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Fabrication of high sensitivity thin-film indium antimonide magnetoresistors
Solid-Safe
Electronics, 1975, Vol. 18, pp. 393-397.
Pergamon Press.
Printed in Great Britain
FABRICATION OF HIGH SENSITIVITY THIN-FILM INDIUM ANTIMONIDE MAGNETORESISTORS” G. S. NADKARNI,
A.
SIMONI
Precision Electronics Components (1971)Ltd., Toronto, Canada
and J. G. SIMMONS Electrical Engineering Department, University of Toronto, Toronto, Canada (Received 22 June 1974)
Abstract-A methodis describedfor fabricatinghi&-sensitivitythin filmof InSb. The fabrication procedure consists of the sequential deposition of chromium, antimony and indium. The films are then heat treated to thermo-chemically produce polycrystalline InSb films. The free-electron mobility of these films is found to be 5.4 x IO’cm’/V. set, and the free carrier density to be 10L6 cm-‘. Magnetoresistors were fabricated from these films with addition of indium, Hall-voltage shorting strips. The magnetoresistance sensitivity of these resistors was found to be 45per cent K G, which compares very favourably with that obtained from single crystal InSb resistors. 1. INTRODUCTION
Magnetoresistors are technologically important because of the promise they offer not only as contactless switches, potentiometers and angular transducers but also for their use in various automatic control systems[l-31. The fact that the resistance of the device may be varied without the use of a wiping contact, eliminates erosion of the resistor element due to wear and tear that conventional potentiometers are subject to; thus, these resistors have long-lie expectancy and high reliability. Furthermore, contact noise associated with conventional resistors is obviated. The magnetoresistance effect is a function of the free carrier mobility. Thus because of their high carrier mobility, intermetallic compound semiconductors have been widely studied as possible materials for use as magnetoresistors. In particular, indium antimonide (InSb) has received wide attention because it has the highest mobility (- 70 x 10’am*/V. set) of the more-common single crystal intermetalic semiconductors. Although crystalline semiconductors have higher carrier mobility than their polycrystalline counterparts, many researchers have concentrated their attentions on intermetallic thinfilm semiconductor films[C8], which are at best polycrystalline in nature. The case ofr thin-film magnetoresistors is that they may be fabricated in a much wider range of geometries than can single crystals, and because of their high surface to-volume ratio, heat generation is much easier to dissipate in thin-film resistors, particularly if *This work was supported by Defence Research Board of Canada.
fabricated on a suitable (high-thermal conductivity) substrate. The fabrication of stoichiometric intermetallic semiconductor thin-films is, however, a difficult problem. This is primarily because of the wide disparity that normally exists between the vapour pressure of the constituent elements making up the compound. Thus, using the semiconductor compound as an evaporant results in preferential evaporation of the higher-vapour-pressure constituents and, hence, a nonstoichiometric film. Furthermore, unless the films are prepared on a appropriate single-crystal substrate, the films are at best polycrystalline. As a consequence of their defect nature, thin-film semiconductors have free carrier mean free paths, mobilities and, hence, in particular magnetoresistance sensitivities that are disappointing compared to those of the corresponding single crystals. The object of this paper is to demonstrate using appropriate fabrication techniques, that it is possible to prepare thin film magnetoresistors of InSb that have magnetoresistance sensitivities approaching those of crystalline InSb magnetoresistors.
2.
FABRICATION
In view of the fact that InSb evaporates preferentially, there is no advantage in using pure InSb crystals as starting material. Thus, the method adopted here is to start with the high-purity elemental materials In and Sb. The magnetoresistors were fabricated on glass substrates (although any substrate material may be used). The substrates were ultrasonically cleaned, first in detergent 393
394
G. S.
NADKARNI,
A.
SIMONI and J. G. SIMMONS
and water, and then in isopropyl alcohol. The substrates were then rinsed using deionized water and dried. Next the substrates were placed in a Balzer vacuum system and gas-discharged (ion bombardment) cleaned in a filtered argon atmosphere. They were then heated to about 200°C for 2 hr at a pressure of 10d6torr, to degas the surface. The vacuum system contained a planetary substrate holder to ensure uniform film coatings. A four-crucible electron-gun assembly was used for vaporizing the elemental materials. The vacuum system was pumped by a turbomolecular pumping system. A thin layer of chromium, about 500 A in thickness, the purpose of which will be discussed later, was first deposited onto the substrate. Next a layer of antimony was deposited on to the chromium layer, followed by a layer of indium (Fig. 2(a)). (Note that the order of depositing the film is important, because indium prevents the evaporation of the antimony during the annealing process, see below). The total thickness of the double layer was varied from 1 to 5 pm, such that the ratio of the masses of the individual layers of indium and antimony were in a close proportion to their atomic weights (121.76: 114.82). All three layers were deposited uniformly over the entire surface of the substrate, with the substrate held at a temperature of about 200°C.The entire process was completed without breaking the vacuum at any time, under a pressure of the order of about 10e6torr. The substrates were then allowed to cool to room temperature before removal from the coating unit. Next, the samples were annealed in a furnace, using the heating cycle shown in Fig. 1, in order for the indium and antimony to thermo-chemically combine into the InSb semiconductor compound. During the heating cycle, argon was passed through the furnace, at a flow rate of about 6l./hr, to prevent oxidation of the elemental materials. During annealing, indium melts at a temperature of approximately 156”C, and as the temperature is raised to above the melting point of InSb (-530°C) the molten indium diffuses into the antimony layer and chemically combines with it to yield polycrystalline InSb.
When the heating cycle was completed, the samples were again placed in the vacuum system, and a uniform layer of indium of thickness between 0.3-0.4 pm was deposited over the entire surface. Using standard photolithographic techniques, the indium layer was etched into uniform strips of width 100pm, separated by various distance, as shown in Fig. 2(c). (Note that it is not necessary to use indium for making these strips, the function of which is discussed later; any metal of good conductivity may be used. Indium was used in our case, because of its relatively high conductivity, its adherence to InSb, and to avoid contaminating the vacuum system with other metals). Resistor patterns were then etched into the InSb film using photolithographic techniques, such that the current path in the resistor was perpendicular to the In strips, as shown in Fig. 2(d). Finally lead contacts were either bonded or soldered to the resistor terminals.
Substrate
(b)
Y
(d)
Fig. 2. Schematic representation of fabrication process: (a) Cr-%-In layers immediately after deposition; (b) system after heat treatment; (c) system with In strips; (sd) magnetoresistor pattern.
E 2 e $ E
45c
c
35c
I
I
I
Time,
Fig. 1.
Heating
cycle
/
/
3. RESULTS
I 90
60
30
min
for thermo-chemical films.
processing
of InSb
sensitivity of the magnetoresistors was found to be dependent on several factors: (a) thickness of Cr layer; (b) thickness of InSb layer; (c) thickness and spacing of the In strips. We shall consider these parameters below. The
395
Thin-filmindiumantimonidemagnetoresistors Finally, we will present more basic data, namely the results of mobility, and carrier density studies. 3.1 Magnetoresistance sensitivity The full curve (a) in Fig. 3 shows a typical characteristic for a thin-f&n InSb magnetoresistor, fabricated using the techniques described above. It is seen that for magnetic fields less than 3K G the characteristic in nonlinear, but at higher fields the curve becomes linear in the magnetic field. The thickness of the InSb layer was 4 pm and the In strips were 100 pm wide separated by gaps 100pm wide. For comparison, curve (b) is for an indential
4
Effect
of InSb thickness
. Q Ql Q” 2
/ /’
I I
0
500
I 2
Film thickness.
Fig.
4. Effect
of
InSb
I 3
I 4
I 5
-I
urn
film thickness sensitivity.
on
magnetoresistance
provides superior adherence of the InSb film to the substrate. Second, it serves to improve the sensitivity of the device, by partially shorting the Hall voltage. Of course, the resistance of ihis layer must be much higher than that in InSb layer otherwise it effectively shunts the InSb resistance and reduces the magnetorestance sensitivity. For example, let RI and R2 be the resistances of the chromium layer and InSb layer respectively, and RT be the total resistance of the device. Since R, and Rz are in parallel, we have RT = R,Rd(Rl t Rz).
(1)
For a given change (AB) in the magnetic field, the change in the total resistance, ART,due to the change AR2,in the InSb film is B,
K. Gauss
Fig. 3. Magnetoresistance sensitivity as a function of magnetic field. Curve (a) is InSb film with In Hallvoltage shorting strips (see text).
resistor, but without the strips. Curve (c) in Fig. 3 are the results obtained from single crystal InSb, replotted from the results in ref. [3]. Curve (d) in Fig. 3 was obtained from thin film recrystallized de&tic InSb films replotted from Fig. 4 of ref. [6]. It is clearly evident that our results are substantially superior to those of curve (d), and are indeed, close to those obtained using the single crystal material (curve (c)). It is found from curve (a) in Fig. 3 that the magnetoresistance sensitivity of these resistors (percentage change per unit change in magnetic field, i.e. the slope of the linear part of the curve), is about forty five per cent per K G. 3.2 Chronium layer The purpose of the chromium layer is two fold. First, it acts as a nucleating agent for the antimony layer and
ART =
(2)
Thus, it is seen that ART is effectively reduced by a factor [R,/(R, t R#, which is less than unity, but tends to unity for RI %-R2. 3.2 Indium and antimony layers The magnetoresistance sensitivity initially increases with the thickness of the InSb layer, but then saturates to a constant value for thicknesses greater than 3 km, as shown in Fig. 4. The reason for this phenomenon is that the carrier mobility is higher in the thicker films, as a consequence of the larger crystallite size and better uniformity of these films, which reduces free-carrier scattering. 3.3 Indium strips The purpose of the indium strips is to short-circuit the Hall voltage and, thus, increase the magneto-resistance sensitivity.
G. S. NADKARNI,
396
A.
SIMONI and
J. G.
SIMMONS
Figure 5 illustrates the effect of strip separation, for a given strip width of 100pm, on the sensitivity of the magnetoresistor. It is seen that the sensitivity improves as the separation decreases, as a consequence of more effective shunting of the Hall voltage.
12 kG _/5
/
kG
500
400
z g
300
2 ." t? .c u 200 P 2 u
B=lOkG \ In strip width = IOOpm
15
IO
5 Sensing
V,“,
voltage,
X10-’
100
Fig. 6. Hall voltage vs applied voltage for InSb films for various magnetic field strengths.
0
I
1
I
2 In strip
I
3 separation.
4 pm.
Fig. 5. Magnetoresistance sensitivity as a function shorting strip separation.
5 Xl00 of Hall voltage
3.4 Mobilities measurements The thin film InSb samples were studied to determine carrier density etc. using Hall effect measurements and the magneto-resistance effect. (a) Hall e$ect methods. Figure 6 shows a graph of input voltage (Vi,) vs Hall voltage (V,,) characteristics for a typical sample without indium strips. The length (L) to width (W) ratio of this sample was L/W = 2.5. The measurements were made for different magnetic fields (B). The direction of the Hall voltage indicated that the carriers are electrons. The electron (in this case) mobility (CL”) was calculated from the relation 0
IO
5 Magnetic
field,
15 Gauss.
NO3
Fig. 7. Hall mobility vs magnetic field strength.
Fig. 7 shows the variation of electron mobility as a function of magnetic field. It is seen that the mobility decreases with increasing magnetic field. Extrapolating this curve to B = 0, p,, was found to be approximately 3 x lo4 cm*/V. sec. The conductivity (Tfor this sample was
300R-‘cm-‘, and the carrier concentration, (n) calculated using the relation 0
=
ep.n
397
Thin-filmindiumantimonide magnetoresistors
where e is electronic charge, was found to be lOI cm-‘. Note that in the case of our samples which are polycrystalline at best, the value does not necessarily imply a donor concentration of 1OL6 cm’; this is because traps in the sample may act as compensating centers. (b) Magnetoresistance method. In this case the mobility of the carriers was calculated before the Hall voltage shorting strips were deposited and after the strips were deposited. In the former case, the mobility calculated from the magnetoresistance change is the real mobility, and in the latter case it is virtual or effective mobility, since there is an increase in the magnetoresistance change (AR/R), due to Hall voltage shorting. These mobilities were calculated for low magnetic field (1 K G). For low fields, the Wilson-Sommerfeld theory [9] predicts for the simple case of an isotropic conduction band, which is a reasonable approximation for our polycrystalline material, that Rs = Ro(1 + 0.273 B2pb),
i.e. $
= 0.273 p;B*,
where R. is the resistance of the sample in zero magnetic field, and B in a magnetic field B. From the curve (b) of Fig. 3 ~~ was calculated to be CL.= 54 X lo4 cm’/V. set
for the sample without the strips. From curve (a) of Fig. 3 an apparent mobility CL.= 8.1 x 10”cm’/V. set is obtained for the same sample with the Hall voltage shorting strips. The former value compares well with the Hall effect measurement obtained earlier, and also compares favourably with single crystal values, which are typically 7 X lo4 cm*/V . sec. 4.CONCLUSIONS
We have described a relatively simple method of preparing thin-film InSb magnetoresistors with the magnetoresistance sensitivity close to that of single crystal InSb magnetoresistors. Magnetoresistance sensitivities as high as 45 per cent per K G were obtained by appropriate short-circuiting of the Hall voltage. The electron mobility was found to be approximately 5.4 X 10”cm’/V . set, and the free carrier density to be 10’6cm-3. REFERENCES
1. L. T. Yuan, Solid-St. Electron 9, 497 (1%6). 2. S. Kataoka, Pm. LEE 111, 1937(1964). 3. S. Kataoka,H. Yamadaand H. Fujisada, Solid State Sensor Symp. Conf Record, p. 56 (1970). 4. H. H. Weider, .I appl. Phys. 40, 3320 (1%9). 5. W. J. Williamson,Solid-St. Electron 9, 213 (1%6). 6. H. H. Wieder, Solid-St. Electron 9, 373 (1%6). 7. N. F. Teede. Solid-St. Electron 10, 1069(1967). 8. J. A. Carroll&d J. F. Spivak, Solid-St. Electron b, 383(1%6). 9. A. H. Wilson, Theory of Metals, p. 235. Cambridge University Press (1953).
Electronics, 1975, Vol. 18, pp. 393-397.
Pergamon Press.
Printed in Great Britain
FABRICATION OF HIGH SENSITIVITY THIN-FILM INDIUM ANTIMONIDE MAGNETORESISTORS” G. S. NADKARNI,
A.
SIMONI
Precision Electronics Components (1971)Ltd., Toronto, Canada
and J. G. SIMMONS Electrical Engineering Department, University of Toronto, Toronto, Canada (Received 22 June 1974)
Abstract-A methodis describedfor fabricatinghi&-sensitivitythin filmof InSb. The fabrication procedure consists of the sequential deposition of chromium, antimony and indium. The films are then heat treated to thermo-chemically produce polycrystalline InSb films. The free-electron mobility of these films is found to be 5.4 x IO’cm’/V. set, and the free carrier density to be 10L6 cm-‘. Magnetoresistors were fabricated from these films with addition of indium, Hall-voltage shorting strips. The magnetoresistance sensitivity of these resistors was found to be 45per cent K G, which compares very favourably with that obtained from single crystal InSb resistors. 1. INTRODUCTION
Magnetoresistors are technologically important because of the promise they offer not only as contactless switches, potentiometers and angular transducers but also for their use in various automatic control systems[l-31. The fact that the resistance of the device may be varied without the use of a wiping contact, eliminates erosion of the resistor element due to wear and tear that conventional potentiometers are subject to; thus, these resistors have long-lie expectancy and high reliability. Furthermore, contact noise associated with conventional resistors is obviated. The magnetoresistance effect is a function of the free carrier mobility. Thus because of their high carrier mobility, intermetallic compound semiconductors have been widely studied as possible materials for use as magnetoresistors. In particular, indium antimonide (InSb) has received wide attention because it has the highest mobility (- 70 x 10’am*/V. set) of the more-common single crystal intermetalic semiconductors. Although crystalline semiconductors have higher carrier mobility than their polycrystalline counterparts, many researchers have concentrated their attentions on intermetallic thinfilm semiconductor films[C8], which are at best polycrystalline in nature. The case ofr thin-film magnetoresistors is that they may be fabricated in a much wider range of geometries than can single crystals, and because of their high surface to-volume ratio, heat generation is much easier to dissipate in thin-film resistors, particularly if *This work was supported by Defence Research Board of Canada.
fabricated on a suitable (high-thermal conductivity) substrate. The fabrication of stoichiometric intermetallic semiconductor thin-films is, however, a difficult problem. This is primarily because of the wide disparity that normally exists between the vapour pressure of the constituent elements making up the compound. Thus, using the semiconductor compound as an evaporant results in preferential evaporation of the higher-vapour-pressure constituents and, hence, a nonstoichiometric film. Furthermore, unless the films are prepared on a appropriate single-crystal substrate, the films are at best polycrystalline. As a consequence of their defect nature, thin-film semiconductors have free carrier mean free paths, mobilities and, hence, in particular magnetoresistance sensitivities that are disappointing compared to those of the corresponding single crystals. The object of this paper is to demonstrate using appropriate fabrication techniques, that it is possible to prepare thin film magnetoresistors of InSb that have magnetoresistance sensitivities approaching those of crystalline InSb magnetoresistors.
2.
FABRICATION
In view of the fact that InSb evaporates preferentially, there is no advantage in using pure InSb crystals as starting material. Thus, the method adopted here is to start with the high-purity elemental materials In and Sb. The magnetoresistors were fabricated on glass substrates (although any substrate material may be used). The substrates were ultrasonically cleaned, first in detergent 393
394
G. S.
NADKARNI,
A.
SIMONI and J. G. SIMMONS
and water, and then in isopropyl alcohol. The substrates were then rinsed using deionized water and dried. Next the substrates were placed in a Balzer vacuum system and gas-discharged (ion bombardment) cleaned in a filtered argon atmosphere. They were then heated to about 200°C for 2 hr at a pressure of 10d6torr, to degas the surface. The vacuum system contained a planetary substrate holder to ensure uniform film coatings. A four-crucible electron-gun assembly was used for vaporizing the elemental materials. The vacuum system was pumped by a turbomolecular pumping system. A thin layer of chromium, about 500 A in thickness, the purpose of which will be discussed later, was first deposited onto the substrate. Next a layer of antimony was deposited on to the chromium layer, followed by a layer of indium (Fig. 2(a)). (Note that the order of depositing the film is important, because indium prevents the evaporation of the antimony during the annealing process, see below). The total thickness of the double layer was varied from 1 to 5 pm, such that the ratio of the masses of the individual layers of indium and antimony were in a close proportion to their atomic weights (121.76: 114.82). All three layers were deposited uniformly over the entire surface of the substrate, with the substrate held at a temperature of about 200°C.The entire process was completed without breaking the vacuum at any time, under a pressure of the order of about 10e6torr. The substrates were then allowed to cool to room temperature before removal from the coating unit. Next, the samples were annealed in a furnace, using the heating cycle shown in Fig. 1, in order for the indium and antimony to thermo-chemically combine into the InSb semiconductor compound. During the heating cycle, argon was passed through the furnace, at a flow rate of about 6l./hr, to prevent oxidation of the elemental materials. During annealing, indium melts at a temperature of approximately 156”C, and as the temperature is raised to above the melting point of InSb (-530°C) the molten indium diffuses into the antimony layer and chemically combines with it to yield polycrystalline InSb.
When the heating cycle was completed, the samples were again placed in the vacuum system, and a uniform layer of indium of thickness between 0.3-0.4 pm was deposited over the entire surface. Using standard photolithographic techniques, the indium layer was etched into uniform strips of width 100pm, separated by various distance, as shown in Fig. 2(c). (Note that it is not necessary to use indium for making these strips, the function of which is discussed later; any metal of good conductivity may be used. Indium was used in our case, because of its relatively high conductivity, its adherence to InSb, and to avoid contaminating the vacuum system with other metals). Resistor patterns were then etched into the InSb film using photolithographic techniques, such that the current path in the resistor was perpendicular to the In strips, as shown in Fig. 2(d). Finally lead contacts were either bonded or soldered to the resistor terminals.
Substrate
(b)
Y
(d)
Fig. 2. Schematic representation of fabrication process: (a) Cr-%-In layers immediately after deposition; (b) system after heat treatment; (c) system with In strips; (sd) magnetoresistor pattern.
E 2 e $ E
45c
c
35c
I
I
I
Time,
Fig. 1.
Heating
cycle
/
/
3. RESULTS
I 90
60
30
min
for thermo-chemical films.
processing
of InSb
sensitivity of the magnetoresistors was found to be dependent on several factors: (a) thickness of Cr layer; (b) thickness of InSb layer; (c) thickness and spacing of the In strips. We shall consider these parameters below. The
395
Thin-filmindiumantimonidemagnetoresistors Finally, we will present more basic data, namely the results of mobility, and carrier density studies. 3.1 Magnetoresistance sensitivity The full curve (a) in Fig. 3 shows a typical characteristic for a thin-f&n InSb magnetoresistor, fabricated using the techniques described above. It is seen that for magnetic fields less than 3K G the characteristic in nonlinear, but at higher fields the curve becomes linear in the magnetic field. The thickness of the InSb layer was 4 pm and the In strips were 100 pm wide separated by gaps 100pm wide. For comparison, curve (b) is for an indential
4
Effect
of InSb thickness
. Q Ql Q” 2
/ /’
I I
0
500
I 2
Film thickness.
Fig.
4. Effect
of
InSb
I 3
I 4
I 5
-I
urn
film thickness sensitivity.
on
magnetoresistance
provides superior adherence of the InSb film to the substrate. Second, it serves to improve the sensitivity of the device, by partially shorting the Hall voltage. Of course, the resistance of ihis layer must be much higher than that in InSb layer otherwise it effectively shunts the InSb resistance and reduces the magnetorestance sensitivity. For example, let RI and R2 be the resistances of the chromium layer and InSb layer respectively, and RT be the total resistance of the device. Since R, and Rz are in parallel, we have RT = R,Rd(Rl t Rz).
(1)
For a given change (AB) in the magnetic field, the change in the total resistance, ART,due to the change AR2,in the InSb film is B,
K. Gauss
Fig. 3. Magnetoresistance sensitivity as a function of magnetic field. Curve (a) is InSb film with In Hallvoltage shorting strips (see text).
resistor, but without the strips. Curve (c) in Fig. 3 are the results obtained from single crystal InSb, replotted from the results in ref. [3]. Curve (d) in Fig. 3 was obtained from thin film recrystallized de&tic InSb films replotted from Fig. 4 of ref. [6]. It is clearly evident that our results are substantially superior to those of curve (d), and are indeed, close to those obtained using the single crystal material (curve (c)). It is found from curve (a) in Fig. 3 that the magnetoresistance sensitivity of these resistors (percentage change per unit change in magnetic field, i.e. the slope of the linear part of the curve), is about forty five per cent per K G. 3.2 Chronium layer The purpose of the chromium layer is two fold. First, it acts as a nucleating agent for the antimony layer and
ART =
(2)
Thus, it is seen that ART is effectively reduced by a factor [R,/(R, t R#, which is less than unity, but tends to unity for RI %-R2. 3.2 Indium and antimony layers The magnetoresistance sensitivity initially increases with the thickness of the InSb layer, but then saturates to a constant value for thicknesses greater than 3 km, as shown in Fig. 4. The reason for this phenomenon is that the carrier mobility is higher in the thicker films, as a consequence of the larger crystallite size and better uniformity of these films, which reduces free-carrier scattering. 3.3 Indium strips The purpose of the indium strips is to short-circuit the Hall voltage and, thus, increase the magneto-resistance sensitivity.
G. S. NADKARNI,
396
A.
SIMONI and
J. G.
SIMMONS
Figure 5 illustrates the effect of strip separation, for a given strip width of 100pm, on the sensitivity of the magnetoresistor. It is seen that the sensitivity improves as the separation decreases, as a consequence of more effective shunting of the Hall voltage.
12 kG _/5
/
kG
500
400
z g
300
2 ." t? .c u 200 P 2 u
B=lOkG \ In strip width = IOOpm
15
IO
5 Sensing
V,“,
voltage,
X10-’
100
Fig. 6. Hall voltage vs applied voltage for InSb films for various magnetic field strengths.
0
I
1
I
2 In strip
I
3 separation.
4 pm.
Fig. 5. Magnetoresistance sensitivity as a function shorting strip separation.
5 Xl00 of Hall voltage
3.4 Mobilities measurements The thin film InSb samples were studied to determine carrier density etc. using Hall effect measurements and the magneto-resistance effect. (a) Hall e$ect methods. Figure 6 shows a graph of input voltage (Vi,) vs Hall voltage (V,,) characteristics for a typical sample without indium strips. The length (L) to width (W) ratio of this sample was L/W = 2.5. The measurements were made for different magnetic fields (B). The direction of the Hall voltage indicated that the carriers are electrons. The electron (in this case) mobility (CL”) was calculated from the relation 0
IO
5 Magnetic
field,
15 Gauss.
NO3
Fig. 7. Hall mobility vs magnetic field strength.
Fig. 7 shows the variation of electron mobility as a function of magnetic field. It is seen that the mobility decreases with increasing magnetic field. Extrapolating this curve to B = 0, p,, was found to be approximately 3 x lo4 cm*/V. sec. The conductivity (Tfor this sample was
300R-‘cm-‘, and the carrier concentration, (n) calculated using the relation 0
=
ep.n
397
Thin-filmindiumantimonide magnetoresistors
where e is electronic charge, was found to be lOI cm-‘. Note that in the case of our samples which are polycrystalline at best, the value does not necessarily imply a donor concentration of 1OL6 cm’; this is because traps in the sample may act as compensating centers. (b) Magnetoresistance method. In this case the mobility of the carriers was calculated before the Hall voltage shorting strips were deposited and after the strips were deposited. In the former case, the mobility calculated from the magnetoresistance change is the real mobility, and in the latter case it is virtual or effective mobility, since there is an increase in the magnetoresistance change (AR/R), due to Hall voltage shorting. These mobilities were calculated for low magnetic field (1 K G). For low fields, the Wilson-Sommerfeld theory [9] predicts for the simple case of an isotropic conduction band, which is a reasonable approximation for our polycrystalline material, that Rs = Ro(1 + 0.273 B2pb),
i.e. $
= 0.273 p;B*,
where R. is the resistance of the sample in zero magnetic field, and B in a magnetic field B. From the curve (b) of Fig. 3 ~~ was calculated to be CL.= 54 X lo4 cm’/V. set
for the sample without the strips. From curve (a) of Fig. 3 an apparent mobility CL.= 8.1 x 10”cm’/V. set is obtained for the same sample with the Hall voltage shorting strips. The former value compares well with the Hall effect measurement obtained earlier, and also compares favourably with single crystal values, which are typically 7 X lo4 cm*/V . sec. 4.CONCLUSIONS
We have described a relatively simple method of preparing thin-film InSb magnetoresistors with the magnetoresistance sensitivity close to that of single crystal InSb magnetoresistors. Magnetoresistance sensitivities as high as 45 per cent per K G were obtained by appropriate short-circuiting of the Hall voltage. The electron mobility was found to be approximately 5.4 X 10”cm’/V . set, and the free carrier density to be 10’6cm-3. REFERENCES
1. L. T. Yuan, Solid-St. Electron 9, 497 (1%6). 2. S. Kataoka, Pm. LEE 111, 1937(1964). 3. S. Kataoka,H. Yamadaand H. Fujisada, Solid State Sensor Symp. Conf Record, p. 56 (1970). 4. H. H. Weider, .I appl. Phys. 40, 3320 (1%9). 5. W. J. Williamson,Solid-St. Electron 9, 213 (1%6). 6. H. H. Wieder, Solid-St. Electron 9, 373 (1%6). 7. N. F. Teede. Solid-St. Electron 10, 1069(1967). 8. J. A. Carroll&d J. F. Spivak, Solid-St. Electron b, 383(1%6). 9. A. H. Wilson, Theory of Metals, p. 235. Cambridge University Press (1953).