RECENT STUDIES ON EPITAXIC IV-VI FILMS

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RECENT STUDIES ON EPITAXIC IV-VI FILMS

Jay Zemel

To cite this version:

Jay Zemel. RECENT STUDIES ON EPITAXIC IV-VI FILMS. Journal de Physique Colloques, 1968,

29 (C4), pp.C4-9-C4-20. �10.1051/jphyscol:1968402�. �jpa-00213606�

JOURNAL DE PHYSIQUE Colloque C 4, supplkment au no 11-12, Tome 29, Nouembre-Dkcembre 1968, page C 4

- 9

RECENT STUDIES ON EPITAXIC IV-V1 FILMS

^{( l )}

JAY N. ZEMEL

The Moore School of Electrical Engineering University of Pennsylvania

Philadelphia, Pennsylvania 19 104

RBsum6. -

Cet expose porte sur les techniques de prkparation kpitaxiale de couches minces pour ['etude des alliages et des surfaces. L'etat prksent de la question de l'etude des alliages

par

les couches kpitaxiales est pass6 en revue et la discussion de I'6tude des surfaces est bas6e sur l'etude des compo- sks tels que PbS, PbSe, PbTe et SnTe.

Abstract. -

This paper deals with the techniques that have evolved for growing epitaxic films for alloy and surface research. The current state of alloy research using epitaxic films is reviewed and the discussion of surface research is based on studies of compounds such as PbS, PbSe, PbTe and SnTe.

I. Introduction. - Thin single crystal films of IV-V1 compounds have found broad application in fundamental research in recent years. There has been important contributions to understanding the band structure, crystal dynamics and some related processes of these materials

^(l).

As the details of the electrical and optical behavior of the IV-V1 compounds have been gradually established (both with bulk and film studies), the emphasis in film research has been shifting to problems for which the films are uniquely well suited, e. g. pseudo-binary alloys of IV-V1 compounds with members of both the IV-V1 and other classes of materials and surface research.

The advantage of hetero-epitaxy in preparing single crystal films of alloys of the IV-V1 on insulating substrates lies in the speed with which a broad range of alloy compositions can be prepared, the relatively high quality of the materials (high crystallographic perfection, good electrical properties, uncontaminated and undamaged surfaces) and the usefulness of films for a variety of measurements. In many areas of potential application, thin films are preferred forms for these materials, as is well known. In the study of the surface behavior of degenerate semiconductors, which

an assured method of preparing specimens for reliable surface transport and field effect measurements.

Therefore, in this paper we review the techniques that have evolved for growing epitaxic films for alloy and surface research. The current state of alloy research using epitaxic films will be reviewed and the discussion of surface research will be based on studies of the pure lead salt compounds

( 2 ) .

It is somewhat interesting to note that it was as far back as 1949 when Elleman and Wilman [2] demons- trated that oriented overgrowths of PbS could be produced on heated NaCl substrates. However, it was not until the early 1960's that extensive research began on epitaxic films of the lead salt family. As has happened many times in the past, research was under- taken almost simultaneously in different laboratories.

2. Film preparation.

-

Epitaxic films of the lead salts have been prepared using three techniques

:

sublimation onto a heated substrate, sputtering onto a heated substrate and chemical deposition from solution. One general observation is that the lead salts prefer to grow in a crystalline form : films grown even on glass show fairly large single crystal grains.

is quite new, epitaxic films are the only reasonable

( 2 )

The substances PbS, PbSe and PbTe are called more

When carrier are in accurately,

⁽⁽

lead chalcogenides

^D.

Current usage

^by

research the 1018/cm3 range, epitaxic thin film methods provide workers in these substances has given the name lead salts

^D

to

the chalcogenides. This modified terminology

will be

adopted

(1)

Partially supported

by

the

U.

S. Army Research Office- here, the family of compounds PbS, PbSe, PbTe and the

IV-V1

Durham under Contract No. DAHCO-68-C-0023. compound SnTe,

will be

called lead salts.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1968402

C 4 - 1 0 JAY N. ZEMEL

Despite the fact that extremely good single crystal

films have been prepared, their preparation is not well understood. There is a good deal of uncertainty about the dependence of crystallinity of the film on the substrate temperature, and little information on the effect of the substrate material on film growth and electrical properties.

2.1 SUBLIMATION

ONTO A HEATED SUBSTRATE.

-

A

schematic of a typical evaporation system is shown in figure 1. The pressure during deposition was

its terminal pressure, the substrate was heated to the growth temperature, usually in the range of 200-250 oC.

With the shutter closed, the source was heated to about 700 OC and a small amount of material evapo- rated. The shutter was then opened and the deposi- tion carried out. The usual deposition rate was 100 A/mn. On completion of the deposition, the shutter was closed land the substrate allowed to cool down in vacuum. The films were stored in dry argon to protect them from moisture. Essentially the same technique was used by the U. S. Naval Ordnance

U

FIG. 1.

-

Schematic diagram of evaporation system used in IV-V1 epitaxic film growth.

usually in the high 1OP6 torr to low IO-' torr range.

Elleman and Wilman [2] were able to grow films at pressures as high as 10F3 torr. Schoolar and Zemel [3]

(hereafter called SZ) cleaved substrates from synthetic single crystal NaC1, although natural NaCl has been used quite satisfactorily by Elleman and Wilman.

Typical substrate dimensions used by

SZ

were 3

X

15

X

30 mm. The quartz oven illustrated in figure 1 was heated by a coil of 0.025 cm diameter molyb- denum wire wrapped aroung the outside.

Typical of the procedure used was that of SZ in which

:

The source oven was loaded with approxima- tely two grams of freshly pulverized material. A freshly cleaved substrate was mounted on the flat bed heater and the entire assembly placed in the vacuum system.

The vacuum system contained a shutter which sub- stantially isolated the source and substrate during the initial outgassing procedure. When the system achieved

Laboratory group in subsequent preparations of PbSe, PbTe, SnTe and several alloys of these materials.

Semiletov and Voronina [4] have made an extensive study of epitaxic films of PbSe and PbTe on various substrates. They used graphite and tantalum source boats. In the case of PbSe the source material varied from 0.5 weight percent (wt. %) excess selenium to 2 wt. % excess lead. Near stoichiometric and up to 0.1 wt. % excess lead, PbTe were sublimed. No comment was made about the effect of source material on the film properties nor was any mention made of the construction of the substrate heater. Substrate temperatures ranging from room temperature up as high as 550 OC were quoted.

Figure 2 shows a back reflection Laue pattern of a

7 p thick PbS film on NaCl [3]. The 4-foId symmetry

and absence of Debye rings is strong evidence that

the film is an undistorted single-crystal, cubic structure.

RECENT STUDIES ON EPITAXIC IV-V1 FILMS C 4 - 1 1

FIG. 2. -Back reflection Laue pattern from a 7 micron thick PbS film on NaCI.

further evidence of the single-crystal character of the film. Substantially the same results have been obtained using electron diffraction measurements [2, 41.

Jensen and Zemel [5] have made use of the electrical properties as a criterion of the perfection of epitaxic PbS films. Voronina and Semiletov [6] described PbSe epitaxic films in terms of their electrical proper- ties and electron diffraction patterns.

Recently, Palatnik, Sorokin and Lebedeva [7]

showed that when Laue diffraction patterns indicated disorder (at low growth temperatures), the free carrier mobility of thick PbTe films at room temperature would be relatively low. At high temperatures, order would predominate and the mobility of the carriers would rise. Furthermore, topographic details of the cleavage face appeared to be important. As might be expected, films grown on surfaces with numerous gross imperfections have degraded free carrier mobi- lities. Holloway and Zemel [8] found no correlation between X-ray rocking crystal half widths of PbS films up to 20 minutes of arc and their room tempe- rature mobilities. This is in substantial agreement with the observations of Scanlon [9] on bulk PbS.

It would appear that relatively small angular mismatches of the mosaic blocks comprising the film will not cause large scale free carrier scattering in Figure 3 shows a Bragg diffractometer recording the lead salts at room temperature. However, high from a 3 p thick PbS film using filtered radiation from angle grain boundaries can cause considerable free an iron target

131.

The lattice constant based on the carrier scattering, e. g. in the case of polycrystalline diffractometer recording is within experimental error films. A typical electron micrograph of an 800 A

of the accepted value of 5 929 A. Furthermore, as can thick PbS film is shown in figure 4, indicating the be seen, the iron Ka doublet is clearly resolved by high degree of perfection in the films even when the the film even at the lower Bragg angle providing mosaic block structure is evident.

FIG. 3. - Bragg diffractometer recording from a 3 p thick PbS film. Filtered Ka Fe radiation was used and the Kcl doublet is clearly resolved by both the NaCI substrate and the PbS film.

C 4 - 1 2 JAY N. ZEMEL

FIG. 4. - Electron micrograph of an 800

A

thick PbS film.

2.2 SPUTTERING

^{IN A N} INERT GAS ONTO A HEATED

SUBSTRATE.

-

Francombe has shown that epitaxic films of lead telluride can be grown by conventional sputtering methods [10, 1 l]. The basic experimental arrangement is shown in figure 5. The properties of

HIGH VOLTAGE SHIELDED LEAD

FIG. 5. - Schematic diagram of a inert gas sputtering apparatus used for growing epitaxic semiconductor films.

these films were not reported in detail but optical micrographs suggest good crystallinity and X-ray patterns confirm the single crystal character of the

films. Additional information on the electrical pro- perties of these films would be desirable.

2.3 CHEMICAL

DEPOSITION FROM SOLUTION. -

The tendency for the lead salts to form crystalline layers isrnowhere better illustrated than in the work of Davis and Knorr [l21 on chemical deposition of PbS on germanium. In this work, the films are depo- sited on well oriented [(loo) and (ill)] Ge substrates from the same types of chemical solutions used in producing photoconductive PbS detectors on glass.

X-ray data using both the Laue back reflection method and Bragg diffractometer recordings indicated a well ordered-single crystalline overgrowth on the germanium surface. The observed lattice constant, from the diffractometer recordings, agreed with the lattice constant obtained for both bulk and epitaxic PbS. The thickness of the PbS films was not measured by the authors, though the prominence of the Ge line in the diffractometer recording suggests that the films were less than I O - ~ cm thick. Only photovoltaic measurements were carried out with these films so that no quantitative evaluation of their electrical properties is available. There was an observed diffe- rence between the photovoltaic properties of the junctions on n-type, p-type or intrinsic substrates.

PbS films were also grown on silicon using the above techniques [13, 141.

2 . 4 ALLOYS.

-

Because of the ease with which epitaxic films of the lead salts could be produced, it was natural to undertake the growth of alloys of the form Pb(VI),(VI),-, and Pb,-,Sn,(VI). Bis and Zemel [IS] have produced alloy films of PbSe,Te, -,.

Bis, Rodolakis and Zemel [l61 have described an alloy evaporation system suitable for any two compound sublimation and a schematic of the two independent oven apparatus is shown in figure 6.

Bylander [l71 has obtained epitaxial films of Pb, -,Sn,Te using both double oven and single source techniques. In the single source method, the alloy is prepared by melting the correct weight proportions together and then evaporating the material as des- cribed earlier [3]. The double oven technique [l71 did not prove any more advantageous than the single source method. It is interesting that the composition of the alloy is preserved during the deposition of the film

^(3).

Both procedures yielded single crystal films.

(3) Note added in proof. Recent unpublished studies by T. Farinre indicate that the films are systematically tin rich.

RECENT STUDIES ON EPITAXIC IV-V1 FILMS

L-

I

COLD TRAP LIQUID N,

IU,BITRATE BLOCK

F=h

\ ^)$&, p\

HEATER C O I L

*

SHUTTER VALVE

WATER COOLED JACKET

V VL I Y

TO PUMP SYSTEM "B,"

FIG. 6. - Schematic diagram of a two source, multi-pumped evaporator for alloy preparation.

occurs in the intermediate x range. This generally agrees with the Hume-Rothery size factor for substi-

3.

Alloys.

- In the past two years, a number of

_0.45

tutional solid solution [19]. Scanlon showed that the band gap of PbS,Se,-, decreased uniformly with x to the value for PbSe and then increased uni- formly with x for PbSe,Te,-, to the value for PbTe [20]. This is shown in figure 7. The non-miscibility of PbS,Te,-, prevented a similar band gap study for all values of x [19].

Joffe and Stil'bans [21] have studied PbSe,Te,-, bulk crystals. The electrical and thermal properties were measured for different values of

X.

It was obser- interesting single phase alloys, or solid solutions of the lead and tin chalcogenides have been prepared as

ALLOY COMPOSITION

- -

FIG. 7. -Dependence of the band gap for the alloy systems PbSzSel-, and PbSezTe on composition [20].

epitaxic films. While only a few papers have been -

published on these materials, their potential impor-

^0.40

- tance as infra-red sources and detectors is considerable,

particularly in the case of the lead-tin chalcogenides. -

a

-

For convenience, the alloys of the lead salts will be

0.35-

discussed separately from the lead-tin chalcogenide

>-

-

C ) -

system.

3.1 ALLOYS

^{OF THE}

LEAD SALTS, P ~ ( v I ) ~ ( v I ) ~ - , . - Bulk studies have shown that the alloy systems PbS,Se, -, and PbSe,Te, -, are fully miscible over the entire range of x from

0

to 1 118-191 PbS,Te,-,

is not fully miscible and segregation into two phases

PbTe 50% PbSe 50% PbS

ved that n-type crystals had uniformly higher mobilities than p-type crystals.

A plot of the mobility versus

composition is shown in figure

8.

Bis and Zemel [l51 were able to grow single crystal, single phase alloy films of the PbSe,Te,-, system.

This was indicated by sharp Laue patterns typical of

NaCl structures and relatively narrow X-ray diffrac-

C 4 - 1 4 JAY N. ZEMEL

100 1 I l

0 50 100

PbTe PbSe

% PbSe

FIG. 8. - Bulk mobility of PbSesTel-z as a function of composition [21].

tion peaks. Laue patterns were obtained of the same quality shown in figure 2 and a Bragg recording is shown in figure 9. Compositions were estimated by Vegard's law based on Yamamoto's work [18].

Almost any sudden change in the environment of the film could cause them to detach from the substrate.

This would occur when the films were exposed to air after growth or applying a stress to the substrate, e. g., bending or cleaving. There were some general indications that reduced growth temperatures assisted in stabilizing the films [22].

The electrical properties of the p-type PbSe,Te,-, films were superior to bulk materials. The temperature variation of the Hall mobility for a PbTeo.,,Se0~,, film is shown in figure 10 along with corresponding data on an n-type bulk PbTeo.,Se0., crystal measured by Joffe and Stil'bans 1211. Only the room temperature mobility of a bulk p-type PbTeo,,Se0., crystal was available and is shown as a point in figure 10. The Hall coefficient of the epitaxic film is also shown.

3.2 ALLOYS

OF

Pb,Snl -,{ Se, Te ).

-

The lead-tin chalcogen system has attracted a great deal of interest recently because of observed decrease in band gap as (1

- X)

increases. This is not a unique property of Pb,Sn,-,{ Se, Te ) alone. Hg,Cd,-,Te is a well

FIG. 9. - Bragg diffractometer recording from a PbSeo. ~Teo. 5 epitaxic film on NaCl using filtered Fe radiation. The Ka doublet is resolved by the films.

Infra-red multiple reflection fringes obtained with PbSe,Te, -, films were as well defined as those obtai- ned on pure materials. Thicknesses were obtained by linear interpolation of the index of refraction between the indices of the pure compounds. It would be desirable to have a more systematic study of the depen- dence of the index of refraction on the composition of the alloy. This comment applies to almost every property of this system.

One interesting observation was the fragility of the alloy films despite attempts to anneal out strain.

known material that also displays a decrease in band gap as (1

- X )

increases for small values of (1 -

X)

[23]. Mazelsky

et al., have shown that Vegard's

law is obeyed by Pb,Snl -,Te using lattice constants obtained by X-ray powder methods [24]. Preliminary measurements by Nikolic 1251 on the fundamental absorption edge of Pb,Sn,-,Te demonstrated the decrease in the edge with ( l

- X)

for small values of

(1

- 4

Bylander [l71 showed that epitaxic films of

Pb,Sn,-,Te could be grown as easily as the pure

RECENT STUDIES ON EPITAXIC IV-V1 FILMS

FIG. 10. -Temperature dependence of the Hall mobility of bulk (dashed line, n-type bulk crystal) and film P b s e , T e ~ - ~ alloys near x 0,5, and Hall coefficient of epitaxic film.

Q is for a bulkp-type crystal with X N 0,5.

compounds using the

((

single-source method descri- bed in 2.4. The electrical properties were comparable or better than bulk material [26]. The Hall mobility, as in the case of PbSe,Te,-,, was as large as those observed in the bulk and is an especially attractive feature of these epitaxic systems. Except for the mate- rials with very low tin concentrations, the Pb,Sn, -,Te films were p-type.

Because of the thickness of the films, it was possible to get reasonable measurements on the onset of the fundamental absorption edge at 300 OK. The depen- dence of the energy gap,

E,,

in the alloys on composi- tion is shown in figure 11. The data of Nikolic is also shown for comparison.

Dimmock, Melngailis and Strauss [27] were able to optically stimulate laser action in Pb,Sn, -,Te samples with radiation from a GaAs diode laser. The laser radiation from the alloys were at 15.9 microns for Pbo,8,Sno.19Te and at 14.9

y

for Pbo.8,Sno~,,Te.

These values fall on the line in figure 1 1.

Strauss [28] has studied epitaxic films of Pb,Sn, -,Se grown by the

⁽⁽

single-source

>>

method. The behavior of this system is quite similar to that of the telluride.

One important difference is that SnSe is not rock salt cubic and so for small

X,

the crystal structure of the films must change. The band gap of this alloy decreases like the telluride.

Recently, Bis and Dixon have shown that there is an

FIG. 11. - Dependence of energy gap of PbsSnl-zTe as a function of composition.

anomaly in the temperature dependence of the electri- cal properties of Pb,Snl-,Te at that temperature where band crossing is expected [29]. The origin of this behavior is not understood at present.

3 . 3

DISCUSSION

OF THE

BAND STRUCTURE

OF THE

ALLOYS. - Further discussion of the band structure will be presented in other papers at this meeting.

We will briefly review some features that have been obtained up to the past year.

Dimmock

et al. [27] have described the band gap

behavior in terms of the band structure of the lead salts. In the rock salt structure, the wave functions of the conduction and valence bands have different ordering but have the same group symmetry. Esaki and Stiles [30] have shown from tunneling experiments that the band gap of SnTe is near 0.3 eV. Dimmock

et al., postulate that the band ordering is reversed

in SnTe but that the group symmetries of the bands are preserved. Using the tight binding picture, the wave functions involve linear combinations of the Pb and Sn sublattices wave functions. If the band gap in SnTe is assigned a

⁽⁽

negative

^>)

value, i. e., plotted as shown in figure 11, then the decrease in band gap with 1

- x

is indeed simply found.

A similar behavior occurs for the selenide alloy sys-

tem [28].

C 4 - 1 6 JAY N. ZEMEL

Changing the chalcogen does not seem to change binding model would be needed to explain the exis- the basic ordering of the bands in the lead chalcogen tence of such states.

alloys. It is interesting to note that the band gap The magnitude of the coulombic interaction can shows no indication of going to zero in Pb,Ge,-,Te be calculated using a zero order model: The interac- alloys 1311. This suggests that the band orderings are tion energy, eint, is given by a two dimensional nearest the same in the lead and germanium chalcogens. neighbor interaction.

4.

Surface phenomena.

- The sensitivity of the 4 q2

Ein =

-

lead salts to gas ambients has been a well known

Eeff 80 d

(2)

fact for many years [l]. Quantitative measurements of

the up-take of oxygen, the gas responsible for the more where eeff is the effective dielectric constant for a dramatic electronic changes at the semiconductor charge at the interface between the oxide and the surfaces, have only recently been carried out [32-331. substrate [38].

Green and Lee [32], and Hillenbrand [33] have shown that the oxygen adsorption process in quite slow on PbTe and PbS, respectively. Indeed, sticking coeffi- cients in the 10-g range appear to be the norm for oxygen on the lead salts. Despite this limited interac- tion between the adsorbate and adsorbent, very high surface charge densities were observed on epi- taxic films in the past two years. The first study was on PbSe by Brodsky and Zemel [34]. Additional confirmation of very high surface charge concentra-

d is the mean distance between ions, is the permitti- vity of free space and q is the electronic charge. The factor 4 takes into account the four nearest neighbor sites.

The values for the effective dielectric constant are based on the assumption that the smide is approxima- tely 20. The values of

E,,,

for the lead salts are given in table I. The charge density observed by various

zeff

^&S, E i n t Csscr 1 Y

md*

Wsv

-

- - - -

- ^L

-

-

PbS 105 190 .485 .40 21 A 33 2.8 .207 .35

PbSe 150 280 .340 .28 31 A 38 1 .O .l09 .41

PbTe 235 450 -217 .31 50 44 1.4 .I35 .30

tions were obtained by Egerton and Juhasz on PbTe authors [34-361 is as large as 5

^X 1013/cm2.

If the [35] and by Brodsky on PbS [36]. Egerton and Juhasz surface charge is distributed on a square two dimen- have obtained convincing data that oxygen is respon- sional lattice, the mean distance between nearest sible for charge changes as high as 5

X

lOI3 holes/cm2 neighbors is

on virgin film surfaces. The origin of this high surface

charge has been considered recently along with the a=-- 1

implications on surface quantization. h ⁽⁴⁾

4.1 OXIDE

OR

SURFACE STATES.

-

There are two explanations for the states responsible for the high surface charge found on the lead salts [37]. The first is a band of levels arising from the oxygen ions on the surface. Because of the spread in energy due to coulombic interaction, it would not be reasonable to expect that this band would be in the forbidden energy gap at the (1 11) Brillouin zone edge, as are the band extrema. These states might be at another point in the Brillouin zone providing such a concept has significance in terms of a single layer of molecules at the surface. A detailed study based on a

tight-

which is of the order of 1.5

X

10-' cm. As an example, the interaction energy is .34 eV for PbSe which is substantially greater than the energy gap of PbSe at room temperature [37]. The interaction energy for the three lead salts along with their room temperature band gaps, E,, are listed in table I. In almost every case, the band gap is less than the interaction energy of the surface ions. This raises the question of where the energy level associated with the surface states might be.

A second approach, based on the established non-

stoichiornetry of lead chalcogenides, envisages

a

RECENT STUDIES O N EPITAXIC IV-V1 FILMS C 4 - 1 7

heavily defected oxide partially stabilized by the

electrostatic interaction between the oxygen ions and the holes in the semiconductor space charge region.

This model requires that the diffusion of the chalcogens and lead atoms through the oxide be both highly temperature dependent and, at room temperature, quite slow. At room temperature, the defected oxide should produce a strong space charge. The space charge field grows leading eventually to a cessation of growth due to electrostatic interactions.

By using the oxide rather than the surface state model, a more consistent explanation of the generation of high surface charge densities on degenerate semi- conductors is possible. The acceptor levels in the oxide are determined by the intrinsic properties of the oxide and can be well below the Fermi level of a p-type degenerate semiconductor. As a result, these states when ionized will produce the observed semi- conductor space charge region. The surface state model founders on the interaction energy calculation, particularly for a p-type accumulation layer on a p-type degenerate semiconductor.

4 . 2 SURFACE

QUANTIZATION. - Another question raised by the high space charge density is the possible quantization of the states in the bottom of surface potential well. The thickness of the space charge region, C,,,,, is of the order of 20-50 A

[37].

The electron or hole DeBroglie wavelengths, A, for the lead salts are listed in table I. In every case, the DeBro- glie wavelength is either comparable to or larger than the space charge region and significant surface quantization effects are expected. The theory of surface quantization has been developed for the case of an inversion layer [39]. The accumulation layer has not been treated to any great extent. In order to treat the accumulation layer problem, an estimate of the classical barrier height for a given charge density is needed. The magnitude of the classical barrier height is compared then to the added barrier-height resulting from quantization of a simple linear well model of the type proposed originally by Schrieffer [40].

The classical barrier height,

^W,,,

can be calculated from an expression derived by Siewatz and Green [41]

for the surface charge in a degenerate system. The lead salts have four valleys located at the (111) Bril- louin zone boundary and each valley contains 114 of the total charge in the system. The same distribution of charge should apply to the surface space charge region. The. arguments of. Brodsky and Zemel I341 for ap-type aegenerate bulk and ap-type accumulation layer, can be used leading to a simplified expression

for the barrier height in terms of film functions.

Where

y

is the

<<

classical density of states in the valence band and

p,

is the bulk density of charge.

Using values for the coefficients given in table I as well as Q,

=

5

X 1013 holes/cm2, W,,

is calculated from eq. (5). As can be seen in figure 12, the barrier height is

FIG, 12. -Energy band at the surface of p-type degener&e semiconductor with a p-type accumulation layer.

W,,

is defined in terms

of

the Fermi integral

and is tabulated in table I for the surface charge density mentioned above,

The quantization of energy levels in a linear well pr~duees wave functions that *behave Hke BessEl functions of order 113. This. model has been-widely used to describe surface quantization effects because of its mathematical simplicity. For a given charge density, the energy of the lowest electric sub-band in this well, provides a measure of the additional barrier height produced by quantization and is given by

where

m:

is the component Qf the effective mass tensor perpendicular to the surface of the crystal.

m:

can be expressed in terms of the longitudinal

C 4 - 1 8 JAY N. ZEMEL

and transverse masses (m: and

m: respectively) of

the ellipsoidal energy surface [39]. Stern and Howard [39] have analyzed the effect of surface quantization on a multi-valley ellipsoidal energy surface and have shown that the high surface electric fields split the valley degeneracy in the quantum limit.

As the crystallographic orientation of the surface varies from one direction to another, it is clear that both m: and g, vary. To determine both the magnitude of the quantum correction to the barrier height and the validity of the linear well model, it is necessary to calculate E, from eq. ( 8 ) using the expressions for m: and values for g, given by Stern and Howard [39].

In a given orientation, there is more than one value of the effective mass depending on the valley orien- tation. Because the lead salts have 4 valleys at the (1 11) Brillouin zone boundaries, for (1 10) and (1 11) surfaces there are two values of

m:

corresponding to a heavy and light mass component. One expects that the lowest value of E, will correspond to the largest value of m:,

m: (1) (call this value of E,, E:).

Then the larger value of E, will be associated with the lighter value of m:,

m: (2) and will be denoted E:.

A brief examination of the expression for E, in eq.

(8) points out that the valley degeneracy factor

can be very important in this model. Zemel has calculated mZfZ (l), m:

(21,

E: and E: and these numbers for the three lead salts for three different values of surface orientation (loo), (110) and (111) are listed in table I1 [37]. In the case of (1 11) oriented surfaces, the model breaks down for PbS and PbSe with

m:

(1) >

m:

(2) but E; >

E:

due to the multiplicity of the light mass valleys. One of the important conclusions to be drawn from this result is that a full self consistent calculation of the energy levels of The electric sub- bands using the coupled Poisson and Schroedinger equations is needed for the multi-valley semiconductors.

The simple linear well model is not accurate under these conditions even for the ordering of the bands.

Another conclusion is that increasing mass ansoi- tropy decreases the crystallographic dependence of

E,.

This is physically reasonable, since as the crys- tallographic orientation shifts from a low mass, high valley degeneracy direction to a high mass-low valley degeneracy direction, a trade off occurs'which tends to limit the magnitude of E,. For the almost spherical case, e. g. PbS, the variation in crystallogra- phic direction most strongly affects the valley degene- racy contribution to E,. Therefore surface quantiza- tion of the SSCR will show the maximum variation going from (100) to ( I l l ) in PbS and PbSe while showing a much weaker variation in PbTe.

While the magnitudes of the quantum contribution to the barrier height are uncertain, the approximate values should be of the order of 0.1 to 0:2 volts.

These are 'sufficiently large so that experimental verification should be possible using contact potential measurements.

5. Conclusions. - This review has attempted to point out a number of areas of solid state research in general and IV-V1 research in particular where the use of epitaxic films are eminently well suited. The

((

band crossing

D

phenomena in the Pb,Sn, -,(Se, Te) system is important from both theoretical and applied viewpoints. A more detailed investigation of both the optical and electrical properties of these alloys are needed to cIarify the origin of the

⁽⁽

band cros- sing

B.

The application to infrared technology will undoubtedly encourage additional effort on the Pb-Sn system as well as other potential band crossing

D

alloy.

In surface phenomena, a new subject area is evolving as a result of the surface quantization research of the past two years. Acceleration of this work can be expected if experiments on IV-V1 compounds demons- trate unambiguously the surface quantization of the surface space charge region.

(1 00)

Mass ratio

E;(eV) P ~ S

m1

(1) .093 .091

m1 ( 3

- -

PbSe m;

(1) .051 .086

m? (2)

-

PbTe

m1 (1) .OS8 .060

m? (2) ⁺

-

( 1 10)

Mass ratio E;(eV)

(111)

Mass ratio

Ej(eV)

RECENT STUDIES ON EPITAXIC IV-V1 FILMS C 4 - 1 9

6 . Acknowledgements. - The author would like t o acknowledge useful discussions with Drs.

M.

Brod- sky,

C.

Juhasz, and

R.

Lee.

References

[l] ZEMEL (J. N.), Epitaxic Films of Lead Chalcogenides and Related Compounds, Chapter 5, Solid State Surface Science, M. Green Editor, Marcell Dekker (In Prep.).

[2] ELLEMAN (A. J.) and WILMAN (H.), Proc. Phys. Soc., 1948, 61, 164.

[3] SCHOOLAR (R. B.) and ZEMEL (J. N.), J. Appl. Phys., 1964, 35, 1848.

[4] SEMILETOV (S. A.) and VORONINA (I. P.), SOV. Phys.

Doklady, 1964,8,960.

[S] JENSEN (J. D.) and ZEMEL (J. N.), Bull. Am. Phys. Soc., 1961,6,437.

[6] VORONINA (J. P.) and SEMILETOV (S. A.), SOV. Phys.

Solid State, 1964, 6, 1204. Ibid., 1964, 1494.

[7] PALATNIK (L. S.), SOROKIN (V. K.) and LEBEDEVA (M.

V.), Sov. Phys. Solid State, 1965, 7 , 1374.

[8] HOLLOWAY (H.) and ZEMEL (J.) (Unpublished).

[9] SCANLON (W. W.) (Unpublished data).

1101 FRANCOMBE (M.), Proc. Am. Vac. Soc., 1963, p. 316.

[l11 FRANCOMBE (M.), Phil. Mug., 1964,10,989.

[l21 DAVIS (J. L.) and RNORR (M.), J. Appl. Phys., 1966, 37,1670.

[l31 DAVIS (3. L.) and KNORR (M.) (Private communi- cation).

1141 SIGMUND (H.) and BERCHTOLD (K.), Phys. Status Solidi, 1967,20,255.

[l51 BIS (R. F.) and ZEMEL (J. N.), J. Appl. Phys., 1966, 37, 228.

1161 BIS (R. F.), RODOLAKIS (A.) and ZEMEL (J. N.), Rev.

Sci. Inst., 1965,36, 1626.

1171 BYLANDER (E. G.), Mat. Science and Eng, 1966,1,190.

[l81 YAMAMOTO (S.), Science Reports of Tohoku University, 1st Series, 1956, 40, 11.

[l91 SCANLON (W. W.), J. Phys. Chem. Solids, 1959, 8,423.

[20] SCANLON (W. W.), Phys. Rev., 1958,109,47.

[21] JOFFE (A. F.) and STIL'BANS (L. S.), Reports on Prog.

in Phys., 1959,22, 167.

[22] BIS (R. F.) (Private Communication).

[23] KRUSE (P. W.), Appl. Optics (USA), 1965,4,687.

[24] MAZELSKY (R.), LUBELL (M. S.) and KRAMER (W. E.), J . Chem. Phys., 1962,37,45.

[25] NIKOLIC (P. M.), Brit. J. Appl. Phys., 1965, 16, 1075.

[26] MACHONIS (A. A.) and CADOFF (I. B.), Trans. AIME, 1964,230, 333.

[27] DIMMOCK (J. O.), MELNGAILIS (I.) and STRAUSS (A. J.), Phys. Rev. Letters, 1966, 16, 1193.

[28] STRAUSS (A. J.), Phys. Rev., 1967, 157,608.

[29] Brs (R. F.) and DIXON (J. R.) (Private communication).

1301 ESAKI (L.) and STILES (P. J.), Phys. Rev. Letters, 1966, 16, 1108.

[31] WOOLLEY (J. C.) and NIKOLIC (P. M.), J. Electro- chem. Soc. 1965, 112, 82.

[32] GREEN (M.) and LEE (M.), J. Phys. Chem. Solids, 1966, 27, 797.

1331 HILLENBRAND (L. J.), J. Chem. Phys., 1964, 41, 3971.

1341 BRODSKY (M. H.) and ZEMEL (J. N.), Phys. Rev., 1967, 155, 780.

[35] EGERTON (R. F.) and JUHASZ (C.), Brit. J. Appl. Phys., 1967, 18, 1009.

[36] BRODSKY (M. H.) (Private communication).

[37] ZEMEL (J. N.), Proceeding of Battelle Memorial Institute Colloquium on Molecular Processes on Solid Surfaces (to be published).

[38] KELLOGG (O.), Foundations of Potential Theory, Dover 1953.

[39] STERN (F.) and HOWARD (W. E.), Phys. Rev., 1967, 163,816.

[40] SCHRIEFFER (J. R.), Semiconductor Surface Physics, Ed. R. H. Kingston (Univ. of Penna. Press, Phila.

Pa.. 1956). v . 68.

[41]

SIEWATZ

(R. j'ind GREEN (M.), J. Appl. Phys., 1958, 29, 1034.

DISCUSSION

PAUL, W. - Would you please amplify for us your remarks o n the relief of thermal strain by defor- mation of the film or substrate ? What is the sort of strain t o be expected in a given lead salt film o n a specified substrate as a function of temperature, after deposition under known conditions of substrate temperature ?

ZEMEL,

J. N.

- The thermal strain is defined as

where

T'

is the temperature where the thermal strain is initiated. This may or may not be the growth tempe- rature depending o n whether there is a strain release mechanism. In alkali halides cleaved surfaces, there are dislocation loops left from the cleavage which exhibit considerable inelastic behavior. As a result, the strain may be quite small. For details the interested reader is referred t o reference [l].

HOWARD, W.

E.

- In discussing the effect of quan- tization in these films, you have emphasized the change with orientation of the energy levels. From an experimental point of view, is not the two-dimensional density of states of more interest ?

ZEMEL,

J. N.

- The most measurable quantity may well be the contact potential difference. This will be determined by

E,'.

Admittedly, the two- dimensional electron gas would be of great interest but there is also some difficulty in catching hold of a measurement for examining it.

CROCKER, A. J.

-

D O you not agree that one should be very careful i n interpreting the results of annealing experiments on films since in the PbTe case one can

C 4 - 2 0 JAY N. ZEMEL

get an apparent range of stoichiometry greater than

the bulk.

ZEMEL, J. N.

-

I quite agree.

BURSTEIN, E.

-

Has the oxygen-induced surface density of holes also been investigated for n-type material where such an effect should lead to the formation of p

-

n junctions

?

ZEMEL, J. N.

-

Yes, there is information available by Brodsky and Zemel and by Brodsky and Schoolar that p-layers form on PbSe and PbS respectively.

Egerton and Juhasz have observed the conversion on a-type PbTe films to p-type.

BAKI, L. -We have failed to see any evidence of hole accumulation an the surface by oxygen in the measurements of tunneling as well as surface field- effect transport.

ZEMEL, J. -N.

^-

The oxygen exposure quoted by Dr. Esaki was 0.1 torr. hours, far less than what is

needed to produce appreciable oxide formation according R. N. Lee (this conference). Furthermore, his films are in contact with an oxide coated with a metal whose work function is smaller than that of the IV-V1 compounds he studies. This will work to counteract any hole excess.

GREEN, M. -What do you suppose the (1 11) surface of PbTe to be

?

ZEMEL, J. N.

-

Egerton and Juhasz find that (1 11) surfaces on mica are p-type.

SERAPHIN, B.

0.

- IS the strong p-type surface layer you mentioned characteristic for

f i l m s

only

?

What do we know about the surface \conditions in bulk samples

?

Electro-reflectance seems to show that bulk samples of PbTe and Pb,Sn,-,Te are closer to the flat band case.

ZEMEL, J. N. - The bulk surface exposed to air and

not etched

but freshly cleaved is likely to be p-type

but we have no direct evidence on this.