ECT 09 091

1 6

CMOS

High-resistance device consisting of subthreshold-operated CMOS differential pair Shin’ichi Asai , Ken Ueno, Tetsuya Asai, and Yoshihito Amemiya, (Hokkaido University)

Abstract

We propose a CMOS circuit that can be used as an equivalent of resistors. This circuit uses a differential pair consisting of diode-connected MOSFETs and operates as a high-resistance resistor when driven in the subthreshold region. Its resistance can be controlled in a range of 1-1000 MΩ by adjusting the driving current for the circuit. For example, we realized a 123 MΩ resistor with a tail current of 1 nA. The results of the fabrication using a 0.35-µm 2P-4M CMOS process technology and measurement of the circuit are described.

(integrated circuit, high resistance, differential circuit, subthreshold)

1.

CMOS10 M

CMOS

1-2 kΩ/100 MΩ 0.5 mm2

CMOS

(1) MOSFET-

100 MΩ

(2) (3) (4)

MOSFET

1

Fig. 1 Outline of resistor circuit equivalent to a resistor with terminals 1 and 2.

CR

M1 M2Ib

Ib /2

1 2M2M1

ΔI ΔI

ΔV

Ib

Ib /2Ib /2

Vdd

2 6

1 2 VI 2 I

IV 2

( )

MOSFET ID MOSFET -VGS - VDS

(5)

ID =I b2

=W

LI0 exp

q (VGS − Vth )

mkT

⎛ ⎝ ⎜ ⎞

⎠ ⎟

⋅ 1 − exp −qVDSkT

⎛ ⎝ ⎜ ⎞

⎠ ⎟

⎛ ⎝ ⎜

⎞ ⎠ ⎟ ,

I0 = μCox (m − 1) ⋅kT

q

⎛ ⎝ ⎜ ⎞

⎠ ⎟ 2

.................... (1)

W/L mk T q Vth

MOSFET µ CoxVDS > 0.1 V ID

ID =I b2

=W

LI0 exp

q (VGS − Vth )

mkT

⎛ ⎝ ⎜ ⎞

⎠ ⎟ ......................... (2)

1-2 VM1

I b2

+ ΔI =W

LI0 exp

q (VGS − Vth + ΔV / 2)

mkT

⎛ ⎝ ⎜ ⎞

⎠ ⎟

=I b2exp

qΔV

2mkT

⎛ ⎝ ⎜ ⎞

⎠ ⎟

........... (3)

qΔV/(2mkT) << 1 (3)

I b2

+ ΔI =I b2

1 +qΔV

2mkT

⎛ ⎝ ⎜ ⎞

⎠ ⎟ .......................................... (4)

R =ΔV

ΔI=4mkT

qIb......................................................... (5)

Ib = 1nA100MΩ

mkT/q

2Ib M1-M5

MOSFET1-2

2

Fig. 2 Resistor circuit with biasing subcircuit.

3 Fig. 3 Offset currents of resistor circuit. Offset currents ΔI1 and ΔI2 consist of common-mode offset current ICM and differential offset current IDIFF.

0 3I10 I20 2

i () ICM ii

IDIFFI10 I20

ΔI10 = IDIFF + ICM ...................................................(6) ΔI20 = IDIFF − ICM ...................................................(7)

ICM M5 M3-M42 1 IDIFF

M1-M3 M2-M4

3.

0.35-µm 2P-4M CMOSMOSFET

M3 M4

M5

M1 M2ΔI1 ΔI2

1 2

Vdd

Ib

Biasing subcircuit Resistor circuit

ΔI10 ΔI20

ICMICM

IDIFF

1 2

VCM

3 6

4 - Fig. 4 Voltage-current characteristic of resistor circuit, measured for Ib = 1 nA, Vdd = 3 V and VCM ( common-mode voltage for terminals 1 and 2 ) = 1.5 V. W/L = 20 µm/4 µm 105 µm × 110 µm

4 Vdd = 3 V( )VCM = 1.5 V Ib = 1 nA

1 - 2 - ( V- I ) 40 mV 40 mV

-a

- b 1I1 ( ) 2 I2

( )

VCM5 Vdd = 3 V Ib = 1 nA

VCM 0-3 VICM ( ) IDIFF ( )

VCM 0.4-2.8 V

Ib 6

(5)Ib Ib

Ib = 10 nA 12 MΩ Ib = 1 nA123 MΩ

4. CR

4 1

CR7

5 -VCM Fig. 5 Offset currents as a function of common-mode voltage VCM for terminals 1 and 2, measured for Ib = 1nA and Vdd = 3 V.

6 Ib - Fig. 6 Resistance of resistor circuit as a function of tail current Ib.

Sold line shows measured data, and dashed line shows theoretical resistance.

3 G

G = 1 − 5R2ω 2C 2 − jRωC (R2ω 2C 2 − 6)...................(8)

R C 1/jωCC (8)

0 π RωC (R2ω 2C 2 − 6) = 0 ................................................(9)

ω =6

CR.......................................................................(10)

0

-40 -20 0 20 40-0.4

-0.3

-0.2

-0.1

0.1

0.2

0.3

0.4C

urre

nt [n

A]

ΔI1

ΔI2

(solid line)

(dashed line)

Voltage ΔV [mV]

VCM = 1.5 V

Res

ista

nce

[MΩ

]

Tail current Ib [nA]

Measured

1

10

100

1000

0.1 1 10 100

4mkTqIb

Offs

et c

urre

nt [n

A]

VCM [V]

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.5 1 1.5 2 2.5 3

ICM

IDIFF

4 6

f =6

2πCR.................................................................. (11)

R = 4mkT/(qIb)Ib f

4 2

8 0.35-µm 2P-4M CMOSCR350 µm × 370 µmRin = 5 kΩ Rf = 170 kΩ 9

Vdd = 3 V E0 = 1.5 V C = 10 pFIb = 10 nA 2.7 kHz Ib = 1 nA 290 Hz

5.

5 1 PTAT 4mkT/(qIb)

Ib

PTAT (Proportional To Absolute Temperature current) Ib

PTAT

10 PTATM6 M7 M8 M9 4

ß (CS CK CK )

PTATVdd M9

M6M8 M9

IPTAT M6 -VGS6 M7 - VGS7

IPTATRS

VGS6= VGS7 + IPTAT RS

RS =1

CS f

.............................................. (12)

7 CR Fig. 7 CR phase-shift oscillator. The elements circled by dashed lines represent resistor circuits.

8 CR Fig. 8 Chip photograph of phase-shift oscillator. Chip size is 350 μm × 370 μm. Parameters used for fabrication were Rin = 5 kΩ, Rf = 170 kΩ, C = 10pF, Vdd = 3 V, and E0 = 1.5 V.

(a) Ib = 1 nA

(b) Ib = 10 nA 9

Fig. 9 Output waveforms of phase-shift oscillator, measured for two values of tail current Ib for resistor circuit.

210

mV

200 μs

1 ms

140

mV

Rin

Rf

Output V0C C CE0

Resistor circuit

Op AmpsOp AmpsOp Amps

370 μm370 μm

350

μm35

0 μm High Resistance ResistorsHigh Resistance ResistorsHigh Resistance Resistors

CapacitorsCapacitorsCapacitors

Rin, RfRin, RfRin, Rf

5 6

10 Fig. 10 Resistor circuit with temperature compensation.

RS ( CS

f ) (12)

IPTAT RS = VGS6 − VGS7

=mkT

qln

IDI0

⋅L

W

⎛ ⎝ ⎜

⎞ ⎠ ⎟ + Vth6

−mkT

qln

IDI0

⋅L

WK

⎛ ⎝ ⎜

⎞ ⎠ ⎟ − Vth7

=mkT

qln K

................... (13)

M6 M7 1 KMOSFET

PTAT IPTAT

IPTAT =mkTCS f

qln K ............................................... (14)

M9 M10 1 : αIPTAT 1/α

1-2 (5) (14)

R =4α

CS f ln K............................................................ (15)

5 2 0.35-μm CMOS

SPICE 11( )

11 Fig. 11 Temperature characteristic of resistor circuit for three tail currents.

0.9 nA - 6 nA(TC) 2610 ppm/°C - 2660

ppm/°C 12 10 PTAT IPTAT

CS = 0.55 pFf 910 kHz - 5.6 MHz

13 , PTAT

10f 20 MΩ - 140 MΩ

CK

1 : K

CK

M6

M1

M9 M4M8

8 st

age

M3M10

M5

M7

M2

f

21

α

α : 1

Start up

PTAT current source Resistor circuit

Vdd

CS

IPTAT IPTAT

0

20

40

60

80

100

120

140

160

Res

ista

nce

[MΩ

]

Temperature [°C]

Ib = 0.9 nA

Ib = 2 nA

Ib = 6 nA

80 60 40 20 0 -20

(2660 ppm/°C)

(2660 ppm/°C)

(TC = 2610 ppm/°C)

353 333 313 293 273 253Temperature [K]

6 6

12 PTAT Fig. 12 Temperature dependence of PTAT current for three switching frequencies.

330 ppm/°C - 690 ppm/°C( ) PTAT

( 1 /(CS f ))CS f

α Kα = 10, K = 2

60

6.

CMOS

1-1000 MΩCR

PTAT

13

Fig. 13 Temperature dependence of resistor with compensation. Parameters used for fabrication were Vdd = 3 V, α = 10,K = 2, CS = 0.55 pF.

PTAT

7.

(VDEC)

( ) A. Wang, B. H. Clhoun, and A. P. Chandracasan Sub-Threshold Design for Ultra Low-Power Systems, Springer, New York (2006)

( ) K. Nagaraj : “New CMOS Floating Voltage-Controlled Resistor”, Electron. Lett., Vol.22, No.12 pp.667-668 (1986)

( ) S. P. Singh, J. V. Hanson, and J. Vlach : “A New Floating Resistor for CMOS Technology”, IEEE Trans. Circuits Syst., Vol.36, No.9 pp.1217-1220 (1989)

( ) S. Sakurai and M. Ismail : “A CMOS Square-Law Programmable Floating Resistor Independent of the Threshold Voltage”, IEEE Trans. Circuits Syst. II, Vol.39, No.8 pp.565-574 (1992)

( ) Y. Taur and T. H. Ning Fundamentals of Modern VLSI Devices, .Cambridge, Cambridge Univ. Press, U.K. (2002)

353 333 313 293 273 253

f = 910 kHz

f = 2 MHz

f = 5.6 MHz

0

20

40

60

70

50

30

10

I PTA

T [n

A]

switching frequency

Temperature [K]

(0.07 nA/°C)

(0.03 nA/°C)

(TC = 0.19 nA/°C)

Temperature [°C] 80 60 40 20 0 -20

0

20

40

60

80

100

120

140

160

Res

ista

nce

[MΩ

]

Temperature [°C]

f = 910 kHz

f = 2 MHz

f = 5.6 MHz

80 60 40 20 0 -20

(500 ppm/°C)

(330 ppm/°C)

switching frequency

(TC = 690 ppm/°C)

w/o temperature compensation

353 333 313 293 273 253Temperature [K]