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A simple method for the determination of impurity concentrations and profiles in semiconductors
710
NOTES
Acknowledgements--The authors wish to acknowledge A. AVAK1AN and D. GOLDSTEIN for their constant encouragement throughout the development of the study summarized in this paper. They also wish to thank J. DIMAURO for hFE-temperature and junction leakage measurements and A. CAPABIANCOfor lifetime and total base dope measurements.
7. A. G. CHYNO\VETHand G. L. PEARSON,J. appl. Picvs. 29, 1103 (1958). 8. A. H. COTTRELL, in Dislocations and Plastic Flow in Crystals. Oxford University Press, London (1953). 9. W. L. KAUFMAN and A. A. BERGH, IEEE Trans. Electron Devices ED-16, 394 (1969).
Sylvania Electric l~roducts Inc. 1O0 Syh,an Road lVoburn Mass., U . S . A .
Solid-State Electronics Pergamon Press 1970. Vol. 13,
P. C. PAREKH E. GAVEL
pp. 710-713.
A s i m p l e m e t h o d for the d e t e r m i n a t i o n o f i m p u r i t y c o n c e n t r a t i o n s a n d profiles in semiconductors
and G.T. and E. Research Laboratories 100 Sylvan Road Woburn Mass., U . S . A .
Printed in Great Britain
V. LYN
(Received 16 October 1969; in revised form 5 December 1969) INTRODUCTION IMPURITY concentrations, profiles and concentra-
References 1. J. M. FAIRFIELDand G. H. SCHWUT'FKE,3. electrochem Soc. 115, 415 (1968). 2. G. H. PLANTINGA, ] E E E Trans. Electron Devices ED-16, 394 (1969). 3. E. SmTL and A. ADLER, Z. :~letall. 52, 529 (1961). 4. P. C. PAREKH and D. M. GOLDSTEIN, Proe. IEEE (to be published). 5. J. P. DE'CosTERD, D. CHAUNG and K. HUB_',m_'R,J. electrochem. Soc. 115, 781 (1968). 6. M. L. JosHI and F. WILHELM, J. electrochem. Soc. 112, 185 (1965).
,
tion fluctuations are i m p o r t a n t properties of s e m i c o n d u c t o r crystals and t h i n films, used for the fabrication of devices. T h e m e a s u r e m e n t of the capacitance of evaporated Schottky contacts is one of the most f r e q u e n t l y used and most exact means of obtaining these data. But the p r o c e d u r e is t i m e c o n s u m i n g , since in most cases the s e m i c o n d u c t o r m u s t be etched s t e p - b y - s t c p and the contacts m u s t be evaporated in high vacuum.
To recorder ( y - oxis)
Vectorvoitrnefer
Iv4,1~,I a4,~
Test frequenc~ so hic.h thGt QJ C O ode >~-. GD,c ~e
~ ~ (~l~z~8= 9 0 a
t /'D;cd6 = QJCD tee " V2 ode
ond
E
!f
I/8= /:,od~ /?Z R:<- I/cJCB:~e
then /q ~
C-
=.~,
~ / ~ = 5oj2
2 Metaltip i
Semiconductor sampe
FIc. 1. Experimental setup for measuring the current through a metal-semiconductor tip contact.
711
NOTES T h e step-by-step etching process can be replaced by a small angle bevelling ( < 5 °) and the evaporated Schottky barrier diode can be replaced by a metal contact to the semiconductor, since it is known that a metal tip set on a semiconductor surface will give diode-like current-voltage characteristics. Both of these modifications reduce the time and effort required to characterize a sample. MEASURING
PROCEDURE
A sliding metal tip (tip radius ~ 1 0 t ~ m ; tungsten, rhodium-plated) is used to measure the capacitance of a semiconductor sample, and thus to determine its doping concentration. Figure 1 shows the measuring setup schematically: Metal tip and semiconductor are each part of the inner conductor of a coaxial line and can be mechanically moved relative to each other. T h e movement of the tip is coupled with the movement of a poteniometer brush. T h e potential at the brush contact serves as a measure for the location of the tip relative to the semiconductor. A high signal frequency is chosen so that the current through the diode (metal point on semiconductor) is purely capacitive (cf. Fig. 1): /diode ~
difference Aq0ABbetween v A and v~ were measured with a Hewlett-Packard vector voltmeter. T h e phase difference was found to be close to 90 ° at frequencies above 100 MHz, thus verifying the assumption wCdioae >~ Gdiod e. RESULTS
The relation between voltage v B and impurity concentration N was investigated with four gallium arsenide samples of different but known impurity concentrations. For this purpose the four samples were soldered onto the inner conductor of the coaxial line and lapped, polished and etched simultaneously. This leads to a planar surface and to a constant pressure of the tip against all four samples. T h e test diagram shows (Fig. 2) that a relation v B ~ N 1'4 (4) holds. Schottky theory gives Cs ~
N 1/2.
(5)
E
,?
L°C'Udiode
E o
o x
o
= ¢oC(VA--~'B).
At the load resistance, measured as VB =
RE,
the voltage
/ d i o d e " RL"
vB
is
8 o
(1)
2.
°
o
If R L
<
1/oJC,
then VB ~
VA,
I i
and iaiod e = ~ o C v A.
(2)
Inserting equation (2) into equation (1) then yields Z'B = ogCVARL, or
v B = const . C.
(3)
T h e voltage v B is proportional to the capacitance C. During the measurements described here, o~/2~r = 250 MHz, v a = 30 mV, v B < 1 mV and R r . = 50 .Q. T h e voltages v A and v B and the phase
,/N,
I 2
,_
arbit"rory units ( log )
FIG. 2. Relation between impurity concentration of four gallium arsenide samples and current through the metalsemiconductor tip contact (v~ = voltage at load resistance proportional to current through contact). T h e discrepancy between the observed dependence of capacitance on impurity concentration and the expected one can be explained, if allowance is made for series or parallel capacitances due to interface layers between metal and semiconductor and due to stray effects. T h e dependence of a total
712
NOTES gallium solutions. T h e impurity concentrations mentioned above were obtained from independent measurements on evaporated Schottky contacts. I n Fig. 4 the d.c. voltage equivalent to the a.c. voltage v B is plotted by means of a recorder. T h i s voltage is measured when the tip slides along the
C2
Cr+Cz
~~~_
c~
~
c,
c~
i J c,
cs
j
f : 200 MHZ Ya ~: 30mV Bevelling ongle 5 ° E
,/N(log)
CT
FIG, 3. Dependence of the t o t a l c a p a c t t a n c e impurity
concentration
l~, if
is a c o m b i n a t i o n
CT Oil of a
Schottky capacitance Cs with stray and series capacitances C1, C2 which are independent of N.
2 ,8~'0 : 2
5 ~10 7!
2
Ii
%
capacitance C r on impurity concentration N is shown in Fig. 3 for three simple cases: (1) Schottky capacitance C s in series with a capacitance C 1 which is independent of N ; (2) C s parallel to a capacitance C 2 which is independent of N, too; (3) C s in series with C 1 and both parallel to C'2. Figure 3 shows that in general
w i t h 0 -< n < 1/2.
¥
÷ 2
.d
4 x ,D:~. Subsfrote
T h e relation v B ~ N 1;4 obtained from our measurements is thus only an approximation valid for a limited range of impurity concentrations. T h e absolute value of the voltage v s depends on the pressure of the tip against the semiconductor, which may vary from m e a s u r e m e n t to measurement. Therefore only data from one measurement may be compared. Yet the relation v B ~ N 1/4 is independent of the tip pressure. As an example for the application of the procedure to the determination of impurity concentrations, measurements on a series of epitaxial gallium arsenide layers are reported here. T h e series was bevelled at an angle of 5°. It consisted of a very low-resistivity substrate ( N = 8"10 iv c m - a ) , a medium-resistivity getter layer ( N = 1.1016 c m - 3 ) , a high-resistivity layer ( N = 3"1015 c m - 3 , e.g. to be used for Gunn-effect) and a very low-resistivity layer of unknown impurity concentration. T h e lavers were grown from tin and
~i5~- i7/4 ~
E X
" ~,rc Surface
J x,
arbitrary units
F'Ic. 4. Impurity concentrations of a series of epitaxial gallium arsenide layers measured with the tip sliding along a bevelled surface. bevelled surface of the semiconductor. T h e four different doping levels lead to clear differences in the voltage v B. T h e absolute i m p u r i t y concentration can be calculated, if one concentration is known. In the present case the concentration of the 5 / , m getter layer was taken as known. T h e other concentrations were calculated according to relation (4). T h e results are plotted at the left abscissa. T h e concentrations obtained from measurements on evaporated Schottky contacts are given at the right abscissa for comparison. A
NOTES useful correlation between both results is found to exist. DISCUSSION
With the procedure described above impurity concentrations can be assessed. T h e accuracy is determined (1) by the constancy of the pressure against the semiconductor during the movement of the tip, (2) by the impurity concentration itself, (3) by the accuracy with which the relation (4) is measured and (4) by the constancy of the series and stray capacitances during the movement of the tip. Since the pressure is not constant during the movement of the tip, fluctuations in v B of about 6 per cent at N = 3"1015 cm -3 can occur (cf. Fig. 4). This results in uncertainties of about 25 per cent in the determination of N. With higher concentrations the relative error 'XN/N decreases to about 10 per cent at N = 1018 cm -3. Small random fluctuations, as are called for by TIaIret(1) for the quenched multiple dipole mode of Gunn devices, cannot be measured with the accuracy obtained here and a tip radius of 10/zm. The described procedure is a small-signal a.c. technique. Since no bias is applied, the impurity concentration perpendicular to the sample surface can only be evaluated by bevelling the sample.
713
For a simple and rapid evaluation of impurity concentrations and profiles the procedure is very useful, especially in the case of epitaxial layers. Moreover, the thicknesses of the layers can easily be measured. As compared to other methods ~z'3) for automatic plotting of impurity concentrations from Schottky measurements, this method has the disadvantage of giving only approximate and relative values. Its advantages are the rapid evaluation of the results and the nondestructive investigation of the sample, except for the small bevelled area. Acknowledgements--Dr. H. SALOW has sponsored the
work. The epitaxial layers were grown by Dr. E. GaonE of this laboratory. Their help and the discussions with Dr. K. MAUSEare acknowledged with thanks. Forschungsinstitut des Dr. K. HEIME Fernmeldetechnischen Zentralamtes der Deutschen Bundespost D 61 Darmstadt A m Kavalleriesand 3 References
1. H. W. THIM, J. appl. Phys. 39, 3897 (1968). 2. J. COPELAND, IEEE Trans. on Electron Devices ED-16, 445 (1969). 3. J. E. CARROLL,Electron. Lett. 4, 260 (1968).
NOTES
Acknowledgements--The authors wish to acknowledge A. AVAK1AN and D. GOLDSTEIN for their constant encouragement throughout the development of the study summarized in this paper. They also wish to thank J. DIMAURO for hFE-temperature and junction leakage measurements and A. CAPABIANCOfor lifetime and total base dope measurements.
7. A. G. CHYNO\VETHand G. L. PEARSON,J. appl. Picvs. 29, 1103 (1958). 8. A. H. COTTRELL, in Dislocations and Plastic Flow in Crystals. Oxford University Press, London (1953). 9. W. L. KAUFMAN and A. A. BERGH, IEEE Trans. Electron Devices ED-16, 394 (1969).
Sylvania Electric l~roducts Inc. 1O0 Syh,an Road lVoburn Mass., U . S . A .
Solid-State Electronics Pergamon Press 1970. Vol. 13,
P. C. PAREKH E. GAVEL
pp. 710-713.
A s i m p l e m e t h o d for the d e t e r m i n a t i o n o f i m p u r i t y c o n c e n t r a t i o n s a n d profiles in semiconductors
and G.T. and E. Research Laboratories 100 Sylvan Road Woburn Mass., U . S . A .
Printed in Great Britain
V. LYN
(Received 16 October 1969; in revised form 5 December 1969) INTRODUCTION IMPURITY concentrations, profiles and concentra-
References 1. J. M. FAIRFIELDand G. H. SCHWUT'FKE,3. electrochem Soc. 115, 415 (1968). 2. G. H. PLANTINGA, ] E E E Trans. Electron Devices ED-16, 394 (1969). 3. E. SmTL and A. ADLER, Z. :~letall. 52, 529 (1961). 4. P. C. PAREKH and D. M. GOLDSTEIN, Proe. IEEE (to be published). 5. J. P. DE'CosTERD, D. CHAUNG and K. HUB_',m_'R,J. electrochem. Soc. 115, 781 (1968). 6. M. L. JosHI and F. WILHELM, J. electrochem. Soc. 112, 185 (1965).
,
tion fluctuations are i m p o r t a n t properties of s e m i c o n d u c t o r crystals and t h i n films, used for the fabrication of devices. T h e m e a s u r e m e n t of the capacitance of evaporated Schottky contacts is one of the most f r e q u e n t l y used and most exact means of obtaining these data. But the p r o c e d u r e is t i m e c o n s u m i n g , since in most cases the s e m i c o n d u c t o r m u s t be etched s t e p - b y - s t c p and the contacts m u s t be evaporated in high vacuum.
To recorder ( y - oxis)
Vectorvoitrnefer
Iv4,1~,I a4,~
Test frequenc~ so hic.h thGt QJ C O ode >~-. GD,c ~e
~ ~ (~l~z~8= 9 0 a
t /'D;cd6 = QJCD tee " V2 ode
ond
E
!f
I/8= /:,od~ /?Z R:<- I/cJCB:~e
then /q ~
C-
=.~,
~ / ~ = 5oj2
2 Metaltip i
Semiconductor sampe
FIc. 1. Experimental setup for measuring the current through a metal-semiconductor tip contact.
711
NOTES T h e step-by-step etching process can be replaced by a small angle bevelling ( < 5 °) and the evaporated Schottky barrier diode can be replaced by a metal contact to the semiconductor, since it is known that a metal tip set on a semiconductor surface will give diode-like current-voltage characteristics. Both of these modifications reduce the time and effort required to characterize a sample. MEASURING
PROCEDURE
A sliding metal tip (tip radius ~ 1 0 t ~ m ; tungsten, rhodium-plated) is used to measure the capacitance of a semiconductor sample, and thus to determine its doping concentration. Figure 1 shows the measuring setup schematically: Metal tip and semiconductor are each part of the inner conductor of a coaxial line and can be mechanically moved relative to each other. T h e movement of the tip is coupled with the movement of a poteniometer brush. T h e potential at the brush contact serves as a measure for the location of the tip relative to the semiconductor. A high signal frequency is chosen so that the current through the diode (metal point on semiconductor) is purely capacitive (cf. Fig. 1): /diode ~
difference Aq0ABbetween v A and v~ were measured with a Hewlett-Packard vector voltmeter. T h e phase difference was found to be close to 90 ° at frequencies above 100 MHz, thus verifying the assumption wCdioae >~ Gdiod e. RESULTS
The relation between voltage v B and impurity concentration N was investigated with four gallium arsenide samples of different but known impurity concentrations. For this purpose the four samples were soldered onto the inner conductor of the coaxial line and lapped, polished and etched simultaneously. This leads to a planar surface and to a constant pressure of the tip against all four samples. T h e test diagram shows (Fig. 2) that a relation v B ~ N 1'4 (4) holds. Schottky theory gives Cs ~
N 1/2.
(5)
E
,?
L°C'Udiode
E o
o x
o
= ¢oC(VA--~'B).
At the load resistance, measured as VB =
RE,
the voltage
/ d i o d e " RL"
vB
is
8 o
(1)
2.
°
o
If R L
<
1/oJC,
then VB ~
VA,
I i
and iaiod e = ~ o C v A.
(2)
Inserting equation (2) into equation (1) then yields Z'B = ogCVARL, or
v B = const . C.
(3)
T h e voltage v B is proportional to the capacitance C. During the measurements described here, o~/2~r = 250 MHz, v a = 30 mV, v B < 1 mV and R r . = 50 .Q. T h e voltages v A and v B and the phase
,/N,
I 2
,_
arbit"rory units ( log )
FIG. 2. Relation between impurity concentration of four gallium arsenide samples and current through the metalsemiconductor tip contact (v~ = voltage at load resistance proportional to current through contact). T h e discrepancy between the observed dependence of capacitance on impurity concentration and the expected one can be explained, if allowance is made for series or parallel capacitances due to interface layers between metal and semiconductor and due to stray effects. T h e dependence of a total
712
NOTES gallium solutions. T h e impurity concentrations mentioned above were obtained from independent measurements on evaporated Schottky contacts. I n Fig. 4 the d.c. voltage equivalent to the a.c. voltage v B is plotted by means of a recorder. T h i s voltage is measured when the tip slides along the
C2
Cr+Cz
~~~_
c~
~
c,
c~
i J c,
cs
j
f : 200 MHZ Ya ~: 30mV Bevelling ongle 5 ° E
,/N(log)
CT
FIG, 3. Dependence of the t o t a l c a p a c t t a n c e impurity
concentration
l~, if
is a c o m b i n a t i o n
CT Oil of a
Schottky capacitance Cs with stray and series capacitances C1, C2 which are independent of N.
2 ,8~'0 : 2
5 ~10 7!
2
Ii
%
capacitance C r on impurity concentration N is shown in Fig. 3 for three simple cases: (1) Schottky capacitance C s in series with a capacitance C 1 which is independent of N ; (2) C s parallel to a capacitance C 2 which is independent of N, too; (3) C s in series with C 1 and both parallel to C'2. Figure 3 shows that in general
w i t h 0 -< n < 1/2.
¥
÷ 2
.d
4 x ,D:~. Subsfrote
T h e relation v B ~ N 1;4 obtained from our measurements is thus only an approximation valid for a limited range of impurity concentrations. T h e absolute value of the voltage v s depends on the pressure of the tip against the semiconductor, which may vary from m e a s u r e m e n t to measurement. Therefore only data from one measurement may be compared. Yet the relation v B ~ N 1/4 is independent of the tip pressure. As an example for the application of the procedure to the determination of impurity concentrations, measurements on a series of epitaxial gallium arsenide layers are reported here. T h e series was bevelled at an angle of 5°. It consisted of a very low-resistivity substrate ( N = 8"10 iv c m - a ) , a medium-resistivity getter layer ( N = 1.1016 c m - 3 ) , a high-resistivity layer ( N = 3"1015 c m - 3 , e.g. to be used for Gunn-effect) and a very low-resistivity layer of unknown impurity concentration. T h e lavers were grown from tin and
~i5~- i7/4 ~
E X
" ~,rc Surface
J x,
arbitrary units
F'Ic. 4. Impurity concentrations of a series of epitaxial gallium arsenide layers measured with the tip sliding along a bevelled surface. bevelled surface of the semiconductor. T h e four different doping levels lead to clear differences in the voltage v B. T h e absolute i m p u r i t y concentration can be calculated, if one concentration is known. In the present case the concentration of the 5 / , m getter layer was taken as known. T h e other concentrations were calculated according to relation (4). T h e results are plotted at the left abscissa. T h e concentrations obtained from measurements on evaporated Schottky contacts are given at the right abscissa for comparison. A
NOTES useful correlation between both results is found to exist. DISCUSSION
With the procedure described above impurity concentrations can be assessed. T h e accuracy is determined (1) by the constancy of the pressure against the semiconductor during the movement of the tip, (2) by the impurity concentration itself, (3) by the accuracy with which the relation (4) is measured and (4) by the constancy of the series and stray capacitances during the movement of the tip. Since the pressure is not constant during the movement of the tip, fluctuations in v B of about 6 per cent at N = 3"1015 cm -3 can occur (cf. Fig. 4). This results in uncertainties of about 25 per cent in the determination of N. With higher concentrations the relative error 'XN/N decreases to about 10 per cent at N = 1018 cm -3. Small random fluctuations, as are called for by TIaIret(1) for the quenched multiple dipole mode of Gunn devices, cannot be measured with the accuracy obtained here and a tip radius of 10/zm. The described procedure is a small-signal a.c. technique. Since no bias is applied, the impurity concentration perpendicular to the sample surface can only be evaluated by bevelling the sample.
713
For a simple and rapid evaluation of impurity concentrations and profiles the procedure is very useful, especially in the case of epitaxial layers. Moreover, the thicknesses of the layers can easily be measured. As compared to other methods ~z'3) for automatic plotting of impurity concentrations from Schottky measurements, this method has the disadvantage of giving only approximate and relative values. Its advantages are the rapid evaluation of the results and the nondestructive investigation of the sample, except for the small bevelled area. Acknowledgements--Dr. H. SALOW has sponsored the
work. The epitaxial layers were grown by Dr. E. GaonE of this laboratory. Their help and the discussions with Dr. K. MAUSEare acknowledged with thanks. Forschungsinstitut des Dr. K. HEIME Fernmeldetechnischen Zentralamtes der Deutschen Bundespost D 61 Darmstadt A m Kavalleriesand 3 References
1. H. W. THIM, J. appl. Phys. 39, 3897 (1968). 2. J. COPELAND, IEEE Trans. on Electron Devices ED-16, 445 (1969). 3. J. E. CARROLL,Electron. Lett. 4, 260 (1968).