Impurity states in n-type Hg1−xCdxTe in high magnetic field and under hydrostatic pressure

Physma 117B & 118B (1983) 428-430 North-HollandPubhshmgCompany

428

IMPURITY STATES IN n-TYPE Hgl_xCdxTe IN HIGH MAGNETIC FIELD AND UNDER HYDROSTATIC PRESSURE x Nm

A. RAYMOND,

J.L. ROBERT,

D.S. KURIAKOS

Centre d'Etudes d'Electronlque des Solldes (LA 21) assocle au C.N.R.S. U.S.T.L. Place Eugene Bataillon, 34060 Montpelller cedex, France M. ROYER S.A.T. 41, rue Cantagrel, 75013 Parls, France

We have recently shown (1) that the magnetlc freeze-out can be observed in narrow gap Hg.l-x Cd Te alloys (0,18 < x < 0,34). For the less doped samples the existence of a resonan~ level xs clearly pointed out. This level is responsible of a large trapping of the electrons when the magnetic field increases. The application of an hydrostatic pressure conflrms the exlstence of this level : in zero magnetlc field, when the pressure increases, the conductivlty decreases strongly and then varies with a smaller slope. This implies a strong decrease of the free carrler density in the low pressure range and a change in the conduction process. We observed an activated conduction from an hydrogenlc donor XMOst of the experlments have been performed at the S.N.C.I./C.N.R.S. Grenoble, France XXon leave from Physlcs Department, Unlverslty of Thessalonlkl, Thessalonlkl, Greece

We have performed transport experiments in ultraquatUm llmit on narrow gap Hg. Cd Te samples with different composition be~w~enXO. 18 and 0.25 In order to account for the decrease of the free carrier density with increasing magnetic field in the less doped samples we have to consider the existence of both an hydrogenlc level and of a resonant level located not far above the Fermi level in zero magnetic field. For the most doped sample the magnetic freeze-out effect is connected only to the existence of the hydrogenlc level, llke in the case of n-type InSb. In order to conflrm these results, we have performed magnetlc freeze-out experlments under hydrostatic pressure on two kinds of samples. For the less doped samples, the conductivlty decreases when the pressure £s applied as a result of a transfer of a part of the conduction band electrons on s resonant impurity level. For the most doped sample, all the states below the Ferml level are occupled and thus, there is no drastic change in the conductivity, when the pressure is applied. I.

EXPERIMENTAL AND THEORETICAL PROCEDURES

The samples we have investigated have been cut perpendicular to the growth axis in a paralleleplpedlc shape. Their characterlstics are given in table (l). All the experiments have been performed in the ohmic region and the samples have been well etched before soldering 9~ @hmlc contacts. mX/m ° Eg ; meV Samples x% (4.2 K) a

25

150

1,2.I0 -2

b

18,2

40

3.10-3

c

23,4

130

0 378.-4363/83/0000-0000/$03 00 © 1983 North-Holland

i0-2

We have obtalned the components ~ and o of the conductlvity tensor from Hal~ x effec~Yand magnetoreslstlvity experiments. These experiments have been performed in magnetic field up to 19 T under hydrostatlc pressure. To get the pressure, we used a BeCu clamp cell in which a mixture of light hydrocarbure acts as the pressure transmltting medlum. The cell is pressurized at room temperature and cooled st helium temperature, the pressure being measured usxng an InSb gauge. To get the free carrler density n in the conduction band, we have used the classical expression n = ]/Rwe in the low field region as far as only one kln~ of carriers partlclpates. The investlgated samples are degenerated at zero field. In the hlgh magnetic free carrier denslty a component, which xy RH B 2 SO, n = e(o/z~ + R~

field region ( ~ >> I) the has been deduced from the can be written ne ~xy B B z)

(I)

is the reslstlvity of the sample xn transverse magnetlc field. To take into account a possible contributlon to the conductlon of the electrons located on the impurlty states, the previous expresslons must be modlfied. In the low magnetic field reglon, the classlcal two band model has been used. To analyze the magnetlc fleld dependence of the free carrier denalty~ we conslder two kinds of nH= I/RHe ; cm -3

~H = RH/Po ; cml/vs

4.2 K

4,2 K

1.8 1016

16 000

1015 7,8.10 I~

17 500 9 000

A Raymond et al / Impurity states In n-type Hgl.xCdxTe donors : the donors x (density Nx) which gzve only hydrogenic states and the donors R (density NR) which gives two energy states : a hydrogenlc one and a resonant one. If we call n ~ the density of neutral hydrogenzc states of doh~rs x, n H R the density of neutral hydrogenic states of donors R and n R the density of neutral resonant states we have : N

x EH_ E F

nHx ffi I

exp

+

NR nHR

-

=

[ + exp

(2)

429

p e n d e n c e of t h e l a s t c o n d u c t i o n s u b b a n d : ~ = E - E(O,0,+) • The neutrality equation can written for all experimental magnetic fields and temperatures : N D = n + nHx + nHR + n R + N A

It is interesting to notice that, if there is no resonant level (N. ffi 0) or if this level is fulfilled (n R ffi N R a~d ~HR = 0); the expression (8) is reduce~ to N x ffi n + n H + N A where n H is glven by equation

kT nR (3)

EH - E F kT

with N H = N x + N R- n R

(9)

(2)

For a glven magnetic field and 4 different temperatures, we eliminate NX - NA, and NX. We obtain :

and NR - ~HR

n R ffi

(4)

l

ER - EF

I + ~ exp

kT

E q u a t i o n (3) c a n be w r i t t e n NR nR ffi l ER- EF I ER _ EH 1 + ~ exp T + ~ exp kT

n I- n 2 n 3- n 4 where X (5)

The equations (2 and 3) do not contain the factor I/2 in front of the exponent : because of the large value of g factor only the states of the last subband O + must be conszdered. At high magnetzc fzeld, the electron energy above the band edge zs an appreciable fraction of the energy gap and the band's nonparabolictiy comes into play. We take the following expression for the lowest magnetic subband (l,2) E E 2 I/2

E(O,ks,÷> o - ÷ where D(0,kz,+) ffi

I M ~-

+

÷

(l + exp X4)-I - (l + exp X3)-T (10)

= EH - EFt

A resolution of this equation gives the alone unknown quantity E H and it is then possible to calculate N . x 2. ANALYSIS OF THE EXPERIMENTAL a- Highly doped sample

RESULTS

(a)

° (.--,) 1016

10 t5

= I + ~2kz2 /2m x and

~ uBIgXlH

. Expression

(6) is valid

for electrons energie E << E + 2 is spin-orbit interaction g ~ energy A , where larger than 0.9 eV for the investigated samples. Relation (6) leads to the followin~ expression for the density of states (per Icm ~) in the lowest spzn subband x~ 2 1 r2m ~ eH ii + 2E E _ t ) -1/2 ~~= " " ~-~j ~ ~-) (EC1 + ~--) (7) g g In the case of nondegenerate statzstics, the free carrier denszty can be written :

n' = .(EF -~.kT)

1014

10t3

1012 Flgure|

I12

I 12~mXkT5 n = - (2n) 2 ( - - - - ~ J where

(l + exp X2)-I - (l + exp XI)-I

eH (1 + ~--~) exp ~' ~ g

10

,,

I

I

,0,(T) I

: Magnetlc fleld dependence o f the free carrzer denslty o f sample a

(8)

is the reduced Fermi energy

In equations (4) and (5) the magnetic field dependence of the activation energy of the resonant level E R is calculated assuming that this level does not "move " in absolute energy (E._ = cte) wlth increasing magnetic field. Usz'~g expression (6) for the magnetic field de-

The magnetic field dependence of the free carrier density for the most doped sample is given figure | for an hydrostatic pressure of 2.2K bar a~d different temperatures. As a reference, we have also reported the results at P ~ 0 and T - 4.2 K. In the maEnetle field range 5T-19 T e m p r e e s l o n ( I ) h a s b e e n u s e d . At v e r y 1crwmagne~i~ f~eld, the free carrier density obtained by n - ~-~ is nearly equal to the value deduced from " ~ t h e p e r i o d o f m a g n e t o r e s l s t a n c e o s c i l l a tions.

A Raymond et al / Impurity states zn n-type Hg l.x CdxTe

430

In the activated region (B > 5 T) using equation (10) or solving the neutrality equation (9) assuming only one hydrogenie donor level, we obtained a good agreement betwen experimental and calculated value of n in the whole temperature range, for the following values of E H

(om)-',o_, 10 -I 1°-|

B(T)

18.71

16

14

12

10

JEHJ(meW

2.7

2.3

1.9

1.4

1

10-z

The values of N D and N obtained from the second general method are : ~D 44 6,9.1016 cm -3 and N A 44 4.6 1016 cm-3.

10-3

lO 3

It is interesting to compare in this magnetic field range the two curves at 4.2 K with P equal to zero and 2.2 kbars. This behaviour wlth pressure Is similar to the one observed on InSb and can be explained by an increase of the binding energy of the hydrogenic donor level due to an increase of the effective Rydberg with pressure.

;

t0-4

3

4

~ p

lO-

, 0

The pressure dependence of the reslstlvlty is approximatly equal to the effective mass one. This variation is lower than the one of the mobility which, for a degenerate statistic and scattering by ionized impurity, varies llke the square of the effective mass.

:o

5

1o

1,

.

.(,)

Fig. 3

Magnetlc fleld dependence o f the °xy component for sample b for dlfferent pressures (only 2 temperatures have been reported) The insert corresponds to varlat2ons up to 5 T.

I/RHe . I/4 ~4 3,5 I0 I~ cm -3. At 4.2 K, for P = 0,

Po = 2.]8 10-2 ~ c m

and for P = 2.2 kbarrs

As a result because of the large value of the ratlo ul/u2 the electron density of the impurity band must be larger than I016cm -3 even at zero pressure. Thls explains the low experimental value of the mobility of this sample. ~ figure 3 we have plotted the magnetic field dependence of the Oxy component (sample (b~, we observe a reverse of the Hall coefficient. Two mechanisms can be invoked to explain this behavlour. First we can assume that the resistivity of the bulk becomes so large that the surface effect are responsible of the p-type character of the conductivlty. This hypothesis Is unlikely : because of the weak thickness of the surface layer the p-type carrier density would be much larger than 1018cm -3. The second hypothesls is that the carriers loc~ized on the resonant states yleld a positive slgn of the Hall coefficient. In anyway, before the c ~ e of slgn of the axy component, and for low enough magnetic field, the contrlbutlon to the ~xy component of the conductlon band is preponderant In thls magnetic field range, we observed a classical magnetlc freeze-out on the hydrogenlc level.

O ° = 2.51 10-2 ~ em

b- Lightly doped samples The existence of a resonant level is clearly pointed out on figure 2 : we observe a decrease of the conductivity and of the Hall coefficient wlth increasing pressure (sample (b~. This behavlour is typical of the one of a semiconductor with two kinds of carriers, the high mobillty electrons being transfered into low moblllty band when the pressure increases.A klnk is observed on the resistivity when the pressure is about I kban This corresponds to the region of pressure in which the two conductivlties are nearly equal. So to interpret the experlmental results, a two band model is needed. We can write indeed for two kinds of carriers 1 and 2 : = ~i(I+~ where

and __R~=(RI+a2R2)/(I+a)2

a = 02/ o]

We can calculate the free carrier concentration in the conduction band at I kbar assuming that the conduetlvity ratio a is egual to 1. This leads to a value of n I which Is equal to : ( ,.,,J_...~--~-~TJK "leK

~ ~ : : : = = ~--e.. _

RH (m'/Cb) ~

10...3

The analysis of these results (§I) allowed us to determine the pos~t~on of the resonant level (ERo 4~ ]0 meV) and the magnetic fleld dependence of the binding energy E H of the hydrogenic level (figure 4). Simllar results had been obtained at P = 0 on sample C (ERo ## 5 meV).

,

,

,

~ ~ ~'-----..

0 .~t0 K ~'"

,mK

meV) P: 0

4

,

Flg. 2 : Pressure dependence of the reslstzvlty and Hall coefflclent for sample b

B~T) 2

0

10

20