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Noise in silicon and FET's at high electric fields
Solid-SIote Elecfmnics,
1977, Vol. 20, pp. l-3.
Pergamon Press.
Printed in Great Britain
NOISE IN SILICON AND FET’S ELECTRIC FIELDS
AT HIGH
KELJI TAKAGI and KATXJYA MATSUMOTO Department of Electronics, Kyushu Institute of Technology, Tobata, Kitakyushu, Fukuoka, Japan 804 (Received 3 May 1976;in revisedform 15July 1976)
Ah&act-The noise temperature of n-type silicon was measured on an epitaxial layer up to a field strength of 10KV/cm from 1 to 20 MHz at 77°K.The result was applied to obtain an approximate form for the drain noise of an FET in the high electric field. We found that the noise increases in proportion to the product of the drain current and voltage in high electric fields. The noise of the FET was also measured and the experimental data show reasonable agreement with the theoretical expressions.
1. INTRODUCTION
It is well known that at high-electric fields the mobility j.~ of semiconductors decreases with increasing field. There are many expressions for the mobility as a function of electric field and Trofimenkoff [l] shows that eqn (1) is a fair approximation to experimental measurements of the mobility, i.e.
2. NOISEMEASUREMENTS IN SILICONAT HIGHELECTRICFIELDS
The noise measurements have been carried out on a device which is essentially a FET without a gate. It consists of a thin low resistivity n-type silicon layer epitaxially grown on a high-resistivity substrate (800 SZcm), with two ohmic contacts lying 25 pm apart (see Fig. 1).
1 ’ =?+E/E, where ~~ is the low-field mobility, E the field strength and EC a critical field strength. This is a simple expression which may be used to calculate the noise of FET’s in closed form. At the same time, the heating of electrons[2] in semiconductors by high fields can be approximately represented by an effective electron temperature [3]
77’K
o va=25v
.
15v 1ov
5v A
2~~~.~.~~~.
A
I
lo’-
zv .7v .25V
7’. ~-X----X--X 5.
where TO is the lattice temperature and /3 a factor. Bougalis and van der Ziel[4] applied the above two equations to single injection space-charge-limited solid state diodes and discussed the noise property of the diodes. However, eqn (2) has not been demonstrated experimentally over the observed frequency range. On the other hand, the noise increase in a saturated FET has been reported by many authors[5]. We have measured the noise temperature of silicon as a function of the applied field on an epitaxial layer from 1 to 20 MHz. It will be shown that the experimental results are in good agreement with eqn (2). Equations (1) and (2) are then used to calculate the drain noise of an FET and prove that the drain noise of the FET operating in the field-dependent mobility region contains a term proportional to the product of drain voltage V, and current I. Such high field effects become observable in FET’s having short channels, at low temperatures. We have carried out the noise measurement on FET’s and have found reasonable agreement with the theoretical predictions.
2.
NOISE
IO’ 100
2
3
S71d f (MHz)
2 ---,
Fig. I. I, vs frequency for the device No. 1. Pulse width= 3.5 mS. Repetition frequency = 50 Hz. !F,,= 77°K.
The noise was measured by applying a pulsed voltage to the ohmic contacts in order to reduce the internal heating effect. The noise measuring procedure is the same as in [6]. The measurements were made by connecting a noise diode in parallel to the device, and doubling the noise power while correcting for the noise of the whole measuring system in each measurement. That is the noise current spectral intensity 7 can be represented by its equivalent diode current Ieg according to
Figure 1 shows the equivalent noise current 1, meas-
K. TAKAGI and K. MATSUMOTO
2
,, Go(u) dx - Go(0)Ec
(7)
77OK 0 x -
Device
#l
Devke
# 2
Calculated
Fig. 2. V,, E vs T./T,; f= 10MHz. The solid line denotes the calculated noise temperature of eqn (2), with B/E,‘= 2.5Xlo-’ [cm’/V’].
ured at 77°K. It is seen that there is practically no l/f noise above 1 MHz. Figure 2 shows applied voltage V, and field strength E vs T,/Z’, at 10MHz for the devices. Also shown is the curve of eqn (2) with p /EC2= 2.5 x lo-’ (cm?‘). Reasonable agreement between eqn (2) and the experiment can be noted, indicating that T,/T, may be approximated by eqn (2).
3. CONSIDERATIONS
OF NOISE IN FET’S AT
HIGH ELECTRIC FIELDS
du
t 02 B $1 - IO. 1
.
3
where x is the horizontal coordinate from the source to drain, u the channel voltage at x and G(u) the channel conductance per unit length at x. Taking into account the fact that G(u) is proportional to the mobility CL,and combining eqn (1) to eqn (4), we obtain
(5) where G,(u) is the low-field channel conductance per unit length. It is noted that the channel conductance becomes {G,(v) - (Z/E,)} in the high field. The drain noise is calculated as follows[7].
where L is the channel length. Putting the effective electron temperature Z’, in eqns (2)-(6), we obtain
77’ K
0
19fK
x
3730K
2
loo
-
-
7 5
lo+
(4)
. l
.
5
As in the above experiments, it is found that the noise temperature vs field E may be approximated by eqn (2). In order to obtain an approximate form of the drain noise at high electric fields, we shall apply eqns (1) and (2) to the calculation of FET drain noise. In the gradual approximation, the d.c. channel current Z of the FET is given by Z = Go
where Cd0= Go(0)/L is the drain conductance for zero drain bias, V, the pinch-off voltage and Z, the drain saturation current. The first term of eqn (7) represents the noise in the low-field mobility case and is unity for zero drain bias but decreases monotonically with increasing V,, reaching its minimum value at saturation. The second term is of the decreased noise due to the decreased drain conductance and it should be relatively small. The third term is of the increased noise due to the high-field effect. This term should become dominant in the high field region, indicating that the noise increases in proportion to the product of drain current and voltage. The noise measurement in FET’s was also made by connecting a noise diode in parallel to the FET, and the equivalent noise diode current ZC,was measured from 1 to 30 MHz. The result shows practically white noise over the frequency range. Figure 3 shows an example of the
NOISE *
3
5
7
,o-’
2
3
5
7 “xp
,oo
2 -
Fig. 3. 1.,/I.,, vs V,,/V, for the FET (2SK16) at 30MHz. The solid line denotes the calculated result of eqn (7). assuming
measured result, Z,/Z,, vs V,/ VP for the FET (2SKl6) at 30 MHz; here ZCqO is the equivalent noise diode current for zero drain bias. The dotted line shows the first term of eqn (7), which represents the thermal noise in the low-field region for MOS FET[8] or junction FET having a hyperabrupt gate junction [9]. It is seen that the measured noise first decreases and then increases rapidly near saturation at low temperature. This is an indication that part of the excess noise is of non-thermal origin. Apparently this non-thermal excess noise is small at T = 373°K and it increases strongly with decreasing temperature. This should be caused by a decrease of the critical field EC with decreasing temperature. The solid line is the calculated result of eqn (7), using the static characteristic of the FET and assuming p ( VP/EcL)2(Zs /Cd0 VP) = 11 and the second term is small. Reasonable agreement was obtained with the measured result as shown in Fig. 3 at 77°K.
Noise in silicon and FET’s at high electric fields
3
4. CONCLUSIONS
REFERENCES
We have demonstravd high field effects on the thermal noise generated in silicon and FET’s. In n-type silicon, the noise temperature was measured at 77°K and agreed reasonably well with eqn (2). The noise should be measured at higher temperatures in future studies. We calculated the drain noise of an FET in the hieh field region and find that it contains a term proportional to the product of the drain current and voltage. The experimental results agreed reasonably well with the theoretical predictions. The drain noise property is much more clear in this study.
1. F. N. Trofimenkoff, Proc. IEEE 53, 1765(1965). 2. E. Erlbach and J. B. Gunn, Phys. Rev. Letl. 8, 280 (1962). 3. W. Baechtold, IEEE Trans. ED-U, 1186(1971). 4. D. N. Bougalis and A. van der Ziel, Solid-St. Electron. 14,265 ,,0,,,L,. (171 5. For example, K. Takagi and A. van der Ziel, Solid-St. Electron. 12, 907 (1%9). 6. K. Takagi and K. Mano, Solid-St. Electron. 14, 524 (1971). 7. A. van der Ziel, Noise; Sources, Characterization, Measuremen& p. 73. Prentice-Hall, Englewood Cliffs (1970). 8. M. Shoji, IEEE Trans. ED-13, 520 (1966). 9. K. Takagi, Bulletin, Kyushu Institute of Tech. 27, 125 (1973).
1977, Vol. 20, pp. l-3.
Pergamon Press.
Printed in Great Britain
NOISE IN SILICON AND FET’S ELECTRIC FIELDS
AT HIGH
KELJI TAKAGI and KATXJYA MATSUMOTO Department of Electronics, Kyushu Institute of Technology, Tobata, Kitakyushu, Fukuoka, Japan 804 (Received 3 May 1976;in revisedform 15July 1976)
Ah&act-The noise temperature of n-type silicon was measured on an epitaxial layer up to a field strength of 10KV/cm from 1 to 20 MHz at 77°K.The result was applied to obtain an approximate form for the drain noise of an FET in the high electric field. We found that the noise increases in proportion to the product of the drain current and voltage in high electric fields. The noise of the FET was also measured and the experimental data show reasonable agreement with the theoretical expressions.
1. INTRODUCTION
It is well known that at high-electric fields the mobility j.~ of semiconductors decreases with increasing field. There are many expressions for the mobility as a function of electric field and Trofimenkoff [l] shows that eqn (1) is a fair approximation to experimental measurements of the mobility, i.e.
2. NOISEMEASUREMENTS IN SILICONAT HIGHELECTRICFIELDS
The noise measurements have been carried out on a device which is essentially a FET without a gate. It consists of a thin low resistivity n-type silicon layer epitaxially grown on a high-resistivity substrate (800 SZcm), with two ohmic contacts lying 25 pm apart (see Fig. 1).
1 ’ =?+E/E, where ~~ is the low-field mobility, E the field strength and EC a critical field strength. This is a simple expression which may be used to calculate the noise of FET’s in closed form. At the same time, the heating of electrons[2] in semiconductors by high fields can be approximately represented by an effective electron temperature [3]
77’K
o va=25v
.
15v 1ov
5v A
2~~~.~.~~~.
A
I
lo’-
zv .7v .25V
7’. ~-X----X--X 5.
where TO is the lattice temperature and /3 a factor. Bougalis and van der Ziel[4] applied the above two equations to single injection space-charge-limited solid state diodes and discussed the noise property of the diodes. However, eqn (2) has not been demonstrated experimentally over the observed frequency range. On the other hand, the noise increase in a saturated FET has been reported by many authors[5]. We have measured the noise temperature of silicon as a function of the applied field on an epitaxial layer from 1 to 20 MHz. It will be shown that the experimental results are in good agreement with eqn (2). Equations (1) and (2) are then used to calculate the drain noise of an FET and prove that the drain noise of the FET operating in the field-dependent mobility region contains a term proportional to the product of drain voltage V, and current I. Such high field effects become observable in FET’s having short channels, at low temperatures. We have carried out the noise measurement on FET’s and have found reasonable agreement with the theoretical predictions.
2.
NOISE
IO’ 100
2
3
S71d f (MHz)
2 ---,
Fig. I. I, vs frequency for the device No. 1. Pulse width= 3.5 mS. Repetition frequency = 50 Hz. !F,,= 77°K.
The noise was measured by applying a pulsed voltage to the ohmic contacts in order to reduce the internal heating effect. The noise measuring procedure is the same as in [6]. The measurements were made by connecting a noise diode in parallel to the device, and doubling the noise power while correcting for the noise of the whole measuring system in each measurement. That is the noise current spectral intensity 7 can be represented by its equivalent diode current Ieg according to
Figure 1 shows the equivalent noise current 1, meas-
K. TAKAGI and K. MATSUMOTO
2
,, Go(u) dx - Go(0)Ec
(7)
77OK 0 x -
Device
#l
Devke
# 2
Calculated
Fig. 2. V,, E vs T./T,; f= 10MHz. The solid line denotes the calculated noise temperature of eqn (2), with B/E,‘= 2.5Xlo-’ [cm’/V’].
ured at 77°K. It is seen that there is practically no l/f noise above 1 MHz. Figure 2 shows applied voltage V, and field strength E vs T,/Z’, at 10MHz for the devices. Also shown is the curve of eqn (2) with p /EC2= 2.5 x lo-’ (cm?‘). Reasonable agreement between eqn (2) and the experiment can be noted, indicating that T,/T, may be approximated by eqn (2).
3. CONSIDERATIONS
OF NOISE IN FET’S AT
HIGH ELECTRIC FIELDS
du
t 02 B $1 - IO. 1
.
3
where x is the horizontal coordinate from the source to drain, u the channel voltage at x and G(u) the channel conductance per unit length at x. Taking into account the fact that G(u) is proportional to the mobility CL,and combining eqn (1) to eqn (4), we obtain
(5) where G,(u) is the low-field channel conductance per unit length. It is noted that the channel conductance becomes {G,(v) - (Z/E,)} in the high field. The drain noise is calculated as follows[7].
where L is the channel length. Putting the effective electron temperature Z’, in eqns (2)-(6), we obtain
77’ K
0
19fK
x
3730K
2
loo
-
-
7 5
lo+
(4)
. l
.
5
As in the above experiments, it is found that the noise temperature vs field E may be approximated by eqn (2). In order to obtain an approximate form of the drain noise at high electric fields, we shall apply eqns (1) and (2) to the calculation of FET drain noise. In the gradual approximation, the d.c. channel current Z of the FET is given by Z = Go
where Cd0= Go(0)/L is the drain conductance for zero drain bias, V, the pinch-off voltage and Z, the drain saturation current. The first term of eqn (7) represents the noise in the low-field mobility case and is unity for zero drain bias but decreases monotonically with increasing V,, reaching its minimum value at saturation. The second term is of the decreased noise due to the decreased drain conductance and it should be relatively small. The third term is of the increased noise due to the high-field effect. This term should become dominant in the high field region, indicating that the noise increases in proportion to the product of drain current and voltage. The noise measurement in FET’s was also made by connecting a noise diode in parallel to the FET, and the equivalent noise diode current ZC,was measured from 1 to 30 MHz. The result shows practically white noise over the frequency range. Figure 3 shows an example of the
NOISE *
3
5
7
,o-’
2
3
5
7 “xp
,oo
2 -
Fig. 3. 1.,/I.,, vs V,,/V, for the FET (2SK16) at 30MHz. The solid line denotes the calculated result of eqn (7). assuming
measured result, Z,/Z,, vs V,/ VP for the FET (2SKl6) at 30 MHz; here ZCqO is the equivalent noise diode current for zero drain bias. The dotted line shows the first term of eqn (7), which represents the thermal noise in the low-field region for MOS FET[8] or junction FET having a hyperabrupt gate junction [9]. It is seen that the measured noise first decreases and then increases rapidly near saturation at low temperature. This is an indication that part of the excess noise is of non-thermal origin. Apparently this non-thermal excess noise is small at T = 373°K and it increases strongly with decreasing temperature. This should be caused by a decrease of the critical field EC with decreasing temperature. The solid line is the calculated result of eqn (7), using the static characteristic of the FET and assuming p ( VP/EcL)2(Zs /Cd0 VP) = 11 and the second term is small. Reasonable agreement was obtained with the measured result as shown in Fig. 3 at 77°K.
Noise in silicon and FET’s at high electric fields
3
4. CONCLUSIONS
REFERENCES
We have demonstravd high field effects on the thermal noise generated in silicon and FET’s. In n-type silicon, the noise temperature was measured at 77°K and agreed reasonably well with eqn (2). The noise should be measured at higher temperatures in future studies. We calculated the drain noise of an FET in the hieh field region and find that it contains a term proportional to the product of the drain current and voltage. The experimental results agreed reasonably well with the theoretical predictions. The drain noise property is much more clear in this study.
1. F. N. Trofimenkoff, Proc. IEEE 53, 1765(1965). 2. E. Erlbach and J. B. Gunn, Phys. Rev. Letl. 8, 280 (1962). 3. W. Baechtold, IEEE Trans. ED-U, 1186(1971). 4. D. N. Bougalis and A. van der Ziel, Solid-St. Electron. 14,265 ,,0,,,L,. (171 5. For example, K. Takagi and A. van der Ziel, Solid-St. Electron. 12, 907 (1%9). 6. K. Takagi and K. Mano, Solid-St. Electron. 14, 524 (1971). 7. A. van der Ziel, Noise; Sources, Characterization, Measuremen& p. 73. Prentice-Hall, Englewood Cliffs (1970). 8. M. Shoji, IEEE Trans. ED-13, 520 (1966). 9. K. Takagi, Bulletin, Kyushu Institute of Tech. 27, 125 (1973).