III–V semiconductor junctions

424

Surface Science 200 (1988) 424-434 North-Holland, Amsterdam

SCHOTFKY BARRIER FORMATION IN DEFECT-FREE M E T A L / I I I - V SEMICONDUCTOR J U N C F I O N S J. S/kNCHFT-DEHESA, F. FLORES, J. ORTEGA Departamento de Fisica de la Materia Condensada (C-XII), Unioersidad Aut6noma de Madria~ Cantoblanco, 28049 Madri~ Spain

and J.D. DOW Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA Received 30 June 1987; accepted for publication 19 August 1987

The Schottky barrier heights for the perfect, abrupt, and defect-free interfaces between silver and two different semiconductors, GaAs and lnP, are calculated self-consistently. The results compare favorably with data for GaAs/Ag and InP/Ag interfaces.

1. Introduction Different experimental evidence [1-10] suggests that semiconductors/metal junctions can be classified into three main groups: (i) abrupt interfaces [2-4], with a well-defined separation between the structures of the metal and the semiconductor, (ii) etched interfaces [11], with a reactant left between the metal and the semiconductor, and (iii) reactive interfaces [5-10], with the metal and the semiconductor interdiffusing a n d / o r forming a new chemical compound at the imerface. A property of these junctions that is amenable to study both theoretically and experimentally is the Schottky barrier height. The purpose of this paper is to present theoretical calculations appropriate to the pexffect abrupt-interface limit for GaAs/Ag and InP/Ag contacts and to show how the Fermi level can be pinned by intrinsic interface states at such interfaces, leading to Schottky barrier formation.

1.1. Models of Schottky barrier formation Several models of Schottky barrier formation have been proposed, and it is not yet clear from the data that a single model can explain all the data. Of the 0039-6028/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Pub!isbJng Division)

J. Sdnchez-Dehesa et at / Schottky barriers in metal~semiconductor junctions

425

many models [3,5,9,10,13,14,19,22-24] that have been proposed for the I I I - V / m e t a l Schottky barrier heights, two general types appear to continue to attract fairly wide support in the scientific community: (i) The defect model [22,25-33], which assumes that the formation of the Schottky barriers results from the creation of a sigafificant number of native defects at or near the semiconductor surface; these defects have deep levels in the gap which determine the surface Fermi energy, causing a Schottky barrier to form when the Fermi energy of the surface aligns with those of the bulk semiconductor and the metal ("Fermi-level pinning" [23]). (ii) The induced density of interface states [24,34-42] model, which attributes the Schottky barrier height to Fermi-level pinning by intrinsic semiconductor/metal interface states that have a significant density of states near the mid-bandgap. Both of these models involve states at the semiconductor/metal interface with characters that are almost independent of the metal, and so they are capable of explaining Schottky barrier heights that are virtually independent of the metals. On purely theoretical grounds it is clear that if Fermi-level pinning occurs, the states that predominantly cause the pinning must be defects states in the limit that the interface contains many defects with deep levels in the furdamental band gap, and must be intnnsic states in the limit of few d e l f t s . (Recall that most of the interface states are not in the fundamental band gap, and so only the fraction of the interface states in the gap contributes to Fermi-level pinning.) Thus there are two major theoretical issues: (i) Does Fermi-level pinning determine the Schottky barrier height of a given semiconductor/metal contact? (ii) If Fermi-level pinning is responsible, are the pinning states intrinsic or defect states? Present evidence suggests that most I I I - V / m e t a l interfaces and Si/transition metal si!icide interfaces [43-45] have a Fermi level pinning [12,14-17,30-33]. Hence the resolution of the issue concerning how Schottky barners are formed at III-V/metals interfaces depends on (i) the III-V semiconductor and the metal (and their reaction chemistry), and (ii) the deposition process, the perfection of the interface, and the number of defects formed during or after the deposition. If there are too few defects, the defect model cannot describe the data (estimates of the required number of defects range from below 0.1% to 10% of the surface atoms); likewise, if there are too few intrinsic interface states in the gap, those states cannot pin the Fermi level either. In the limit of few defects, the questions remain: (i) For III-V semiconductors, can intrinsic interface states n l n t h e ~o.rm;. lava.1 a r dae..~ t h e a l d Schottky work-function model aovlv? (ii) In cases such that Fermi-level pinning by intrinsic interface states occurs, what are the Schottky barriers heights to be expected and how do they compare with the existing data? The purpose of this paper is to address the latter question. A few experiments appear to have produced very good interfaces, most notably GaAs/Ag [3,46] and possibly InP/Ag [12,47], and so a comparison of theory and data for these interfaces is warranted.

426

J. Simchez.Dehesa et al. / Schottky barriers in metal~ semiconductor junctions

1.2. The perfect semiconductor~ metal interface Following early theoretical studies of perfect semiconductor/metal interfaces, Cohen and coworkers [48] calculated the electronic structures of such interfaces, using self-consistent pseudopotential theory. By means of an equivalent method, Tejedor et al. [38] proposed a mechanism of Schottky barrier formation based on the concept of charge neutrality at the interface; in this mechanism, the semiconductor-metal barrier height is determined by a high density of states located at an energy near the surface energy bands of a clean surface: For the clean surface, there is a high density of states associated with the surface band; when the semiconductor and the metal are coupled, that density of surface states broadens but keeps its center of gravity almost constant. Hence the interface's Fermi level almost coincides with the Fermi level for the free surface. Recently, two different methods have been applied to the semiconductor-metal junction, following the seminal idea of local charge neutrality. S[mchez-Dehesa et al. [39-41] used a tight-binding approach, while Tersoff [42] employed a Green's function method. In both methods, local charge neutrality conditions were used to calculate the charge neutrality level [38], the interface Fermi level, and the Schottky barrier height. The Green's function method of Tersoff [42] is independent of the particular metal forming the junction, while the method of Sfinchez-Dehesa et al. [39-41] provides a mechanism for introducing the small corrections associated with a particular metal. The results of both methods are similar and produce Schottky barrier heights for abrupt semiconductor/metal contacts as well as band offsets for semiconductor/semiconductor heterojunctions [49,50] in agreement with appropriate measurements and with other more sophisticated calculations based on the local density approach [51]. The aim of this work is to calculate the electronic structures of defect-free abrupt interfaces for different III-V heteropolar semiconductors. Various workers [25,26,30-33] have stressed that the defect model seems to adequately describe the bulk of the Schottky barrier data involving these semiconductors. Nevertheless, since some abrupt, defect-free interfaces may occur for III-V semiconductors (an example is GaAs/Ag [46] and a more controversial case is I n P / A g [19~.471~ it i.~ annrnnriate to determine if the ln~.al e.haroe, neutrality concept can describe the Schottky barriers of these high-quality junctions also.

2. The model We describe the electronic structures of the semiconductors and the metal by means of tight-binding models. For GaAs and InP we use a basis of sp3s* orbitals [52] at each atom and include interaction parameters extending up to

3. S~nchez-Dehesa et al. / Schottky barriers in metal/semiconductor junctions

(110) :

427

OGo QAs OAg

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Fig. 1. Geometry of the GaAs (or InP) (ll0)/Ag metal-semiconductor junction for the deposition of two metal layers. The diagonal perturbations V~ for each layer are plotted. The distance between the last semiconductor layer and the first metal layer is taken equal to a / 2 ¢ ~ while the distance between neighbounng metal layers is a / 4 , with a = 5.66 A (5.45 ~,).

the first neighbours. For the metal, we use two orbitals at each atom, trying to simulate a broad and a narrow band associated with an s - a n d a d-band, respectively. In particular, we have followed the simple Harrison model to obtain the parameters that mimic the appropriate densities of states [53]. The crystallographic structure of the semiconductor/metal interface is rather complicated. The deposited silver forms crystallites on the (441) plane [46] parallel to the (110) face of GaAs. A complete calculation for this structure would be rather cumbersome. For simplicity, we assume that the Ag atoms form a (110) face-centered-cubic structure matching tlae (110) face of the heteropolar semiconductor. The structure has been chosen having the (001) direction of the metal parallel to the (110) direction of the ' emiconductor in order to have an atomic density close to the actual density ~'Jr Ag (see fig. 1). Note that the first Ag layer is determined by the cation-cor, tinued position of the ideal semiconductor. For the Hamiltonian of the interface, we assume the ~ame tight-binding interaction parameters for the metal and the semiconductoJ's as were chosen for the bulk. The junction is formed by introducing new in' eraction parameters between the outermost semiconductor atoms and the m~,tal atoms of the last layer. These parameters have been calculated using two different models: (a) we use a simple arithmetical mean value between metal and semiconductor bulk interactions, corrected if neccesary by the scaling laws of Harrison [53],

428

J. $dnchez-Dehesa et al. / Schottky barriers in metal~semiconductor junctions

(b) the tunneling cm~rent between the metal and semiconductor atomic wave functions is employed in order to calculate the interaction [54].

3. Method of calculation In the calculations we introduce diagonal perturbations at different layers of the interface. In practice only 2 layers of G a A s and 3 of Ag are perturbated.

Then, the calculations are iterated to self-consistency, relating the diagonal perturbations to the transfer of charge between the two crystals [39,41]. In executing the calculations, we follow the procedure explained in ref. [39]. In summary, our method consists of looking for the surface matrix elements of the Green's function of the system. By means of a decimation technique, we can define for the metal and the two semiconductors effective matrices

associated with the last 3 semiconductors layers and the last 4 metal layers. These matrices define effeq.'3ve interactions for the surface atoms of each crystal and we analyze the junction by considering the interaction of the renormalized metal and semiconductor layers. The hopping interactions between the metal and the semiconductor, as well as the diagonal perturbations for the different layers around the interface of both crystals specify completely our Hamiltonian for the junction; the effective Hamiltonian has been reduced by this procedure to a 46 × 46 matrix.

4. Resets and discussion The results presented in this paper have been obtained by assuming that the junction is built up as an ideal semiconductor crystal. It is well known that I I I - V semiconductor surfaces reconstruct and relax. (For GaAs, the surface relaxation removes the unrelaxed surface electronic states from the bulk fundamental gap.) However, small numbers of atoms deposited on the surfaces are known to quench the geometrical relaxation and reconstruction [46,55]. Therefore, in this paper we have assumed that the semiconductor at the semiconductor/metal contact is ideal and unrela:~:ed. The ideal electronic semiconductor structures are defined by the parameters ~"~'" ^. at. _1 t.,z], r~.,, .,._ _1. . . . :,__ the two-band electronic structure of Ag , ~ , ~ u by it.._1 v ,o~,~ ~t i O uescnoe we have used the tight-binding parameters [39]: V~ = -- 1.00 eV,

V~d= -- 0.25 eV,

Vdd = -- 0.25 eV,

cd - % = - 3.00 eV. Here, ~s, ~sd and Vdd are interactions between the nearest neighbours s-s, s - d and d - d orbitals, respectively, while c a and c s are the d and s orbital levels (diagonal matrix elements).

3'. Sdmchez-Dehesa et al. / Schottky barriers in metal~ semiconductor junctions

429

Table 1 Interactions between the orbitals of GaAs (or InP) and the nearest metal atom orbitals (in eV) Atom

Vss a)

K~ a)

Vds a)

Vdp a)

Meanb)

ModelC)

Meanb)

ModelC)

Meanb)

ModelC)

Meanb)

ModelC)

- 1.47 - 1.10

- 1.10 - 1.19

1.92 1.63

1.63 1.60

- 1.01 - 0.61

- 1.20 - 0.66

1.45 0.71

1.73 0.94

P

- 1.33

- 1.08

1.15

1.58

- 0.88

- 0.94

1.42

1.50

In

- 1.00

- 1.24

1.71

1.86

- 0.53

- 0.63

0.42

0.83

As Ga

The first subscript refers to the metal orbital (s or d) and the second one refers to the semiconductor orbital (s or p). The interaction with the semiconductor s* orbitals are taken equal to zero. b) Calculated using a scaled aritmetic mean value. c) Calculated using the model described in ref. [54].

a)

As discussed above, we have chosen an ideal (110) face-centered-cubic structure for Ag matched to be (110) heteropolar semiconductor. In table 1 we give the different parameters defining the semiconductor-metal junction for 2./, 2.0-

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ENERGY (e.V.) Fig. 3. Local density of states (in arbitrary units) in the interface InP layer for (a) clean surface (idea~) and (b) a I n P / A g interface. ~ "

the kind of interface shown in fig. 1. Notice that both sets of parameters are similar. In figs. 2 and 3 we show the densities of states for the semiconductors surface layer, as calculated with the parameters (b) given in table 1. Fig. 2 shows the results for a G a A s / A g junction for the following cases- (i) an unrelaxed free surface; (ii) the metal-semiconductor interface. Fig. 3 shows the free surface and the semiconductor-metal coupling case for an I n P / A g j-nctlnn

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different layers of the metal and the semiconductor are given for GaAs and InP. The charge transfers calculated self-consistently are given in table 3. From figs. 2 and 3 we draw the following conclusions" (i) For free surfaces we find, near the fundamental gap, two peaks in the local d~nsities of states associated with two surface bands: the well-known anion-l.ike and ca:ion-hke surface states. (ii) For the semiconductor-metal interface we find that surface state peaks are smaller and that the density of states at the Fermi level

J. S~nchez.Dehesa et al. / Schottky barriers in metal~semiconductor junctions

431

Table 2 V a l u e s o f t h e d i a g o n a l p e r t u r b a t i o n s (in eV) for the l a y e r s n e a r the i n t e r f a c e o f a G a A s ( o r InP)(111)-Ag junction

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Semiconductor

Ag

v_2

v_~

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v2

v3

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- 1.10 - 0.89

- 1.07 - 0.97

- 1.04 - 0.95

-0.96 - 0.87

increases. The Fermi level at the interface is pinned by this strong resonance, at an energy a little shifted with respect to the free-surface Fermi level. This effect has been observed by Viturro et al. [56] during the interface formation for metals on I I I - V semiconductor surfaces. Our calculations show that the final charge neutrality le,rel does not coincide with the initial one [42]; for GaAs we find &k0 = 0.2 eV and for InP 8~ o = 0.11 eV, 8~0 being the change in the charge neutrality level. We have also calculated the electronic structure of the semiconductor/metal interface by switching off either the Ag-cation or the Ag-anion interactions. For these cases our calculations yield the following results: (i) for the junction with the anion-metal interaction switched off, the interface Fermi level is shifted to 0.4 eV lower in energy, while (ii) for a junction with the cation-metal interaction switched off, the interface Fermi level is shifted upward by almost the same amount. These results can be easily understood by noticing that the metal-cation interaction pushes the cation surface states towards lower energies, while the l~etal-arfioi~ ;.nteracfion introduces the opposite effect for the anion surface states. As regards the junction barrier heights we are interested in, we have calculated that the Fermi level is changed as a function of the semiconductor-metal couplings. From our calculations, we obtain the movement of the interface Fermi level referred to the Fermi energy E F ~;or a clean surface. (Not:,ce that we cannot expect to have a very accurate charge neutrality level for the semiconductor hating used parameters ~hat only include interactions up to first neighbours.) Taking for the initial Fermi energy (clean surface) the charge neutrality level given by Tersoff [42], we have

Table 3 Excess o r d e f e c t of c h a r g e in t h e l a y e r s n e a r the m e t a l - s e m i c o n d u c t o r i n t e r f a c e ( e - / a t o m )

AsGa InP

8n_ 3

8n_ 2

8n_ 1

8n I

8n2

8n 3

8n4

- 0.002 - 0.001

0.013 0.014

0.014 0.004

- 0.027 - 0.013

0.000 - 0.005

- 0.0C2 - 0.003

0.003 0.004

J. $dnchez-Dehesa et al. / Schottky barriers in metal/semiconductor junctions

432

obtained that the barrier heights for the junctions GaAs/Ag and InP/Ag are given by: 0bn(GaAs/Ag) = 0.70 4- 0.05 eV, Cbn(InP/Ag) = 0.42 4-0.05 eV, both values measured from the conduction band bottom. I-rere the 0.05 eV uncertainty is the numerical uncertainty in the calculations for this model, and it must not be confused with the theoretical uncertainty of the model which is about 0.1 eV. These values are to be compared with the following experimental results [18,47,571 Cb,(GaAs/Ag) = 0.79 + 0.1eV, ~b,(InP/Ag) = 0.40-0.55eV. The agreement for GaAs/Ag is good, demonstrating that the present model can indeed describe the Schottky barrier height of high-quality GaAs/Ag interfaces. Our results for InP/Ag are also in good agreement with the data for that interface, indicating that the same comment made for GaAs/Ag might apply to InP/Ag as well. However, a word of caution is in order, because there is experimental evidence [47] strongly suggesting that the InP/Ag interface is not at all ideal. Still, the observed non-ideality of the interface ¢ot~!d he reconciled with the theory by the proposal that the barrier height is mainly determined by small islands of InP/Ag junctions. Note that the good agreement between our theoretical results and the experimental data suggests that Ag atoms deposited on the surface interact with both ions, as the geometry given above implies. As discussed previously, predominant interactions with cations (anions) would shift the Fermi level to lower (higher) energies contrary to the experimental evidence. In conclusion, our theoretical analyses for the perfect, abrupt, and defect-free interfaces between Ag and GaAs and between Ag and InP show good agreement with the experimental barrier heights. This means that one need not appeal to a defect model to explain these data for high-quality GaAs/Ag or • m - / r ~ interfaces. ~ e s e resmts mso highlight me need of experiments that will (i) correlate Schottky barrier heights with the quality of semiconductor/ metal contacts and (ii) determine the experimental conditions under which observed Schottky barriers are determined by the intrinsic interface states and by defects. In particular, we hope that future experimental work will focus on the qualiw of tke interface in a semiconductor/metal contact and determine the extem tc which the quality causes the present kind of model or a defect model to be appropriate for Schottky barrier formation. lr~rb

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J. S~nchez-Dehesa et al. / Schottky barriers in metal~semiconductor junctions

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Acknowledgements One of the authors (J.S.-D.) gratefully acknowledges the hospitality of the Physics Department of the University of Notre Dame, where part of this work was done. This work was partially supported by Comisifn Asesora de Investigaci6n Cientifica y Tdcniea (contract No. PR83-2798) and the European Communities (contract No. ST2J-0254-7-E (EDB)).

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111 C.A. Mead and W.G. Spitzer, Phys. Rev. A134 (1964) 713.

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J. Sdnchez-Dehesa et ai. / Schottky barriers in metal~semiconductor junctions

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