Matching properties of MOS transistors

624

Nuclear Instruments and Methods m Physics Research A305 (1991) 624-626 North-Holland

Section VI(b) . Readout circuit design

Matching properties of MOS transistors Marcel J.M. Pelgrom

Philips Research Laboratories WA Y519, P.O. Box 218, 5600 MD Eindhoven, The Netherlands

In measurement systems which use a large number of parallel channels equipped with MOS electronic subsystems (like amplifiers, A/D converters, etc.), the (mis)matching of MOS transistors is the ultimate limitation in performance. We identified 3 parameters that

contribute to the mismatch of MOS transistors which are designed to be identical: the threshold voltage VT, the current factor # and what we call the substrate factor K (body effect). For a large number of devices the values of one parameter follow a normal distribu-

10 MV

a(VT)

t

8 6 4 2 0 700110 20120 1015 515 - 1/

313

WL

af)

.8 a (/31 13 t .6%

3% 2%

700110 20120

c

1015 515 1/ W

20 120

313

d

10 15 515 ~11~

313

Fig. 1 (a) Standard deviation of the threshold VT as a function of the inverse transistor area for a pair of NMOS transistors; (b) idem for the substrate factor K; (c) idem for the normalized current factor ß; (d) comparison of the standard deviations for the normalized current factor /3 for parallel and rotated placement of the pair of NMOS transistors. 0168-9002/91/$03 .50 © 1991 - Elsevier Science Publishers B.V . (North-Holland)

M.J M Pelgrom /Matching properties of MOS transistors

tion characterized by a mean value and a variance a . One can suppose that the resultant value of each of the parameters is dependent on many randomly localized "events" such that the value becomes more accurate for a larger area device . The variance thus becomes a function of the inverse transistor dimensions W and L. Defects in the substrate and in the oxide cause "bath" type or parabolic distributions of the parameters over the wafers . For devices close to each other the mismatch contribution is small, but it grows with the distance D between devices. The following functions, taken from ref. [1] describe the mismatch, using the factors mentioned above: D2, a2(VT)=A22 IWL+S22 , a2(K) =AKIWL+SKD2, ° 2 (ß)lß 2= A 2 1WL+Sß2 D 2 .

With these functions one can determine the expected mismatch, e.g ., the spread on comparator thresholds, the offset on a long-tailed pair, the precision of current sources, etc. One could then predict the yield on certain circuits for a given production process. The predictability is of the order of 10% . Practical measurements are done on several wafers in a batch, on several transistors per wafer. Data are shown in figs . la to lc for each of the mismatch factors VT , K and ß respectively, as a function of the inverse WL . A linear relation exists between the variance of the distribution and the inverse square root of the transistor gate area as is seen in the figures. This holds for all 3 factors separately . This is contrary to the

a(VT) coefficients of several tests " own measurements x measurement by others

AVTO

625

Table 1 Matching data for NMOS and PMOS transistor pairs in a 50 rim gate oxide, 2 .5 wm n-well process Parameter

Standard deviation n-channel

p-channel

Unit

A vm AQ AK

30 2 .3 0 .016

35 3 .2 0.012

MV [Cm

S~ Se

4

4

4

4

2

SK

2

% l~m

F ~L m

~.V/~m

10-6/[Lm

10 -6 fV /gm

common belief that the geometry variations dominate the current factor mismatch . The rotation of transistors influences the matching as is shown in fig. Id but it is not widely understood why. In fact, only the current factor is seriously affected and not the VT and the substrate factor K. So rotation is possible if care is taken with respect to the current. In summary, the matching parameters which we determined are described in table 1. The comparison of measurements from various processes in figs . 2a and 2b shows that there exist a universality of matching characteristics even for processes in different factories. This fact is so far unexplained. The VT mismatch apparently is related to a quantity of 10 12 particles cm -2 which is in common for all processes. The study of limits on the matching can be used to obtain the ultimate circuit performance, e.g ., in design-

°1)

Aß

3%,um

coefficients of several tests

50 mV pm 40mVpm

2% ,um

30mVpm 20mVl.lm

1 %,um

10mv,l .lm 0 a

25nm 35nm 50nm 65nm 100nm - nominal gate oxide

0 b

25nm 35nm50nm65nm -= nominal gate oxide

Fig . 2. (a) Threshold mismatch factors as measured by the author (") and by others (X). Each point corresponds to the data of

several wafers in one batch; (b) idem for the current factor f3 .

VI . ROUND TABLE SESSIONS

M.J.M. Pelgrom / Matching properties of MOS transistors

626

a_(Il

1%

I 0.8 10.6% 0.4%

VOO= 5V VSB = OV WIL= 20/20 VTO = 085V Q (VTO) = 0.85 mV °(l3) =0.13% ß

02%

Fig. 3. Normalized standard deviation of the current in an NMOS transistor pair connected to 5 V drain. Dots are the measurement points, the solid curve is calculated using extracted mismatch data .

ing a temperature-independent reference voltage source,

which is found to have a variance of 18-19 mV as predicted. In fig. 3 the prediction for a current mirror is compared with the actual performance

E. Heijne (CERN) : Does your detailed study of the rmsmatch parameters lead to improvements on the matching of devices? M. Pelgrom: One obtains in this way more reliable rules to predict the mismatch, so one has the possibility to adapt the devices to the desired values . One can calculate for example the size of the gate area to obtain a certain degree of matching . One can also see that a reduced gate oxide thickness will improve the matching of the threshold voltage but it will not help in the mismatch of ß. The fascinating thing is the observation that every process in the world is on the straight line of 10 12 doping atoms (?)/particles cm -z , and there is no under-

standing why this is so . Therefore it is questionable if one can get somehow better . E. Heijne (CERN) : Is it then right to say that a submicron process will give improvement, due to the thinner gate oxide, as long as one keeps the gates long . M. Pelgrom: If one can make use of the extremely thin oxides available in some processes, e.g . for EPROMs, one can improve on mismatch by a large factor . It should be remarked that the numbers given here represent the minimal mismatch available, in an industrial history of many years of manufacturing. Quite regularly, the matching is an order of magnitude worse than shown here, due to identifiable mistakes in the factory. Therefore, I can not indicate how to improve the matching but I could indicate you many ways of how to degrade it .

Reference [11 M.J .M . Pelgrom et al ., IEEE J. Solid State Circ. 24 (1989) 1433 .

Discussion L. van den Berg (EG&G) : If doping nonumformities play a role in the mismatch effects that you observe, what happens if the device temperature is changed? M. Pelgrom: We did vary the temperature in the range 0 to 100° C but none of the mismatch parameters were affected by this . The doping related problem is not an insufficient ionization but more basically the presence or absence impurities in a given depleted region .

K. Kandiah (RAL): You expressed the degree of mismatch between areas with a number which involves charge and this is usually large. Normal variations on this may not be big enough to explain your observed fluctuations . Does this imply that there is a correlation distance in your process which is related to the area? M. Pelgrom: Do you realize that there are only several thousand doping atoms in the depletion region of a 1 ~t m X 1 Wm transistor? The statistical variations on such low numbers can be very important. K. Kandiah (RAL): So your conclusion is that statistical variations are the most important contribution to mismatch? M. Pelgrom: Yes, and the cause is expressed as a particle concentration, but I cannot indicate which could be these "particles", e.g. if they are in the oxide or elsewhere.