Quantum oscillations of photothermomagnetic power in two dimensional electron gas at block boundaries in Hg1−xCdxTe

~o~

~ ~

~ Solid State Communications, Vol. 68, No. i0, pp.891-895, 1988. Printed in Great Britain.

QUANTUM OSCILLATIONS OP PHOTOTHERMOMAGNETIC

0038-1098/88 $3.00 + .00 Pergamon Press plc

POWER IN TWO DIMENSIONAL

ELECTRON GAS AT BLOCK BOUNDARIES IN Hgl_xCdxTe V.A.Pogrebnyak,

D.D.Khalameida and V.M.Yakovenko

Institute of Radiophysics and Electronics, Academy of Sciences of the Ukrainian SSR, Kharkov, 310085, USSR (Received August 29, 1988 by V.M.Agranovich) The photothermomagnetic

effect (PTME) in two-dimensional

(2D) electron gas at block boundaries in n-Hgl_xCdxTe single crystals has been investigated. Photothermomagnetic power (VpTM) oscillations caused by quantization of the 2D electron spectrum in magnetic field have been found. It is shown that oscillations of V p T ~ r e determined by oscillations of the derivative of the electron gas density of states in a magnetic field, D~ ( ~ p is the Permi energy of the 2D gas). ~£~

Investigation of effects of transport in the 2D electron gas is of great interest because it has unique properties and is most promising as

This paper deals with I~CT samples exhibiting two-dimensional conductivity along BB's. The existence of 2D channels at BB's leads to the fact that MCT single crystals possess the p-or n-type bulk conductivity ~ and the n-type two-dimensional one ~s along BB's. The bulk conductivity can be decreased by changing the external parameters. In p-type samples, this can be achieved by decreasing the temperature to below the accepter ionization temperature; and in compensated n-type samples by placing them in a strong magnetic field. This leads to localization of bulk electrons in flu-

applied to microelectronics. It has been shown 1'2 that in addition to the well known 2D systems ~, two-dimensional electron gas also appears at block boundaries (BB) in Hgl_xCdxTe (MCT) single crystals. As was pointed out 1'2, 2D conductivity at block boundaries was not observed on all samples cut from a single MCT disk. One of the reasons of such a statistics of conductivity in 2D channels follows from the percolation theory which describes conductivity of a random net of BB's. Another reason may be that in some samples, potential wells at BB's can be insufficiently deep for a 2D channel to form. In this case, concentrated n-type layers with bulk conductivity arise at BB's. Such layers can be evidenced by anisetropy of the magnetoresistance appearing with decreasing thickness of the

ctuation potential wells. For example, in narrow-gap semiconductors samples of n-MCT's with n ~ 1 0 l@ cm -3 at T = = 4.2K, localization starts at H 5 kOe 5. In higher fields, the conductivity is localized in the frame formed by 2D channels at BB's. Naturally, the magnetoresistance of such a frame in a bulk samples does not depend on the angle between H and ~ . However, if the thickness of the samp-

sample4. 891

PHOTOTHERMOMAGNETIC POWER IN TWO DIMENSIONAL ELECTRON GAS

892

le is decreased age block size

Vol. 68, No. i0

to less than the aver(IOO - ~ 0 0

mkm) then in A

such a sample rential

there appears

a prefe-

direction which is perpendicu~

lar to the film surface.

The reason

is

that BB's in the film, which is a monolayer

in relation

to blocks,

mainly perpendicular face

3

are

to the layer sur-

(see Fig.1 and the below explana-

tion to Eq.(1)). I0

This paper deals with the photothermomagnetic

effect in such a sys-

tem of 2D channels single-crystal were prepared tals.

in n-Hgl_xCdxTe

layers.

Thin layers

from bulk single

The thickness

brought

20 H (kOe)

crys-

of the layers was

FIG.2. Dependence of the derivative ofsthe transverse magnetoresistance ~H on the magnetic field in a thin layer for various values of the 8 angle: 1-~, 2-52 ~ , 3-62 ° , 4-90 °.

to 60 - 80 mkm by consecutive

mechanical etching. onality

polishing

Te sample measured

and chemical

The criterion

of two-dimensi-

The electron

concentration

ty for T=4.2K,

of the electron gas at BB's

6xl.SxO.065

mm 3.

and mobili-

as found from galvano-

of the Shubnikov-de

Haas oscillations

magnetic measurements, are n = 1.4x 1014 cm -3 and Jx=l.OSxlO 5 cm2/(V.s),

(SdH0)

~

respectively.

was the dependence

of the frequency

on the angle

between

the

The SdHO frequency

pends on the angle

normal to the layer surface and the magnetic field direction, l~ig.2 shows

normal

such a dependence

the two-dimensional

the transverse on the magnetic samples

of the derivative

magnetoresistance

movement

field for one of the

in which oscillations

ter pronounced.

of

component

ver,

are bet-

at BB's.

, viz. on the

~&L~e

, thus proving

character

influence might

In this case, howe-

in the film plane.

seem that a uniform (in Fig.l,

is between H

the angle

and the normal

5"Y

smearing.

so. Indeed, component

it is not field is

of the 2D magnetoresistance . is averaged with respect

, then we can easily

angle integration longitudinal

FIG.i.Schematic of 2D channels at block boundaries in a thin singlecrystal layer of Hg I Cd Te, where n ( n , n , O) is the 56rm~l to the 2D c h a ~ e l Y p l a n e . The idealization of the real layer by the condition n~O is discussed in the analysis of formula (I).

to the in oscil-

along the X-axis and the oscillating

to ~ ×

However,

if the magnetic

~-COS) ( ~_c _

/

It

distributi-

x 2D channel ~) should result lation

of the

of the random orientation

on in angles

I

of the

there arises the question

of 2D channels

The n-Hgo.s15Gdo.185

8

de-

tegration

quasi-momentum

in the calculation

the three-dimensional averaging, "extreme

see that

is similar

case.

p~

in-

of ~

in

In the

it is only SdHO of the

sections",

i.e. of channels

which are perpendicular "survive" :

to the

to H, that

Vol. 68, No. iO

a~

Sk(2~ZKTI

H y~

(1) ~o

where

893

PHOTOTHERMOMAGNETIC POWER IN TWO DIMENSIONAL ELECTRON GAS

is the

_,~m°n°t°nic

tance c o m p o n e n t , ~ = m ~ a

ovvv/VV

resis-

, ~ the Boltz-

mann constant and ~

2 >

the relaxation

I

time in zero field. The averaging leads,

as does the

p,

integration in

the three-dimensional

case, to a de-

crease of the amplitude by a factor of ! ~ . Thus, alteration of the magnetic field direction in the film pla-

PIG.3. Dependence of the photothermomagnetic power V=,,~on the magnetic field in 2D chanh~Ts (thin layer) - 2 and for a bulk sample - 1.

ne must not result in substantial changes of the oscillation pattern; this is indeed observed in the experiment. By analogy with we can perform

~

averaging,

~(m) averaging,

~(n)

being the angle between n and the Zaxes. Since the number of block boundaries with ~(n)=90 ° is approximateLx ly r z times larger than that of BB's with ~(n)=O ( L x ~ L y , Lz are the sizes of the sample along the X, Y and

field for a thin layer and curve 1 for a bulk sample, from which this layer was produced.

systems, which have several subbands filled with electrons.

To analyze this

curve, let us use the expression describing the field

E~

of the iso-

thermal NE effect 7. It is calculated from the condition of the zero current

Z-axes),

then there results the anisotropy of 0~ ~-~ in ~ , which is seen in the experiment

The oscillations on

curve 2 have a shape typical of 2D

-

V

Te

and

= 0

•

(Fig.2).

Now let us turn our attention to

(a)

description of the experiment on the photothermomagnetic

effect. A sample

where ~

the electromagnetic wave vector

the basis of the quantum transport

was perpendicular to the thin layer

~

The

was placed in a waveguide so that K

and

is the NE coefficient.

G~

should be calculated on

theory for 2D systems. However,

as we

surface (Fig.l). The radiation fre-

shall show below,

quency was f=136 GHz and the radiati-

quantum oscillations we can distingu-

on power was P ~ l O mW. The wave attenuation produces an electron tem-

ish the main term in

perature gradient

V~Ta

in two-dimen-

in the region of ~

without

exact calculation and thus carry out

sional channels. The magnetic field

a qualitative analysis of the VpTM(H) behaviour 8. Let us analyze formula(2)

is directed along the X-axis. The

for the strong field region

thermomagnetic field appears in the

~l~

direction perpendicular to H and V~Te. The PTME is essentially the transverse

fined as usual: ~Z = ecms/H , ns being the surface density of electrons

Nernst-Ettingshausen

(NE) effect at

~>>

. The Hall conductivity is de-

in the 2D channel. The quantity

hot electrons 6. Curve 2 in Fig.3 shows

~m/g~z=o~

the dependence of the photothermomag-

coefficient of the electron 2D gas in

which is the thermoelectric

netic power signal on the magnetic

a magnetic field, can be calculated as

PHOTOTHERMOMAGNETIC POWER IN TWO DIMENSIONAL ELECTRON GAS

894

for the three-dimensional

case 9'10 and

~r~ K ~ T 3 ew~

= ~(~F)

F(~I

is a smooth function.

Formula (6) explains the alternating-

represented as

where

where

Vol. 68, No. I0

0(t4

(3)

is the density of states

of the electron 2D gas in a magnetic

sign character of VpTM(H) and the origination of the phase shift between VpT~OScillations

and SdH0 or oscilla-

tions of thermoelectric coefficient

field at the Fermi level. When consi-

in a strong magnetic field. In the

dering the diagonal components

harmonic law approximation

and

~II

~il

we remember that the density

~(&~)

of states, which is responsible for

0 0 5 ( £ ~ I ~ c ) the phase shift is which is usually observed in the ex-

the oscillations of the kinetic coef-

periment.

ficients, twice:

enters into these components

in the thermodynamic averaging

In the general case of the

$(£~) form, the Landau level width depends upon the number N and, there-

and in terms of the scattering proba-

fore, the phase shift depends on the

bility:

magnetic field. Analysis of oscillation curve 2

(4)

in Fig.3 permits the elctron concentrations in 2D subbands of the channels to be determined:

where

~17

£1°l

and

sion coefficients, of an electron,

are the dimen-

&

is the energy

~(g)

the distributi-

on function of 2D electrons,

and W(E)

the smooth function describing the quantum diffusion of the orbit of the

in the ground

0.7 n s, and in the

three excited subbands, nl=O.19 ns, n2=0.07 n s and n~=O.O@ n s . The ~ ~ total surface density is ns=2.7xl0±~ cm -2. To estimate the mobility in 2D channels,

the electron masses were deter-

mined from the temperature dependence

electron in a transverse magnetic field due to the interaction with a scattering potential.

subband, n g =

In the case of

of the SdHO: mg=O.046 mo, ml=O.041 mo, m o being the free electron mass. On the assumption that at T=4.2K,

a highly degenerate gas

the re-

laxation time of 2D electrons is of

.I>,,
~F

(5)

Since the density of states for the electron 2D gas in strong magnetic

the same order of magnitude as that for bulk electrons, T ~ lO-12s, we shall obtain

~ s ~ @xlO 4 cm2/(V • s)

which is close to the values obtained

fields is 3

for 2D channels on the MCT crystal

z_ 1 L~. ~-F. t r,,, ) 1

surface as a result of natural or artificial oxidation 12. In conclusion, we note that as is

where

~

is the degeneracy multipli-

city,

~N

the Landau level width,

then it is obvious that the term containing ~-~ becomes predominant in the oscillation region ll. Thus, the VpT M oscillations are determined~sby oscillations of the derivative ~

4>

~i~

8CF

(6)

seen from the experimental curves and the calculation,

the photothermomagne-

tic effect is a more sensitive method of investigation of the region of quantum oscillations of kinetic coefficients than that based on magnetoresistance, because in the former case, oscillating component greatly exceeds the monotonic one.

Vol. 68, No. i0

PHOTOTHERMOMAGNETIC POWER IN TWO DIMENSIONAL ELECTRON GAS References

I. V.A.Pogrebnyak, D.D.Khalameida and V.M.Yakovenko. Pis'ma v ZhETF, ~6, 167, (1987) 2. V.A.Pogrebnyak, D.D.Khalameida and V.M.Yakovenko. Solid State Comman., 65, 1307, (1988) 3. T.Ando, A.Powler and P.Stern. Electronic Properties of Two-dimensional Systems. Reviews of Modern Physics, 5~, 437, (1982) 4. V.A.Pogrebnyak, D.D.Khalameida and V.M.Yakovenko. Abstracts of the 9-th All-Union Symposium "Electronic processes at the surfaces and thin layers of semiconductors", part 2, p.ll7, Novosibirsk, 1988 ~in Russian) 5. I.M.Tsidil'kovskii. Uspekhi Fiz. Nauk, 152, 583, (1987) 6. A.N.Vystavkin, Sh.M.Kogan, T.M.Lifshits and P.G.Melnyk. Radiotekhnika i Elektronika, 8, 994, (1963)

7. I.M.Tsidil'kovskii. Thermomagnetic effects in semiconductors. Fizmatgiz, Moscow, (1960) (in Russian) 8. An exact result, which has the simpliest form in the case of scattering on a short range potential, confirms the qualitative calculation 9. Yu.N.Obraztsov. Fiz.Tverd.Tela, 7, 573, (1965) 10.A.I.Ansel'm and B.M.Askerov. Fiz. Tverd.Tela, 9, 30, (1967) ll.Otherwise speaking, the term with the derivative contains a larger quantity, i.e. the oscillation frequency 12.Wen-qin Zhao, F.Koch, I.Ziegler and H.Maier. Phys.Rev.B.,31, 2416,

(1985)

895