Charge Transfer in ChargeCoupled DevicesChoongKi Kim and Martin Lenzlinger Citation: Journal of Applied Physics 42, 3586 (1971); doi: 10.1063/1.1660774 View online: http://dx.doi.org/10.1063/1.1660774 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/42/9?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Observation of charge storage and charge transfer in a GaAlAsSb/GaSb chargecoupled device Appl. Phys. Lett. 36, 458 (1980); 10.1063/1.91506 GaAs chargecoupled devices Appl. Phys. Lett. 32, 383 (1978); 10.1063/1.90062 Accumulationmode chargecoupled device Appl. Phys. Lett. 25, 568 (1974); 10.1063/1.1655313 Effects of gamma radiation on chargecoupled devices Appl. Phys. Lett. 23, 400 (1973); 10.1063/1.1654934 Chargecoupled memory device Appl. Phys. Lett. 22, 650 (1973); 10.1063/1.1654541

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JOURNAL OF APPLIED PHYSICS VOLUME 42, NUMBER 9 AUGUST 1971

Charge Transfer in Charge-Coupled Devices*

Choong-Ki Kim and Martin Lenzlingert

Research and Development Laboratory, Fairchild Camera and Inststrument Corporation, Palo Alto, California 94304 (Received 18 February 1971)

The transfer characteristics of charge-coupled devices have been investigated theoretically and simulated experimentally. The transport of minority carriers along the Si-Si02 interface can be described by a diffusion equation where the effective diffusion coefficient is composed of two terms representing the drift and the diffusion currents. There are two time constants associated with the two current components. For typical operating conditions, the drift time constant is about 100 times smaller than the diffusion time constant. The charge transfer can theoretically be separated into a charging and a discharging process, and the final stages are described by the drift and the diffusion time constants, respectively. Transfer efficiencies for charge-coupled devices have been calculated from the discharging phenomena. The drift current increases the transfer efficiency significantly. For high transfer efficiencies (>99%), however, the increase of the transfer efficiency with transfer time is limited by the diffusion time constant. A simple scheme which overcomes this limitation is described. Experimen­tally, the charging and discharging conditions have been simulated by using gated diodes. Good agreement between theory and experiment has been found by a reasonable adjustment of the surface mobility alone.

I. INTRODUCTION good device, the storage time is of the order of 1 sec. 3

A charge-coupled device l , 2 consists of an array of closely spaced metal-oxide-semiconductor (MOS) capacitors. Minority carriers forming an inversion layer are stored in the potential well at one of the MOO capacitors and then transferred to an adjacent capacitor by adjusting the relative potentials to create a deeper well. The storage and transfer of minority carriers take place at semiconductor­insulator interface. During the transfer, the MOS capacitor where the carriers are stored is being discharged while the adjacent one is being charged. Therefore, the characteristics of the charging and discharging phenomena are directly reflected in the transfer characteristics of a charge-coupled device.

The surface potential 1> s during the transient period can be obtained from the three basic equations for an MOS capacitor. 4 USing the depletion approxima­tion, they are

In this paper the charging and discharging phenom­ena are studied separately by considering the trans­port of carriers along the Si -SiOz interface in a transient state. The continuity equation including both diffusion and drift terms is solved with appro­priate initial and boundary conditions. The solution is then compared with the experimental measure­ments made on gated diodes in terms of charging and discharging currents. Finally, the transfer characteristics of charge-coupled devices are found from the properties of the charging and discharging phenomena.

n. DEVELOPMENT OF EQUATIONS

A. MOS Capacitor in Transient State

Consider an MOS capacitor with n-type substrate. When a pulse with a sufficiently large negative vol­tage is applied to the metal electrode, a deep de­pletion region is initially created under the elec­trode. As time goes on, thermally generated mi­nority carriers are collected at the Si-Si02 inter­face and form an inversion layer. The time required for this process is called the storage time. For a

3586

Or-----~----._----_.-----.-----.

-I

CPs (V)

-2

-3

-4

-5

-6

---- EQUATION (6)

--- EQUATION (7)

FIG. 1. Two expressions of the surface potential, ND = 1015 cm-3, xo= 0.11-1, VT = - 2V, VFB = -1 V.

(1)

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CHARGE TRANSFER IN CHARGE-COUPLED DEVICES 3587

OXIDE ------, +++++~-----r----' r----

.... ____ .,,: t<O I '~ ____ )

I I I I \._----'

t > 0

n-TYPE SUBSTRATE

FIG. 2. Schematic diagram showing the operation of a charge-coupled device.

(2)

Qs=Qp +qNvxa' (3)

where V G is the voltage applied to the electrode, V F B

is the flat-band voltage, Co is the oxide capacitance per unit area, q is the electronic charge, N v is the donor concentration, Xd is the width of the depletion region, Eo is the permittivity, Ks is the dielectric constant of the substrate, and Qp is the charge per unit area due to minority carriers at the interface. The solution of the above three equations gives l

where B = (K/K)qNvxo' and Ko and Xo are dielectric constant and thickness of the oxide layer.

In the steady state,

(5)

where V T is the threshold voltage. Using Qps' Eq. (4) can be rewritten

CPs= VG - VFB +.2£QQ (VT - Vc ) PS

+~J[I-~(VG- VFB +~(VT- Vc})T/2 -If· (6)

For a typical device and typical electrode voltages, the surface potential is a nearly linear function of the minority-carrier concentration. Therefore, the dependence of CPs on Qp can be approximated by

CPs'"" CPso + (CPSl - CPsQ)(Q/Qps) , (7)

where CPS! and CPso are the surface potentials in equi­librium and in deep depletion, respectively.

The two expressions [Eq. (6) and Eq. (7)] are shown in Fig. 1 for a typical device. The error involved in the approximation has been found to be less than 5% for

Nv =1015-1016 cm-s , xo =0.1-0.2 Ji.,

Vc= 5 -10 V.

In Sec. III the approximation of the surface potential will be used to study the general characteristics of charging and discharging phenomena. The exact relationship will be used for the theoretical calcu­lation to be compared with the experimental results.

B. Transport of Carriers

(4) In a single MOS capacitor, the minority carriers are

Qp Qps 1~~~~----------________________________ ~2~.0L-____ ~

0.8 1.0

0.6

0.4

0.2

x T

FIG. 3. Minority-car­rier concentration vs distance for charging.

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3588 C-K. KIM AND M. LENZLINGER

TABLE 1. Parameters for two test devices with different gate lengths.

Device number

Gate length (mil) Junction radius (mil) Substrate doping level (cm-3)

Flat-band voltage (V) Threshold voltage (V) Oxide thickness (Al

06

2.5 3.6

2.0x1015

-1.1 -2.4

950

53

5 3.6

2.sx1015

-1. 35 - 3.1 1400

generated uniformly throughout the depletion region and are uniformly collected at the Si-Si02 interface. Therefore, Q p and <P s are functions of time only. In a charge-coupled device, however, the minority car­riers are transported along the interface. Conse­quently, Qp and <Ps are functions of both time and distance.

The transport of carriers can be described by the continuity equation

a~P=a~ (Dp~+/J.pQp aa~s} (8)

The rate of carrier generation is neglected because the transport of carriers occurs in a much shorter time than the storage time. In Eq. (8) the first term inside the parentheses represents the diffusion cur­rent and the second term represents the drift cur­rent. Accurate determination of the surface poten­tial at any given instant should be based on the so­lution of the two-dimensional Poisson's equation. Under an electrode, however, the two-dimensional problem can be separated into two independent one­dimensional problems as is usually done in MOSFET analyses. 5 When we make this approximation, the variation of <P s with x arises only through the varia­tion of Qp with x. (Note that this relationship does not apply to the space between two electrodes where

the potential at the oxide surface is some function of x.) Therefore

o<Ps_d<Ps aQp ax-dQ; ax'

From Eqs. (8) and (9),

(9)

~_ a ( aQp) at -ax Deff dx ' (10)

D Q d<Ps D eff = p+/J. p PdQ/ (11)

where D eff' the effective diffusion coefficient, is concentration dependent and is a function of t and x.

To find the initial and boundary conditions for Eq. (10) we consider the operation of a three-phase charge-coupled device shown in Fig. 2. For t < 0, the potential at electrodes 2 and 3 is V3 which is negative and larger than V2 , the potential at elec­trode 1. As a result, there is a potential well under electrode 1 and the minority carriers are stored there (V2 < V T)' At t = 0 the potential of electrode 2 is changed from V3 to VI' which is more negative than V2 • Then, a deep depletion region is initially formed under electrode 2 and, subsequently, the carriers are transferred from electrode 1 to elec­trode 2. As the carriers are transferred, the sur­face potential under electrode 2 rises while that under electrode 1 falls. For an effective transfer, VI should be sufficiently negative so that after the completion of the transfer, the surface potential under electrode 2 is still more negative than under electrode 1. This transfer of carriers can be con­sidered as a combination of charging and discharging phenomena of two closely spaced MOS capacitors.

Let us first study the charging and the discharging problems separately by conSidering electrode 1 as an

t - -T -=. 0.00?5(j~C:::::::===------===========1

0.8

0.4

0.1 x

T

3

6

1.0

FIG. 4. Minority-car­rier concentration vs distance for discharg­ing.

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CHARGE TRANSFER IN CHARGE-COUPLED DEVICES 3589

I­Z W 0: 0: ::::> u

o W N

<i ICf I

:2 0: o Z

I ~ t- 1/2

~-L - 71'2 , I~exp(---)

'/ 4 T

, T

~

FIG. 5. Charging current vs time.

infinite source of carriers for the charging of elec­trode 2, and by considering electrode 2 as an infinite sink of carriers for the discharging of electrode 1. How the solutions to these problems can be combined to predict the performance of charge-coupled devices will be discussed in Sec. IV. The appropriate initial and boundary conditions are

Qp(x ,0) =:0, 0 $.x $. L

Qp(O,t)=:QPs' t>O

~(L, t) =:0, t> 0

for the charging problem and

Qp(x,O)=:Qps' O;Sxs.L

Qp(O,t)=O, t>O

a~p(L,t)=O, t>O ux

(12)

(13)

for the discharging problem, where L is the length of the electrode. The infinite source and sink of car-

III. CHARACTERISTICS OF CHARGING AND DISCHARGING

PHENOMENA

In this section the general characteristics of charging and discharging phenomena will be dis­cussed USing the approximation for ¢s [Eq. (7)J. As will be seen later, the use of Eq. (7) gives an ex­tremely simple form for the effective diffusion co­efficient, thereby allowing us to find the general characteristics without too much mathematical com­plication.

From Eqs. (7) and (11)

Deff = fl/1 ¢ (QI +-8-::), where

A¢ = ¢Sl - ¢,sO'

QI _ fl/Dp - --;sq;- .

Using Einstein's relation,

kT/q £:\'=--A¢ .

(14)

For a typical device operation, A¢ is of the order of 5 V. Therefore, QI is about 0.005 at room tempera-

10-1

I-Z W 0: 0: ::::> u

0 W 10-3 N

-1 <!

(7r2 t) :2 0: I~exp -4 aT 0 10-4 Z

riers are represented by the boundary conditions at 10-5

X = O. The boundary conditions at x = L are obtained by noting that the flux is zero at the end of the elec-trode.

The charging and discharging currents are found by

after solving Eq. (10) subject to Eqs. (12) and (13).

t T

FIG. 6. Discharging current vs time. Note the difference in time scale from Fig. 5.

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3590 C-K. KIM AND M. LENZLINGER

DIODE GATE

! I !

r r ~ p+ ~ I I I I--L--' I I

n-TYPE SUBSTRATE

I FIG. 7. Cross section of the experimental gated diode

with circular geometry.

ture and the drift current is dominant when Q p

> 0.01 Qps'

The numerical solutions of Eq. (10) subject to initial and boundary conditions given by Eqs. (12) and (13) are shown in Figs. 3 and 4. For this solution, Eq. (14) is used for Deff and (]I is taken to be 0.01. The time tis normlaized with respect to the character­istic time constant for the drift component

T=V/ IIp':l.rp.

During the initial period of time, the electrode can be regarded as being infinitely long. Then the prob­lems are equivalent to sorption and desorption prob­lems in a semi-infinite medium. (Detailed discus­sions of sorption and desorption in a semi-infinite medium can be found in Ref. 6.) For this case Boltzmann's transformation can be applied and Q / Q ps is a function of x/2t 1/2 only:

Q/Qps = j(x/2f1/ 2).

Therefore, the charging and the discharging currents are proportional to 1/ tl/2 in this period.

For t» T, Q/QPs approaches unity for the charging problem and zero for the discharging problem. Therefore, Deff approaches IlP'~'rp and 1lP'::.rp(]l =:Dp for the charging and discharging problems, respec­tively. Since Deff is constant in this period, both charging and discharging currents will decrease ex­ponentially and the ratio of the charging time con­stant to the discharging time constant will be equal to (]I.

In the intermediate region, the effective diffusion coefficient increases with time for the charging problem and decreases with time for the discharging problem. This gives a distinguishing characteristic to the charging current:

d 2[

dt 2 <0

for some period of time. This characteristic which can be readily observed in experiment is a direct consequence of the effective diffusion coefficient being proportional to the carrier concentration.

(When the diffusion coefficient is a constant, d 2[/dt 2

> 0 at all times during the charging process. )

Figures 5 and 6 show the charging and discharging currents normlaized to

fo = QpslJ./",rp(Z/L) ,

where Z is the width of the electrode. The three different phases of the charging current are clearly shown in Fig. 5. The r l/2 dependence of the dis­charging current cannot be seen clearly in Fig. 6 simply because of the large time scale used.

Experimentally, the infinite source and sink of mi­nority carriers which were assumed for charging and discharging of an MOS capacitor can be most conveniently simulated using gated diodes. Figure 7 shows the cross section of the test device fabricated by standard processes. The experimental arrange­ments of measuring the charging and the discharging currents are shown in the inserts of Figs. 8 and 9. For the charging condition, negative pulses of var­ious amplitudes are applied to the gate with the diode connected to the substrate by a 50-0 resistor. For the discharging condition, a large negative pulse is applied to the diode with various dc negative vol­tages applied to the gate. The currents are found by measuring the potential drop across 50-0 resistors using a sampling scope. The discharging current is found by adding the substrate and the gate currents.

For the theoretical calculation to be compared with the experimental measurements, we use the exact equation for the surface potential, Eq. (6). The test

I (rnA)

7

6

--THEORY

---EXPERIMENT

80 100

(n sec)

FIG. 8. Charging current vs time for the test device No. 06.

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CHARGE TRANSFER IN CHARGE-COUPLED DEVICES 3591

6r-----.-----.------r-----.-----.------,-----,------,-,

5

I (rnA)

4

--THEORY

-- - EXPERIMENT

=

80 100

t (n sec)

devices have circular geometry and the cylindrical coordinate system is used accordingly.

120

Two devices with different gate length L have been used for the experiment. The doping level of the substrate, oxide thickness, flat-band voltage, and threshold voltage are determined from the standard C - V measurements, and the geometrical dimensions are found from the masks used. These parameters are given in Table I. The surface mobility which is

--THEORY

--- EXPERIMENT

I

0.2

o 0.5 0.6

(fL- 5 ee)

FIG. 10. Charging current vs time for the test device No. 53.

FIG. 9. Discharging current vs time 50.11 for the test device No. 06.

140 160

the only unknown parameter for the theoretical cal­culation has been determined by matching the theo­retical results to the experimental measurements. For the comparisons shown in Figs. 8-11, a con­stant value of 250 cm2 Iv sec has been used. This is in reasonable agreement with the results obtained by others. 7

Figures 8 and 10 show the charging currents for the two test devices. Since the charging time constant is approximately proportional to the inverse of the gate voltage, the charging current decays faster for larger gate voltages. The dependence of the charging time constant on the gate length can also be seen by comparing these two figures.

The discharging currents shown in Figs. 9 and 11 decay slower than the charging current as we have discussed before. As the magnitude of the current decreases, however, the error in the experimental measurements become relatively large and the long time constant for the discharging currents cannot be clearly observed.

IV. TRANSFER CHARACTERISTICS OF CHARGE-COUPLED

DEVICES

To find the transfer characteristics of a charge-cou­pled device, two adjacent MOS capacitors should be considered at the same time with the additional re­quirement that the sum of the charges stored in each capacitor remains constant. This is a difficult prob­lem requiring the solution of a two-dimensional time-dependent Poisson's equation because the sur­face potential under the gap between the electrodes depends not only on the carrier distribution but also on the potential difference between the electrodes. Even arbitrarily assuming a potential distribution at the oxide surface between the electrodes results in an equation much more difficult than the one treated

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3592 C-K. KIM AND M. LENZLINGER

1.4 r-----,----,---,---,----,-----r----r---

--THEORY

I (rnA)

0.8

--- EXPERIMENT

0.5

(fL sec)

before, since Eq. (9) does not hold between the elec­trodes.

However, some of the limitations of charge transfer in charge-coupled devices can be found from the charging and discharging phenomena studied in the previous section. When the two adjacent electrodes in a charge-coupled device are very close and the potential difference between them is large, a high electric field will be established between them. In this situation, the transfer time and the transfer ef­ficiency will be determined predominantly by the discharging electrode because discharging occurs more slowly than charging. Because of the high elec­tric field between the electrodes, the charging elec­trode can be regarded as an infinite sink of minority ,carriers. Therefore, the results of a single dis­charging MOS capacitor can be directly applied to find the transfer characteristics of a charge-coupled device.

The transfer time and the transfer efficiency can be most conveniently discussed in terms of QT' the total charge left under the discharging electrode:

QT(t) = Z foL Qp(x, t) dx.

In Fig. 12 Q T is shown for four different values of o!. O! = 00 corresponds to the hypothetical case where the discharging occurs by diffusion only. The lower curve for O! = 10-2 is obtained from the initial con­dition

Q p (x, 0);: Q po = 0 .1 Q t>s"

For all the other curves, Qpo=Qps ' The time is normalized by

0.6 0.7 0.8

Tdiff=V/Dp

FIG. 11. Discharging current vs time for the test device No. 53.

which is the characteristic time constant for the diffusion current.

During the initial period of the discharging process, when

Q/Qps»O!'

the drift current is dominant because of the large effective diffusion coefficient associated with it. This part of the discharging process can be charac­terized by the time constant

T=V/ IV~:"¢ =O!(V/Dp)

which is proportional to Ct. As the carrier concen­tration decreases, however, the diffusion current becomes dominant and QT decreases expontentially with time. The time constant for this exponential decay is determined by Tdiff which is independent of o!. The tail part of the curve for Ct = 00 can be ex­pressed as

QT 8 (7T 2 t )

QpsZL =7T2exp -"4 Tdif ; .

When O! has some finite value, we may express the exponential tail as

Q T 8 ( rr2 t ) QpsZL =7T

2Kexp -"4 Tdlff '

where K is the fraction of Q psZL which is discharged by diffusion. From Fig. 12 it is observed that K ~ 20! which is in reasonable agreement with the ear­lier observation that the discharging is diffusion limited when Q/Qps <O!. The results of two different

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CHARGE TRANSFER IN CHARGE-COUPLED DEVICES 3593

10- 1 90 -I :0 l> Z UJ '1

99 [Tl

:0

'" [Tl

a. '1 0 '1

"- (")

610-3 99.9~

(")

-<

10- 4 ~

FIG. 12. Total charge stored in the discharging electrode and transfer efficiency vs transfer time.

[Tl

'1 '1 [Tl (")

10- 1 90 -I

< [Tl

..J -I :0

N l> ~10-2 99 Z

0 UJ

"- '1 [Tl

0 ::u I-0 [Tl

,~ 10-3 '1 I- 99.9~

0 (")

[Tl

z (")

10- 4 -<

~

T diff

FIG. 13. The effective transfer efficiency of a "one" vs transfer time for three different values of Qpo for "zero".

initial conditions for Ci = 10-2 in the figure, and other numerical experiments, show that K is not a strong function of Q po as long as

Qp/Qps » Ci.

Also indicated in the figure is a scale for the trans­fer efficiency 1) defined as

1) = 1 - QT/QpoZL.

This scale applies only for the initial condition Q po

=Qps '

The effect of the drift current, which was called the "field-enhanced component", 1 can be observed by comparing the curves for finite values of (J with that

for Ci = o(). The drift current is important only during the initial period of the charge transfer and in­creases the transfer efficiency considerably. B As an example, the transfer effiCiency increases from 93% for Q = 0() to 99.8% for Ci = 10-2 when the transfer time is equal to Td1ff • If we are interested in high transfer efficiency (> 99%), however, the increase of the transfer efficiency with transfer time is lim­ited by the diffusion current and the upper limit of the operating frequency will be determined by the diffusion time constant. From these observations it is clear that there is a significant tradeoff between the transfer time and the transfer efficiency. This tradeoff is much more pronounced here than it would be for a simple exponential dependence because of the decrease of the effective diffusion coefficient in the discharging process.

In digital applications of charge-coupled devices, 1 and 0 can be represented by different amounts of charge stored under an electrode. 9 This leads to an improvement in transfer efficiency, e. g . , when a "zero" is followed by a "one", the charge left be­hind by the" zero" will be added to the charge of the " one". Since the amount of charge left behind is almost independent of the initial charge, as illus­trated in Fig. 12, the net amount of charge lost per transfer is decreased considerably. In this situation, the effective transfer efficiency can be defined as

1)eff = 1 - (QTl - QTO)/QpsZL,

where Q T1 and QTO are the total charge left behind by the" one" and the" zero" , respectively. Figure 13 shows the effective transfer efficiency for Ci = 10-2

and for three different values of Q po for the" zero" while Q po = Q ps for the" one". The curve for Q po

= 0 .1Qps is simply the difference between the two curves of Fig. 12 for Q = 10-2 • Significant improve­ments in transfer characteristics can be achieved with this scheme, e. g. , the transfer time necessary for 1)eff =99 .5% is reduced by a factor of 7 using Qpo = O. 5Q ps instead of Q po' The distinguishability of 1 and 0, however, will set the limit to this scheme.

V. CONCLUSIONS

The charge transfer in charge-coupled devices has been studied by conSidering the charging and the dis­charging phenomena. The drift current has been found to reduce the transfer time considerably for a rather low transfer efficiency. For high transfer efficienCies, however, the operating frequency is limited by diffusion with a characteristic time con­stant T=L2/D. A simple scheme, which overcomes this limitation, has been described.

Because of the trapping of minority carriers at the surface states, the transfer efficiency of a real de­vice will be lower than calculated here. The present study, however, shows the inherent limitations of charge-coupled devices associated with charging and discharging phenomena.

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3594 C-K. KIM AND M. LENZLINGER

*This paper was presented at the 1971 IEEE International Solid-State Circuit Conference, Philadelphia, Pa.

tPresent address: Faselec AG, Zurich, Switzerland. lW.J. Boyle and G.E. Smith, Bell System Tech. J. 49, 587 (1970).

2G. F. Amelio, M. F. Tompsett, and G. E. Smith, Bell System Tech. J. 49, 593 (1970).

3F. P. Heiman, IEEE Trans. Electron Devices ED-14, 781 (1967),

4A. S. Grove, B. E. Deal, E. H. Snow, and C. T. Sah, Solid-State Electron. 8, 145 (1965).

5H. K. J. Ihantola and J. L. Moll. Solid-State Electron. 7, 423 (1964).

6J. Crank, The Mathematics of Diffusion (Oxford U. P., Oxford, England, 1957).

70. Leistiko, A. S. Grove, and C. T. Sah, IEEE Trans. Electron Devices ED-12, 248 (1964).

BW.E. Engeler, J.J. Tiemann, and R.D. Baertsch, Appl. Phys. Letters 17, 469 (1970).

9R. J. Strain, IEEE International Electron Devices Meet­ing, Washington, D. C., 1970 (unpublished).

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