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Front Title

Choudhury, D K

Dhar, Pijush Kanti

Indian J. Phys.Sl (8), 819-830(2007) 
Non-singlet structure function at low and high x in the next-
to-leading order and CCFR neutrino data 
D K Choudhury* and Pijush Kanti Dhar* 
Department of Physics, Gauhati University, 
Guwahati-781 014, Assam, India 
E-mail : dkcphys^yahoo.co in 
Recewed 27 April 2007, accepted 8 August 2007 
Abstract . We find the complete solutions of the DGLAP equations for non-singlet structure function at low 
and high x using Lagrange's auxiliary method in the next-to-leading order and find analytical expressions for xF^ 
Through our formalism, we have been able to separate out qualitatively low and high x regimes of deep inelastic 
neutrino scattering. Comparison with CCFR neutrino data as well as exact solutions is also made 
Keywords : Non-singlet structure functions, low and high x, next-to-leading order. 
PACSNos. : 12.38 -t, 12.38. Bx, 13.60-Hb 
1. Introduction 
Recently [1] we reported the complete solutions of DGLAP equations [2] in the leading 
order for non-singlet structure functions at low and high x. Using the Lagrange's auxiliary 
methods [3], we made phenomenological analysis with the CCFR data [4] with reasonable 
success. The formalism enables one qualitatively to separate the low and high x regions 
explored in deep inelastic neutrino scattering. 
In the present paper, we incorporate the next-to-leading order [NLO] effects in the 
formalism and re-analyze the CCFR data. 
Despite the maturity of the field and its long history [5,6] possible new analytical 
insight into the solutions of DGLAP evolution equations, if obtained, are expected to 
clarify the question of how much the results of such formalism can be made flexible 
'Corresponding Author 
t On leave of absence from Arya Vidyapeeth College, Guwahati-781 016, Assam, India 
©2007IACS 
820 D K Choudhury and Pijush Kanti Dhar 
enough to bring them to the close proximity of the exact results with least number of 
parameters. This is the aim of the present paper. 
In Section 2, we record the essential formalism while Section 3 contains the results 
and discussions. 
2. Formalism 
2.1 The DGLAP equation for non-singlet structure function in next-to-leading order is 
[5,6] 
dFNb(x,t) «s(f) 
dt 2n 
| { 3
 + 4log(1-x)}FNS(x,0-^^{(l + z2)FNS(x/z,r)-2FNS(x,0} 
2K 
( x - 1)Fws(x,f)j7(z)dz+\f{z)FNS (x/z,t)dz (D 
with 
f(z) = ^ PF(z) + 2PG(Z) + lnfPNi(z) + lpA(z) (2) 
where PF(z), PG(z), PNi(z) and PA(z) are taken from [5,6]. 
Ineq.(1), f = log O
2} 
Running coupling constant in next-to-leading order (NLO) is [5,6] 
a,(0 = 4K fiytogt fit J 
for one loop with 
. 33-2n, 306-38a 
Po=—f-L and # = — 1 
n, being the number of flavours. 
Using Taylor expansion [7-10] and using eqs. (2)-(4) of Ref. [1] we obtain from eq. (1), 
8 F
 a f
( X
' ° - [T(t)A(x) + r 2 ( f )B ( x ) ] 8 F ^ X ' f ) - [T(t)C(x) + T2(t)D(x)]FNS(x, t) = 0 (3) 
Non-singlet structure function at low and high x in the next-to-leading order etc 
where 
821 
and 
2* fat 
1 ft tog* 
I Pot (4) 
A(x) = - (-2x log x + x(1 - x2)) (5) 
f 1 - z B(x) = x j f(z)dz (6) 
C(x)^[3+4log(1-x) + (x-1)(x+3)] (7) 
D(x) = -Jf(z) dz+ xJ7(x) dz (8) 
where f(z) is defined in eq. (2). 
In order to solve eq. (3), it is recast in the standard form [3] 
dt dx 
to be compared with eq. (5) or Ref. (1). 
Here, 
0(x,f) = 1 
P(x,t) = -T(t)[Aix) + T(t)B(x)] 
R(x,t) = T(t)[C(x) + T(t)D(x)] 
R'(x,t) = R(x,t)FNS(x,t). 
(9) 
(10) 
(11) 
(12) 
(13) 
The general solution of eq. (9), frequently referred to as Lagrange's equation [3] is obtained 
from the solutions of the equation [eq. (9) of Ref. [1]] viz. 
dx dt -NS dF !3(x,t) 
P(x,t) Q(x,t) R(x,t)FNS(x,t) (14) 
822 OK Choudhury and Pijush Kanti Dhar 
Here the expressions for P[x,t) and R(x,t) defined in eq. (11) and eq. (12) are not factorizable 
in x and t unlike the corresponding equations of Ref. [1]. [eq. (6) and eq.(8)]. For a 
possible analytical solution, ^ ( f ) is linearised [11] through the ansatz 
T2(t)zTQT(t) (15) 
where 7"0 is a numerical parameter to be determined from experiment. 
This results in 
P(x,t) = -T(t)[Alx) + B(x)T0] (16) 
R(x,t) = T(t)[C(x) + D(x)TQ] (17) 
The general solution of eq. (3) is 
F(UNLOlVNLO) = 0 (18) 
where F is an arbitrary function and UNLO[xXFNS^Cy, VNLO(x,t,FNS)J = C2 are two 
independent solutions of eq. (14) 
(Here CA and C2 are two arbitrary constants.) 
The first equation of the system of eq. (14) is 
dx
 = dt_ 
-T(t)[A(x) + B(x)T0] 1 09) 
the solutions of which is 
M»tf-)JH«pr£tM«>-t (20) 
Another equation of the same system is 
dx _ _flFAf(x,f) 
-f(t) [A(*) + B(x)~)T0] " 7 ( 0 [C(x)~+ D(x)7- 0 ]F" s (x , f ) <21> 
the solution of which is 
VNLO{xJ.FNS)=FNS(x,t) exp [M(x)J (22) 
where 
a- 2 h - A 
R ' *2 and 
Non-singlet structure function at low and high x in the next-to-leading order etc 823 
N{X)
~1 Mx) + B(x)Tr (23) 
C(x)
 + D(x)T0t 
and M{x) = lA(x)VB[x)f0dX (24) 
The most general form of eq. (18) linear in F^ (i.e. in VNLC) has structure similar to eq. 
(19) of Ref. [1], viz. 
VNLo=aUnNLO + P (25) 
where a and fl are two arbitrary constants n' = n'(x,t) and is any real function of x 
and t. 
From eqs. (20), (22) and (25), one gets, 
FNS(x,f)exp[/W(x)] = a 
Using eq. (21) of Ref. (1), viz 
Fws(1,f) = 0 
for any f, we get 
>W{^} +fi. 
/?=-« /H b N1 expi- + —— 1 1 a 
Putting the values of p in eq. (26), one gets 
FN*(x,f )exp[M(x)] : 'exp expn N(x)l 
(26) 
(27) 
(28) 
-exp /7 «} (29) 
Now defining, 
FNS(x, t0) exp[M(x)] = a tQ ^ J exp U J, n'b exp "1 W(x)l a - e x p n N(1)l a (30) 
824 D K Choudhury and Pijush Kanti Dhar 
we finally get, 
-NS NS, F"*(x,t) = F":>(x,t0) t I ' exp rftii t tn (31) 
In Ref. [1], it has been suggested that the general solution of non-singlet structure function 
for low x ( x « 1) in LO of as is given by (eq. (26) of Ref. (1)). 
FNS(x,t) = FNS(x,tQ) < t^
n 
(32) 
where n = n (x, /) is any real function of x and t such that n > 0 numerically. The solution 
given by eq. (31) in the leading order limit (b=pjp$ -> o) should yield eq. (32) and that 
is possible if n'(x,f) = n(x,f). 
2.2. High x solution: 
Using the approximation for high x pursued in Ref. (1), we get an equation similar to eq. 
(3) except the function >4(x) defined in eq. (5) gets modified to 
A(x) -* A\x) = | x ( 1 - x) (x2 + x + 4) . (33) 
Similarly, the functions N(x) and M{x) defined in eqs. (23) and (24) are also modified 
N(x)->N'(x)= f - - dx— 
' J^ ( x ) + S(x)rc 
and 
W ( x ) ^ W ' ( x ) = f C ( x ) - + D ( x ) r o dx. 
JA'(x)
 + B(x)Tn 
(34) 
(35) 
As in low x, demanding linearity of the solutions in ^(x, Q as defined in eq. (18), we get 
the following form similar to eq. (25) 
where 
VNLO ~ a1UNLO + A 
U'NLO(x,t,FNS) = l^) exp 
t a 
(36) 
(37) 
Non-singlet structure function at low and high x in the next-to-leading order etc 825 
and 
VNLOMF™) = FNS(x,t)exp [M'(x)]. (38) 
in eq. (36), k'=k{x,t) is any real function of x and f similar to n'= n'{x,t) of eq. 
(31). 
From eqs. (36), (37) and (38), one gets 
FNS(x,0exp[M'(x)] = o1 >
1)exp{^
 + M4 + A (39) 
which has a term similar to eq. (26) for low x limit. 
We now use the boundary conditions eq. (27) to finally obtain the -^evolution of FNS(x,t) 
at high x : 
NS, FNI,(x,t) = F^(x,t0) 
,"(?*•) 
*1^+ i 
exp k'b 
' to j-i 
(40) 
As the general solution of non-singlet structure function for high x (x -» 1) in LO is (eq. 
(47) of Ref. (1)] 
-NS NS, F™(x,f) = F'v*(x,f0) 
(
 t V**'0 
<o) 
p(x,t)<0, (41) 
The solution eq. (40) in the leading order limit (b -» 0) must conform to eq. (41), one 
again has the equality 
/c'(x,f) = p(x,f). 
We can also reexpress eq. (31) and eq. (40) in the following form 
FNS(x,t) = F»s(x,t0){± 
\H*oW) 
(42) 
826 D K Choudhury and Pijush Kanti Dhar 
where 
n(xj)\og\ 
"yvLtf(*>') = -
* + i 
+ n{xj)b (\ l l 
t /n 
log ( t^ 
yKj 
(43) 
for x -> 0 and 
p(xj)\og\ A
1 
HNL0(X'r)--
[»• . 
+ p(jc,r)6 r i L^ 
log 
v < « , 
(44) 
for high x(x -» 1) limits respectively. 
The ratio of HNLO to n (for low x) and p (for high x) is defined as R(f) 
log 
,(H 
*(JM) = -
i + . o; 
log 
(45) 
yields 
HNW(,xj)=HU)l.xj)R{t) (46) 
where for x -» 0, HLO(x,t)-+ n(x,t) and for x -> 1, Hw(xj) -> />(*,*). 
As f?(r) 's positive for r > ^ as shown in Figure (1), it implies that the exponent 
H^otx.f) defined in eq. (42) has features identical to those of n(x,t) and p(x,r) defined 
earlier (in eqs. (32) and (41) respectively) i.e. n(x,0 > 0 for low x and p(x,Q < 0 for high x. 
This suggests that even in the next-to-leading order, the present formalism enables one 
Non-singlet structure function at low and high x in the next-to-leading order etc 827 
qualitatively to separate out low x and high x regimes explored in deep inelastic scattering 
It is worthwhile to note that the main results of the present work eq (31) and eq (40) are 
improvement over those of Ref. (11) as the present form of evolutions are both T0 and x 
independent, which were not so there. It is also more general than those of Ref (12) 
based on adhoc relation y? = ay(y = 2,3,4,5 ) 
0 84 
R(t) 
0 82-j 
0 80-J 
) 
0 78-
0 76-
0 74-I 
0 72 J 
0 70< 
n, = 6 
n, = 4 
n • r-
6 7 
Figure 1. We plot f?(f) (eq 45) vs t for two distinct quark flavours n, = 4 and nt = 6 respectively 
3. Results and discussions 
In order to make phenomenological analysis, we use eq (42) to define HLXpt(xj) as 
^expt W ) ~ T^N ( 
log 
(47) 
The numerical value of Hcxp{(x,t) will be obtained by the analysis of recent CCFR 
experiment [4] and taking A = 323 MeV. 
Similarly we can define Hexact(x, 0 as 
HexaLt(xj)~ 
_ logF e x a c t ( jc ,ono g F(* , / 0 ) (48) 
log 
which is obtained from HEP data base [13] using MRST 2004 NLO parton distributions 
[13]. 
828 D K Choudhury and Pijush Kanti Dhar 
In Figure 2(a-d), we plot Wexpt(x, /) vs 0 2 for four representative values of low x : x = 
0.0075, 0.0125, 0.0175, 0.0250. It shows that most of the data for it is found to be 
positive as suggested by the theory. However, in the following few (x.Q2) values, 
Hexpt(x,f) for low x turns out to be negative : (0.0075, 1 3), (0.0075, 3.2), (0.00125, 3.2), 
(0.0175, 1.3), (0.0250, 1 3), which is anomalous in the context of the present 
formalism. 
For high x, we make similar analysis for four representative values of x : x = 0.4500, 
0.5500, 0.6500, 0.7500 as in Figure 2(e-h). In this case, however Hexpt(x,f) comes out to 
be invariably negative, suggesting the validity of the present formalism. 
In Ref [1], we have suggested most general form of HL0(x,t) while a simple empirical 
form of it was found to be 
#cxp« (i.O = ° ^801-5 796* + 0 996(1 - v)l (49) 
t o 
05-1 
ooJ 
H*.tr°ej 
-10 
.15 
.2 0 
-2H 
-30 
-3S-j 
-4 0 J 
Q'jGtV2) 
(a) 
4 = 
x-0.0175 
3 1 
2 -
1 -
0 -
- 1 -
H(«.t) l ] 
-4-
-6-
-6-
-7-
-8-
-10-
•11-
1 
i 
0 
• 
1 
15 
I 
1 -
X-0JD075 
H.Jx.tJCCFR 
- Our work (HNl0(x,t)) 
i ' i 
20 26 
i 
• 
3.0 
i 
i 
3 
4 - i 
3 -
2 -
H(x.t) 
1 -
0 -
1 -
1 
I i 
0 
i 
15 
l" 
I 
-1--
1 0 
x«0 0125 
• H ^ <x,t) CCFR 
- - OunworMH^.1)) 
<Hto(x,t)) 
t • • J • • • • ! f ' 
25 30 
i 
i • i 
35 40 4 5 
J 
-] 
5 0 55 
H<M) 
• H^JMCCFR 
— Our work (h^JM) 
10 
05 
00 
-oo-j 
- ion 
•15 
-2 0 
2 5-1 
3 0 
-3 5 
Q'CGeV3) 
(b) 
X-0 02S0 
H^x.OCCFR 
Our work (H^Jjtf) 
(HJx.t)) 
i • * i ' » 
4 5 6 
Q'^V*) 
0 2 4 6 6 10 
Q'CGW3) 
(C) (d) 
Figure 2 (a-d). We plot H#Jjpt(x,f) vs Q2 for four representative values of low x : x = 0.0075, 0.0125, 
0.0250 For high x, we make similar plotting for four representative values of x : x = 0 4500, 0.5500, 
0.7500 in Figure 2(e-h). 
0 0175, 
0.6500, 
Non-singlet structure function at low and high x in the next-to-leading order etc 829 
A reanalysis of the data with NLO MRST distributions [13] modifies eq. (49) to 
r N L O #cxpt =0.412 [-4.5U + 0.913(1-Jt)] (50) 
In Figure 2(a-d), we compare for low x the predictions of eq. (49) (dotted line) and eq. 
(50) (dashed dot line) with exact results eq. (48) (solid line) while in Figure 2(e-f) a 
similar comparison is done for high x. For low x, the NLO effects of eq. (50) are found to 
be negligible as its predictions nearly coincide with those of eq. (49). However, for high x, 
the predictions of eq. (50) are closer to exact one eq. (48) except for the point x = 
0.4500 where eq. (49) is favoured. 
H<K,t) 
0.1 
0 0 
•0.1 
- 0 2 
-0.9 
-0.4' 
-0.5 
•0,0 
-0.7. 
-0.9 
-09 
-1.0 
x-0.4500 
H„JM> 
• H^JxflCCFR 
OurworfcC^Jx,!)) 
n~7T 
100 13) 
Q'COeV1) 
W 
H(x,t) 
4 . 4 -
-0 .6-
) -
- Q 8 -
-1 .0 -
- 1 2 -
I 
l 
-i-i- -»-
0 SO 
X-.5500 
H ^ x . t ) 
• H ^ (x.t) CCFR 
Our^orMH^fr.t)) 
" <l\o0c.t)) 
• • 4. 
F i , . . . . . . . j .... F 
100 150 200 
QtGeV2) 
(0 
H(X,t) 
-1.0-
,1 
x-0.6500 
H . J M 
• H^(x,t)CCFR 
• Our work (K^JM) 
<Hj[xft)) 
-OS-i 
-1 .0-
-1 5 -
-2 0 -
i 
I 
i • r 
x-0.7500 
1
 HBip,(x,t)CCFR 
Our work (HNlo(x.t)) 
I "(HJx.t)) 
I 
, , , . , , , 
1 
60 BO 100 
Q*(GeV*) 
(0) 
Q'(GeV') 
Figure 2 (e-h). We compare for low x the predictions of eq. (49) (dotted line) and eq.(50) (dashed dot line) with 
exact results eq. (48) (solid line) while in Figure 2(e-h) a similar comparison is done for high x. 
4. Comments and conclusions 
To conclude we have shown that the exponent of {t/t0) in the expression for the structure 
function in the next-to-leading order is positive for low x and is negative for high x, as in 
leading order. Through our formalism, we have been able to separate the low and high x 
830 DKChoudhuryandPijush KantiDhar 
region respectively. In contrast to the result of the previous work (Refs. 7-11), we have 
suggested that the exact form of the exponent can be much more general than the mere 
geometrical numbers ±1 . As its exact form is not given by the theory, we suggested a 
general structure and obtained a simple empirical form consistent with CCFR data. Our 
analysis above suggests that such empirical form with NLO effects is closer to exact 
results for most of the data at high x, while for low x, such effects are insignificant. 
References 
[1] D K Choudhury and P K Dhar Indian. J. Phys. 81(2) 259 (2007) 
[2] V N Gribov and L N Lipatov Sov. J. Nucl. Phys. 15 438 (1972); Yu L Dokshitzer Sov. Phys. JETP 
46 64 (1977); G Altarelli and G Parisi Nucl. Phys. B126 298 (1977); L N Lipatov Sov. J. Nucl. Phys 
20 94 (1975); G Alterelli Phys. Rep. 81 1 (1981) 
(3] I Sneddon Elements of Partial Differential Equations (New York : Mcgraw-Hill) p50 (1957) 
[4] CCFR Collab : W J Seligman et al Phys. Rev. Lett. 79 1213 (1997); http:/durpdg.dur.ac.uk/hep data 
on-line (Structure function data from CCFR) 
[5] W Furmanski and B Petronzio Phys. Lett. B97 437 (1980) 
(6] G Curci, W Furmanski and R Petronzio Nucl. Phys. B175 27 (1980) 
[7] D K Choudhury and J K Sarma Pramana-J. Phys. 38 481 (1992); ibid 39 273 (1992) 
[81 J K Sarma, D K Choudhury and G K Medhi Phys. Lett. B403 139 (1997) 
[91 Atri Deshamukhya and D K Choudhury Indian J. Phys. 75A(5) 573 (2001) 
[101 D K Choudhury and Atri Deshmukhya Indian J. Phys. 75A(2) 175 (2001) 
[11] A Deshamukhya and D K Choudhury Proc. of the 2nd Regional Conference on Physics Research 
in North-East, Guwahati, India p34 October (2000) 
[12] R Rajkhowa and J K Sarma Indian J. Phys. 79(1) 55 (2005) 
[13] http://durpdg.dur.ac.uk /cgi-bin/hep data 


English

Non-Singlet Structure Function at Low and High x in the Next-to-Leading Order and CCFR Neutrino Data

Singh, N S

Singh, W Shambhunath

Singh, Sh Dorendrajit

Okram, G S

Indian J. Phys- 81 (2), 225-231 (2007) 
Preparation and characterisation of nanocrystalline CdSe 
N Shanta Singha*, W Shambhi|nath Singha, 
Sh Dorendrajit Singhb and G S Okramc 
•Department of Physics, Manipur College, Imphal-795 008, Mampur, India 
bDepartment of Physics, Manipur University, Canchipur, Imphal-795 003, Manipur, India 
CUGC-DAE Consortium for Scientific Research, lndore-452 017, Madhya Pradesh, India 
E-mail shantasinghl(f^yahoo.coin 
Received 14 July 2006, accepted 1 December 2006 
Abstract : Nanostructured CdSe crystals have been prepared by wet chemical method in alkaline medium 
at 65 - 70°C using cadmium acetate and freshly prepared sodium selenosulphite as Cd and Se ion sources. XRD 
pattern of the prepared sample shows cubic zinc blende structure with average particle size of 3 4 nm. EDX 
measurement determines nearly equal atomic concentrations of Cd and Se. The powdered sample of CdSe is 
characterised using SEM and AFM. Optical absorbance study of thin film of CdSe deposited on glass substrate 
using chemical bath deposition method shows the blue shift of the band gap of energy of 0 12 eV from the bulk 
value of 1 7 eV due to quantum confinement effect. The average crystallite size is estimated using effective 
mass approximation (EMA) as 3 8 nm which agrees well with that obtained using the XRD pattern. 
Keywords : Nanoparticles, optical absorbance, semiconductors 
PACS Nos. : 81 07.Bc, 78 67,Bf 
1. Introduction 
Nanocrystalline semiconductor materials have attracted many researches for their intriguing 
physical properties which arise due to the spatial confinement of carriers and increase in 
the number of surface atoms. Among them group ll-VI binary semiconductors in 
nanocrystalline form occupy a prominent place in the semiconductor physics as they 
show wide range of applications in optoelectronic devices, solar energy conversions etc. 
Cadmium Selenide nanocrystal among ll-VI semiconductors is of great interest for its 
potential applications owing to its excellent optical conductivity, such as non linear optical 
properties, luminescent properties and quantum size effect [1, 2]. In thin film form they 
* Corresponding Author 
©2007 I ACS 
226 N Shanta Singh, W Shambhunath Singh, Sh Dorendrajit Singh and G S Okram 
are used as thin film transistors, gas sensors [3], gamma ray detectors and large screen 
liquid crystal display [4]. Further, deliberate doping of impurity influences their optical, 
electronic, structural and other characteristic properties [5-8]. Cadmium Selenide quantum 
dots have also shown the sensitive dependence of their optical and electrical properties 
on size, shape, size distribution and morphologies. Such properties attract research workers 
[9, 10] for fundamental and technological interest. 
Among a number of methods for the preparation of the CdSe, wet chemical method 
offers an inexpensive and simple means to synthesize such particles with good control 
over size and size distribution by optimising various parameters. Many workers [1, 3, 7, 
8] use ammonia for its dual role of forming complex metal ion and varying the pH of the 
reaction bath and thereby slowing down the reaction rate. 
Preparations of CdSe in various shapes, namely, nanorods, nanocables, nanoballs, 
hollow nanospheres have been investigated by a number of workers [9-12]. R Maity and K 
K Chattopadhyay reported the preparation of nanocrystallme ZnS and ZnS:Mn by chemical 
synthesis process without using any capping agent [13]. Ghosh et al [14] have also 
reported the chemical bath deposition of transparent polycrystalline ZnS nonobelts within 
the pores of polyvinyl alcohol on glass and Si substrates. In this paper we report the 
synthesis and characterisation of nanostructured CdSe crystals and thin films using wet 
chemical method without using capping agent. Cadmium Acetate and freshly prepared 
sodium selenosulphite are used as cadmium and selenium ion sources and liquor ammonia 
(25%) solution is used as a complexing agent as well as to make the bath alkaline. XRD, 
SEM and AFM are used to characterize the air-dried powder sample. Thin film of CdSe 
has been deposited onto the glass substrate using chemical bath deposition method for 
study of optical absorbance properties. The band gap of CdSe calculated using the 
absorbance is found to be 1.82 eV. The size of the nanograms of CdSe has been determined 
using both XRD pattern and effective mass approximation (EMA) using the increase in the 
value of bandgap from the value of bulk CdSe (1.7 eV). The values are found to agree 
well. 
2. Experimental details 
2.1 Sample preparation: 
All reagents used are of analytical grade. Cadmium Acetate Cd(CH3COO)2 and freshly 
prepared sodium selenosulphite Na2SeS03 are used as the sources of Cd and Se ions 
respectively. To prepare fresh Na2SeS03 solution 3 gm of Na2S03 is dissolved in 250 ml 
of distilled water. 0.5 gm of Se metal powder is added to this solution and heated at 90°C 
under constant stirring for 8 hours and cooled to room temperature to obtain fresh 
Na2SeS03 solution. To 250 ml of 0.005M Cd(CH3COO)2 is added 0.05M NH4COOCH3 
buffer solution in which 25% liquor ammonia is then added to this until the pH of the bath 
becomes 9.6. Glass substrates are cleaned following the steps reported by Oladeji and 
Chow [15]. The cleaned glass substrates are held vertically in the solution with the help 
of teflon holders and tapes. The solution is now heated upto 65°C and 30 ml of the 
Preparation and characterisation ofnanocrystalline CdSe 227 
freshly prepared Na2SeS03 is then added slowly at the rate of 1 ml per minute. The 
reaction continues for 4 hours while red CdSe thin film gets deposited on the glass 
substrate. The glass substrate with the thin film of CdSe is taken out of the bath, cleaned 
with distilled water in an ultrasonic bath and air dried at room temperature for its optical 
absorbance measurement. The temperature of the bath is now increased to 70°C for the 
homogeneous reaction to start and precipitation of CdSf starts taking place in the solution. 
The CdSe colloids in the bath is centrifuged and extracted with methanol. The CdSe 
precipitate is washed with several times with distilled watar and air dried at room temperature 
and kept in desiccators for its characterisation. 
2.2 Reaction mechanism 
The reaction mechanism involved in the formation of CdSe [16, 17] is as follows : 
NH; + OH-<-»NH3+H2O 0) 
Cd2 + 4NH3 <-> Cd(NH3 ) f (2) 
In an alkaline solution, the inorganic sodium selenosulphite hydrolyses to give Se2* 
ions and reacts with Cd2+ to form the CdSe. 
Na2SeS03 + 20HT <-» Na2S04 + H20 + Se2" (3) 
and cd2 + Se2 ' *-> CdSe (4) 
If the ionic product [Cd2+][Se2_] exceeds the solubility product, K
 9 of CdSe 
(4.0x10'36), then CdSe will form as solid phase [4,16]. 
2.3 Characterisation : 
The particle size and crystal structure of the samples are determined from XRD data 
using a Rigaku 18 kW Rotating X-ray generator equipped with Rigaku D-Max-300 0-20 
Goniometer with CuKa X-radiation. The ionic composition is determined using energy 
dispersive X-rays (EDX) data. The micrographs of the sample dispersed on the glass 
substrate are recorded using SEM (JSM-5600) and a Digital Instruments Nanoscope AFM 
(E Verson-245). The optical absorbance of CdSe deposited on glass substrates is recorded 
using UV-Visible Spectrophotometer (Systronics-2202). 
3. Results and discussions 
Figure 1 shows the XRD pattern of the nanostructured CdSe crystals. The diffraction 
peaks are observed at the 20 values of 25.665°, 42.650°, 49.650°, 67.709° and 78.021° 
corresponding to the crystal planes of (111), (220), (311), (331) and (422) respectively, 
showing the cubic zinc blende structure of CdSe [18]. CdSe has been reported to exist 
both in cubic phase [1,3,6,10] and in hexagonal phase [19]. Different workers have revealed 
the co-existence of hexagonal and cubic CdSe crystallites with preferential orientation 
228 N Shanta Singh, W Shambhunath Singh, Sh Dorendrajit Singh and G S Okram 
600 
^ 500 A 
3 
CO 
c 
CD 
400 
300 
200 H 
100 H u V \****^^ 
along c-axis and (111) direction 
respectively [4,20]. In this work, CdSe 
nanocrystals are found to exist only in 
cubic phase. The prominent peaks have 
been utilised to estimate the grain size 
of the samples with the help of Scherrer 
formula [21], D = KA//3cos0, where D 
is the average crystallite size, K is a 
constant (-1), p is the full width at 
half maximum and e is the Bragg's 
angle. The grain size estimated using 
the (111) peak is found to be 3.4 nm 
The ionic concentrations of cadmium 
and selenium of the prepared CdSe 
sample are determined using EDX. Cadmium ion concentration exceeds slightly that of 
the selenium ion by about 9% with a small trace of sulphur ion of about 6%. Figure 2 
shows the SEM picture of the powdered sample of CdSe. The picture shows that the 3 4 
nm nanograins have agglomerated to form a bigger particle of nearly 1 micron size with 
sharp boundaries. The SEM picture shows that bigger agglomerated particles are 
homogeneous in size. 
20 40 60 
26 (degree) 
80 100 
Figure 1. XRD pattern of nanostructured CdSe crystals 
Figure 2. SEM picture of CdSe powder. 
Figures 3(a) and 3(b) shows two dimensional (2D) and three dimensional (3D) AFM 
images of CdSe powder samples dispersed in acetone over a glass substrate. The particles 
are found to form small spherical islands of an average diameter of 150 nm. However, 
section analysis of two spherical islands shows that the islands have vertical distances of 
preparation and characterisation of nanocrystalline CdSe 229 
5.991 nm and 11.701 nm. This shows that although a single particle could not be selected 
for the AFM observation the particles he in the range of 6-12 nm. Kale et al [22] attributed 
the formation of small islands of ZnSe to the indication of three dimensional growth of the 
film of ZnSe deposited using modified chemical bath deposition method. 
nm Section Analysis 
o 
o 
K 
. . • ' N I -
1 00 2 00 
Surface distance 
Honz distance(L) 
Vert distance 
Angle 
Surface distance 
(foriz distance 
Vert distance 
Angle 
87 205 nm 
85 938 nm 
11 701 nm 
7 754 0 
86.351 nm 
85.938 nm 
5.991 nm 
3 988 0 
<a)p (b) 
Figure 3. Two dimensional (2D) and three dimensional (3D) AFM images of CdSe powder 
1.0-K 
0.8J 
The absorbance of the CdSe thin 
film deposited on the glass 
substrate is shown in figure 4. The 
band gap of the sample is 
calculated from the absorption 
spectra shown in figure 4 using the ^ 
relation [23] (ahv)Vn - A{hv - Eg) £ 0.6 
where a is the absorption co-
efficient, hv is the photon energy, 
A is a constant and £ is the band 
gap of the material. The value of n 
in the exponent is 1/2 for direct, 
allowed transitions. 
0) 
< 0.4 
0.2H 
Figure 5 shows the plots of 
{ahvf versus hv. The linear 
portion of the plot of (ahv)2 versus 
v 
\ 
400 500 600 
Wavelength (nm) 
700 
Figure 4. Absorbance spectra of thin film of CdSe deposited 
on a glass substrate. 
230 N Shanta Singh, W Shambhunath Singh, Sh Dorendrajit Singh and G S Okram 
1.8 2.0 
MeV) 
Figure 5. Curve showing (ahv)2 versus hv (open 
circles) of CdSe thin film. The solid line shows the 
extrapolation of the linear portion of the strong 
absorption region. 
hv in the region of strong absorption has 
been extrapolated to obtain the intercept 
on the hv axis. The intercept gives the 
value of the band gap Eg. The value of E 
is found to be 1.82 eV, which exceeds 
the band gap 1.70 eV of bulk CdSe. This 
is attributed to the quantum confinement 
effect as the particle size becomes 
smaller [24]. The grain size of 3.4 nm 
obtained from the XRD data shows that it 
is appreciably smaller than the Bohr 
exciton radius 5.6 nm of CdSe. The 
exciton energy E$ obtained using effective 
mass approximation (EMA) for strong 
confinement is given by [23, 25] 
E$ = Eg + h2n2l2»R2 - 1.786e2/4;rc0eR 
-0.248Epy, where ju is the reduced 
effective mass, e is the dielectric constant of CdSe and e0 is the permittivity in vacuum, 
E*Ry is the effective Rydberg energy. Using this relation the grain size of the prepared 
CdSe is found to be 3.8 nm, which is quite near to the size 3.4 nm obtained from XRD 
data. 
4. Conclusion 
Nanostructured CdSe both in powder form and thin film has been prepared using chemical 
method. The grain sizes obtained using XRD (3.4 nm) and EMA (3.8 nm) are found to 
agree well. The particles are found to be in cubic phase. SEM pictures shows the grown 
samples are homogeneous in size. AFM picture of the sample shows spherical islands 
having heights of 6-12 nm. The band gap calculated using the absorbance spectra of the 
deposited CdSe film gives a value of 1.82 eV. 
Acknowledgments 
One of the authors (WSS) wishes to thank the University Grants Commission, New Delhi 
for financial assistance [vide its letter R No. 30-5/2004(SR)] and UGC-DAE CSR, Indore 
for partial financial assistance through its collaborative research scheme. We also would 
like to thank V Ganesan, N P Lalla and D M Phase, UGC-DAE CSR, Indore for AFM, 
XRD and EDX measurements. 
References 
[1] R B Kale and C 0 Lokhande Appl. Surf. Sci. 223 343 (2004) 
[2] M Chen and L Qao Inorg. Chem. Comrn. 7 673 (2004) 
[3] B Pejova, A Tanusevski and I Grozdanov J, Sol. Stat Chem. 172 381 (2003) 
Preparation and characterisation ofnanocrystalline CdSe 231 
[4] C D Lokhande, E H Lee, K D Jung and 0 S Joo Mat. Chem. Phys. 91 200 (2005) 
[5] G Pema, V Capozzi, A Minafra, M Pallara and M Ambrioo Eur. Physical J. B32 339 (2003) 
[6] V M Bhuse Mat. Chem. Phys. 91 60 (2005) 
[7] p p Hankare, A D Jadhar V M Bhuse, A S Khomapene and K M Garadkar Mat. Chem. Phys. 80 
102 (2003) 
[8] K C Sharma, R Sharma and J C Garg Jpn. J. Appl. Phy$ 31 742 (1992) 
[9] X Peng, L Manna, W Yang, J Wickham, E Scher, A Kadananich and A P Alivisatos Nature 404 59 
(2000) 
[10] M Chu and G Liu Mat. Lett. 60 11 (2006) 
[11] Y Xie, Z Qiao, M Chen, X Lin and Y Qian Adv. Mater. 11 1512 (1999) 
[12] 0 Palchik, R Kerner, A Gedanken, A M Weiss, M A Slifkjnand V Palchik J. Mat. Chem. 11 874 
(2001) 
[13] R Maity and K K Chattopadhyay Nanotechnology 15 812 (2004) 
[14] P K Ghosh, M K Mttra and K K Chattopadhyay Nanotechnology 16 107 (2005) 
[15] I 0 Oladeji and L Chow J. Electrochem. Soc. 144 2342 (1997) 
[16] G Hodes Chemical Solution Deposition of Semiconductor Films (New York : Marcel Dekker) 
(2003) 
[17] K L Chopra and S R Das Thin Film Solar Cells (New York : Plenum) (1983) 
[18] JCPDS # 19-0191 
[19] C Wang, W X Zhang and X F Qian Mat. Chem. Phys. 60 99 (1999) 
[20] F Raoult, B Fortin and Y Colin Thin Sol. Films 182 1 (1989) 
[21] Ch Hammond The Basis of Crystallography and Diffraction (Oxford : Oxford) (1887) 
[22] R B Kale, C D Lokhande, R S Mane and Sung-Hwan Han Appl. Surf. Sci. 252 5768 (2006) 
[23] J I Pankove' Optical Processes in Semiconductors (New Jersey, USA : Prentice Hall) (1971) 
[24] A D Yofee Adv. In Phys. 42 173 (1993) 
[25] K Subha Ramaiah, Y K Su, S J Chang, F S Juang, K Ohdaira, Y Shiraki, H P Liu, I G Chen and A 
K Bhatnagar J. Crystal Growth 224 74 (2001) 


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Indian J. Phys. 81(3) 371-376 (2007) 
Elemental analysis of some antioxidant-rich medicinal 
Zingiberales of Manipur usingproton induced X-ray 
emission (PIXE) technique 
K Nomita Devi1*, H Nandakumar S^rma1 and Sanjiv Kumar2 
'Department of Physics, Manipur University, Canchipur, Impha!-795 003, Manipur, India 
2National Centre for Compositional Characterization of Materials (CCCM), 
Hyderabad-500 062, Andhra Pradesh, India 
E-mail : nomita_k@rediffmail.com 
Received 27 February 2006, accepted 8 February 2007 
Abstract: Rhizomes of seven medicinal Zingiberales commonly used in Manipur have been analysed by the 
proton induced X-ray emission (PIXE) technique. The elements K. Ca, Mn, Fe, Cu, Zn, Rb and Sr are found to be 
present in varying concentrations. K and Ca have been estimated at percentage level while other elements are 
quantified at ppm level. Among the trace elements, Mn, an antioxidant rich element, is found to be present in high 
amount in most of the studied samples. Strong positive correlations are observed between K and Mn, K and Cu, 
Ca and Fe and Mn and Cu. 
Keywords : PIXE, medicinal Zingiberales, antioxidant, trace element. 
PACS Nos : 78.70.En, 23.90.+W 
1. Introduction 
Medicinal herbs have been used from antiquity by humanity. Over three quarters of the 
world's population relies mainly on plants and plant extracts for primary heath care and 
there is a global resurgence of interest in the use of plant products to treat almost all 
diseases including cancer. Herbal medicines have stood the test of time for their safety, 
efficacy, cultural acceptability and lesser side effects. They are rich source of synthetic 
and herbal drugs and contain a wide range of chemical compounds, commonly referred to 
as photochemicals. In addition, medicinal plants contain essential and trace elements, 
which can be available to the human body from any kind of consumptions of herbs and 
their extracts. Hence, it is desirable to establish the levels of elements in medicinal plants. 
Further, as certain elements at elevated levels are toxic, such an assessment would also 
be helpful in regulating their use. 
* Corresponding Author O 2007 (ACS 
372 K Nomita Devi, H Nandakumar Sarma and Sanjiv Kumar 
Medicinal Zingiberales are hot herbs today and a number of studies have shown that 
the rhizomes of these species possess a variety of potential antioxidant molecules [1-4]. 
These aromatic plants are not only used as food, spices and condiments, but they are also 
used in the traditional system of medicines for curing various human diseases [5,6]. The 
antioxidant and anticarcinogenic properties of curcumin, the chrome orange yellow coloring 
compound present in turmeric rhizome have been reported [7,8]. Rhizome extracts of 
Alpinia galanga, Zingiber cassumunar, Kaempferia galanga, Curcuma caesia and Zingiber 
officinale have been shown to possess antioxidant [9] properties. Supplementation of 
natural antioxidants through a balanced diet could be more effective and also more 
economical than the supplementation of an individual antioxidant, such as vitamin C or 
vitamin E, in protecting the body against oxidative damage under various conditions. 
Another advantage of using antioxidant agents of plant origin is that it can control the 
oxidative damage without any side effects. It is also reported that various elements present 
in plants have either direct or indirect role in the control and maintenance of the antioxidant 
defence system of the body. The trace elements copper, manganese, selenium and zinc 
act as co-factors of antioxidant enzymes to protect the body from oxygen free radicals that 
are produced during oxidative stress. It is necessary to maintain a balance between the 
harmful pro-oxidant components produced and the antioxidant compounds that counter 
these effects [10-12]. A delicate balance also exists for the redox trace elements such as 
copper, which can initiate free radical reactions but is also a co-factor of copper/zinc-
superoxide dismutase, a free radical scavenging enzyme. Manganese is an antioxidant 
nutrient and is important in the breakdown of amino acids and the production of energy. 
It is an essential requirement for the metabolism of vitamin B1, C and E and for activation 
of various enzymes, which are important for proper digestion, and utilization of foods. 
In the present study, the major and trace element content of seven medicinal 
Zingiberales commonly used in Manipur, a north-east state of India, have been determined 
by proton induced X-ray emission (PIXE) technique. PIXE is a powerful ion-beam analysis 
technique for the sensitive determination of elements and it has been used extensively in 
various fields [13-18]. 
2. Experimental 
2.1 Sample preparation: 
Fresh rhizomes of seven medicinal Zingiberales, namely, Curcuma domestica, Zingiber 
officinale, Zingiber cassumunar (Roxb), Alpinia galanga, Heduichium marginatum C.B 
Clarke, Kaempferia galanga Linn and Curcuma caesia were collected from different parts 
of Manipur. The outer skin of the rhizomes were removed, thoroughly washed with distilled 
water, cut into thin slices with a sharp steel knife, dried in an incubator at 40°C and 
subsequently, ground into fine powder. The powdered samples were thoroughly mixed with 
high purity graphite powder in the ratio 4:1 by weight. This step is necessary for charge 
integration with better accuracy and eliminating the problems associated with charging 
during PIXE measurement. The samples thus obtained were further mixed with 200fil of 
Elemental analysis of some antioxidant-rich medicinal Zingiberales etc. 373 
2-wt % polyvinyl alcohol, a binder, dried under an IR-lamp and subsequently pressed into 
pellets of 18mm diameter and 2mm thickness. The thick targets of Certified Reference 
Materials (CMRs) of cabbage (GBW 08504, China), viheat flour (NIST-8436) and bovine liver 
(NIST-1577b) used as calibration standards in the present study, were also prepared in a 
similar way. 
2.2 Analysis: \ 
I 
PIXE measurement was performed at the Surface apnd Profile Measurement Laboratory at 
CCCM, BARC, Hyderabad using a 3MV Tandetron ^ accelerator. A well collimated 2.4MeV 
proton beams of diameter 5mm and current 5-7nA v$as incident normally on targets placed 
inside an evacuated scattering chamber and the X-rays are detected by a planer high purity 
germanium (HPGe) (Eurisys Measures type EGX10O-O1, Be window thickness of 40 pm, 
FWHM of 150 keV at 5.9 keV) placed at 45° to the beam axis. A 25 nm mylar foil served 
as the X-ray exit window. The vacuum in the scattering chamber, pumped by a 
turbomolecular pump, was about 2x10"6 torr. An electron suppressor with a voltage of -
900V was placed in front of the samples. The data were recorded on a PC based MCA 
and the spectral data were analysed by the GUPIX [19] software package which provides 
nonlinear fitting of the spectra. 
In thick target PIXE (TT-PIXE), calibration standards having matrix composition identical 
to that of the sample under investigation are required for quantification with better accuracy. 
Therefore, three biological standard reference materials, as mentioned earlier, were used 
as calibration standards in the present study. In order to ascertain the accuracy of the 
analysis, the calibration standards were analysed against each other. The overall uncer-
tainty in the estimation of all elements except Fe, on repetitive measurements, was 
observed to be 3-8%. It may be ascribed to errors in the measurement of peak areas and 
relative accumulated charges. In the case of Fe, the uncertainty was about 15%, which 
may be largely due to its inhomogeneous distribution in the targets. It is to be noted that 
sufficient care was exercised to avoid contamination during the preparation of the samples. 
374 K Nomita Devi, H Nandakumar Sarma and Sanfiv Kumar 
3. Results and discussion 
The PIXE spectrum obtained from Zingiber officinale having peaks for various elements 
such as K, Ca, Mn, Fe, Cu, Zn, Rb is presented in Figure 1. The results of the elemental 
composition analysis of the samples are given in Table 1. 
Table 1. Elemental concentrations of the medicinal rhizomes under study. 
Sample 
Curcuma domestica 
Zingiber officinale 
Kaempferia gaianga Linn 
Zingiber cassumunar (Roxb.) 
Alpinia gaianga 
K (%) 
4.84 
0.77 
3.92 
2.33 
7.69 
Hedychium marginatum C.B Clarke 2.59 
Curcuma caesia 1.62 
Ca(%) 
0.329 
0.165 
0.22 
1.94 
0.43 
0.56 
0.069 
Mn 
24 
313.4 
632 
203 
1803.3 
451 
215 
Fe 
142 
216.6 
177 
83 
231 
295 
27 
Cu 
8 
4.5 
8.4 
2.7 
28 
1.9 
3.4 
Zn 
46 
72.5 
66.5 
45 
60 
155.7 
153.5 
Rb 
5.3 
12.9 
16.4 
11.6 
8.2 
Sr 
59.2 
Concentrations of elements are in ppm except for those major elements given in %. 
From the data, it can be inferred that all the samples under study contain the trace 
elements Mn, Fe, Cu, Zn along with K and Ca as the major elements. The spectra of most 
of the samples also show the presence of Ti, Cr and Ni at very low concentration. Table 
1 also shows the presence of high amounts of Mn, an antioxidant rich element, ranging 
between 203 ppm and 1803.3 ppm except in Curcuma domestica where the content is 
24 ppm. But this value is also well within the common values reported elsewhere [20-25] 
for medicinal plants which range between 18 ppm and 700 ppm. Alpinia gaianga contains 
a higher amount of Mn than the common values reported with 1803.3 ppm. An earlier 
analysis of tea leaves [26], reported values between 350 ppm and 900 ppm, concluding 
that tea drinks can provide a rich dietary intake of this metal. Another study [27] also 
reports an anomalous value of Mn reaching upto 2134 ppm in Eucalyptus globules. Among 
all the studied rhizomes, the K content is also highest in A. gaianga. H. marginatum 
contains high concentration of Fe and Zn. As high levels of essential elements such as 
Fe, Mn, Zn and Ca have been demonstrated to influence the retention of toxic elements 
in animals or human beings [28, 29], we carefully searched for certain toxic elements such 
as Pb, As, Hg, Cd, etc. which are of prime interest in toxicological studies [28] but none 
was found in the rhizomes under study. Hence, these rhizomes could be considered safe 
to consume. 
Table 2. Karl Pearson correlation matrix 
Elements 
K 
Ca 
Mn 
Fe 
Cu 
Zr\ 
K 
1.000 
.489 
.757* 
.273 
.894* 
-.409 
Ca 
.489 
1.000 
.451 
.820* 
.327 
.157 
Mn 
.757' 
.452 
1.000 
.443 
.915* 
-.146 
Fe 
.273 
.820* 
.443 
1.000 
.284 
.054 
Cu 
.894* 
.327 
.915* 
.284 
1.000 
-.378 
Zn 
-.409 
.157 
-.146 
.054 
-.378 
1.000 
Marked correlations are significant at p< .05 
Elemental analysis of some antioxidant-rich medicinal Zingiberales etc. 375 
To investigate any kind of correlation between elemental concentrations and dependence 
of these concentrations amongst the studied Zing|>erale$, the Karl Pearson correlation 
matrix was calculated. Based on the correlation mftrix (Table 2), it can be said that Mn 
is positively correlated with other elements except Z|i. Ca and Fe have positive correlation 
with all the other elements. Correlations at statically significant level are observed 
between K and Mn, K and Cu, Ca and Fe and Mrf and Cu. 
From the above discussions, it may be undershiod that the elements K, Ca, Mn, Fe, 
Cu and Zn might have played a significant role in tHe antioxidant property possessed by 
the medicinal Zingiberales. The high content of Mil, Fe, and Zn in these rhizomes may 
again support their effective use in the traditional system of medicine by the local people 
of Manipur. The low incidence of various tumors among the populations in north-east India, 
particularly in Manipur [30], may be linked with the high level consumption of these plant-
based foods rich in high antioxidant elements in routine dietary intake. Further extensive 
investigation on the relationship of organic content and trace elements is in progress, and 
will be reported with better statistics in near future. 
4. Conclusions 
A PIXE investigation was carried out on some members of medicinal Zingiberales. The 
elements K, Ca, Mn, Fe, Cu, Zn Rb and Sr were found to be present in varying 
concentrations. The Karl Pearson correlation matrix of the common elements K, Ca, Mn, 
Fe, Cu and Znwas determined, from which the correlation co-efficient of two particular 
elements was observed. Most of the studied samples are found to contain high amount of 
Mn, Fe and Zn. 
Acknowledgement 
The authors are grateful to the authority and supporting staffs of the Surface and Profile 
measurement Laboratory, CCCM, Hyderabad for providing the PIXE facility and the help 
rendered. 
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J.P/XE3229(1993) 
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N.E. States, Imphal, Axtiap39(2001) 


Elemental Analysis of some Antioxidant-Rich Medicinal Zingiberales of Manipur Using Proton Induced X-Ray Emission (PIXE) Technique

Path, K D

Thool, U S

Mohod, A N

Indian J. Phys. 81 (4) 485-493 (2007) j ^ ^ . 
W 
Analysis of the spacetime singularities arising in higher 
dimensional monopole-Vaidya Collapse 
K D Patil1*, U S Thool2 and A N Mohod3 
'Department of Mathematics, B D College of Engineering, Sewagram, Wardha-442 102, Maharashtra, India 
^Department of Mathematics, Dr Ambedkar College, Chandrapur-442 401, Maharashtra, India 
'Department of Mathematics, S S S K R Innani Mahavidyalay, Karanja-444 105, Washim, Maharashtra, India 
E-mail kishordpatiK'J'yahoo com 
Received 25 January 2006, accepted 13 February 2007 
Abstract : We consider the end state of collapsing null radiation together with monopole field in higher 
dimensional spacetime The condition for the formation of a naked singularity as a result of the collapse has 
been obtained It is found that under certain restriction on the mass function, the collapse leads to a strong 
curvature naked singularity, violating CCH 
Keywords : Cosmic censorship, gravitational collapse, naked singularity, black hole 
PACS Nos. : 04 20 Dw, 04 20 Cv, 04 20 Jb 
1. Introduction 
In the framework of the Einstein Theory of relativity, spacetime singularities can be formed 
by gravitational collapse. If a singularity forms, it is crucial to consider physical phenomena 
around it, whether the singularity is covered by event horizon of the gravity or not. The 
Cosmic Censorship Hypothesis (CCH) [1] states that such singularities will always be 
covered by event horizons and hence can never be visible from the outside. Despite 
several attempts by many researchers, neither general proof nor precise mathematical 
formulation of this hypothesis has been available so far. On the contrary, several 
examples of naked singularities have been found. The examples of naked singularities 
known in spherical collapse arise from various forms of matters. These include dust [2 -
5), radiation [6-10], perfect fluid [11,12], null strange quark fluid [13,14] etc. 
Vaidya solution is one of the most important solution among the above solutions. 
papapetrou [15] first showed that this solution could yield a naked singularity. Since then, 
'Corresponding Author © 2607 IACS 
486 K D Paul, U S Thool and A N Mohod 
this solution is being used to analyse the scenario of gravitational collapse in general 
relativity Wang and Wu [16] generalized the Vaidya solution to a more general case 
which include most of the known solutions to the Einstein field equations, such as 
monopole solution, charged Vaidya solution, Husain solution Later on, Patil et al [17] 
have shown that under certain conditions on mass function, the gravitational collapse of 
generalized Vaidya solutions may yield naked singularities which appear in Vaidya and 
Tolman-bondi spacetimes are of the same nature Various important features such as the 
degree of in-homogeneity of the collapse necessary to produce a naked singularity the 
Cauchy horizon equation, the apparent horizon equation, and the strength of the singularity 
have a mutual correspondence in both metrics [cf 18] Recently, Sijie Gao and Lemos 
[19] have shown that it is possible to match the two solutions in one single spacetime 
the Tolman-Bondi-Vaidya spacetime 
There is a considerable motivation provided in the past few years for considering 
the possibility for the spacetime to have extra dimensions String theory has created the 
interest in higher dimensional spacetimes Although the extra dimension is not directly 
observable, but TeV-scale theory [20,21] suggests that our universe, may have large extra 
dimensions Hence to prove or to disprove cosmic censorship hypothesis, it becomes 
necessary to study the gravitational collapse in the higher dimensions as well In this 
respect many research papers have been appeared on higher dimensional gravitational 
collapse [22-28], which show that either naked singularities or black holes may form in 
higher dimensional collapse depending upon the nature of the initial data 
In the present paper, we discuss the gravitational collapse of null fluid around 
monopole field in the higher dimensional spacetime Our aim is to investigate the 
influence of a monopole field on Vaidya collapse and to study the naked singularities that 
may possibly form in this collapse 
This work is organized as follows In the Section 2, we describe the tive 
dimensional monopole-Vaidya spacetime In Section 3, we discuss the nature of the 
collapse, finally in Section 4 we conclude the paper 
2. Monopole-Vaidya solution in five dimensional spacetime 
Let us consider five dimensional spherically symmetric spacetime described by the metric 
[28,29] 
f 
ds2 = 
\ m(vtr)\ dv2 + 2dvdr + r2(d()? + s\n<iQidO% + s\n2o,$\r)262d02)i (1) 
where v is an advanced Eddington time coordinate, r is the radial coordinate with 
0</•<«>, and m{v,r) is the mass function giving gravitational mass inside the sphere of 
radial coordinate r 
Non-vanishing components of the Einstein tensor for the above metric are given by 
Analysis of the spacetime singularities arising in higher dimensional monopole-Vaidya Collapse 487 
where{x"}=r{v,r,0lt02,03}, (H = 0,1,2,3,4) and( ) and ( ' ) represent partial derivatives with 
respect to v and r respectively 
Combining eq (2) with field equations 
G/» =KT^ . (3) 
we find that the corresponding energy momentum tensfcr can be written in the form 
[16,30] i 
J = 7(n) + T{m), (4} 
where 
and 
^
w )
- ( p + P ) ( / ^ + t ^ ) + P ^ (5) 
Using eqs (2-5), we can write the expressions for <T, p and P as 
3m(v,r) _3/7?'(v,r)
 p_-/rt"(v.O 
"2T71" • P ' ™ 2 K 7 r " ' "~2Kr2 * = ~zhr >  - - o - . ^
 p
- - o . . ; 2 - . (6) 
where />, P are energy density and pressure, while cr is the energy density of the Vaidya 
null radiation 
We have considered null vectors /,,, ^, such that 
m(v,r)~ l**8l'% = l 1- -*:.• 
/,/* = ^ = 0 , /,*?*--1 (7) 
r(nl, can be considered as the component of the matter field that moves along the null 
hyper surface v = constant When p = P = 0, the solutions reduce to the higher 
dimensional Vaidya solution with m = m(v) [31] This fluid in general belongs to the type 
II fluids and the energy conditions for this type of fluids are given by [28-30,32] 
(i) The weak and strong energy condition 
a > 0, p > 0, P > 0 (8) 
(ii) The dominant energy condition 
a > 0, p ^ P > 0, P > 0 (9) 
Following Refs. [16,29], we define the monopole solution in five dimensional spacetime 
gM^ar2, (10) 
where a is an arbitrary positive constant 
Monopoles are formed due to a gauge-symmetry breaking and have many properties 
488 K D Patil, U S Thool and A N Mohod 
of elementary particles Most of their energy is concentrated in a small region near 
monopole core [33] 
Mass function in five dimensional Vaidya space is defined by [31, 34] 
0 v <0 
f(v)= Xv2 0<v<T 
m0 v>T 
where A is a positive constant 
Since the energy momentum tensor is linear in terms of the mass functions, a 
linear superposition of particular solutions is also a solution of the Einstein field equations 
[16] In particular, the combination 
An(v,r) = Ai'2 + ar2, (12) 
would represent the monopole-Vaidya solution in five dimensional spacetime 
For v < 0, the spacetime is higher dimensional monopole solution with f(v) = o 
The radiation is focussed into a central singularity at r = 0, v = 0, of growing mass f(\) 
At v = 7, say, the radiation is turned off For v > 7, the exterior spacetime settles to the 
higher dimensional Schwarzschild field embedded in a monopole field Thus v = 0 to i 
= 7, the metric is monopole-Vaidya, whereas for v > T it is an Schwarzschild-monopole 
spacetime Note that presence of monopole breaks the asymptotic geometry of the 
spacetime 
To investigate the structure of the collapse we need to consider the radial null 
geodesies defined by ds2 = 0 taking 0, = o2 = o3 = 0 into account 
Radial null geodesic equations (taking the null condition KaK^ = 0 into account 
where K*~dx*ldk is the tangent vector of a geodesic) for the metric (1) are 
(13) 
l/C/C' = 0 (14) 
Let 
dIC 
+ 
dk 
l ^ i K r - o , 
dK' ( m mm' mm' 
~dr+\2r*?~2?+~2?r~ 
/ R(v,r) 
( r 
m2) 
' r5 (*?+[?• 2m' ' r3 , 
(15) 
Using the null condition, KaKa = 0 , we get 
Analysis of the spacetime singularities arising in higher dimensional monopole-Vaidya Collapse 489 
where R satisfies the differential equation 
3. Nature of the collapse 
To investigate the nature of the collapse, we follow the rr|Bthod described in Ref [10] 
Roughly speaking naked singularities are singularities that* may be seen by physically 
allowed observer / e outgoing light rays starting from the singularity terminate on the 
singularity in the past. The central shell-focussing singularity (/ e that occurring at r = 0) 
is naked, if the radial null geodesic equation admits one or more positive real roots [35] 
With the choice of the mass function (12), the m«|tnc (1) admits a homothetic 
Killing field given by 
which satisfies the equation 
^ ^ a ^ S o a = 2 0 a * , ( 1 9 ) 
where L denotes the he derivative 
It can be seen that %dKa is constant along radial null geodesies, that is 
£*Ka=vKx +rKr=S, (20) 
where S is constant 
Eq (20), because of the eqs (12), (15) and (16) yields 
* . - * * . (2D 
A X 3 - ( 1 - a ) X + 2 
where we have put X = v/r and is known as a self similarity variable 
To investigate the nature of the singularity we need to consider the radial null 
geodesies defined by cfe2 = 0 
Equation for the radial null geodesies for the metric (1) are given by 
GrV (22) dr \-mjr2 
With the choice of the mass function (12), above equation becomes 
dv
 „ 2 (23) 
* 1-A(v / r ) 2 -a* 
It can be observed that the above differential equation has a singularity at r = 0, v = 0 
For the geodesic tangent to be uniquely defined and to exist at this point, we must 
have [35] 
X0 = lim - «hm — = 2 (24) 
490 K D Pat/I, U S Thool and A N Mohod 
that is 
AX2-(l-a)X0 + 2 = 0. (25) 
The above algebraic equation decides the nature of the singularity. If the above equation 
has a real and positive root, then there is a future directed radial null geodesic originating 
from r = 0, v = 0; in this case, the singularity will be naked. If eq. (25) has no real and 
positive root, then the singularity will be covered and the collapse proceeds to form a 
black hole. 
From the theory of equations, it can be checked that eq. (25) has two real and 
positive roots if 
0<a<1 andO<A< 0-*f 
27 (26) 
Thus if the above condition is satisfied, then the higher dimensional monopole-Vaidya 
collapse leads to a naked singularity, otherwise the collapse ends into a black hole. In 
particular if we choose A = 0.01, a = 0.5 then we get two positive real roots X, = 6.1005 
and X2 = 3.4373. Table 1 shows the positive roots corresponding to different values of 
a and X. 
Table 1. 
and A. 
a 
0.3 
0.5 
0.7 
0.9 
. Roots of the eq (25) corresponding to different values of a 
A 
0.010000 
0.009000 
0.008000 
0.004000 
0.003000 
0.002000 
0.001000 
0.000900 
0.000800 
0.000030 
0.000020 
0.000010 
Positive real roots 
Root X, 
6.1005 
6.6667 
7.2963 
7.8078 
10.0000 
13.2001 
10.0172 
12.4347 
14.0281 
41.6047 
56.9593 
87.8885 
Root X2 
3.4373 
3.3333 
3.2492 
5.0000 
4.5742 
4.3232 
9.9892 
8.5259 
8.0661 
24.3100 
22.1832 
20.9149 
Four dimensional monopole-Vaidya collapse has been discussed in Ret. [17] and it 
has been shown that, the collapse leads to a naked singularity if 
0 < A « £ i '-
8 
(27) 
Analysis of the spacetime singularities arising in higher dimensional monopo/e-Vaidya Collapse 491 
Thus comparison with the analogous 4D case shows that naked singularity occurs for a 
slightly smaller value of the parameter X in 5D. 
Strength of a naked singularity : " 
Strong curvature singularity is regarded as a more serious ^ violation of cosmic censorship 
as compared to a weak one. It is believed that spacetimi cannot be extended through 
a strong singularity, but is possibly extendible through a w^ak one [36]. In Tipler's sense 
[37], singularity is said to be a strong curvature singularity'if collapsing volume elements 
crushed to zero at the singularity. According to Clarke and Krolak criteria [38], a 
singularity is strong curvature type if 
^aB|imfc2/?al/C-/C*>0f (28) 
where Ka is tangent to the radial null geodesic, Rab is the fiicci tensor and k is an affine 
parameter. 
In order to examine the strength of a singularity along radial null geodesies, we 
observe that 
dk~ rdk r2 dk ' ( ' 
Using eqs. (15) and (16), above equation becomes 
From eqs. (15) and (16), we obtain 
<p = lim k2RabK*Kb = lim k2 get 
= 3AX0 lim ' ^ ? (32) 
At the singularity, k -> 0, r -> 0 and X -> a+, where a, is a root of eq. (25). Hence applying 
'^Hospital's rule and using some algebra, we obtain 
"m(Z?)- , - (33) 
*-o[
 f * ' l - A X 0 2 - a 
inserting the above equation into eq. (32), we get 
3AXn ( 3 4 ) 
( l -AX 0 «-a) * 
Thus Clarke and Krolak condition for the strong curvature singularity [38] is satisfied. 
Hence, the naked singularity arising in this spacetime is strong. 
492 K D Patil, U S Thool and A N Mohod 
4. Conclusion 
We have presented the scenario for the gravitational collapse of a monopole field together 
with Vaidya null radiation in higher dimensional spacetime. The possible occurrence of a 
naked singularity has been investigated and it has been shown that at least for a 
particular choice of the parameters, a naked singularity is formed. 
We have estimated the strength of a naked singularity by Clarke and Krolak criteria 
[38] and it is found that these singularities are of strong curvature type. 
Since in the absence of monopole field, spacetime becomes asymptotically flat, one 
can argue that the condition of asymptotically flatness does not play any significant role 
in the formation of the naked singularity. 
Occurrence of a strong curvature singularity in the higher dimensional monopole-
Vaidya spacetime suggests that this solution violates the CCH. 
Similar solutions in four dimensions have been obtained earlier [17] and it has been 
shown that under certain conditions on the mass function m(v%t)y these solutions admit 
naked singularities. In fact, we can find a class of the functions m(v,r) such that 
m(v,r) = Av + F(v, r) 
where F(v,r)/r is a polynomial in r(or in v)t then the only contribution to the condition 
for the existence of the null geodesies emanating from the central singularity is from AW 
the Vaidya mass. However, while choosing the function m(vtr), one has to take the care 
that the energy conditions mentioned in eqs. (8) and (9) should not be violated. The same 
idea of choosing m(v,f) can be extended to higher dimensions as well. 
Acknowledgment 
One of the authors (KDP) would like to thank IUCAA, Pune (India) for kind hospitality 
under Associate-ship program, where part of this work was done. 
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[13] T Harko and K S Cheng Phys. Lett. A266 249 (2000) 
[14] S G Ghosh and N Dadhich Gen. Rel. Grav. 35 359 (2003) 
Analysis of the spacetime singularities ansing in higher dimensional monopole-Vaidya Collapse 493 
(15) A Papapetrou in A Random Walk in Relativity and Cosmology (eds) N Dadhich, J K Rao, J V Narlikar 
and C V Vishveshwara (New York Wiley) p184 (1985) 
[16] An Zhong Wang and Yumei Wu Gen Rel Grav 31 107 (1999) 
[17] K D Patil, R V Saraykar and S H Ghate Pramana-J Phys 52 $53 (1999) 
[18] T Harka Phys Rev D68 064005 (2003) 
[19] Sijie Gao and J P S Lemos Phys Rev D71 084022 (2005) , 
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[21] S B Giddings and S Thomos Phys Rev D65 056010 (2002) * 
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Analysis of the Spacetime Singularities Arising in Higher Dimensional Monopole-Vaidya Collapse

From Editor's Desk

Gogoi, P

Konwar, K

Baishya, B

Indian J. Phys. 81 (5 & 6), 567-572 (2007) 
Effect of copper interlayer on thermally deposited 
polycrystalline Ge-thin film transistors fabricated 
on glass substrates 
P Gogoi*, K Konwar and B Baishya 
Department of Physics, Dibrugarh University, Dibrugarh-786 004, Assam, India 
E-mail: paragjyoti_g(^rediffmail.com 
Received 27 December 2006, accepted 17 May 2007 
Abstract : Here we reported the performance of Ge- thin film transistors (TFTs) with a copper interlayer in 
the channel region. All the TFTs are fabricated in staggered electrode structure on perfectly cleaned glass 
substrates using thermal evaporation process. Rare earth oxide Dy203 is used as gate insulator. The TFTs are 
annealed at 370°C at high vacuum. The TFT exhibits a better mobility of 0.646 cm2V ^ s \ than the TFT, fabricated 
without copper interlayer, mobility of which is found as 1.44 X lO^crrvV's1. The characteristics and some 
electrical parameters of the TFTs with copper interlayer are evaluated and compared with that of TFTs fabricated 
without copper interlayer. 
Keywords : Poly Ge-TFT, copper interlayer, Dy203, mobility. 
PACS Nos. : 73.61 .Cw, 73.40. Qv 
1. Introduction 
In the recent years, TFTs are widely used as driving devices in large area electronics 
circuits. Particularly in active matrix liquid crystal displays (AMLDs), TFTs are used as 
pixel transistors [1]. The passivation of grain boundary states by atomic hydrogen is a 
well-established technique to reduce the grain boundary potential barrier in poly-Si [2]. An 
enlargement of the grain size and a reduction of the barrier height at the grain boundaries 
by means of hydrogen passivation have been investigated in order to improve the carrier 
mobility in poly-Si TFTs [3]. It has been reported that, copper passivation of dislocation in 
polycrystalline silicon reduces the potential barrier height at the grain boundaries [4]. 
* Corresponding Author 
© 2007 IACS 
568 P Gogoi, K Konwar and B Baishya 
Many investigators [5-7] have shown that rare earth oxides play an important role in 
thin film transistors as gate insulators due to their high chemical stability, high dielectric 
constant and high resistivity. 
In this investigation we have reported the performance of poly Ge-TFTs with copper 
interlayer fabricated on glass substrates with Dy203 as gate insulator. Also the 
characteristics of the TFTs with copper interlayer are compared with the TFTs fabricated 
without copper interlayer. 
2. Experimental details 
In this investigation the TFTs were fabricated using thermal evaporation process in high 
vacuum better than 4x10*6 torr. All the TFTs were deposited in staggered electrode structure 
on glass substrates. Aluminium was deposited first as source-drain electrodes. A channel 
of 50-nm lengths was produced with the help of a wire grill, fixed on the mask. A 1055 A 
channel layer was formed between the source-drain gap by deposition of Ge (512 A), Cu 
(23 A) and Ge (520 A) layers in steps. The Ge/Cu/Ge layers are deposited at substrate 
temperature of 250°C with a deposition rate of 0.5 As1. A layer of Dy203 of thickness 
715 A was deposited as gate insulator over the Ge/Cu/Ge layers. Finally, a layer of Al 
was deposited on the oxide layer as gate electrode. The fabricated TFTs were annealed 
in high vacuum at 370°C for 5 to 6 hours. Figure 1 shows a schematic structure of the 
TFT with a copper interlayer. 
Figure 1. Schematic diagram of the staggered electrode structure of the TFT fabricated with a copper 
interlayer. 
Ge- Dy203 TFTs without copper interlayer have also been fabricated with the similar 
procedure as mentioned above. These TFTs are also annealed to a temperature of 370°C 
for 5 to 6 hours. 
The film thicknesses were measured by multiple beam interference method. The gate 
capacitance was measured using auto computer LCR sortester (APLAB, Model 4912). 
The drain current, drain voltage and gate voltage were measured using the digital 
nanoammeters and digital multimeters. 
Effect of copper interlayer on thermally deposited polycrystalline etc 569 
3. Results and discussions 
3.1. Electrical characteristics of the TFTs . 
Well-modulated drain current (ld) vs. drain voltage%(Vy characteristics of the TFTs, with a 
copper interlayer with constant gate voltages (Vg) hjave been observed which are shown in 
Figure 2. Figure 3 shows the typical drain currer^ (/^ vs gate voltage (Vg) curve for the 
TFT at drain voltage Vd= 8V. 
1 2 3 4 5 6 7 8 
Drain voltage (V<y) in volt 
Figure 2. Id - Vd curves of the TFTs with copper 
interlayer 
-1 -3 -5 -7 -9 -11 
Gate voltage (VK) in volt 
-13 
Figure 3. Id - Vg curves of the TFTs with copper 
interlayer. The inset shows variation of //d at 
different Vn 
The transconductance (gm) of the devices is estimated from the eq. (1) given by [8] 
dl
" -u r V« 
9 Jvd=consL 
0) 
where C^ is the gate capacitance per unit area, / is the channel length, Vd is the drain 
voltage and MFET i s t h e f i e l d e f f e c t mob i l i ty-
The electrical parameters of TFTs can be calculated using the following expressions: 
output drain resistance 
r -£& 
°
 H
 Vg=const 
(2) 
amplification factor 
» = 9m*rd (3) 
570 P Gogoi, K Konwarand B Baishya 
and gain-bandwidth (G.BW) product 
GBw = 
2nC„ (4) 
From eq. (1), the mobility iifB1 can be estimated. The calculated values of output 
drain resistance (r^), transconductance {gj, amplification factor (n ), mobility fiFET and 
the gain-bandwidth product (G.BW) of the TFTs are presented in Table 1. 
3.2. Comparison with TFTs fabricated without copper interlayer: 
The characteristics and the calculated parameters of the TFTs fabricated with copper 
interlayer are compared with that of the TFTs fabricated without copper interlayer. The 
drain current (/^ vs. drain voltage ( i y characteristics of the TFTs, without copper interlayer 
are shown in Figure 4. It is apparent from Figures 2 and 4 that the family of drain current 
of the TFTs with copper interlayer exhibits higher drain current than the TFTs without 
copper interlayer. This is due to their higher mobility and lower threshold voltage (VT). 
0 12 
51 
1 
6 3 
o 
c 
D
ra
i 
0.12 
0.1 -
0.08 
0.06 
0.04 
0.02 
0 i 
C 
~ *• 
) 1 2 
Drain 
^ 
3 
" " 
4 
— 
5 
voltage (Vd) 
~ 
6 
in 
7 
volt 
"3* 
-jyi 
jyl 
^2yl 
y^ovl 
8 9 
Gate voltage (Vg) in volt 
Figure 4. Id - Vd curves of the TFTs without copper 
interlayer. 
Figure 5. Id - Vg curves of the TFTs without 
copper interlayer. The inset shows variation of 
V/d at different Vg 
Figure 5 shows the drain current (/^ vs. gate voltage (V') curve at drain voltage Vd= 
8V for the TFT without copper interlayer. The threshold voltage (VT) of the TFTs with 
copper interlayer and without interlayer have been evaluated by plotting <ld vs. gate voltage 
(Vy at constant drain voltage (Vd), which are shown in the inset of Figures 3 and 5 
respectively. In the inset of Figures 3 and 5, a straight line is drawn through the linear 
region of the vfd vs. gate voltage (Vy curves. From the intercepts with the horizontal axis, 
the threshold voltages (VT) of the TFTs with copper interlayer and without copper interlayer 
are determined and these are noted as 3V and 6.4V respectively. The estimated values of 
Effect of copper interlayer on thermally deposited potycrystalline etc 571 
the electrical parameters of the TFTs without copper interlayer are also presented in Tablel. 
Using eq. (1), the mobilities are estimated and fqund as 0.646 cmV1s1 for TFTs with 
copper interlayer and 0.4x10*3 for TFTs without cop|>er interlayer. The enhance mobility of 
the TFTs with copper interlayer can be explained a|s follows. In this investigation we may 
say that, during the heat treatment, the grain bot|idary states in the case of poly- Ge 
TFTs are passivated by copper in Ge. During the passivation, copper atom diffuses along 
the grain boundaries and completes some of t&e opened bonds (dangling bonds). 
Consequently the interface states density drops anjb the potential barrier is lowered. The 
resulting effect is that the poly-Ge electrically progresses towards single crystal Ge 
characteristics, yielding higher mobility. 
The gain-bandwidth products of the devices are found very low. The gain- bandwidth 
product depends on mobility and is a function of the channel length. Improvement in the 
gain-bandwidth product can be accomplished by reducing the channel length. An attempt 
to use too small a channel length will give trouble if the resulting gap region is not 
sharply defined. Hence to get the high value of gain-bandwidth product, the mobility of 
the carrier must be increased [8]. In this investigation, the TFTs exhibit low mobility, 
hence the devices exhibit low gain-bandwidth product. 
Table 1 . Comparison of some parameters of the TFTs with copper interlayer and without copper interlayer. 
Type of Output resistance Transconductance Amplification Mobility Gain bandwidth 
TFTs rd gm factor n nFET product G.Bw 
(ohm) (mho) (cm2V V 1 ) (KHz) 
with Copper 0.125 X 106 3.86 X 10"6 0.49 0.646 1.31 X 10'2 
interlayer 
without 
copper 89.29 X 106 0.0083 X 10'6 0.70 1.44 X 10"3 29.35 X10'2 
interlayer 
4. Conclusion 
TFTs with copper interlayer exhibit a higher mobility than the TFTs without copper interlayer. 
It is observed that the threshold voltage (Vr) is significantly improved in case of TFTs with 
copper interlayer. The other electrical properties such as output resistance (rd) and 
transconductance (gfm) are also found better in case of TFTs with copper interlayer, but 
amplification factors (11) are comparable for both types of TFTs. From this observation it 
may also be concluded that the rare earth oxide Dy203 can be used as a dielectric layer 
in TFTs. 
Acknowledgment 
Authors P Gogoi and K Konwar are grateful to the Govt, of Assam for financial 
assistance. 
572 P Gogoi, K Konwarand B Baishya 
References 
[1] A W Wang and K C Saraswat IEEE Transaction on Electron Devices 47 5 1035 (2000) 
[2] C H Seager and D S Ginley J. Appl. Phys. 52 1005 (1981) 
[3] S D S Malhi, H Shichijo, S K Banerjee, R Sundaresan, M Elahy, G P Polack, W F Richardson, A H 
Shah, L R Hite, R H Womack, P K Chatterjee and H Wailam IEEE Transaction on Electron Devices 
32 2 258 (1985) 
[4] J G Lee and S R Morrison J. Appl. Phys. 64 6679 (1988) 
[5] P K Deka and B Baishya Thin Solid Films 112 L5 (1984) 
[6] P Singh and B Baishya Thin Solid Films 141 179 (1986) 
[7] P Singh and B Baishya Thin Solid Films 47 25 (1987) 
(8] P K Weimer Phys. Thin Films (Eds) G Hass and R E Thun 2 149 (1964) 


Effect of Copper Interlayer on Thermally Deposited Polycrystalline Ge-Thin Film Transistors Fabricated on Glass Substrates

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