Ultraviolet photoemission experiments on HgTe (110) cleaved surfaces

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ELSEVIER

CRYSTAL GROWTH

Journal of Crystal Growth 159 (1996) 736-740

Ultraviolet photoemission experiments on HgTe (110) cleaved surfaces M. Banouni, M. Nasser, G. Leveque * Laboratoire d'Analyse des Interfaces et de Nanophysique (LAIN) - URA CNRS 1881, Universit~ Montpellier II, F-34095 Montpellier Cedex 5, France

Abstract We present the experimental results obtained by angular resolved photoemission on HgTe monocrystals, for a photon energy of 23 eV. The results are compared with other experiments on Cd0.6Hgo.4Te, obtained under the same experimental conditions, and a common scheme is proposed for the emission of the HgTe-CdTe mixed compounds. We computed theoretical emission spectra, using the tight-binding model and show that emissions originate mostly from bulk " T e p " orbitals, with a minor component due to umklapp processes. Surface states were not observed at the top of the valence band (near F), as previously reported for CdTe.

1. Introduction Ultraviolet photoemission, in the angular resolved mode is commonly used to provide data on the band structure of solids, giving the energy of the valence bands in significant part of the Brillouin zone. For instance the electronic structure of CdTe which has the same electronic structure as HgTe, is now well documented [1-6]. Small gap materials such as CdxHgl_xTe alloy or semimetallic HgTe have been studied much less frequently [7-9]. It is thus difficult to obtain precise values of band dispersion, for the CdHgTe alloys, as required for device development [10-12]. Below we give detailed experimental results for HgTe and a comparison with results for CdxHg]_xTe materials. In the second part, we discuss the capacity of the tight-binding scheme to describe photoemis-

* Corresponding author. Fax: + 3 3 67 52 15 84.

sion spectra, which are often complex and confused, given the simultaneous presence of bulk, surface and diffracted emissions.

2. Experimental procedure Angle resolved photoemission experiments were performed with synchrotron radiation coming from the Super ACO storage ring at LURE (Orsay). Electrons were received by a photoemission system with multidetection [13]. All electrons emitted in a plane (called the emission plane in Fig. 1 and determined by an azimuthal angle 9) are dispersed and focused onto a fluorescent screen. The two-dimensional image is directly related to the band structure in the E k, k plane. Image treatment is carried out subsequently to correct the defects of the system and enhance band contrast [14]. An energy resolution is 200 meV and an angular resolution of 2 ° is assumed.

0022-0248/96/$15.00 © 1996 Elsevier Science B.V. All fights reserved SSDI 0 0 2 2 - 0 2 4 8 ( 9 5 ) 0 0 8 3 4 - 9

M. Banouni et al./Journal of Crystal Growth 159 (1996) 736-740

737

3. Observation of bulk bands

Photoemission experiments were performed for various azimuthal angles ¢p, for h v = 23 eV, energy at which electrons of the top of the valence band are emitted from F, and are compared with tight-binding calculation (Fig. 2). We can follow easily the direct bulk bands (A,B,C) across the photoemission image (Fig. 3). These bands are theoretically split in some pans of the Brillouin zone but our resolution was not enough to observe the effect. Calculated bands are dependent on a constant V0 appearing in the free electron model of the final states: ~2

u

,x

Ef='~mlk+Gl2+Vo=Ei(k ) +hr.

~incident photon

Fig. 1. Surface reciprocal lattice for zincblende compounds, defined by translation vectors A and B. F X ' M X are high symmetry point in the surface Briliouin zone. The projection of the bulk Brillouin zone is indicated by dotted lines and letters without a bar. Hatched areas correspond to the irreducible part of the (1 × 1) surface Brillouin zone. The projection of the emission plane and the incident plane are given for the azimuthal angle ~p.

HgTe(110) surfaces were obtained by cleavage in UHV of a monocrystalline sample (1 × 1 × 5 mm). In our experiment, the incident photon beam was inclined at 45 ° relative to the surface, at right angles to the emission plane and with a " p " polarisation.

(1)

The small discrepancies between fitted and experimental bulk bands cannot be eliminated by adjusting V0 or the effective mass m*, but are probably due to a gap in the final state [5]. The bulk band energy values for high symmetry points in the Brillouin zone are given in Table 1 and are close to the corresponding values observed with CdTe and ZnTe. As the experimental energy and dispersion of " T e s " bands are not well known [15], we have considered the "Sa" bands as deep levels, not coupled to the upper valence bands. This approximation has no apparent effect on other calculated valence bands.

b

a

0.5

0

1

1.5

...')/'y,,.,x \ \

~.:.-

/-,("vL~g_.,~:-"N,

-2

~

~

7

...~

- ~C i/2

-4

L

A

FI

A

-... "

'

/

C)~v,X.:".::'C

X

Fig. 2. Bands in the tight-binding scheme. (a) Dispersion of the bands along the [001] direction (FX) and [111] (FL). (b) Calculated bands for photoemission at hv = 23 eV and ¢p = 90 ° as deduced from expression (1). Note the hulk hands (ABC) are not periodic in kip Umklapp hands g B ' C ' are represented by dashed lines and A"B"C" by dots.

M. Banouni et al./ Journal of Crystal Growth 159 (1996) 736-740

738

Results obtained using the same experimental set up on HgTe and on the semiconducting alloy Cd0.6Ho.4Te are compared. Outside of a small difference in the band dispersion amplitude, the photoemission images are virtually identical. This implies

-1

0

+1

I

I

I

that the photoemission process is only slightly sensitive to the type of material (semimetal or semiconductor) and to the local order of the crystal (we did not observe band splitting and widening as predicted in the coherent potential model [16]).

k,l!kzB

-1

0

+1

I

I

I

kll!k B

'0

Exp.

--1

¸

i!?

!i~i¸¸!

.-2 .-3 .-4

.-5

-1~

0,

+1~

k JBk ,

-1

0

+1

I

I

I

kll!k B

T

'0

S

.-1

Pc

C .-2

!i~,~i~i~~¸¸ i

!~

.-3

.--4 "--5

HgTe Fig. 3. Experimental data ("exp") for hv = 23 eV and ~ = 90° compared to the calculation usmg expression (2). "so", "Pc" and "Pa" refer to separate atomic contributions. The emission from "Sa" is ignored in our model. A 0.2 eV Gaussian broadening is applied to the theoretical emissions.

M. Banouni et al./Journal of Crystal Growth 159 (1996) 736-740

features also appear on CdTe and ZnTe and are interpreted either as surface states [1,6] or as bulk umklapp bands [3,7]. Both show the same energy dispersion as A and B bands with amplitudes 1/3 to 1/10 of the corresponding bulk structure. In Fig. 2 are reported the calculated umklapp emissions, obtained by adding surface lattice vectors to krl, the bands are labelled g , B', C' for Akll = (0,__ 1) and ,~', B", C" for Aklp = ( + v~-,0). We immediately observe that these umklapp bands reproduce the secondary emission in Fig. 3. In order to obtain ever more conclusive arguments, we computed the intensity of the emissions bands, in the tight-binding scheme, as explained in the next section. We note in Fig. 3. that the calculated bands fit nearly perfectly the observed secondary emission, allowing a definite umklapp origin to be given. Other faint structures are present on our emission images as for instance the small point n e a r ktl = - 1, E i = - 3 . 5 eV, which is a true surface state.

Table 1 E n e r g y o f bulk v a l e n c e b a n d s in e V Band

L o c a t i o n in the

Z n T e [17]

C d T e [6]

HgTe

Brillouin z o n e A B

C

-0.9

-0.6

-0.7

X 7

-2.2

-2.0

- 1.0

t

-

L4.

5

- 1.3

- 1.2

X6

-2.5

-2.3

-2.3

mini ~

- 2.8

- 2.7

- 2.7

F7 L6

- 0.9 -5.0

- 0.9 -4.6

- 0.9 -4.7

X6

-5.2

-4.6

-4.7

6

1.5

In consequence, a continuous tight-binding scheme can be applied for the CdxHg I_xTe valence band, over the whole range of composition 0 < x < 1.

4. Secondary emissions In most photoemission experiments, secondary emissions are observed. These structures correspond to transitions towards final states (Eq. (1)) with different G values and can be interpreted as a crystal lattice diffraction (umklapp) of bulk electrons. Fig. 3 shows distinct emissions around kll/kzB = + 1 (around F) at the top of the valence band. These -1

0

+1

I

I

-"

739

5. Emission intensity As a first approximation, we consider that the emission intensity is proportional to the optical tran-

klllk s r

-1

0

I

I

-

'0 .-1 .-2 ,--3

--4t -5~

HgTe Fig. 4. S a m e as Fig. 3, for q~ = 0 °.

-

klllkzB

+1 I

~" ,

,

740

M. Banouni et aL /Journal of Crystal Growth 159 (1996) 736-740

sition matrix element, which can be developed in the tight-binding model as

l( kf ,a ) ~ 'kf al2 ~-~l ~" C"'~'~"'~(kf ) [

(2)

where C is the component of the eigenvector describing the initial state and • the Fourier transform of the initial wave functions (referring to atom /x, orbital a , and spin tr). A is the potential vector of the incident electromagnetic wave. As the functions • are not explicitly given in the tight-binding scheme an exact value of the above expression cannot be determined. However a simple approximation can be used: for the small range of Ikfl values covered in our experiment (for instance 2.5 < Ikfl < 2.8 .~-i for the valence band in normal photoemission, with 23 eV photon energy) the Fourier transform of each orbital wave function can be taken as constant v e r s u s kf. In Fig. 3, we present the theoretical images, corresponding to the separate contribution made by each type of orbital. By comparison with the experiment, we can deduce that - F i g . 3 " P a " appears closest to the experimental image, giving the correct balance between the A, B and C band intensities. -Mixing the " P a " contribution with one of the others results in interference effects between the orbitals (due to the complex sum in Eq. (2)) and induces a strong dissymmetry between the right and left side of the theoretical photoemission images, not seen in Fig. 3 " e x p " . We concluded that most of the intensity in our experiments are related to anion " p " orbitals. The overall agreement between the calculated intensities and the experiment can be verified in other geometry, as in Fig. 4 for q~= 0.

6. Conclusion The emission of HgTe, CdxHg~_xTe and CdTe are very similar, which allows the use of a common scheme for the interpretation of all photoemission structures, whatever the x value. The optical matrix elements between the tight-bi-

nding initial states and free electron final states are in close agreement with observed emission intensities. This model can be extended to the umklapp bands, which clearly simulate the secondary emissions observed at the top of valence band.

Acknowledgements We are very grateful to J. Bonnet, LURE (Orsay) for his support during the experiments.

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