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Hall mobility and field effect mobility studies on PbTe HWE thin films
Applications of Surface Science 22/23 (1985) 731-736 North-Holland, Amsterdam
HALL
MOBILITY
AND FIELD EFFECT
731
MOBILITY
STUDIES ON PbTe
HWE THIN FILMS P.R. VAYA,
J. M A J H I
*, B . S . V . G O P A L A M
*
a n d C. D A T I ' A T R E Y A N
Centre for Systems and Devices, Indian Institute of Technology, Madras-600 036, India Received 27 August 1984; accepted for publication 12 November 1984
Hall mobility (,ttH) and field effect mobility (P,FE) studies were carried out on PbTe films of different thickness grown on KCI (100) substrates by the hot wall epitaxy (HWE) technique. The Hall mobility was obtained using the standard Van der Pauw technique. The diffused scattering mobility, /ttD, due to size effect was calculated and compared with /ZH. A large discrepancy between /xu and /z o was explained on the basis of a residual mobility contribution which was attributed to the scattering due to grain boundaries, dislocations, cleavage steps and other surface effects. For AC field effect studies an MIS structure with a thin mica spacer between the film surface and metal electrode was used. The field effect mobility, #FE, was obtained at different temperatures from 98 to 156K in the frequency range of 40 to 200kHz. The variation of /-tFE with frequency was found to be largely due to the relaxation of fast surface states having time constants from 1.84 to 0.96 ~s in the above temperature range. The activation energy and capture cross-section of these surface states were calculated to be 0.02eV and 10-19 cm 2 respectively. Unlike the Hall mobility, the effective DC field effect mobility derived from the experimental results was found to be independent of film thickness.
1. Introduction The lead chalcogens have been the subject of considerable attention over t h e p a s t t w e n t y y e a r s o w i n g t o t h e i r t e c h n o l o g i c a l i m p o r t a n c e in t h e i n f r a r e d field [1]. T h e e p i t a x i a l g r o w t h t e c h n i q u e s p r o v i d e a n a s s u r e d m e a n s o f p r e p a r i n g s p e c i m e n s f o r r e l i a b l e s u r f a c e t r a n s p o r t a n d field e f f e c t m e a s u r e m e n t s . T h i n e p i t a x i a l films a r e p r e f e r r e d in m a n y a r e a s f o r d i f f e r e n t a p p l i c a t i o n s a n d in f u n d a m e n t a l r e s e a r c h t o f u r t h e r o u r u n d e r s t a n d i n g o f electronic band structure and conduction phenomena in s e m i c o n d u c t o r s . T h e g r o w t h o f e p i t a x i a l films o f P b T e o n KC1 ( 1 0 0 ) s u b s t r a t e s u s e d in t h i s work has been reported by Vaya and Ramachandran [2,3]. T h e p r e s e n t s t u d y is c o n c e r n e d w i t h t h e t h i c k n e s s d e p e n d e n c e s o f H a l l m o b i l i t y a n d field e f f e c t m o b i l i t y in P b T e f i l m s g r o w n b y H W E t e c h n i q u e s . * Department of Physics, Indian Institute of Technology, Madras-600 036, India. 0378-5963/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
P.R. Vaya et al. / PbTe HWU. thin films
732
2. H a l l m e a s u r e m e n t s
To study the effect of film thickness on Hall mobility, sixteen samples of different thickness were grown on KCI substrates by the H W E technique as described by Ramachandran and Vaya [3] and Lopez Otero [4]. Since the Van der Pauw method gives unambiguous results of electrical measurements on films grown on insulating substrates, this method was used for the measurements of resistivity (p) and Hall constant (Rn) in the temperature range of 77 to 300 K. All the samples were found to be n-type by the hot-probe technique as well as by the sign of the Hall voltage. R H was found to be practically constant in this temperature range indicating the extrinsic nature of PbTe films with carrier concentrations of the order of 10~cm 2 The Hall mobility, #H, obtained from the product of R n and 1/p, was found to decrease with temperature, but none of the samples followed the T s/2 law. The value of the exponent varied from 1.5 to 2.3 with film thickness ranging from (1.5 to 5 #m. It was also observed that the rate of increase of /~H with decreasing temperature becomes slower as the thickness of the film decreases. This shows that the contribution of the surface dependent scattering process (diffused scattering) in limiting the mobility is more significant for thinner films. The diffused mobility, /.ZD, depends on film thickness as follows: /z tZD = 1 + (3/27r)~/2A/d '
(1)
where A is the mean free path of carriers and d is the film thickness. #D was calculated for various thicknesses at different temperatures. Fig. 1 shows a plot of /z D versus d at different temperatures along with the corresponding experimental Hall mobility. The curves coincide at the higher thickness (>5/~m) but deviate at lower thickness. This indicates that some other factors are also contributing to the mobility apart from the diffused scattering. To quantify this deviation, the size effect or diffused mobility was subtracted from the experimental mobility data using the relation: 1 /'Z exp
-
I #D
q
1
(2)
~l'Lr
where #r is the residual mobility. The variation of log #r with film thickness is linear up to 5 # m are shown in fig. 2. For thicker films ( > 5 / , m ) . as #e,p approaches P'D, /Xr tends to infinity and hence the effect of p.~ becomes negligible. A detailed study o f / z r variation with temperature, T, leads to the following empirical fit: # ~ - #~,(d)
T -'(d) ,
(3)
P.R. Vaya et al. / PbTe H W E thin films
733
50 -...0..--....0-- E x p e r i m e n t c t l . . . .
Calcu
Io, t e d 75½
40
J / /
/ /
J
f
f
t
/
•
/ /
/
/
/i/
~o 30
/
/
// E u
"/_
~5 2O o
lz
E /
//
I
10
0
/
/
_ /
/
I ~
I 2
I I 3 4 Thickness (~um)
I 5
1 6
I 7
I
Fig. 1. Thickness d e p e n d e n c e of the (calculated) Hall mobility of thin PbTe films together with the corresponding experimental data, at constant temperatures.
where /~,0(d) and n(d) are thickness-dependent terms. This study also reveals that the effect of [£r is more predominant in the case of thin films. # , can be thought of as an overall scattering due to grain boundary potential, dislocations, defects, cleavage steps, and surface defects which limit the carrier mobility. At lower thicknesses these scattering effects restrict the free m o v e m e n t of carriers to a sizeable extent and consequently reduce the carrier mobility in the film.
734
P.R. Vaya et al. / PbTe H W E thin fihns
125
bq 1
> ~
5 10 f
/
200K
/ /
."2_
/
0
E
-s
-o 104
0
1
2
3
4
5
6
7
Thickness ()3m) Fig. 2. T h i c k n e s s d e p e n d e n c e of residual mobility al constant temperatures.
3. Field effect measurement To study the mobility of the charge carriers on the free surface of these PbTe epitaxial films, an A C field effect technique was employed. The MIS structure used was obtained by placing freshly cleaved thin mica between the gold-plated gate electrode and the film surface. The ohmic contacts were made at the two ends of the film cut into a rectangular shape ( 1 0 m m × 5 mm). A small transverse A C signal (100 mV) was applied between the gate electrode and the surface. Changes in surface conductance of the film were measured and, hence, the field effect mobility, # w , which is defined as the
P.R. Vaya et al. / PbTe H W E thin films
735
ratio of change in conductance to charge induced on the surface, was obtained. The details of the experimental setup are given by Vaya [2] and Vaya et al. [5]. The field effect mobility was studied as a function of temperature and frequency. The field effect signal was found to be appreciable only in the higher frequency range (40-200 kHz) and low temperature (98-156 K), indicating the effectiveness of only fast surface states. Fig. 3 shows the variation of ~ with frequency at different temperatures in a typical film (sample 2). Following Garrette's theory [6] of frequency dependence of ~ E , the relaxation time, r, of these states was estimated and found to vary from 1.84 to 0.96/.~s in this temperature range. Using Rupprecht's relation [7] for temperature dependence of r, the activation energy E T and capture cross-section of these surface states were estimated to be 0.02 eV and 10 19 c m 2 respectively. From the magnitude of energy level and capture cross-section, the surface states encountered in this temperature range seem to be shallow and of repulsive type. The effective DC field effect mobility, ~DC, was obtained by extrapolating the curve in fig. 3 to low frequency regions ( f ~ 0). 32 o------
28
It3 K
% 2z~
E
98K
o----- 103 K
123 K
20
o---'- 132 K
16
1/-.,8 K ,,-----156 K
140 K
v
0
E •~
t2
',7
Oi
40
I
I
I
I
60
BO
I00
120
l
140
I
l
I
160
180
200
Ff e q u ~ n c y ( k Hz )
Fig. 3. Frequency dependence of field effect mobility at different temperatures.
P.R. Vaya et al. / PbTe H W F thin films
736
Table 1 V a l u e s of r, ET, IXn and /XDC at 9N K for three s a m p l e s of different t h i c k n e s s S a m p l e No.
Thickness (#m)
Carrier concentration
/xH (cm2/V • s)
#D~ (cm2/V • s)
~" (10 "s)
t:" (cV)
2300 4800 741)0
400() 5500 451111
1.91 1.,X4 1.79
(L01N 0.020 0.l)19
(cm 3) 1 2 3
1.0 1.5 ___.11
1.5 × Ill ~s 6.6 × l0 w g.(t x I() j7
These measurements were repeated on three samples of thickness ranging from 1 to 2/,,m. No measurable field effect signal could be obtained for films having a thickness greater than 2 / , m due to the very low resistance of the films. The thickness dependence of #De" r, and E f is given in table I along with Hall mobility data.
4. Discussion
The residual mobility, #r, is highly sensitive to defects and also the film thickness, whereas the field effect mobility, #rE, depends directly on the active states on the surface. Therefore a direct comparison of /*De and #H would be misleading as /*DC is the mobility of carriers confined to the surface space charge layer which, in the present case, is very small compared to the film thickness, and hence depends mainly on the surface scattering mechanisms such as surface condition, surface phonons, ionized impurities on the surface and potential fluctuations within the surface layers under the influence of an external gate field. On the other hand, P'H depends predominantly on the lattice scattering in the bulk and the diffused scattering at the surface. Hence the properties of the initially grown layer of film are exhibited by /-tFE, while those of the total thickness are given by the Hall mobility, #H-
References I1] [2] [3] [4] [5] [6] [71
J.N. Z e m e l , Solid State Surface Sci. 1 (1969) 291. P.R. Vaya, P h D Thesis, Indian I n s t i t u t e of T e c h n o l o g y , M a d r a s (1984). V. R a m a c h a n d r a n a n d P.R. Vaya, J. A p p l . Phys. 54 (1983) 5358. A. L o p e z O t e r o , Thin Solid Films 49 (1978) 3. P.R. Vaya, V. R a m a c h a n d r a n a n d J. M a j h i , Solid State E l e c t r o n . 27 (1984) 553. C.G.B. G a r r e t t , Phys. Rev. 1(17 (1957) 478. G. R u p p r e c h t , J. Phys. C h e m . Solids 14 11960) 208.
HALL
MOBILITY
AND FIELD EFFECT
731
MOBILITY
STUDIES ON PbTe
HWE THIN FILMS P.R. VAYA,
J. M A J H I
*, B . S . V . G O P A L A M
*
a n d C. D A T I ' A T R E Y A N
Centre for Systems and Devices, Indian Institute of Technology, Madras-600 036, India Received 27 August 1984; accepted for publication 12 November 1984
Hall mobility (,ttH) and field effect mobility (P,FE) studies were carried out on PbTe films of different thickness grown on KCI (100) substrates by the hot wall epitaxy (HWE) technique. The Hall mobility was obtained using the standard Van der Pauw technique. The diffused scattering mobility, /ttD, due to size effect was calculated and compared with /ZH. A large discrepancy between /xu and /z o was explained on the basis of a residual mobility contribution which was attributed to the scattering due to grain boundaries, dislocations, cleavage steps and other surface effects. For AC field effect studies an MIS structure with a thin mica spacer between the film surface and metal electrode was used. The field effect mobility, #FE, was obtained at different temperatures from 98 to 156K in the frequency range of 40 to 200kHz. The variation of /-tFE with frequency was found to be largely due to the relaxation of fast surface states having time constants from 1.84 to 0.96 ~s in the above temperature range. The activation energy and capture cross-section of these surface states were calculated to be 0.02eV and 10-19 cm 2 respectively. Unlike the Hall mobility, the effective DC field effect mobility derived from the experimental results was found to be independent of film thickness.
1. Introduction The lead chalcogens have been the subject of considerable attention over t h e p a s t t w e n t y y e a r s o w i n g t o t h e i r t e c h n o l o g i c a l i m p o r t a n c e in t h e i n f r a r e d field [1]. T h e e p i t a x i a l g r o w t h t e c h n i q u e s p r o v i d e a n a s s u r e d m e a n s o f p r e p a r i n g s p e c i m e n s f o r r e l i a b l e s u r f a c e t r a n s p o r t a n d field e f f e c t m e a s u r e m e n t s . T h i n e p i t a x i a l films a r e p r e f e r r e d in m a n y a r e a s f o r d i f f e r e n t a p p l i c a t i o n s a n d in f u n d a m e n t a l r e s e a r c h t o f u r t h e r o u r u n d e r s t a n d i n g o f electronic band structure and conduction phenomena in s e m i c o n d u c t o r s . T h e g r o w t h o f e p i t a x i a l films o f P b T e o n KC1 ( 1 0 0 ) s u b s t r a t e s u s e d in t h i s work has been reported by Vaya and Ramachandran [2,3]. T h e p r e s e n t s t u d y is c o n c e r n e d w i t h t h e t h i c k n e s s d e p e n d e n c e s o f H a l l m o b i l i t y a n d field e f f e c t m o b i l i t y in P b T e f i l m s g r o w n b y H W E t e c h n i q u e s . * Department of Physics, Indian Institute of Technology, Madras-600 036, India. 0378-5963/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
P.R. Vaya et al. / PbTe HWU. thin films
732
2. H a l l m e a s u r e m e n t s
To study the effect of film thickness on Hall mobility, sixteen samples of different thickness were grown on KCI substrates by the H W E technique as described by Ramachandran and Vaya [3] and Lopez Otero [4]. Since the Van der Pauw method gives unambiguous results of electrical measurements on films grown on insulating substrates, this method was used for the measurements of resistivity (p) and Hall constant (Rn) in the temperature range of 77 to 300 K. All the samples were found to be n-type by the hot-probe technique as well as by the sign of the Hall voltage. R H was found to be practically constant in this temperature range indicating the extrinsic nature of PbTe films with carrier concentrations of the order of 10~cm 2 The Hall mobility, #H, obtained from the product of R n and 1/p, was found to decrease with temperature, but none of the samples followed the T s/2 law. The value of the exponent varied from 1.5 to 2.3 with film thickness ranging from (1.5 to 5 #m. It was also observed that the rate of increase of /~H with decreasing temperature becomes slower as the thickness of the film decreases. This shows that the contribution of the surface dependent scattering process (diffused scattering) in limiting the mobility is more significant for thinner films. The diffused mobility, /.ZD, depends on film thickness as follows: /z tZD = 1 + (3/27r)~/2A/d '
(1)
where A is the mean free path of carriers and d is the film thickness. #D was calculated for various thicknesses at different temperatures. Fig. 1 shows a plot of /z D versus d at different temperatures along with the corresponding experimental Hall mobility. The curves coincide at the higher thickness (>5/~m) but deviate at lower thickness. This indicates that some other factors are also contributing to the mobility apart from the diffused scattering. To quantify this deviation, the size effect or diffused mobility was subtracted from the experimental mobility data using the relation: 1 /'Z exp
-
I #D
q
1
(2)
~l'Lr
where #r is the residual mobility. The variation of log #r with film thickness is linear up to 5 # m are shown in fig. 2. For thicker films ( > 5 / , m ) . as #e,p approaches P'D, /Xr tends to infinity and hence the effect of p.~ becomes negligible. A detailed study o f / z r variation with temperature, T, leads to the following empirical fit: # ~ - #~,(d)
T -'(d) ,
(3)
P.R. Vaya et al. / PbTe H W E thin films
733
50 -...0..--....0-- E x p e r i m e n t c t l . . . .
Calcu
Io, t e d 75½
40
J / /
/ /
J
f
f
t
/
•
/ /
/
/
/i/
~o 30
/
/
// E u
"/_
~5 2O o
lz
E /
//
I
10
0
/
/
_ /
/
I ~
I 2
I I 3 4 Thickness (~um)
I 5
1 6
I 7
I
Fig. 1. Thickness d e p e n d e n c e of the (calculated) Hall mobility of thin PbTe films together with the corresponding experimental data, at constant temperatures.
where /~,0(d) and n(d) are thickness-dependent terms. This study also reveals that the effect of [£r is more predominant in the case of thin films. # , can be thought of as an overall scattering due to grain boundary potential, dislocations, defects, cleavage steps, and surface defects which limit the carrier mobility. At lower thicknesses these scattering effects restrict the free m o v e m e n t of carriers to a sizeable extent and consequently reduce the carrier mobility in the film.
734
P.R. Vaya et al. / PbTe H W E thin fihns
125
bq 1
> ~
5 10 f
/
200K
/ /
."2_
/
0
E
-s
-o 104
0
1
2
3
4
5
6
7
Thickness ()3m) Fig. 2. T h i c k n e s s d e p e n d e n c e of residual mobility al constant temperatures.
3. Field effect measurement To study the mobility of the charge carriers on the free surface of these PbTe epitaxial films, an A C field effect technique was employed. The MIS structure used was obtained by placing freshly cleaved thin mica between the gold-plated gate electrode and the film surface. The ohmic contacts were made at the two ends of the film cut into a rectangular shape ( 1 0 m m × 5 mm). A small transverse A C signal (100 mV) was applied between the gate electrode and the surface. Changes in surface conductance of the film were measured and, hence, the field effect mobility, # w , which is defined as the
P.R. Vaya et al. / PbTe H W E thin films
735
ratio of change in conductance to charge induced on the surface, was obtained. The details of the experimental setup are given by Vaya [2] and Vaya et al. [5]. The field effect mobility was studied as a function of temperature and frequency. The field effect signal was found to be appreciable only in the higher frequency range (40-200 kHz) and low temperature (98-156 K), indicating the effectiveness of only fast surface states. Fig. 3 shows the variation of ~ with frequency at different temperatures in a typical film (sample 2). Following Garrette's theory [6] of frequency dependence of ~ E , the relaxation time, r, of these states was estimated and found to vary from 1.84 to 0.96/.~s in this temperature range. Using Rupprecht's relation [7] for temperature dependence of r, the activation energy E T and capture cross-section of these surface states were estimated to be 0.02 eV and 10 19 c m 2 respectively. From the magnitude of energy level and capture cross-section, the surface states encountered in this temperature range seem to be shallow and of repulsive type. The effective DC field effect mobility, ~DC, was obtained by extrapolating the curve in fig. 3 to low frequency regions ( f ~ 0). 32 o------
28
It3 K
% 2z~
E
98K
o----- 103 K
123 K
20
o---'- 132 K
16
1/-.,8 K ,,-----156 K
140 K
v
0
E •~
t2
',7
Oi
40
I
I
I
I
60
BO
I00
120
l
140
I
l
I
160
180
200
Ff e q u ~ n c y ( k Hz )
Fig. 3. Frequency dependence of field effect mobility at different temperatures.
P.R. Vaya et al. / PbTe H W F thin films
736
Table 1 V a l u e s of r, ET, IXn and /XDC at 9N K for three s a m p l e s of different t h i c k n e s s S a m p l e No.
Thickness (#m)
Carrier concentration
/xH (cm2/V • s)
#D~ (cm2/V • s)
~" (10 "s)
t:" (cV)
2300 4800 741)0
400() 5500 451111
1.91 1.,X4 1.79
(L01N 0.020 0.l)19
(cm 3) 1 2 3
1.0 1.5 ___.11
1.5 × Ill ~s 6.6 × l0 w g.(t x I() j7
These measurements were repeated on three samples of thickness ranging from 1 to 2/,,m. No measurable field effect signal could be obtained for films having a thickness greater than 2 / , m due to the very low resistance of the films. The thickness dependence of #De" r, and E f is given in table I along with Hall mobility data.
4. Discussion
The residual mobility, #r, is highly sensitive to defects and also the film thickness, whereas the field effect mobility, #rE, depends directly on the active states on the surface. Therefore a direct comparison of /*De and #H would be misleading as /*DC is the mobility of carriers confined to the surface space charge layer which, in the present case, is very small compared to the film thickness, and hence depends mainly on the surface scattering mechanisms such as surface condition, surface phonons, ionized impurities on the surface and potential fluctuations within the surface layers under the influence of an external gate field. On the other hand, P'H depends predominantly on the lattice scattering in the bulk and the diffused scattering at the surface. Hence the properties of the initially grown layer of film are exhibited by /-tFE, while those of the total thickness are given by the Hall mobility, #H-
References I1] [2] [3] [4] [5] [6] [71
J.N. Z e m e l , Solid State Surface Sci. 1 (1969) 291. P.R. Vaya, P h D Thesis, Indian I n s t i t u t e of T e c h n o l o g y , M a d r a s (1984). V. R a m a c h a n d r a n a n d P.R. Vaya, J. A p p l . Phys. 54 (1983) 5358. A. L o p e z O t e r o , Thin Solid Films 49 (1978) 3. P.R. Vaya, V. R a m a c h a n d r a n a n d J. M a j h i , Solid State E l e c t r o n . 27 (1984) 553. C.G.B. G a r r e t t , Phys. Rev. 1(17 (1957) 478. G. R u p p r e c h t , J. Phys. C h e m . Solids 14 11960) 208.