Noise reduction method for a semiconductor device

A 1/f noise coefficient characteristic with respect to an operating point of a semiconductor device is measured, and a control voltage corresponding to an operating point of the semiconductor device with which the 1/f noise coefficient is minimized is applied to a MOSFET. Further, using a MOSFET which has known element dimensions, a relationship of a 1/f noise coefficient to a channel area is calculated, and the resistance value of the MOSFET is calculated using the channel width and the channel length as well as a constant peculiar to the MOSFET. Then, the 1/f noise coefficient of the semiconductor device is calculated using the 1/f noise coefficient with respect to the channel area of the MOSFET and the resistance value, and the channel width and the channel length of the MOSFET are set so that the 1/f noise coefficient of the semiconductor device may be minimized.

BACKGROUND OF THE INVENTION
 1. Field of the Invention
 This invention relates to a noise reduction method for reducing 1/f noise
 of a semiconductor device which includes an element having an impedance
 and a MOSFET (Metal Oxide Semiconductor Field Effect Transistor).
 2. Description of the Related Art
 Usually, noise components of a semiconductor device include 1/f noise and
 Johnson noise, and where the semiconductor device is a sensor or a like
 element of the temperature detection type for use with an infrared
 detector, thermal fluctuation noise caused by thermal energy inputted to
 it is produced additionally.
 In order to improve the signal to noise ratio (hereinafter referred to
 simply as S/N ratio) of a semiconductor device, in a device which at least
 includes an element having an impedance and a MOSFET, which is reputed to
 have high 1/f noise, the 1/f noise in particular above must be reduced.
 It is to be noted that (S/N ratio)=(effective value of signal)/(effective
 value of noise).
 If noise of a semiconductor device is noise on current, then noise current
 spectrum density Sn1/f [A.sup.2 /Hz] and noise current effective value
 In1/f [A] representative of the magnitude of 1/f noise can be represented
 by the following expressions:
EQU Sn1/f=K.multidot.Ib.sup.2 /f (1)
EQU In1/f=(.intg..sub.f1.sup.f2 Snidf).sup.1/2
 ={K.multidot.Ib.sup.2.multidot.1n(f2/f1)}.sup.1/2 (2)
 where K is the 1/f noise factor, Ib is the bias current [A] to flow through
 the semiconductor device, f is the frequency [Hz], f1 is the lowest
 frequency [Hz] in a measurement band, and f2 is the highest frequency [Hz]
 in the measurement band.
 As seen from expressions (1) and (2), noise current spectrum density Sn1/f
 [A.sup.2 /Hz] and noise current effective value In1/f [A] of 1/f noise
 rely upon the value of bias current Ib to flow through the semiconductor
 device, and if bias current Ib increases, also 1/f noise increases.
 Meanwhile, noise current effective value InJ of Johnson noise and noise
 current effective value Inth of thermal fluctuation noise can be
 represented, when an infrared sensor of the bolometer type used in an
 infrared detector or the like as a semiconductor device is taken as an
 example, by the following expressions:
 InJ={4.multidot.k.multidot.T.multidot.(f2-f1)/R}.sup.1/2 (3)
EQU Inth=Ib.multidot..alpha..multidot.T.multidot.(k/Cth).sup.1/2 (4)
 where R is the total resistance value [.OMEGA.] of the semiconductor
 device, k is the Boltzmann's constant [eV/K], T is the temperature [K]
 upon measurement, .alpha. is the temperature coefficient of the bolometer
 type infrared sensor resistance [1/K], and Cth is the heat capacity [J/K].
 By the way, the magnitude of signal component Is outputted from the
 semiconductor device can be represented, where a bolometer type infrared
 sensor which is used with an infrared ray detector or the like is taken as
 an example (refer to, for example, Brugess R. Johnson et al., "Silicon
 Microstructure Superconducting Microbolometer Infrared Arrays", SPIE, Vol.
 2,020, Infrared Technology XIX, 1993), by the following expression:
EQU Is=.alpha..multidot..DELTA.T.multidot.Ib (5)
 where .alpha. is the temperature coefficient [1/K] of the resistance of the
 bolometer type infrared sensor, .DELTA.T is the temperature rise [K] of a
 diaphragm when an object of measurement having a temperature difference of
 1.degree. K from the surroundings is observed, and Ib is the bias current
 [A] to flow through the semiconductor device.
 Using noise current effective value In1/f of 1/f noise, noise current
 effective value InJ of Johnson noise and noise current effective value
 Inth of thermal fluctuation noise, the S/N ratio of the semiconductor
 device can be represented by the following expression:
 ##EQU1##
 Of the noise components of a semiconductor device, the thermal fluctuation
 noise has a value much lower than those of the Johnson noise and the 1/f
 noise, and therefore, the thermal fluctuation noise can be ignored. The
 thermal fluctuation noise is noise peculiar to a sensor of the temperature
 detection type such as an infrared detector, and matters only when the
 Johnson noise and the 1/f noise are very low.
 By the way, when bias current Ib to flow through the semiconductor device
 is low, Johnson noise becomes a principal noise component of noise of the
 semiconductor device. On the other hand, when bias current Ib to flow
 through the semiconductor device is high, since also the 1/f noise
 increases as bias current Ib increases, the 1/f noise becomes a principal
 noise component of the semiconductor device.
 In a range of bias current Ib in which Johnson noise is outputted as a
 principal noise component, if bias current Ib is increased, then signal
 component Is increases, and therefore, the S/N ratio can be improved. This
 is due to the fact that, as seen from expression (3) above, the Johnson
 noise is fixed without relying upon bias current Ib.
 However, if bias current Ib is further increased to a value in another
 range of bias current Ib in which 1/f noise is outputted as a principal
 noise component, then improvement of the S/N ratio can no longer be
 expected. This arises from the fact that, if bias current Ib increases,
 then simultaneously as signal component Is increases as seen from
 expression (5), also the 1/f noise increases as seen from expression (2).
 Accordingly, in order to improve the S/N ratio, signal component Is must be
 increased while suppressing an increase of the noise components.
 This is described taking a bolometer type infrared sensor as an example. In
 order to increase signal component Is, as can be seen from expression (5),
 temperature coefficient .alpha., temperature rise .DELTA.T of the
 diaphragm and bias current Ib should be increased.
 In order to increase temperature rise .DELTA.T of the diaphragm, it is
 necessary to reduce the thermal conductance or increase the absorption
 factor of infrared rays of the diaphragm to improve the sensitivity of the
 sensor. Meanwhile, in order to increase temperature coefficient .alpha. of
 the resistance, it is necessary to develop an infrared sensor of the
 bolometer type having a high temperature coefficient. However, the
 countermeasures just described cannot be realized readily because a high
 development cost and a long development time are required. Therefore, in
 order to increase signal component Is, the most easy and effective
 countermeasure is to increase bias current Ib.
 On the other hand, in order to suppress an increase of noise components, a
 method such as forming each element of a semiconductor device from a
 material which produces a minimized amount of noise or to devise the
 structure of elements to suppress an increase of noise seem to be
 applicable.
 For example, since the magnitude of Johnson noise relies upon the
 resistance value of an element, production of Johnson noise can be
 suppressed by making the resistance value of the element high. However, if
 the resistance value of the element is made high, then the operating
 voltage of the element becomes high and the margin for the dielectric
 strength is reduced, and consequently, the applied voltage is limited and
 bias current Ib cannot be increased. Therefore, signal component Is cannot
 be increased.
 Meanwhile, although the 1/f noise can be reduced by forming the element
 from a material having a low 1/f noise coefficient, this gives rise to
 another problem in that temperature coefficient .alpha. of the resistance
 and so forth are deteriorated.
 Another method of devising the structure of an element to suppress the
 noise production amount is disclosed, for example, in Japanese Patent
 Laid-Open No. 186253/96. In the conventional noise reduction method
 disclosed in Japanese Patent Laid-Open No. 186253/96, impurity diffusion
 regions are formed at locations spaced from the surface of a silicon
 substrate and are used as the source and the drain such that the channel
 may not contact with a gate oxide film to reduce the 1/f noise of the
 MOSFET.
 With such a conventional noise reduction method for a semiconductor device
 as described above, since the noise increases and the S/N ratio cannot be
 improved in the range of bias current Ib in which 1/f noise is outputted
 as a principal noise component. Bias current Ib must be limited to a range
 within which 1/f noise does not become a principal noise component.
 Accordingly, in order to obtain a high S/N ratio in this condition, an
 increase of signal component Is is inevitable. However, in order to
 increase signal component Is, it is necessary to develop a material having
 a high temperature coefficient of the resistance or a new element or
 structure for improving the sensitivity. Consequently, there is a problem
 that a high cost and much time are required in order to develop a material
 or a structure or establish a production method which satisfies this
 requirement.
 Here, while it may be a possible idea to use, as a material for the
 element, a metal oxide or the like which has a high temperature
 coefficient of the resistance such as vanadium oxide (VOx), in order to
 form an element from vanadium oxide, a special manufacture line is
 required and the production cost is increased because it is difficult to
 use a manufacture line which is used for formation of elements using
 silicon.
 Also where an element is formed from a material having a low 1/f noise
 coefficient to reduce noise components to improve the S/N ratio or where
 the structure of an element is devised to reduce noise components to
 improve the S/N ratio, in order to develop the material and establish a
 manufacture method, a high cost and much time are required. Consequently,
 there is a problem that the production cost becomes high. If a special
 structure which reduces the 1/f noise coefficient as in a MOSFET which is
 disclosed, for example, in Japanese Patent Laid-Open No. 186253/96 is
 adopted, then the structure and the production process of the element are
 complicated. Consequently, an increase of the production cost cannot be
 avoided.
 SUMMARY OF THE INVENTION
 Accordingly, it is an object of the present invention to provide a noise
 reduction method for a semiconductor device which can suppress an increase
 of noise components by an increase of bias current to improve the S/N
 ratio.
 It is another object of the present invention to provide a noise reduction
 method for a semiconductor device which can improve the S/N ratio without
 using a special material or without adding a special driving circuit.
 In order to achieve the objects described above, according to the present
 invention, there is provided a noise reduction method for a semiconductor
 device for suppressing a noise component of a semiconductor device which
 includes an element having an impedance and a MOSFET circuit which
 includes at least one MOSFET, comprising the steps of measuring a 1/f
 noise coefficient characteristic indicative of a relationship of a 1/f
 noise coefficient to an operating point of the semiconductor device using
 a control voltage to be applied to a gate of the MOSFET as a parameter,
 and applying, based on the 1/f noise coefficient characteristic, a control
 voltage corresponding to an operating point of the semiconductor device
 with which the 1/f noise coefficient is minimized within a range within
 which the MOSFET is operable. By the construction just described, even if
 bias current of the semiconductor device is increased to increase a signal
 component, the amount of 1/f noise which may be produced is suppressed.
 Further, when the MOSFET circuit is composed of a P-channel MOSFET and an
 N-channel MOSFET connected in parallel, by applying a second control
 voltage which is a predetermined optimum voltage to the substrate of the
 P-channel MOSFET, the 1/f noise coefficient can be further reduced.
 On the other hand, when a noise reduction method for a semiconductor device
 comprises the steps of calculating, using a MOSFET having known element
 dimensions, a relationship of a 1/f noise coefficient to a channel area of
 the MOSFET, calculating resistance values of the MOSFET and a MOSFET
 circuit using a channel width and a channel length set from the channel
 area and a peculiar constant of the MOSFET, calculating a 1/f noise
 coefficient of the semiconductor device using thus calculated values, and
 setting the dimensions of the MOSFET so that the 1/f noise coefficient of
 the semiconductor device may be minimized, an external circuit for
 minimizing the 1/f noise coefficient becomes unnecessary and the
 construction of the semiconductor device can be simplified.
 The above and other objects, features, and advantages of the present
 invention will become apparent from the following description with
 references to the accompanying drawings which illustrate example of the
 present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
 (First Embodiment)
 First, a first embodiment of the present invention is described.
 The first embodiment provides a method wherein, taking note of the fact
 that, when a gate voltage (control voltage) of a MOSFET of a semiconductor
 device is used as a parameter, the 1/f noise coefficient of the
 semiconductor device relies upon the operating point determined by bias
 current of the semiconductor device, a signal component is increased while
 suppressing an increase of 1/f noise to improve the S/N ratio by causing
 the semiconductor device to operate with the operating point and control
 voltage which minimize the 1/f noise coefficient.
 (First Working Example)
 While the first embodiment of the noise reduction method for a
 semiconductor device of the present invention can be applied to various
 semiconductor devices, the present working example is described taking a
 case where the noise reduction method is applied to an infrared sensor of
 the bolometer type as an example.
 Referring to FIG. 1, semiconductor device 1 of the present working example
 includes bolometer 11 formed from a thermoelectric conversion element,
 horizontal switch 14 formed from first P-channel MOSFET Q1 and first
 N-channel MOSFET Q2 connected in parallel, and vertical switch 10 formed
 from second N-channel MOSFET Q3 grounded at the source thereof and
 connected at the drain thereof to an end of bolometer 11.
 Here, an end of horizontal switch 14 is connected to the other end of
 bolometer 11, and the other end of horizontal switch 14 is connected to
 output terminal 15.
 Connected to the gate of first P-channel MOSFET Q1 of horizontal switch 14
 is first buffer 17 which outputs one of predetermined control voltage VDD
 applied to a power supply terminal and ground potential Vss in response to
 horizontal switch selection signal .phi.H. Meanwhile, to the gate of first
 N-channel MOSFET Q2, second buffer 18 which outputs one of control voltage
 VDD applied to the power supply terminal and ground potential Vss in
 response to a negated value of horizontal switch selection signal .phi.H
 is connected.
 Further, a substrate (body) of first P-channel MOSFET Q1 is connected to
 voltage control circuit 3 so that control voltage VDD is applied to the
 substrate of first P-channel MOSFET Q1. Meanwhile, a substrate of first
 N-channel MOSFET Q2 is grounded.
 Meanwhile, a substrate of second N-channel MOSFET Q3 of vertical switch 10
 is grounded, and to the gate of second N-channel MOSFET Q3, third buffer
 16 which outputs one of control voltage VDD applied to the power supply
 terminal and ground potential Vss in response to vertical switch selection
 signal .phi.V is connected.
 It is to be noted that, for bolometer 11, titanium or a material which
 contains titanium as a principal component or else a metal oxide film
 having a thermoelectric conversion characteristic may be employed.
 In a construction such as described above, vertical switch 10 and
 horizontal switch 14 exhibit on-states only when vertical switch selection
 signal .phi.V has the High level and horizontal switch selection signal
 .phi.H has the Low level, respectively. In this instance, control voltage
 VDD is applied to the gate of second N-channel MOSFET Q3 of vertical
 switch 10 and ground potential Vss is applied to the gate of first
 P-channel MOSFET Q1 of horizontal switch 14, and control voltage VDD is
 applied to the gate of first N-channel MOSFET Q2.
 Read-out circuit 2 includes transistor Q4 for reading out a signal detected
 by semiconductor device 1, capacitor C1 for integrating and outputting the
 signal read out by transistor Q4, reset circuit 22 which connects an
 output of capacitor C1 to power supply Vr to charge capacitor C1 so that
 charge accumulated in capacitor C1 may be equal to the potential of power
 supply Vr, and bias voltage supply 23 connected to the base of transistor
 Q4 for controlling bias current Ib to be supplied to semiconductor device
 1.
 It is to be noted that reset circuit 22 performs a switching operation in
 response to predetermined periodical pulse .phi.R transmitted thereto from
 control means not shown to connect the potential of capacitor C1 to power
 supply Vr in a predetermined period.
 In a construction such as described above, predetermined bias current Ib is
 supplied from transistor Q4 of read-out circuit 2 through output terminal
 15 to horizontal switch 14, bolometer 11 and vertical switch 10 of
 semiconductor device 1. In this instance, the value of bias current Ib to
 be supplied from the emitter of transistor Q4 is determined and operating
 point Vop of semiconductor device 1 is determined by the value of voltage
 Vb applied to the base of transistor Q4.
 It is to be noted that the relationship between operating point Vop and
 bias current Ib is Vop=Ib.times.R where the total resistance of
 semiconductor device 1 is R. In the case of semiconductor device 1 shown
 in FIG. 1, since the resistance value is approximately 3,300 [.OMEGA.],
 Vop=3,300.times.Ib.
 Referring to FIG. 2, voltage control circuit 3 of the present working
 example includes A/D converter 31 for receiving voltage Vb of bias voltage
 supply 23 of read-out circuit 2 as an input voltage and converting voltage
 Vb into a digital signal, storage apparatus 32 for storing data to be used
 for outputting control voltage VDD corresponding to the value of voltage
 Vb of bias voltage supply 23, D/A converter 33 for converting data
 outputted from storage apparatus 32 into an analog value, and driver 34
 for receiving an output voltage of D/A converter 33 as an input thereto
 and supplying control voltage VDD to first buffer 17, second buffer 18,
 third buffer 16 and the substrate of first P-channel MOSFET Q1 of
 semiconductor device 1.
 Storage apparatus 32 receives digital data outputted from A/D converter 31,
 for example, as address data, reads out data recorded corresponding to the
 address in accordance with a lookup table system and outputs the data.
 In order to record data into the storage apparatus 32, based on a
 characteristic (hereinafter referred to as 1/f noise coefficient
 characteristic) of 1/f noise coefficient K with respect to operating point
 Vop of semiconductor device 1 measured in advance, optimum control voltage
 VDD with which 1/f noise coefficient K is minimized at arbitrary operating
 point Vop is determined, and from the relationship among them, data of
 control voltage VDD corresponding to voltage Vb of bias voltage supply 23
 corresponding to operating point Vop are recorded.
 Since read-out circuit 2 such as described above is provided, also when it
 is tried to reduce 1/f noise of, for example, a semiconductor device which
 includes an element which is different from semiconductor device 1 of the
 present embodiment and has an impedance and a MOSFET, such reduction can
 be achieved by modifying the data of storage apparatus 32 or by replacing
 storage apparatus 32 with another storage apparatus in which modified data
 are stored.
 Now, the principle of the noise reduction method for a semiconductor device
 of the present invention is described with reference to FIGS. 3 and 4.
 Referring to FIG. 3, curves a, b and c illustrate characteristics when
 control voltage VDD is used as a parameter and varied to VDD=10, 13 and 15
 [V], respectively. It is to be noted that FIG. 3 illustrates a graph
 produced based on actually measured values.
 As seen from FIG. 3, 1/f noise coefficient K indicates a characteristic
 which relies upon operating point Vop and exhibits a maximum value at a
 predetermined operating point. If control voltage VDD is set to a higher
 voltage, then voltage Vopmax of an operating point at which 1/f noise
 coefficient K exhibits a maximum value is shifted to a higher voltage.
 In FIG. 3, when VDD=10 [V], Vopmax=6.6 [V], when VDD=13 [V], Vopmax=8.6
 [V], and when VDD=15 [V], Vopmax=10.5 [V].
 From the relationships just mentioned, between voltage Vopmax [V] of an
 operating point at which 1/f noise coefficient K exhibits a maximum value
 and control voltage VDDpeak [V] then, there is a relationship given by
 ##EQU2##
 where (Sp/Sn) is the ratio between current driving capacity Sp of P-channel
 MOSFET Q1 and current driving capacity Sn of N-channel MOSFET Q2 which
 form horizontal switch 14 of semiconductor device 1. It is to be noted
 that FIG. 3 illustrates a graph where (Sp/Sn)=2.
 Accordingly, when operating point Vop of semiconductor device 1 is to be
 set, control voltage VDD is set so that it may be different from VDDpeak
 obtained based on expression (7).
 It is to be noted that, where the voltage of the operating point is lower
 than Vopmax (on the left side of a peak of FIG. 3), the 1/f noise
 coefficient characteristic of semiconductor device 1 depends principally
 upon the 1/f noise coefficient characteristic of N-channel MOSFET Q2.
 On the other hand, when the voltage of the operating point is higher than
 Vopmax (on the right side of a peak of FIG. 3), the 1/f noise coefficient
 characteristic of semiconductor device 1 depends principally upon the 1/f
 noise coefficient characteristic of P-channel MOSFET Q1.
 By the way, as can be seen from FIG. 3, when semiconductor device 1 is
 rendered operative with the operating point set to a value lower than
 Vopmax (on the left side of a peak), in order to make 1/f noise
 coefficient K low, control voltage VDD should be set to a high value.
 However, with an actual MOSFET, since the voltage (=control voltage VDD)
 to be applied to the gate is limited to a value which depends upon the
 process of manufacture of the semiconductor device, the value of control
 voltage VDD is set to voltage VDDmax which depends upon the process of
 manufacture of the semiconductor device.
 Meanwhile, when semiconductor device 1 is rendered operative with the
 operating point set to a value higher than Vopmax (on the right side of a
 peak), in order to make 1/f noise coefficient K low, control voltage VDD
 should be set to a low value. However, with an actual MOSFET, since, from
 the structure, control voltage VDD cannot be set lower than a source
 voltage (voltage Vop at the operating point) of the P-channel MOSFET, the
 control voltage and the operating point are set to a substantially equal
 voltage.
 In summary, in order to allow semiconductor device 1 to operate with low
 1/f noise coefficient K, the relationship between control voltage VDD and
 operating point Vop should be set such that
 VDD=VDDmax where Vop&lt;4/{3.times.(Sp/Sn)}.times.VDDmax, but
 VDD=Vop where Vop.gtoreq.4/{3.times.(Sp/Sn)}.times.VDDmax.
 Since 1/f noise coefficient K of semiconductor device 1 is suppressed to a
 low value by setting control voltage VDD with respect to operating point
 Vop in this manner, an increase of 1/f noise when bias current Ib is
 increased is suppressed. Accordingly, an increase of signal component Is
 is allowed, and the S/N ratio can be improved.
 That the method of setting 1/f noise coefficient K to a low value described
 above can be applied also to a case other than where (Sp/Sn)=2 has been
 confirmed by a circuit simulation conducted by the applicant of the
 present application.
 It is to be noted that, where channel length Lp of a P-channel MOSFET and
 channel length Ln of an N-channel MOSFET are equal to each other, the
 ratio (Sp/Sn) between current driving capacities Sp and Sn is equal to the
 ratio (Wp/Sn) of channel width Wp of the P-channel MOSFET and channel
 width Wn of the N-channel MOSFET.
 Now, that reduction of 1/f noise of the horizontal switch of semiconductor
 device 1 shown in FIG. 1 presents similar effects to those presented by
 reduction of 1/f noise of entire semiconductor device 1 is described with
 reference to FIG. 4.
 Referring to FIG. 4, curves d, e and f indicate characteristics when, where
 control voltage VDD is used as a parameter, it is varied to VDD=10, 13 and
 15 [V], respectively.
 Comparing the graph of FIG. 4 with the graph of FIG. 3, the 1/f noise
 coefficient characteristics illustrated in FIG. 4 exhibit maximum values
 at the same operating points as those of FIG. 3. This arises from the fact
 that, since the resistance value of bolometer 11 is approximately 2.7
 K.OMEGA. and is larger approximately by only one place than the resistance
 value of horizontal switch 14, the 1/f noise coefficient characteristic
 only of horizontal switch 14 has a significant influence on the 1/f noise
 coefficient characteristic of entire semiconductor device 1.
 Accordingly, merely by suppressing the 1/f noise coefficient K of
 horizontal switch 14 of such semiconductor device 1 as shown in FIG. 1 to
 a low value, an equal effect to that obtained by suppressing the 1/f noise
 coefficient K of entire semiconductor device 1 to a low value is achieved.
 It is to be noted that, while read-out circuit 2 of the present working
 example is described taking a construction wherein an integral waveform is
 outputted as an example, it may otherwise have another circuit
 construction wherein a variation in resistance of semiconductor device 1
 is detected. In this instance, voltage control circuit 3 should detect the
 voltage at operating point Vop of semiconductor device 1 and output
 control voltage VDD corresponding to the detected voltage.
 Further, while voltage control circuit 3 of the present working example
 detects base voltage Vb of transistor Q4 of read-out circuit 2 in place of
 operating point Vop, for example, a voltage detection circuit (not shown)
 which detects the emitter voltage of transistor Q4 may be used or else a
 current detection circuit (not shown) for detecting bias current Ib or the
 like may be used between the emitter of transistor Q4 and output terminal
 15 of semiconductor device 1 instead.
 Further, while, in the present working example, the construction of
 semiconductor device 1 is described in connection with a case wherein
 vertical switch 10, bolometer 11 and horizontal switch 14 are connected in
 series in this order from the ground side, also a different construction
 wherein they are connected in series in order of bolometer 11, vertical
 switch 10 and horizontal switch 14 or in order of bolometer 11, horizontal
 switch 14 and vertical switch 10 can be applied. Further, a further
 construction which does not employ vertical switch 10 and includes
 bolometer 11 and horizontal switch 14 connected in series in this order
 from ground potential Vss side can be applied.
 Further, while the present working example is described in connection with
 an example constructed such that horizontal switch 14 is composed of first
 P-channel MOSFET Q1 and first N-channel MOSFET Q2 connected in parallel,
 also where it is otherwise composed only of first P-channel MOSFET Q1 or
 only of first N-channel MOSFET Q2, similar effects can be achieved by
 measuring the relationship of the 1/f noise coefficient to the operating
 point in advance and controlling the value of control voltage VDD based on
 the relationship.
 Furthermore, while the present working example is described in connection
 with an example wherein semiconductor device 1 is an infrared sensor of
 the bolometer type, the present invention can be applied not only to
 bolometer 11 but also to an element which has an impedance and with which
 1/f noise matters. In particular, the noise reduction method for a
 semiconductor device of the present invention can be applied to a
 semiconductor device which includes an element having an impedance and a
 MOSFET.
 An example of such a semiconductor device as just described is an image
 sensor. With an image sensor, if a circuit or an equivalent circuit for an
 element (corresponding to one pixel) having a sensing function is formed
 in an equal construction to that of the present working example, then 1/f
 noise can be suppressed similarly as in the present working example.
 Accordingly, the present invention can be applied to a two-dimensionally
 arranged semiconductor device, a one-dimensionally arranged semiconductor
 device, a semiconductor device composed of a single element and so forth.
 For example, the present invention can be applied to a semiconductor
 device wherein bolometers are arranged two-dimensionally and one
 horizontal switch is arranged for each column of the bolometers (refer to
 Japanese Patent Laid-Open No. 105794/96).
 (Second Working Example)
 In the following, a second working example of the first embodiment of the
 present invention is described with reference to the drawings. The present
 working example is different from the first working example in
 construction of the voltage control circuit. The other construction of the
 present working example is omitted here since it is similar to that of the
 first working example.
 Referring to FIG. 5, voltage control circuit 4 of the present working
 example includes first voltage source 41, second voltage source 42, third
 voltage source 43 and fourth voltage source 44 for out putting
 predetermined voltages in response to voltage Vb of a bias voltage source
 of a read-out circuit, and switch 40 which receives voltage Vb of the bias
 voltage source as an input thereto, selects one of terminals to which
 first to fourth voltage sources 41 to 44 are connected and outputs the
 voltage of the selected terminal as control voltage VDD.
 In the construction described above, the output voltages of first voltage
 source 41, second voltage source 42 and third voltage source 43 are set to
 control voltages VDD set optimally from a 1/f noise coefficient
 characteristic (refer to FIGS. 3 and 4) of a semiconductor device measured
 in advance so that 1/f noise coefficient K may have minimum values in
 accordance with an operating point of the semiconductor device determined
 by voltage Vb of the bias voltage source of the read-out circuit.
 It is to be noted that the output voltage of fourth voltage source 44 is
 set to a voltage equal to the voltage of operating point Vop.
 Since such voltage control circuit 4 as described above is provided,
 optimum control voltage VDD corresponding to an operating point of the
 semiconductor device can be applied to the gate and the substrate of a
 MOSFET which forms the semiconductor device, and consequently, an increase
 of 1/f noise can be suppressed similarly as in the first working example.
 It is to be noted that, while the present working example is described in
 connection with an example wherein four voltage sources are involved, the
 number of voltage sources need not be limited to 4, but a plural number of
 voltage sources may be provided in accordance with a situation of a
 circuit scale or the like.
 Further, each of first to fourth voltage sources 41 to 44 may be formed
 from a simple circuit such as a voltage dividing circuit composed of
 resistors.
 (Third Working Example)
 Now, a third working example of the first embodiment of the present
 invention is described with reference to the drawings. The present working
 example is different from the first working example in construction of the
 semiconductor device. Since the other construction is similar to that of
 the first working example, description thereof is omitted here.
 Referring to FIG. 6, semiconductor device 6 of the present embodiment
 include impedance element 60 having an impedance, and horizontal switch 64
 composed of P-channel MOSFET Q5 and N-channel MOSFET Q6 connected in
 parallel. An end of impedance element 60 is connected to ground potential
 Vss. Meanwhile, an end of horizontal switch 64 is connected to the other
 end of impedance element 60, and the other end of horizontal switch 64 is
 connected to output terminal 62. The substrate of P-channel MOSFET Q5 is
 connected to first external terminal 65, and predetermined control voltage
 VBB is inputted from a voltage control circuit (refer to FIG. 1) to first
 external terminal 65. Meanwhile, the substrate of N-channel MOSFET Q6 is
 connected to ground potential Vss.
 Further, first buffer 67 which outputs one of predetermined voltage VDD0
 applied to a power supply terminal and ground potential Vss in response to
 horizontal switch selection signal .phi.H is connected to the gate of
 P-channel MOSFET Q5 of horizontal switch 64 while second buffer 68 which
 outputs one of predetermined voltage VDD0 applied to the power supply
 terminal and ground potential Vss in response to a negated value of
 horizontal switch selection signal .phi.H is connected to the gate of
 N-channel MOSFET Q6.
 Power supply terminals of first buffer 67 and second buffer 68 are
 connected to second external terminal 63, and predetermined voltage VDD0
 is inputted from the voltage control circuit or an external constant
 voltage circuit.
 It is to be noted that impedance element 60 is a circuit composed of a
 plurality of elements such as, for example, a vertical switch or a
 bolometer described hereinabove in connection with the first working
 example.
 In such a construction as described above, semiconductor device 6 of the
 present working example is characterized in that predetermined control
 voltage VBB can be applied independently to the substrate of P-channel
 MOSFET Q5 through first external terminal 65. As described above in
 connection with the first working example, control voltage VDD is normally
 applied to the substrate of P-channel MOSFET Q5.
 Where such a construction as described above is employed, similar effects
 to those achieved by controlling the potential between the gate and the
 source (electrode connected to output terminal 62) of P-channel MOSFET Q5
 by a substrate effect can be achieved by controlling voltage VBB to be
 applied to the substrate of P-channel MOSFET Q5.
 Consequently, control of operating point Vop which determines the 1/f noise
 coefficient characteristic of P-channel MOSFET Q5 is equivalent to control
 of the potential between the gate and the source of P-channel MOSFET Q5,
 and the 1/f noise coefficient characteristic of P-channel MOSFET Q5 can be
 controlled by control voltage VBB to be applied to the substrate.
 Accordingly, as described hereinabove in connection with the first working
 example, when semiconductor device 6 is rendered operative with the
 voltage of the operating point set to a value higher than Vopmax (on the
 right side of a peak of FIG. 3), since the 1/f noise coefficient
 characteristic of horizontal switch 64 depends principally upon the 1/f
 noise coefficient characteristic of P-channel MOSFET Q5, the 1/f noise
 coefficient characteristic of horizontal switch 64 can be controlled by
 control voltage VBB to be applied to first external terminal 65.
 It is to be noted that, in this instance, since the voltage to be applied
 to second external terminal 63 does not have an influence on the 1/f noise
 coefficient characteristic of horizontal switch 64, predetermined voltage
 VDD0 is applied to second external terminal 63.
 Consequently, by setting voltage VBB to be applied to first external
 terminal 65 to a voltage lower than control voltage VDD to be applied to
 the gate of N-channel MOSFET Q6 and preferably equal to operating point
 Vop, an increase of 1/f noise of semiconductor device 6 can be suppressed
 similarly as in the first working example.
 Further, since the voltage control circuit is required to apply voltage VBB
 only to the substrate of P-channel MOSFET Q5 which has an influence on the
 1/f noise coefficient characteristic, optimization of the driving capacity
 of a driver circuit and so forth in the voltage control circuit is
 allowed.
 (Fourth Working Example)
 In the following, a fourth working example of the first embodiment of the
 present invention is described with reference to the drawings.
 Semiconductor device 7 of the present working example is different from the
 third working example in that, as seen in FIG. 7, it includes voltage
 conversion circuit 75 for applying control voltage VBB to the substrate of
 P-channel MOSFET Q7 which forms horizontal switch 74. Since the other
 construction is similar to that of the third working example, description
 thereof is omitted here.
 Referring to FIG. 7, voltage conversion circuit 75 in the present working
 example converts predetermined voltage VDD0 inputted thereto from external
 terminal 73 into voltage VBB and applies voltage VBB to the substrate of
 P-channel MOSFET Q7. By controlling voltage VBB to be applied to the
 substrate of P-channel MOSFET Q7 by voltage conversion circuit 75 in this
 manner, an increase of 1/f noise can be suppressed similarly as in the
 third working example.
 Further, since voltage conversion circuit 75 is provided in semiconductor
 device 7, the first external terminal described in connection with the
 third working example is not required, and the area required for a pad or
 a wiring line in the semiconductor device can be eliminated.
 Furthermore, since it is required to apply, in addition to an operating
 point, only predetermined voltage VDD0 to semiconductor device 7,
 semiconductor device 7 has a good operability.
 Further, since only predetermined voltage VDD0 is required to be applied to
 the external terminal, an external circuit for supplying voltage VDD0 can
 be implemented with a variable voltage circuit or the like, and the
 circuit construction is simplified.
 It is to be noted that, while voltage conversion circuit 75 of the present
 working example has a circuit construction which generates voltage VBB in
 response to an input of predetermined voltage VDD0, another circuit
 construction wherein the voltage of operating point Vop is detected by a
 detection circuit provided outside semiconductor device 7 and is inputted
 to voltage conversion circuit 75 to generate voltage VBB may be employed.
 Alternatively, a different circuit construction wherein the voltage of
 output terminal 72 is detected in the inside of semiconductor device 7 and
 inputted to voltage conversion circuit 75 to generate predetermined
 control voltage VBB may be employed.
 As described above, by measuring a 1/f noise coefficient characteristic of
 a semiconductor device in advance and applying, to a MOSFET of the
 semiconductor device, control voltage VDD with which 1/f noise coefficient
 K of the semiconductor device has a low value in response to operating
 point Vop of the semiconductor device from the measured characteristic, an
 increase of 1/f noise can be suppressed also when bias current Ib is
 increased. Accordingly, an increase of the signal component is allowed and
 the S/N ratio can be improved.
 In this instance, similar effects can be achieved even if control voltage
 VDD is applied only to the MOSFET which has a significant influence on 1/f
 noise of the entire semiconductor device.
 Further, since a special material for improving the S/N ratio need not be
 used and the structure of an element is not complicated, the time and the
 cost required for development of an element are not required, and the
 production cost is reduced.
 (Second Embodiment)
 In the following, a second embodiment of the noise reduction method for a
 semiconductor device of the present invention is described with reference
 to the drawings.
 The second embodiment provides a method which reduces 1/f noise of a
 semiconductor device by setting element dimensions (channel length L and
 channel width W) of a MOSFET which is a component of the semiconductor
 device so that the 1/f noise coefficient may be minimized. It is to be
 noted that, since the constructions of the semiconductor device, read-out
 circuit and voltage control circuit are similar to those in the first
 embodiment, description thereof is omitted here.
 The 1/f noise coefficient (refer to FIG. 4) of the semiconductor device is
 composed of 1/f noise coefficients of individual components as recognized
 from expression (12) given hereinbelow.
 Particularly, the 1/f noise of the horizontal switch has the most
 significant influence on the magnitude of 1/f noise of the semiconductor
 device due to the facts that the horizontal switch is formed from a MOSFET
 which is reputed to be high in 1/f noise and that a variation of the
 operating point varies the resistance value.
 This can be recognized from the fact that, of the 1/f noise coefficient
 characteristic illustrated in FIG. 4 (1/f noise coefficient characteristic
 with respect to the operating point where only the horizontal switch is
 involved), the operating point at which the 1/f noise coefficient exhibits
 a maximum value and, of the 1/f noise coefficient characteristic
 illustrated in FIG. 3 (1/f noise coefficient characteristic with respect
 to the operating point of the semiconductor device), the operating point
 at which the 1/f noise coefficient characteristic exhibits a maximum
 value, have an equal voltage. Accordingly, in order to reduce the 1/f
 noise of the semiconductor device, it is effective to reduce the 1/f noise
 of the horizontal switch.
 It is to be noted that, in the following description, for simplified
 description, it is assumed that channel length Lp of the P-channel MOSFET
 and channel length Ln of the N-channel MOSFET are individually fixed to
 predetermined values (Lp0 and Ln0) and the total channel width of the
 P-channel MOSFET and the N-channel MOSFET is fixed to 600 .mu.m (Wp+Wn=600
 .mu.m). Further, control voltage VDD is fixed to 13 [V].
 Usually, since a MOSFET has a lower resistance and exhibits a higher
 current driving capacity as the ratio (W/L) of channel length W to channel
 width L decreases, this is preferable as a characteristic of an element.
 Therefore, taking characteristics of an element such as a layout area and
 channel length modulation, design rules and other necessary conditions
 into consideration, usually channel length L is set short and channel
 width W is set large.
 Consequently, here, channel length L is set to a value as low as possible
 within a range which can be realized based on design rules. Further, since
 channel width W is limited by the layout area of an element and so forth,
 here the total value of channel widths W is fixed, and as an example, it
 is set to 600 .mu.m (Wp+Wn=600 .mu.m).
 In the following, a method of optimizing channel widths Wp and Wn and
 channel lengths Lp and Ln of the P-channel MOSFET and the N-channel MOSFET
 which compose the horizontal switch so that the 1/f noise coefficients of
 them may be minimized is described with reference to a flow chart of FIG.
 8.
 Referring to FIG. 8, first in step S1, a temporary horizontal switch is
 formed using a P-channel MOSFET and an N-channel MOSFET having known
 element dimensions, and the relationship of the 1/f noise coefficient to
 the operating point of each of the P-channel MOSFET and the N-channel
 MOSFET is measured.
 In this instance, the control voltage to the horizontal switch composed of
 the MOSFETs having known element dimensions is set to a voltage equal to
 control voltage VDD of a semiconductor device to be designed (here,
 VDD=13[V]). It is to be noted that the channel width of the P-channel
 MOSFET having known element dimensions is represented by Wp0, the channel
 length by Lp, the channel width of the N-channel MOSFET by Wn0, and the
 channel length by Ln.
 FIG. 9 illustrates relationships of the 1/f noise coefficients to the
 operating points of the P-channel MOSFET and the N-channel MOSFET which
 compose the horizontal switch and have known element dimensions. It is to
 be noted that curve a in FIG. 9 indicates the 1/f noise coefficient
 characteristic of the P-channel MOSFET while curve b indicates the 1/f
 noise coefficient characteristic of the N-channel MOSFET.
 As can be seen from FIG. 9, 1/f noise coefficient (curve a) Kp of the
 P-channel MOSFET exhibits a tendency in which it decreases as operating
 point Vop increases (because the ON resistance of the P-channel MOSFET
 decreases). Meanwhile, 1/f noise coefficient characteristic (curve b) Kn
 of the N-channel MOSFET exhibits another tendency in which it increases as
 operating point Vop increases (because the resistance of the N-channel
 MOSFET increases).
 Then, in step S2, from the 1/f noise coefficient characteristics of the
 P-channel MOSFET and the N-channel MOSFET, which have known element
 dimensions, measured in step S1 (refer to FIG. 9), the 1/f noise
 coefficient at an operating point of the semiconductor device to be
 designed is calculated.
 From FIG. 9, it can be seen that, when the operating point is set to Vop0
 (=8.3 [V]), the 1/f noise coefficient of the P-channel MOSFET is
 determined to be Kp0 and the 1/f noise coefficient of the N-channel MOSFET
 is determined to be Kn0.
 Then, in step S3, relationships of the 1/f noise coefficients to channel
 areas L.times.W of the P-channel MOSFET and the N-channel MOSFET which are
 components of the semiconductor device to be designed are calculated.
 FIG. 10 illustrates the relationships of the 1/f noise coefficients to the
 channel areas of the MOSFETs. It is to be noted that curve c in FIG. 10
 indicates the characteristic of 1/f noise coefficient Kp to channel area
 Lp.times.Wp of the P-channel MOSFET while curve d indicates the
 characteristic of 1/f noise coefficient Kn to channel area Ln.times.Wn of
 the N-channel MOSFET. Determination of those two curves c and d is
 described below.
 First, channel area Lp0.times.Wp0 of the P-channel MOSFET and channel area
 Ln0.times.Wn0 of the N-channel MOSFET which have been used in step S1 and
 have known element dimensions are calculated.
 Then, from channel area Lp0.times.Wp0 and 1/f noise coefficient Kp0 of the
 P-channel MOSFET calculated in step S2, point P0 on the graph is
 determined. Similarly, from channel area Ln0.times.Wn0 and 1/f noise
 coefficient Kn0 of the N-channel MOSFET calculated in step S2, point N0 on
 the graph is determined.
 Thereafter, the gradients of curves c and d are determined. It is generally
 known that the 1/f noise coefficient of a MOSFET increases in proportion
 to channel area L.times.W to the mth power (-1.5.ltoreq.m.ltoreq.-0.5). It
 is to be noted that FIG. 10 illustrates the curves where m=-1.
 Accordingly, curves c and d are straight lines which pass point P0 and
 point N0, respectively, and have a predetermined gradient given by m=-1.
 It is to be noted that, where the operating point is not Vop0, since the
 values of 1/f noise coefficient Kp of the P-channel MOSFET and 1/f noise
 component Kn of the N-channel MOSFET are individually different as seen in
 FIG. 9, the characteristics of 1/f noise coefficients K with respect to
 channel areas L.times.W are drawn as curves having different intercepts
 from those of curves c and d shown in FIG. 10.
 Here, the value of m may be determined measuring the 1/f noise coefficient
 characteristic of a different MOSFET which has different channel area
 L.times.M but has known element dimensions.
 Then, in step S4, the channel widths of the P-channel MOSFET and the
 N-channel MOSFET of the semiconductor device to be designed are set to
 arbitrary values Wp1 and Wn1 (here, Wp1+Wn1=600 .mu.m), respectively.
 Then, in step S5, channel area Lp0.times.Wp1 and channel area Lp1.times.Wp0
 for channel width Wp1 of the P-channel MOSFET and channel width Wn1 of the
 N-channel MOSFET set in step S4 are calculated, and point P1 and point N1
 are calculated from the characteristics of the 1/f noise coefficient with
 respect to the channel area illustrated in FIG. 10 are calculated,
 whereafter 1/f noise coefficients Kp1 and Kn1 then are calculated.
 Thereafter, in step S6, where the channel width of the P-channel MOSFET to
 be designed is represented by Wp1 and the channel width of the N-channel
 MOSFET by Wn1, resistance Rp1 of the P-channel MOSFET, resistance Rn1 of
 the N-channel MOSFET and resistance RH of the horizontal switch are
 calculated.
 Resistance Rp of the P-channel MOSFET is calculated based on the following
 expressions known popularly with various corrections performed thereto so
 that it may coincide with an actual device characteristic:
 ##EQU3##
 where Vds is the source-drain voltage, Id is the drain current, Wp is the
 channel width, Lp is the channel length, .mu.p is the mobility of holes in
 the channel, C0 is the gate capacitance, Vgs is the gate-source voltage,
 Vth is the threshold voltage, .phi.f is the Fermi potential difference,
 Vfb is the flat band voltage, .epsilon.k is the dielectric constant,
 .epsilon.0 is the dielectric constant of the vacuum, q is the charge
 quantity of an electron, Na is the ionized acceptor concentration, and Vbs
 is the substrate-source voltage.
 Also resistance Rn of the N-channel MOSFET is calculated similarly
 replacing the constants in expressions (8) and (9) with constants peculiar
 to the N-channel MOSFET.
 Further, resistance RH of the horizontal switch is calculated in accordance
 with the following expression:
EQU RH=Rp.times.Rn/(Rp+Rn) (10)
 FIG. 11 illustrate an example of characteristics of resistance Rp of the
 P-channel MOSFET at operating point Vop, resistance Rn of the N-channel
 MOSFET and resistance Rh of the horizontal switch where channel width Wp
 of the P-channel MOSFET and channel width Wn of the N-channel MOSFET are
 used as parameters.
 Curves a1, b1 and c1 in FIG. 11 indicate characteristics of resistance RH
 of the horizontal switch and characteristics where the ratio of channel
 width Wp of the P-channel MOSFET/channel width Wn of the N-channel MOSFET
 is set to 400/200, 450/150 and 500/100 (the units are Wp [.mu.m]/Wn
 [.mu.m]). It is to be noted that, in FIG. 11, the characteristics of
 resistance Rp of the P-channel MOSFET are indicated by alternate long and
 short dash lines and the characteristics of resistance Rn of the N-channel
 MOSFET are indicated by broken lines.
 From FIG. 11, it can be seen that, as channel width Wp of the P-channel
 MOSFET increases, resistance Rp of the P-channel MOSFET decreases, but as
 channel width Wn of the N-channel MOSFET increases, resistance Rn of the
 N-channel MOSFET decreases.
 Further, resistance values RH of the horizontal switch exhibit a reversal
 in magnitude at a boundary in the proximity of operating point Vop=7.6
 [V].
 In particular, where operating point Vop is lower than 7.6 [V], curve
 a1&lt;b1&lt;c1, and as channel width Wp of the P-channel MOSFET increases,
 resistance value RH of the horizontal switch increases. On the other hand,
 where operating point Vop is equal to or higher than 7.6 [V], curve
 c1&lt;b1&lt;a1, and as channel width Wp of the P-channel MOSFET increases,
 resistance value RH of the horizontal switch decreases.
 It is to be noted that FIG. 11 additionally indicates resistance Rp1 of the
 P-channel MOSFET, resistance Rn1 of the N-channel MOSFET and resistance
 RH1 of the horizontal switch where the channel width of the P-channel
 MOSFET is Wp1 and the channel width of the N-channel MOSFET is Wn1.
 Then, in step S7, 1/f noise coefficient KH of the horizontal switch is
 calculated in accordance with the following expression:
 ##EQU4##
 where Kp is the 1/f noise coefficient of the P-channel MOSFET, Rp the
 resistance value of the P-channel MOSFET, Kn the 1/f noise coefficient of
 the N-channel MOSFET, and Rn the resistance value of the N-channel MOSFET.
 Since the horizontal switch is formed from a P-channel MOSFET and an
 N-channel MOSFET connected in parallel, 1/f noise coefficient Kp of the
 P-channel MOSFET and 1/f noise coefficient Kn of the N-channel MOSFET are
 multiplied by the squares of the resistance values of the other MOSFETs as
 weights, respectively, as seen from expression (12).
 FIG. 12 illustrates relationships of 1/f noise coefficients to operating
 points of the horizontal switch. In FIG. 12, relationships of 1/f noise
 coefficient KH to an operating point of the horizontal switch where
 channel width Wp of the P-channel MOSFET and channel width Wn of the
 N-channel MOSFET are used parameters, and curves a2, b2 and c2 indicate
 characteristics where channel width Wp of the P-channel MOSFET and channel
 width Wn of the N-channel MOSFET are set to Wp/Wn=400/200, 450/150 and
 500/100, respectively.
 Here, 1/f noise coefficients Kp1 and Kn1 and resistance values Rp1 and Rn1
 obtained by the processing in the steps up to step S6 are substituted into
 expression (11) to calculate 1/f noise coefficient KH1 only of the
 horizontal switch.
 It is to be noted that 1/f noise coefficient KH of the horizontal switch at
 any other operating point than Vop0 is a value obtained by calculating 1/f
 noise coefficients Kp and Kn for each operating point from the
 characteristic (FIG. 9) measured in step S1 and performing the processing
 in steps S2 to S6 using thus calculated 1/f noise coefficients Kp and Kn.
 As seen from FIG. 12, where the operating point is at Vop0 (=8.3 [V]), even
 if the channel widths of the MOSFETs vary, little difference appears with
 1/f noise coefficient KH of the horizontal switch.
 On the other hand, where the operating point is at Vop1 (=6.6 [V]), the
 magnitude of 1/f noise coefficient KH of the horizontal switch exhibits
 the relationship of curve a2&lt;b2&lt;c2, but where the operating point is at
 Vop2 (=10 [V]), the magnitude of 1/f noise coefficient KH of the
 horizontal Sw exhibits the relationship of curve c2&lt;b2&lt;a2.
 Thereafter, in step S8, 1/f noise coefficient KALL of the entire
 semiconductor device is calculated in accordance with the following
 expression:
 ##EQU5##
 where KV, KB and KH are the 1/f noise coefficients of the vertical switch,
 bolometer and horizontal switch, respectively, and RV, RB and RH are the
 resistance values of the vertical switch, bolometer and horizontal switch,
 respectively. It is to be noted that KV, KB, RV and RB are values measured
 in advance, and KH and RH are values calculated in the processing up to
 step S7. Further, while expression (12) indicates 1/f noise coefficient
 KALL of the entire semiconductor device where the semiconductor device is
 composed of a vertical switch, a bolometer and a horizontal switch
 connected in series, where the semiconductor device is composed otherwise
 of a plurality of elements connected in series and each having an
 impedance and a MOSFET circuit (for example, a horizontal switch)
 including a MOSFET, 1/f noise coefficient KALL of the entire semiconductor
 device is calculated in accordance with
 ##EQU6##
 where KH1 is the 1/f noise coefficient of the MOSFET circuit, RH1 is the
 resistance value of the MOSFET circuit, Ki (i=positive numbers of 1 to N)
 are the 1/f noise coefficients of the elements each having an impedance,
 and Ri (i=positive numbers of 1 to N) are the resistance values of the
 elements each having an impedance.
 In a semiconductor device such as shown in FIG. 1, since a vertical switch,
 a bolometer and a horizontal switch are connected in series, each of the
 1/f noise coefficients is multiplied by the square of a resistance as a
 weight as seen from expression (12). Therefore, if the resistance is low,
 then even if the 1/f noise coefficient is high, the influence upon the 1/f
 noise of entire semiconductor device 1 is little.
 By the processing in step S8, 1/f noise coefficient KALL of the entire
 semiconductor device with respect to channel lengths L and channel widths
 W of the MOSFETs is determined.
 FIG. 13 is a graph illustrating relationships of the 1/f noise coefficient
 to the operating point of the semiconductor device where channel width Wp
 of the P-channel MOSFET and channel width Wn of the N-channel MOSFET are
 used as parameters.
 Curves a3, b3, c3, d3, e3, f3, g3 and h3 of FIG. 13 indicate
 characteristics where channel width Wp of the P-channel MOSFET and channel
 width Wn of the N-channel MOSFET are set to Wp/Wn=400/200, 450/150,
 500/100, 525/75, 550/50, 575/25, 600/0 and 0/600, respectively.
 It is to be noted that curve g3 indicates a characteristic where the
 horizontal switch is composed only of a P-channel MOSFET, and curve h3
 indicates a characteristic where the horizontal switch is composed only of
 an N-channel MOSFET.
 From FIG. 13, it can be seen that, as the operating point varies, the
 relationship in magnitude between channel widths Wp/Wn of the MOSFETs and
 1/f noise coefficient KH.
 1/f noise coefficient KALL1 of the entire semiconductor device can be
 obtained by substituting resistance value RH1 and 1/f noise coefficient
 KH1 of the horizontal switch calculated in steps S6 and S7 into expression
 (12).
 Further, channel width Wp of the P-channel MOSFET and channel width Wn of
 the N-channel MOSFET are varied, and then the control returns to the
 processing of step S4 to repetitively and successively perform the
 processing in the steps up to step S8.
 By executing processing in accordance with the flow chart described above,
 channel lengths and channel widths of the MOSFETs with which 1/f noise
 coefficient KALL of semiconductor device 1 is minimized with respect to an
 operating point of the semiconductor device can be determined.
 It is to be noted that, while a case wherein channel length Lp of the
 P-channel MOSFET and channel length Ln of the N-channel MOSFET are fixed
 is described here, the channel widths and the channel lengths of the
 MOSFETs can be optimized by setting channel lengths Lp and Ln
 simultaneously with the setting of channel widths Wp and Wn.
 Meanwhile, where a semiconductor device does not include a vertical switch,
 calculation should be performed with KV and RV of expression (12) set to
 zero (0).
 Further, while a horizontal switch which includes a P-channel MOSFET and an
 N-channel MOSFET connected in parallel is described as an example here,
 the application of the present invention is not limited to such a
 construction as just described, but the present invention may be applied
 to various circuits which includes a MOSFET.
 Consequently, by applying dimension optimization of a MOSFET described
 above to a semiconductor device which is composed of an element having an
 impedance and a MOSFET, the 1/f noise coefficient can be minimized, and an
 increase of 1/f noise can be prevented.
 Now, an example of a result of optimization of channel width Wp of the
 P-channel MOSFET and channel width Wn of the N-channel MOSFET by the
 processing described above is described.
 Where channel length Lp of the P-channel MOSFET and channel length Ln of
 the N-channel MOSFET are fixed (Lp=Ln=2.4 [.mu.m]) and the sum of the
 channel widths of the P-channel MOSFET and the N-channel MOSFET is 600
 [.mu.m] (Wp+Wn=600 [.mu.m]), a preferable range of the ratio (Wp/Wn)
 between the channel widths of the MOSFETs to operating point Vop can be
 determined as described in (1) to (4) below:
 (1) Where Vop.ltoreq.0.5.times.VDD, the ratio (Wp/Wn) between the channel
 widths of the P-channel MOSFET and the N-channel MOSFET is set to
 approximately 0/600.ltoreq.(Wp/Wn).ltoreq.500/100.
 The reason is that, as seen in FIG. 13, where the operating point is
 Vop.ltoreq.0.5.times.VDD, the 1/f noise coefficient exhibits a minimum
 value at (Wp/Wn)=0/600. Further, where
 0/600.ltoreq.(Wp/Wn).ltoreq.500/100, the 1/f noise coefficient exhibits an
 increase only by approximately 3 dB comparing with that where
 (Wp/Wn)=0/600.
 (2) Where 0.5.times.VDD&lt;Vop&lt;0.8.times.VDD, the ratio (Wp/Wn) between the
 channel widths of the P-channel MOSFET and the N-channel MOSFET should be
 set approximately to 550/50.ltoreq.Wp/Wn.ltoreq.600/0.
 The reason is that, as seen in FIG. 13, where the operating point is
 0.5.times.VDD&lt;Vop&lt;0.8.times.VDD, the 1/f noise coefficient exhibits a
 minimum value at (Wp/Wn)=0/600, but where
 550/50.ltoreq.(Wp/Wn).ltoreq.600/0, the 1/f noise coefficient exhibits an
 increase only by approximately 3 dB comparing with that where
 (Wp/wn)=600/0.
 (3) Where Vop.gtoreq.0.8.times.VDD, the channel width ratio (Wp/Wn) between
 the P-channel MOSFET and the N-channel MOSFET should be set approximately
 to 500/100.ltoreq.(Wp/Wn) .ltoreq.600/0.
 The reason is that, as seen in FIG. 13, where the operating point is
 Vop.gtoreq.0.8.times.VDD, the 1/f noise coefficient exhibits its minimum
 value at (Wp/Wn)=600/0, but where 500/100.ltoreq.(Wp/Wn).ltoreq.600/0, the
 1/f noise coefficient exhibits an increase only by approximately 3 dB
 comparing with that where (Wp/Wn)=600/0.
 (4) Where operating point Vop is set to an arbitrary value within the range
 of 0 to VDD, the ratio (Wp/Wn) between the channel widths of the P-channel
 MOSFET and the N-channel MOSFET should be set to 525/75
 (Wp/Wn).ltoreq.575/25, and approximately to (Wp/Wn)=550/50.
 The reason is that, as seen in FIG. 13, where operating point Vop is within
 the range of 0 to VDD, the characteristic of (Wp/Wn)=550/50 (curve e3)
 exhibits a substantially flat characteristic over the entire operation
 range, and an increase only by approximately 3 dB is exhibited where
 525/75.ltoreq.Wp/Wn.ltoreq.575/25.
 If the horizontal switch is composed only of a P-channel MOSFET, then the
 1/f noise coefficient exhibits a sudden increase within the range of
 Vop.ltoreq.0.5.times.VDD as seen from curve g3 of FIG. 13, but if the
 horizontal switch is composed only of an N-channel MOSFET, the 1/f noise
 coefficient exhibits a sudden increase within the range of
 Vop.gtoreq.0.5.times.VDD as seen from curve h3 of FIG. 13. Accordingly,
 operating point Vop is set so that it may not fall within the ranges
 mentioned above irrespective of the channel width.
 It is to be noted that, while the present embodiment is described in
 connection with an example wherein control voltage VDD is fixed to 13 [V],
 if control voltage VDD increases, then the characteristics of 1/f noise
 coefficients Kp and Kn of the P-channel MOSFET and the N-channel MOSFET
 illustrated in FIG. 9 are shifted to higher operating point Vop side (to
 the right side in FIG. 9), but the resistance characteristic of the
 horizontal switch illustrated in FIG. 11 is shifted to higher operating
 point Vop side (to the right side in FIG. 11). On the contrary, if control
 voltage VDD decreases, then the characteristics of 1/f noise coefficients
 Kp and Kn of the P-channel MOSFET and the N-channel MOSFET illustrated in
 FIG. 9 are shifted to lower operating point Vop side (to the left side in
 FIG. 9), but the resistance characteristic of the horizontal switch
 illustrated in FIG. 11 is shifted to lower operating point Vop side (to
 the left side in FIG. 11). Accordingly, the noise reduction method of the
 present embodiment can be applied also to a case other than where control
 voltage VDD is 13 [V].
 By the way, where channel length Lp of the P-channel MOSFET and channel
 length Ln of the N-channel MOSFET are equal to each other, the ratio
 (Wp/Wn) between channel width Wp of the P-channel MOSFET and channel width
 Wn of the N-channel MOSFET is equal to the ratio (Sp/Sn) between current
 driving capacities Sp and Sn of them.
 In other words, the ratio (Wp/Wn) between the channel widths of the
 P-channel MOSFET and the N-channel MOSFET can be replaced by the ratio
 (Sp/Sn) between the current driving capacities in accordance with the rule
 of scaling.
 Accordingly, a preferable range of the ratio (Wp/Wn) between the channel
 widths of the P-channel MOSFET and the N-channel MOSFET with respect to
 operating point Vop is set as a range of the ratio (Sp/Sn) in current
 driving capacity as given in (5) to (8) below:
 (5) Where Vop.ltoreq.0.5.times.VDD, the ratio (Sp/Sn) in current driving
 capacity should be set approximately to 0 .ltoreq.(Sp/Sn).ltoreq.5.
 (6) Where 0.5.times.VDD.ltoreq.Vop.ltoreq.0.8.times.VDD, the ratio (Sp/Sn)
 in current driving capacity should be set approximately to
 11.ltoreq.(Sp/Sn).
 (7) Where Vop.gtoreq.0.8.times.VDD, the ratio (Sp/Sn) in current driving
 capacity should be set approximately to 5.ltoreq.(Sp/Sn).
 (8) Where operating point Vop is set to an arbitrary value within the range
 of 0 to VDD, the ratio (Sp/Sn) in current driving capacity should be set
 to 7.ltoreq.(Sp/Sn).ltoreq.23, and approximately to (Wp/Sn)=11.
 Since the dimensions of the MOSFETs which compose the semiconductor device
 are optimized in accordance with the procedure described above so that the
 1/f noise coefficient may be minimized, an external circuit for minimizing
 the 1/f noise coefficient becomes unnecessary, and the construction of the
 semiconductor device can be simplified. Accordingly, minimization and
 reduction in power dissipation of the semiconductor device can be
 achieved.
 While a preferred embodiments of the present invention has been described
 using specific terms, such description is for illustrative purposes only,
 and it is to be understood that changes and variations may be made without
 departing from the spirit or scope of the following claims.