Indi an Journal or Pure & App lied Physics Vol . 40. October 2002. pp . 726-73 1

( C /

\

Electrical properties of ~oron delta-layers in silicon I._M 0 Hakim\& M Mozibur Rahman \

, De l~anment o?Phy~ i c s. Uni'v'ersity"To r Raj shahi. Raj shahi 6205 . l3anglade~h - . e-mai l:lllohakimbd @yahoo .com

Recei ved 12 December 2001: revi sed 12 June 2002

Electrical propert ies or MI3E grown horon I)- layer in Si have been in vestigated in the temperature range 10-300 K and a comparati ve study with their uniform doping counterpart has heen presented . Various horon doping level s rrom 1012_101

.1

cm ~ in the I)- layer show thal. wi th the fall of temperature from 300 to 50 K. Hall mobilit y first increases rol lowed by a rapid decrease. and at temperature ::::50 K. it becomes alillost constant. Hi gher doping leve l in the sample grossly lowers the value or Hall mohility but its variat ions with temperalUre are almost similar to each other. Existence or the dominant caITier scalle ring mechani sm has also been reported. In al l the sampl es. freeze-out of calTiers have been clearly noticed he low 100 K. Ex istence or a MOll metal -non-metal transition in the sample has been observed at low temperature region when the doping eonce ntrati ~n exceeds a criti cal high value of 6x I 0 1

' cm·2• and thi s has been found consistently wit h the other observations like zero acti vation energy and negat ive TCR . The value of minimal metallic conductance for the samples has al so heen reponed. ' I -

...J

1 Introduction

Delta function shaped doping profile in s ilicon is current ly attracting interes t because of its use in many novel e lectron ic dev ices like , MOSFET I

,

FET2. infrared detectors' , etc . Thi s technique of atomi c layer doping (ALD) is also ve ry important for studying two-dimensional e lec tronic transport in silicon , GaAs and Ge c rysta ls. The fabricati on of extremely thin doping laye rs has become possible because of the development of advanced growth techniques such as molec ular beam epitaxy (MBE) and metal oxide chem ical vapour deposition

(MOCV D). Boron 8-doping in silicon by MBE is a recent progress in this line.!. Properties of Sb and B

8-layer have a lready been reported in litera ture5.6

.

Va rious aspects of growth and structural charact.eristics of these layers have been obtained from those reports.

In thi s paper, a detailed study on Hall effect and

e lect rica l conductivity of 8- layers in silicon, have been presented. Effects of various doping concentrations and temperature on the e lectrical transport properties of this layer are reported.

2 Experimental Details

Boron de lta layers were depos ited on Si 11001 wafer in a modified VG Semicon 905 MBE system fitted with an e lementa l boron evaporat ion source in

which, the res idual gas pressure during growth was 10 9 mbar, 99% of which was due to hydrogen. The substrates were low-doped n-silicon chips of 100

mm dia and res ist ivity 16-24 Qcm. Afte r the substrate preparation at 850 DC, 400 nm of un-doped S i was deposited during which, the temperature was red uced to 475 DC. The substrate was then exposed to a boron flux of 6x 10" atoms cm·2sec·1 fo r a certain pre-determined length of time whilst the Si source was shuttered. The resulting doping-spike was then buried beneath a capping layer of 32.5-100 nm of un-doped Si. Various doping concentrations were ach ieved by adjusting the time period of boron expos iti o n to the chip. Two-dimensiona l dop ing concentrat ions for the present set of sa mples va ry from l xlO12 to l x lO l .l cm·2 .

The e lectrical p roperties of the samples were studied by means of temperature-dependent Hall effect and resisti vity measure ment carri ed out between 10 and 300 K. For this purpose, an automated, computer-controlled system was used. The sample was mo unted on a thick copper block in a variable temperature, continuous flow' c losed cycle helium cryostat with automatic te mperature control. The constant magnet ic induction for Hall measurement was 4 KGauss. Ohmic contact with

the 8-layer was fo rmed by sputte ring AI dot on the sample and annealed at 550 DC for a minute in N2 at mosphere. In-Ga eutectic with a gold pad was then

fIAKIM & RAHMAN : ELECTRICAL PROPERTIES OF BORON DOPED SILICON 727

pressed on the AI dot to take out connection leads. Van der Pauw's method has been used for the e lectrical measurements.

-\l) \l) i:: (j) 10'

1000 0

'\

\

50

:.. \ ~ \

100 150 200

Temp . (K)

--N2D=lE+12

-tt- N2D=3E + 12

.-...- N20=7E+12

- Ill-- N2D=3E + 13

250 300 350

Fi g. I (a) - Plot of sheet resistance R€ versus temperature for Si:B <'i- layer

14

0 12 a::

o .

/ ;Li 0/ I l~/ /0 t

'

/ 'J 0 I 0 0 N20=1 E+12

/ 0 0 N20 =3E+ 12

I . 0 N20=7E +12 I ,} , N203E+13

10 Vi ,,.0 -tJ x N2D=7F. +1 3 1/ t:, N20=1E +14

/ () ~~_,_"L-'--'_-

8 l-~-_ --;'iww,",'*.."n ~ , i4 ~~_fL_

Fig. I (b)- Plot oflnR€ as a function of 1000lT

3 Results and Discussion

Electrical conductivity -The variation of sheet res istance R with temperature T is shown in Fig.

1 (a) . The nature of variation of R changes with the

different B doping concentration N1D in the 8-layer. It can be noticed that, a strong freeze-out of carriers occurs at a temperature below 200 K for samples having N1D :S; l x I012 cm2

. This freeze-out limit shifts towards a lower te mperature as the N1D increases. At

300 K this can be observed by a rapid fall of R with the increase of N1D [Fig 2(a)]. At temperature 50-300 K , the conduction may occur due to thermall y activated hopping of electron in a state near the Fermi energy Er (except for Mott transition) and may be defined as7

:

En (J = (Jo exp(- - )

kT . .. (1 )

where Eu=EA-EF+W, EA is the impurity energy and W is the activation energy for hopping. Similar hopping conduction was observed by Koch8 for Si delta-layer in GaAs [N1D= 7 .8x 1010 to 2x 10 11 cm2]. The conductivity activation energy Eu, has been ca lculated from a plot of InR (TI) as shown in Fig l (b). The values obtained in the temperature range 50-300 K are shown in Table 1. This shows that , Eu slowly goes down and vanishes at some higher doping concentration N CRIT ~6x 1013 cm·2 as shown in Fig. 2(b). The variation of the measured carrier concentration, n2D with temperature is shown in Fig. 3. From 300 to 100 K, Hall effect shows that, /l2O

gradually decreases. As the doping concentration N1 D increases, this variation becomes relatively fl at and at N2D:::: l x 1014 cm2 it becomes independent of

temperature. Samples with N1D ~ 10 13 cm-2 show a ri se in n2D between 100 and SO K, but, below SO K , it is either freezed out or become almost independent of te mperature . A very good correspondence of the applied doping concentration N1D with the measured catTier concentration n2D indicates a complete ionization of the dopant atoms in the 8-layer at room temperature.

The values of acceptor ionization energy Ej can be obtained from a plot of Inn2D versus T ·I (Fig. 3). The values in the te mperature range 200-300 K are given in Table I. This shows again that, Ej similar to Eu slowly goes down with the increase of N1D and vanishes at about - 1014 cm·2 [Fig 2(b)]. The values of measured TCR (temperature coefficient of

728 INDI AN J PURE & APPL PHYS, VOL 40, OCTOBER 2002

res istance) as a functi on of tf-D has been plotted in Fig. 4. This shows clearl y that, the sign of TCR changes at N1D? 6x 10 13 cm 2 where E" va ni shes as menti oned above.

Table I - Values of acceptor ion ization energy. acti vation energy and TCR with doping concen tration N1D in the Ii -l ayer

Doping Acceptor Activation TC R concentrat ion ioni zation energy F;i

( 10 ' /deg) N1DCIll ·2 energy E" (llleV) (llleV)

Ix l 012 293 .2 3346 - 11 .0 3x l Ol2 53.4 44.5 -6.2

7x l 012 30.4 26.3 -4 .6 3x 101:1 28.7 3.3 -0.73 7x I 0 13 24. 1 0 0. 18

Ix l 014 0 0 106

Metal-Iloll -metal transition - Three significant sigm for thi s type of transiti on in semiconductors as have been noticed here are: (i) The disappearance of acceptor ionizati on energy with the increase of B doping level in the sample, (ii ) the ex istence of a minimal metallic conductance (J M at low temperature and (iii ) the changing of sign of TCR with tuning th rough dopant additi on. All these are in favour of Mott metal-non-metal (MNM) transition7

in the samples .

In Fig. 2(b), it has been shown that, E" smeared out at the zero leve l at doping concentrat ion tf-1\ ,::6x l0 i:1 cm-2 at which TCR just changes its sign. It is noticed in Fig. l(b) that, sa mples with doping level lower than thi s critica l va lue (NcRIT) show clearl y a common intercept in the lnR (TI) curve, which is an indication of the ex istence of a minimal metallic conductance (J M in the low temperature limi t. The va lue of (J M was obtained to be 3.3x 10 4 (0.1 )-1. According to Mott, the two-dimensional minimal conductance should have va lue 0_ 1 e21h [=2.4x lO-5 (Q! )" IJ which is about an order of magnitude lower than our observed value in Si delta laye r. Thi s implies the possi bili ty of suppress ion of metallic conductance even at higher impurity density than their uni fo rml y doped counterpart9

,

where, thi s type of transition was observed at about 5x 10 13 cm J (=2.9x 1012 cm "). The average separati on of impurity centres fo r this concentrati on is 3.5 nm which is obviously much higher than that of its value in 8-doped samp les viz ., 0.8 nm. Thi s can be further noticed that, after such a phase transition

> Ql

E W

w

•

t---........ • ----1000 ~~~~WL~~~~~~~~

o 21013

41013

61013

81013

1 10 14 1.210 14

Fig. 2(a) - Plot of sheet res istance R€ versus doping concentrati on N20 in the layer at 300 K

350

300

250

200

ro

150

100

50

0

10 11 1012

1013

1014

1015

N2D cm-2

Fig. 2(h) - Variation of acceptor ioni zat:on energy (E i) and activation energy (Ea) wi th doping concentration N2D at 300 K

from semiconductor to the meta ll ic regime, the va lue of (J (0) at T=O should not lie be low (J M . The present set of samples clearl y foll ow this criteri a as we ll , which ca n be noticed in F ig. lea). Thus, fo r B

HAKIM & RAHM AN: ELECTRICAL PROPERTIES OF BORON DOPED SILICON 729

8-l ayer in Si the critica l doping concentrati on fo r MNM transiti on may be 6x 1O lJ cm-".

Temp K

100 50 33.33 25 20 34 ~~~~~~~~~~~·

32 tI

30

0 [ -- N2D=l E~;l ~ N

c 28 - :- N2D=3E+12 i -+- N2D=7E+1 2 i

"' E: >.

4, --1l- N2D=3E+13 , I

26 n --+- N2D=7E+13 !

Q ---,',- N2D=lE+14 : c\. ... ..;

24

o 10 20 30 40 50

1000/T

Fig . 3 - Pl ot of Inl/21) as a func tion o f looorr

, , 0 .... /I

~ / A '";"

. / I OJ -1 (J)

"0 / 6x10 '3 cm -2

-2 I

'0 / ;

-3 , (Y: / () -4 / f- I ...

-5

-6 / ! ,

-7

1012

1013 10

14 10

15

N2Dcm -2

Fig. 4 - Vari ation or tcmpe ratu re coe fficien t o f R€ (TC R) with doping concent ration N2D

Hall mobiliry - Fi g. 5 shows the variati on of Hall mobility Ill! with temperature T. As the temperature changes from 300 to 120 K, Ill! slowly increases for ali the sa mples (except one with lowest doping

concentration I X 1012 cm·2). ft then rapid ly decreases with a further fall of temperature and fin a ll y becomes constant at T <:::; 50 K. At room temperature (300 K), it is interes ting to note that ~lH increases rapid ly with the dec rease of area l doping concentrati on, fVlD as shown in Fi g. 6. Th is behav iour is a lso common to uniforml y doped Si:B (Ref. 9). £t is also noted in Fig. 6 that. at 120 K (when the III I va lues are the max imum for most of the sa mp les) Il l! increases a litt le at first then fall s down with the increase of doping leve l.

,-.. U ~ rJ)

> " N

E u '-"

I :1

250 -+- N20=1E+12

-+- N2D=3E+ 12

200 -.-N20=7E+12

-:!'- N2D=3E+ 13

-+- N20=7E+13

- J-- N2D=1E+14 150

100

50

o o 50 100 150 200 250 300 350

Temperature,T (K)

Fig. 5 - Variati on o r Hall mohi lity Ji l! as a function of temperature T

At 300 K, the meas ured Hall mobi lity in the layer is 49 cm2/V sec for sample with carrier concentrati on 3.8x lO '9 cm') which is well comparable to the value 53 cm2N sec obtained for the uniforml y-doped Si:B layer9 with carrier concentrati on 2x 1019 cm" . At low temperature - 77 K, the reported Hall mobility fo r uniformly-doped samp le is sli ght ly hi gher than our 8-doped samples. Samples with the lower 8-doping concentmti on show relati vely high mobility - 200 cm2N sec at room temperature, but it rapidl y dec reases with the fall of temperature and fin all y freeze-out at about 200 K.

Scattering process - For uniforml y-doped Si sample with a very low doping concentration, Hall

730 INDIAN J PURE & APPL PHYS, VOL 40, OCTOBER 2002

mo bility of the carrie rs is norma ll y limited by the latti ce phonon scatte ring in the high te mperature

region above room temperature (~ 300 K) (Ref. 10), and by the ionized impurity scatte ring in the temperature be low 300 K. In an ideal situation, f.!11 should show a T 3fl depe ndence for the former while in the latte r, it is '(312. In a prac tica l s ituati on, dev iati ons are al ways observed. For Ge lattice phonon scattering, howe ver, sta rts at about 100 K whic h is lower than for S i samples l l

.

--<:- T=1 20K :

200 " -- T=220K

-- T=240K

Li ....,rT=300K CI)

~ 150 > --N

E u 100 ~

0: :1

o 2 4 6 8 10 12

Fig. 6 --- Variation of Hall mobility JlH as a func ti on of doping concentrat ion N2D

In the case of boron 8-doped layers, an important diffe rence exists. Here, a large number of impurity atoms are concentrated over a fraction of a mono-layer of atoms and thus the ionized fl aws are numerous in a localized regio n of the epi-Iayer. In our sa mples, the most probable impurity separations are about 0.6-3 nm. In the absence of any para lle l conduction paths in such a medium, the effici ency of scattering by the impuri ty fl aws should be higher and may eas il y be .observed at 150-300 K. If this idea is taken into account, then, in thi s te mperature range, in the presence of both the latti ce phonon and ioni zed impurity scattering, the latte r should dominate and lead to a te mperatu re dependence of Jill u r with x ",,-0.5 (Ref. 12), Thi s has actuall y been observed in our samples with higher doping levels in the temperature range 150-300 K where x is found to lie be tween -0.4 and -0 .5 (Fig . 7), This is in exce llent agreement with the theory,

II 100 (l) C/)

> ......

N

E II

I :1

10 100 Temperature , T (K)

Fig. 7 - Logarithmic plot of JlH as a function of 1.emperature T

In the low te mperature region, between 50-100 K, the influence of lattice phonon scatte ring should be dimini shed and mostl y ion ized impurity scatte ring in addition of other similar mechani sms may take over leading to x ",,3/2. It was found that, x to lie between 1.2 and 2 .6 in thi s te mperature region. T his is a lso in fa ir agreement with t e theory. Tn a

sa mple with the lowest doping level :sIx 1 0 12 c m 2,

the impurity atoms are further apart -6 nm and a temperature dependence of JiHUr s is expected in the higher te mperature range. In their sample, the

autho rs observed JillUr 7 in thi s reg ion. Thi s is aga in an excellent agreement with the theory. Thus, the authors conclude that, io ni zed impuri ty scatte ring is the main scatte ring mechani sm in boron 8-doped S i in the te mperature range 50-300 K which limits the Hall mobility.

4 Conclusions

From electrical properties of MBE grown boron 8-l ayer in silicon, in the temperature range 10-300 K, it is found that, the conducti vity acti vation energy

E,. of the 8-layer decreases with the increases of doping concentration. A strong freeze-out of carrie rs was observed at a temperature be low 200 K fo r samples having N'lD ~ 1012 cm·2 . But, thi s freeze-o ut te mperature shifts towards a lower value as the doping concentration increases and at higher doping

HAKIM & RAHMAN : ELECTRICAL PROPERTI ES OF BORON DOPED SILICON 73 1

concentrati on, no freeze-out effect was indicated . Mott meta l-non-meta l phase trans ition in the samples has been observed at a critical carrier

conce ntrati on of 6x 10 1:1 c m·2, as a consequence of

zero ac ti vat ion energy, negati ve T CR and the

ex istence of a minimal metallic conductance 0 llIin at low temperature limit. Thi s critical value al so implies the poss ibility of suppress ion of meta llic conductance even at hig her impurity density than its uniforml y doped counterpart. Ha ll mo bility of the samples slowly increase with the decrease of te mperature, in the range 300- 120 K, and then goes down with a further decrease of te mperature be low 100 K and become almost constant at te mperature .s50 K. 1111 dec reases with the inc rease of doping level as well. Ioni zed impurity scatte ring may have a dominant role to control the Hall mobility in the investigated te mperature region.

Acknowledgement

One of the authors (MOH ) gratefull y acknowledges the financial support of the Commonwea lth Commi ss ion, UK and the tec hni ca l facilities of the Advance Silicon Researc h Laboratory of Warwick Uni versity to ca rry out the work.

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