Single crystal InSb thin films by electron beam re-crystallization

Solid-State

Pergamon

Electronics

SINGLE

Press 1967. Vol. 10, pp. 1069-1076.

CRYSTAL BEAM

InSb

THIN

Printed

FILMS

in Great Britain

BY ELECTRON

RE-CRYSTALLIZATION N. F. TEEDE

Department

of Electrical

Engineering,

The University (Receiwd

of Western

24 March

Australia,

Nedlands,

Western

Australia

1967)

Abstract-Single crystals in excess of 1 mm2 in area have been grown in evaporated InSb thin films by electron beam microzone melting. The electrical and galvanomagnetic properties have been studied as a function of temperature between 300 and 90°K. In 3.6 p films electron mobilities of 61,000 cma/V-see at room temperature rising to 71,000 cme/V-set at 85°K have been measured. Both the values and temperature dependence of mobility are comparable with those reported for single crystal bulk material of similar net donor concentration of 4 x 10’e/cm3. This is in contrast with the anomalous mobility temperature dependence previously reported for thin films of InSb. A thickness dependence of mobility has been found in the range 1 to 58 p; however magnetoresistance measurements suggest that the lower mobilities in the thinner films could be due to the inhomogeneity of these samples. R&umB-Des cristaux simples ayant une surface superieure a 1 mm* ont ete developpes dans les pellicules fines dvaporees de SbIn par la fonte microzone a faisceau electronique. Les proprietes Clectriques et galvanometriques ont et6 etudites en fonction de la temperature entre 300 et 90°K. Dans les pellicules de 3,6 p on a mesure des mobilites d’electrons allant de 61.000 ems/V-set a temperature ambiante a 71.000 cmz/V-set a 85OK. Les valeurs et la dependance de mobilite sont comparables a celles repartees pour un materiau de masse g cristal simple ayant une concentration nette de donneurs de 4 x lO’a/cm s. Ceci contraste avec la temperature de mobilite anormale precedemment report&e pour les pellicules fines de SbIn. La dependance de la mobilite en fonction de l’epaisseur a Btci trouvee dans la gamme entre 1 et 5,s; toutefois, les mesures de magnetoresistance suggerent que les mobilites plus basses dans les pellicules plus fines seraient dues aux inhomogeneites de ces Cchantillons. Zusammenfassung-Aus der Dampfphase niedergeschlagene diinne I&b-Schichten wurden voriibergehend durch Elektronenbestrahlung aufgeschmolzen. Auf diese Weise entstanden Einkristallschichtcn mit einer FlPchenausdehnung van mehr als 1 mm 2. Die elektrischen und galvanomagnetischen Eigenschaften wurden als Funktion der Temperatur zwischen 300 und 90°K untersucht. Die Elektronenbeweglichkeit in 3,s p dicken Schichten stieg von 61 000 cm’/V-s bei Raumtemperatur auf 71 000 cma/V-s bei 85°K. Die Beweglichkeiten und .ihre Temperaturabhangigkeit sind vergleichbar mit den Werten, welche ftir Einkristalle aus Vollmaterial mit lhnlicher Donator-konzentration, namlich 4.10i6/cm3, angegeben werden. Dieser Befund steht im Gegensatz zu dem ftiher berichteten anomalenTemperaturverhalten der Beweglichkeit diinner InSb-Schichten. Eine Dicken-abhangigkeit der Beweglichkeit wurde zwar zwischen 1 und 5,s p gefunden. Jedoch lassen Messungen der Widerstandsanderung im Magnetfeld vermuten, d&s die kleineren Beweglichkeiten in den dtinneren Schichten von Inhomogenitlten hervorgerufen werden kiinnten. INTRODUCTION ~NDIUM

ANTIMONIDE

thin films prepared by vacuum evaporation of either the compound(l) or the elemental component@ have been polycrystalline in structure and have electrical properties which are inferior to those of the bulk material. CorrelationsPn3) between mobility and 3

crystallite size suggest that scattering at grain boundaries is important in limiting the electron mobility to about one quarter that of single crystal bulk InSb. Long annealing cycles at temperatures below the melting point of the compound have not succeeded in promoting extensive crystal in such polar semiconductor films. growth(l) 1069

1070

N.

F. TEEDE

However, polydendritic films consisting of an array of crystals which are large in relation to the electron mean free path, have been prepared by remelting vacuum deposited films under a protective In,O, cover layer. (4*5) CLAWSON and WIEDER@) have reported electron mobilities of 5.56 x lo4 cm2/V-set in thin single crystal dendrites isolated from polydendritic films prepared by this-method. The films reported in this paper have been re-crystallized from the molten’state by electron beam microzone melting.(7s, Large single crystal areas have been grown in evaporated InSb films on glass substrates which have electron mobilities and conductivities approaching to within 5 per cent of their values in single crystal bulk material having a similar net donor concentration. The InSb films were initially prepared by the rapid evaporation of. the compound on to glass substrates held at 350-4OO”C in a vacuum of about 5 x 10M6 torr. When the film had cooled to 3OO”C, the indium rich surface layer was oxidized by admitting air to the system at a pressure of 10 torr for approx. 4 min. After re-evacuating the system, the film was allowed to cool until it reached about 50°C when it was mechanically removed from the oven, rotated and brought into the focal plane of an electron beam. In the re-crystallization process, the energy of a scanning electron beam was used to melt a narrow zone 40 p wide across the film. The zone was moved slowly.through the film in the quadrature direction allowing the molten material to re-crystallize on to the advancing solid-liquid interface. The most uniform crystals were produced when using scanning speeds of 3 p/set in the slow growth direction and between 20 and 100 mm/set in the cross scan direction. The effects of changes in the various scanning parameters on crystal growth, and the electron optics of this system have been discussed more fully in a previous paper. (lo) Areas 5 x 5 mm have been recrystallized in films with thicknesses ranging from 1 to 6 CL. This slow, progressive growth technique imposes more favourable crystal growth conditions in the film than does the method reported by ~VIEDER and CLAU.SON’~~ allowing random c!endritic re-crystallization from extensive molten areas. In zone re-crystallized films dendritic growth was not usual except where excessively high scanning speeds or beam powers were used,

or where the initial film was grossly non-stoichiometric as indicated by the presence of Sb lines in Debye-Scherrer X-ray patterns. In both techniques of re-crystallization from the melt, the In,O, surface layer is necessary to prevent surface tension in the molten InSb causing the film to agglomerate into isolated mounds. Of a series of 40 films prepared by the zone recrystallization technique, 85 per cent yielded electron mobilities in the range of 30,00061,300 cm’/V-set near 300°K having net donor concentrations between 1 and 8 x 1016/cm3. In this paper the electrical and galvomagnetic properties of seven samples which are representative of the thickness range l-6 p are reported. PROPERTIES

OF UNIFORM

SINGLE

CRYSTAL

InSb FILMS

Using jet abrasion, areas of 4x 1 mm with the long axis parallel to the direction of fast scan were isolated from the central portion of 5 x 5 mm recrystallized films. The surface oxide layer was reimoved by gently polishing the surface, with levigated alumina. The abraded surface of one such sample, identified as sample il, is shown in Fig. 1. X-ray oscillation diffraction patterns show this area to be single crystal with the (111) orientation parallel to the plane of the substrate, This conclusion has been suppoLted by etch studies”” using 0.2 per cent iodine in acetic acid. Electrical measurements were made on sample A using low resistance current, potential and Hall contacts of vacuum deposited silver. The homogeneity of samplg A was checked in two ways: (a) macroscopically-the film was found to be uniform to within 5 per cent by an analysis of resistivity between six contacts applied to the film; (b) the microscopic homogeneity was checked by an analysis of the magnetoresistance, AR]R,. High field magnetoresistance is especially sensitive to random special fluctuations of carrier concentrations”“) and carrier concentration gradients.‘13) In Fig. 2 the magnetoresistance of sample A is shown as a function of magnetic Au:< density. It is quadratic in B for weak fields tending to linear function for B > 0.4 \Vb/m2. The increase in magnetoresistance between 300 and 85’K is accounted for by the increase in mobility which follows from an expression developed by LIPPMAN and I
SINGLE

I

0

0.1

CRYSTAL

InSb

THIN

0.4

a,

1071

FILMS

,

0.2

0.3 8

Cl6

0.7

WblM2)

FIG. 2. The magnetoresistance of sample A as a function of magnetic flux density with temperature as the parameter.

magnetoresistance

as:

a(B) AR --= ~/j@)*Btf(LIW)]-1 o(O) &,

L

(1)

where 0(0)/c(B) is the physical magnetoresistance, L/W is the length-to-width ratio of the film, _f(L/W) is a function of the geometry, p(B) is the mobility, and B is the flux density at which the measurement is made. Assuming the physical magnetoresistance to be zero [i.e. o(B) = o(O)] and using the published values(r4) off(L/ W), the geometric magnetoresistance of sample A at 0.65 Mb/m2 was calculated to be 0.68 at 300°K and 0.74 at 85°K which compare well with the measured values of O-71 and 0.79 respectively. This indicates that the greatest part of the measured magnetoresistance is due to the macroscopic geometric configuration. There is ,also a distortion of current streamlines where the Hall and potential electrodes protrude

slightly into the edge of the film which could account in part for the 3 per cent discrepancy between measured AR/R, and calculated geometric magnetoresistance. This sample is therefore assumed to be homogeneous in mobility and carrier concentration over the area measured to within the limits of experimental error. The thickness of sample A has been measured on a mechanical stylus Talysurf surface roughness gauge and has been found to be 3.65 _+O-05 CL. The surface was flat to within 500 A over a distance of 100 p before polishing. The scratches seen on the surface in Fig. 1 due to polishing are of similar depth. Figure 3 shows the temperature dependence of Hall coefficient, R,, and conductivity, CT, measured at 0.1 Wb/m 2. A minimum value of o in this range of temperature is reached at 238°K increasing slightly with decreasing temperature down to 85’K. The R, curve shows R, monotonically increases with decreasing temperature and

N.

1072

TEEDE

F.

*d

1 9

6

7

-6

FIG. 3. The Hall coefficient and conductivity of sample A as a function of inverse temperature. tends

to a value - 165 cm3/C at 85°K. These curves give a temperature dependence of mobility shown in Fig. 4. Figure 5 shows the field dependence of R, in sample A. The low temperature Ri, rises from a saturation value of -150 cm3/C at inweak approx 0.7 Wb[m 2 byafactorr=l.l fields. The value

6-

6-

R

H&O ------==

R HB-lm corresponds to the ratio of Hall to conductivity mobility. The net donor concentration has been calculated in all cases from RHO = rjne to eliminate uncertainty in scattering. Similarly the Hall mobility defined by pn = coRHo has been calculated using the weak field Hall voltage from

7-

2-

V HB-10 1

I-

lh = --F-x’-F 1 O.

60

1

120

la0

200

2.0

224

320

T (‘K, FIG. 4. The electron mobility of seven re-crystallized samples as a function of absolute temperature.

V, being potential to-width “n. IU_. IO’ R xl”’

lo* (2)

the applied voltage measured between probes and l/w is the appropriate lengthratio. From the curves for sample A, en. V’ and the net donor concentration.

SINGLE

0

0.1

CRYSTAL

0.2

InSb

0.4

0.3

THIN

0.1

1073

FILMS

0.6

0.7

B (Wb/M2)

FIG. 5. Field dependence of Hall coefficient in sample A at 300°K (lower curve) and W’K (upper curve). ND-NA, have been calculated, and are shown in Table 1 together with the values expected in bulk single crystal which were interpolated from the curves of mobility vs. carrier concentration for various orientations in Te doped samples, reported by RUPPRECHT et a1.(15) A comparison of the mobilities shows that in uniform single crystal films both the mobility value and its temperature dependence are comparable with those in bulk InSb of the same net donor concentration, the discrepancy here beulg about 3 per cent. THICKNESS DEPENDENCE OF MOBILITY The electrical and galvanomagnetic properties of other samples selected from the same series as sample A with thicknesses varying from 1 to 5.8 p have been measured. These samples were

again non-dendritic films, though up to 4 crystals, generally with the (111) direction perpendicular to the plane of the substrate and random orientation in the plane, were present in some areas measured. Twinning appeared to be common in the thicker films. The net donor concentrations and thickness of seven re-crystallized samples are shown in a summary of properties in Table 2. The temperature dependence of electron mobility has been plotted in Fig. 4. In thicker films with 2.5 p < d < 6.0 TV, pn( T) increases monotonically with decreasing temperature down to the limit of measurement at 85°K. In thinner films with 1 p < d < 2 p the mobility is essentially flat over the temperature range from 300 to 85°K. The behaviour of p,,(T) in these zone re-crystallized samples is comparable to that reported for

Table 1. The electrical properties of sample A at 300 and 85°K compared zbith the bulk mobility reported by RUPPRECHTet a1.‘15) Bulk InSb(ls’

Sample A T, “K

cZ?C

300 85

- 127 -165

(*-CL) -I 480 430

ND--N.& cme3

4.12:10’6

Pn?

Pnv cma/V-set

cm2/V-sec.

6.08~10~ 7.18 x 104

6.3x10* 7.3 x lo* (at 78°K)

F.

N.

1074

TEEDE

Table 2. The electrical and galvomagnetic properties of seven re-crystallized samples at 300 and 90°K Z Sample

d, p

T, “K

R~oiRwm

Geometric AR/Ro*

Measured AR/R*

A

3.65_

85 300

1.12 1.05

0.74 0.58

0.79 0.61

4.17 x 10’6

B

5.8

90 300

1.16 1.06

0.45 0.40

0.92 0.78

1.05 x 1016

c

2,s

9i) 300

1.34 1.08

0.40 0.35

1.54 1.14

1.76 x 1 Ora

D

1.85

90 300

1.26 1.16

0.49 0.50

0.55 0.54

2.40 x 10’0

E

1.3

90 300

1.18 1.07

0.47 0.48

0.81 0.66

I .86 x 10’6

F

1.25

90 300

1.13 1.05

0.42 0.40

1.07 0.74

2.42 x 1 Ora

G

1.05

90 300

1.20 1.08

0.18 0.16

o-77 0.49

3.5 x 10’6

* The geometric magnetoresistance Wb/m2 from equation (1).

calculated

for L/W

= 3.2,

ND-

and B = 0.65

0

O

00

1

*

3

THICKNESS

5

4

6

Na, cm-s

7

(pm)

FIG. 6. The thickness dependence of electron mobility in seven m-crystallized samples at 300°K.

SINGLE

CRYSTAL

bulk InSb but is in contrast to the behaviour previously reported for InSb thin films. By comparison, polycrystalline filmsc2) generally have a mobility maxima around 300°K. The position of the maxima shifts to higher temperatures as the crystallite size decreases and at temperatures on either side of the maxima in p,(T) the mobility decreases rapidly. In polydendritic films thicker than 2 I”, shallow mobility maxima occur at temperatures near 300°K. (5s11) WIEDER(‘~) has interpreted the anomalous mobility temperature dependence in his dendritic films in terms of carrier scattering at edge dislocation. The thickness dependence of mobility in the re-crystallized zone samples is shown in Fig. 6. At 300°K the mobility rises from 3.35 x lo4 cm2/V-see in a 1.0 p sample to 6.13 x 104 cm2/V-set in a sample of +5.8 p. At 90”K, however, this simple thickness dependence does not persist. An analysis of magnetoresistance of each sample, shown in Table 2 indicates that the samples are not all homogeneous. This conclusion is supported by microscopic investigation, especially in samples C and G where the grain boundaries run across the samples in the direction of crystal growth (i.e. the direction of slow scan). It is expected that impurities present in the film would segregate out at the grain boundaries producing strips of high carrier concentration running across the film much in the fashion of a magnetoresistive raster plate. These strips would have the effect of shorting out the Hall voltage giving a lower effective mobility and strongly enhancing the magnetoresistance. One would expect, therefore, the true electron mobilities of the more inhomogeneous thinner samples to be higher than those shown in Fig. 6. BATE et aLcl”) have investigated the influence of discontinuities in resistivity in the direction perpendicular to the current in bulk InSb. Such discontinuities are shown to significantly decrease the measured electron mobility. The thickness dependence of mobility found here can therefore be partly explained by the inhomogeneous nature of the thinner samples. DISCUSSION

The evidence presented in this paper suggests that large area single crystals can be grown in a controlled manner from near stoichiometric InSb

InSb

THIN

FILMS

1075

thin films on amorphous substrates using a scanning electron beam as the heat source. The electron mobility, its temperature dependence, and the magnetoresistance of homogeneous samples are in agreement with those reported for bulk material of comparable net impurity concentration and are higher than reported values in thin films prepared by other methods. A thickness dependence of mobility has been found in the range 1-6~ which can be partly explained by the inhomogeneous distribution of current carriers in some of the samples. The thinness of the sample may affect the electrical properties of thin films in different ways. HANNEMANet a1.(17) have found that in thin wafers of InSb bond distortion on the free (111) A surface causes bending of the sample, the radius of curvature being thickness dependent. In films constrained to a flat plane by the substrate, the plastic strain associated with the surface may induce ionized vacancies and interstitials, considerably reducing the mobility without changing the Hall coefficient. This has been suggested by DUCA et a.Lcl*) for plastically induced strain dislocations in bulk samples. The strain energy associated with the differential expansion of film and substrate could have a similar effect. Furthermore, the ratio of surface to volume is also thickness dependent. Surface states are known to significantly affect the electrical properties even in bulk material.(lg) Finally, the effect of surface scattering is expected to become important in thinner films. The electron mean free path length governed by acoustic scattering has been calculated@) to be 0.57 p at 300°K. Even where partially diffuse scattering exists at the surface this limitation should become appreciable in films of comparable thickness. Although a thickness dependence of mobility has been found, it is concluded that its effect is secondary, at least down to 1 p. As yet no attempt has been made to determine the nature of electron scattering at film boundaries in the films reported above. An insuficient number of thin crystals with the required homogeneity have been prepared to draw any consistent,information on this aspect. However, the oxide cover layer technique introduced by WIEDER(~)has made it technologically feasible to re-crystallize layers thinner than 0.5 p by electron beam microzone melting. In this laboratory work is proceeding in this direction.

1076

N.

F.

Acknowledgements-The author is indebted to Professor A. R. BILLINGS and Mr. R. H. HARTLEY for their many helpful discussions and critical remarks, and to Mr. G. DAUTH for his technical assistance. This project has been principally supported by the Radio Research Board ‘and supplemented by funds from the Australian Research Grants Committee. REFERJZNCES 1. W. J. WILLIAMSON, Solid-St. Electron. 9,213 (1966). 2. K. G. GUNTHER,Compound Semiconductorl (Willardson and Goering Eds.) , p. 3 13, Reinhold, Germany (1962). 3. R. KOIKE and R. UEDA, Jap. J. appl. Phys. 3, 191 (1964). 4. H. H. WIEDER and A. R. CLAWSON, Solid-St. Electron. 8, 467 (1965). 5. J. A. CARROLL and J. F. SPIVAK, Solid-St. Electron. 9, 383 (1966). 6. A. R. CLAWSON and H. H. WIEDER, Solid-St. Electron. 10, 57 (1967). 7. J. MASERJIAN, Solid-St. Electron. 6, 473 (1963).

TEEDE 8. S. NAMBA, J. appl. Phys. 37, 1929 (1966). 9. N. M. DAVIS and H. H. WIEDER, “Electron Beam Synthesis and Recrystallization of InSb films”, Eighth Annual Symposium on Electron and Laser Beam Technology (A.B. El Kareh Ed.) Pennsylvania (1966). 10. N. F. TEEDE, Proc. Instn. Radio Enars Aust. 28. 115 (1967). 11. H. H. WIEDER, Solid-St. Electron. 9, 373 (1966). 12. C. HERRING, J. appl. Phys. 31, 1939 (1960). 13. R. T. BATE and A. C. BEER, J. appl. Phys. 32, 800 (1961). 14. H. J. LIPPMAN and F. KUHRT, 2. Naturforsch. 13a, 462 (1958). 15. H. RUPPRECHT,R. WEBER and H. WIESS, 2. Nuturforsch lSa, 783 (1960). 16. R. T. BATE, J. C. BELL and A. C. BEER, J. appl. Phys. 32, 806 (1961). 17. R. E. HANNENIAN,M. C. FINN and H. C. GATOS, J. Phys. Chem. Solids 23, 1553 (1962). 18. J. J. DUGA, R. K. WILLARDSON and A. C. BEER, J. appl. Phys. 30, 1798 (1959). 19. I. M. MACKINTOSH,J. Electron. 1, 554 (1956).