Some Schottky barriers on clean-cleaved silicon

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SOME SCHOTTKY BARRIERS ON

CLEAN - CLEAVED SILICON

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SOME SCHOTTKY BARRIERS ON

CLEAN - CLEAVED SILICON

PROEFSCHRIFT

TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE HOGESCHOOL DELFT, OP GEZAG VAN DE RECTOR MAGNIFICUS PROF. IR. L. HUISMAN, VOOR EEN COMMISSIE AANGEWEZEN DOOR HET COLLEGE VAN DEKANEN TE VERDEDIGEN OP

WOENSDAG 26 OKTOBER 1977 TE 14.00 UUR

DOOR

JOHANNES DIRK VAN OTTERLOO

ELEKTROTECHNISCHINGENIEUR / GEBOREN TE ROTTERDAM //O^-^ S 3> S^iy

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1. GENERAL INTRODUCTION

A hundred years ago Braun observed that point contacts (a thin wire) on a variety of natural crystals showed a total resistance depending on the polarity of the applied voltage and on the surface conditions. In contrast to his contemporaries, Braun realized that this rectification process was located at the point contact. The fact that the rectification took place at the point contact and not in the interior of the crystal was only accepted in the late twenties as a result of more extensive experiments on semiconductors such as cuprous oxide and selenium. The importance of the geometrical form of the contact area was investigated by Schottky and his co-workers in the years 1930-1935, but it was not until 1939 that the interface properties were well understood and it was realized that the rectification process was independent of the contact form.

The tunnel theory of Wilson' ^, Nordheim' ' and Frenkel and Joffe' '* in 1932 had failed to explain the rectification process because it predicted the wrong direction of rectification as was pointed out by Davydov'"^ in 1938.

In 1939 Mott' ^, Schottky' ' and Davydov' ° independently formulated theories of rectification for metal-semiconductor contacts which explain the observed phenomena correctly. Because Schottky's' theory was the most universal one, metal-semiconductor diodes are often referred to as Schottky barrier diodes. In these theories it was suggested that a built-in potential barrier was responsible for the observed rectification processes. That is, the height of this barrier could be lowered or raised depending on the polarity of the applied bias voltage across the contacts. Furthermore, it was predicted that the zero-bias potential height largely depended on the difference between the thermionic work functions on the two materials.

However, more systematic investigations on the semiconductors silicon and germanium after the Second World War did not reveal the expected large influence of the work function difference on the barrier height. A very important contribution to the solution of this problem was

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given by Bardeen' ^. He postulated another possibility for the origin of the barrier: namely that the barrier was produced by the presence of surface states. The concept of surface states, i.e., allowed levels for electrons in the forbidden gap of the semiconductor at the surface of this semiconductor, was introduced by Tamm' " and developed by

Schockley' '' in 1939. This concept is essentially based on the finite size of the crystal lattice. Bardeen ^ pointed out that, depending on the position of the Fermi level at the surface, some extra charge could be accomodated in the surface states. Because the charge was removed from the bulk of the semiconductor, a potential barrier already existed in the semiconductor before the metal contact was deposited. This potential barrier screened the influence of the metal work function.

The (adverse) influence of the surface states on the semiconductor surfaces forced developments towards devices with rectifying properties in the bulk of the material. This led to the p-n junction theory of Schockley' '^ which was based on the early work of Davydov' ^ in 1938. The rapid development of both the p-n junction theory and technology pushed the development of metal-semiconductor structures into the background.

Yet, metal-semiconductor structures cannot be overlooked in semi-conductor technology. First of all, there is the familiar application of a metal-semiconductor contact as an ohmic contact (degenerate rectifying behavior). In the second place, there are semiconductors (such as GaAs)

in which p-n junctions are hard to prepare and where Schottky contacts seem attractive. There is, however, another important reason for the application of Schottky barrier diodes. Because the current in metal-semiconductor diodes is almost entirely carried by majority charge carriers (this is in contrast to p—n junctions where minority charge carriers play the crucial role), the slow process of the diffusion of minority charge carriers is absent. Therefore, the actual switching speed of Schottky barrier diodes is only limited by the charging and dischar-ging of the barrier capacitance, and thus the Schottky barrier diode makes an ideal device for high frequency applications.

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contacts one must have an insight into the physical background of the potential barrier at the interface of the metal and the semiconductor. Obviously, the absorption of contaminants on the surfaces of the semi-conductors before the metal contact is fitted will affect the properties of these Schottky diodes. Therefore, it is necessary to study the proper-ties of metal contacts on oZean semiconductor surfaces.

This thesis deals with the properties of metal contacts on clean silicon, which are obtained by cleaving the silicon in an ultra high vacuum in a stream of evaporating metal atoms. The influence of the silicon surface states on the height of the potential barrier of the metal-silicon contact has been investigated by varying the kind of metal

(Ag, Au, Al, Mg, Na, K and C s ) . The height of the barrier has been measured in different ways, and the accuracy of the applied methods has also been the subject of investigations. To insure reproducible results, the diode fabrication and the barrier height measurement were performed in the same ultra high vacuum. It will be shown that the measured barrier heights can be explained by assuming that each metal induces a specific interface state distribution as a function of energy. The term i-ntevfaae states will be used to refer to silicon covered with a metal overlay; the term surface states will be used to refer to uncovered silicon surfaces.

References

I- 1 F. Braun, Pogg. Ann. _1_53, 556 (1874).

1- 2 A.H. Wilson, Proc. Roy. Soc, A 136, 487 (1932). 1- 3 L. Nordheim, Z. Phys, 75^, 434 (1932).

1- 4 J. Frenkel and A. Joffe, Phys. Z. Sowietunion _1_, 60 (1932). 1- 5 B. Davydov, J. Tech. Phys. USSR 5^, 87 (1938).

1- 6 N.F. Mott, Proc. Roy. Soc. A 171, 27 (1939). 1- 7 W. Schottky, Z. Phys. _ m , 367 (1939). 1- 8 B. Davydov, J. Phys. USSR J_, 167 (1939). 1- 9 J. Bardeen, Phys. Rev. 1\_, 1\1 (1947). 1-10 I. Tamm, Phys. Z. Sowietunion J_, 733 (1932). 1-11 W. Schockley, Phys. Rev. 56, 317 (1939).

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2. SURVEY OF THEORIES ON SCHOTTKY BARRIERS

2.1. Introduction

The theoretical aspects of metal-silicon diodes can be separated into two categories. First there is the potential barrier formation theory, and secondly there is the theory concerning current transport over this barrier. The basic theoretical aspects of the barrier formation are found in the comprehensive book of Henisch which appeared in 1957. Because surface (and interface) states play a crucial role in the

formation of the barrier, a considerable part of this chapter deals with the physical background of surface states. Knowledge of surface states has been recently increased by the appearance of spectroscopic surface analysis techniques.

Therefore, the reader is referred to the more recent review of Meyer and Sparnaay as well as to the classical paper of Davison and

Levine^ ^. In conjunction with Davison and Levine^ ^ only those surface states which are intrinsic will be considered. Intrinsic states stand for those states present on a clean silicon surface free from foreign atoms. Furthermore these surface states can be non-loaalized or localized states. Non-localized states are arranged in bands and describe those states

resulting from a periodic surface. This is in contrast to localized states which appear in discrete levels and result from imperfections on the surface.

Not only was the barrier formation mechanism identified by Henisch^ ' but also the historical development of the metal-semiconductor contact and the current transport theories were described. It will be shown that, although two current transport theories for metal-semiconductor contacts are available, neither of these theories predict the observed current-voltage behavior. This discrepancy between theory and practice was for the first time systematically investigated by Padovani^""*. An explanation for this discrepancy has been formulated by Rhoderick . Because the height of the potential barrier is measured with various techniques based

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on the current transport mechanism, the validity of the results is in question, this is also discussed in the second part of this chapter.

Furthermore, a distinction has to be made between Schottky barriers on veal silicon surfaces and those on clean silicon surfaces. Real silicon surfaces are defined as those surfaces prepared by chemical etching, followed by exposure to the atmosphere or to other gases. These surfaces are only clean to a certain extent because the surface is covered with contaminating chemical residues and a thin oxide layer. The latter is caused by the high oxidation rate^ ^ of silicon even at room temperature. Within several minutes the silicon is covered with an oxide thickness of 1 nm when exposed to air. The possible instability of Schottky barrier heights on real silicon surfaces is exemplified by the investigations of Turner and Rhoderick . They showed that the potential barrier height of a Au contact on w-type Si varied between 0.67 eV and 0.90 eV depending on the chemical treatment. Consequently the spread found in the literature for values of Schottky barrier heights on real silicon surfaces may be attributed to the difference in the structure of the interfacial layer. A striking example is found for hafnium p-type silicon interfaces, where a value of 0.90 eV for the barrier height was reported by Saxena in contrast to the value of 0.58 eV of Beguwala and Crowell^ ^ . Clean surfaces, on the other hand, are less simple to prepare. Initially a special method must be applied to obtain a clean silicon surface, and then it must be kept clean. The latter condition is easily met by the application of ultra high vacuum (UHV) techniques, although small quantities of residual gases remain present (Sec. 3.2.2.).

Among the current methods used to obtain an initially clean surface, there are three methods^ ^ especially suitable for the formation of metal-silicon diodes, viz:

1. ion bombardment followed by a subsequent annealing at 900°C in UHV,

2. high temperature heating (above 1000 C) of real silicon surfaces in UHV,

3. cleavage in UHV,

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surface is created by cleaving the silicon in a stream of evaporating metal atoms, thus forming the metal-silicon contacts (Sec. 3.2.). Only Schottky barrier contacts on the (111) plane of the silicon can be inves-tigated, because silicon only cleaves along the (111) plane. Furthermore, a cleaved silicon surface does not guarantee that the surface is perfect, i.e., the surface exhibits "cleavage steps". This surface roughness can be considered as consisting of a series of parallel terraces (parallel to

the (111) plane) bordered by steep risers (the cleavage steps). As stated previously in this thesis, much attention will be paid to a cleavage method (Ch. 4.) which minimizes the density of cleavage steps. The influence of the cleavage steps on the electronic properties of the silicon surfaces is anticipated and is discussed in Sec. 2.2.2.3. Finally, it must be remembered that the properties of cleaved silicon surfaces are different from those of annealed clean silicon surfaces. Consequently, the properties of Schottky barrier diodes on both surfaces will also differ.

2.2. Barrier formation

2.2.1. Basic concepts

2.2.1.1. Energy r e l a t i o n s w i t h o u t the p r e s e n c e of s u r f a c e states Figure 2.1(a) shows the energy levels for an electron in a metal and in a n-type semiconductor (silicon). The electrons in the metal and in the silicon are in thermal equilibrium, but the metal and the silicon are not in equilibrium with respect to each other. The thermionic work function (t (in eV) is defined as the difference between the

electro-m

chemical potential of the electrons just inside the metal here at the Fermi level position and the electrostatic potential energy of an electron just outside it. A similar definition holds for the electron affinity x

(in eV) of the silicon, except that the electrons are at the position of the conduction band edge. The level of zero energy is marked by the dashed line, representing the state of an electron at rest in vacuo.

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Metal E electron ' ^ F "

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Fig. 2.1. Electronic energy relations in a metal and a n-type semi-conductor vithout surface states; (a) separated from one another, (b) in close proximity and in thermal equilibrium.

When electronic equilibrium is established between the two

materials , the Fermi levels must coincide and a contact potential (by definition, the difference between the two thermionic work functions) <t> ~ (X + ?^p will arise. Electrons will travel from the silicon to the metal (because the Fermi level in the metal is lower than in the semicon-ductor) . If the materials are allowed to approach each other an

increasing negative charge is built up at the surface of the metal and an equal, but opposite charge, must exist in the silicon (Fig. 2.1(b)). If the interdistance t (henceforth called the interfacial layer") is small enough, the gap becomes transparent to electrons and the potential barrier which it represents can be disregarded. The contact potential takes place mainly then in the silicon with a limiting value given by:

?^,-

(x

+

qv^)

,

2.1

where V.. is called the built-in barrier voltage and qV,. denotes the distance between the conduction band edge and the Fermi level in the bulk of the silicon. This built-in barrier voltage K, . formes a potential

bz

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If a bias voltage V is applied across the contact and the Fermi level in the metal is taken as the zero constant reference level, this potential barrier can be raised or lowered depending on the polarity of the applied bias. The junction becomes forward biased with an external voltage Y if the contact potential is lowered by 1/ (the n-type semicon-ductor is negative with respect to the metal). The junction becomes reverse biased if the contact potential is raised by V (n-type semiconduc-tor positive with respect to the metal) . In both cases the barrier d) - Y

m for the movement of electrons from the metal into the n-type silicon, remains unaffected by the applied voltage and, therefore, is taken as the

barrier height qV.

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contact is considered to be ohmic (non-rectifying).

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semi-conductor without surface states; (a) separated from one another, (b) in close proximity and in thermal equilibrium.

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A similar analysis can be made for p-type silicon (Fig. 2.2). After establishing an electronic equilibrium and bringing the materials into close contact. Fig. 2.2(b) is obtained with opposite polarities of course. The space charge in the silicon is now negative (due to ionized acceptor centers) and the junction is forward biased when the semiconductor is positive with respect to the metal. The barrier height qV. is found from

qV, = X + E - if , 2.3

^ bp ^ g ^m

with E being the band gap of the silicon. This general picture ' was the first (idealized) description of barrier formation in metal-semiconductor contacts, mentioned in Ch. 1.

From Eq. 2.2 and Eq. 2.3, it can be concluded that the barrier height on silicon should depend on the work function of the metal. This is the crucial point in the theory. In the first place it is difficult to verify Eq. 2.2 and Eq. 2.3 because of the wide spread in the values of the various work functions in literature, and secondly, from extended experiments on silicon, it must be concluded that the relations do not hold. This is illustrated in Table 2,1, where some work function values are compiled from a literature search. The values in the second row were obtained using straight forward techniques; that is either by cleaning of the specimen by outgassing in a vacuum or by the evaporation of thin metal films in a vacuum. The introduction of ultra high vacuum systems has led to some striking new values (e.g. gold ) , which are compiled in the third row. The Schottky barrier heights in the last row were obtained from experiments on cleaved (in vacuum) n-type silicon and bear no relation with the values in the fourth row based on Eq. 2.2. The theoretical barrier heights in the fourth row have been calculated from the work function values in the third row with the use of

X = 4.03 eV (this value is found for cleaved silicon in UHV^ ' " ) . A comparison between the calculated barrier heights (fourth row of Table 2.1) obtained using the simple theory presented in the above and the measured barrier heights (last row of Table 2.1) shows that this simple theory does not hold. This, in fact, is not surprising because

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TABLE 2. 1

Comparison between barrier heights after the Schottky theory and

experimentally obtained barrier heights on cleaved n-type Si

surfaces.

metal Ag Au Al Pb Pd Pt Cu Ni Na older work function values d) (eV) m 4,31^"" 4.70^"" 4.20^"" 4.02^"'^ 4.9 ^"'2 5.3-5.8 ^"'^ 4.52^"" 4.74^"" 2.3-2.4 2"'' recent determinations

K

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4.32=''3 5.10^""* 4.17^"'^

—

5.55^"'^ 5.65^"'^ 4.65^"'^ 5.15^"'^ 2.75^""^ barrier height after Eq. 2.2

? V (eV)

0.29 1.07 0.14

—

>Eg >Eg 0.62 1 .12 ohmic experimental values

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0.76^-'' 0.84^"'' 0.77^"'' 0.79^" « 0.78^"" 0.86^"'" 0.77^-'' 0.68^"" 0.43^""

interface states play a dominant role in Schottky barriers on silicon.

2.2.1.2. Energy r e l a t i o n s in the p r e s e n c e of surface states In the presence of surface states the equilibrium relations at the silicon surface can be quite different . The situation of Fig. 2.3(a) occurs if the Fermi level at the surface is above the so-called neutral level E (for a detailed discussion see Sec. 2.2.2.1.) resulting in a negative charge in the surface states. The negative charge is created by

filling extra levels (from E to E in the case of uniformly distributed

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levels over the forbidden gap) with electrons originating from the bulk. This negative surface charge is compensated by an equal but opposite charge in the silicon. The charge of the ionized donor atoms cause a band bending to occur before contact is made between the silicon and the

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E e l e c t f o n ^^

S e m i - ^ conductor /^m

a) b)

Fig'. 2.3. Electronic energy relations in a metal and a n-type

semi-conductor with surface states; (a) separated from one another and (b) in close proximity and in thermal equilibrium.

metal. The value of this band bending depends on the number of the surface state levels. When electronic equilibrium is established between the two materials, the band bending will only slightly change as the metal and the silicon approach each other (Fig. 2.3(b)). In the case of a high density of states, most of the electrons travel to the metal from the surface states. The potential drop will take place mainly in the vacuum which results (in the limiting case of very small t , this barrier is again transparent for electrons) in a nearly unaffected barrier height.

The insensitivity of the barrier height to the work function difference, in the case of a high density of surface states, was first pointed out by Bardeen. However, because it was observed in the

literature (see also the last row of Table 2.1) that the barrier height of metal contacts on cleaved silicon was not a constant, this model needs to be investigated further (Sec. 2,2.3.). Moreover, the picture of uniformly distributed surface states in the forbidden gap of the silicon is only a simplification of the real situation (Sec. 2.2.2,).

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2.2.2. The clean silicon surface

2.2.2.1. S u r f a c e s t a t e s on c l e a n - c l e a v e d s i l i c o n

The first reliable experiments on the surface states of silicon were performed (independently) in 1962 by van Laar and Scheer^ '^ and by Allen and Gobeli^ '". In their work, silicon was cleaved in UHV and the photoemission of the cleaved surfaces was studied as a function of the bulk dopant concentration.

Following the pioneering work of Allen and Gobeli , it was concluded that their experiments could be best explained by assuming a two-band structure for the surface states in the silicon band gap. One band lies above the Fermi level at the surface and the other one below

the Fermi level at the surface. This was in marked contrast to prevailing opinion. At that time surface states were considered to be homogeneously distributed in the band gap of the silicon.

3 2 1 0 states,Im' eV)'

1 05 0 states, (m^ eV)''

Fig. 2.4. Distribution of surface states on olean-oleaved silicon; (a) after Allen and Gobeli^ ' ° j (b) after Meyer and Kroes^ ^^.

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In the two-band structure (Fig. 2.4(a)) the upper unoccupied band behaves like acceptor levels and is referred to as acceptor-like states^ ^, and the lower occupied band behaves like donor levels and is referred to as donor-like states^ '. The acceptor-like states are neutral when empty and negatively charged when filled with one electron. The donor-like states are neutral when filled with one electron and positively charged when empty. The bands are symmetrically arranged around the so-called neutral level E (Fig. 2.4(a)). Which means that, when the Fermi level is at E , the charge in the surface states is zero.

o °

Consequently, when the Fermi level is at a position somewhat higher than E , extra acceptor-like states are filled with electrons and the surface

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states are negatively charged. Conversely, when the Fermi level is at a position somewhat lower than E , the surface states will be positively charged.

In these early years it was assumed that both bands were located exclusively inside the silicon band gap . This picture was drastically changed by the photoemission energy distribution experiments of Eastman and Grobman " and by those of Wagner and Spicer^ . They showed that the surface state bands are not only located in the silicon band gap, but also that the donor-like states extend into the valence band. This picture was further completed by the ellipsometric measurements of Meyer and Kroes who found that the acceptor-like states extend beyond the conduction band edge. The resulting surface state bands are depicted in Fig. 2.4(b) with the following properties:

(i) The total number of acceptor-like surface states equals the total number of donor-like surface states (in other words, the areas under the two curves in Fig. 2.4(b) are equal).

(ii) The gap between the two bands appeared to be 0.26 eV as confirmed experimentally by Chiarotti et al.^ ^^. (iii) The maximum of the donor-like states is 0.6 eV below

the valence band edge, and the distance to the maximum of the acceptor-like states is 2.8 eV,

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(iv) The two secondary peaks around the band gap lie 0.45 eV apart.

Until 1973, theoretical calculations about the surface states on silicon had not revealed a model which was consistent with the experiments. In particular, the gap between the donor-like and the acceptor-like states did not arise in the theoretical models. Qualitative agreement between the theoretical distributions and the measured ones was only obtained by assuming more or less realistic atomic arrangements of the surface and sub-surface layer^"^"'^^'^^ .

2.2.2.2. E f f e c t of s u r f a c e atom a r r a n g e m e n t on the s u r f a c e state d i s t r i b u t i o n

The Low Energy Electron Diffraction (LEED) investigations of Lander et al. on cleaved (at room temperature) silicon surfaces in UHV showed that Che positions of the surface atoms must be altered with respect to their bulk positions. Instead of the normal bulk mesh, they found extra diffraction spots resultin in a 2x 1 surface unit mesh. Which means that the surface mesh had twice the linear dimensions of the substrate unit mesh. The difference in surface mesh with respect to the bulk mesh is called surface reconstruction and is considered as a lateral displacement of the surface atoms in the surface plane. Surface reconstruction is not only found on silicon surfaces but is also found on the majority of clean semiconductor surfaces (Tosatti^ ^ ° ) .

It must be noted that the surface reconstruction depends on the clean surface preparation method. For example, a clean silicon surface obtained by ion-bombardment with subsequent annealing exhibits a 7 x 7 structure. In addition it appears that in general cleaved semiconductor srufaces show an unstable surface reconstruction ^ . For cleaved Si surfaces the 2 x l structure changes into 7 x 7 upon heating above 480 C ^. When the sample is cooled to room temperature, the surface structure remains 7 x 7 .

A possible explanation for the observed 2 x ] structure on cleaved Si was also proposed by Lander et al.^ ^^. An ideal Si (111) surface is depicted in Fig. 2.5(a). In this unreconstructed case, one dangling bond

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surface plane^

c/MvIvK;:z:,

Layer i d e a l (111) s u r f a c e ideal (111) s u r f a c e - ^ , - ^ ~r^^ [ v a c u u m O.OlSlnm 5 5 0012|nm

S"-^^

I b u l k ® r e c o n s t r u c e d (111) surface after Lander el oL reconstructed {111 1 surface after Haneman

Fig. 2.5. Surface structure proposed for the (111) surface of silicon; (a) the "vacancy" model proposed by Lander et al."^ ^^, (b) the "rumpled" surface model proposed by Haneman^ '°.

lobe is perpendicular to the surface plane and three back bonds are connected to the sub-surface. Lander et al.^ ^' suggested that the dangling bond lobe could interact with a neighbouring lobe or with one of the back bond lobes (by breaking it). This pairing of surface atoms (now two electrons in a bonding state) could account for the ( 2 x 1 ) periodicity.

Another possibility was proposed by Haneman (see his review

article^ ^ " ) . He argued that the covalent sp bond in the Si bulk mainly results from the tetrahedral arrangement of the Si atoms. However, at the surface this arrangement is disturbed and therefore the bonds at the surface must be different. According to Haneman's^ ^° proposal the dangling surface bonds are either p or s type. If the dangling bond is

. . . 2 p type, then the three back bonds must be modified into sp . However,

these bonds are planar causing the dangling bond to be pulled downward. If, on the other hand, the dangling bond tends to be s type, the back bond will change into pure p type. However, these bonds are at 90 with respect to each other, causing the s dangling bond to be pushed upward. In conclusion, the resulting strain can be accommodated if there are

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alternating s and p type rows of dangling bonds. This is shown in Fig. 2.5(b),

The resulting displacements were recalculated by Schliiter et al, ^ They found that the raised atoms are displaced vertically by 0.018 nm, while the lowered ones are displaced vertically by 0.011 nm. Note that the atoms in the second layer are laterally displaced. It was calculated by Schliiter et al.^ ^^ that this surface atom arrangement resulted in a theoretical surface state distribution which is in good agreement with the experiments. Particularly they also found the surface state band gap of 0.26 eV.

In contrast Selloni and Tosatti '' found that a good agreement between a theoretical surface state distribution and the experimental one could be obtained by only incorporating laterally displaced surface atoms, in the surface plane of the silicon.

The Haneman model of Fig. 2.5(b) has been subject to many further investigations. Appelbaum and Hamann "* pointed out that, if the bond lengths between the surface and the sub-surface were not taken as being equal, a surface state distribution could be calculated in close agree-ment with the measured one. Furthermore, they proposed that alternating

3 . . . .

sp and p type rows occur because this is energetically more likely than s and p rows. Pandey and Phillips^ ^, on the other hand, calculated that, if in the Haneman model the sub-surface layer was taken closer to the surface layer (by « 0.03 n m ) , a surface state distribution resulted which was in close agreement with the measured one. This alteration of the perpendicular spacing between surface and sub-surface layers is known as relaxation. They found that the surface states which extend into the valence band result from the strengthened back bonds. These states are, therefore, called back bond states; the surface states which lie in the forbidden bap of the silicon were found to originate from the dangling bonds and are called dangling bond states.

The Haneman model of Fig. 2.5(b) was not only preferred theoretical-ly over the Lander et al.^ ^' model and the Selloni and Tosatti^ " model, but also it was preferred experimentally. For example, the results in the optical absorption experiments of Chiarotti and

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Nannarone on cleaved Ge surfaces could be best explained in terms of the Haneman model of surface reconstruction. A similar conclusion was found by Ibach and Rowe from their hydrogen adsorption experiments on clean silicon surfaces. On their cleaved samples they observed that the 2 X 1 superstructure disappeared after complete coverage with hydro-gen. This can be explained by assuming that the adsorbed hydrogen

3 . .

restores the sp -hybridization of the silicon surface atoms and that, therefore, the buckled surface will cease to exist. Moreover, they

observed that the deeper lying back bond states also disappeared upon hydrogen coverage which is also consistent with the Haneman model.

2.2.2.3. I n f l u e n c e of c l e a v a g e steps on the surface state d i s t r i b u t i o n

Until now the cleaved silicon surface has been treated as being strictly periodic and without any irregularity. But in reality cleavage steps are present to a large extent.

In the work of Henzler^ ^'* two types of cleavage steps are distinguished: large cleavage steps and cleavage steps of nearly mono-layer height arranged as regular step arrays. The large cleavage steps originate from the onset of cleavage (discussed in Ch. 4.) and are clear-ly visible on the surfaces as heavy lines (see Fig. 4.2). The monolayer steps are not visible with the naked eye and were concluded from LEED investigations^ '"'.

From a characteristic splitting of the spots in the normal LEED pattern into doublets, Henzler^ ^'* concluded that the regular step arrays were perpendicular to the large cleavage steps and in a direction normal

to the cleavage direction. The step edge (Fig. 2.6 and 2.7) of such an array is in the [ 110] direction, while it was observed '"* that the steps themselves are oriented only towards the [112] direction. This is

peculiar because an orientation towards [ 1 12] seems also likely. The edge atoms in the observed [112] direction have, however, two dangling bonds, while those in the [112] have only one (Fig. 2,7), In other words, these

edge atoms destroy the covalent character of the bonding of the edge atoms.

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[ill]

i i i

_{• •}

• o

• o step fieigtit • • O

Fig. 2.6. Regular array of steps (Henaler^ ^^).

^ , edge position with single dangling bond

% top layer atoms O Lower layers atoms

Fig. 2.7. Model for atomic steps on the (111) face of silicon^

The regular step array, after Henzler*^ ^ "* , was only found on those portions of the cleaved surface which were inclined (> 1 ) with respect to the (111) plane. If the misorientation between cleavage plane and (111) plane was less than 1 , no regular step array was found.

It was observed^ if^'* that several surface properties of the silicon depended on this inclination angle. For example, the already mentioned irreversible conversion from a 2 x I structure to a 7 x 7 structure on cleaved silicon is influenced by steps. The larger the angle, the higher the conversion temperature for the transition of the 2 X 1 superstructure to the 7 x 7 superstructure will be 9'3't_

The chemical properties of the silicon depended also on the angle of misorientation. The sticking coefficient for oxygen was found^ ^^ to increase for larger angles. Commonly, the step concentration is assigned

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by tan a, where a is the misorientation between the cleavage plane and the (111) plane and a is measured with an optical reflection method^ sinS For small a tan a corresponds to the density of edge atoms in

the surface. A strong deviation of a = 7 gives tan a = 0.15 corres-ponding to about 15% edge atoms in the surface.

Rowe et al. investigated the influence of steps on the surface state distribution of silicon surfaces. They concluded that both the dangling bond surface states and back bond surface states depended on the step density. For a stepped surface with 10% edge atoms, they^ '^ found an extra surface state peak 0.4 eV higher than the normal maximum of the occupied band in Fig. 2.4(b). This means that this surface state band has a tail extending above the bulk valence band edge into the forbidden gap. A similar extension of the occupied surface state band into the band gap was found in the theoretical work of Schliiter et al.^ ^^. They assumed an unreconstructed Si (111) surface with monatomic steps in a similar way to Henzler . The presence of these steps affected the position of the Fermi level at the surface. It appeared that the Fermi level was shifted towards the valence band edge by 0.3 eV, which was experimentally confirmed by Rowe et al.^ ^^.

2.2.S. The metal-silicon interface

2.2.3.1. R e v i e w of c u r r e n t m o d e l s

In the case of a very high density of surface states, the Fermi level at metal-silicon interfaces is fixed in one position, regardless of the metal work function value. This model is known as the Bardeen-pinning mode model (after Bardeen ^ ) .

Since it appeared from experimental work that there was a slight dependence of the barrier height on the metal work function (see Table 2.1), a less stringent model was proposed by Cowley and Sze '. They showed that this dependency could be explained by assuming a lower density of interface states. In this model '' the interface states were taken to be uniformly distributed in the forbidden gap and the value of the

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A pinning theory based on quite different theoretical considerations was proposed by Heine °. Heine disputed the existence of surface states in the case where the silicon is covered by a metal overlay. He argued that the solutions of the Schrodinger equation responsible for the appearance of the surface states on uncovered silicon now can exist in the metal as Bloch states " . These volume states in the metal have tails extending into the silicon forming resonant or virtual states in the band gap. The coupling of these states with the metal depends on the electronic structure of the metal and can be strong or weak, thus creating a slight dependence of the Fermi level on the type of metal. The mean length of the tails of the virtual states was estimated^ "*" to be 0.8 nm. This model was also consistent with the barrier heights known at that time. However, it is difficult to decide which model is the correct one, because much of the work is based on unreliable barrier height values. To be specific, the various classical barrier heights measuring methods (Sec. 3.3.) give results which are not consistent. This aspect will be further emphasized in Sec. 3.3.

The situation has been changed with the introduction of spectro-scopic surface analysis methods (in 1975), with which the change in Fermi level position can be observed during the Schottky barrier formation. From their experiments with a Pd overlay on cleaved III-V compounds, Eastman and Freeouf "* concluded that the final Fermi level position was related to the edge of the empty surface state band of the corresponding compounds. Consequently, the intrinsic surface states play the dominant role, thus giving support for the Bardeen ^^ model.

The validity of the Bardeen mechanism in turn was discussed by Spicer et al. . From their experiments '* on cleaved GaAs surfaces, it was concluded that the position of the Fermi level in the band gap on the clean surface changes upon increasing Cs coverage. Therefore, they concluded that new Cs-induced states were created causing a different Fermi level position. A further contribution to this problem is found in the work of Huyser and van Laar "*'. From their work function measure-ments on cleaved GaAs surfaces, it was concluded that there was no surface state band at all in the forbidden gap. They suggested that the

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reported^ "*' empty surface state band in the band gap of GaAs is induced by cleavage steps. Consequently, the Bardeen model cannot hold for metal-GaAs interfaces. However, it is quite possible that cleavage-step -induced surface states play the crucial role in the work of Eastman and Freeouf ^~'*' .

Recently several new pinning theories '•'•''* ' ^ have been proposed, which do not make use of interface states.

Inkson '*'* calculated the change in the image potential of an

electron in a metal-semiconductor structure, going from the semiconductor towards the metal. For the case of a covalent semiconductor, such as silicon, he concluded that at the metal-silicon interface the band gap shrunk to zero. The disappearance of the gap was caused by a upward bending of the valence band and a downward bending of the conduction band, resulting in a pinning of the Fermi level in one position.

Phillips^ "* proposed a pinning model entirely based on the chemical bonding forces between metal and semiconductor. In ionic semiconductors such as SiO , the internal bonds are so strong that the metal is only weakly bonded on the semiconductor. Here the Schottky model holds

because in the model no chemical bonding is assumed between the metal and the semiconductor; i.e., the electron is raised virtually to the vacuum level and then returned to the conduction band (see also Fig. 2,1). Consequently, a large dependency of the barrier height on the metal work function is expected in the case of an ionic semiconductor. In contrast the internal bonds in covalent semiconductors are not so strong, resul-ting in a strong interaction between the metal and, for example, the silicon. Thus, the Schottky model no longer holds.

The dependency of these properties together with others on the ionicity of the semiconductor was also recognized by Kurtin et al. '*^. All these properties exhibit the same characteristic abrupt change at the transition of semiconductors with a low ionicity (e.g.. Si) to those with a high ionicity (e.g., SiO.).

In the work of Harrison^ "*' it is also argued that the Fermi level can be pinned in the band gap of covalent semiconductors whether or not there are surface states. From his calculation on the 2 x ) structure of silicon (111) surfaces, he concluded that dangling bond hybrids are

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alternately shifted in the valence band and in the conduction band, thus balancing the Fermi level in the band gap.

Recent theoretical work^ '*^ on the nature of the interface states of Al-Si interfaces has questioned the Bardeen model as well as the Inkson

model. In these self-consistent calculations, the Al-Si structure is treated as several parallel slabs, extending from bulk Si to bulk Al with the real interface in between. With this model, Louie and Cohen "* concluded that the Inkson model can be disregarded because it is not meaningful to speak about a band picture as a function of distance (from the interface) on such a microscopic scale as conceived by Inkson . The Bardeen model was also rejected because Louie and Cohen^ "* ^ found in their model that the intrinsic surface states of the silicon were annihilated by the Al overlay and were replaced by four types of interface states.

First there are the bulk Al and Si states, secondly there are bulk-like states in the Si but rapidly decaying in the Al, thirdly there are bulk-like states in the Al but rapidly decaying in the Si, and finally there are states decaying in the Al as well as in the Si. These latter states were labeled as truly localized interface states. However, these states have a neglible influence on the pinning of the Fermi level because they are found well below the Fermi level (-8 eV).

The states which are responsible for the pinning of the Fermi level are the third type of states, and they resemble the characteristics of the intrinsic surface states in a Heine "-like way.

The same method of calculation^ "*' has been applied for Al contacts on semiconductors with an increasing ionicity (GaAs, ZnSe and ZnS) to check whether or not the Phillips^ ** ^ theory holds. These authors, Louie et al.^ "*', concluded that the dependency of the barrier height on the metal work function, in the case of the ionic semiconductor ZnS, could also be explained in terms of interface states (namely a low density). In conclusion Louie et al. "*' stated that the behavior of the various classes of metal-semiconductor interfaces can best be explained by the presence of a characteristic density of new metal-induced states.

The presence of new metal-induced states is confirmed by the Elec-tron Energy Loss Spectroscopy (ELS) experiments of Rowe and his

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co-workers^ so»51,52^ From these experiments it was concluded that, upon coverage with a metal overlay, the intrinsic surface states on (ion bombarded and subsequently annealed) Si (111), GaAs (111) and Ge (11!) surfaces were completely annihilated and replaced by new metal-induced states. Only in the case of Ge (110) surfaces, were the intrinsic

surface states found to be partly removed. From the detailed experiments on ion bombarded and annealed Si(lll) surfaces ^ , it was concluded that the metal atoms saturate the Si dangling bonds, creating new interface states with a low density tail extending into the Si band gap. These states probably are the result of the chemical bond between the metal and the silicon atoms. This bond has a more covalent character rather than metallic bond character. After coverage with the metal overlay, the 7 x 7 structure persisted. Finally, they ^ concluded that their metal-induced states which caused the Fermi level pinning, do not precisely agree with the states of Louie and Cohen^ "*' (because in the latter work the states were found to extend into the silicon).

2.2.3.2, R e l a t i o n b e t w e e n i n t e r f a c e state c h a r g e and b a r r i e r he i ght

From the previous section it can be concluded that the pinning of the Fermi level in metal-silicon interfaces is caused by charged interface states. Consequently, the problem of Sec. 2.2.1.2. must now be solved: namely, how the charge in these interface states is related to the barrier height. A relationship between the interface state charge and barrier height value is found by introducing the interface-model of Archer and Atalla"^ '^ and Goodman^ '', which is depicted in Fig. 2.8. In this model it is assumed that there is always an interfacial layer between the metal and the silicon. However, it is so thin that the Fermi

level in the metal is continuous with that at the surface of the silicon (in the case of equilibrium). Furthermore, the character of interface states is assumed to be purely two-dimensional, that is, with neglible dimensions perpendicular to the interface. This assumption is justified by the observations of Margaritondo , mentioned in the previous section, which was that the interface states originate from the

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semiconductor metal ? .

S Ii

distance from interface

Fig. 2.8. Electronic energy relations at the interface of a

metal-semiconductor contact.

chemical bonding between metal and semiconductor, thus indicating that the interface states do not penetrate into the metal or silicon. Further simplifications are that

(i) the electrons in the interface states are in equilibrium with the electrons in the metal,

(ii) the space charge is uniform and continuous, (iii) the interfacial layer itself is charge free, (iv) the work function and electron affinity value is the

free surface value in vacuum,

(v) an applied bias voltage acrocs the contact causes a neglible voltage change across the interfacial layer with respect to that across the space charge region.

The last condition corresponds to the requirement that the capacitance resulting from the interfacial layer is large with respect to that of the space charge region.

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found by applying Gauss' law:

Y =_{' e} -^— (Q_£._{so vs} + e . ) , 2.4

o t

where t is the thickness of the interfacial layer (m), E the permit-tivity of free space (8,85 x 10~ F/m), £. the relative dielectric constant of the interfacial layer, Q. the charge in the interface states, and Q the charge in the space charge region.

The charge in the space charge region (per unit area) is found by solving Poisson's equation ' (the effect of the reverse layer ' is incorporated by introducing the familiar term kTlq):

3g^ = / ^"i^d^o^s ^"^r ^ ^m'"^ ~ ^X/<? + l'^) - Y - ^^/^^ . 2.5

where V is the applied reverse bias (V), A; the Boltzmann constant (8.62 X iQ-s eV/K), T the absolute temperature, q the magnitude of electronic charge (1.6 x 10~'^ C ) , M^ the doping of the n-type Si (m~^), and E the relative dielectric constant of the silicon (= 11.8).

The barrier height can be calculated from the differential capacitance C of the contact. When a small ac voltage is superimposed upon a reverse dc bias voltage V , charges of one polarity are induced on the metal surface and charges of opposite polarity in the silicon. Consequently the differential capacitance can be written as

6Q 6(6 + e . )

^ - m _ sc ts , ,

^ - &V &V ' ^-^

r r

where Q is the compensating charge on the metal plate. As stated previously, SQ. /6V is negligible and the differential capacitance is

found by differentiating Eq. 2.5 with respect to voltage. After that, Eq. 2.4 can be substituted in the resulting equation. Consequently,

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*'^' ^ ^

iV^^^Jq-iXlq^Vj-kTlq-^-Q.].

2.7

2 2 ,7 r m ^ ' ^ f ^ zs

O Z ^ d O S OS

And conforming to the initial simplifications, Eq. 2,7 reduces to

^ d o s •' o z

If the reciprocal of the capacitance squared is plotted against the Led bias,

voltage axis:

applied bias, a straight line results (Eq. 2.8) with intercept V. on the

-V^ = ^Jq-ixlq-V^)-^_Q.^-kTlq - V.. 2.9

Note that the intercept voltage is positive. From this method, known as the capacitance {C~^-V) method, the barrier height can be determined, several other methods are discussed in Sec. 3.3. From Fig. 2.8 it appears that the barrier height qV^ can be expressed as

qv, = <\> -x-qy • 2.10

^ bn m ^

If Eq. 2.4 is substituted into Eq. 2.10, this results in

qV-, = * -X--^^Q --^^Q. , 2.11

^ bn m ^ e c . ^sc E e. ts

0 1 o %

which in turn gives, with the use of Eq. 2.9

V, = V. + V.+ kT/q--^ Q . 2.12

bn ^ f ^ £ e. se

•' o %

However, in this case of thin interfacial layers (0.1-1 n m ) , the last term in Eq. 2.12 c^n be neglected (of the order 10 '*), which reduces the

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relation in Eq. 2.12 to

I'l, = y. + K^ + kTlq . 2.13

bn 1' f

The relation between the charge in the interface states and the barrier height is found by substituting Eq. 2.9 into Eq. 2.13 resulting in

hn '-

V ^

-

X/^

-

F T :

«^a

• 2-'^

The charge in the interface states is found by assuming that the levels in the interface state distribution are occupied according to Fermi statistics. The details of the interface state distribution can be distinguished by measuring the temperature dependence of the barrier height "* . This method was first proposed by Davison and Levine in order to reveal the details of the surface state distribution on silicon. The charge in the interface states also depends on the temperature because the occupation of the states is determined by the Fermi statistic after

3. = q \ N{E) F(E) dE 2.15

zs

where N(E) is the distribution of the interface states as a function of energy and F{E) is the Fermi function.

Based on the considerations of the previous section, two types of possible interface state distributions must be investigated : one type restricted only to the forbidden gap of the silicon (Fig. 2.9(a)) and the other with energy distributions extending into the bulk bands (Fig. 2.9(b)). On first sight, the two proposed fundamental interface state distributions of Fig. 2.9 resemble those of the free silicon surfaces. However, it will be shown in Ch. 6. that the details are quite different. For both

distributions it is asserted that they are fixed within the band gap with respect to the intrinsic Fermi level E.. The distance E.-E (E is the

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reference level) is an invariant. 10 S

4 ^

® 15 10 0 f , - 0 5 •10

states,(m' eV)' states,(m' eVP

Fig. 2.9. Proposed fundamental interface state distributions;

(a) energy distribution restricted to the forbidden gap of the silicon,

(b) energy distribution extending into the bulk bands of the silicon.

The net interface charge for the distribution in Fig. 2.9(a) is

Q. = qn^ j

(1 + exp[(£',-£')/feT]}-'

dE

"2 "b

-qn j {1 + exp[ (£•-£•)/?:?']}"' dE

2.16

with E and E representing the band edges, E, representing the widths of the band, and n and n representing the density of states (/m .eV) in the acceptor band and donor band, respectively. For simplicity, assume

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n, = n^ = n and define^ ^ (see Fig. 2.9(a))

E^=i(E^^E^), ^p = E^-E^, LE^=E^-E^ = LE^=E^-E^-t£.

The integral in Eq. 2.16 can now be solved in closed form together with Eq. 2.13 to give

q\n<-1) = ^„(T)-xiT) - ^ ^ p n [ { l + exp[(A£ + £^- E )/kTl}

i o •'

X {1 + exp[(A£' + A£' )//;?]}] 2.17

- ln[{l + exp[(Aff + £'^ +A£' )/feT]} x {] + exp[ (Aff - Aff )/fey]}]]]

The several values in Eq. 2.17 are found in the literature (see Ch. 6 . ) , and the theoretical barrier height qV, can be plotted as a function of temperature with t/e., tsE, E, and n as parameters. By a trial-and-error method, the best fit with the experimental barrier heights is found and results in an interface state distribution^ ^'*. This is presented in Ch. 6

A similar procedure is applied to the distribution depicted in Fig. 2.9(b). This results in an interface charge:

E, E. ₁₊ b \. Iq = - \ n,{l + exp[ (£•-£• J/fey]}-' il ^s ^ ' 1 " f E^.E^.E^ f n {] + exp[(£'-£' )/fer]}-' d£" E+E,+E^+E, 1 o 3 4 -1 / n.{l + ex-pl{E-E )/kT]] ' dE

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+ / ^ 3 ( 1 + exp[(£' -£)/feT]}"' dE

h-h

j nA\ + exp[(£ -£')/feT]}"' dE

h-h-h

/ n {\ + exp[(Z7 -E)/?;?]}"' d£ .

F -F •'

2.U

The resulting barrier height after Eq. 2.13 becomes

'^"fcn^") = ^ ( ^ ) - X(^) ^ _{£ .£} X II n ^ l n ] 1 + e x p [ (Aff + AK + K + £ 3 + £ )/feT] 1 + exp[(A£' +A£ + £', + £ ' g ) / J : r ] n ^ l n j 1 + exp[(A£' + A£ + £ , + £ " ) / / c T ] 1 + e x p [ ( A £ ' ^ + A E + f, )/feT] + n ,

p _ 1 + exp[(A£' +A£: + £'^)/fe!r] l n { - I n

1 + expC(A£' + A£' )/fe2]

1 + e x p [ ( A £ ' - A £ ' )/fey] 1 + expr(A£' + ^, - A£ J / f e y ] + n^ l n ( 1 + exp[(AE' + S ^ - A £ ' , ) / f e T ] 1 + ^-x.Y:l{t£ + E,+E^-t\E^|kT^ + n l n ( 1 + exp[(Aff + £', +£• -A£'^)//<:T] 1 + exp[ (t£ + E,+E^ + E, - hE J /kTl b i h f

'1

2 . 19

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Consequently the closest fit to the experimental data is found by varying tjz., tsE, E , E,, E , E and the respective densities n., n , n, and n . An extra condition, in both trial-and-error methods, is that the total density of states (m"^) must be physically acceptable (see Ch. 6.).

2.3. Direct current transport

2.3.1. Diffusion and thermionic emission

theory-Basically there exist two theories which govern transport in Schottky barrier diodes. The first is called the diffusion theory and was proposed by Wagner and in a more general form by Schottky and Spenke . The second one is called the diode theory (or thermionic emission theory) and was proposed by Bethe^ " . The diffusion theory supposes a mean free path of the charged carriers that is small in comparison with the barrier thickness. The current is then limited by the ordinary processes of diffusion and drift. The diode theory supposes the contrary, namely, a mean free path that is large in comparison with the distance within which the potential energy changes by kT near the top of the barrier.

In fact these processes are in series, and the current flow is determined by that process which causes the larger resistance. Several authors (see the review article of Rhoderick^ ^) have combined these theories into one. However, it turns out that the current transport in metal-silicon diodes is mainly governed by the thermionic emission theory because the condition

p B » y/4 2.20

max

is seldom violated. In this equation E is the maximum electric field

max

in the barrier, y is the mobility of the charged carriers,-and v is their average velocity. This condition is usually satisfied in high mobility semiconductors such as silicon. However, for low barrier heights and low dopant concentrations, the maximum electric field may be so low that,

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even for silicon, the condition in Eq. 2.20 is not satisfied. In that case the current transport is described by the diffusion theory.

The current (density) -voltage relationship predicted by the thermionic emission theory is shown to be '

J = A*T'^ &x^{-qV IkT) l&x-piqVlkT)- \1 , 2.21

where J is the current density (A/m ) , A the Richardson constant

(112 X lo"* A/m^.K^ for n-type Si and 32 x jO"* A/m^.K^ for p-type S i ) , and V the applied bias voltage. A similar relationship is found from the diffusion theory except that the current density predicted by the diffusion theory exceeds that predicted by Eq. 2.21 by a factor of 4y E Iv (see Rhoderick^"').

max

However, in practice many deviations from the predicted current-voltage relation in Eq. 2.21 are observed; the responsible mechanisms will be identified below.

2.Z.2. Image force lowering and quantum mechanical tunneling

From thermionic emission experiments on two parallel metal electrodes in 1914, Schottky became aware of a lowering of the thermionic work function due to the applied field between the metal plates. This so-called Schottky effect or image force lowering plays a role also in

metal-semiconductor interfaces and makes the barrier height dependent on the field in the space charge layer. Consequently the reverse current, as predicted by Eq. 2.21, will not saturate because the barrier height is dependent on the external bias. This was first formulated by Henisch^ ' and recently corrected by Padovani "* . The change in the barrier height Al/, ^ "* is found to be bs A7, = [ a ' / V , ( l / , - 7 - 1 / - - A : 7 / o ) / 8 T r 2 £ => E-^ £ ] ' , 2 . 2 2 bs ^ d bn f ^ o d w h e r e Z-, i s t h e image f o r c e d i e l e c t r i c c o n s t a n t ( i n g e n e r a l £ , i s a p p r o x i m a t e d by t a k i n g £ , = £ = 1 1 . 8 ) . a s

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Another apparent decrease in barrier height, which was already incorporated in the early transport theories of Schottky and Spenke and Bethe^ ^', is the quantum mechanical tunneling of charged carriers through the top of the barrier. Assume for the sake of simplicity that the barrier above a certain critical barrier thickness x is completely transparent to electrons. Then (after Henisch^ ') the diminution of the barrier height Al/, ^ can be stated as

^ bt

A K , = X l2qN,iV. -V-V„)lc'l' . 2.23

bt a ^ d bn f

This bias dependent barrier lowering becomes more important at high doping levels and large reverse voltages {V is negative). As a consequen-ce, it can be expected that electron tunneling penetration of the barrier will become predominant in barriers made on semiconductors with a heavy dopant concentration. The current transport is then no longer properly described by the thermionic emission theory, but is replaced by field emission theories as formulated by Padovani , These theories will be disregarded in this thesis because the Schottky barriers considered here are all made on moderately doped (< 10^' atoms/m^) silicon.

Not only are the reverse characteristics affected by the image force lowering and the tunnel effect, but also the shape of the forward

characteristic is changed. From extensive experiments on Au n-type GaAs Schottky barrier diodes, Padovani^ "* concluded that the current-voltage relation is best represented by

J A T^ exp{-qV, ImkT) LexpiqVlmkT) - \1 , 2.24

where m is a dimensionless parameter close to unity, resulting from the combined voltage dependence of Al/, and AF, (Eq. 2.22 and 2.23). This empirical relation was also observed for metal-silicon diodes by

Saxena . The diode factor m is calculated from the slope in a plot of the logarithm of the forward current density as a function of applied bias. For qV » kT, a straight line will appear and the deviation of the slope of this line from qlkT determines m. Theoretically the factor m is

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also calculated. Rhoderick^ ^ showed that m = 1.02 only if the image force lowering was incorporated. On the contrary, the measured values of m, determined by Padovani"^ "* and Saxena^ " revealed much larger

deviations from unity.

2.2.2. Observed anomalies

2.3.3.1. A n o m a l i e s in the forward current

Investigations concerning the saturation current revealed that the factor m must be temperature dependent. This saturation current density J is defined, from Eq, 2.24 as

J = A*T^ exp(-qV, ImkT) . 2.25

From Eq. 2.25 it is concluded that a plot of the logarithm of J IT^ versus qlkT should yield a straight line with slope (-7, /m) . Padovani^ '* and Saxena^ ^', however, pointed out that for GaAs and silicon, respectively, a plot of log(J' /T^) versus qlk(T + T ) resulted in a straight line. So the factor m is expressed as

m = {T + T )IT , 2.26

o o

where T is called the excess temperature, which is a characteristic of the applied semiconductor.

Saxena ^' investigated various metal-silicon combinations and suggested that the origin of the excess temperature T was a specific temperature dependence of the barrier height (jl/, . By applying the simple Schottky theory to his barriers, Saxena determined from this temperature dependence the temperature coefficient of the work function. However, the agreement with the values in the literature of the temperature coefficient of the work function for the various metals was not good.

An elaborate analysis of the origin of the excess temperature T has been given by Levine . He supposes an exponental interface state energy distribution with a characteristic energy E (not to be confused

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with our E = neutral level). This energy E uniquely determines the

o "•' o

excess temperature T . He claimed that a proof for his theory was that T must be both a function of temperature and applied bias, as was indeed concluded from the data of Saxena^ ^^. The energy E is determined from the plot \IT versus applied bias. In a later publication ^ Levine showed that the energy E could be determined also from the reverse

^^ o

characteristics.

A severe objection to the Levine theory comes from Rhoderick ^ who pointed out the lack of a balancing interface state charge on the metal. The introduction of such a charge in the theory of Levine ^° is quite possible , but the determination of the energy E is then much more complicated.

A more realistic explanation for the curvature in the plot of the logarithm of the forward current as a function of the applied bias has been given by Yu and Show . They showed that the forward current in metal-silicon contacts consists of two components: a recombination

(taking place in the space charge region) term and the normal thermionic emission term. The recombination current arises in much the same way as in silicon p-n junctions (Grove^ ^ ' * ) , namely, through recombination centers near the middle of the band gap. The recombination current density J is (after Ref. 2-63,64)

•^ rea

'^rec = ^'5'"i^/'^o exp(^y/2fey) , 2,27

where n. is the intrinsic carrier concentration, I is the width of the space charge region, and T is the effective lifetime within the space charge region.

The relative importance of thermionic emission and recombination in the space charge region depends on the barrier height (^l', , the doping concentration A', (which determines Z.), the lifetime T , the temperature T and the applied bias voltage V. This is exemplified in Pig. 2.10 for a Pt contact on chemically etch-polished Si (after Yu and Snow"" ^ ^ ) . At room temperature and low forward bias, the recombination term and thermionic emission term are comparable, and the factor m has an

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inter-10' <,10' C T3 a | i o ' 10 = 10'° 0 01 02 03 04 forward bias. V

Fig. 2.10. Forward characteristics of a Pt-Si Schottky barrier diode (after Yu and Snow^~^^).

mediate value of 1.3 (Fig. 2.10). However, for higher bias voltages the thermionic emission term dominates and m tends to unity. Conversely, for a reduced temperature (-30 C) recombination becomes relatively more important, and a region with m = 2 appears at low forward biases (Fig. 2.10). From Fig. 2.10 it is concluded that the factor m is both

temperature and bias dependent.

However, the present case of Schottky barriers on cleaved silicon is more involved. As stated in Sec, 2,2,2,1. clean-cleaved silicon already has a barrier before contact with a metal is made. This means that the surface is depleted resulting in a surface space charge region.

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depleted, and this extra surface space charge region will also have an influence on the current-voltage relationship. The influence of such surface space charge regions is known from the elaborate studies of Grove^ ^'* and Whelan^ ^ ^ on gated p-n structures. In a gated p-n structure, an annular metal-SiO -Si capacitor is closely located around the p-n diode and is employed to study the characteristics of the surface areas around the metallurgical diode area.

Yu and Snow^ ^' adopted this structure to study similar effects on the current-voltage relationship in Schottky barrier diodes (Fig. 2.11).

Scfiottky barrier l/g(negative) , S i O , I n-type SI 'y

r

® l/g>0

Fig. 2.11. (a) Creation of an annular surface space charge region around the Schottky barrier diode, by means of a biased gate; (b) Resulting forward current as a function of the gate voltage.

When a voltage is applied on the gate, the width a;, of the surface space charge region can be varied independently of the diode voltage. If the gate voltage is negative, a situation appears which is similar to our diodes on cleaved silicon. Following Grove "* , two extra contributions to the forward current density will be observed.

Firstly, a current density arising from the bulk recombination centers in the surface space charge region, will appear in a similar manner to the one described in Eq. 2.27. Upon an increasing negative gate voltage, the increasing inverted surface (p- type layer) is connected to

Some Schottky barriers on clean-cleaved silicon

SOME SCHOTTKY BARRIERS ON

CLEAN - CLEAVED SILICON

y/&^ X^

^y

CLEAN - CLEAVED SILICON

n

o o

•4 O

II !l II If.!

ii!i:ii:!!l!itl

in

III | i i

iiiiili

M « | t

SOME SCHOTTKY BARRIERS ON

CLEAN - CLEAVED SILICON

PROEFSCHRIFT

JOHANNES DIRK VAN OTTERLOO

CONTENTS

1. GENERAL INTRODUCTION

2. SURVEY OF THEORIES ON SCHOTTKY BARRIERS

2.1. Introduction

2.2. Barrier formation

r T

Y~^

0.

r

^

<

\

k

?^,-

(x

+

qv^)

,

AT

Wsl

Comparison between barrier heights after the Schottky theory and

experimentally obtained barrier heights on cleaved n-type Si

surfaces.

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2.2.S. The metal-silicon interface

Fig. 2.8. Electronic energy relations at the interface of a

metal-semiconductor contact.

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Fig. 2.9. Proposed fundamental interface state distributions;

(a) energy distribution restricted to the forbidden gap of the silicon,

(b) energy distribution extending into the bulk bands of the silicon.

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