IV-VI COMPOUND DOPING SUPERLATTICES

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IV-VI COMPOUND DOPING SUPERLATTICES

G. Bauer, W. Jantsch

To cite this version:

G. Bauer, W. Jantsch. IV-VI COMPOUND DOPING SUPERLATTICES. Journal de Physique Col-

loques, 1987, 48 (C5), pp.C5-293-C5-300. �10.1051/jphyscol:1987564�. �jpa-00226768�

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JOURNAL DE PHYSIQUE

Colloque C5, suppl6ment au n o l l , Tome 48, novembre 1987

I V - V I COMPOUND DOPING SUPERLATTICES G. BAUER and W. JANTSCH*

Institut fiir Physik, Montanuniversitat, A-8700 Leoben, Austria

" ~ n s t i t u t fiir Experimentalphysik, Johannes Kepler Universitat, A-4040 Linz, Austria

ABSTRACT

Doping superlattices ("nipi's") made of IV-VI compounds are interesting both with respect to their extraordinary physical properties and their possible applications for infrared optoelectronic devices. The properties of PbTe nipi's are reviewed with emphasis on band structure, lifetime of non-equilibrium carriers and photo-sensitivity.

1. INTRODUCTION

Cubic IV-VI compound semiconductors exhibit a number of outstanding electronic properties: Although direct semiconductors, their minimum energy gap of 0

...

³⁰⁰^meVoccurs at the L-point of the Brillouin zone. A s a consequence* the constant energy surfaces are ellipsoids of revolution with a mass anisotropy m l /mt*

of up to 10 in the case of PbTe Ell. In addition, this class of materials has a tendency for a ferroelectric phase transition from the NaCl structure to a low temperature rhombohedra1 modification 121. A s a consequence, the static dielectric constant is very large and temperature dependent.

Both properties, the anisotropic multivalley structure and the paraelectric behavior make PbTe an interesting material for artificial doping superlattices. Due to the narrow energy gap and the large dielectric constant, ionized impurity scattering is very weak even for high doping concentrations. Apart from technological considerations, the resulting high carrier mobilities enable the application of such valuable experimental methods a s far-infrared magneto-spectroscopy in contrast to the well investigated GaAs doping superlattices (nipi's) E31. In addition, the strong temperature dependence of the static dielectric constant and the energy gap imply also a strong temperature dependence of the nipi potential [4,51.

In this paper, we review recent work on the preparation of PbTe nipi's and their electronic properties. The latter are investigated by cyclotron-resonance and photoconductivity experiments. Finally, the applicability a s high sensitivity IR detectors is demonstrated.

2. PREPARATION

The nipi samples are grown on cleaved (111) oriented BaF, substrates using the Hot-Wall technique E61. The n- and p-layers are grown either by adjusting the stoichiometry using proper PbTe sources and by an additional control of the Te pressure or by using Bi o r T1 a s dopants 171. These materials a r e evaporated from Bi,Te, and T12Te sources. Despite the fact that the diffusion constants of these dopants in PbTe are not known precisely, Partin 181 has demonstrated that even with high doping levels up to 5 x

l o t 8

cm3 the Bi and T1 interdiffusion is still negligible on a nm length scale for substrate temperatures around 3000C.

For the nipi crystal first a buffer layer of either n- or p-type of typically 100

-

500 nm is deposited on the BaF, substrate. Then 10 to 15 n-i-p-i periods are grown with typical thicknesses between 30 and 200 nm each.

The deviations from stoichiometry, due to either Pb or Te vacancies, are associ- ated with resonant states well within the valence- or conduction band, respectively.

Two free holes o r two electrons are released into the valence- or conduction band

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987564

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C5-294 JOURNAL DE PHYSIQUE

from each of the vacancy states, respectively. Carrier freeze out a t these resonant levels is not possible. Thus, in contrast to GaAs nipi's, no impurity band separated from the valence band occurs. Also PbTe structures doped with Bi and T1 do not exhibit any evidence of impurity bands since the extremely high static dielectric constant of PbTe prevents the formation of hydrogen-like bound impurity states.

The films are characterized by Hall-effect and conductivity measurements using bar shaped samples [9,101. with typical dimensions of 0.1 x 1 mm2 with potential probe contacts on each side prepared by photolithography.

3. ELECTRONIC STRUCTURE

The periodic doping by donors and acceptors, respectively, which constitutes the nipi crystal causes an alternating background-charge density, which may be compensated partially by free carriers. This one-dimensional periodic space charge, in turn, causes an electrostatic potential, V(z), a s described by Poisson's equation, which is superimposed on the periodic lattice potential and therefore alters the electronic states within the nipi crystal. In an one-electron-effective-mass approximation, the Schrodinger equation, describing the quantization along the z-direction (growth) is given by:

where mj,, is the effective mass of the carriers in the valley type j of the multivalley conduction ("c") or valence band ("v") for kl lz in the i-th electric subband. The nipi potential V(z) obeys:

where ND+ and NA- are the densities of localized positive and negative charges due to uncompensated donors and acceptors in the n- and p-layers, respectively. In Eqs.

(1) and (2), the Hartree term and the exchange correction to the potential is negligible for PbTe because of the high value of the static dielectric constant 151.

The spatial distribution of the free carriers is described by the resulting wave functions:

where n , f j and p,ij are the numbers of carriers per layer within the j-valley and the i-subband. Eqs. (1)

-

^{(4) have} to be solved self-consistently taking also into account macroscopic charge neutrality:

. f [ ~ o + ( z ) - n(z)ldz =

IN*-(^)

^-^p(z)]dz,

n-layer p-layer

and z-independent quasi-Fermi levels, E ~ C * and E ~ v * , defined by:

and:

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Here gj stands for valley degeneracy and mo k for the density of states masses. For PbTe nipi's grown on a C1111 substrate, d e r e are two types of L-valle~s (see Fig. 1):

r i i i l

171 kx

I 1121 Fig. 1. Surfaces of constant energy in reciprocal space for growth direction z I I 1 11 11. The a-valley is oriented parallel to z-direction, the 3 D and 20 cyclotron orbits (circular) are indicated. For the three oblique b- valleys the 2D orbit (projection of the ellipsoids on the (111) plane) has a larger area than the 3D cyclotron orbits indicated by the dash-dotted ellipses.

Fig. 2. Dependence of the nipi potential on layer thickness (d,

=

dp) for. several donor and acceptor concentrations for a compensated (dn.No

=

dp.NA) nipi structure.

the "a"-valleys (g,

=

1) are oriented along the growth (2) direction, whereas the triply degenerate "b"-valleys correspond to the remaining equivalent oblique [1111 directions. In this situation, the 2D-density of states effective masses are given by

[11,121:

and:

m t c ~ v r n ~ , ~ c ? v =

-

3

where m t k and mtk denote longitudinal and transverse effective masses of PbTe. The effective masses mj,,csv used in E q . ( l ) are given by 111,121:

and

In Figs. 2 and 3, results are given for the selfconsistent nipi potential a s obtained

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C5-296 JOURNAL DE PHYSIQUE

from Eqs.(l)

-

(11). Fig. 2 shows the dependence of the amplitude on the desigr parameters assuming for simplicity d,

=

d p and NA-

=

No+. In this case of a compensated nipi in the low temperature limit chosen, these results can be obtained from:

without free carriers 141.

The static dielectric constant, which enters Eqs.(2) or (12), depends also on the defect concen- tration 123. A t low temperatures values of typically 300

-

⁶⁰⁰

appear reasonable for the concen- tration range of interest. A t fin- ite temperatures, 2V0 increases almost linearly with temperature because of the paraelectric behav- iour of sS, according to the Curie- Weies law:

Fig. 3. Selfconsistent model calculation of quasi-parabolic band-gap modulation for an uncompensated n-type nipi structure

(d

=

^d,

+

^dp

=

^{150 nm)} ^with

electric subbands for the a- and b-valleys and corresponding wave functions +'(z). The influence of nonequilibrium electron and hole sheet concentrations of An,, Ap,

=

^Z and 4 x decreases the nipi potential and increases the wave-function overlap in real space a s indicated by the shaded area for the i

=

²

subband of the b-valley. EF and EF* denote the Fermi- and quasi- Fermi energies, respectively.

where T,

<

0. Eq.(12) holds for

T

>

40 K, below E , saturates be-

cause of zero-point fluctuations c21.

In bottom part of Fig. 3, results for the more realistic situation of a slightly uncompensated n-type nipi crystal a t low temperatures are given. Wave functions, nipi potential and subband energies (separation:

Bu, y8*b) both for a- and b- valieys are indicated schema-

C ^I ^I

0 50 100 150

Z- COORDINATE (nm)

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tically. For the upper two diagrams, additional electron-hole (e--h+) pairs have been introduced in order to describe also the effect of band-gap illumination. The tunability of the nipi potential, the effective energy gap and the overlap of conduction- and valence band wavefunctions, which determine the recombination probabilities, is clearly visible.

Experimentally, the occupation of the various conduction- and valence-band states of a PbTe nipi can be investigated using far-infrared cyclotron-resonance investigations. Fig. 4 shows results of such measurements. Since, for practical reasons, the laser wavelength is within the Reststrahlen regime, the gross features are caused by dielectric anomalies, which accompany the cyclotron resonances [111.

The resonance positions are indicated by arrows in Fiq 4: for their identifi- cation, nonparabolicity has to be taken into account. For the Faraday configuration, all electric subbands are split into sets of Landau states. The occurence of different resonances in one type of valley can be explained by transitions in Landau states originating from different electric subbands C131.

For h

=

118.8 p, three distinct structures are clearly separable in the range of 4.5

...

⁵T, which can be attributed to the transitions indicated in the fan-chart on the right-band side (r.h.s) of Fig. 4. For higher wavelengths, the closely lying

MAGNETIC FIELD ( T I

Fig. 4. Far infrared magnetotransmission for three laser wave lengths (X

=

118.8 pm; 163 pm and 254 pm) in Faraday configuration.

Arrows indicate cyclotron resonance transitions. R.h.s.: Calculated Landau states vs. B for two electric subbands for b-valleys. Arrows correspond to the experimentally observed resonances (1.h.s.).

resonances merge together. For the calculation of the Landau states, nonparabolicity is taken into account Cll, which explains the separation of equivalent transitions in different electric subbands. In calculating the electric subbar.d energies according to Eqs.(l)-(ll), band nonparabolicity has been omitted for simplicity. Its main effect would be a reduction of the subband spacings ho,,,a,b. (These spacings are not equidistant even for parabolic bands because of the nonparabofic selfconsistent

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C5-298 JOURNAL DE _PHYSIQIJE

potential V ( z ) in real space.) For the three transitions within the b-valleys, close to 4.5

...

⁵^T^(A

⁼

118.8 pm), which are practically equidistant in experiment, the band nonparabolicity would render a lowering of the the i

=

2 subband and hence of the resonance field for the (i

=

^2,^0- + I-) transition.

4. LIFETIME AND PHOTOCONDUCTIVITY

An important consequence of the periodic nipi potential and the resulting confinement of the wavefunctions in growth direction is the reduction in overlap of the latter in the conduction- and the valence band a s indicated by the shaded areas in Fig. 3 for the b-valleys. (For the a-valleys, the overlap is much smaller because of the larger mass component, m l c l v , in z-direction.) The reduction in overlap, in

TEMPERATURE [ K l WAVELENGTH [pml

Fig. 5. Comparison of lifetime vs. Fig. 6. Detectivity vs. wave length temperature for a PbTe nipi for a photoconducting PbTe-nipi (<n>=8x101 ern-=) C 14,151 with data (180° field of view, 800 Hz modulation for bulk samples (n=4x10L6 cm-=). frequency and 1 Hz bandwidth) for Intrinsic (A) and extrinsic (a) bulk three temperatures (solid lines). The lifetimes are given C 171. broken line represents the theore-

tical limit for photoconductors a t 77 K.

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turn, causes an increase in the lifetime of nonequilibrium e--ht pairs. Lifetime measurements have been performed both with chopped electron beams (pulsed EBIC experiments) [14,151 and pulsed laser photoconductivity 1161. Results for the weak intensity limit are given in Fig. 5 together with literature data obtained for bulk material [ 17

I.

For bulk material, photoconductivity transients exhibit two different decay times (s. Fig, 5), the shorter one is attributed to the intrinsic Auger mechanism C171, whereas the longer one, which has been observed also by Schlicht et al. C181 is obviously of extrinsic origin caused by deep traps. Effects due to the later mechanism have been observed also for PbTe nipi's 191. However, due to the spatial separation of e--ht pairs and the strong localization of deep states, the Shockley- Read-Hall mechanism becomes very ineffective and the extrins'ic time constants are much longer than in the bulk case: a t room temperature time constants of seconds up to several minutes are observed, which increase substantially on cooling. Below 150 K, persistent photoconductivity is observed 191.

For a discussion of the influence of the periodic nipi potential on the eletronic properties of such structures, the intrinsic time constants should be compared. The exponential time constants observed both in EBIC and photoconductivity experiments on PbTe nipi's agree very well with those obtained from magneto-optical experiments a t low temperatures C151. By comparison to the intrinsic bulk data 1171 (s. Fig. 5), we obtain an increase in lifetime by nearly two orders of magnitude, which agrees well with estimates for the "intrinsic" lifetime enhancement assuming thermal activation of electrons and holes across the nipi barriers C4,51, which depends only little on temperature for 100 K

<

T

<

200 K because of the nearly linear dependence of 2V0 on temperature.

For higher illumination intensities the e--h+ pair lifetime decreases strongly 1161. This effect is expected from the influence of free carriers on the nipi potential and hence on the overlap (s. Fig. 3). With increasing excitation intensity, the nipi lifetime approaches the intrinsic bulk lifetime, which i s reached if the excess carrier density exceeds the donor or acceptor concentrations. The lifetime enhancement of non-equilibrium e--ht pairs implicates also excellent small-signal response of photoconductive IR-detectors [3,41. Fig. 6 shows typical experimental results for the detectivity of PbTe nipi's a s a function of wavelength. A t 90 K sample temperature, the detectivity a t the peak wavelength of 5.8 p is close to the theoretical limit of 10" cm H Z ~ / Z W-I C191. In the determination of D*, reflection losses a t the BaF,-cryostat-window and a t the uncovered nipi surface are not taken into account 1151. Properly chosen anti-reflection coatings will further improve D*.

5. CONCLUSIONS

I n summary, the present experimental investigations on the electronic structure of PbTe doping superlattices can be described very well by extending the nipi model, developed originally for GaAs and related compounds by including the many valley band structure and the paraelectric temperature dependence of the static dielectric constant.

Among other reasons, the good quality of the samples may be a consequence of the ineffectiveness of random potential fluctuations in this highly polarizable material, a s pointed out by Dohler C41. First investigations on photoconductivity indicate interesting practical applications a s opto-electronic and nonlinear devices.

ACKNOWLEDGEMENTS

It is a pleasure to thank H. Clemens for generously providing nipi samples and to K. Lischka, J. Oswald and P. Pichler for their contributions in this project. Work supported by the "Fonds zur Forderung der wissenschaftlichen Forschung", Austria.

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