donor-llke native defect (5-6). However, both early results of Laff and Fann(5) and recent ones of Seller et al (7) give too
A Kadr~ et aL / New results in transport phenomena
large values of the activation energy (about 120 meV) to consider that the level we observed is the same. In the intermediate region (15 K - 40 K) the observed plateau corresponds to the exhaustion of the hydrogenzc level before activation of the deep one. 4. CONCLUSION In conclusion, these results lead to a new field of investzgation of transport phenomena in ntype InSb. Our experiment allowed us to obtain the lowest free carrier never reached in n-type InSb without compensation or stress, and to observe the metal-non metal transition in the same sample where the free electron concentration was changed by freezing electrons on metastable state . Due to the high purity of the sample , an activation energy corresponding to the effective Rydberg has been observed. Evidence is also glven of a deep donor-like impurity level.
237
REFERENCES I. E. Lxtwing-Staszewska, W. Szymanska and R. Piotrzkowskl, Proc. 4th Int. Conf. Physics Narrow gad semlcond. Linz. Austrla,SeDt. 1981 2. M. Konczykowskl, S. Porowskl and J. Chroboczek High Temp.-High pressure 6 (1971) I11 3. S. Porowskl, L. Konczewlcz, M. Konczykowski, R.L. Aulombard and J.L. Robert Proc. 15th Int. Conf. Physics of SC, Kyoto (1980) J . Phys. Soc. Japan 49 (1980) 271 4. R. Kaplan Narrow Gap Semicond. Phys. and a p p l i c a t i o n s , Nimes (1978) 138 5. R.A. L a f f and H. Y. Fan, Phys. Rev. 121 (1961) 53 6. J . E . L . H o l l i s , S.C. Choo and E.L. H e a s e l l J . Appl. Phys. 38 (1967) 1626 7. D.G. S e i l e r , M.W. Goodwing and A. M i l l e r Phys. Rev. L e t t . 44 (1980) 807
235
HEW RESULTS IN TRANSPORT PHENOMENA IN UNCOMPENSATED n-TYPE InSb WITH EXTREMELY LOW CARRIER DENSITY A. KADRI, R.L. AULOMBARD,
C. BOUSQUET,
A. RAYMOND,
J. L. ROBERT
Centre d'Etudes d'Electronlque des Solides , assocle au C.N.R.S. ( L.A. n ° 21) U.S.T.L. Place Eugene Batalllon, 34060 MONTPELLIER C~dex (France) S. POROWSKI, High Pressure Research Center,
L. KONCZEWICZ
Pollsh Academy of Sclences,
WARSAW (Poland)
We report new experimental results of low temperature (4.2 K - 95 K) transport phenomena in uncompensated n-type InSb sample, where very low free carrier concentratlons are obtained using the properties of a metastable impurity state. By varying free electron density in the same sample, from ]0 II cm -3 to 1014 cm -3 the metal-non metal transition is observed. The evidence of an activation energy of the hydrogenlc level corresponding to the effective Rydberg is given. Above 40 K the role of a donor-llke impurity level is shown.
I.
INTRODUCTION
A great interest has been devoted to the studies of low free carrier density n-type InSb, and different methods have been used to obtain such samples using either growing techniques (purification, compensation ...) or external perturbations (magnetic field, compression...). Recently, some workers (l) performing experiments on n-type InSb at 77 K have shown the possibility to obtain low electron concentrations and hlgh mobIiIties by freezing electrons on a metastable state (connected with X minimum) using hlgh pressure techniques and an appropriate temperature treatment. In the present work, we use this method to induce large changes of the free carrier density on a very low compensated n-type InSb sample on which transport experiments have been performed in the temperature range from 4.2 K to 95 K. By uslng this previous method on a very pure sample, we have obtained very interesting new results, which lead to a new progress in the study of transport phenomena in n-type InSb.
hydrostatlc pressure is removed. If temperature is then raised to 100 - ||0 K, a reexcltation of carriers is observed, giving different "states" for the same sample characterized by different free carrier density. Our experiments were performed on a very weakly compensated sample of n-type InSb with an initi~ free carrier density of 7.5 lO 13 cm -3 at low temperature and a compensation ratio of about 5%. The sample was put in a Cu-Be bomb, where hydrostatic pressure up to 15 Kbars were given by a gas compressor using He as transmitting medium. The sample under high hydrostatic pressure was cooled to 80 K. Then the temperature was slowly decreased to 4.2 K, while the pressure was gradually removed, taking care not to freeze the helium gas. Hall measurements were performed in the 100 5000 Gauss magnetic field range, to be sure that the formula n - |/ RHe holds i.e at the Hall coefficient saturation (r = |) which appears before the beginning of the magnetic freeze-out regime. -
2.2
Experimental results
2. EXPERIMENTS 2.1
Experimental procedure
The basls of the prevlous mentlonned method is the use of the properties of a metastable impurity state, which is associated with the X minimum and whose existence in n-type InSb has been shown in several transport experlments (l,2,3). If hydrostatic pressure above |3 Kbars is applied at a temperature higher than |40 K, electrons of the conduction band are trapped on thls level in such a way that the decrease of the temperature below 100 K will prevent ~ny reexcitatlon of the carriers, even when the
0 378--4363/83/0000-0000/$03.00 © 1983 North-Holland
In fig. I, the free electron concentration versus temperature is shown for five different "states" of the same sample. As it can be seen the free carrier density decreases strongly when the temperature is lowered from 95 K to 40 K, then it reaches a plateau in the 40 K - 15 K range, followed by a small drop down to the lowest available temperature 4.2 K. In fig. 1(a) a very low carrier density never reached in n-type Ingb has been obtained without ~ny external stress or compensation. For this low~st concentration, below 30 K, we could not measure the Hall coefficient. On the contrary, the resistivity (fig. 2(a) ) has been measured down to 4.2 K.
A Kadn et al / N e w results zn transport phenomena
236
1014
104 x
!.
w
×
10 3
x
: '
w M
10 2
M i x .
:
fl:
.
t 01
: "~oI • (a) ,
o
t21 I*
'°!l:
8
,s .~llqg • il
dis J • • • •
•
.""
•
" "[el
•
10"1
,,
,6 2
I0 000 Fig.
]
005 Electron perature,
010
015
concentrations
versus
tem-
Points are experimental, solid lines are calculated with N A = 6. |012 cm -3
This can be due to the existence of a hopping process. 3.
1/T I,,K
020
ANALYSIS OF THE EXPERIMENTAL RESULTS
In fig. l-f we have plotted the temperature dependence of the intrinsic carrier concentr~ion. It clearly appearsthat in the 4.2 K - 95 K range no contribution to the conduction can be expected from these carriers. A detailed analysis has been done on the basis of the neutrality equation, taking into account the contribution of three levels : a hydrogenic one which is active at low temperature, a deep level, active above 40 K, and one or several acceptor levels always ionized. - In a first step, we don't take into account any level broadnlng or band tailing effect. The best fit to the data is obtained at low temperatures if the acceptor density N. is equal to • . A 6.1012 cm -3. Thls result is In good agreement wlth the one obtained from the analysis of the magnetic freeze out experiments done on the same sample. Moreover the high experimental moblllties we have measured, are in agreement with the theoretical predictions of LitwinStaszewska et al (]) for low compensated samples. - In a second step, we consider a broadnlng of the hydrogenic level and a band tailing of the r conduction band assuming in both cases a gausslan llke distribution function with a respectively 7 and y' half width. In this caae
Fig. 2
Variations of experimental resistivity with temperature
too, calculations show that the compensation remains low. In the case of low free carrier density (fig. l-b, l-c), the values of y and 7' we have obtained must be lower than 0.5 meV with N A = 6.1012 cm -3. This seams reasonnable since both the effect of disorder and electron interaction for our high pure sample must be low, with increasing free electron concentrations (flg. l-d, l-e) the best fitting are obtained assuming higher values of 7 and y' up to 2 meV. As a result, In the low temperature range (4.2 K - ]5 K), we have shown the existence of an activation energy of 0.6 meV for the case of fig. |-b. Thls value is close to the theoretical lonisatlon energy of the hydrogenlc level (effective Rydberg) which is about 0.63 meV in n-type InSb (4). From fig. ]-b to flg. I-c, it can be seen a decrease of the activation energy wlth increasing free carrier density. In the case of flg. ]-d no activation energy appears. This result shows a metal-non metal transition due to the changes of the free carrier denslty without applying any stress. In the high temperature range (40 K - 95 K), the conductivity is controlled by the donor like impurity level, characterized by a density of states of 3.10 13 em -3 and an activation energy of 55 meV. Though we are not aware of any transport experiment which has detected such a level, experlmental evidences from pbotoeonduetivity and photoelectromagnetlc measurements have indicated a deep donor-llke native defect (5-6). However, both early results of Laff and Fann(5) and recent ones of Seller et al (7) give too
A Kadr~ et aL / New results in transport phenomena
large values of the activation energy (about 120 meV) to consider that the level we observed is the same. In the intermediate region (15 K - 40 K) the observed plateau corresponds to the exhaustion of the hydrogenzc level before activation of the deep one. 4. CONCLUSION In conclusion, these results lead to a new field of investzgation of transport phenomena in ntype InSb. Our experiment allowed us to obtain the lowest free carrier never reached in n-type InSb without compensation or stress, and to observe the metal-non metal transition in the same sample where the free electron concentration was changed by freezing electrons on metastable state . Due to the high purity of the sample , an activation energy corresponding to the effective Rydberg has been observed. Evidence is also glven of a deep donor-like impurity level.
237
REFERENCES I. E. Lxtwing-Staszewska, W. Szymanska and R. Piotrzkowskl, Proc. 4th Int. Conf. Physics Narrow gad semlcond. Linz. Austrla,SeDt. 1981 2. M. Konczykowskl, S. Porowskl and J. Chroboczek High Temp.-High pressure 6 (1971) I11 3. S. Porowskl, L. Konczewlcz, M. Konczykowski, R.L. Aulombard and J.L. Robert Proc. 15th Int. Conf. Physics of SC, Kyoto (1980) J . Phys. Soc. Japan 49 (1980) 271 4. R. Kaplan Narrow Gap Semicond. Phys. and a p p l i c a t i o n s , Nimes (1978) 138 5. R.A. L a f f and H. Y. Fan, Phys. Rev. 121 (1961) 53 6. J . E . L . H o l l i s , S.C. Choo and E.L. H e a s e l l J . Appl. Phys. 38 (1967) 1626 7. D.G. S e i l e r , M.W. Goodwing and A. M i l l e r Phys. Rev. L e t t . 44 (1980) 807